Seismic Fragility & Risk Assessment Guidance | EPRI Report

Seismic Fragility and Seismic Margin Guidance for Seismic Probabilistic Risk Assessments 2018 TECHNICAL REPORT 13633436 February 23, 2023 Errata 2 for 3002012994, Seismic Fragility and Seismic Margin Guidance for Seismic Probabilistic Risk Assessments The following corrections have been made to this technical report: • Pages and 5-22: The second section labeled 5.3.5.3, was changed to 5.3.5.4 Variability in Other Structure Response Parameters • Page 3-21–3-22: In Equations 3-17, 3-18, and 3-19, FHDPR was replaced with 1/FHDPR. • Page 4-8: The product number for 1025287 was corrected in the third paragraph. • Page 4-17: The following footnote was added: The capacities in Tables 4-2 and 4-3 are horizontal accelerations and should be compared to horizontal demands to develop the capacity factor. Vertical demands can generally be neglected when calculating equipment fragilities using earthquake experience, except 1) when analyzing equipment known to be sensitive to vertical input (for example, batteries, wall-mounted MCCs), or 2) when the vertical demands are significantly greater than horizontal. a • Page 4-21: The following values in red were corrected: If plant-specific test data are unavailable, a median concrete compressive strength equal to 1.5 times the minimum specified strength at 28 days and logarithmic standard deviation of 0.17 are recommended for members less than 3 ft thick. The 0.17 logarithmic standard deviation is estimated as the SRSS of a 0.14 COV for cylinder tests and corresponding 0.10 logarithmic standard deviation for the aging factor consistent with Equation 4-7. For thicker members… • Page 5-22: The following footnote was added: Alternatively, the overall logarithmic standard deviation can be estimated based on the 84% NEP and median responses calculated per the guidance above. Both deterministic methods for estimating 84% NEP response and variability will produce reasonable results. b • Page 5-30: In the last row of Table 5-3, the  was moved from the βU column to the βR column. • Page 5-33: New content was added to Table 5-6. • Page 6-53: In-text references to Eq. 6-23 and Eq. 6-24 were corrected. • Page 7-2: The product number for 1025287 was corrected. • Page M-1: Previously omitted section M.2 Verification of Original Spectra to be Scaled was added to the report. • Page M-6: Figure M-4 was replaced. 13633436 Errata/Corrections for 3002012994, Seismic Fragility and Seismic Margin Guidance for Seismic Probabilistic Risk Assessments February 23, 2022 Page 2 • Page S-50: Table S-6 was replaced. • Page S-56: In the “Tank effective frequency” calculation, the variable fs was replaced with fe. • Page T-5: Table T-2 contains the following change: Anchor Bolts (ASTM A307 A36 threaded rod) • Page X-4: The first paragraph contains the following change: “The logarithmic standard deviations associated with functional fragility are presented in this section. Relevant logarithmic standard deviations in this example account for variability in the structure response, clipping factor, demand reduction factor, capacity increase factor, and broad frequency input spectrum device capacity factor.” • Page X-7: Figure X-4 was replaced. June 7, 2019 Errata 1 for 3002012994, Seismic Fragility and Seismic Margin Guidance for Seismic Probabilistic Risk Assessments The following corrections have been made to this technical report: Source credits were added to Figures M-1 through M-4 on pages M-2 through M-5 to acknowledge that they are from Bruce Power Report No. 973/NK29-21001, “Bruce GS B Reactor Building Seismic Analysis by the Lumped Mass Model,” September 1983. These figures are drawings of the reactor building model and floor response spectra at Node 11 in the eastwest, north-south, and vertical directions, respectively. 13633436 13633436 Seismic Fragility and Seismic Margin Guidance for Seismic Probabilistic Risk Assessments 3002012994 Final Report, September 2018 EPRI Project Manager J. Richards All or a portion of the requirements of the EPRI Nuclear Quality Assurance Program apply to this product. ELECTRIC POWER RESEARCH INSTITUTE 3420 Hillview Avenue, Palo Alto, California 94304-1338 ▪ PO Box 10412, Palo Alto, California 94303-0813 ▪ USA 800.313.3774 ▪ 650.855.2121 ▪ askepri@epri.com ▪ www.epri.com 13633436 DISCLAIMER OF WARRANTIES AND LIMITATION OF LIABILITIES THIS DOCUMENT WAS PREPARED BY THE ORGANIZATION(S) NAMED BELOW AS AN ACCOUNT OF WORK SPONSORED OR COSPONSORED BY THE ELECTRIC POWER RESEARCH INSTITUTE, INC. (EPRI). NEITHER EPRI, ANY MEMBER OF EPRI, ANY COSPONSOR, THE ORGANIZATION(S) BELOW, NOR ANY PERSON ACTING ON BEHALF OF ANY OF THEM: (A) MAKES ANY WARRANTY OR REPRESENTATION WHATSOEVER, EXPRESS OR IMPLIED, (I) WITH RESPECT TO THE USE OF ANY INFORMATION, APPARATUS, METHOD, PROCESS, OR SIMILAR ITEM DISCLOSED IN THIS DOCUMENT, INCLUDING MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE, OR (II) THAT SUCH USE DOES NOT INFRINGE ON OR INTERFERE WITH PRIVATELY OWNED RIGHTS, INCLUDING ANY PARTY'S INTELLECTUAL PROPERTY, OR (III) THAT THIS DOCUMENT IS SUITABLE TO ANY PARTICULAR USER'S CIRCUMSTANCE; OR (B) ASSUMES RESPONSIBILITY FOR ANY DAMAGES OR OTHER LIABILITY WHATSOEVER (INCLUDING ANY CONSEQUENTIAL DAMAGES, EVEN IF EPRI OR ANY EPRI REPRESENTATIVE HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES) RESULTING FROM YOUR SELECTION OR USE OF THIS DOCUMENT OR ANY INFORMATION, APPARATUS, METHOD, PROCESS, OR SIMILAR ITEM DISCLOSED IN THIS DOCUMENT. REFERENCE HEREIN TO ANY SPECIFIC COMMERCIAL PRODUCT, PROCESS, OR SERVICE BY ITS TRADE NAME, TRADEMARK, MANUFACTURER, OR OTHERWISE, DOES NOT NECESSARILY CONSTITUTE OR IMPLY ITS ENDORSEMENT, RECOMMENDATION, OR FAVORING BY EPRI. THE FOLLOWING ORGANIZATION, UNDER CONTRACT TO EPRI, PREPARED THIS REPORT: Simpson Gumpertz & Heger THE TECHNICAL CONTENTS OF THIS PRODUCT WERE NOT PREPARED IN ACCORDANCE WITH THE EPRI QUALITY PROGRAM MANUAL THAT FULFILLS THE REQUIREMENTS OF 10 CFR 50, APPENDIX B. THIS PRODUCT IS NOT SUBJECT TO THE REQUIREMENTS OF 10 CFR PART 21. NOTE For further information about EPRI, call the EPRI Customer Assistance Center at 800.313.3774 or e-mail askepri@epri.com. Electric Power Research Institute, EPRI, and TOGETHER…SHAPING THE FUTURE OF ELECTRICITY are registered service marks of the Electric Power Research Institute, Inc. Copyright © 2018 Electric Power Research Institute, Inc. All rights reserved. 13633436 ACKNOWLEDGMENTS The following organization, under contract to the Electric Power Research Institute (EPRI), prepared this report: Simpson Gumpertz & Heger 4695 MacArthur Court, Suite 500 Newport Beach, CA 92660 Principal Investigators F. Grant G. Hardy S. Short This report describes research sponsored by EPRI. EPRI gratefully acknowledges the following individuals and their companies for their support in the development of this report: Robert Kennedy, RPK Structural Mechanics Consulting Robert Campbell, Consultant This publication is a corporate document that should be cited in the literature in the following manner: Seismic Fragility and Seismic Margin Guidance for Seismic Probabilistic Risk Assessments. EPRI, Palo Alto, CA: 2018. 3002012994. iii 13633436 13633436 ABSTRACT Seismic fragility methods were developed almost 40 years ago as part of the first seismic probabilistic risk assessments (SPRAs) for the nuclear power industry. Since then, seismic fragility methodology has evolved dramatically with advances in computational techniques and the industry’s understanding of earthquake effects—most recently, in SPRAs performed following the 2011 Tohoku earthquake/tsunami in Japan that damaged the Fukushima nuclear power plant. Seismic fragility is also becoming a more common tool in the engineering community and has expanded to non-nuclear industries. The Electric Power Research Institute (EPRI) has published several reports addressing the seismic margin and seismic fragility of structures, systems, and components, with these reports actively used in current SPRAs. Drawing from existing EPRI reports and other industry references, this report represents a single, comprehensive repository of the most relevant, state-of-the-art methods needed by plants that develop seismic fragilities in support of an SPRA. This report supersedes the EPRI reports Methodology for Developing Seismic Fragilities (TR-103959), Seismic Fragility Applications Guide (1002988), and Seismic Fragility Application Guide Update (1019200). Other EPRI reports on the topic have been incorporated in part. The approach to develop the present report included the following processes:  The relevant seismic fragility aspects of five reports were combined into the new document.  Duplicated technical material and descriptions were removed.  Methods that have changed or been replaced by new, more appropriate ones have been updated.  Errors have been corrected. This report documents fragility methods so that they are understandable to the well-trained utility structural mechanics engineer. Guidance is provided to develop fragilities and margins in an efficient, effective manner that conforms to the intent of the American Society of Mechanical Engineers/American Nuclear Society Standard for Probabilistic Risk Assessments for Nuclear Power Plants. The variables associated with seismic fragility and seismic margin analysis are defined, and the methodologies for their development and application are described. In addition, key example calculations are provided in the appendices. Keywords Earthquake Fragility methods Seismic fragility Seismic margin Seismic probabilistic risk assessment (SPRA) v 13633436 13633436 EXECUTIVE SUMMARY Deliverable Number: 3002012994 Product Type: Technical Report Product Title: Seismic Fragility and Seismic Margin Guidance for Seismic Probabilistic Risk Assessments PRIMARY AUDIENCE: Engineers performing or reviewing seismic margin calculations for seismic margin assessments (SMAs) or seismic fragility calculations for seismic probabilistic risk assessments (SPRAs) SECONDARY AUDIENCE: Project managers involved in managing SMA or SPRA projects KEY RESEARCH QUESTION What are the state-of-the-art methods for calculating seismic margins and seismic fragilities for use in SPRAs? RESEARCH OVERVIEW This report provides guidance for performing seismic margin and seismic fragility calculations for use in SPRAs. Guidance is provided for developing fragilities and margins in an efficient, effective manner that is intended to meet the criteria of the American Society of Mechanical Engineers/American Nuclear Society Standard for Probabilistic Risk Assessments for Nuclear Power Plants. The variables associated with seismic fragility and seismic margin analysis are defined, and the methodologies for their development and application are described. KEY FINDINGS • The report consolidates seismic margin and seismic fragility guidance into a single resource that addresses the main aspects of seismic margin and seismic fragility calculations. • Section 2 provides background on how seismic fragilities and seismic margins fit within the context of SPRAs and SMAs. • Section 3 presents methods for developing seismic fragilities, including the fundamental fragility concepts (Section 3.1), the lognormal fragility model (Section 3.2), and the separation of variabilities (Section 3.3) and hybrid (Section 3.4) fragility formulations. • Guidance for determining structure and equipment seismic capacities and the key parameters is provided in Section 4. Criteria are provided for stress-based failure modes (Sections 4.3–4.5 and 4.8), equipment anchorage failure modes (Section 4.7 and Appendices E and F) and equipment functional failure modes using earthquake experience data (Section 4.2), and seismic test data (Section 4.9 and Appendix J). • Methods for determining seismic response and the parameters affecting response variability are provided in Section 5 and Appendices M and N. Guidance for determining an initial seismic input reference earthquake for response calculations is provided in Section 5.2. • Seismic walkdown guidance is provided in Section 6.1 and Appendices B–D. Recommended walkdown forms are included as electronic attachments to the report. • Guidance for performing structure and equipment screening assessments is provided in Section 6.2, along with recommendations for performing initial estimates of representative fragility values. vii 13633436 EXECUTIVE SUMMARY    Guidance is provided for performing relay evaluations (Section 6.3 and Appendix L) as well as criteria for performing seismic demand and capacity response spectra peak clipping (Section 6.5). A collection of methods for considerations associated with high-frequency ground motions and instructure response spectra are described in Sections 6.4.1–6.4.4. Eleven example fragility calculations illustrate the fragility methods, as follows:  Structures: shear wall (Appendices O, P, R), masonry wall (Appendix Q)  Equipment: flat-bottom tank (Appendix S), heat exchanger (Appendix T), pump (Appendix U), inverter using test data (Appendix X), motor control center using earthquake experience data (Appendix Y)  Anchorage: expansion anchor (Appendix V), fillet weld (Appendix W) WHY THIS MATTERS Previous guidance for calculating seismic margins and seismic fragilities for use in SPRAs was developed over time and published by EPRI. Until now, the latest criteria could be obtained only by combining information from several EPRI reports. This report assembles all of the current guidance into one report. Also, it incorporates updated guidance and lessons learned from several recent SPRAs performed at sites with particularly high seismic hazards relative to their design basis. HOW TO APPLY RESULTS The basics of the seismic margin and fragility calculation processes are unchanged from previous EPRI guidance, although some parameters and techniques have been updated. The general criteria are covered in the body of the report, with the appendices providing supplemental guidance for seismic walkdowns (Appendices A–C), fragility calculation methods (Appendices E–K), response analysis methods (Appendices L–Q), and example evaluations (Appendices R–Y). LEARNING AND ENGAGEMENT OPPORTUNITIES  EPRI offers seismic fragility training, which is the best way for new fragility analysts to learn about the methods. Contact John Richards for additional information. EPRI CONTACTS: John Richards, Technical Executive, jrichards@epri.com PROGRAM: Risk and Safety Management, 41.07.01 IMPLEMENTATION CATEGORY: CATEGORY 2 Together...Shaping the Future of Electricity® Electric Power Research Institute 3420 Hillview Avenue, Palo Alto, California 94304-1338 • PO Box 10412, Palo Alto, California 94303-0813 USA 800.313.3774 • 650.855.2121 • askepri@epri.com • www.epri.com © 2018 Electric Power Research Institute (EPRI), Inc. All rights reserved. Electric Power Research Institute, EPRI, and TOGETHER...SHAPING THE FUTURE OF ELECTRICITY are registered service marks of the Electric Power Research Institute, Inc. 13633436 LIST OF ACRONYMS AC alternating current ACI America Concrete Institute AEP annual exceedance probability AFE annual frequency of exceedance AISC American Institute of Steel Construction ALARA as low as (is) reasonably achievable ANS American Nuclear Society AOV air-operated valve ASCE American Society of Civil Engineers ASD allowable stress design ASME American Society of Mechanical Engineers B&PV boiler and pressure vessel B&W Babcock & Wilcox BE best estimate BNL Brookhaven National Laboratory BOP balance of plant BWR boiling water reactor c.g. center of gravity CC Capability Category CCD concrete capacity design CCDP conditional core damage probability CDF cumulative distribution function CDFM conservative deterministic failure margin CE Combustion Engineering CEUS Central and Eastern United States CIP cast in place ix 13633436 COV coefficient of variation CRD control rod drive DBE design basis earthquake D/C demand-to-capacity ratio DEGB double-ended guillotine break DFEM detailed finite element model ECC earthquake component combination EMC electrical metal conduit EP exceedance probability EPP elastic perfectly plastic EPRI Electric Power Research Institute ESI equipment-structure interaction FIRS foundation input response spectra GE General Electric GERS generic equipment ruggedness spectra GIP Generic Implementation Procedure GMI ground motion incoherence GMRS ground motion response spectra HCLPF high confidence of low probability of failure HCU hydraulic control unit HDPR horizontal direction peak response HVAC heating, ventilation, and air conditioning ICC International Code Council IGSCC intergranular stress corrosion cracking IPEEE Individual Plant Examination for External Events ISI in-service inspection ISRS in-structure response spectra LB lower bound LERF large early release frequency LHS Latin hypercube simulation LLNL Lawrence Livermore National Laboratory x 13633436 LMSM lumped mass stick model LOCA loss-of-coolant accident LOOP loss of offsite power LRFD load and resistance factor design MCC motor control center MOV motor-operated valve NEMA National Electrical Manufacturers Association NEP non-exceedance probability NPP nuclear power plant NRC U.S. Nuclear Regulatory Commission NSSS nuclear steam supply system NTTF Near-Term Task Force P&ID piping and instrumentation diagram PGA peak ground acceleration PRA probabilistic risk assessment PSHA probabilistic seismic hazard assessment PWR pressurized water reactor RCL reactor coolant loop RE reference earthquake RLE review level earthquake RMS root mean square RPV reactor pressure vessel RRS required response spectra/reference response spectrum RVT random vibration theory RWST refueling water storage tank SCDF seismic core damage frequency SCE seismic capacity engineer SDOF single degree of freedom SEL seismic equipment list SEWS screening evaluation worksheet SI spatial interaction xi 13633436 SLERF seismic large early release frequency SLOCA small loss-of-coolant accident SMA seismic margin assessment SMACNA Sheet Metal and Air Conditioning Contractors’ National Association SME seismic margin earthquake SOV separation of variables SPRA seismic probabilistic risk assessment SPRAIG Seismic Probabilistic Risk Assessment Implementation Guide SQUG Seismic Qualification Utility Group SQURTS Seismic Qualification Reporting and Testing Standardization SRSS square root of the sum of the squares SRT seismic review team SRV steam relief valve SSC structure, system, or component SSE safe shutdown earthquake SSI soil-structure interation SSLOCA small-small-loss-of-coolant accident SSMRP Seismic Safety Margins Research Program SSRAP Senior Seismic Review and Advisory Panel SW service water SWC seismic walkdown checklist TRS test response spectra UB upper bound UBC Uniform Building Code UHRS uniform hazard response spectrum USI Unresolved Safety Issue V/H vertical-to-horizontal ratio VSLOCA very small loss-of-coolant accident VSV vertical spatial variation WN white noise ZPA zero period acceleration xii 13633436 LIST OF DEFINITIONS AND SYMBOLS Definitions Term Definition active SSC A structure, system, or component that must perform mechanical motion or undergo a change of state to accomplish its function credited in the SPRA. Examples include pumps and electrical relays. annual exceedance probability The likelihood that a specified level of earthquake ground motion will be exceeded in a given year. capacity The ability of an SSC to sustain a load measured in terms of the load level (such as stress, moment, displacement, or acceleration) below which the SSC continues to perform its credited functions. Capacity is not the same as fragility, and the two are not to be confused. core damage Uncovery and heatup of the reactor core to the point at which prolonged oxidation and severe fuel damage are anticipated and involving enough of the core, if released, to result in offsite public health effects. exceedance probability The likelihood that a random process will produce a result greater than a specified value. failure Basic abnormal occurrence that precludes the successful operation of an SSC or otherwise prevents it from performing its credited function (such as fails to start, fails to run, or leaks). failure mode Any of the processes that result in failure, including electrical, mechanical, physical, thermal, and human error. Failure modes should be realistic and consistent within the context of the system operational requirements, environmental factors, and SPRA systems analysis model. Equivalent to failure mechanisms defined in the PRA standard. xiii 13633436 Term Definition fragility Conditional probability that an SSC would fail for a specified ground motion or response parameter as a function of that value. Fragilities for SPRA are typically expressed in terms of the PGA of the reference earthquake. The fragility calculation typically uses a double lognormal model with three parameters, which are the median acceleration capacity (Am), the logarithmic standard deviation of the aleatory (randomness) uncertainty in capacity (βR), and the logarithmic standard deviation of the epistemic (modeling and data) uncertainty in the median capacity (βU). The aleatory and epistemic variability can be combined into a composite variability (βC). The fragility using a composite variability is referred to as the mean fragility. high confidence of low probability of failure (HCLPF) A HCLPF capacity is defined as the ground motion level at which there is a high (95%) confidence of a low (at most 5%) probability of failure. In fragility terms, it is defined as HCLPF = Am*exp [-1.656(R + U)]. When the fragility is expressed as a single curve using a composite variability, the HCLPF could be approximated as the ground motion level at which the composite probability of failure is at most 1% and is defined as HCLPF = Am*exp [-2.33(C)]. large early release The rapid, unmitigated release of airborne fission products from the containment to the environment occurring before the effective implementation of offsite emergency response and protective actions such that there is a potential for early health effects. median value The value of a random variable that represents the 50th percentile of the variable’s probability distribution function. That is, for any given subset of the population, it is equally likely that the result of a trial will yield a value above or below the median. nonexceedance probability The likelihood that a random process will produce a result that does not exceed a specified value. passive SSC A structure, system, or component that performs one or more credited functions fully or partially through passive means (that is, relying on natural physical processes, such as natural convection, thermal conduction, radiation, gravity or pressure differentials, or depending on the integrity of a pressure boundary or structural component). Examples include piping systems used to maintain an inventory of fluid and deliver flow along a fluid path as well as structural supports for SSCs. xiv 13633436 Term Definition peak ground acceleration (PGA) The maximum ground acceleration, which can be obtained from a ground response spectrum as the spectral acceleration occurring at high frequencies (typically greater than 100 Hz but historically considered the spectral acceleration at frequencies greater than 33 Hz). In this report, and in most nuclear power plant–related seismic risk studies, the size of an earthquake is measured in terms of the PGA rather than magnitude, intensity, or any other geophysical parameter. randomness The variability in seismic capacity or demand arising from the randomness of the earthquake’s characteristics for the same acceleration and to the structure and equipment response parameters that relate to these characteristics. Randomness is associated with the aleatory uncertainty inherent in a nondeterministic (stochastic, random) phenomenon and is reflected in fragility analysis by modeling the phenomenon in terms of a probabilistic model. In principle, randomness cannot be reduced by accumulation of more data or information. reference earthquake (RE) In a seismic probabilistic risk assessment, the reference earthquake is the UHRS 1 at a specified control point that defines: (1) the response spectrum shape that is: a. used as seismic input to structure response and fragility analyses b. anchored to seismic fragility parameters, such as median or HCLPF capacity, whether the fragilities are expressed in terms of PGA or spectral acceleration at a specified frequency range (2) the level or amplitude of seismic input that: a. is used in structure response analyses to develop ISRS, which will serve as input to equipment fragility analyses b. determines the stress level at which structures are analyzed (such as cracked or uncracked stiffness for concrete members and level of structure damping) and the strain level at which the underlying soil is analyzed when SSI effects are important The amplitude of the RE should be in the region that is important to the seismic risk of the plant. seismic core damage frequency Expected number of core damage events initiated by seismic events per unit time. 1 Although the GMRS is not technically a UHRS because the hazard return period for each response spectrum frequency is not necessarily uniform, for purposes of the reference earthquake discussion in this report, the GMRS is included as an acceptable option. xv 13633436 Term Definition seismic demand A quantification of the service requirements due to earthquake loads on the SSC being evaluated. Earthquakes produce complex time-varying motion of the ground and structures. The measures used to quantify seismic effects on structures and equipment are characterized in terms of acceleration time histories, acceleration response spectra, and equivalent peak accelerations or forces. Response spectra and equivalent static forces are the most commonly used seismic demand measures in nuclear applications. seismic equipment list The list of all SSCs that require seismic fragility evaluation for SPRA. seismic hazard analysis The process of estimating the expected exceedance frequency (over some specified time interval) of various levels of some characteristic measure of a hazard’s intensity (for example, peak ground acceleration to characterize ground shaking from an earthquake). The period of interest is typically one year, in which case the estimate is called the annual frequency of exceedance. seismic large early release frequency Expected number of large early release events initiated by seismic events per unit time. seismic margin assessment A deterministic process to estimate the seismic margin of plant safety systems and to identify any seismic vulnerabilities of the plant. Seismic margin is expressed in terms of the earthquake motion level that compromises plant safety, specifically leading to core damage. seismic probabilistic risk assessment (SPRA) A probabilistic risk assessment (PRA) is a qualitative and quantitative assessment of the risk associated with plant operations and maintenance that is measured in terms of frequency of occurrence of risk metrics such as core damage for radioactive material release and its effects on public health (also referred to as a probabilistic safety assessment [PSA]). An SPRA is a PRA in which a seismic event (typically, a range of seismic events) is the initiating event. structure, system, or component A general term used for a system, structure, or component that has been identified as potentially important to plant risk. Examples include a structural element, electrical or mechanical piece of equipment, piping system, or electrical cable system. uncertainty The variability in the median seismic capacity arising from imperfect knowledge about the models and model parameters used to calculate the median capacity. Also called epistemic uncertainty, it is reflected in fragility analysis by ranges of values for parameters, a range of viable models, the level of model detail, multiple expert interpretations, and statistical confidence. In principle, epistemic uncertainty can be reduced by the accumulation of additional information. xvi 13633436 Symbols A1 and A2 constants defined for ASCE 43-05/Barda equation for low-rise concrete shear wall strength A1% 1% NEP ground acceleration capacity A10% 10% NEP ground acceleration capacity Ab tank anchor bolt cross-section area Abe boundary element area ACDFM CDFM ground acceleration capacity AD design static coefficient Aeff effective area AF amplification factor or function AFC cabinet amplification factor AFE effective amplification factor AFEM median effective amplification factor AFh median amplification factor for a device mounted with its top at height hd AFp peak amplification factor AFpm median peak amplification factor Af weighting factor used in calculating effective frequency from elastic frequency Ag gross cross-sectional area Ags gross area of reinforcing steel Ain constant for computing effective frequency for high-frequency ductility of anchorage Am median ground acceleration capacity AP ground acceleration capacity at the PF failure probability Ap area of wall pier As stressed area of bolt (either shank or threads, as appropriate) Ast steel area per unit width of masonry wall Astif gross cross-sectional area of stiffeners Asvm median steel reinforcing area Av wall pier shear area Avlv valve acceleration vector Aw web area xvii 13633436 a input level expressed in terms of the reference parameter (typically PGA) am half the distance from the compression face of a shear wall in flexure to the first yielded reinforcement bar in tension ao dimensional parameter for evaluating Whitney stress distribution B bandwidth to central frequency ratio Bin constant for computing hysteretic damping for high-frequency ductility of anchorage b width of plate beff effective flange width C capacity associated with failure mode under evaluation C1% 1% NEP capacity C50% median estimate of component’s seismic capacity according to Section C1.3.1 of ASCE/SEI 43-05 C’B lower bound estimate of bandwidth correction factor CB bandwidth correction factor CBK tank shell buckling strength per unit length CBK,-1β median minus-one standard deviation value for tank shell buckling strength CC clipping factor for narrow-banded RRS CCDFM CDFM capacity associated with failure mode under evaluation CF strong motion duration factor used in calculating Af in effective frequency/effective damping method CFL tank impulsive mode frequency coefficient Cg1% 1% NEP capacity expressed in terms of ground spectral acceleration Cgm median capacity expressed in terms of ground spectral acceleration CI capacity increase factor CMI modal interaction correction factor C’m maximum tank shell compression force Cm median capacity CmC median spectral acceleration capacity in terms of motion at cabinet base CmD median spectral acceleration capacity in terms of motion at device mounting location COV coefficient of variation CSTD standard seismic capacity according to Section C1.3.1 of ASCE/SEI 43-05 xviii 13633436 CT clipping factor for narrow-banded TRS Cu uncertainty constant for inelastic energy absorption factor model CW tank impulsive mode frequency coefficient for water-filled tanks c depth from compressive flanges to neutral axis ca1 distance from the center of the anchor shaft to the concrete edge, as defined in ACI 349-13 D demand associated with failure mode under evaluation, or tank shell diameter D50% median seismic demand for DBE input according to Section C1.3.1 of ASCE/SEI 43-05 D84% 84th NEP seismic demand according to Section C1.3.1 of ASCE/SEI 43-05 DCDFM CDFM demand Dm median demand DNoHDPR seismic demand computed without consideration of HDPR DNoHDPR,84% 84th percentile value of DNoHDPR DNoHDPRm median value of DNoHDPR DNS nonseismic demand DS seismic demand DSTD deterministic demand according to Section C1.3.1 of ASCE/SEI 43-05 DW deadweight of tray and contents d distance between overturning axis and critical anchor in the direction of seismic input da anchor bolt diameter dah anchor bolt hole diameter dc depth of cabinet dh head diameter dm distance from extreme compression fiber to center of force of all reinforcement in tension do outside diameter ds tank fluid slosh height dsR total fluid slosh height due to horizontal seismic component E Young’s modulus (that is, modulus of elasticity) Eb modulus of elasticity of tank anchor bolt material xix 13633436 EC modulus of elasticity of concrete EL axial seismic load in electrical raceway Em Young’s modulus for masonry ERE seismic inertial loading ES modulus of elasticity of steel Es modulus of elasticity of tank shell material e(·) or exp(·) natural exponential function (base e ≈ 2.718) e eccentricity eh distance from inner face of hook bolt shaft to furthest tip of hook eX eccentricity about transverse axis eY eccentricity about longitudinal axis FAX multi-axis to single-axis conservatism factor Fbe force carried by vertical boundary element reinforcement Fbe95 95% EP force carried by vertical boundary element reinforcement FC capacity factor FC,CDFM CDFM capacity factor Fc(h/d) factor for calculating best estimate drift ratio of masonry walls FCm median capacity factor FCm,Zσ median capacity factor corresponding to plus-Z lognormal standard deviations FD broad frequency input spectrum capacity factor FECCe equipment earthquake component combination factor FECCs structure earthquake component combination factor FER equipment response factor FEXX minimum code nominal tensile strength for weld material Ffe equipment frequency factor Ffs structure frequency factor FGMI ground motion incoherence factor FH horizontal directionality factor FH horizontal membrane force in the tank bottom plate FHDPR ground motion horizontal direction peak response factor FHDPRm median ground motion horizontal direction peak response factor xx 13633436 CDFM FHDPR CDFM ground motion horizontal direction peak response factor FIR inelastic structure response factor Fi ith scaling or weighing factor Fij force at node i for mode j Fin inelastic capacity increase factor for anchorage of equipment responding at high frequencies FinPL inelastic capacity increase factor for tension due to longitudinal seismic input FinPT inelastic capacity increase factor for tension due to transverse seismic input FinPV inelastic capacity increase factor for tension due to vertical seismic input FinVL inelastic capacity increase factor for shear due to longitudinal seismic input FinVT inelastic capacity increase factor for shear due to transverse seismic input Fj jth scaling factor Fk knockdown factor to estimate system ductility from ductility of governing story Fkd knockdown factor for estimating HCLPF as a function of GERS test experience data FMC structure mode combination phasing factor FMCe equipment mode combination factor FMCs structure mode combination factor FMs structure model fidelity factor FMe equipment model fidelity factor Fm median factor of Fi individual factors FNI% nominal factor of safety against a 1% conditional probability of failure FPV factor to correct HCLPFPV to avoid double counting of βPV,R FQM qualification method factor FR capacity reduction factor for expansion anchors in concrete with hairline and small cracks FRS structure response factor FRSm median structure response factor FS safety factor FS strength factor; also known as elastic RE scale factor FS,CDFM CDFM strength factor FSσ 84% NEP or EP strength factor xxi 13633436 FSσ,R 84% NEP or EP strength factor considering only randomness variability FScode conservative ratio of median to code strength for ASME pressure vessels FSA ground motion spectral shape factor FSm median elastic strength factor FSm,R median elastic strength factor considering only random variability FSS equipment spectral shape factor FSSI inertial soil-structure interaction factor FTC structure torsional coupling factor FTH time-history phasing factor FS,P strength factor for tensile failure mode FS,PV strength factor for tensile-shear interaction failure mode FV ground motion vertical to horizontal acceleration ratio (V/H) factor FVSV vertical spatial variation factor Fvw force carried by vertical web reinforcement Fvw95 95% EP force carried by vertical web reinforcement Fδe equipment damping factor Fδs structure damping factor Fμ inelastic energy absorption factor Fμ,CDFM CDFM inelastic energy absorption factor Fμm median inelastic energy absorption factor FμZ inelastic energy absorption factor corresponding to Z f frequency f±1σ plus- or minus-one logarithmic standard deviation equipment frequency f(·) function that relates SF to basic variables xi f’c concrete compressive strength f’c28 average 28-day concrete compressive strength from tests f’c60 average 60-day concrete compressive strength from tests f’cCDFM CDFM concrete compressive strength f’cm median concrete compressive strength f’cmin minimum specified concrete compressive strength f’m,CDFM CDFM masonry strength xxii 13633436 fC tank sloshing mode frequency fc central frequency fe effective frequency ff frequency of floor response spectral ordinate Sanf fI tank impulsive mode frequency fj frequency of mode j flong frequency in longitudinal direction fs secant frequency ft cracking tension in flexure ftran frequency in transverse direction fu ultimate tensile strength fV tank vertical fluid mode frequency fwCDFM CDFM equation strength reduction factor for welds fy tensile yield strength fym median steel yield strength fymin minimum specified steel yield strength G modulus of rigidity (that is, shear modulus) Gc shear modulus of concrete GERS capacity level from generic equipment ruggedness spectra GSSE equivalent static g force used for the SSE qualification g acceleration of gravity H tank fluid height HC height of cabinet HD dome height of a domed roof tank Hcg height to center of gravity HF available freeboard for tank fluid sloshing Hf floor-to-floor height Hs tank shell height h beam depth h1 stiffener height—outside pair h2 stiffener height—inside pair xxiii 13633436 hc tank anchor bolt chair height hd height of top of device within a cabinet he effective bolt stretch length hef effective embedment depth hp plate thickness ht height to bottom of tank hw effective height of wall HCLPF high confidence of low probability of failure capacity HCLPF50 HCLPF calculated using median input ground motion spectrum HCLPF84 HCLPF calculated using 84% NEP input ground motion spectrum HCLPF’ HCLPF corrected to avoid double counting of βPV,R HCLPFC HCLPF capacity in terms of motion at base of cabinet HCLPFCDFM CDFM HCLPF capacity HCLPFD HCLPF capacity in terms of motion at device mounting point HCLPFPV HCLPF not corrected to avoid double counting of βPV,R I moment of inertia of wall or pier Ib out-of-plane moment of intertia of tank bottom plate Ie effective moment of inertia Ig gross moment of inertia IT cracked section transformed moment of inertia Iyy moment of inertia in saddle’s weak direction Iθ moment of inertia in the transverse (rocking) direction i generic index is stress intensification factor j generic index K elastic stiffness Kb tank anchor bolt axial stiffness Kf bulk modulus of tank fluid Kp peak reduction factor for converting peak amplification to broadband amplification factor Ks secant stiffness xxiv 13633436 Ks1 stiffness of outside pair of stiffener plates Ks2 stiffness of inside pair of stiffener plates Ksad fixed saddle support stiffness in weak direction Kµ ductility reduction factor Kθ rocking stiffness kbolt bolt stiffness kc coefficient for basic concrete breakout strength in tension L length LN(xm, β) lognormal distribution with median xm and logarithmic standard deviation β Lp distance between wall piers LX side-to-side dimension LXcg distance between center of gravity and cabinet side panel LY front-to-back dimension LYcg distance between center of gravity and cabinet front panel lb saddle plate to edge of base plate distance le load-bearing length of an anchor leff effective wall length of cylindrical concrete wall ls stiffener width lw length of wall or wall pier in direction of shear force applied ℓ span length M overturning moment M+ maximum positive moment demaned in the uplifted portion of tank bottom plate MA resultant moment on cross-section due to weight and other sustained loads MB resultant moment loading on cross-section due to earthquake inertial loads and steam relief valve (SRV) loads M’C tank overturning moment below the bottom plate due to fundamental sloshing mode MC tank overturning moment above the bottom plate due to fundamental sloshing mode Mcap,m median ultimate moment capacity Mcap,nom nominal ultimate moment capacity MCDFM CDFM moment capacity xxv 13633436 MCR cracking moment Mc tank overturning capacity MD bending moment due to deadweight Mf moment demand in tank shell at the intersection with the bottom plate M’I tank overturning moment below the bottom plate due to fundamental impulsive mode MI tank overturning moment above the bottom plate due to fundamental impulsive mode Mi mass of ith node MP∆ P∆ moment Mpb plastic out-of-plane moment strength of tank bottom plate Mps plastic out-of-plane moment strength of tank shell MR total tank overturning moment above the tank bottom plate Ms seismic bending moment MT seismic bending moment in the transverse plane MUT allowable moment in the transverse plane MUV allowable moment in the vertical plane MXX overturning moment about X-axis MYY overturning moment about Y-axis Mym median yield moment capacity MV seismic bending moment in the vertical plane MθX overturning component along θ direction due to X-direction seismic input MθY overturning component along θ direction due to Y-direction seismic input Mθ overturning moment about θ direction m mass per unit height N number of samples included in the Monte Carlo or Latin Hypercube simulations NA total number of tank anchor bolts Na axial force in wall Nb basic concrete breakout strength in tension Nc,NUREG mean concrete breakout strength for deeply embedded anchors from NUREG/CR5563 NDL axial force in a pier due to dead load (non-seismic) xxvi 13633436 NSH median seismic axial force in a pier due to horizontal input NSV median seismic axial force in a pier due to vertical input NB number of anchor bolts at each location NEP(·) non-exceedance probability of x NL number of anchor bolt locations at each saddle NS number of tank supports n number of observations P pressure P(·) probability of an event Pa axial load Pau axial capacity Pavg average fluid pressure over the tank bottom plate Pay beam or column elastic axial capacity PC hydrodynamic pressure on tank shell due to fundamental sloshing mode PC+ maximum fluid pressure on tank shell at the toe of an overturning tank PC- minimum fluid pressure on tank shell at the toe of an overturning tank PCDFM CDFM tensile strength PCr probability of concrete being cracked in the vicinity of post-installed anchor Pcb base fluid pressure at tank toe (shell in compression) PcCDFM CDFM tensile capacity of anchor bolt in concrete Pcm median tensile capacity of anchor bolt in concrete Pcmean mean tensile capacity of anchor bolt in concrete PDL axial force due to dead load PF' probability of failure including both epistemic and aleatory variability PF probability of failure PFf probability of failure obtained by performing convolution using hazard and fragility defined at frequency f PGA peak ground acceleration PGARE reference earthquake peak ground acceleration Pgj peak factor for ground motion and structure mode j PH total hydrodynamic pressure on tank shell due to horizontal seismic component xxvii 13633436 PI hydrodynamic pressure on tank shell due to fundamental impulsive mode Pi probability of non-exceedance for ith sample of random variable xi in a Monte Carlo simulation Pi,jRE seismic load in element i for mode j for the RE Pi,jSSE seismic load in element i for mode j for the SSE Pl axial demand due to longitudinal input Plong combination of axial demands assuming longitudinal direction controls Pnf peak factor for node n and equipment frequency ff PPlate anchor tensile capacity based on yield line analysis of base plate Pp operating pressure Ppullout pullout strength of hook anchor PRE seismic load in element i by appropriate modal combination of Pi,jRE for all modes Ps axial force due to seismic load in three orthogonal directions Ps3σ axial force due to seismic load in three orthogonal directions corresponding to three standard deviations PsX axial force due to seismic load input in horizontal x-direction PsY axial force due to seismic load input in horizontal y-direction PsZ axial force due to seismic load input in vertical z-direction Pst hydrostatic pressure at tank base PT+ maximum fluid pressure on tank shell at the heel of an overturning tank PT- minimum fluid pressure on tank shell at the heel of an overturning tank Pt axial demand due to transverse input Ptb base fluid pressure at tank heel (shell in tension) Ptran combination of axial demands assuming transverse direction controls Pum median ultimate tensile capacity PV hydrodynamic pressure on tank shell due to the vertical fluid mode Pv axial demand due to vertical input P−σ tensile capacity corresponding to minus-one standard deviation in strength factor Pθ base fluid pressure at tank azimuth angle θ Q confidence level R structure response quantity, or tank shell radius RA ratio of actual bolt capacity to mean capacity xxviii 13633436 Ra ratio of axial to effective ultimate stresses R abs response based on absolute sum of direction contributions RC overall median conservatism ratio associated with the CDFM method RD median demand conservatism ratio associated with the CDFM method Ri% ratio of capacity with i NEP to CDFM capacity, for example, for i = 1, 5, 10, and 50% NEP Rm median response based on SRSS or 100-40-40 combination of direction contributions Rmc,abs response based on absolute sum of modal contributions Rmc,m median response using median-centered modal contribution method RN computed load or response to normal operating loads Rn parameter for converting from μ to μ’ RRS reference response spectrum demand RRSB clipped RRS at base of cabinet RRSC clipped RRS RRSqual mounting-point response spectrum to which the component must be qualified by testing RS median strength conservatism ratio associated with the CDFM method RSSE computed load or response to the GSSE loading RT total response to the RE plus normal operating loads RT/L ratio of transverse to longitudinal weld strength RT/P ratio of tested to predicted strength RU ratio of actual to mean bolt capacity in uncracked concrete RβU ratio of amplification factor uncertainty to device capacity uncertainty RβR ratio of amplification factor randomness to device capacity randomness Rθ/L ratio of weld strength at angle θ to longitudinal strength Rμ median inelastic energy absorption conservatism ratio associated with the CDFM method rndi random number selected between 0 and 1 (different for each ith sample) S section modulus S50% median estimate of the component’s seismic strength according to Section C1.3.1 of ASCE/SEI 43-05 S98% 98% EP strength according to Section C1.3.1 of ASCE/SEI 43-05 xxix 13633436 S99% 99% EP strength according to Section C1.3.1 of ASCE/SEI 43-05 SCDFM CDFM strength for low ductility modes according to EPRI NP-6041-SLR1 SAF structural amplification factor SAFm median structural amplification factor Sa spectral acceleration Sa5 spectral acceleration at 5 Hz Sa84% 84% NEP spectral acceleration SaC fundamental tank sloshing mode spectral acceleration demand SaCm median clipped spectral acceleration SaCm84 84% NEP spectral acceleration using median clipping factors SaC84 84% NEP clipped spectral acceleration SaC84m median clipped spectral acceleration using CDFM clipping factors Sac spectral acceleration capacity SaD effective nonlinear spectral acceleration demand SaD (ξD) design spectral acceleration at design equipment damping for the dominant equipment frequency(ies) Sag ground spectral acceleration Sagj ground spectral acceleration input for mode j Sagm median ground spectral acceleration capacity SaI fundamental tank impulsive mode spectral acceleration demand Saj spectral acceleration of mode j at frequency fj SajRE spectral acceleration from the RE for mode j at RE modal damping SajSSE spectral acceleration for the SSE for mode j at SSE modal damping Sam median spectral acceleration Sam,R median peak spectral acceleration considering only random variability Sam (ξm) median spectral acceleration at median equipment damping for the dominant equipment frequency(ies) Sanf floor spectral acceleration at node n and frequency ff Sanfj floor spectral acceleration at node n, frequency ff, and mode j SaPEAK peak spectral acceleration vector SaRE spectral acceleration at RE SaRRS spectral acceleration from the applicable RRS floor spectrum xxx 13633436 SaS in-structure spectral acceleration SaSL peak 5% damped horizontal ground Sa representing the EPRI NP-6041-SLR1 [1] Table 2-4 HCLPF level that the equipment satisfies SaSSE spectral acceleration at SSE SaTV vertial inertial spectal acceleration response of the tank shell SaV vertical fluid mode spectral acceleration demand Saσ,R 84% NEP peak spectral acceleration considering only random variability Sa alternating stress range Sa (ξm) RE or ISRS spectral acceleration for median structure or equipment damping at the significant structure or equipment frequency(ies) Sa (ξ-1σ) RE or ISRS spectral acceleration for minus-one logarithmic standard deviation structure or equipment damping at the significant structure or equipment frequency(ies) Sd spectral displacement SF scale factor to obtain the ground motion capacity from the RE ground motion SFavg mean value of SF SFm median value of SF SFr elastic response scale factor for flat-bottom storage tank SFZσi value of SF that is Z standard deviations above or below SFm Sg gross section modulus Sh basic material allowable stress at operating temperature SMER reference seismic margin earthquake level SSTD deterministic strength according to Section C1.3.1 of ASCE/SEI 43-05 SX spacing in X-direction SY spacing in Y-direction s ratio of post-yield stiffness to elastic stiffness K sb bolt spacing ss saddle spacing sw weld spacing Tbi tensile force in ith tank anchor bolt Tbp pretension force in tank anchor bolt Tbs tank anchor bolt tensile strength xxxi 13633436 Tbs,-1 median minus-one standard deviation value for tank shell buckling strength Tf tank fluid hold-down force including membrane effects Tfi intercept of best-fit line to Tf vs. cos(θ) curve Tfm slope of best-fit line to Tf vs. cos(θ) curve Tfn tank fluid hold-down force at the neutral axis Tfo tank fluid hold-down force at the tank heel Tfs tank fluid hold-down force based on small displacement theory, that is, excluding membrane effects TRS test response spectrum TRSC clipped TRS TRSCDFM CDFM test response level t weld leg dimension tb base plate thickness tn thickness of wall or wall pier tnp nominal pipe wall thickness ts tank shell thickness tsb tank shell thickness at base ts_avg average tank shell thickness ts_min minimum tank shell thickness tse tank shell equivalent uniform thickness tst stiffener thickness tt thickness of tank shell V shear force VB maximum shear vector at weld-base metal interface VB,CDFM CDFM capacity for base metal at weld connection Vb concrete breakout strength VC tank base shear due to fundamental tank impulsive mode VCCDFM CDFM shear capacity of expansion anchors VCDFM CDFM shear capacity VCm median shear capacity of expansion anchors VCmean mean shear capacity of expansion anchors xxxii 13633436 Vc shear capacity contribution from concrete strength Vcap,m equivalent shear capacity representing moment capacity Vcy yield wall concrete capacity for diagonal shear failure VDL dead load shear VI tank base shear due to fundamental tank impulsive mode Vj base shear for mode j VL longitudinal shear load Vl shear demand due to longitudinal input Vlong combination of shear demands assuming longitudinal direction controls Vlong,84% combination of 84% NEP shear demands assuming longitudinal direction controls VNS shear demand due to non-seismic loads VR total tank base shear Vs seismic shear force Vsc tank sliding shear capacity VsX shear force due to seismic load input in horizontal x-direction VsY shear force due to seismic load input in horizontal y-direction VsZ shear force due to seismic load input in vertical z-direction Vs3σ shear force due to seismic load in three orthogonal directions corresponding to three standard deviations VT larger of VTX and VTY VTX transverse load in X direction VTY transverse load in Y direction Vt shear demand due to transverse input Vtran combination of shear demands assuming transverse direction controls Vu shear ultimate capacity Vuc median concrete contribution to ultimate shear capacity Vuc95 95% EP concrete contribution to ultimate shear capacity VuL,CDFM CDFM longitudinal weld capacity Vum median ultimate shear capacity VuT,CDFM CDFM transverse weld capacity Vu95 95% EP ultimate shear capacity xxxiii 13633436 Vθ load applied at angle θ Vuθ,CDFM CDFM ultimate shear force capacity at angle θ Vuθm median ultimate shear force capacity at angle θ V−σ shear capacity corresponding to minus one standard deviation in strength factor vave average shear stress vc1σ minus-one standard deviation strength contribution from concrete (stress) vcm median strength contribution from concrete (stress) vc95 95% EP strength contribution from concrete (stress) vsm median strength contribution from steel reinforcement (stress) vs95 95% EP shear strength contribution from steel (stress) vum median ultimate shear strength (stress) vu95 95% EP ultimate shear strength (stress) W weight WC effective sloshing fluid weight WE effective tank weight WI effective impulsive fluid weight Wi weight of story i Wr tank roof weight Ws tank shell weight WT total tank fluid weight WTE effective empty tank weight X’C height to centroid of effective sloshing fluid weight, including fluid pressures on the bottom plate XC height to centroid of effective sloshing fluid weight, excluding fluid pressures on the bottom plate X’I height to centroid of effective impulsive fluid weight including fluid pressures on the bottom plate XI height to centroid of effective impulsive fluid weight excluding fluid pressures on the bottom plate Xg” ground motion acceleration time-history vector Xj” absolute acceleration response vector of a ground mounted oscillator with frequency fj and damping ξj Xr height to centroid of tank roof xxxiv 13633436 Xs height to centroid of tank shell Ẍ 1 absolute acceleration of first stage of cascaded two-SDOF system Ẍ 2 Ẍ 1RMS absolute acceleration of second stage of cascaded two-SDOF system vector of absolute RMS accelerations of first stage of cascaded two-SDOF system Ẍ 2RMS vector of absolute RMS accelerations of second stage of cascaded two-SDOF system x lognormally distributed random variable xave mean of x xi ith lognormally distributed random variable in a set xiavg mean of xi xim median of xi xm median of x YL allowable axial load in electrical raceway Yn” structure absolute acceleration response vector for node n Ynj” structure modal acceleration response component for node n and mode j y lognormally distributed random variable that is a product of lognormally distributed random variables xi yH depth below the fluid surface ym median of lognormal distribution on y Z standard normal variable Z95%EP standard normal variable corresponding to 95% exceedance probability Z98%EP standard normal variable corresponding to 95% exceedance probability Znf” absolute acceleration response of floor-mounted oscillator with frequency ff Znfj” absolute acceleration response of floor-mounted oscillator with frequency ff due to mode j Zni” absolute acceleration response of floor-mounted oscillator at node n, for response direction i Znir” absolute acceleration response of floor-mounted oscillator at node n, for input direction r and response direction i Znirj” absolute acceleration response of floor-mounted oscillator at node n, for input direction r, response direction i, and structure mode j ZPA zero-period acceleration xxxv 13633436 ZPA84% 84% NEP structure ZPA ZPA84%,R 84% NEP structure ZPA from probabilistic analysis simulations that consider only random variables ZPACOH structure ZPA from the coherent SSI analysis ZPAINC structure ZPA from the incoherent SSI analysis ZPAMAX maximum ZPA from the five earthquake acceleration time-history sets assumed to lie at the 90% NEP level ZPAm median ZPA ZPAm,R median structure ZPA from probabilistic analysis simulations that consider only random variables ZPA (ξm) structure ZPA from the SSI analysis using best estimate soil and structure properties ZPA (ξ-1σ) structure ZPA from an SSI analysis modified to use the minus-one logarithmic standard deviation structure damping with best estimate soil and structure properties Zp plastic section modulus α ratio of gross to effective cross-sectional area for cylindrical concrete walls α1, α2, α3 regression parameters αA0 axial compression imperfection factor for tank shell with no internal pressure αB0 bending imperfection factor for tank shell with no internal pressure αp bending imperfection factor for tank shell with internal pressure β logarithmic standard deviation βAB,U logarithmic standard deviation for capacity uncertainty due to variability in anchor bolt strength βAF,R logarithmic standard deviation for randomness in cabinet amplification factor βAF,U logarithmic standard deviation for uncertainty in cabinet amplification factor βAX,U logarithmic standard deviation for uncertainty in multi-axis to single-axis conservatism factor βab,U logarithmic standard deviation for total anchor bolt strength uncertainty βab_eq,U logarithmic standard deviation for equation uncertainty in anchor bolt strength βab_mat,U logarithmic standard deviation for material strength uncertainty in anchor bolt strength βBK,U logarithmic standard deviation for capacity uncertainty due to variability in tank shell buckling strength xxxvi 13633436 βbar,U logarithmic standard deviation for strength uncertainty due to errors in rebar placement βbk,U logarithmic standard deviation for total uncertainty in tank shell buckling strength βbk_eq,U logarithmic standard deviation for equation uncertainty in tank shell buckling βbk_mat,U logarithmic standard deviation for material strength uncertainty in tank shell buckling strength βC composite logarithmic standard deviation βCcRS,C composite logarithmic standard deviation for structure response and clipping factor variability βCcRS,U logarithmic standard deviation for structure response and clipping factor uncertainty βCc,U logarithmic standard deviation for uncertainty in the clipping factor βCI,U uncertainty logarithmic standard deviation associated with the capacity increase factor βĈ logarithmic standard deviation for Cm βĈ,R contribution of randomness variability to βĈ βĈ,U contribution of uncertainty variability to βĈ βconc logarithmic standard deviation for concrete breakout strength of deeply embedded anchors βD seismic demand logarithmic standard deviation for a specified seismic input βDNoHDPR,C composite logarithmic standard deviation in DNoHDPR βDS,C composite logarithmic standard deviation in DS βECCe,R logarithmic standard deviation for earthquake component combination randomness for equipment βECCs,R logarithmic standard deviation for earthquake component combination randomness for structure βEC,R randomness logarithmic standard deviation for equipment capacity factor βEC,U uncertainty logarithmic standard deviation for equipment capacity factor βEQN,U logarithmic standard deviation for strength equation uncertainty βER,R combined variability due to equipment response randomness βER,U combined variability due to equipment response uncertainty βFAB,U logarithmic standard deviation due to uncertainty in fabrication tolerances βFD,R logarithmic standard deviation for randomness in the broad frequency input spectrum device capacity factor xxxvii 13633436 βFD,U logarithmic standard deviation for uncertainty in the broad frequency input spectrum device capacity factor βFH,R logarithmic standard deviation for randomness in tank fluid height βFH,U logarithmic standard deviation for uncertainty in tank fluid height βFP,R logarithmic standard deviation for randomness in tank fluid pressures βFP,U logarithmic standard deviation for uncertainty in tank fluid pressures βfe,U logarithmic standard deviation in equipment response due to uncertainty in equipment frequency βfs,U logarithmic standard deviation in structure response due to uncertainty in structure frequency βGMI,U logarithmic standard deviation for uncertainty in GMI βGM,R logarithmic standard deviation for ground motion randomness βGM,U logarithmic standard deviation for ground motion uncertainty βgĈ lgarithmic standard deviation for Cgm βHDP,R logarithmic standard deviation for randomness in horizontal direction peak response βIR,R logarithmic standard deviation for randomness in nonlinear structure response βIR,U logarithmic standard deviation for uncertainty in nonlinear structure response βi logarithmic standard deviation of the lognormal random variable xi βMC,R logarithmic standard deviation for randomness in mode combination phasing of structure βMCe,R logarithmic standard deviation for randomness in mode combination phasing of equipment βMe,U logarithmic standard deviation for equipment response due to uncertainty in the fidelity of equipment modeling (mode shape) βMs,U logarithmic standard deviation for structure response due to uncertainty in the fidelity of structure modeling (mode shape) βPV logarithmic standard deviation for peak and valley variability βPV,C composite logarithmic standard deviation for peak and valley variability in earthquake ground motion βPV,R logarithmic standard deviation for peak and valley randomness in earthquake ground motion βPV,U logarithmic standard deviation for peak and valley uncertainty in earthquake ground motion xxxviii 13633436 βpullout logarithmic standard deviation for uncertainty in strength equation for pullout failure in hook anchors βQM,U logarithmic standard deviation for uncertainty in the qualification method βR ’ corrected logarithmic standard deviation for randomness after removing peak and valley variability βR logarithmic standard deviation for randomness (aleatory variability) βRC logarithmic standard deviation for randomness in capacity expressed at cabinet base βRD logarithmic standard deviation for randomness in capacity expressed at device mounting point βRS,C composite logarithmic standard deviation for structure response variability βRS,R logarithmic standard deviation for structure response randomness βRS,U logarithmic standard deviation for structure response uncertainty βS logarithmic standard deviation associated with strength variability βS,R randomness logarithmic standard deviation associated with strength variability βS,U uncertainty logarithmic standard deviation associated with strength variability βSAF logarithmic standard deviation structural amplification factor βSA,U logarithmic standard deviation in structure response due to uncertainty in the spectral shape βSSI,U logarithmic standard deviation for soil property variability βSS,U logarithmic standard deviation in equipment response due to uncertainty in spectral shape βTC logarithmic standard deviation due to torsional coupling βTC,R logarithmic standard deviation for tank seismic capacity randomness βTC,U logarithmic standard deviation for tank seismic capacity uncertainty βTH,R logarithmic standard deviation due to time-history phasing randomness βTH,U logarithmic standard deviation due to time-history phasing uncertainty βTR,U logarithmic standard deviation for tank seismic response randomness βU’ corrected logarithmic standard deviation for uncertainty after removing peak and valley variability βU logarithmic standard deviation for uncertainty (epistemic variability) βUC logarithmic standard deviation for uncertainty in capacity expressed at cabinet base xxxix 13633436 βUD logarithmic standard deviation for uncertainty in capacity expressed at device mounting point βULT,U logarithmic standard deviation for uncertainty in material ultimate strength βVSV,U logarithmic standard deviation for uncertainty in vertical spatial variation βy logarithmic standard deviation of the lognormal random variable y βyield logarithmic standard deviation for uncertainty in material yield strength βδe,U uncertainty logarithmic standard deviation associated with equipment damping βδo,R logarithmic standard deviation for permissible tank uplift height randomness βδo,U logarithmic standard deviation for permissible tank uplift height uncertainty βδs variability in structure response due to variability in structure damping βµ,C composite logarithmic standard deviation due to inelastic energy absorption factor βµ,R randomness logarithmic standard deviation due to inelastic energy absorption factor βµ,U uncertainty logarithmic standard deviation due to inelastic energy absorption factor Γ participation factor Γj participation factor for mode j Γjr participation factor for mode j and input direction r γ yield line capacity parameter, or unit weight γs steel unit weight γw water unit weight HOR ΔCDIAG VERT ΔCDIAG change in diagonal shear cracking capacity for horizontal earthquake effect change in diagonal shear cracking capacity for vertical earthquake effect ΔCS reduction in capacity due to concurrent seismic loading Δf0.8 frequency bandwidth at 0.8 times peak spectral acceleration ∆NaH change in median diagonal shear cracking due to the incremental change in Na ∆Tf difference between fluid pressures at the tank heel and the neutral axis ∆Vu reduction in shear capacity due to seismic axial force ∆vu reduction in shear strength due to seismic axial force δ tank uplift displacement δe elastic horizontal drift at the tank center of gravity due to tank uplift δei elastic deflection of story i at yield xl 13633436 δf | δxi xiavg derivative of f with respect to xi evaluated at the mean values of xi δI horizontal drift at the tank center of gravity due to tank uplift δin system inelastic displacement capacity δin,a inelastic displacement capacity of critical anchor element δir Kronecker delta function δo permissible tank uplift height δs story displacement (shear drift) δT maximum permissible story deflection δTi deflection of story i when nonlinear drift limit is reached by one or more stories δu wall ultimate drift at the onset of significant degradation δus system ultimate displacement (δu/hw) drift ratio (δu/hw)CDFM CDFM drift ratio δy elastic story deflection at yield δys system yield deflection δθ tank uplift displacement at tank azimuth angle θ ε error ζ shear-tension interaction exponent θ angle θi azimuth angle to tank ith tank anchor bolt θn azimuth angle to tank neutral axis μ ductility ratio μf coeffcient of friction μlim ductility limit μs ductility ratio for a single story λl acceleration coefficient in longitudinal direction λp square root of ratio of yield strength to classical buckling strength adjusted for imperfections λt acceleration coefficient in transverse direction λv acceleration coefficient in vertical direction ν Poisson’s ratio xli 13633436 ξ elastic damping ratio ξe effective damping ratio ξf damping ratio for equipment response at frequency ff ξh pinched hysteretic damping, or system hysteretic damping ξj damping ratio for structure mode j π universal constant pi ≈ 3.14 (ρfym)AVER average effective steel ratio for cylindrical concrete wall ρ steel reinforcement ratio ρf tank fluid density ρh horizontal steel reinforcement ratio ρhp hoop steel reinforcement ratio ρm meridional steel reinforcement ratio ρs tank shell material density ρse effective steel reinforcement ratio ρv vertical steel reinforcement ratio ρw water density σ standard deviation σau ultimate axial stress σCL classical tank shell buckling strength σcr critical buckling stress σeu effective ultimate stress σh hoop stress σhP hoop pressure stress σi standard deviation of xi σm meridional stress σmDL meridional dead load stress σmP meridional pressure stress σmSV meridional seismic stress σp tank shell classical buckling strength adjusted for imperfections σsf standard deviation characterizing the distribution of SF σu ultimate strength (stress) xlii 13633436 σu,B minimum specified ultimate strength of base metal in welded connection (stress) σub median ECCS buckling strength with no internal pressure σum median ultimate strength (stress) σx standard deviation of lognormally distributed random variable x σxi standard deviation of lognormally distributed random variable xi σy yield strength (stress) σy,-1β median minus-one standard deviation value for yield strength σym median yield strength (stress) τwL,m median longitudinal weld shear strength (stress) τwL,CDFM CDFM weld shear strength (stress) Φ(·) standard normal cumulative distribution function Φ-1 inverse standard normal cumulative distribution function ϕ strength reduction factor ϕCDFM CDFM strength reduction factor ϕconc strength reduction factor for concrete breakout equation for deeply embedded anchors ϕpullout CDFM strength factor for pullout failure of hook anchors φs CDFM strength reduction factor for shear φt CDFM strength reduction factor for tension φvs CDFM tank sliding shear strength reduction factor ϕwCDFM CDFM material strength reduction factor for welds φ Eigenvector (mode shape) φnj Eigenvector component for node n and mode j φo maximum mode shape amplitude Ψec,N modification factor from ACI 349 for eccentric loading Ψed,N modification factor from ACI 349 for edge distance effects Ψc.N modification factor from ACI 349 for uncracked concrete Ψcp,N modification factor from ACI 349 for post-installed anchors ω circular frequency ωf circular frequency of floor response spectral ordinate Sanf ωj circular frequency of mode j xliii 13633436 13633436 CONTENTS ABSTRACT ................................................................................................................................. III EXECUTIVE SUMMARY ..............................................................................................................V LIST OF ACRONYMS ................................................................................................................VII LIST OF DEFINITIONS AND SYMBOLS ..................................................................................XIII 1 INTRODUCTION AND SCOPE .............................................................................................. 1-1 1.1 Introduction ..................................................................................................................... 1-1 1.2 Objective ......................................................................................................................... 1-2 1.3 Scope and Report Organization ...................................................................................... 1-3 2 BACKGROUND ...................................................................................................................... 2-1 2.1 SPRA Background .......................................................................................................... 2-1 2.1.1 Overall SPRA Methodology ..................................................................................... 2-1 2.1.2 Fragility Evaluation in an SPRA............................................................................... 2-3 2.2 SMA Background ............................................................................................................ 2-5 2.2.1 Overall SMA Methodology ....................................................................................... 2-5 2.2.2 HCLPF Evaluation ................................................................................................... 2-7 2.3 Hybrid Approach.............................................................................................................. 2-7 3 FRAGILITY METHODOLOGIES ............................................................................................ 3-1 3.1 Fragility Concept ............................................................................................................. 3-1 3.1.1 Failure Modes .......................................................................................................... 3-1 3.1.2 Seismic Capacity ..................................................................................................... 3-3 3.1.3 Seismic Response and Seismic Demand ................................................................ 3-3 3.1.4 Seismic Fragility ...................................................................................................... 3-5 3.2 Lognormal Fragility Model ............................................................................................... 3-8 3.2.1 Equations for a Single Lognormal Variable ............................................................. 3-8 xlv 13633436 3.2.2 Double Lognormal Seismic Fragility Model ........................................................... 3-13 3.2.3 Useful Properties of the Lognormal Distribution .................................................... 3-17 3.3 Separation of Variables Fragility Approach ................................................................... 3-19 3.3.1 Median Capacity as a Product of Factors .............................................................. 3-20 3.3.2 Analytical Procedures for Developing Fragility Curves .......................................... 3-24 3.3.2.1 Approximate Second Moment Procedure ...................................................... 3-25 3.3.2.2 Other Second Moment Procedures ............................................................... 3-27 Second Moment-First Order .................................................................................. 3-27 Second Moment-Second Order Mean .................................................................. 3-28 Approximate Second Moment – Generalized ....................................................... 3-29 3.3.2.3 Monte Carlo Simulation.................................................................................. 3-30 3.3.2.4 Latin Hypercube Simulation ........................................................................... 3-35 3.3.2.5 Example Analyses Comparing Analytical Procedures ................................... 3-36 3.4 Hybrid Fragility Approach .............................................................................................. 3-38 3.4.1 Conservative Deterministic Failure Margin Method ............................................... 3-39 3.4.2 Approximating Fragility Curves .............................................................................. 3-43 4 SEISMIC CAPACITY .............................................................................................................. 4-1 4.1 Capacity Factor ............................................................................................................... 4-2 4.1.1 Fragilities Based on Seismic Experience ................................................................ 4-2 4.1.2 Fragilities Based on Analysis ................................................................................... 4-3 4.1.2.1 Elastic Strength Factor..................................................................................... 4-3 4.1.2.2 Inelastic Energy Absorption Factor .................................................................. 4-4 4.1.2.3 Criteria for SOV and CDFM Evaluations.......................................................... 4-5 4.1.3 Fragilities Based on Test ......................................................................................... 4-5 4.2 Seismic Capacities Based on Experience ....................................................................... 4-7 4.2.1 Seismic Capacities for Equipment ........................................................................... 4-9 4.2.2 Capacities for Structures ....................................................................................... 4-15 4.2.3 Application of Capacity Tables in SPRA ................................................................ 4-17 4.3 Material Strengths ......................................................................................................... 4-19 4.3.1 Concrete Material Strength.................................................................................... 4-19 4.3.2 Steel Material Strength .......................................................................................... 4-22 4.4 Structure Failure Modes and Capacities ....................................................................... 4-23 4.4.1 Concrete Shear Wall Strength Equations .............................................................. 4-25 4.4.1.1 Diagonal Shear Cracking ............................................................................... 4-26 xlvi 13633436 Shear Walls with Boundary Elements ................................................................... 4-26 Rectangular Shear Walls ...................................................................................... 4-31 4.4.1.2 Flexural Capacity ........................................................................................... 4-31 4.4.1.3 Shear Friction Capacity.................................................................................. 4-33 4.4.1.4 Out-of-Plane Shear Capacity ......................................................................... 4-33 4.4.2 Tangential Shear Strength of Cylindrical Concrete Walls ...................................... 4-34 4.4.2.1 Pressurized Cylindrical Concrete Walls ......................................................... 4-35 4.4.2.2 Unpressurized Cylindrical Concrete Walls ..................................................... 4-36 4.4.3 Masonry Walls ....................................................................................................... 4-37 4.5 Structure Inelastic Energy Absorption ........................................................................... 4-37 4.5.1 Ductile Failure Modes ............................................................................................ 4-38 4.5.2 Inelastic Deformation Limits .................................................................................. 4-39 4.5.3 System Ductility ..................................................................................................... 4-42 4.5.4 Approximate Method of Calculating Inelastic Energy Absorption .......................... 4-43 4.5.4.1 Effective Frequency/Effective Damping Method ............................................ 4-44 4.5.4.2 Logarithmic Standard Deviations ................................................................... 4-45 4.5.5 Conservative Representative Inelastic Energy Absorption Factors ....................... 4-46 4.6 Equipment Failure Modes and Capacities..................................................................... 4-48 4.6.1 Passive Equipment ................................................................................................ 4-48 4.6.2 Active Equipment................................................................................................... 4-50 4.6.3 Distribution Systems .............................................................................................. 4-51 4.6.3.1 Piping ............................................................................................................. 4-51 4.6.3.2 Electrical Raceways ....................................................................................... 4-54 4.6.3.3 HVAC Ducting ................................................................................................ 4-55 4.6.4 Sampling Evaluation of Equipment and Subsystems ............................................ 4-56 4.7 Anchorage Failure Modes and Capacities .................................................................... 4-57 4.7.1 Steel Anchorage Failure Modes ............................................................................ 4-57 4.7.1.1 Cast-in-Place Bolts ........................................................................................ 4-59 4.7.1.2 Welds ............................................................................................................. 4-59 4.7.1.2.1 Capacity Under Longitudinal Shear Load .............................................. 4-60 4.7.1.2.2 Capacity Under Transverse and Combined Shear Loads ...................... 4-61 4.7.1.3 Plates in Bending ........................................................................................... 4-62 4.7.2 Concrete Failure Modes ........................................................................................ 4-63 4.7.2.1 Concrete Breakout of Cast-in-Place Anchors ................................................ 4-63 4.7.2.2 Concrete Breakout of Post-Installed Anchors ................................................ 4-64 xlvii 13633436 4.7.2.3 Splitting Failure .............................................................................................. 4-64 4.7.3 Pullout Failure Modes ............................................................................................ 4-65 4.7.3.1 Post-Installed Anchors ................................................................................... 4-65 4.7.3.2 Hook Anchors ................................................................................................ 4-65 4.7.4 Tension-Shear Interaction Equation ...................................................................... 4-67 4.8 Equipment Inelastic Energy Absorption ........................................................................ 4-67 4.9 Seismic Capacities Based on Test ................................................................................ 4-69 4.9.1 TRS Clipping Factor .............................................................................................. 4-70 4.9.2 Capacity Increase Factor....................................................................................... 4-71 4.9.3 Multi-Axis to Single-Axis Conservatism Factor ...................................................... 4-72 4.9.4 Broad Frequency Input Spectrum Device Capacity Factor ................................... 4-73 4.9.5 Additional Test Experience .................................................................................... 4-75 5 SEISMIC DEMAND ................................................................................................................ 5-1 5.1 General ........................................................................................................................... 5-1 5.2 Reference Earthquake .................................................................................................... 5-3 5.2.1 Definition of Reference Earthquake ......................................................................... 5-3 5.2.2 Nonlinear Effects in Structure Response ................................................................. 5-4 5.2.3 Determination of Reference Earthquake ................................................................. 5-5 5.2.4 Application of the Reference Earthquake ................................................................ 5-7 5.2.5 Validation of the Reference Earthquake Selection .................................................. 5-7 5.2.6 Reference Earthquake Control Point ....................................................................... 5-7 5.2.7 Alternatives to Reference Earthquake Approach .................................................... 5-9 5.3 Evaluation of Median and 84th Percentile Seismic Demand........................................... 5-9 5.3.1 Structure Modeling ................................................................................................ 5-10 5.3.1.1 Structure Material Properties ......................................................................... 5-11 5.3.1.2 Structure Stiffness.......................................................................................... 5-11 5.3.1.3 Structure Mass ............................................................................................... 5-13 5.3.1.4 Structure Damping ......................................................................................... 5-14 5.3.2 Soil-Structure Interaction ....................................................................................... 5-14 5.3.3 Ground Motion Incoherence .................................................................................. 5-15 5.3.4 Scaling of Existing Analytical Results .................................................................... 5-16 5.3.5 Deterministic Seismic Response Analyses ........................................................... 5-18 5.3.5.1 Soil Property Variation ................................................................................... 5-20 5.3.5.2 Structure Property Variation........................................................................... 5-21 xlviii 13633436 5.3.5.3 Median and 84% NEP Response .................................................................. 5-22 5.3.5.4 Variability in Other Structure Response Parameters ..................................... 5-22 5.3.6 Probabilistic Seismic Response Analyses ............................................................. 5-23 5.4 Response Variables for Structure Fragilities ................................................................. 5-29 5.4.1 Ground Motion ....................................................................................................... 5-30 5.4.1.1 Earthquake Response Spectrum Shape........................................................ 5-30 5.4.1.2 Horizontal Direction Peak Response Variability............................................. 5-31 5.4.1.3 Vertical Response Variability ......................................................................... 5-33 5.4.2 Structure Damping................................................................................................. 5-33 5.4.3 Structure Modeling ................................................................................................ 5-35 5.4.3.1 Structure Frequency ...................................................................................... 5-35 5.4.3.2 Model Fidelity ................................................................................................. 5-35 5.4.3.3 Torsional Coupling ......................................................................................... 5-36 5.4.4 Structure Response Phasing ................................................................................. 5-36 5.4.4.1 Time-History Phasing..................................................................................... 5-36 5.4.4.2 Mode Combination Phasing ........................................................................... 5-38 5.4.5 Foundation-Structure Interaction ........................................................................... 5-38 5.4.5.1 Ground Motion Incoherence .......................................................................... 5-39 5.4.5.2 Soil Structure Interaction................................................................................ 5-40 5.4.5.3 Vertical Spatial Variation ................................................................................ 5-40 5.4.6 Earthquake Component Combination ................................................................... 5-40 5.4.7 Structure Response Variability from Probabilistic Analysis ................................... 5-41 5.5 Response Variables for Equipment Fragilities .............................................................. 5-43 5.5.1 Structure Response for Equipment Fragilities ....................................................... 5-45 5.5.1.1 Structure Frequency ...................................................................................... 5-45 5.5.1.2 Earthquake Component Combination ............................................................ 5-46 5.5.1.3 Inelastic Structure Response Factor .............................................................. 5-47 5.5.1.4 Probabilistic Structure Response Analysis .................................................... 5-48 5.5.2 Equipment Response for Fragility Based on Analysis ........................................... 5-48 5.5.2.1 Qualification Method ...................................................................................... 5-49 5.5.2.2 Equipment Damping ...................................................................................... 5-51 5.5.2.3 Equipment Modeling ...................................................................................... 5-52 Frequency ............................................................................................................. 5-52 Fidelity (Mode Shape) ........................................................................................... 5-52 5.5.2.4 Equipment Response Phasing (Mode Combination) ..................................... 5-52 xlix 13633436 5.5.2.5 Earthquake Component Combination ............................................................ 5-53 5.5.3 Equipment Response for Fragility Based on Testing ............................................ 5-53 5.5.3.1 Response Spectra Clipping ........................................................................... 5-54 5.5.3.2 Cabinet Amplification ..................................................................................... 5-59 5.5.3.3 Boundary Conditions ..................................................................................... 5-60 5.5.3.4 Building Response ......................................................................................... 5-61 6 FRAGILITY IMPLEMENTATION TOPICS ............................................................................. 6-1 6.1 Seismic Walkdown .......................................................................................................... 6-1 6.1.1 Past Seismic Walkdown Approaches and Strategies .............................................. 6-2 6.1.2 Composition and Qualifications of Seismic Review Team ...................................... 6-3 6.1.3 Pre-Walkdown Preparation...................................................................................... 6-5 6.1.4 Detailed Walkdowns vs. Walk-Bys .......................................................................... 6-8 6.1.5 Component Capacity Estimation ............................................................................. 6-9 6.1.6 Walkdown Documentation ..................................................................................... 6-10 6.2 Screening and Representative Fragilities...................................................................... 6-11 6.2.1 Screening of Inherently Rugged SSCs .................................................................. 6-11 6.2.2 Screening of High-Capacity Components ............................................................. 6-13 6.2.3 Representative Fragilities ...................................................................................... 6-15 6.2.4 Example Approach for Developing Representative Fragilities .............................. 6-16 6.2.4.1 Selecting Representative Fragility Data ......................................................... 6-16 6.2.4.2 Filtering and Screening of the SEL ................................................................ 6-17 6.2.4.3 Developing Seismic Capacities...................................................................... 6-17 Rugged Rank ........................................................................................................ 6-17 High Rank ............................................................................................................. 6-18 Medium Rank ........................................................................................................ 6-18 Low Rank .............................................................................................................. 6-18 6.2.4.4 Develop Seismic Response and Representative Fragilities .......................... 6-19 6.3 Outline of Relay Evaluation ........................................................................................... 6-19 6.4 Special Considerations for High-Frequency Seismic Demands .................................... 6-21 6.4.1 High-Frequency Test Capacities for Fragility Evaluation ....................................... 6-22 6.4.2 High-Frequency Inelastic Effects on Anchorage Systems ..................................... 6-24 6.4.2.1 Equipment Subjected to Single Direction Seismic Input ................................ 6-25 6.4.2.2 Equipment Subjected to Multi-Directional Seismic Input ............................... 6-29 6.4.3 Seismic Response Considerations ........................................................................ 6-31 l 13633436 6.4.3.1 Spectral Averaging for In-Structure Response Spectra ................................. 6-31 6.4.3.2 Equipment-Structure Interaction .................................................................... 6-32 6.4.4 Qualitative Methods for Considering High-Frequency Motions ............................. 6-32 6.5 Methods for Spectral Clipping ....................................................................................... 6-33 6.5.1 Spectral Clipping for Deterministic ISRS ............................................................... 6-33 6.5.1.1 Deterministic Method 1 .................................................................................. 6-34 6.5.1.2 Deterministic Method 2 .................................................................................. 6-34 6.5.2 Spectral Clipping for Probabilistic ISRS ................................................................ 6-35 6.6 Structure Models for Seismic Response Analysis ......................................................... 6-36 6.7 Response Analysis Scaling Methods ............................................................................ 6-38 6.7.1 Scaling Structure Seismic Demands ..................................................................... 6-39 6.7.1.1 Scaling Structure Forces................................................................................ 6-39 6.7.1.2 Scaling In-Structure Response Spectra ......................................................... 6-42 6.7.2 Scaling Seismic Demands for Components and Subsystems ............................... 6-44 6.7.2.1 Fifteen Response Analysis Scaling Cases .................................................... 6-45 Scaling for Case 1 ................................................................................................. 6-46 Scaling for Case 2 ................................................................................................. 6-46 Scaling for Case 3 ................................................................................................. 6-47 Scaling for Case 4 ................................................................................................. 6-47 Scaling for Case 5 ................................................................................................. 6-47 Scaling for Case 6 ................................................................................................. 6-49 Scaling for Case 7 ................................................................................................. 6-50 Scaling for Case 8 ................................................................................................. 6-50 Scaling for Case 9 ................................................................................................. 6-50 Scaling for Case 10 ............................................................................................... 6-50 Scaling for Case 11 ............................................................................................... 6-50 Scaling for Case 12 ............................................................................................... 6-50 Scaling for Case 13 ............................................................................................... 6-51 Scaling for Case 14 ............................................................................................... 6-51 Scaling for Case 15 ............................................................................................... 6-52 6.7.2.2 Alternatives to Scaling ................................................................................... 6-52 6.8 Combining Fragilities for Multiple Failure Modes .......................................................... 6-52 7 REFERENCES ....................................................................................................................... 7-1 li 13633436 A ENGLISH TO SI UNIT CONVERSION ................................................................................. A-1 B WALKDOWN GUIDANCE .................................................................................................... B-1 B.1 Walkdown Checklists ..................................................................................................... B-1 B.1.1 Motor Control Centers and Low and Medium Voltage Switchgear Units ............... B-2 B.1.2 Batteries and Racks ............................................................................................... B-4 B.1.3 Battery Chargers and Inverters .............................................................................. B-5 B.1.4 Transformers .......................................................................................................... B-6 B.1.5 Control and Instrumentation Panels ....................................................................... B-7 B.1.6 Instrument Racks ................................................................................................... B-9 B.1.7 Distribution Panels ............................................................................................... B-10 B.1.8 Local Instruments and Sensors............................................................................ B-11 B.1.9 Engine Generators ............................................................................................... B-11 B.1.10 Motor Generators ............................................................................................... B-13 B.1.11 Horizontal Pumps ............................................................................................... B-14 B.1.12 Vertical Pumps ................................................................................................... B-15 B.1.13 Air- or Fluid-Operated Valves (Diaphragm or Piston Type) or Dampers ............ B-16 B.1.14 Motor-Operated Valves or Dampers .................................................................. B-18 B.1.15 Solenoid-Operated Valves ................................................................................. B-19 B.1.16 Air Compressors ................................................................................................ B-19 B.1.17 Fans and Air Handlers ....................................................................................... B-20 B.1.18 Chillers ............................................................................................................... B-22 B.1.19 Frame or Skirt Supported Vertical Tanks and Heat Exchangers (also Flat Bottom Tanks) ............................................................................................................... B-24 B.1.20 Horizontal Saddle or Cradle Supported Tanks or Heat Exchangers .................. B-25 B.1.21 Horizontal Suspended Tanks ............................................................................. B-26 B.1.22 Buried Tanks ...................................................................................................... B-26 B.1.23 Building Penetrations of Underground Utilities ................................................... B-27 B.1.24 Strainers and Filters ........................................................................................... B-27 B.1.25 NSSS Components and Primary Coolant Loops ............................................... B-27 B.1.26 Control Rod Drive Assemblies ........................................................................... B-28 B.1.27 Building Seismic Gaps ....................................................................................... B-28 B.1.28 Control Room Ceilings ....................................................................................... B-29 lii 13633436 B.1.29 Traveling Screens and Sluice Gates .................................................................. B-29 B.1.30 Manual Valves or Dampers ................................................................................ B-30 B.1.31 Generic Components ......................................................................................... B-30 B.2 Area Walkdown Reviews ............................................................................................. B-30 B.2.1 Electrical Conduit and Cable Tray Raceways ...................................................... B-31 B.2.2 Balance-of-Plant Piping........................................................................................ B-31 B.2.3 HVAC Ducting ...................................................................................................... B-32 B.3 Seismic Spatial Systems Interactions .......................................................................... B-33 B.3.1 Proximity .............................................................................................................. B-33 B.3.2 II/I Interactions...................................................................................................... B-35 B.3.3 Spray and Flooding .............................................................................................. B-36 B.4 Walkdown Data Sheets................................................................................................ B-37 B.5 References................................................................................................................... B-39 C WALKDOWN CRITERIA: BASIS FOR SEISMIC CAPACITY GUIDELINES FOR STRUCTURES, EQUIPMENT, AND SUBSYSTEMS............................................................... C-1 C.1 General Discussion........................................................................................................ C-1 C.2 Background and Discussion of Capacity Guidelines ..................................................... C-2 C.2.1 Reactor Containment Structures............................................................................ C-3 C.2.1.1 Primary Containment...................................................................................... C-3 C.2.1.2 Internal Structures .......................................................................................... C-4 C.2.2 Category I Concrete Structures Designed for Seismic Loads ................................ C-4 C.2.2.1 Shear Walls and Footings .............................................................................. C-4 C.2.2.2 Diaphragms (Includes Roofs) ......................................................................... C-5 C.2.2.3 Steel and Concrete Frame Construction ........................................................ C-6 C.2.3 Non-Category I Structures ..................................................................................... C-6 C.2.4 Masonry (Block) Walls ........................................................................................... C-6 C.2.5 Control Room Ceilings ........................................................................................... C-7 C.2.6 Impact Between Structures .................................................................................... C-7 C.2.7 Other Structure Failure Modes............................................................................... C-7 C.2.8 NSSS Primary Coolant System and Supports ....................................................... C-8 C.2.9 Reactor Internals .................................................................................................... C-9 C.2.10 Control Rod Drives............................................................................................... C-9 C.2.11 Piping ................................................................................................................. C-10 C.2.12 Valves ................................................................................................................ C-11 liii 13633436 C.2.13 Heat Exchangers ............................................................................................... C-12 C.2.14 Tanks ................................................................................................................. C-12 C.2.14.1 Atmospheric Storage Tanks ....................................................................... C-12 C.2.14.2 Pressure Vessels ....................................................................................... C-12 C.2.14.3 Buried Tanks .............................................................................................. C-13 C.2.15 Batteries and Racks ........................................................................................... C-13 C.2.16 Diesel Generators .............................................................................................. C-13 C.2.17 Pumps ................................................................................................................ C-14 C.2.18 HVAC Systems .................................................................................................. C-14 C.2.19 Cable Trays and Cabling ................................................................................... C-15 C.2.20 Electrical Conduit ............................................................................................... C-16 C.2.21 Active Electrical Equipment ............................................................................... C-17 C.2.22 Other Electrical Components ............................................................................. C-17 C.3 Earthquake Experience Data ....................................................................................... C-17 C.4 Seismic Qualification Data ........................................................................................... C-20 C.5 Aging Effects................................................................................................................ C-23 C.6 Probabilistic Risk Assessment Fragilities .................................................................... C-27 C.7 Fragility Data from SAFEGUARD Program ................................................................. C-29 C.7.1 Shock Environment .............................................................................................. C-30 C.7.2 Applicable of Shock Test Data ............................................................................. C-33 C.7.3 Fragility Results of Shock Tests ........................................................................... C-34 C.7.3.1 Mechanical and Passive Electrical Equipment ............................................. C-34 C.7.3.2 Active Electrical and Electro-Mechanical Equipment ................................... C-35 C.7.3.3 Motor Control Centers .................................................................................. C-44 C.7.3.4 Low-Voltage Switchgear............................................................................... C-44 C.7.3.5 Medium-Voltage Switchgear ........................................................................ C-44 C.7.3.6 Distribution Panels ....................................................................................... C-45 C.8 Electrical Cable Raceways .......................................................................................... C-46 C.8.1 Tests of Modern Commercial Raceways and Conduit ......................................... C-46 C.8.2 Rod Hung Raceways ........................................................................................... C-48 C.9 Piping Systems ............................................................................................................ C-48 C.10 References ................................................................................................................ C-50 liv 13633436 D WALKDOWN CRITERIA: SAMPLING GUIDELINES .......................................................... D-1 D.1 Introduction .................................................................................................................... D-1 D.2 Capacity Table Sampling ............................................................................................... D-2 D.3 Walkdown Sampling ...................................................................................................... D-3 D.4 Sampling Analyses ........................................................................................................ D-5 D.5 References .................................................................................................................... D-6 E FRAGILITY METHODS: BACKGROUND ON RECOMMENDATIONS FOR HOOK ANCHORS AND DEEPLY EMBEDDED ANCHORS ............................................................... E-1 E.1 Background .................................................................................................................... E-1 E.2 L-Bolts ............................................................................................................................ E-2 E.2.1 Test Data................................................................................................................ E-2 E.2.2 Pullout Failure Prediction Equations ...................................................................... E-2 E.2.3 Pullout Failure Prediction Equation Recommendation ........................................... E-3 E.2.4 Recommended Strength Reduction Factor ............................................................ E-4 E.2.5 Conclusion ............................................................................................................. E-4 E.3 J-Bolts ............................................................................................................................ E-5 E.4 Deeply Embedded Headed Bolts and Studs.................................................................. E-6 E.4.1 Test Data................................................................................................................ E-6 E.4.2 Concrete Breakout Strength Equations .................................................................. E-7 E.4.3 Developing a Strength Equation ............................................................................ E-7 E.4.4 Recommended Strength Reduction Factor ............................................................ E-8 E.4.5 Conclusion ............................................................................................................. E-9 E.6 References..................................................................................................................... E-9 F FRAGILITY METHODS: CDFM CAPACITY CRITERIA FOR EXPANSION ANCHORS ......F-1 F.1 Introduction .....................................................................................................................F-1 F.2 Factor of Safety for Uncracked Concrete ........................................................................F-1 F.3 Influence of Small Concrete Cracks on Capacity ............................................................F-2 F.4 References ......................................................................................................................F-5 G FRAGILITY METHODS: COMPARISON OF ASCE/SEI 43 DESIGN CRITERIA AND CDFM CRITERIA FOR LOW DUCTILITY FAILURE MODES ................................................. G-1 G.1 Introduction .................................................................................................................... G-1 G.2 ASCE/SEI 43-05 Design Strength and Demand Criteria for Low Ductility Failure Modes .................................................................................................................................. G-2 lv 13633436 G.3 EPRI NP-6041-SLR1 CDFM Strength and Demand Criteria for Low Ductility Failure Mode ........................................................................................................................ G-4 G.4 Recommendation for Estimating the Mean 1% Probability of Failure in a Fragility Evaluation ............................................................................................................................ G-5 G.5 References .................................................................................................................... G-6 H FRAGILITY METHODS: ISSUES CONCERNING THE INCLUSION OF RESPONSE SPECTRAL PEAK AND VALLEY VARIABILITY IN DEVELOPMENT OF FRAGILITY AND HCLPF CAPACITY ESTIMATES .................................................................................... H-1 H.1 Introduction .................................................................................................................... H-1 H.2 Recommendation for Modifying Existing Fragility Analyses .......................................... H-2 H.3 Recommendation for New Fragility Analysis ................................................................. H-4 H.4 Recommendation for use of HCLPF Capacities Computed by the Conservative Deterministic Failure Margin Methodology ........................................................................... H-4 H.5 Discussion of the Terms HCLPF50 Versus HCLPF84 ..................................................... H-6 H.6 Use of Screening Tables in SPRA ................................................................................. H-7 H.7 Summary of Recommendations .................................................................................... H-9 H.8 References .................................................................................................................. H-10 Supplement A – Updated Description of the Conservative Deterministic Failure Margin Method for Computing Seismic Capacity ............................................................... H-11 H-A.1 Background ......................................................................................................... H-11 H-A.2 General Criteria of CDFM Method ....................................................................... H-12 H-A.3 Estimation of the Conservatism Introduced by the CDFM Method Generally Applied........................................................................................................................... H-14 H-A.3.1 Basic Approach............................................................................................ H-14 H-A.3.2 Median Strength Conservatism Ratio .......................................................... H-15 H-A.3.3 Median Demand Conservatism Ratio .......................................................... H-15 H-A.3.4 Median Nonlinear Conservatism Ratio ........................................................ H-16 H-A.3.5 Resulting CDFM Capacity Conservatism .................................................... H-16 H-A.4 Conclusion........................................................................................................... H-18 Supplement B – Other Related HCLPF and Fragility Issues.............................................. H-19 H-B.1 Correction of Randomness R and Uncertainty U............................................... H-19 H-B.2 Conversion of EPRI NP-6041-SLR1 Table 2-4 to Terms of 5% Damped Peak Spectral Acceleration at Base of Component ....................................................... H-19 lvi 13633436 I FRAGILITY METHODS: HORIZONTAL DIRECTION PEAK RESPONSE VARIABILITY ............................................................................................................................. I-1 I.1 Background ....................................................................................................................... I-1 I.2 HDPR Factor for Seismic Fragility Analyses ..................................................................... I-1 I.2.1 Case 1: Specific Direction Response ........................................................................ I-2 I.2.2 Case 2: Collinear Vector Response .......................................................................... I-2 I.2.3 Case 3: General Vector Response ............................................................................ I-3 I.2.4 Case 4: Axisymmetric Largest Direction Response .................................................. I-3 I.3 HDPR Factor for Seismic Margin Analyses....................................................................... I-5 I.4 References ........................................................................................................................ I-7 J FRAGILITY METHODS: DEVELOPMENT OF TEST-BASED FRAGILITY PARAMETERS .......................................................................................................................... J-1 J.1 HCLPF Capacities Derived from GERS .......................................................................... J-1 J.1.1 High Confidence Low Probability of Failure Capacities from Generic Equipment Ruggedness Spectra ...................................................................................... J-2 J.2 Effective Amplification Factors ........................................................................................ J-5 J.2.1 Effective Amplification Factors for Motor Control Centers and Switchgear ............. J-6 J.3 Seismic Margin Capacity of Components Based upon Seismic Testing ......................... J-9 J.3.1 Guidance for Capacity Determination for Tested Components ............................... J-9 J.3.1.1 Example Component Subjected to Broad Frequency Input Spectrum........... J-19 J.3.1.2 Example Component Subjected to Narrow Frequency Input Spectrum......... J-22 J.4 References .................................................................................................................... J-25 K FRAGILITY METHODS: TREATMENT OF SMALL-SMALL LOSS OF COOLANT ACCIDENTS IN FRAGILTY ANALYSIS .................................................................................. K-1 K.1 Background .................................................................................................................... K-1 K.2 Objective ........................................................................................................................ K-2 K.3 Approach ....................................................................................................................... K-2 K.4 SSLOCA Walkdown and Fragility Experience ............................................................... K-2 K.4.1 Plant A: B&W Lowered Loop PWR 2010s SPRA ................................................... K-4 K.4.2 Plant B: WEC 4-Loop PWR 2010s SPRA .............................................................. K-6 K.4.3 Plant C: WEC 4-Loop PWR 2010s SPRA .............................................................. K-6 K.4.4 Plant D: WEC 4-Loop PWR 2010s SPRA .............................................................. K-7 K.4.5 Plant E: WEC 4-Loop PWR 1987 SMA .................................................................. K-8 K.4.6 Plant F: WEC 2-Loop PWR 1994 SPRA and 2004 Update ................................... K-8 lvii 13633436 K.4.7 Plant G: WEC 2-Loop PWR 1990s Safety Upgrade Program ................................ K-8 K.4.8 Plant H: GE Mark I BWR 2010s SPRA .................................................................. K-9 K.4.9 Plant I: Candu 6 PHWR 2010s SPRA .................................................................... K-9 K.4.10 Plant J: Framatome PWR 2000s SPRA ............................................................. K-10 K.4.11 Plant K: Siemens PHWR 2010s SMA ................................................................ K-10 K.5 Summary and Recommendations................................................................................ K-11 K.6 References................................................................................................................... K-13 L RESPONSE ANALYSIS: REFINEMENT OF IN-CABINET AMPLIFICATION FACTORS ..................................................................................................................................L-1 L.1 Comparison of Mounting Point Seismic Demand with Test Capacity ............................. L-1 L.2 Mounting Point Seismic Demand .................................................................................... L-1 L.3 Refinement of Demand Estimates................................................................................... L-2 L.3.1 Low- and Medium-Amplification Cabinets ............................................................... L-3 L.3.2 Low- and Medium-Amplification Cabinets with Top Bracing ................................... L-4 L.3.3 High-Amplification Cabinets .................................................................................... L-4 M RESPONSE ANALYSIS: BENCHMARK STUDIES TO VERIFY AN APPROXIMATE METHOD FOR SPECTRA SCALING ...................................................................................... M-1 M.1 Background ................................................................................................................... M-1 M.2 Verification of Original Spectra to be Scaled ................................................................. M-1 M.3 Development of Scaled Spectra by Rigorous and by Simplified Means ..................... M-10 M.4 References .................................................................................................................. M-15 N RESPONSE ANALYSIS: DEVELOPMENT OF IN-STRUCTURE RESPONSE SPECTRA FOR SEISMIC MARGIN OR SPRA EVALUATION BY SCALING ........................ N-1 N.1 Introduction .................................................................................................................... N-1 N.2 Spectral Estimation Method ........................................................................................... N-1 N.3 References .................................................................................................................... N-5 O EXAMPLE: FRAGILITY ANALYSIS OF A REINFORCED CONCRETE SHEAR WALL........................................................................................................................................ O-1 O.1 Overview........................................................................................................................ O-1 O.2 Seismic Demand and Median Structure Response Factor............................................ O-3 O.3 Median Capacity Factor................................................................................................. O-4 O.3.1 Median Elastic Strength Factor .............................................................................. O-4 O.3.1.1 Diagonal Shear Strength ................................................................................ O-4 lviii 13633436 O.3.1.2 Flexure ........................................................................................................... O-7 O.3.1.3 Median Elastic Strength Factor Summary.................................................... O-11 O.3.2 Median Inelastic Energy Absorption Factor ......................................................... O-13 O.3.3 Median Capacity Factor Summary ...................................................................... O-17 O.4 Logarithmic Standard Deviations................................................................................. O-17 O.4.1 Structure Response Variability ............................................................................ O-18 O.4.1.1 Ground Motion ............................................................................................. O-19 O.4.1.1.1 Earthquake Response Spectrum Shape ................................................... O-19 O.4.1.1.2 Horizontal Direction Random Variability.................................................... O-19 O.4.1.1.3 Vertical Response Variability .................................................................... O-19 O.4.1.2 Structure Damping ....................................................................................... O-20 O.4.1.3 Structure Modeling ....................................................................................... O-20 O.4.1.3.1 Structure Frequency ............................................................................. O-20 O.4.1.3.2 Model Fidelity ............................................................................................ O-20 O.4.1.3.3 Torsional Coupling .................................................................................... O-20 O.4.1.4 Structure Response Phasing ....................................................................... O-20 O.4.1.5 Foundation-Structure Interaction.................................................................. O-21 O.4.1.6 Earthquake Component Combination .......................................................... O-21 O.4.2 Structure Capacity Variability ............................................................................... O-21 O.4.2.1 Elastic Strength Factor ................................................................................. O-22 O.4.2.2 Inelastic Energy Absorption ......................................................................... O-22 O.5 Shear Wall Fragility Parameters .................................................................................. O-23 O.6 References .................................................................................................................. O-23 P EXAMPLE: CYLINDRICAL CONCRETE WALL CDFM CAPACITY ................................... P-1 Q EXAMPLE: CDFM ANALYSIS OF LIGHTLY REINFORCED NON-LOAD BEARING MASONRY WALLS .................................................................................................................. Q-1 Q.1 Introduction .................................................................................................................... Q-1 Q.2 Ultimate Moment Capacity ............................................................................................ Q-2 Q.3 Limit on Permissible Drive ............................................................................................. Q-5 Q.3.1 Best Estimate......................................................................................................... Q-6 Q.3.2 CDFM Permissible Drift Limit ................................................................................. Q-7 Q.4 Seismic Capacity ........................................................................................................... Q-7 Q.5 Secant Frequency ......................................................................................................... Q-8 lix 13633436 Q.6 Effective Nonlinear Demand .......................................................................................... Q-8 Q.7 Ground Motion CDFM Capacity .................................................................................... Q-9 Q.8 References .................................................................................................................. Q-10 R EXAMPLE: COMPARISON OF ASCE/SEI 43-05/BARDA AND GULEC/WHITTAKER STRENGTHS FOR AN EXAMPLE LOW-RISE SHEAR WALL ............................................... R-1 R.1 ASCE 43-05/Barda Strength.......................................................................................... R-1 R.2 Gulec and Whittaker Strength........................................................................................ R-3 R.3 Conclusion ..................................................................................................................... R-6 S EXAMPLE: FRAGILITY AND CDFM ANALYSIS OF A METAL FLAT-BOTTOM VERTICAL LIQUID STORAGE TANK ..................................................................................... S-1 S.1 Overview ........................................................................................................................ S-1 S.2 Tank Seismic Response Analysis .................................................................................. S-3 S.2.1 Horizontal Impulsive Mode Response .................................................................... S-3 S.2.1.1 Effective Fluid Weight ..................................................................................... S-3 S.2.1.2 Frequency and Damping ................................................................................ S-4 S.2.1.3 Base Shear and Overturning Moment ............................................................ S-6 S.2.1.4 Hydrodynamic Fluid Pressures....................................................................... S-6 S.2.2 Horizontal Sloshing Mode (Convective Mode) ....................................................... S-7 S.2.2.1 Effective Weight of Liquid ............................................................................... S-7 S.2.2.2 Frequency and Damping ................................................................................ S-7 S.2.2.3 Base Shear and Overturning Moment ............................................................ S-8 S.2.2.4 Hydrodynamic Fluid Pressures....................................................................... S-8 S.2.2.5 Fluid Slosh Height .......................................................................................... S-8 S.2.3 Vertical Fluid Mode ................................................................................................ S-8 S.2.3.1 Frequency and Damping ................................................................................ S-8 S.2.3.2 Hydrodynamic Fluid Pressures....................................................................... S-9 S.2.4 Total Seismic Demands ......................................................................................... S-9 S.2.4.1 Base Shear and Overturning Moment ............................................................ S-9 S.2.4.2 Total Fluid Pressures ................................................................................... S-10 S.2.4.3 Total Fluid Pressures ................................................................................... S-10 S.3 Tank Seismic Capacity Evaluation............................................................................... S-11 S.3.1 Overturning Moment Strength .............................................................................. S-11 S.3.1.1 Tank Shell Compressive Buckling Strength ................................................. S-11 S.3.1.2 Bolt Hold-Down Strength .............................................................................. S-14 lx 13633436 S.3.1.3 Permissible Tank Uplift Height ..................................................................... S-14 S.3.1.4 Fluid Hold-Down Forces ............................................................................... S-15 S.3.1.5 Anchor Bolt Hold-Down Forces .................................................................... S-20 S.3.1.6 Overturning Moment Strength ...................................................................... S-21 S.3.1.7 Inelastic Energy Absorption Factor............................................................... S-22 S.3.2 Tank Sliding Evaluation........................................................................................ S-23 S.3.3 Freeboard Evaluation ........................................................................................... S-24 S.4 Example Tank CDFM Evaluation ................................................................................. S-24 S.4.1 Tank Seismic Response Evaluation ..................................................................... S-25 S.4.1.1 Horizontal Impulsive Mode Response .......................................................... S-25 S.4.1.2 Horizontal Sloshing Mode Response ........................................................... S-27 S.4.1.3 Vertical Fluid Mode Response...................................................................... S-29 S.4.1.4 Total Seismic Demands................................................................................ S-29 S.4.2 Tank Seismic Capacity Evaluation ....................................................................... S-32 S.4.2.1 Tank Shell Buckling Strength ....................................................................... S-32 S.4.2.2 Bolt Hold-Down Strength .............................................................................. S-34 S.4.2.3 Permissible Tank Uplift Height ..................................................................... S-35 S.4.2.4 Fluid Hold-Down Forces ............................................................................... S-35 S.4.2.5 Bolt Hold-Down Forces................................................................................. S-40 S.4.2.6 Overturning Moment Strength ...................................................................... S-40 S.4.2.7 Tank Sliding Evaluation ................................................................................ S-41 S.4.2.8 Freeboard Evaluation ................................................................................... S-42 S.4.2.9 HCLPF Capacity of Example Tank ............................................................... S-42 S.5 Example Tank Fragility Evaluation............................................................................... S-43 S.5.1 Tank Seismic Response Evaluation ..................................................................... S-43 S.5.1.1 Median Horizontal Impulsive Mode Response ............................................. S-43 S.5.1.2 Median Horizontal Sloshing Mode Response............................................... S-43 S.5.1.3 Median Vertical Fluid Mode Response ......................................................... S-44 S.5.1.4 Total Seismic Demands................................................................................ S-44 S.5.2 Tank Seismic Capacity Evaluation ....................................................................... S-46 S.5.2.1 Median Tank Shell Buckling Strength........................................................... S-46 S.5.2.2 Bolt Hold-Down Strength .............................................................................. S-48 S.5.2.3 Median Permissible Tank Uplift Height......................................................... S-49 S.5.2.4 Fluid Hold-Down Forces ............................................................................... S-49 S.5.2.5 Bolt Hold-Down Forces................................................................................. S-52 lxi 13633436 S.5.2.6 Median Overturning Moment Strength ......................................................... S-53 S.5.2.7 Tank Sliding Evaluation ................................................................................ S-54 S.5.2.8 Freeboard Evaluation ................................................................................... S-54 S.5.3 Median Seismic Capacity ..................................................................................... S-54 S.5.4 Variabilities ........................................................................................................... S-57 S.5.4.1 Response Variables ..................................................................................... S-57 Ground Motion ..................................................................................................... S-57 Tank Damping ...................................................................................................... S-57 Tank Frequency ................................................................................................... S-58 Tank Model Fidelity .............................................................................................. S-58 Mode Combination ............................................................................................... S-58 Earthquake Component Combination .................................................................. S-59 Tank Fluid Height ................................................................................................. S-59 Total Response Variabilities ................................................................................. S-59 S.5.4.2 Capacity Variables ....................................................................................... S-60 Tank Shell Buckling Strength ............................................................................... S-61 Anchor Bolt Hold-Down Strength ......................................................................... S-62 Fluid Pressures .................................................................................................... S-63 Permissible Tank Uplift Height ............................................................................. S-65 Inelastic Energy Absorption Factor ...................................................................... S-66 Total Capacity Variabilities ................................................................................... S-66 S.5.5 Seismic Fragility of Example Tank ....................................................................... S-67 S.6 References................................................................................................................... S-67 T EXAMPLE: HEAT EXCHANGER FRAGILITY BY SEPARATION OF VARIABLES AND HYBRID APPROACHES ..................................................................................................T-1 T.1 Introduction .....................................................................................................................T-1 T.2 Equipment Response Analysis .......................................................................................T-4 T.3 Separation of Variables Method ....................................................................................T-10 T.3.1 Median Capacity ....................................................................................................T-10 T.3.1.1 Failure Through the Steel Anchor Bolt...........................................................T-10 T.3.1.2 Failure of the Anchor Bolt in the Concrete .....................................................T-10 T.3.1.3 Failure of the Support Base Plate Due to Bending ........................................T-11 T.3.1.4 Failure of the Weld Connection Between the Base and Vertical Support Plates near the Anchor Bolt .......................................................................................T-12 T.3.1.5 Reference Earthquake Scale Factor and Median Capacity ...........................T-12 lxii 13633436 T.3.2 Logarithmic Standard Deviations ..........................................................................T-13 T.4 Hybrid Approach ...........................................................................................................T-15 T.4.1 Failure Modes........................................................................................................T-15 T.4.1.1 Failure Through the Steel Anchor Bolt...........................................................T-15 T.4.1.2 Failure of the Anchor Bolt in the Concrete .....................................................T-16 T.4.2 HCLPF and Median Capacities .............................................................................T-16 T.5 References ....................................................................................................................T-17 U EXAMPLE: FRAGILITY FOR SERVICE WATER PUMP ..................................................... U-1 U.1 Description of Equipment............................................................................................... U-1 U.2 Capacity Factor.............................................................................................................. U-3 U.3 Equipment Response Factor ......................................................................................... U-4 U.3.1 Qualification Method .............................................................................................. U-4 U.3.2 Damping................................................................................................................. U-5 U.3.3 Modeling ................................................................................................................ U-5 U.3.3.1 Frequency ...................................................................................................... U-5 U.3.3.2 Equipment Model Fidelity ............................................................................... U-6 U.3.4 Mode Combination ................................................................................................. U-6 U.3.5 Earthquake Component Combination .................................................................... U-6 U.3.6 Equipment Response Factor ................................................................................. U-7 U.4 Structural Response Factor ........................................................................................... U-7 U.4.1 Ground Motion ....................................................................................................... U-7 U.4.2 Damping................................................................................................................. U-8 U.4.3 Modeling ................................................................................................................ U-8 U.4.3.1 Frequency ...................................................................................................... U-8 U.4.3.2 Structure Model Fidelity.................................................................................. U-9 U.4.3.3 Torsional Coupling ......................................................................................... U-9 U.4.4 Time History Phasing ............................................................................................. U-9 U.4.5 Foundation Structure Interaction ............................................................................ U-9 U.4.5.1 Ground Motion Incoherence ........................................................................... U-9 U.4.5.2 Soil-Structure Interaction ................................................................................ U-9 U.4.5.3 Vertical Spatial Variation of Ground Motion ................................................... U-9 U.4.6 Inelastic Structure Response ............................................................................... U-10 U.4.7 Structural Response Factor ................................................................................. U-10 lxiii 13633436 U.5 Fragility for Service Water Pumps ............................................................................... U-10 U.6 References .................................................................................................................. U-10 V EXAMPLE: EXPANSION ANCHOR FRAGILITY BY SEPARATION OF VARIABLES AND HYBRID APPROACHES ................................................................................................. V-1 V.1 Equipment Description ................................................................................................... V-1 V.2 Separation of Variables Method..................................................................................... V-3 V.2.1 Demand on the Expansion Anchor Bolts ............................................................... V-3 V.2.2 Capacity of the Expansion Anchor Bolts ................................................................ V-6 V.2.2 Median Strength Factor for the Expansion Anchor Bolts ....................................... V-8 V.2.3 Expansion Anchorage Fragility .............................................................................. V-9 V.2.3.1 Equipment Capacity Factor ............................................................................ V-9 V.2.3.2 Equipment Response Factor ........................................................................ V-11 V.2.3.3 Structure Response Factor........................................................................... V-14 V.2.3.3 Summary of Expansion Anchor Bolt Fragility ............................................... V-15 V.3 Hybrid Approach .......................................................................................................... V-16 V.3.1 Demand on the Expansion Anchor Bolts ............................................................. V-16 V.3.2 Capacity of the Expansion Anchor Bolts .............................................................. V-18 V.3.3 HCLPF and Median Capacities ............................................................................ V-19 V.4 References................................................................................................................... V-19 W EXAMPLE: CDFM EVALUATION FOR FILLET WELD ANCHORAGE ............................ W-1 X EXAMPLE: FRAGILITY ANALYSIS FOR EQUIPMENT QUALIFIED BY TESTING ........... X-1 X.1 Introduction .................................................................................................................... X-1 X.2 Separation of Variables Method..................................................................................... X-1 X.2.1 Test Response Spectrum and Reference Response Spectrum ............................ X-1 X.2.2 Functional Fragility ................................................................................................. X-4 X.3 Hybrid Approach ............................................................................................................ X-6 X.3.1 Test Response Spectrum and Reference Response Spectrum ............................ X-7 X.3.2 CDFM and Median Capacities ............................................................................... X-8 X.4 References..................................................................................................................... X-8 lxiv 13633436 Y EXAMPLE: FRAGILITY DERIVED FROM EXPERIENCE DATA ........................................ Y-1 Y.1 Demand ......................................................................................................................... Y-1 Y.2 Capacity ......................................................................................................................... Y-2 Y.3 Capacity Factor .............................................................................................................. Y-2 Y.4 Structure Response Factor ............................................................................................ Y-3 Y.5 Fragility .......................................................................................................................... Y-3 Y.6 References..................................................................................................................... Y-4 lxv 13633436 13633436 LIST OF FIGURES Figure 1-1 Roadmap of superseded and retained EPRI reports ................................................ 1-2 Figure 2-1 Seismic risk assessment methodology ..................................................................... 2-3 Figure 2-2 Seismic fragility curves showing Am and logarithmic standard deviations ................ 2-4 Figure 2-3 Seismic fragility curves showing HCLPF and logarithmic standard deviations......... 2-8 Figure 3-1 Example spectral acceleration and PGA hazard curves .......................................... 3-4 Figure 3-2 The effect of aleatory (βR) and epistemic (βU) variability on fragility curves ............. 3-6 Figure 3-3 Flowchart of separation of variables and hybrid fragility approaches ....................... 3-7 Figure 3-4 Transformation between lognormal and standard normal distributions .................... 3-9 Figure 3-5 Non-exceedance probability, NEP, vs. standard normal variable, Z ...................... 3-12 Figure 3-6 Example probability density function and cumulative distribution function ............. 3-13 Figure 3-7 Example fragility curves based on the lognormal distribution ................................. 3-14 Figure 3-8 Results from fragility illustrations ............................................................................ 3-16 Figure 3-9 Separation of variables fragility evaluation process ............................................... 3-19 Figure 3-10 Results of example Monte Carlo simulation ......................................................... 3-32 Figure 3-11 Best fit plot to example Monte Carlo simulation ................................................... 3-34 Figure 3-12 Example Latin hypercube sampling process ........................................................ 3-35 Figure 3-13 CDFM evaluation parameters ............................................................................... 3-43 Figure 4-1 Section 4 roadmap ................................................................................................... 4-2 Figure 4-2 Elastic strength factor (FS) ........................................................................................ 4-4 Figure 4-3 Reference Spectrum ............................................................................................... 4-10 Figure 4-4 Extended Reference Spectrum .............................................................................. 4-10 Figure 4-5 Extended Capacity Spectrum ................................................................................. 4-12 Figure 4-6 Concrete compressive strength increase with time; air-cured, dry at test condition ................................................................................................................ 4-20 Figure 4-7 Strength of concrete shear walls ............................................................................ 4-28 Figure 4-8 Reinforcement capacity coefficients, A1 and A2 ...................................................... 4-30 Figure 4-9 Flexural capacity properties .................................................................................... 4-32 Figure 4-10 Comparison of Japanese scale model test data to predictive formulations .......... 4-36 Figure 4-11 Cyclic shear wall test initial and subsequent loading peaks ................................. 4-42 Figure 4-12 Idealized force deflection diagram for concrete shear walls ................................. 4-44 Figure 4-13 Fillet weld schematic ............................................................................................ 4-59 Figure 4-14 L-bolt anchor ......................................................................................................... 4-66 lxvii 13633436 Figure 4-15 J-bolt anchor ......................................................................................................... 4-66 Figure 4-16 Typical sine beat and sine sweep time histories .................................................. 4-70 Figure 4-17 Realistic demand and capacity response spectra at failure for equipment qualified by testing ........................................................................................................... 4-72 Figure 5-1 Seismic demand evaluation in the fragility process .................................................. 5-2 Figure 5-2 Reference earthquake .............................................................................................. 5-4 Figure 5-3 Three measures for identifying the dominant seismic input levels ........................... 5-6 Figure 5-4 Example reference earthquake control point at the site surface .............................. 5-8 Figure 5-5 Example reference earthquake control point at the foundation of a key structure ................................................................................................................ 5-8 Figure 5-6 Horizontal coherency functions from EPRI 1014101 .............................................. 5-16 Figure 5-7 Example of ground response spectra that are similar ............................................ 5-17 Figure 5-8 Example of ground response spectra that are not similar ...................................... 5-18 Figure 5-9 Filling valleys between peaks of deterministic analysis cases ............................... 5-21 Figure 5-10 Thirty scale factors, F, for median of 1.0 and  of 0.35 by Latin hypercube sampling ......................................................................................................... 5-24 Figure 5-11 Example response spectra from thirty sets of time histories matching the RE ..... 5-27 Figure 5-12 Example response spectra from thirty sets of time histories including horizontal direction variability ........................................................................................... 5-27 Figure 5-13 Example ISRS from probabilistic seismic response analyses .............................. 5-28 Figure 5-14 Effects of shift in structure fundamental frequency on in-structure response spectra .............................................................................................................. 5-46 Figure 5-15 In-cabinet response spectra for cabinet with single ~10 Hz frequency panel mode ...................................................................................................................... 5-55 Figure 5-16 In-cabinet response spectrum for multiple cabinet modes ................................... 5-55 Figure 5-17 Example response spectrum clipping ................................................................... 5-57 Figure 6-1 Capacity based criteria for fragility analysis ........................................................... 6-12 Figure 6-2 Composite test capacity (TRS) for an example component ................................... 6-24 Figure 6-3 Limiting high-frequency spectral accelerations to 20 Hz spectral ordinate ............. 6-33 Figure 6-4 Scaling structural loads .......................................................................................... 6-42 Figure 6-5 Cumulative distribution function for the ratio of the maximum valve acceleration vector to the peak spectral acceleration vector (Avlv/Sapeak)......................... 6-49 Figure B-1 Limits of experience data for air-operated diaphragm valves and pistonoperated valves of light-weight construction ................................................................... B-17 Figure B-2 Limits of experience data for motor-operated valves, substantial pistonoperated valves, and solenoid valves ............................................................................. B-17 Figure C-1 Seismic motion bounding spectra horizontal ground motion ............................... C-19 Figure C-2 Comparison of GERS with ruggedness TRS data: operability for battery chargers .......................................................................................................................... C-22 Figure C-3 Comparison of GERS with TRS data: failure for battery chargers ....................... C-23 Figure C-4 Generic hazard curves ......................................................................................... C-28 lxviii 13633436 Figure C-5 Typical hard-mounted spectrum for mechanical equipment, horizontal spectrum ......................................................................................................... C-31 Figure C-6 Typical shock-mounted spectrum for electrical equipment .................................. C-32 Figure C-7 Synthesized shock waveform responses for varied damping .............................. C-33 Figure C-8 Specimen performance General Electric HFA relay Y axis vert........................... C-37 Figure C-9 Specimen performance General Electric HFA relay Z axis F-B ........................... C-38 Figure C-10 Typical shock input and response level for electrical devices ............................ C-40 Figure C-11 Typical shock spectrum for medium voltage switchgear .................................... C-45 Figure E-1 Embedded anchor types: headed bolt; L-bolt; J-bolt .............................................. E-2 Figure E-2 J-bolt anchor to concrete........................................................................................ E-6 Figure I-1 Resultant base overturning moment for a circular tank ............................................. I-4 Figure J-1 Plot of logarithms of Sa versus cumulative probability ............................................ J-4 Figure J-2 In-cabinet response spectra for cabinet with single 10 Hz frequency panel mode ...................................................................................................................... J-11 Figure J-3 In-cabinet response spectrum for multiple cabinet modes .................................... J-11 Figure J-4 Horizontal floor spectra .......................................................................................... J-23 Figure L-1 Amplification factor for switchgear with flexible panels (high-amplification cabinets)............................................................................................................................. L-5 Figure M-1 Lumped mass model of reactor building ................................................................ M-2 Figure M-2 Reactor building east-west floor spectra, Node 11 ................................................ M-3 Figure M-3 Reactor building north-south floor spectra, Node 11 ............................................. M-4 Figure M-4 Reactor building vertical floor spectra, Node 11 .................................................... M-5 Figure M-5 RG 1.60 spectrum-compatible time histories ......................................................... M-6 Figure M-6 Reactor building east-west floor spectra reconstructed model, Node 11 .............. M-7 Figure M-7 Reactor building north-south floor spectra reconstructed model, Node 11............ M-8 Figure M-8 Reactor building vertical floor spectra reconstructed model, Node 11 .................. M-9 Figure M-9 East-West floor response spectrum developed from eigensolution of DBE analysis using RG 1.60 time histories ................................................................. M-10 Figure M-10 Comparison of DBE with UHRS ........................................................................ M-11 Figure M-11 Reactor building – estimated SDOF oscillator response – Node 11.................. M-12 Figure M-12 Reactor building – estimated SDOF oscillator response – Node 11.................. M-12 Figure M-13 Reactor building – UHRS scale factors – Node 11 ............................................ M-13 Figure M-14 Scaled DBE spectra – Node 11 ......................................................................... M-13 Figure N-1 Response spectra relationships ............................................................................. N-2 Figure O-1 Elevation view of shear wall section for example analysis .................................... O-1 Figure O-2 Free body diagram of wall section above inflection point ...................................... O-8 Figure O-3 Building deflected shapes and relative story weights .......................................... O-14 Figure O-4 Force deflection diagrams for Piers 1 and 2 and the first story............................ O-15 Figure Q-1 Load deflection curve showing pinched hysteresis behavior typical of masonry walls ............................................................................................................... Q-1 lxix 13633436 Figure Q-2 Horizontal floor response spectra .......................................................................... Q-2 Figure S-1 Example vertical metal flat-bottom liquid storage tank ........................................... S-1 Figure S-2 Schematic illustration of tank bottom behavior near tensile region of the tank shell ............................................................................................................... S-16 Figure S-3 Cross-section forces on tank shell at base .......................................................... S-20 Figure S-4 Horizontal ground motion response spectra ........................................................ S-25 Figure S-5 Fluid hold-down forces for tank uplift of 0.53 in. ................................................... S-39 Figure S-6 Fluid hold-down forces for median tank uplift of 1.60 in. ...................................... S-51 Figure T-1 Geometry of the heat exchanger and its support ....................................................T-3 Figure T-2 Five percent damped GMRS ...................................................................................T-4 Figure T-3 Base plate yield model ..........................................................................................T-12 Figure U-1 Model of the service water pump ........................................................................... U-2 Figure U-2 Simplified motor stand model ................................................................................. U-3 Figure U-3 DBE in-structure response spectrum, 5% damping ............................................... U-5 Figure V-1 Schematic view of the inverter sectioned to show anchors .................................... V-1 Figure V-2 Inverter dimensions and center of gravity .............................................................. V-2 Figure V-3 Eccentricities between center of gravity and center of rigidity................................ V-3 Figure V-4 5% damped median-centered unclipped ISRS ...................................................... V-6 Figure V-5 5% damped 84th percentile unclipped ISRS ........................................................ V-18 Figure W-1 Example cabinet anchorage ................................................................................. W-2 Figure W-2 Fillet weld loading ................................................................................................. W-2 Figure X-1 5% damped TRS and clipped median RRS in side-to-side direction ..................... X-2 Figure X-2 5% damped TRS and clipped median RRS in the front-to-back direction.............. X-3 Figure X-3 5% damped TRS and clipped median RRS in the vertical direction ...................... X-3 Figure X-4 5% damped TRS and clipped 84th percentile RRS in the vertical direction........... X-7 Figure Y-1 In-structure response spectra for Building E Node 162610 ................................... Y-1 lxx 13633436 LIST OF TABLES Table 3-1 Sample values from a lognormal distribution with a median of 1.0 and a logarithmic standard deviation of 0.20, x = LN (xm = 1.0, β = 0.20) .................................. 3-10 Table 3-2 Standardized normal variable, Z, for common probabilities ..................................... 3-12 Table 3-3 Summary of capacity factor variables ...................................................................... 3-22 Table 3-4 Summary of equipment response factor variables .................................................. 3-23 Table 3-5 Summary of structure response factor variables ..................................................... 3-23 Table 3-6 Samples of two independent random variables ....................................................... 3-31 Table 3-7 Randomly ordered and summed random variables ................................................. 3-31 Table 3-8 Results for median study ......................................................................................... 3-37 Table 3-9 Results for logarithmic standard deviation study ..................................................... 3-38 Table 3-10 Summary of CDFM method criteria for hybrid fragility applications in SPRA ........ 3-42 Table 3-11 Recommended logarithmic standard deviations to use in the hybrid fragility approach .............................................................................................................. 3-44 Table 4-1 Capacity factor criteria for SOV and hybrid fragilities ................................................ 4-5 Table 4-2 Summary of equipment and subsystems seismic capacities ................................... 4-13 Table 4-3 Improved seismic capacities based on earthquake experience for eight equipment classes ........................................................................................................... 4-15 Table 4-4 Summary of civil structures representative HCLPF (C1%) capacities ....................... 4-16 Table 4-5 Concrete tensile strength ......................................................................................... 4-21 Table 4-6 Material strengths for common materials ................................................................. 4-22 Table 4-7 Concrete reinforcement yield strength ..................................................................... 4-23 Table 4-8 Allowable drift limits for Limit State C ...................................................................... 4-39 Table 4-9 Allowable hinge rotation limits for Limit State C per ASCE/SEI 43-05 ..................... 4-40 Table 4-10 Drift limits for low rise shear walls subjected to cyclic loading ............................... 4-41 Table 4-11 Inelastic energy absorption factors, Fµ, for Limit State C ....................................... 4-47 Table 4-12 Loading combination and acceptance criteria for electrical raceway ..................... 4-54 Table 4-13 Loading combination and stress limits for HVAC ducting ...................................... 4-56 Table 4-14 Strength capacity equation and uncertainty for common structural elements ....... 4-58 Table 4-15 Equipment and distribution systems inelastic energy absorption factor, Fµ ........... 4-68 Table 4-16 Broad frequency input spectrum device capacity factors ...................................... 4-75 Table 5-1 Effective stiffness of reinforced concrete structural components ............................. 5-13 Table 5-2 Deterministic soil and structure stiffness case designations .................................... 5-19 Table 5-3 Response variables for structure fragility evaluation ............................................... 5-30 lxxi 13633436 Table 5-4 Median horizontal direction peak response factors and logarithmic standard deviations .......................................................................................................... 5-32 Table 5-5 Horizontal direction peak response factors for CDFM Evaluations ......................... 5-32 Table 5-6 Structure damping values ........................................................................................ 5-33 Table 5-7 Structure response variables for equipment fragility evaluation .............................. 5-44 Table 5-8 Equipment response variables for equipment fragility evaluation by analysis ......... 5-44 Table 5-9 Equipment damping values ..................................................................................... 5-51 Table 5-10 Cabinet amplification factor, AFC (5% damped – worst-case location) .................. 5-60 Table 6-1 Outline of implementation topics ................................................................................ 6-1 Table 6-2 Inherently rugged SSCs ........................................................................................... 6-12 Table 6-3 Inelastic deformation capacity of fillet welds ............................................................ 6-26 Table 6-4 Inelastic deformation capacity of anchors failing due to concrete breakout in tension .......................................................................................................................... 6-26 Table 6-5 Inelastic deformation capacity of concrete anchors failing due to concrete breakout in shear ............................................................................................................. 6-26 Table 6-6 Component seismic demand scaling cases ............................................................. 6-45 Table B-1 SSRAP guidelines for valve weight and eccentricity limits ..................................... B-18 Table C-1 Topics discussed in Appendix C .............................................................................. C-2 Table C-2 Equipment categories for seismic margin studies .................................................. C-20 Table C-3 Devices tested ........................................................................................................ C-24 Table C-4 Fragility descriptions developed from Corps of Engineers methodology ............... C-34 Table C-5 Summary of required retrofit to survive shock environment ................................... C-35 Table C-6 Fragility descriptions by failure mode for electrical and control equipment ............ C-36 Table C-7 Fragility descriptions by failure mode for electrical and control equipment ............ C-36 Table C-8 Electrical component fragility test ........................................................................... C-39 Table C-9 Motor control centers ............................................................................................. C-41 Table C-10 Switchgear – low voltage ..................................................................................... C-42 Table C-11 Switchgear – medium voltage .............................................................................. C-43 Table C-12 Distribution panels ................................................................................................ C-43 Table D-1 Example of categorizing active valves for capacity evaluation................................. D-3 Table E-1 Statistics comparing tested to predicted pullout strengths ....................................... E-4 Table F-1 Estimated coefficients of variation for expansion bolts in uncracked concrete ..........F-2 Table F-2 Recommended expansion bolt safety factors to be used in CDFM evaluations........F-3 Table F-3 Estimated probability distribution function for capacity reduction factor FR for expansion bolts due to concrete cracking ..........................................................................F-4 Table F-4 Estimated expansion bolt failure probabilities for tension in potentially cracked concrete .............................................................................................................................F-5 Table G-1 Nominal factor of safety, FN1%, for low ductility failure modes based on ASCE/SEI 43-05 ............................................................................................................... G-4 lxxii 13633436 Table G-2 Nominal factor of safety, FN1%, for low ductility failure modes based on EPRI NP-6041-SLR1 ........................................................................................................ G-5 Table H-1 HCLPF correction factor FPV .................................................................................... H-4 Table H-2 HCLPF84/HCLPF50 ratio............................................................................................ H-7 Table I-1 Median HDPR factor and associated randomness ...................................................... I-5 Table I-2 CDFM HDPR factors for varying βC_DNoHDPR ................................................................. I-7 Table I-3 Recommended CDFM HDPR factors .......................................................................... I-7 Table J-1 Representative estimates for knockdown factor Fkd ................................................... J-3 Table J-2 Effective cabinet amplification factors ...................................................................... J-15 Table J-3 Test response spectra (TRS) knockdown factor (Fkd) .............................................. J-16 Table M-1 Scaling results ....................................................................................................... M-14 Table O-1 Deterministic properties of piers .............................................................................. O-2 Table O-2 Comparison of shear capacities at 2.5 times the reference earthquake ................ O-12 Table O-3 Calculation of strength factor where Pier 2 is controlled by flexure ....................... O-13 Table O-4 Structure response variable logarithmic standard deviation .................................. O-18 Table O-5 Structure capacity factor logarithmic standard deviations ...................................... O-21 Table Q-1 Displacement capability of masonry walls ............................................................... Q-5 Table Q-2 Strength factor as a function of the permissible drift level for the example problem ............................................................................................................... Q-9 Table S-1 Impulsive mode frequency coefficient, CW, for steel tanks containing water ............ S-5 Table S-2 Weight takeoff for example tank ............................................................................. S-24 Table S-3 Fluid hold-down force calculations ......................................................................... S-37 Table S-4 Fluid hold-down forces for tank uplift of 0.53 in. ..................................................... S-38 Table S-5 Anchor bolt hold-down forces for tank uplift of 0.53 in. .......................................... S-40 Table S-6 Fluid hold-down forces for median tank uplift of 1.60 in. ........................................ S-50 Table S-7 Anchor bolt hold-down forces for median tank uplift of 1.60 in. .............................. S-52 Table S-8 Tank response variabilities ..................................................................................... S-60 Table S-9 Variability case studies* ......................................................................................... S-61 Table S-10 FHFP variabilities .................................................................................................... S-64 Table S-11 FVFP Variabilities ................................................................................................... S-65 Table S-12 16% NEP estimates of PC- and PT ........................................................................ S-65 Table S-13 Tank capacity variabilities .................................................................................... S-66 Table T-1 Fragility analysis demand variables for heat exchanger ............................................T-2 Table T-2 Properties of the heat exchanger ..............................................................................T-5 Table T-3 Material capacity properties .......................................................................................T-6 Table T-4 Demand on critical anchor bolt (tension positive) ......................................................T-9 Table T-5 Summary for the four failure modes ........................................................................T-13 Table T-6 Logarithmic standard deviations ..............................................................................T-14 Table V-1 Equivalent lognormal distribution properties for capacity of expansion anchors ...... V-7 lxxiii 13633436 13633436 1 INTRODUCTION AND SCOPE 1.1 Introduction Seismic fragility methods were developed almost forty years ago as part of the first seismic probabilistic risk assessments (SPRAs) developed for the nuclear power industry. The seismic fragility methodology evolved tremendously over that period as computational techniques and understanding of earthquake effects improved. Most recently, use of seismic fragility methods within the nuclear power community has increased dramatically as a result of the 2011 Tohoku earthquake/tsunami in Japan that damaged the Fukushima nuclear power plant. Seismic fragility is becoming a more common tool in the engineering community and has expanded to nonnuclear industries, as risk-informed approaches are becoming the norm for new seismic design (e.g., performance-based methods) and for seismic evaluation of existing nuclear facilities. Electric Power Research Institute (EPRI) has developed several documents associated with the seismic margin and seismic fragility of structures, systems, and components (SSCs) that are actively being used within current SPRAs. The major EPRI documents that provide seismic fragility or seismic margin guidance include:  EPRI NP-6041-SLR1, A Methodology for Assessment of Nuclear Power Plant Seismic Margin (Revision 1), August 1991 [1]  EPRI TR-103959, Methodology for Developing Seismic Fragilities, June 1994 [2]  EPRI 1002988, Seismic Fragility Applications Guide, December 2002 [3]  EPRI 1019200, Seismic Fragility Application Guide Update, December 2009 [4]  EPRI 3002000709, SPRA Implementation Guide, December 2013 [5] The methods in these documents are necessary to complete the fragility portion of an SPRA or seismic margin assessment (SMA). The purpose of this seismic fragility and seismic margin guide is to provide a single document that contains the relevant state of the art methods needed to develop seismic fragilities in support of an SPRA. As such, the process used to develop this new EPRI guide includes: 1. Combining the relevant seismic fragility aspects of these five documents into a new single document. 2. Removing the technical material and descriptions that are duplicated in these documents. 3. Updating methods that have been changed or where new, more appropriate methods have been developed. 4. Correcting errors. 1-1 13633436 Introduction and Scope In addition to the five documents cited above, there are additional industry references that contain material associated with specific elements of the fragility process and that are useful to the fragility analyst. These fragility technical elements are either included in this fragility guide or are referenced for the user. Figure 1-1 shows a roadmap of which EPRI reports are incorporated and superseded and which are incorporated in part and retained. Figure 1-1 Roadmap of superseded and retained EPRI reports 1.2 Objective The objective of this report is to provide users with the state of the art methodology for developing seismic fragilities and seismic margins. The intent of this report is to document the fragility methods, so they are understandable to the well-trained utility structural mechanics engineer. Guidance is provided to develop fragilities and margins in an efficient and effective manner that conforms to the intent of the American Society of Mechanical Engineers (ASME)/ American Nuclear Society (ANS) Standard for Probabilistic Risk Assessments for Nuclear Power Plants Code Case #1 [6]. The variables associated with seismic fragility and seismic margins analysis are defined, and the methodologies for their development and application are described within this report. In addition, key example calculations are provided in the appendices. 1-2 13633436 Introduction and Scope 1.3 Scope and Report Organization This report focuses on development of seismic fragilities and seismic margins for use in SPRAs and SMAs. Discussion of other aspects of these seismic risk assessment methodologies is limited to their interface with fragility evaluation. Section 2 of this report contains background on how seismic fragilities and seismic margins fit within the context of SPRAs and SMAs. The overall SPRA methodology is discussed in Section 2.1 to highlight the overall context of fragility analysis and to identify the SPRA considerations that shape fragility methods and decisionmaking. Similarly, the overall concepts involved in an SMA, including high confidence of a low probability of failure (HCLPF), are introduced in Section 2.2. Application of seismic margin methods within an SPRA is introduced in Section 2.3. Methodologies for developing seismic fragilities are presented in Section 3. Variables considered in seismic fragility analysis are discussed in Section 3.3.1. Guidance is provided for developing probability distributions for these variables. Variables affecting seismic capacity are discussed in Section 4, and variables affecting seismic response are discussed in Section 5. Fragility implementation topics are presented in Section 6. One of the key implementation topics is the seismic walkdown. Recommendations are made for seismic walkdown methodology, and strategies are suggested for prioritizing fragility analyses in an SPRA. The appendices to this report contain detailed technical information and background for a variety of fragility topics. The appendices are intended to provide users with representative examples and data to assist in the development of fragilities for specific SSCs commonly found in nuclear power plants (NPPs). 1-3 13633436 13633436 2 BACKGROUND Nuclear power plants have been designed to withstand a conservatively selected earthquake (i.e., the safe shutdown earthquake (SSE)), with adequate margins introduced at different stages of design, analysis, qualification, and construction. However, it is understood that larger earthquakes, although rare, could occur. The objective of both the SPRA and the SMA is to provide insights into how these larger earthquakes may affect the plant and to assess the plant response to such earthquakes. The SPRA provides a probabilistic characterization of these larger earthquakes’ effects on the plant, while the SMA provides primarily a deterministic characterization of the larger earthquakes’ effects. Previous SPRAs have shown that the seismic contribution to the overall core damage frequency and large early release frequency at some NPPs could be significant. Occasionally, seismic risk could even be dominant compared to other internal and external event hazards. Therefore, a quantitative assessment of the seismic risk (such as an SPRA) can be an important aid in the overall risk-informed decision-making process. Background discussions of both the SPRA and SMA are included in this section to provide context for the development of seismic fragilities and seismic margins and to explain how the fragility and margin results are used in these programs. 2.1 SPRA Background An SPRA is a multidisciplinary program combining the inputs and experience of different analysts. SPRA team members will need to interface effectively to develop defendable results consistent with the overall objectives of the program being conducted (which typically includes risk-informed decision-making concepts). As such, the SPRA team should have a basic understanding of the scope, interfaces, data needs, and results of each of the different SPRA activities. A brief description of the SPRA process, along with how seismic fragilities integrate into the overall SPRA, is provided to facilitate that understanding. 2.1.1 Overall SPRA Methodology The key elements of an SPRA are:  Seismic Hazard Analysis: To develop annual probabilities (or “frequencies”) of exceeding various levels of earthquake ground motion (e.g., peak ground acceleration) at the site.  Seismic Fragility Evaluation: To estimate the conditional probability of failure of important structures and equipment whose failure may lead to unacceptable damage to the plant (e.g., core damage). 2-1 13633436 Background  Systems/Accident Sequence Analysis: To model the combinations of structural and equipment failures that could initiate and propagate a seismic core or large early release damage sequence.  Risk Quantification: To assemble the results of the seismic hazard, seismic fragility, and systems analyses to estimate the frequencies of core damage, large early release, and plant damage states. Assessment of the impact of seismic events on the containment and consequence analyses, and integration of these results with the core damage analysis to obtain estimates of seismic risk in terms of effects on public health (e.g., early deaths and latent cancer fatalities). Figure 2-1 shows the key elements of seismic risk assessment methodology:  Box 1 shows the result of a seismic hazard analysis (i.e., a family of seismic hazard curves relating the frequency of exceedance to different levels of ground motion). Note that regionspecific seismicity data is required for this analysis. Important outputs of this step are uniform hazard response spectra (UHRS) used as the seismic input for fragility analyses.  Box 2 is a pictorial representation of the systems analysis; it consists of event trees, fault trees, and containment analysis. The data needed to perform the system analysis includes the random structure and equipment failure probabilities, as well as operator failure probabilities modified to reflect the severe stress induced by earthquakes. An important output of this step is a seismic equipment list (SEL) of SSCs that will be included in the systems model for risk quantification.  Box 3 shows the result of component fragility evaluation (i.e., a family of seismic fragility curves). These are developed using plant design information and realistic response analysis. The data used for fragility analysis include earthquake experience data, generic equipment ruggedness spectra (GERS), and fragility test results. Important outputs of this step are the median capacities at which SSCs on the SEL fail and the variability in the capacities.  Box 4 shows the probability density functions of core damage and large early release frequencies. These are obtained using the sequences of component failures, fragilities of components, and seismic hazard curves. Note that the quantification procedure is different from the internal event analysis in that the entire range of possible earthquakes is considered so that the varying component failure probabilities and dependencies between different component failures are explicitly included in the analysis.  Box 5 refers to the dispersion analysis that uses weather data to estimate the consequences of a core damage accident resulting in a radiological release to the atmosphere. Population distribution around the site and emergency evacuation procedures are considered in assessing the consequences in terms of health effects and property damage.  Box 6 shows the risk curves. For each level of damage (e.g., number of deaths, cancer fatalities, and property damage), the risk curve gives the annual frequency of exceedance of damage. The uncertainties in the risk assessment are displayed by means of a family of risk curves. Therefore, the annual frequency of exceeding a given level of damage is distributed, and one could state this frequency with different levels of confidence. 2-2 13633436 Background The results of an SPRA are typically given as seismic core damage frequency (SCDF) or seismic large early release frequency (SLERF). Intermediate results from the fragility evaluation are the median capacities of SSCs identified in Box 2 along with the variability in the capacity. Figure 2-1 Seismic risk assessment methodology 2.1.2 Fragility Evaluation in an SPRA Safety-related SSCs are designed to withstand the SSE. There are intentional conservatisms introduced in the design, analysis, qualification testing, and construction of these SSCs to provide high confidence that they will not fail to perform their intended function if earthquakes moderately larger than an SSE occur. Therefore, the realistic seismic capacity of an SSC is typically much higher than the SSE acceleration. Because of the uncertainties in the design, analysis, qualification testing, and construction, the actual seismic capacity is unknown and can only be expressed in probabilistic terms represented by a “fragility curve.” This curve depicts the conditional probability of failure of the component for any given ground motion level. Section 3 contains a very detailed description of the fragility curve and includes a mathematical characterization of how fragilities are derived. 2-3 13633436 Background Fragility is the conditional probability of failure as a function of earthquake motion level for any SSC that might contribute to seismic risk. The earthquake motion level parameter could be peak ground acceleration (PGA), peak spectral acceleration, floor spectral acceleration, or others. Seismic fragility is evaluated in a probabilistic manner. It is standard practice to model the seismic fragility by a lognormal cumulative probability distribution. This S-shaped lognormal distribution closely approximates the actual fragility distribution for most SSCs, as would be evidenced, for example, by shake table test data. As such, the fragility calculation typically uses a double lognormal model with three parameters: the median acceleration capacity (Am), the logarithmic standard deviation of the aleatory (randomness) uncertainty in capacity (βR), and the logarithmic standard deviation of the epistemic (modeling and data) uncertainty in the median capacity (βU). The aleatory and epistemic uncertainty can be combined into a composite variability (βC). The fragility using a composite variability is referred to as the mean fragility. Figure 2-2 depicts these elements of the fragility curve using an example Am of 0.87g, βR of 0.25, and βU of 0.35. The example fragility curve in Figure 2-2 shows that the conditional probability of failure of a component increases with the ground motion level to which the site is subjected and approaches 1.0 at high accelerations. The conditional probability is small but not zero at relatively low ground motion values. So even at ground motions less than the SSE acceleration, there will be some low probability of failure given the uncertainties in the fragility process. By knowing the median capacity and logarithmic standard deviations (R and βU) representing the aleatory and epistemic uncertainties in the fragility, the full set of conditional probabilities of failure at different ground motion levels can be calculated. Figure 2-2 Seismic fragility curves showing Am and logarithmic standard deviations 2-4 13633436 Background This report outlines two common approaches for calculating seismic fragilities in an SPRA. First, the separation of variables (SOV) approach explicitly characterizes a probability distribution (median value, aleatory variability, and epistemic variability) for each parameter affecting the SSC’s response and capacity (Section 3.3). The final fragility distribution is obtained from the individual variables using the mathematical properties of lognormal distributions outlined in Section 3.2. Second, a simplified method known as the hybrid approach uses deterministic rules to estimate a conservative capacity near the low-acceleration tail of the fragility distribution and then uses conservative variability estimates to characterize the full fragility distribution (Sections 2.2.2, 2.3, and 3.4). 2.2 SMA Background An SMA is an alternate approach to assess the effects of earthquakes that exceed the seismic design basis. The SMA is based on probabilistic data and concepts but is inherently more deterministic than the SPRA. SMA team members will also need to interface effectively with technical specialists on the SMA team to develop defendable results of the SMA consistent with the overall objectives of the program being conducted. As such, the SMA team should have a basic understanding of the scope, interfaces, data needs, and results of each of the different SMA activities. A brief description of the SMA process along with how the calculation of a HCLPF level integrates into the overall SMA is provided to help facilitate that understanding. 2.2.1 Overall SMA Methodology Seismic margin methodologies were developed based on the results and insights from the early SPRAs. An SMA addresses the question of whether the capacity of the plant exceeds a target earthquake input selected for review. The objectives are then to show that the plant can withstand the effects of this review level earthquake (RLE)2 with high confidence and to identify any potential seismic vulnerabilities. The original EPRI SMA approach as described in EPRI NP-6041-SLR1 [1] was developed to demonstrate margin beyond the design basis earthquake (DBE). In this approach, an RLE was considered that was greater than the DBE but not so great that no SSCs could survive it. The evaluated SSCs were selected using success path modeling rather than event tree/fault tree modeling. The EPRI SMA approach [1] consists of a set of deterministic rules for evaluating a facility’s seismic margin. However, the deterministic approach is implicitly derived from probabilistic considerations, as is the case for many design codes. The SMA approach is conceptually based on demonstrating the adequacy of the SSCs designated as plant safety systems required to maintain plant shutdown following the postulated earthquake and prevent radiological release. One important goal of the SMA approach is the identification of any seismic weak links and remediation if the calculated margin is inadequate. The terms review level earthquake (RLE) and seismic margin earthquake (SME) are used interchangeably in various documents. 2 2-5 13633436 Background The SMA approach involves the use of earthquake experience data, generic equipment qualification and fragility test data, and insights from past SPRAs to develop screening guidelines. Screening of SSCs limits the effort required for higher capacity items such that the focus can be on lower capacity items that affect the plant seismic risk. Screening is accomplished using walkdowns of the plant by a trained assessment team to ensure that the SSCs have characteristics consistent with the screening criteria. Items that are not screened out are evaluated by the conservative deterministic failure margin (CDFM) method that is similar to conservative design used for NPPs. From screening or CDFM analysis, the capacities of the SSCs are determined as the RLE acceleration level at which there is very low probability of failure. This capacity is termed the HCLPF capacity. The SMA method has several advantages:  Evaluations can be conducted with procedures very similar to the design process and thus familiar to practicing engineers.  Evaluations are deterministic, prescriptive, and repeatable between review teams of trained engineers.  Calculations are more limited in scope than seismic fragilities. However, an SMA cannot directly be used to quantify risk because it does not include development of a risk model. The documented results of an SMA need to be transformed into PRA-type summary results to address risk related questions. Several technical reports exist with suggested approaches on how to address this transformation of the seismic margin results into PRA-type summary results (e.g., EPRI 1003121 [7] and EPRI 1009648 [8]). An SMA consists of the following steps: 1. Selection of the RLE and its level 2. Selection of assessment team 3. Preparatory work prior to walkdowns 4. Systems and equipment selection ("success paths") walkdown 5. Seismic capability walkdown 6. Subsequent walkdowns (as-needed) 7. SMA calculations and evaluations (incorporating CDFM methods) 8. Documentation In addition to the EPRI SMA approach, the U.S. Nuclear Regulatory Commission (NRC) outlines another SMA approach in interim staff guidance DC/COL-ISG-020 [9]. In the NRC approach, SSCs are selected for evaluations using event tree/fault tree modeling similar to an SPRA. Despite the differences from the EPRI SMA approach, the SSC capacities are nonetheless conservatively established in the same manner as the original EPRI SMA approach. 2-6 13633436 Background 2.2.2 HCLPF Evaluation The seismic margins approach uses as its figure of merit a HCLPF. The HCLPF capacity is a measure of seismic ruggedness. The HCLPF is a conservative representation of capacity and in simple terms corresponds to the earthquake level at which it is extremely unlikely that failure will occur. The HCLPF is defined as the capacity level at which there is 95% confidence that less than 5% of actual capacity levels will fall below. The SMA method requires estimation of HCLPF capacities of every SSC that might contribute to a specified plant damage state. The method uses the CDFM method for seismic evaluation. The CDFM method along with the HCLPF calculation approach is described in more detail in Section 3 of this report. 2.3 Hybrid Approach An alternative approach to develop fragilities that requires somewhat less effort than the SOV method (Section 2.1.2) uses the CDFM approach for generating HCLPF levels as performed in an SMA. Because only a handful of components are risk-significant enough to justify the additional effort required by the SOV approach (Section 3.3), the CDFM method can provide efficiencies in the overall effort. Therefore, use of the CDFM approach is useful and beneficial for calculating fragilities of SSCs for use in SPRAs. In the CDFM fragility approach, the HCLPF capacity3 is computed, and conservatively biased generic estimates of the composite logarithmic standard deviation βC are used to estimate the mean fragility curve (Figure 2-3). The composite standard deviation βC can be divided into random variability βR and uncertainty βU, which are used to estimate the more complete set of fragility curves in Figure 2-3. Typical generic β values for use in the hybrid approach are provided in Section 3.4.1. 3 The HCLPF capacity, which is the 95% confidence of a 5% probability of failure, is approximately equal to the 1% probability of failure capacity on the mean fragility curve (A1%), which is defined using the median capacity Am and composite variability βC (Equation 3-15). 2-7 13633436 Background Figure 2-3 Seismic fragility curves showing HCLPF and logarithmic standard deviations 2-8 13633436 3 FRAGILITY METHODOLOGIES 3.1 Fragility Concept The term, “seismic fragility” refers to a set of failure probabilities conditional upon a range of earthquake ground motions. Fragilities are commonly plotted as a function with the failure probability on the ordinate (vertical) axis and a ground motion parameter on the abscissa (horizontal), as illustrated in Figures 2-2 and 2-3. Each point on a fragility curve quantifies the probability that an SSC will fail given the occurrence of an earthquake ground motion of a specified amplitude. The underlying concepts and definitions necessary for developing seismic fragilities are discussed in this section. 3.1.1 Failure Modes In the context of an SPRA, failure is defined as the result of any earthquake-induced event or process that precludes the successful operation of an SSC or otherwise prevents it from performing its function that is credited in the systems model (e.g., fails to start, fails to run, leaks, etc.). Failure may result from several processes, including electrical, mechanical, physical, thermal, and human error; these processes that result in failure are referred to as failure modes. Some analysts may be accustomed to referring to failure modes as “failure mechanisms,” and communication between all parties involved in an SPRA should be sure to clarify a mutual understanding of what is meant by these terms. The first step in developing a fragility is to develop a clear definition of what constitutes failure for the SSC being evaluated. This definition of failure must be agreeable to both the fragility analyst, who evaluates seismic capacity and demand associated with various failure modes, and the systems analyst, who must assess the consequences of those failure modes. Several modes of failure (each potentially with different consequences) may have to be considered, and fragility curves may have to be generated for each of these modes. For example, a motor-operated valve (MOV) may fail in any of the following ways:  Failure to operate due to binding of the valve stem due to distortion  Failure of the pressure boundary due to overstress of the flange joint  Failure of the valve motor  Failure of the structure housing the valve  Failure of an adjacent masonry wall that impacts the valve  Failure of power or controls to the valve 3-1 13633436 Fragility Methodologies Although all the above failure modes are possible, not all have equivalent consequences in the SPRA systems model. The fragility analyst and systems analyst must therefore coordinate to determine which failure modes require the development of fragilities. In the example above, the systems analyst may identify that the valve is closed and normally in a safe state. For this case, it is only important that the valve stay closed and the pressure boundary not rupture. Therefore, failure of the motor or failure of power or controls to the valve will not affect the valve’s credited function in the SPRA, and it is unnecessary to develop fragilities for these failure modes. On the other hand, a different valve may be normally closed but required to open to perform the credited function. In this case, the valve must retain operability. Depending on how the systems analyst has treated the valve in the systems model, it may be necessary to develop separate fragilities for failure modes with different consequences. For a valve that must remain operable, failure of power to the valve and binding of the valve stem both impede the valve’s operability. However, manual operation of the valve may still be possible should the former failure mode occur, whereas the latter failure mode may also preclude manual valve operation. The systems analyst may have included manual valve operation as a success path in the plant logic model, in which case the two failure modes discussed above have different consequences to the SPRA. Therefore, the level of detail in the systems model will affect which failure modes require fragility evaluation. Often, it is not immediately obvious whether the failure mode considered in the fragility analysis will certainly preclude the function credited in the SPRA. For example, if an earthquake fails a tank’s anchorage, it is possible that the tank could maintain its pressure boundary. Typically, a fragility evaluation will begin with a relatively simple, straightforward, and sometimes conservative failure mode (e.g., anchorage failure of a tank). Then, if the SSC is shown to be important in the risk quantification, the systems analyst and fragility analyst can jointly consider whether the failure mode evaluated realistically precludes the function modeled. Developing a fragility for a more sophisticated characterization of failure (e.g., pressure boundary failure due to relative displacements after anchorage failure) can involve significantly more effort than the simpler failure modes. Therefore, the decision to refine the failure mode characterization typically involves consideration of project constraints such as schedule, budget, risk importance, and the overall objectives of the SPRA, which are beyond the scope of this guidance document. Nonetheless, it is important to ensure that the fragility analyst and systems analyst both understand the failure mode represented by the seismic fragility, as well as how that failure mode is modeled in the SPRA. The details of failure mode selection discussed above must be considered for each SSC requiring fragility analysis. Although valves are presented as an example, similar issues must be clarified between the systems and fragility analysts regarding treatment of failure modes for other equipment classes and structures. Among a set of failure modes identified as having the same consequences, some may be very unlikely to occur in an earthquake, and in this case, they are not considered credible. Most often, a single governing failure mode will be significantly more likely to occur than the others. It is usually possible to identify this governing failure mode based on observations during seismic walkdown or by reviewing the SSC design or seismic qualification documents. The fragility can then be developed considering only the governing failure mode. If the SSC has multiple failure modes with similar fragilities, fragility curves are developed for each potentially governing 3-2 13633436 Fragility Methodologies failure mode based on the premise that the component could fail in any one of the many potential failure modes. The fragility curves can then either be included in the systems model individually or combined into a single fragility curve for the SSC. Section 6.8 provides an example approach for combining two failure modes that are independent but mutually exclusive. Identification of the credible failure modes is largely based on the analyst’s experience and judgment. Review of plant design criteria, calculated stress levels in relation to the allowable limits, qualification test results, seismic fragility evaluation studies done on other plants, and reported failures (e.g., in past earthquakes, in licensee event reports, fragility tests) are useful in this task. 3.1.2 Seismic Capacity The seismic capacity of an SSC is its ability to sustain a seismic load. It is expressed as a seismic load level (e.g., stress, moment, force, displacement, acceleration) below which the SSC continues to perform its credited functions (i.e., the capacity is the load at which failure is expected). Since SSCs typically have operating loads (e.g., dead weight, pressure, temperature) in addition to seismic loads, it is often important to distinguish between the total capacity and the capacity available to resist seismic loads, or the seismic capacity. In this report, “capacity” is generally used to denote the seismic capacity unless noted otherwise. An SSC has a capacity for each of its possible failure modes. For the MOV example described in Section 3.1.1, the capacity associated with the valve stem failure mode can be expressed in terms of a deformation load (displacement of the valve yoke and therefore the valve stem). The maximum valve stem deformation at which the valve remains capable of opening and closing is the capacity for this failure mode. On the other hand, the capacity associated with pressure boundary failure may be expressed as a stress at some location on the casing (e.g., at the flange joint). The capacity in this case is the stress resulting in leakage or rupture. Methods of estimating capacities of various common failure modes are presented in Section 4. Since a failure mode’s seismic capacity is never perfectly known, it is treated as a probabilistic distribution rather than a single deterministic value. The capacity is conventionally modeled as a lognormal distribution as described in Section 3.2. 3.1.3 Seismic Response and Seismic Demand The seismic demand in the context of fragility analysis is the seismic load level (e.g., stress, moment, force, displacement, acceleration) that challenges an SSC’s seismic capacity. The term “seismic response” refers to a seismic demand resulting from the dynamic response of a structure or component (e.g., the seismic-induced stress at a particular location on a valve’s casing). Alternatively, it can refer to the process used to estimate the seismic demand or the dynamic behavior that produces the demand. For example, “seismic response analysis” refers to the engineering techniques such as response spectrum analysis, dynamic time-history analysis, or equivalent static analysis, which are used to estimate the seismic-induced force or stress in a particular SSC. 3-3 13633436 Fragility Methodologies Fundamentally, the seismic demand in an SPRA is defined by the seismic hazard at the NPP site. The seismic hazard defines the annual exceedance probability (AEP) for a range of ground motion parameter values. Typically, the hazard is provided for several ground motion parameters, including ground spectral accelerations at various structural frequencies (1 Hz, 5 Hz, 10 Hz, etc.) and PGA. Figure 3-1 shows an example set of hazard curves defined at 1 Hz, 2.5 Hz, 5 Hz, 10 Hz, 25 Hz, and PGA. The hazard may be defined at a single control point at the site (a single location within a single soil/rock profile), or multiple sets of hazard curves may be required for multiple control points. Figure 3-1 Example spectral acceleration and PGA hazard curves The objective of the seismic response analysis is to estimate the seismic demands on individual SSCs in terms of loads that challenge their specific failure modes. The response analysis therefore effectively transforms the seismic hazard, which is defined in terms of ground motion parameters, into loads, or responses, on individual SSCs (e.g., stresses, moments, forces, in-structure displacements, in-structure accelerations). Typically, response analysis is performed for a single ground motion level, i.e., the “reference earthquake” (RE) level (Section 5.2). The RE level is defined at a reference control point in terms of a reference ground motion parameter (e.g., PGA, spectral acceleration at a particular structural frequency, or average spectral acceleration across a range of frequencies). For example, the RE level for a given SPRA may be defined as 0.3g PGA at the bottom of the reactor building foundation. In this case, the reference ground motion parameter is PGA, and the reference control point is the bottom of the reactor building foundation. 3-4 13633436 Fragility Methodologies To date, most SPRAs have used PGA as the reference parameter. Accordingly, this guide uses PGA as an example unless noted otherwise. If the seismic hazard curves are available in terms of spectral accelerations at different frequencies, they could be used as the reference parameter as long as they are used consistently in the hazard, fragility, and systems analyses. The best reference parameter is the one that is the best predictor of damage to the SSCs that dominate risk. For example, if the responses of the dominant risk contributors are all governed by 5 to 10 Hz ground accelerations, then using the PGA as the reference parameter can be either conservative or unconservative, depending on the slope of the 5 to 10 Hz acceleration hazard curve relative to the PGA hazard curve. If the two hazard curves are parallel, then either parameter can be used without affecting the SPRA results. The RE is then defined as a particular ground response spectrum shape normalized to the RE level. Typically, the RE shape is defined as either a uniform hazard spectrum having the same AEP as the RE level, or as a Ground Motion Response Spectra (GMRS) developed following ASCE/SEI 4-16 [10]. The RE defines the input to the seismic response analysis, which develops SSC seismic responses associated with the RE. The RE responses may then be scaled to estimate responses associated with other ground motion levels (Section 5.2). Since the RE seismic responses are not perfectly known, they are treated as probabilistic distributions rather than single deterministic values. Responses are conventionally modeled as lognormal distributions, as described in Section 3.2. Ultimately, the seismic responses challenging each SSC’s important failure modes are characterized as probabilistic distributions. The responses are associated with the RE level ground motion and can be scaled to other ground motion levels. The seismic response distributions (Section 3.1.3) are combined with the seismic capacity distributions (Section 3.1.2) to determine the probability of failure over the range of ground motion levels, which is the seismic fragility (Section 3.1.4). 3.1.4 Seismic Fragility For a given ground motion level (e.g., 0.3g PGA), the seismic response analysis determines the distribution of seismic demands challenging each SSC. Combining the seismic demand distribution with the seismic capacity distribution discussed in Section 3.1.2, the probability of failure for the given ground motion level is the probability that the demand exceeds the capacity. When this comparison of seismic capacity and demand is performed over a range of ground motion levels, the result is a seismic fragility function: the probability of failure as a function of the ground motion reference parameter. The seismic capacity and demand distributions each include two types of variability. The part of the variability that is potentially reducible is defined to be epistemic variability. It includes those sources of variability due to lack of knowledge of structural response and capacity that could be reduced by more detailed studies. Examples are uncertainties in the dynamic modeling of the structure, lack of understanding of material capacity, and uncertainties due to use of engineering judgment. For example, the analytically predicted strength of a shear wall could be improved with test data, which would reduce the epistemic variability (βU). 3-5 13633436 Fragility Methodologies The part of the variability that cannot be practically reduced is called aleatory variability (randomness, βR). For example, the variability in structure response for a known RE input spectrum includes an aleatory component. Different earthquakes with the same PGA and spectral shape could produce different maximum responses, for example, depending on whether the two horizontal directions have their peak accelerations at the same time or at different times. It is unlikely that any amount of testing or analysis will reduce this randomness, within the confines of the current analytical model. The effects of aleatory and epistemic variability on the fragility can be distinguished by quantifying them separately throughout the fragility analysis. To illustrate the distinction, it can be instructive to view the fragility as a “family” of fragility curves. An example family of fragility curves is shown in Figure 3-2. The shape of a single curve represents the aleatory variability in ground acceleration capacity due to randomness. The dispersion of fragility curves across various confidence levels reflects epistemic uncertainty. The mathematical framework used to define the family of fragility curves is known as a “double lognormal” model. Section 3.2.2 provides the details of the double lognormal fragility model. Figure 3-2 The effect of aleatory (βR) and epistemic (βU) variability on fragility curves Theoretically, if sufficient resources were available to diminish epistemic variability to a negligible lower bound, then the fragility could be expressed as a single “true” fragility curve that included aleatory variability alone. In Figure 3-2, fragility curves at different confidence levels are shown (e.g., 95%, 50% or median, and 5%). The 95% confidence curve means that the analyst has 95% confidence that the "true" fragility curve lies to the right of (i.e., higher than) the 3-6 13633436 Fragility Methodologies 95% curve. The mean fragility curve is also shown as a dashed line in Figure 3-2; it is the average of all possible fragility curves. The attached Microsoft Excel spreadsheet can be used to easily plot families of fragility curves like those shown in Figure 3-2. Fragility curves can be developed by a variety of methods. This guide discusses two methods of fragility analysis: the SOV and hybrid fragility approaches. Both fragility approaches use a double lognormal model for defining the shape and dispersion of the calculated fragility curves. The two approaches are schematically illustrated in Figure 3-3 and detailed in Sections 3.3 and 3.4. Figure 3-3 Flowchart of separation of variables and hybrid fragility approaches Each approach defines the fragility curve in terms of two ground motion capacity parameters: 1. The median ground acceleration capacity, Am, which is the median capacity on the median fragility curve, giving the ground acceleration for which there is 50% confidence that the conditional probability of failure is less than 50%. 2. The HCLPF ground acceleration capacity, which is a point at low conditional failure probability on the high confidence fragility curve. For an SPRA, by convention, low conditional probability is taken to be 5% or less, and high confidence is taken to be 95%, such that the HCLPF capacity is the value of ground acceleration for which there is 95% confidence that the conditional probability of failure is less than 5%. 3-7 13633436 Fragility Methodologies Median and HCLPF capacities are indicated on the fragility curves shown in Figure 3-2. Although it conveys less information about the fragility, the mean fragility curve shown in Figure 3-2 can be useful in many applications. By representing the fragility with a single curve, the distinction is lost between aleatory and epistemic variabilities. The probability distribution represented by a mean fragility curve therefore reflects the composite effects of aleatory and epistemic variability. Convolution of the mean fragility curve with the mean hazard curve provides a point estimate of mean unconditional failure probability. For the double lognormal fragility model, the mean fragility curve has some characteristics that are important for some applications. As shown in Figure 3-2, the 50% probability of failure on the mean fragility curve occurs at the median ground acceleration capacity, Am. Additionally, the 1% probability of failure on the mean fragility curve occurs approximately at the HCLPF ground acceleration capacity. The mathematical basis for these relationships is discussed in Section 3.2. 3.2 Lognormal Fragility Model The entire fragility family for an SSC corresponding to a particular failure mode can be expressed in terms of the median ground acceleration capacity, Am, and two parameters representing the variabilities, βR and βU. The variabilities represent the inherent randomness (aleatory variability) about the median and the uncertainty in the median value (epistemic variability). SPRAs have traditionally used the lognormal distribution to develop fragility curves. Other types of probability distributions (e.g., Weibull or normal) also can be used; however, the lognormal distribution has properties that make it convenient to implement in a fragility analysis. The assumption of a lognormal distribution allows efficient development of the family of fragility curves that appropriately represent fragility uncertainty. Properties of the lognormal distribution pertinent to fragility curves are discussed below. More information on the lognormal distribution can be found in many places, such as Probability, Statistics and Decision for Civil Engineers [11]. 3.2.1 Equations for a Single Lognormal Variable Lognormal distributions can be represented by the notation LN (xm, ), which indicates that the probability distribution of random variable x is lognormal with median, xm, and logarithmic standard deviation, . This notation is used throughout this guide. The median value, xm, models the central tendency while the logarithmic standard deviation represents the dispersion about the median. The larger the value of , the more spread out (i.e., flat) the probability distribution becomes. The lognormal distribution is related to the normal distribution (also referred to in textbooks as the Gaussian distribution). If the random variable is lognormally distributed, then the logarithms of sampled values on the distribution will be normally distributed. All logarithms referred to in this guide are natural logarithms (i.e., base e) unless otherwise stated. Further, any normal distribution can be represented as a standard normal distribution by normalizing the distribution such that its mean is zero and its standard deviation is unity. By transforming the properties of the lognormal distribution into the standard normal form, standard equations and the tables for the standard normal distribution can be used to solve for the values of the lognormal distribution. 3-8 13633436 Fragility Methodologies For example, the logarithmic standard deviation,  is just the “common" standard deviation of the logarithms of the sampled values. Also, the antilogarithm of the mean of the logarithms of the sampled values is the median capacity. Figure 3-4 shows a transformation of a lognormal probability density distribution with median xm = 0.87g and logarithmic standard deviation  = 0.43 (consistent with the cumulative distribution in Figure 2-3) into standard normal space. Figure 3-4 Transformation between lognormal and standard normal distributions Table 3-1 shows a demonstration of these relationships for a dataset of twenty-five capacity values sampled randomly from a lognormal distribution (they have been sorted in ascending order). These values were sampled from a lognormal distribution x = LN (xm = 1.0, β = 0.20). As can be seen from this table, the calculated  value (i.e., standard deviation of the logarithms) is 0.20 (i.e., 0.199 rounded), and the median (i.e., antilogarithm of 0.000) is 1.0. Note that the median of the sample values (i.e., the thirteenth value in the ordered set) is 1.0, as expected. 3-9 13633436 Fragility Methodologies Table 3-1 Sample values from a lognormal distribution with a median of 1.0 and a logarithmic standard deviation of 0.20, x = LN (xm = 1.0, β = 0.20) Sample Values Logarithms of Values 1 0.662 -0.412 2 0.732 -0.312 3 0.774 -0.257 4 0.805 -0.216 5 0.833 -0.183 6 0.857 -0.155 7 0.879 -0.129 8 0.900 -0.105 9 0.921 -0.083 10 0.941 -0.061 11 0.960 -0.040 12 0.980 -0.020 13 1.000 0.000 14 1.020 0.020 15 1.041 0.040 16 1.063 0.061 17 1.086 0.082 18 1.110 0.105 19 1.137 0.128 20 1.167 0.154 21 1.201 0.183 22 1.241 0.216 23 1.292 0.256 24 1.364 0.311 25 1.506 0.410 Mean 1.019 0.000 Standard Deviation 0.204 0.199 3-10 13633436 Fragility Methodologies The basic equations for calculating values from a lognormal distribution are presented below. These equations are used to obtain the non-exceedance probability, NEP(x), that the value of the lognormal variable is less than x. NEP x Φ Z where: Z Eq. 3-1 x ln x β The variable "Z" is the transformation of the lognormal parameters to the standard normal variable (or “standard normal variate”) and is necessary to be able to use standard normal distribution tables. The cumulative standard normal distribution function, (Z), is tabulated in many handbooks and texts on probability and statistics and is a common function in many computer programs. Thus, knowing the standard normal variable Z, the value for (Z), and hence the non-exceedance probability (NEP) for a value of x, can easily be found (e.g., see Figure 3-5). The inverse operation of knowing the probability and then finding the corresponding value of Z is often represented as: Z Φ Φ NEP is the inverse cumulative standard normal distribution function x x ∙e where: NEP Eq. 3-2 The inverse of Equation 3-2 leads to the value of x corresponding to a given non-exceedance probability as given by the following equation: where: Eq. 3-3 Z is the standard normal variable corresponding to NEP(x) Table 3-2 gives the standard normal variable, Z, for common non-exceedance probabilities. They are plotted in Figure 3-5. The standard normal variables from Table 3-2 of Z = 2.33, 1.65, and 1.00, and their associated NEPs of 0.99, 0.95, and 0.84 are used extensively throughout this report and other fragility literature. See, for example, Equations 3-14 and 3-15 where the 1.65 and 2.33 values are used in the definition of HCLPF and A1%. The 1.00 value associated with 84% NEP is central in the definition of the CDFM method, where seismic response is required to be at about the 84% NEP level as defined in Section 3.4.1. 3-11 13633436 Fragility Methodologies Table 3-2 Standardized normal variable, Z, for common probabilities Standard Normal Variable, Z Non-Exceedance Probability, NEP 2.33 0.99 2.05 0.98 1.65 0.95 1.28 0.90 1.00 0.84 0.00 0.50 -1.00 0.16 -1.28 0.10 -1.65 0.05 -2.05 0.02 -2.33 0.01 Figure 3-5 Non-exceedance probability, NEP, vs. standard normal variable, Z 3-12 13633436 Fragility Methodologies 3.2.2 Double Lognormal Seismic Fragility Model In this section, relationships of lognormal parameters in Equations 3-2 through 3-4 are applied to the double lognormal fragility model. The conventional fragility model distinguishes between epistemic and aleatory variability, with each modeled as an independent distribution. Decomposition of the fragility distribution into two independent distributions for aleatory and epistemic variability is known as the “double” lognormal seismic fragility model. The ground acceleration capacity is treated as a lognormal random variable with median seismic capacity Am, and logarithmic standard deviation βR due to aleatory variability (randomness). Figure 3-6 shows a lognormal probability density function on the ground acceleration parameter “a” and a cumulative distribution function for the ground acceleration capacity, LN(Am, βR), of an SSC. The total area under the density function is unity, and the shape of the function represents the relative likelihood of different capacity values. Figure 3-6 Example probability density function and cumulative distribution function (i.e., fragility curve) As shown in Figure 3-6, the cumulative distribution evaluated at acceleration "a" is the area under the density function between the acceleration equal to zero and the acceleration equal to a. Equivalently, the cumulative distribution function is the probability that the ground acceleration capacity is less than or equal to a. In other words, the cumulative distribution function is equal to the conditional probability of failure at each given ground acceleration value, which is the definition of a fragility curve. Since the cumulative distribution function LN(Am, βR) is anchored to the median ground acceleration capacity and includes only randomness variability, it is equivalent to the SSC’s median (50% confidence) fragility curve. 3-13 13633436 Fragility Methodologies Assuming negligible epistemic uncertainty (i.e., only accounting for the random variability, R), the median conditional probability of failure, PF, for a given ground acceleration, a, is given by applying Equation 3-1 to the median fragility curve defined by LN (Am, βR): P  a ln A Eq. 3-4 β As an example, the relationship between PF and a is shown by the median fragility curve plotted in Figure 3-2 for a component with a median ground acceleration capacity Am = 0.87g and R = 0.25. For the median conditional probability of failure range of 5% to 95%, the ground acceleration capacity is within a range that is found by applying Equation 3-3. From Table 3-2, the standard normal variates, Z, for the 5% and 95% NEPs are -1.65 and 1.65: A ∗e . ∗ 0.58g a a A ∗e . 1.31g ∗ These capacities correspond to the value of the green (50% confidence) fragility curve in Figure 3-2 where it intersects the conditional probability of failure values of 5% and 95%. Figure 3-7 shows several example fragility curves based on the lognormal distribution. The curves in Figure 3-7 all have the same median capacity but with different R values. Higher βR values suggest more random variability (variability that cannot be reduced); therefore, the probability of failure is distributed over a broader acceleration range. Lower βR values suggest less random variability, and the probability of failure is more narrowly distributed around the median capacity value (Am). Figure 3-7 Example fragility curves based on the lognormal distribution 3-14 13633436 Fragility Methodologies Fragility curves at higher or lower confidence levels can be developed by centering the distribution on a ground acceleration capacity other than Am (i.e., with confidence of exceedance greater or less than 50%). These alternative fragility curves account for imperfect knowledge of Am due to epistemic uncertainty. At each acceleration value, the fragility PF can be represented by a probability density function with logarithmic standard deviation U. Equation 3-5 accounts for both random variation in the seismic capacity (aleatory variability) and uncertainty in the median seismic capacity of the distribution for randomness (epistemic variability). a ln A  P β ∗ β Q Eq. 3-5 where Q is the subjective probability (confidence) that the conditional probability of failure, PF, is less than PF' for a ground acceleration a, which is expressed as: Q PP P ′|a Conditional probability of failure considering both aleatory and epistemic variability in the ground motion capacity is calculated below for an example fragility. Example Given: Am = βR = βU = 1.5 g 0.2 0.3 What is the probability of failure with 50% confidence for ground acceleration of 2.0g? P  ln a Am βU ∗  1 0.5 βR After evaluating the standard normal variate for confidence of 50%, it is clear that this failure probability is on the median fragility curve: P  a ln A  ln 2.0 1.5 0.2 β =  [1.438] = 0.93 β ∗0 Obtained from standard normal distribution function table Benjamin and Cornell [11] 3-15 13633436 Fragility Methodologies For the same fragility, what is the ground acceleration for which the probability of failure is 5% with 95% confidence? 0.05  a 1.5 0.3 ∗  0.95  0.05 ∗ 0.2 0.3 ∗ 1.65 ln ln a 1.5 a 0.66g a ln 1.5 ∗ e 0.2 1.65 ∗ 0.2 . ∗ . . 0.3 ∗ 1.65 a 1.5 The results from this example are illustrated in Figure 3-8 below. The first result is shown at a = 2.00g and 93% probability of failure on the 50% confidence (green) fragility curve. The second result of 0.66g is shown as the 5% probability of failure capacity on the 95% confidence fragility curve, which is identical to the HCLPF capacity. Figure 3-8 Results from fragility illustrations 3-16 13633436 Fragility Methodologies 3.2.3 Useful Properties of the Lognormal Distribution Although the lognormal distribution is defined with a median and logarithmic standard deviation, lognormal random variables can also be expressed in terms of the corresponding mean and "common" standard deviation values by the following two equations: x σ where: x x ∗e ∗ e ⁄ Eq. 3-6 1 Eq. 3-7 xave is the mean of the lognormal distribution LN(xm, β) σx is the standard deviation of the lognormal distribution LN(xm, β) Two useful approximations that can be used in fragility analysis are: x β x Eq. 3-8 COV Eq. 3-9 where COV is the coefficient of variation: σ x COV Eq. 3-10 For the example in Table 3-1, these approximations are accurate to within a few percentage points. These approximations are reasonably accurate as long as COV (or ) is less than about 0.4. The lognormal distribution has unique properties that make it easy to work with when calculating fragility curves. For a normal distribution, the mean of a sum of independent, normally distributed random variables is equal to the sum of the means (Benjamin and Cornell [11]). Analogously, the median of a product of independent, lognormally distributed random variables is equal to the product of the medians (Benjamin and Cornell [11]). This is expressed in equation form as follows: y where: x ∗x ∗ …x Eq. 3-11 ym is the median of the lognormal distribution on y, which is the product of n lognormally distributed random variables xi xim is the median of the lognormal random variable xi Also, in a manner analogous to the properties of the normal distribution, where the variance of a sum of normally distributed random variables is equal to the sum of the variances, the lognormal distribution has a similar property. Note that the variance is just the "common" standard 3-17 13633436 Fragility Methodologies deviation squared. The square of the logarithmic standard deviation of a product of lognormally distributed random variables is equal to the sum of the squares of the individual logarithmic standard deviations. This is expressed in equation form as follows: β β where: β ⋯ β Eq. 3-12 βy is the logarithmic standard deviation of the lognormal distribution on y that is the product of n lognormally distributed random variables, xi. βi is the logarithmic standard deviation of the lognormal random variable xi. These last two equations are important for many earthquake capacity problems where the effects of the various underlying variables (i.e., capacity and demand) can be put into a multiplicative format. Based on Equation 3-12, an important short cut is available for calculating the mean fragility curve shown in Figure 3-2 without having to average the suite of individual curves at different confidence levels. The mean curve is also lognormal with properties LN(Am, C), where C, the composite logarithmic standard deviation, is given by the following equation: β β β Eq. 3-13 where βR and βU are the logarithmic standard deviations for randomness and uncertainty, respectively. As can be seen in Figure 3-2, both the 50% confidence and the mean fragility curves pass through the median capacity value. However, the mean curve has a shallower slope compared to the median curve because the latter has a smaller logarithmic standard deviation (i.e., R compared to C). Also shown in Figure 3-2 is the HCLPF capacity, which is defined in SPRA to be the 95% confidence of a 5% probability of failure. Using Equation 3-4, the median is selected at the 95% confidence (i.e., Am * exp [-1.65 * βU]) and this high confidence median is then multiplied by the factor required to reach a 5% probability of failure value (i.e., exp [-1.65 * βR]). Multiplying these two terms leads to the following equation for the HCLPF ground acceleration capacity: HCLPF A ∗e HCLPF A % . ∗ Eq. 3-14 Using the definition for C from Equation 3-13 and considering all possible ratios of R to U, the minimum HCLPF value (i.e., most conservative) is found when R is equal to U. For this case, the HCLPF can be approximated by the 1% NEP capacity (A1%) using only C and the median capacity as follows since √2*1.65 = 2.33: A ∗e 3-18 13633436 . ∗ Eq. 3-15 Fragility Methodologies The 2.33 standard normal variate that results from the bounding case where R is equal to U corresponds to a 1% probability of failures (Table 3-2). Therefore, the 1% probability of failure on the composite (“mean”) fragility curve is considered a reasonable estimate of the HCLPF. This relationship is only slightly conservative for most realistic values of R and U found in fragility analyses. 3.3 Separation of Variables Fragility Approach The SPRA fragility methodology known as the SOV approach is described in detail in this section. The SOV approach entails evaluating median factors of safety and corresponding logarithmic standard deviations βR and βU for each variable affecting the response and capacity. The overall process is illustrated schematically in Figure 3-9. Figure 3-9 Separation of variables fragility evaluation process 3-19 13633436 Fragility Methodologies 3.3.1 Median Capacity as a Product of Factors The SOV fragility approach is a method of developing fragility curves wherein the first objective is to estimate a realistic median ground acceleration capacity, Am. The ground acceleration capacity is evaluated as the product of several random variables. These fragility variables quantify the SSC capacity and seismic response. The next objective is to quantify the aleatory and epistemic variability in the ground acceleration capacity. Based on the properties of lognormal random variables discussed in Section 3.2.3, the separation of the ground motion capacity into a product of several variables in this manner allows efficient evaluation of the variability. The fragility variables presented in this section have been selected to account for the most common significant sources of aleatory and epistemic variability (randomness and uncertainty, respectively) tending to affect fragilities. The basic high-level fragility variables for evaluating the ground acceleration capacity are summarized in this section. In Equation 3-16 and the remaining fragility equations in this guide, it is assumed that PGA is selected as the reference ground parameter for the SPRA. The symbol PGARE indicates that the median ground acceleration capacity is evaluated relative to the PGA of the selected RE. A F ∗F ∗F ∗ PGA Eq. 3-16 The variables FC, FER, and FRS are the capacity factor, equipment response factor, and structure response factor, respectively. The capacity factor, FC, for a particular failure mode of the SSC being investigated is the scale factor on the RE response that will result in failure. The median capacity factor can be estimated by scaling the results of an older analysis or by conducting new analysis of the SSC capacity and seismic response due to the RE. Logarithmic standard deviations in the capacity factor account for variability in the physical properties and methods used to calculate the SSC capacity. The median values of the structure and equipment response factors scale the results of the response analyses to remove conservatism or unconservatism in the corresponding properties and methods. Logarithmic standard deviations in the response factors account for the corresponding variability. When median physical properties and analysis methods are used in a new seismic response analysis, median values of the response factors are typically 1.0. Median values of the response factors are typically non-unity when the response is scaled from an analysis that was developed for a separate application. For example, when seismic demand from a design analysis is scaled for use in fragility analysis, it is likely that significant conservatism existed in the original design analysis that must be removed to obtain the median response due to the RE. In some instances, elements of the response may have been un-conservative, which must also be reflected in the response factors. The evaluation of FC, FER, and FRS depends on the type of SSC and failure mode for which the fragility is being developed. Each of these three variables is approximated as lognormally distributed and can be further factored as summarized in Equations 3-17, 3-18, and 3-19. 3-20 13633436 Fragility Methodologies The meaning of each variable is summarized in Tables 3-3 through 3-5. These tables provide the following information about the variables:  The types of fragilities to which the variable is applicable.  The association of the variable with aleatory variability, epistemic variability, or both. Section 3.1.4 defines the difference between aleatory and epistemic variabilities. Some variables, particularly those related to ground motion, are associated primarily with aleatory variability. Others are purely epistemic. Many include both aleatory and epistemic variability.  The sections of this guide that provide guidance for determining the variable’s median value and logarithmic standard deviations. The variables defined and discussed in this document account for all significant sources of conservatism and variability for most fragility evaluations. In most SPRAs, however, a few fragility evaluations require additional, case-specific variables that are not enumerated here. The fragility analyst must have a sufficient understanding of the fragility methodology and the governing structural mechanics to be able to identify and quantify any additional, case-specific, relevant variables beyond those defined in this document. Fragility Variables for Structures Am = FC * FRS * PGARE Eq. 3-17 = [FS*Fμ]*… [(FSA*(1/FHDPR)*FV)*Fδs*(Ffs*FMs*FTC)*(FTH*FMCs)*(FGMI* FSSI* FVSV)*FECCs]*… PGARE Fragility Variables for Equipment Evaluated by Analysis Am = FC * FER * FRS * PGARE Eq. 3-18 = [FS*Fμ]*… [FQM*FSS*Fδe*(Ffe*FMe)*FMCe*FECCe]*… [(FSA*(1/FHDPR)*FV)*Fδs*(Ffs*FMs*FTC)*(FTH*FMCs)*(FGMI*FSSI* FVSV)*FIR]*… PGARE The structure response factor, FRS for equipment fragilities consists of the same factors as for structure fragilities, with the exception that earthquake component combination, FECCe is evaluated for the equipment response rather than structure response, and an additional factor, FIR, is included to account for the effect of inelastic structure response on equipment response. 3-21 13633436 Fragility Methodologies Fragility Variables for Equipment Evaluated by Testing Am = FC * FRS * PGARE ୘ୖୗ Eq. 3-19 = ቂୖୖୗి ቃ*… ి [(FSA*(1/FHDPR)*FV)*Fδs*(Ffs*FMs*FTC)*(FTH * FMCs)*(FGMI*FSSI*FVSV)*FIR]*… PGARE For equipment evaluated by testing, the structure response factor is the same as for equipment evaluated by analysis. A separate equipment response variable is not included because aspects of equipment response affecting the fragility analysis are accounted for as part of the capacity factor. Table 3-3 Summary of capacity factor variables Variable Symbol Variable Meaning Applicable Fragility Types Structures Equipment (AnalysisBased) FS Elastic Strength Factor*   Fµ Inelastic Energy Absorption Factor   Equipment (TestBased) Variability βR βU Report Sections  4.2, 4.3   4.5, 4.8 TRSC Test Response Spectral Acceleration Capacity    4.1.3, 4.9 RRSC Reference Response Spectral Acceleration Demand    5.5.3 * FS may also be referred to as the elastic RE scale factor. FS may depend on one or more material properties and one or more strength equations. Epistemic variability in all material properties and strength equations should be considered when calculating βU for fragility curves following the methods in Section 3.3.2. 3-22 13633436 Fragility Methodologies Table 3-4 Summary of equipment response factor variables Variable Symbol Variable Meaning Applicable Fragility Types FQM Qualification method factor  FSS Equipment in-structure spectral shape factor  Fδe Equipment damping factor Ffe Structures Equipment (AnalysisBased) Equipment (TestBased) Variability βR βU Report Sections  5.5.2.1  5.5.2.1   5.5.2.2 Equipment model frequency factor   5.5.2.3 FMe Equipment model fidelity factor   5.5.2.3 FMCe Equipment mode combination factor   5.5.2.4 FECCe Earthquake component combination factor for equipment response   5.5.2.5 Variability Report Sections  Table 3-5 Summary of structure response factor variables Variable Symbol Variable Meaning Applicable Fragility Types Structures Equipment (AnalysisBased) Equipment (TestBased) βR βU FSA Ground motion factor for spectral shape     5.4.1.1 FHDPR Ground motion factor for horizontal direction peak response     5.4.1.2 FV Ground motion factor for vertical to horizontal ground acceleration ratio     5.4.1.3 Fδs Structure damping factor     5.4.2 Ffs Structure model frequency factor     5.4.3.1 FMs Structure model fidelity factor     5.4.3.2 FTC Structure model torsional coupling factor     5.4.3.3 FTH Time-history phasing factor     5.4.4.1  3-23 13633436 Fragility Methodologies Table 3-5 (continued) Summary of structure response factor variables Variable Symbol Variable Meaning FMCs Applicable Fragility Types Variability Report Sections Structures Equipment (AnalysisBased) Equipment (TestBased) βR Structure mode combination factor     FGMI Foundation structure interaction factor for ground motion incoherence     5.4.5.1 FSSI Foundation structure interaction factor for soilstructure interaction     5.4.5.2 FVSV Foundation structure interaction factor for vertical spatial variation     5.4.5.3 FECCs Earthquake component combination factor for structure response   5.4.6 FIR Inelastic structure response factor  5.5.1.3     βU 5.4.4.2 3.3.2 Analytical Procedures for Developing Fragility Curves In the SOV fragility approach, it is necessary to calculate three parameters to define the fragility curves for SSC failure modes: Am, βR, and βU. Sections 3.3.2.1 through 3.3.2.4 present several methods for determining these fragility parameters from the median values and logarithmic standard deviations of the individual variables listed in Tables 3-3 through 3-5. Section 3.3.2.5 compares median parameters and corresponding logarithmic standard deviations calculated using the various methods. The several methods presented here are not necessarily mutually exclusive; multiple methods can be used in a single fragility evaluation. For example, Latin hypercube simulation (LHS) or Monte Carlo can be used to calculate the median and variability in structure response, which can then be used as input to an SSC fragility evaluation using the approximate second order procedure. The study concludes that all the investigated methods produce acceptable results, but the approximate second moment procedure described in Section 3.3.2.1 is the easiest to use and is therefore recommended for most situations. At the other extreme, Monte Carlo simulation is the most rigorous approach. It can be time consuming, and its use is justified only in special situations. The general second moment procedures represent an intermediate level of sophistication in fragility analysis. They are particularly useful when closed form expressions for βR and βU values are desired. 3-24 13633436 Fragility Methodologies 3.3.2.1 Approximate Second Moment Procedure Fragility Equations 3-16 through 3-19 express calculation of the median ground acceleration capacity Am following the approximate second moment procedure, which is a practical method of calculating fragility curve parameters that is recommended for most situations. In the approximate second moment procedure, the median seismic capacity, Am, is obtained by a deterministic calculation using median values for all the variables. This procedure follows the same steps that an engineer would normally perform in a conventional analysis or design, except different loads, material properties, and capacity equations are used. In a plant design, the engineer calculates the stresses for a given input and compares the combined seismic plus other loads to allowable values, either directly or indirectly through an interaction equation. If the combined loads are below the allowable values, then the component is adequate. As discussed in Section 3.1.2, the goal of fragility analysis is to express the median capacity in terms of the reference ground motion parameter (e.g., PGA or spectral acceleration) selected for the SPRA. In one approach, the analyst may use the original design results as the basis for the fragility analysis. Here, the conservatism is removed at each step, and the RE responses are scaled to the median capacity. For example, one conservatism that must be removed is the difference between an RG 1.60 [12] response spectrum and the RE selected for the SPRA. In another approach, the RE is directly used, and a new response analysis performed to obtain more realistic demands. In this approach, realistic judgments are made at each analysis step, and the problems of conservatism in the original design are avoided. In either case, the RE input is scaled until the component just reaches the median failure level. The median capacity is just the scaled RE, where the scale factor is based on a deterministic analysis substituting median values for each of the basic variables listed in Tables 3-3 to 3-5. While the median capacity is expressed as a ground acceleration value, the median capacity can also be thought of as a median scale factor times the ground motion level associated with the RE, as expressed by the following equation: Am = SFm * PGARE Eq. 3-20 where SFm is the median scale factor SF, and PGARE is the PGA of the RE. In general, SF is developed as the product of a capacity factor, structure response factor, and equipment response factor as discussed in Section 3.3.1. Per Sections 3.1.2 and 3.2.1, PGA is most commonly used as the reference ground motion parameter for SPRA; therefore Equation 3-20 expresses seismic capacity in terms of PGA. However, PGARE in Equation 3-20 could be replaced by whichever reference parameter has been chosen for the SPRA. The median scale factor is obtained by using median values for all the basic variables in the analysis. In the approximate second moment procedure, the logarithmic standard deviations for randomness, βR, and uncertainty, βU, are obtained by the following equation: β Eq. 3-21 β 3-25 13633436 Fragility Methodologies In this equation, β represents either βR or βU. The term βi represents the part of the final β-value due to the effect of the variability in the i-th underlying basic variable (i.e., any of the basic variables in Tables 3-3, 3-4, or 3-5). The final value for β is the square root of the sum of the squares (SRSS) combination of the individual βi values, which is a property of lognormal variables, as discussed in Section 3.2.3 (Equation 3-12). Each individual βi value is obtained from the following equation: β SF 1 ∗ ln Z SF Eq. 3-22 The parameter SFZσi is the scale factor applied to the RE to reach failure when the i-th variable is defined at Z standard deviations from its median. All other basic variables are kept at their median values. The parameter Z is usually set to one on the side of the median that leads to the lowest capacity. For example, if the strength of steel is the variable, it is changed to the minusone (i.e., Z = -1) standard deviation value, and the analysis is rerun to obtain a revised scale factor. Equation 3-22 is then used to obtain βi corresponding to uncertainty in the steel strength. The process is repeated for each of the basic variables in the analysis. It is recommended that demand variables be increased (i.e., evaluated at the plus-one standard deviation level) and that capacity variables be decreased (i.e., evaluated at the minus-one standard deviation level). In other words, should always be less than unity. This may be slightly conservative, depending on the effect on the median capacity from the relative variability of the underlying basic variable. The computational aspects of this procedure are very similar to sensitivity analysis, which design engineers in the nuclear industry are familiar with. In sensitivity analysis, the analyst asks "what if" the variable has a different value. In fragility analysis, the interpretation of the effect of a change in the variable is quantified using Equation 3-22. In practical terms, the engineer first performs the analysis for the scale factor using median values for all the input parameters. The result of this analysis is the median capacity. The analysis is then repeated by changing each of the underlying variables in Tables 3-3, 3-4, and 3-5, one at a time, and the βi values are obtained using Equation 3-22. These βi values are sorted in a group for βR and a group for βU, and Equation 3-21 is used with each group to calculate the final fragility parameters βR and βU. This procedure works well if the relationship between the various random variables is well behaved. One example where this does not work well is when the fragility analysis involves the difference of two variables (at least one of which is random), and their nominal values are about the same (i.e., the difference is close to zero). The difference can be very small as the parameters are varied, and sometimes can even be negative. When this situation occurs, the approximate second moment procedure can give erroneous results. For this situation, a Monte Carlo procedure should be performed for that part of the analysis. Another situation where this procedure may not work well is when the response of a component is controlled by very peaked ISRS and the fundamental frequency is near the peak. A very slight change in the building or equipment frequency can cause radically different input to the component. For this case, the βi value due to uncertainty in the structure and equipment frequencies should be determined by Monte Carlo simulation. 3-26 13633436 Fragility Methodologies 3.3.2.2 Other Second Moment Procedures The approximate second moment procedure described in Section 3.3.2.1 is recommended for calculating median capacities and logarithmic standard deviations for fragilities in most cases. The second moment approach can also be formulated in other ways, which may be desirable for certain situations. In general, the second order procedures discussed in this section are useful for developing closed-form solutions for fragility curves as functions of the underlying random variables but do not generally offer significant advantages to the approximate second moment procedure described in Section 3.3.2.1. A second moment procedure uses the means and standard deviations of the basic variables to obtain the mean and standard deviation values of the fragility curve. Since ultimately the fragility curve is expressed in terms of medians and logarithmic standard deviations, conversions between mean and median, as well as between standard deviation and logarithmic standard deviation (and vice versa), must be made in the rigorous second moment procedure. This process can be simplified using approximations, as discussed in this section. There are several ways in which the second moment approach can be formulated. The resulting procedures are categorized as follows:  Second moment-first order  Second moment-second order mean  Approximate second moment The second moment procedures start with a Taylor series expansion of the equation that relates the basic variables to the scale factor on the RE. If only the linear terms are retained, then it is called a first order procedure. If the second order terms are retained, then it is called a second order procedure. In general, the second order terms affect both the mean and the standard deviation of the component capacity. However, using second order terms generally only benefits the mean (hence the median) and is not worth carrying along in the calculation for the standard deviation (hence 0). Thus, the second way in which second moment procedures can be categorized refers only to "second order mean." Second Moment-First Order One approximate second moment procedure has already been given in Section 3.3.2.1. Another simplification is given here, which reduces the work when the second moment-first order procedure is used. The second moment-first order procedure starts with the relationship for scale factor, SF, as a function of n basic demand and capacity variables, xi: SF f x ,x ,…x Eq. 3-23 3-27 13633436 Fragility Methodologies The mean, SFavg, and the variance, (σsf)2 (i.e., square of the standard deviation) of the scale factor, assuming a first order Taylor series expansion of Equation 3-23, is: SF σ where: f x ,x δf | δx ,…x Eq. 3-24 ∗σ Eq. 3-25 xiavg is the mean of variable xi σi is the standard deviation of variable xi δf | δx is the derivative of f with respect to xi evaluated at the mean values of xi Since the underlying basic variables are usually expressed as lognormal distributions LN(xim, βi), Equations 3-6 and 3-7 must be used to obtain the mean and standard deviation of each variable. In Equation 3-25, the derivative terms can be evaluated either explicitly or numerically. The former result is useful when a closed form solution for the fragility parameters is desired. A numerical approach is appropriate when numerical answers are needed. Second Moment-Second Order Mean If the functional relationship between SF and the underlying basic variables contains random variables in the denominator of the expression or involves complex terms (e.g., power expressions such as in an interaction equation), then the median capacity will often be low compared to an "exact" result (i.e., using Monte Carlo simulation). This is because using only the linear terms from the Taylor series expansion is not sufficient for these cases. To remedy this problem, a second order Taylor series expansion can be used for the calculation of the mean (hence median) capacity. The following second order equation for the mean should be used to replace Equation 3-24 for these special problems: SF where: δ f | δx f x1avg , x2avg , … xnavg 1 2 ∗ δ f | δx ∗ σ Eq. 3-26 is the second derivative of f with respect to xi, evaluated at the mean values of xi This procedure is the same as for the second moment-first order procedure except when calculating the median capacity, Equation 3-26 should replace Equation 3-24 when calculating the mean. 3-28 13633436 Fragility Methodologies When calculating the logarithmic standard deviation, β, the first order procedure should be used exactly as given above. In other words, when calculating β, Equation 3-24 should be used to obtain the mean. This may seem inconsistent; however, the second order terms are not included in the variance equation (i.e., Equation 3-25). Thus, in the calculation for the logarithmic standard deviation, first order expressions must be used consistently for both the mean and the variance. A second order formulation can be derived for the standard deviation, but it offers very little benefit and is unreasonably complex. Therefore, the second order procedure generally is only recommended when calculating the median. Approximate Second Moment – Generalized The approximate second moment procedure given at the beginning of this section is one example of how the second moment approach can be simplified. A more general simplification can be made, which is useful when a closed form solution to a problem, or part of a problem, is desired. In the general approximation given here, the mean is assumed to be the same as the median, and the standard deviation is set equal to the logarithmic standard deviation times the median. These approximate relationships are represented in Equations 3-8, 3-9, and 3-10 in Section 3.2.3. Making use of the approximate relationships avoids having to make the transformation between lognormal and normal parameters (and vice versa). The same approximations are also made for the parameters of distribution on the scale factor. With these substitutions, the median scale factor, SFm, and logarithmic standard deviation for the scale factor, β, are obtained directly: SF σ f x β σ SF x x ,x ,…,x δf | δx ∗β ∗x Eq. 3-27 Eq. 3-28 Eq. 3-29 As an example application of the approximate second moment approach, the sum of two random variables x1 and x2 that are lognormal LN(x1m, β1) and LN(x2m, β2), respectively, is given in Equations 3-30 to 3-32. Defining x3 as the sum of x1 and x2 as follows: x Eq. 3-30 Using Equations 3-27 through 3-29, the approximate median and logarithmic standard deviation are: x x x Eq. 3-31 3-29 13633436 Fragility Methodologies β x x x ∗β 3.3.2.3 Monte Carlo Simulation x x x ∗β Eq. 3-32 Monte Carlo simulation is a rigorous procedure for calculating fragility curve parameter values. It can be used for developing fragility curves or applied to specific parts of a fragility analysis when the approximate second moment procedure is inaccurate. This method is also not limited to lognormal distributions since any type of distribution from which sample values can be easily obtained can be used. It is also helpful for gaining insights into the analysis and helps to understand intuitively the effects of variability of the underlying basic variables on the fragility curves. If a deterministic relationship can be developed for either the capacity of a component or for the scale factor applied to a RE input, then a Monte Carlo analysis can be performed. This is true since a Monte Carlo analysis only requires:  Probability distributions on the underlying variables  Deterministic equation that is repeated many times using different values taken from the probability distributions Monte Carlo analysis can be thought of as a "smart" sensitivity analysis. The values selected for each deterministic analysis are neither arbitrarily large nor unconstrained, as often occurs in sensitivity analysis, but must be consistent with the underlying distributions on the basic variables. Obviously, the analyst can change the properties of the underlying distributions (i.e., make the median and logarithmic standard deviation larger or smaller). This would then be sensitivity analysis on the Monte Carlo process, but once the distributions are fixed, the sampling process follows procedures that are consistent with those distributions. There are different ways in which sample sets can be produced. In this discussion, a sample set is one realization of the random variables that are used to perform a single deterministic analysis. In most cases it is only practical to obtain the sample values for the basic variables using a computer since many sample sets are required to produce stable results in the final values that are calculated. A simple example shows the power of the Monte Carlo simulation procedure. In this example, a random variable x3 is equal to the sum of two independent random variables x1 and x2, which is the same as the example given above using Equation 3-30. The two basic variables are assumed to be lognormally distributed LN(2, 0.4) and LN(3, 0.5) for x1 and x2, respectively. A total of 1000 samples were obtained using Equation 3-30 as follows: x 2∗e x 3∗e 3-30 . ∗ i = 1 to 1000 . ∗ j = 1 to 1000 13633436 Fragility Methodologies Following are some of the samples that were obtained. Each pair of x1 and x2 values is a sample set: Table 3-6 Samples of two independent random variables x1 x2 0.438 0.568 0.612 0.704 0.658 0.755 0.690 0.772 0.698 0.804 0.721 0.839 0.742 0.861 0.755 0.892 0.770 0.916 0.785 0.920 … … Before these values can be combined using Equation 3-30, they must be randomly ordered relative to each other to preclude introducing any artificial correlation because in this example it is assumed that these two variables are independent of each other. Only the values for one variable must be randomly mixed to make the samples independent. In general, if there are n independent random variables in a problem, only n minus 1 of them must be randomly mixed. In this example, the samples for the variable x2 were randomly mixed, and the sample sets of x1 and x2 values and their sums were found to be: Table 3-7 Randomly ordered and summed random variables x1 x2 x3=x1+x2 0.438 3.319 3.802 0.612 4.420 5.032 0.658 3.156 3.814 0.690 2.371 3.061 0.698 2.976 3.674 0.721 4.181 4.902 0.742 1.327 2.069 0.755 10.318 11.073 0.770 2.998 3.768 0.785 1.969 2.754 … … … 3-31 13633436 Fragility Methodologies Figure 3-10 shows a plot of the histogram of the sample sums (1,000 total values) and the corresponding cumulative probability distribution function. Note that the x3i values are first arranged in ascending order with the first value being the lowest number obtained from the simulations. The rearranged x3i values are plotted against the corresponding probability Pi values to form the distribution function using the following equation for Pi, where N is equal to 1,000 for the example case: P i N 1 2 Eq. 3-33 Some analysts use the following equation for Pi since it has the property of being an unbiased estimator: P N i Eq. 3-34 1 Equation 3-33 works equally as well and in some cases has been found to give more accurate results for a small number of samples. For a large number of simulations, both equations give essentially the same results. The accuracy of this example simulation is checked by comparing the mean and standard deviation of the computed samples x3i to the theoretical values. The mean and standard deviation of the Monte Carlo results for x3 were calculated and found to be 5.564 and 2.019, respectively. The theoretical mean and standard deviation are calculated here using Equations 3-6 and 3-10 from Section 3.2.3. Figure 3-10 Results of example Monte Carlo simulation 3-32 13633436 Fragility Methodologies Theoretical Mean x 2∗e x 3∗e x 3∗e x 2.167 . 2.167 . 3.399 . 3.399 3.399 5.566 (compare to 5.564 from the Monte Carlo simulation) Theoretical Standard Deviation σ 2.167 ∗ e σ 0.902 σ 3.399 ∗ e . 1 . 1.812 1 0.902 1.812 2.024 (compare to 2.019 from the Monto Carlo simulation) The Monte Carlo-based values compare very closely to the theoretical results. In many cases, once the cumulative probability distribution is found, it is then represented by a "best fit" lognormal distribution (e.g., to obtain a lognormal fragility curve). This is done by first putting the results of the simulation in a linear format assuming that the samples fit a lognormal distribution. The equation to obtain the probability of a random variable from the lognormal distribution, LN(x3m, β3) for specific values of x3 is given next. P Φ ln x x β Eq. 3-35 Rearranging the terms of this equation, it can be transformed into a linear format: ln x ln x β ∗Φ P Eq. 3-36 Equation 3-36 shows that the x3 values should be transformed to ln(x3), and the P values transformed to Φ-1(P), using the inverse normal (Gaussian) cumulative distribution function. This transformation is applied to the x3 and P values obtained in the simulation, and the transformed values are plotted in Figure 3-11 along with a "best fit" straight line obtained by linear regression analysis. From Equation 3-36, the slope of the line is equal to the logarithmic standard deviation value, β, and the antilogarithm of the intercept point (i.e., the value of ln(x3) when Φ-1(P) is equal to zero) is the median. For this example, the median and β from the linear regression line were found to be 5.24 and 0.34, respectively. 3-33 13633436 Fragility Methodologies Figure 3-11 Best fit plot to example Monte Carlo simulation In some problems, the simulation results do not nicely fit a straight line, such as shown in Figure 3-11. When a simulation process is performed for the entire fragility curve, it is best to fit the regression line between the median value and a point corresponding to about the minus 2 standard deviation level (i.e., probability of 0.5 and 0.02, respectively) since this is the portion of the fragility curve that typically makes the most contribution to the frequency of failure when integrated with the hazard curve. When this procedure is used for intermediate parts of a fragility analysis (e.g., to simulate in-structure response demand values from a "peaked" curve) then it is best to fit the regression line between the ±2 standard deviation levels, unless the variability of the part dominates the fragility curve. For this case it is better to fit the regression line between the median and the minus 2 standard deviation level. Using Equations 3-31 and 3-32 from the example given above to obtain an approximate second moment estimate of the median and logarithmic standard deviation of x3, it is found that the approximate results are very close to the Monte Carlo results: x β 2 3 2 2 (compare to 5.24) 5 3 ∗ 0.4 3-34 13633436 2 3 3 ∗ 0.5 0.34 (compare to 0.34) Fragility Methodologies 3.3.2.4 Latin Hypercube Simulation One simple procedure for performing Monte Carlo analysis is called Latin hypercube simulation, which is a form of stratified sampling (NUREG/CR-1397 [44]). To obtain N samples of a single random variable, the probability distribution for that variable is divided up into N equal probability regions. For example, if N is equal to 10, then there are ten probability regions each equal to a probability of 0.1 (i.e., 1/10 since the probability values must sum to 1.0). In each probability region one value is randomly selected. Figure 3-12 shows graphically how this process works. A cumulative probability distribution function for a random variable is shown, and a box on the left side is divided up into ten equal area regions. In Figure 3-12, a random value is shown, being selected randomly from within the eighth region from the bottom and the corresponding value of the variable obtained from the distribution function. This process is repeated for each of the ten regions. If the probability distribution is lognormal, LN(xm, β), then the N samples, xi, can be formed using the following equation: x x ∗e ∗ Eq. 3-37 Figure 3-12 Example Latin hypercube sampling process In Equation 3-37, the random number rndi between 0 and 1 is obtained independently for each sample from a random number generator. A good test to see whether the samples are truly random is to calculate the median and logarithmic standard deviation from the N samples. If the calculated values are the same (or nearly so) as the original parameter values that defined the distribution, then the sample has been properly developed. One example is presented in Table 3-1. 3-35 13633436 Fragility Methodologies 3.3.2.5 Example Analyses Comparing Analytical Procedures The purpose of this subsection is to give the fragility analyst some feeling for the relative results when using each of these procedures. The following five equation forms for the scale factor, SF, were studied to see how the accuracy of the various procedures discussed in Sections 3.3.2.1 through 3.3.2.3 compare to each other. 1. SF x ∗x ∗x 3. SF x 2. SF 4. SF 5. x ∗ SF ∗ x x x SF ∗ x 1 For all three of the random variables xi considered, the median values were assumed to be 1.0. The effect of the logarithmic standard deviation is investigated by assuming that β for all three of the random variables is either 0.2, 0.4, or 0.6. The first value is representative of the typical values for the basic variables that normally occur (e.g., see fragility variable values given in Sections 4 and 5). The last value is very extreme, and most fragility problems do not have basic variables with logarithmic standard deviations as high as 0.6. This value severely tests the approximate methods. The median parameter is investigated, and the following four cases are studied: 1. Second moment - first order 2. Second moment - second order mean 3. Approximate second moment [i.e., SF = f (x1m, x2m, x3m)] 4. Monte Carlo simulation Table 3-8 shows the results for the median study. The results for the first and second equation forms give an indication of the accuracy of the Monte Carlo procedure since the results for Case 3 are exact for these two equation forms (i.e., the median of a product (or quotient) of lognormal random variables is equal to the product (quotient) of the medians). Three thousand simulations were obtained in the Monte Carlo approach. 3-36 13633436 Fragility Methodologies Table 3-8 Results for median study Equation Form SF x ∗x ∗x SF SF SF ∗ x x ∗ x SF Median Value, SFm x x x x x x x SF ∗ x 1 Case 1 Case 2 Case 3 Case 4 β = 0.2 1.002 1.002 1.000 1.001 β = 0.4 1.031 1.031 1.000 1.001 β = 0.6 1.132 1.132 1.000 1.002 β = 0.2 0.963 1.002 1.000 1.002 β = 0.4 0.897 1.031 1.000 1.003 β = 0.6 0.789 1.132 1.000 1.005 β = 0.2 3.040 3.040 3.000 3.039 β = 0.4 3.160 3.160 3.000 3.153 β = 0.6 3.357 3.357 3.000 3.337 β = 0.2 1.941 2.021 2.000 2.009 β = 0.4 1.782 2.091 2.000 2.052 β = 0.6 1.557 2.232 2.000 2.128 β = 0.2 0.970 0.990 1.000 0.992 β = 0.4 0.886 0.963 1.000 0.997 β = 0.6 0.757 0.907 1.000 0.932 The results for β equal to 0.2 for all cases lead to essentially the same median values. This indicates that any of the procedures for calculating the median can be used for typical problems. However, note that for the last two equation forms, which either have variables in the denominator or of a complex form (i.e., the last equation), the second order expansion for the mean produces better results than the first order expansion when compared to Monte Carlo simulation. A significant observation is that Case 3 (i.e., the approximate second moment procedure), which is the easiest to use, produces very acceptable results for all equation forms. The logarithmic standard deviation is also investigated, and the following four cases are studied: 1. Second moment – first order 2. Approximate second moment 3. β ∗ ln ; where Z 4. Monte Carlo Simulation 1 3-37 13633436 Fragility Methodologies Table 3-9 shows the results for the logarithmic standard deviation study. Again, the results for the first and second equation forms give an indication of the accuracy of the Monte Carlo results since both Cases 2 and 3 are exact for these equation forms. The results for β equal to 0.2 for all cases produce essentially the same values. This indicates that any of the procedures for calculating the logarithmic standard deviation can be used for typical problems. As with the median value procedures, Case 3, which is the easiest to use, produces very acceptable results for all equation forms. Table 3-9 Results for logarithmic standard deviation study Equation Form SF x ∗x ∗x SF SF SF ∗ x x ∗ x SF Logarithmic Standard Deviation, β x x x x x x x SF ∗ x 1 Case 1 Case 2 Case 3 Case 4 β = 0.2 0.340 0.346 0.346 0.351 β = 0.4 0.647 0.693 0.693 0.703 β = 0.6 0.913 1.039 1.039 1.054 β = 0.2 0.340 0.346 0.346 0.351 β = 0.4 0.721 0.693 0.693 0.702 β = 0.6 0.913 1.039 1.039 1.052 β = 0.2 0.116 0.115 0.129 0.117 β = 0.4 0.237 0.231 0.285 0.236 β = 0.6 0.367 0.346 0.469 0.358 β = 0.2 0.244 0.245 0.252 0.243 β = 0.4 0.481 0.490 0.518 0.487 β = 0.6 0.708 0.735 0.797 0.733 β = 0.2 0.142 0.141 0.153 0.146 β = 0.4 0.287 0.283 0.329 0.312 β = 0.6 0.442 0.424 0.525 0.476 3.4 Hybrid Fragility Approach The SOV fragility approach discussed in Section 3.3 is universally applicable. However, it requires the fragility analyst to individually estimate the median values and logarithmic standard deviations of several different variables affecting capacity and demand. The hybrid fragility approach is a simplified method for estimating fragility curves. Although the hybrid approach is more approximate than the SOV approach, hybrid fragilities are sufficiently accurate for first order estimates of plant seismic risk measures and relative significance of various SSCs to plant seismic risk. Since typically only a handful of components dominate plant seismic risk, these dominant risk contributors can be identified by risk quantifications using hybrid fragilities; plant 3-38 13633436 Fragility Methodologies risk estimates can later be refined using SOV fragilities to calculate more realistic fragility parameters for the dominant risk contributors. This approach can provide efficiencies in the fragility stage of an SPRA by circumventing the additional effort required by the SOV approach for the majority of SSCs. For those SSCs that are determined to be the dominant risk contributors or are risk significant in the seismic accident sequences, estimates of median capacity (C50%) and variabilities (βU and βR) should be done using the separation of variables approach. The basis for the hybrid fragility approach is the HCLPF capacity relationship expressed in Section 3.2.3 by Equations 3-14 and 3-15. The 1% conditional probability of failure ground acceleration capacity on the mean fragility curve (A1%) is approximately equivalent to the 5% conditional probability of failure ground acceleration capacity on the 95% subjective confidence fragility curve (HCLPF). In the hybrid approach, the CDFM method is used to estimate A1%. From the A1% estimate, the family of fragility curves is estimated based on conservatively biased generic values of βR and βU. Background and criteria are presented for the CDFM method in Section 3.4.1, and generic logarithmic standard deviations for use in the hybrid approach are recommended in Section 3.4.2. 3.4.1 Conservative Deterministic Failure Margin Method The CDFM method is a deterministic method for estimating ground acceleration capacity aimed at achieving a seismic capacity corresponding to about the 1% NEP for a specified target response spectrum. The 1% probability of failure capacity defined by the CDFM approach is referenced to the specified target response spectrum. For its application to SPRA as part of the hybrid fragility approach, the specified target response spectrum is the RE. The CDFM method is versatile and has historically been used in many applications. Different response spectra are specified for application of the CDFM method in other situations. For example, ASCE/SEI 43-05 [14] has adopted the CDFM method of calculating seismic capacity for use in seismic design of nuclear facilities, with seismic capacities referenced to the design response spectrum. Some applications of the CDFM method are listed here, along with each application’s primary reference:  Hybrid fragility approach (this guide)  Seismic design of nuclear facilities (ASCE/SEI 43-05 [14])  EPRI SMA (EPRI NP-6041-SLR1 [1])  NRC SMA (NUREG/CR-4334 [15], -4482 [16], and -5076 [17])  PRA-based SMA (NRC ISG DC/COL-ISG-020 [9]) The historical aspect of the CDFM method has resulted in some confusion, of which the fragility analyst should be aware when reviewing older fragility and CDFM calculations. One source of confusion is the outdated terms “HCLPF50” and “HCLPF84,” which were applicable when the HCLPF capacity was being compared to deterministic design or evaluation response spectra defined with either 50% or 84% NEP amplification, respectively. These terms have no relevance to modern application of the CDFM method in an SPRA as part of the hybrid fragility approach. The terms may be encountered in older calculations, however, so Appendix H is included in this guide for historical purposes to explain the associated issues. 3-39 13633436 Fragility Methodologies Calculating A1% is similar to calculating a median seismic capacity for the SOV fragility approach. The difference is the CDFM method introduces targeted levels of conservatism to the physical properties and analysis methods used to calculate seismic capacity and demand. The levels of conservatism are similar or identical to those incorporated in typical structural design methods, which makes the CDFM method a more familiar approach that can be consistently performed by most engineers familiar with design evaluation methods. The general equation for calculating A1% is expressed as follows: A % FC,CDFM ∗ PGARE A % FS,CDFM ∗ F , Eq. 3-38 Similar to Equation 3-16 for calculating median seismic capacities, the CDFM capacity factor FC,CDFM for a particular failure mode of the SSC being investigated is the scale factor on the ground motion defined by the RE that will result in failure. The capacity factor is fundamentally a comparison of the SSC’s capacity to the seismic demand due to the RE. For structures and equipment fragilities based on analysis, FC,CDFM can be further broken down into the elastic strength factor, FS, and the inelastic energy absorption factor, Fμ. ∗ PGARE Eq. 3-39 Conservative (rather than median) values of parameters affecting the capacity factor are used to determine the A1% seismic capacity. The method for calculating FC,CDFM depends on the type of SSC and failure mode being investigated. Specific methods are provided in Section 4 for calculating FC,CDFM alongside corresponding guidelines for median-centered analysis. Unlike Equation 3-16 for the SOV approach, calculating A1% does not require development of the response factors listed in Tables 3-4 and 3-5 or their associated variabilities. General criteria for introducing conservatism in CDFM capacity and demand are presented here. To achieve a 1% NEP seismic capacity, the CDFM method attempts to approximate the following levels of conservatism by the following deterministic criteria: 1. For the RE, the elastic computed response of structures and components mounted thereon should be defined at about the 84% NEP. 2. SSC capacities for a given failure mode (e.g., capacities in terms of force, stress, displacement, acceleration) should be defined at about the 98% exceedance probability (EP) so that even if the CDFM demand slightly exceeds this capacity by more than a permissible, conservatively specified, inelastic energy absorption factor, there will still result a very low probability of failure. However, for brittle failure modes (e.g., weld failure, relay chatter) which have essentially no inelastic energy absorption capability, the capacity should be reduced to about the 99% EP. 3-40 13633436 Fragility Methodologies 3. Inelastic distortion associated with a Demand/Capacity ratio greater than unity is permissible for ductile failure modes. The permissible level of inelastic distortion should be specified at about the 5% failure probability level. The inelastic energy absorption factor Fµ,CDFM should be slightly conservatively estimated at about the 84% EP for this permissible level of inelastic distortion (e.g., use the 84% EP factor from Monte Carlo simulations, or use a slightly conservative method or equation to calculate Fµ). The intended result is an Fµ,CDFM factor at about the 95% EP. 4. The inelastic energy absorption factor, Fμ,CDFM, is the additional demand beyond the elastic capacity that the SSC can undergo before reaching the 1% probability of failure capacity. For CDFM analysis, it is acceptable to use estimate Fμ,CDFM conservatively. Because of the conservatism introduced at the various steps, the result is a HCLPF seismic capacity at about 1% conditional probability of failure on the mean fragility curve (i.e., introduced conservatisms account for a mix of randomness and uncertainty in the capacity and demand). Any seismic evaluation that introduces approximately the level of conservatism as defined in the above criteria meets the intent of the CDFM method and would be expected to achieve a 1% NEP capacity. Theoretical derivation of this NEP for the above criteria is presented in Appendix H. In this approach, most of the conservatism is introduced in the capacity evaluation and in the limited degree of inelastic distortion that is permitted. Only sufficient conservatism is introduced in the seismic response to the RE to achieve computed demands at about the 84% NEP level. Under certain conditions, namely when response variability significantly exceeds capacity variability, the CDFM criteria outlined in this report can produce unconservative estimates of the 1% probability of failure capacity, A1%. Appendix G explains how these conditions affect conservatism in the CDFM method and outlines typical variability ranges within which the CDFM method reliably estimates A1%. For applications where response variability is large, additional conservatism should be introduced into the CDFM methodology to ensure reliable estimates of A1%. Ideally, the damping used in CDFM analysis would be slightly conservative; however, this guide recommends using median damping as a simplification for the following reasons: 1. There is significant uncertainty in how to define “median” and “slightly conservative” values since the viscous damping model is itself an approximation to very complex physical phenomena, and empirical data on measured equivalent viscous damping is sparse. 2. There is significant flexibility in the application of the damping values since damping is dependent on stress levels in various elements of an SSC; this flexibility allows for wider variations in the applied damping values than would any slight conservatism in the CDFM damping values. 3. Any conservatism that would be introduced by using slightly conservative damping values would be small compared to the conservatism introduced via other response variables such as structure and soil stiffness. Therefore, using median damping has negligible effect on the CDFM approach. 3-41 13633436 Fragility Methodologies Table 3-10 provides a detailed summary of the CDFM criteria for the parameters used to calculate capacity and demand. The criteria in Table 3-10 are applicable to the CDFM method when it is applied to the development of seismic fragilities by the hybrid fragility approach for SPRA applications. Table 3-10 also references the sections of this guide providing further explanation of each criterion. Figure 3-13 shows a schematic illustration of the CDFM evaluation process. Table 3-10 Summary of CDFM method criteria for hybrid fragility applications in SPRA Criterion Treatment for CDFM Method Report Sections Load Combination Normal operation + reference earthquake. 4.1.2, 5.2 Ground Response Spectrum Reference the seismic capacity to the chosen SPRA reference acceleration parameter (PGA or spectral acceleration) of the RE. Do not account for spectral shape peak and valley variability. Horizontal direction peak response should be included. 5.2, 5.4.1.2, Appendix H, Appendix I Seismic Demand Perform seismic response analysis in accordance with latest version of ASCE/SEI 4 [10]. 5.3 Damping Median damping. Structural Model Best Estimate (Median) + Parameter Variation. 5.3, 5.4.3 Soil-Structure-Interaction Best Estimate (Median) + Parameter Variation. 5.3, 5.4.5 Material Strength Non-brittle failure modes: Code specified minimum strength or 95% EP actual strength if test data are available. 5.3.1.4, 5.4.2, 5.5.2.2, 4.3, Appendix G Brittle failure modes*: 98% EP material strength. Static Strength Equations Non-brittle failure modes: Code ultimate strength (ACI), maximum strength (AISC), Service Level D (ASME), or functional limits. If test data are available to demonstrate excessive conservatism of code equation, then use 84% EP from test data for strength equation. 4.2, 4.4, 4.6, 4.7, 4.9, Appendix G Brittle failure modes*: 95% EP strength equations. Inelastic Energy Absorption For non-brittle failure modes and linear analysis, use appropriate inelastic energy absorption factor from ASCE 43-05 [14] to account for ductility benefits, or perform nonlinear analysis and go to 95% exceedance ductility levels. 4.5, 4.8 In-Structure (Floor) Spectra Generation ISRS should be developed at the 84% NEP level considering the criteria for variations in structure and SSI parameters. 5.3 *Section 4.7.2.1 describes an exception for concrete breakout failure of cast-in-place anchors. 3-42 13633436 Fragility Methodologies Figure 3-13 CDFM evaluation parameters 3.4.2 Approximating Fragility Curves The hybrid fragility approach is based on the observation that the mean unconditional annual probability of unacceptable performance (PF) for any SSC is relatively insensitive to βC. This annual probability (seismic risk) can be computed with adequate precision from the CDFM A1% and an estimate of βC. Typically, βC lies within the range of 0.3 to 0.6. In fact, if all the sources of variability are appropriately considered, it is not possible to obtain an estimated βC less than approximately 0.3. Kennedy [13] compares values of PF calculated for mean fragility curves with different values of βC and the same A1%. For the comparison, the unconditional failure probabilities are calculated using a representative mean seismic hazard curve. The comparison shows that the computed seismic risk at β = 0.3 is approximately 1.5 times that at β = 0.4, while at β = 0.6 the computed seismic risk is approximately 60% of that at β = 0.4. Appendix D to EPRI 1025287 [18] contains a sensitivity study confirming that PF is insensitive to βC over the full practical range of seismic hazard curve slopes. 3-43 13633436 Fragility Methodologies Due to the relative insensitivity of unconditional failure probability to βC, approximate fragility curves developed with generic logarithmic standard deviations can be used to reasonably estimate plant seismic risk measures. Table 3-11 provides recommended values for βC, βR, βU, and the ratio of the median capacity to A1% capacity computed by the CDFM method (Am / A1%). The recommended βC values are based on NEI 12-06 [90] recommendations and on average are biased slightly conservative (i.e., slightly low βC on average). Therefore, it is important that the logarithmic standard deviations in Table 3-11 only be used to estimate median seismic capacities from CDFM A1% capacities. If the same logarithmic standard deviations were applied to median seismic capacities, the resulting fragility curves may tend to over-predict A1% (i.e., the resulting fragilities would be unconservative). Table 3-11 Recommended logarithmic standard deviations to use in the hybrid fragility approach Type SSC Composite βC Randomness βR Uncertainty βU Am / A1% Structures & Major Passive Mechanical Components Mounted on Ground or at Low Elevation Within Structures 0.35 0.24 0.26 2.26 Active Components Mounted at High Elevation in Structures 0.45 0.24 0.38 2.85 Lower Bound Case4 0.30 0.24 0.18 2.00 Other SSCs 0.40 0.24 0.32 2.54 Random variability βR is primarily due to ground motion variability, and therefore a constant βR value of 0.24 is recommended irrespective of the SSC being considered. The recommended βU values are back-computed from the recommended βC and βR values. The logarithmic standard deviation values listed in Table 3-11 are appropriate for fragilities expressed in terms of ground motion acceleration capacity (e.g., PGA or spectral acceleration at important structure frequencies). Alternatively, the composite logarithmic standard deviations may be more directly estimated by calculating the median ground acceleration capacity Am according to Section 3.3 and the A1% ground acceleration capacity according to the CDFM method. The logarithmic ratio of these two capacities represents 2.33 standard deviations on the mean fragility curve. βR can be estimated as 0.24, and βU can be back-calculated from βC and βR as explained above. This refinement to the hybrid approach involves additional computations but may be cost-effective if it is desired to reduce the conservatism in the estimated variabilities without implementing the more rigorous SOV approach. These lower bound values can be used for relays, block walls, and SSCs with brittle failure modes if more realistic logarithmic standard deviations cannot be estimated. 4 3-44 13633436 4 SEISMIC CAPACITY As discussed in Sections 3.3.1 and 3.4.1, an SSC’s seismic fragility is calculated as the ratio of capacity over demand (the capacity factor, FC) multiplied by response factors and the RE ground motion parameter (e.g., PGARE). This section provides guidance on determining the capacity aspect of FC inherent to SSCs (e.g., material properties, strength equations, and test data). Figure 4-1 outlines a roadmap for this section. Guidance for determining seismic response is provided in Section 5. The capacity factor is described at a high level in Section 4.1, where equations are introduced for comparing seismic capacity and seismic demand. Section 4.1 also introduces three distinct methodologies for calculating component-specific seismic capacities:  Experience-based  Analysis-based  Test-based Section 4.2 provides experience-based seismic capacities for several types of SSCs. The capacities are based on various types of experience, including expert judgment, past analyses, and earthquake experience (observations of the seismic performance of equipment and structures in real earthquakes). Capacities based on test experience (empirical capacities compiled from historical shake table test results) are covered separately in Section 4.9. Analysis-based fragilities use material properties, component or structure configurations, and strength equations to calculate capacities for specific SSC failure modes. Sections 4.3 to 4.8 provide guidance for calculating analysis-based capacities, including material strength properties and strength equations for common failure modes. In contrast, test-based fragilities make use of shake table test data as experimental evidence of a lower bound on the capacity of all potential failure modes challenged by the test. Section 4.9 provides guidance for calculating capacities from test data and suggests some sources of shake table test data for use in fragility analysis. 4-1 13633436 Seismic Capacity Figure 4-1 Section 4 roadmap 4.1 Capacity Factor The fragility analyst may calculate the capacity factor using either experience-based, analysisbased, or test-based methods. In any case, the general form of the capacity factor is a quotient of capacity over demand. If sufficient data is available, it may be possible to calculate the fragility of an SSC following two or more of these methods. In this case, selection of the fragility methodology is at the discretion of the fragility analyst. Most often, however, availability of information will dictate the choice of one or the other. For example, test data is generally unavailable for full-scale nuclear structures, so structure fragilities are developed based on analysis. Capacities can be developed using SOV or hybrid fragility approaches regardless of whether they are based on experience, analysis, or test. 4.1.1 Fragilities Based on Seismic Experience The seismic capacity part of a fragility can be developed using seismic experience information. This seismic experience includes earthquake experience data, shake table testing, and seismic analyses. Two types of experience-based capacities are currently being used in generating seismic fragilities; the first is based on the seismic capacity tables developed in EPRI NP-6041SLR1 [1], and the second is the state-of-the-art approach for developing capacities from earthquake experience data documented in EPRI 3002011627 [19]. Appendix C describes the basis for the capacities derived from EPRI NP-6041-SLR1 [1]. The capacities from EPRI 3002011627 [19] are based on a Bayesian inference method applied to earthquake experience data collected as part of the SQUG research efforts. The experience-based capacity factor for both cases is defined as the ratio of capacity over demand and is characterized in terms of 5% damped spectral acceleration. Demands should be developed in the same terms. Experience based capacities for equipment are expressed in terms of in-structure spectral acceleration, whereas structure capacities are in terms of ground spectral acceleration. The capacities are broad-banded, so demands should be clipped per Section 5.5.3.1. The median capacity factor is: F C D Eq. 4-1 4-2 13633436 Seismic Capacity For SOV evaluations, the capacity C is the median capacity, Cm, provided in Tables 4-2 to 4-4. The demand D is the median clipped spectral acceleration demand, SaCm. For CDFM, the capacity is the 1% probability of failure level, C1%, and the demand is the 84% NEP clipped spectral acceleration demand, SaC84. Since no equipment response analysis is performed for experience-based fragilities, the equipment response factor, FER, is unity with no variability. Another type of experience-based capacity known as test experience are based on the EPRI GERS. The capacity factor for developing fragilities from test experience is the same as the test-based fragility method, which is provided in Section 4.1.3. 4.1.2 Fragilities Based on Analysis Analysis-based fragilities are best suited for failure modes whose limit states are defined in terms of physical parameters that can be evaluated by engineering analysis (e.g., stress, displacement). Examples of such failure modes include anchor pullout, which occurs at a tensile force capacity, and shear wall flexural failure, which occurs at a nonlinear deformation capacity. The capacity factor for an analysis-based fragility can be calculated following the same general form, regardless of the type of SSC (e.g., structure or equipment), and can be broken down into elastic and inelastic parts: F F ∗F Eq. 4-2 4.1.2.1 Elastic Strength Factor The elastic strength factor, FS, is the scale factor required to scale the RE demand to the elastic capacity (Figure 4-2). The elastic strength factor may be formulated as follows: F C DS DNS ΔCS C D D ΔC = = = = Eq. 4-3 Elastic capacity associated with the seismic failure mode being evaluated Elastic demand due to the RE Non-seismic demand Reduction in capacity due to concurrent seismic loading 4-3 13633436 Seismic Capacity Figure 4-2 Elastic strength factor (FS) Rearranging Equation 4-3 highlights the conceptual definition of FS as the elastic RE scale factor corresponding to failure: C F ∗ ΔC D F ∗D Eq. 4-4 In most cases, the capacity C is independent of the level of seismic loading. In the uncommon situation where capacity is increased or decreased by concurrent seismic loading, CS accounts for the change in capacity as the RE is scaled. As an example, consider a sliding failure mode for an unanchored component. The capacity for this failure mode is due to friction resistance against sliding, which is proportional to the normal force at the base of the structure. Assume for this example that failure occurs at the initiation of sliding, even though in most cases some sliding displacement would be acceptable. Therefore, the capacity, C, is equal to the available friction resisting force. For normal (non-seismic) load conditions, this is dependent only on the dead load of the component and the friction coefficient at the sliding surface. During an earthquake, the ground motion will induce forces on the component in both horizontal and vertical directions. The horizontal force in this example is the seismic demand, DS. Meanwhile, the vertical force affects the normal force at the base of the component and will therefore change the available friction resisting force. Depending on the direction of vertical seismic force, the capacity will either increase or decrease. The direction of loading is generally assumed such that the value of ΔCS is positive in Equations 4-3 and 4-4, meaning the capacity decreases for increasing seismic loading. 4.1.2.2 Inelastic Energy Absorption Factor In some instances, failure does not occur when the elastic capacity is reached (i.e., there is additional inelastic capacity beyond the elastic limit state). Therefore, a separate factor, the inelastic energy absorption factor, Fμ, accounts for any further increase in ground acceleration that can occur before failure. Nearly all structures and components exhibit at least some ductility (i.e., ability to strain beyond the elastic limit) before failure. Because of the limited energy content and oscillatory nature of earthquake ground motion, this ductility can be highly beneficial in increasing the seismic capacity for structures and components. The inelastic energy absorption factor, Fμ, represents the ratio of the earthquake level at which a certain system 4-4 13633436 Seismic Capacity ductility, μ, is reached, to the earthquake level for which a limit state (e.g., yield) would be predicted by linear elastic analysis. The additional seismic capacity due to this inelastic energy absorption factor should be considered in any fragility evaluation whose failure could exhibit some significant ductility. Ignoring this effect will lead to unrealistically low estimates of the failure margin. It is impossible to correlate performance of structures and equipment in past earthquakes with capacities predicted by elastic analyses without considering the Fμ factor. The following section identifies the criteria for evaluating the inelastic energy absorption factor in CDFM and SOV fragilities. 4.1.2.3 Criteria for SOV and CDFM Evaluations The criteria for calculating the strength factor, FS, and the inelastic energy absorption factor, Fµ, differ between the SOV or hybrid fragility approaches. Table 4-1 defines the SOV and CDFM criteria for FS and Fµ. The criteria result in a median capacity factor for the SOV criteria (50% EP), and an approximately 99% EP capacity for the CDFM criteria. Table 4-1 Capacity factor criteria for SOV and hybrid fragilities Variable SOV Criteria Hybrid Criteria C Calculate elastic capacity using median centered material strengths and strength equations. Calculate elastic capacity using design values for material strengths and strength equations, or values that will determine C at about 98% EP. For brittle failure modes, reduce C to about 99% EP following the criteria in Table 3-10 for material strengths and strength equations. DS Calculate demands from median response. Calculate demands from response with about 84% NEP. DNS Calculate non-seismic loads based on normal operating conditions5. Calculate non-seismic loads based on normal operating conditions. ΔCS Calculate reduction in capacity due to loads from median response. Calculate reduction in capacity due to loads from response with about 84% NEP. Fµ Calculate inelastic energy absorption based on median limits for nonlinear distortion Calculate inelastic energy absorption factor at about the 84% NEP for a nonlinear distortion limit corresponding to 5% probability of failure. This is intended to result in an inelastic energy absorption factor at about 95% EP. 4.1.3 Fragilities Based on Test Test-based fragilities are calculated from applied test levels and analytically determined demands. Qualification testing is typically conducted when the capacity for a failure mode cannot practically be calculated by engineering analysis. This is typically the case for functional failure modes of active equipment, such as electrical and control components, electric motors, 5 Normal operating conditions are typically considered for at-power SPRA fragility analysis. The probability is very low that more severe faulted or emergency level conditions would occur simultaneously with peak earthquake loads. It would therefore be conservative to consider the more severe conditions concurrent with seismic demands. 4-5 13633436 Seismic Capacity and in some cases pumps and valves. In most cases, these types of components have had their seismic performance qualified by shake table testing. Test-based capacities are represented by the response spectra calculated from the shake table input motion, called the test response spectra (TRS). TRS may be developed from component-specific test data or generic test data. The primary sources of generic equipment test data used in fragility analyses are the EPRI/ANCO GERS [20, 21]. Component-specific test data is typically obtained from seismic qualification reports. For relays, component-specific test data can be obtained from the EPRI Seismic Qualification Reporting and Testing Standardization (SQURTS) database (EPRI 1019309 [22]), or from the EPRI High Frequency Program (EPRI 3002002997 [23] and 3002004396 [24]). EPRI 3002010668 [25] also provides a summary of SQURTS test data formulated for fragility calculations. When the TRS for an SSC are obtained from qualification tests, it is typically qualified for either a single input motion or the maximum of several input motions for which the SSC did not fail (i.e., a proof test). In this case, the quantification of a fragility level must be based on expert judgement. The TRS is sometimes interpreted as a lower bound capacity (i.e., 100% confidence the true capacity is higher), but because there is little statistical significance to a single proof test, it is not truly a lower bound capacity. The true spectral acceleration capacity is uncertain and may be significantly higher than the TRS. As such, estimating seismic fragility curves based on qualification test data is one of the most difficult and debated tasks in an SPRA. This section presents an acceptable procedure for developing test-based fragilities. The general capacity factor formulation for test-based fragilities is given by the following equations, which depend on whether the source of testing information is for an entire cabinet (which includes devices) or for a standalone device test. F TRS RRS Eq. 4-5 Cabinet-Based Test Data Device-Based Test Data TRSC = TRS * CT * CI * FD TRSC = TRS * CT * CI * FAX * FD RRSC = RRS * CC RRSC = RRS * CC * AFC where: TRS RRS CC CT CI AFC FAX FD = = = = = = = = Equipment test response spectrum Reference response spectrum demand (in-structure demand due to the RE) Clipping factor for narrow-banded RRS Clipping factor for narrow-banded TRS Capacity increase factor Cabinet amplification factor Multi-axis to single-axis conservatism factor Broad frequency input spectrum device capacity factor 4-6 13633436 Seismic Capacity Both median and CDFM capacity factors can be calculated using Equation 4-5. The median and CDFM factors that modify TRSC are discussed in Section 4.9. The factors that modify RRSC are discussed in Section 5.5.3. 4.2 Seismic Capacities Based on Experience To be cost-efficient, an SPRA should incorporate a step where SSC fragilities are quickly estimated based upon experience and judgment concerning their seismic ruggedness to withstand seismic loads. An initial fragility estimation effort like this (see Section 6.2 for further description) enables the SPRA to quickly concentrate on those SSCs for which there is a legitimate concern about seismic capacity. Thus, the fragility evaluation effort is focused producing useful risk insights. Essential steps for this quick initial evaluation are: 1. A plant walkdown by an experienced team capable of exercising the necessary judgment to estimate seismic capacities within a specific plant. 2. A general industry and regulatory consensus that, in fact, there are wide classes of SSCs in NPPs which have demonstrated a substantial seismic capacity either because of their performance in past earthquakes, available generic ruggedness or fragility data, or because generally accepted seismic capacity evaluations have been previously performed on similar SSCs in previous seismic margin or SPRA studies. This first step is covered by the walkdown described in Section 6.1. The second step requires the establishment of some guidelines that are generally accepted for capacity estimation. Tables 4-2 and 4-4 are based on Tables 2-3 and 2-4 of EPRI NP-6041-SLR1 [1] and can be used to estimate approximate median or HCLPF seismic capacities of SSCs. The tables list caveats for various types of SSCs that must be met to demonstrate the seismic capacities are applicable. The caveats should be addressed with input from a seismic walkdown of plant-specific SSCs by experienced seismic capability engineers (Section 6.1). The tables should be used as a guide to assist the walkdown team in making seismic capacity judgments during the walkdown. The walkdown team should be very familiar with these tables and the material in this guidance document but must exercise their own experience and judgment in the use of this material for any specific SSC. Appendices B and C provide additional background material to assist the fragility analyst in understanding the bases for these SSC groupings, as well as the caveats and restrictions associated with the use of the acceleration capacity values in these two tables. These tables do not address anchorage, which must be addressed separately. For structures and for some equipment items, seismic capacities estimated from Tables 4-2 and 4-4 may be conservative and not realistic. SPRA requires using realistic fragilities as much as possible to properly rank accident sequences and get accurate insights. However, the Table 4-2 and 4-4 capacities can be used initially, and the need to calculate explicit fragility parameters should be determined jointly with the systems analyst via sensitivity analyses at a later stage of the SPRA. 4-7 13633436 Seismic Capacity The capacities in Tables 4-2 and 4-4 are very heavily based on expert judgements and experience of the NRC-sponsored Expert Panel on the Quantification of Seismic Margins (NUREG/ CR-4334 [15]). However, the tables include additional classes of structures, equipment, and subsystems that were not addressed in NUREG/CR-4334 [15]. Also, some of the footnoted exceptions and restrictions have been modified from the NUREG/CR-4334 [15] content, and other small changes have been made where such changes were believed to be warranted. The tables were introduced in EPRI NP-6041-SLR1 [1] to provide a basis for screening SSCs from an SMA. In an SMA, an SSC may be screened if its HCLPF capacity can be shown to exceed the SME established for that SMA. The tables were, therefore, introduced as an economical and expedient method of demonstrating SSCs had HCLPF capacities exceeding generic, conservative levels. Whereas this method has been extremely useful to screen SSCs from SMAs, their application in an SPRA is different. Screening SSCs in an SPRA is somewhat more complicated than an SMA, since an SPRA has no deterministic capacity threshold above which SSCs will be screened out. Instead, in an SPRA, SSCs may be screened based on having negligible importance to seismic risk, as described in EPRI 1025287 [18]. As such, depending on the seismic hazard and seismic capability of a given plant, the HCLPF capacities demonstrated via Tables 4-2 and 4-4 may not be sufficiently high to screen SSCs from an SPRA. Nonetheless, they may still be used to establish approximate fragilities that can be used in risk quantification to identify those SSCs that contribute most to risk. Tables 2-3 and 2-4 of EPRI NP-6041-SLR1 [1] provide HCLPF capacities expressed in terms of 5%-damped peak spectral ground acceleration (average of two orthogonal horizontal components). In NUREG/CR-4334 [15], the NRC Expert Panel defined the screening tables in terms of mean PGA, which is only a very approximate damage predictor, even for stiff components mounted in stiff buildings. Damage is heavily influenced by the duration and breadth of frequency content of the ground motion (for example, see NUREG/CR-3805 [26]) and the component mounting location within a building subjected to the ground motion. Spectral acceleration in the range of about 2 to 8 Hz is more significant to the potential for an earthquake to cause damage than the PGA. The basis of the spectral acceleration limits in Tables 2-3 and 2-4 of EPRI NP-6041-SLR1 [1] have roots in the original development of the SMA screening guidelines (NUREG/CR-4334 [15]). At that time, SQUG was formed in response to the NRC issue referred to as USI A-46 [27]. Experience data was being gathered and corresponding seismic input in the form of response spectra were compared, which led to both a Reference and a Bounding Response Spectrum (SAND92-0140 [28]). The corresponding spectral limits were developed (EPRI NP-7498 [29]) consistent with the level of conservatism provided in the SMA screening guidelines in NUREG/CR-4334 [15]. It was recommended in EPRI NP-6041-SLR1 [1] to use ground spectral acceleration bins (i.e., <0.8g, 0.8g to 1.2g, and >1.2g) instead of the original PGA limits, which are poor descriptors of the potential for earthquake damage as compared to spectral limits. More detailed discussion on the basis of the ground spectral limits is provided in EPRI-NP-7498 [29]. Appendix C provides the historical basis for the HCLPF capacities that can be demonstrated using the EPRI NP-6041-SLR1 capacity tables, and discusses any deviations 4-8 13633436 Seismic Capacity made from the Expert Panel consensus (NUREG/CR-4334 [15]). Also contained in Appendix C are discussions of additional seismic ruggedness data, including earthquake experience data, which were collected, analyzed, and found to support the capacities in the EPRI NP-6041-SLR1 capacity tables after the publication of NUREG/CR-4334 [15]. Subsequently, EPRI developed a method to express the equipment capacities in terms of local spectral acceleration (Sa) at the mounting point of individual equipment items rather than ground Sa. Mounting point Sa is a better damage predictor than ground Sa. The following sections outline the method, and the equipment capacities in Table 4-2 are expressed in terms of local mounting point Sa. Additionally, EPRI derived a survival statistics methodology in Appendix C to EPRI 1002988 [3] capable of analytically demonstrating that the EPRI NP-6041-SLR1 capacity tables indeed represent HCLPF capacities (95% confidence of 5% probability of failure). The survival statistics method requires that at least thirty samples of equipment survival exist in the SQUG earthquake experience database to demonstrate the EPRI NP-6041-SLR1 capacity levels represent HCLPFs. More recently, EPRI improved the survival statistic approach, and developed a new approach for updating seismic capacities using Bayesian inference and SQUG earthquake experience (EPRI 3002011627 [19]). The Bayesian approach is considered to give more realistic seismic capacities than Table 4-2 and the survival statistics method. For the eight equipment classes for which the Bayesian capacities are available (Control Panels, Engines, Fans, Horizontal Pumps, Inverters and Battery Chargers, Motor Control Centers, Motor-Operated Valves, and Medium Voltage Switchgear), it is recommended that these improved capacities be used in lieu of those in Table 4-2. The improved capacities for these eight classes are summarized in Table 4-3. An ongoing EPRI research program is underway to use the Bayesian approach to update seismic capacities for additional equipment classes. 4.2.1 Seismic Capacities for Equipment Data on the earthquake performance of several generic categories of mechanical and electrical equipment in power plants and heavy industrial facilities demonstrate that they are capable of withstanding significant ground motion levels without functional damage, provided certain conditions are met. These earthquake experience data were compiled in EPRI NP-7149D [30]. The Seismic Qualification Utility Group (SQUG) Generic Implementation Procedure (GIP) [31] used earthquake experience data to address NRC Unresolved Safety Issue (USI) A-46. For the GIP, the seismic capacity of equipment based on earthquake experience is represented by the Reference Spectrum (Figure 4-3). The Reference Spectrum has a PGA of 0.5g and a maximum 5% damped horizontal Sa of 1.2g at frequencies between 2.5 Hz and 7.5 Hz. As noted above, the 1.2g maximum Sa of the Reference Spectrum is the basis of the 1.2g ground Sa limit in EPRI NP-6041-SLR1 [1] Tables 2-3 and 2-4. Therefore, the SQUG Reference Spectrum reasonably represents the HCLPF capacity that is demonstrated by meeting the criteria in the EPRI NP6041-SLR1 capacity tables. 4-9 13633436 Seismic Capacity Figure 4-3 Reference Spectrum Appendix B to EPRI NP-7498 [29] demonstrated that the characteristic shape of the Reference Spectrum beyond 7.5 Hz is due to the energy content of the records used to construct the Reference Spectrum. There is considerable evidence (e.g., EPRI 3002004396 [24]) that the 1.2g spectral acceleration capacity could be conservatively extended into the high-frequency range beyond 7.5 Hz as a demonstrated post-earthquake functional level for anchored components. The Extended Reference Spectrum may consequently be defined by extending the 1.2g spectral acceleration to frequencies exceeding 7.5 Hz, as shown in Figure 4-4. Figure 4-4 Extended Reference Spectrum 4-10 13633436 Seismic Capacity For the equipment capacities in EPRI NP-6041-SLR1 [1] Table 2-4, SaSL is taken to be HCLPF expressed in terms of ground Sa, as discussed above. These generic capacities are subject to verification that the specific SSC meets the class descriptions in the SSRAP report (SAND92-0140 [28]) and conforms to the criteria listed in the tables and in Appendix B, including evaluating anchorage and systems interactions separately. They represent “Function After” capability only; device chatter is not covered by the capacity tables. Table 4-2 capacities are expressed in terms of local mounting point Sa rather than ground Sa, as discussed above. The EPRI NP-6041-SLR1 [1] ground Sa capacities are increased by the following factors as derived in Supplement B to Appendix H, and should be compared with the in-structure response spectra (ISRS) at the base of the component: C1% Cm βĈ SaSL = HCLPF spectral acceleration capacity in terms of horizontal ISRS at the equipment support location = 1.5SaSL = Median spectral acceleration capacity in terms of horizontal ISRS at the equipment support location = 4.0SaSL = Logarithmic standard deviation for Cm = 0.42 = Peak 5% damped horizontal ground Sa representing the EPRI NP-6041-SLR1 [1] HCLPF level that the SSC satisfies These relationships can be readily validated using the frequentist statistical approach outlined in Section 3.1 of EPRI 3002011627 [19] using the following set of conservative assumptions:  At least thirty survivals in the earthquake experience database  Logarithmic standard deviation on capacity, βĈ, of 0.42  Lognormally distributed structural amplification factor with a 98% EP value of 1.0 and a 16% EP value of 1.67  Logarithmic standard deviation on database site demands of 0.30 Based on the data above, the HCLPF or median seismic capacity may be defined by the Extended Capacity Spectra shown in Figure 4-5 for equipment satisfying the criteria for the 1.2g ground Sa level of EPRI NP-6041-SLR1 [1] Table 2-4. These Extended Capacity Spectra are compared to the ISRS at the equipment support location. The HCLPF seismic capacity is 1.5 times the Extended Reference Spectrum and has a peak 5% damped spectral acceleration of 1.8g. The median seismic capacity is four times the Extended Reference Spectrum and has a peak 5% damped spectral acceleration of 4.8g. 4-11 13633436 Seismic Capacity Figure 4-5 Extended Capacity Spectrum Using this approach, Table 4-2 expresses the equipment seismic capacities in terms of local mounting point Sa (Cm and C1%), based on the ground Sa levels from EPRI NP-6041-SLR1 [1] Table 2-4 (SaSL = 0.8g, SaSL = 1.2g, and SaSL > 1.2g). 4-12 13633436 Seismic Capacity Table 4-2 Summary of equipment and subsystems seismic capacities (p. 1 of 3) 5% Damped Peak Mounting Point Sa C1% = 1.2g C1% = 1.8g C1% > 1.8g Cm = 3.2g Cm = 4.8g Cm > 4.8g NSSS Primary Coolant System (piping and vessels) no (a) no (a) yes NSSS Supports (b) (b) (c) yes Reactor Internals (y) yes yes Control rod drive housings and mechanisms (d) yes yes Category I piping (e) (e) yes Active valves no2 (f) yes Passive Valves no no (g) Heat Exchangers (h) (i) yes Atmospheric storage tanks yes yes yes Pressure vessels (h) (i) yes Buried tanks (j) (j) yes Batteries and racks (k) (k) yes Diesel generators (includes engine and skidmounted equipment (l) (l) yes Horizontal pumps no no yes Vertical pumps no (m) yes Fans (n) (o) yes Air handlers (n) (o) yes Chillers (n) (o) yes Air compressors (n) (o) yes HVAC ducting and dampers (e) (e) (p) yes Cable trays no (q) yes Electrical conduit no (r) yes Active electrical power distribution panels, cabinets, switchgear, motor control centers (s) (t) (s) (t) yes Equipment Type 4-13 13633436 Seismic Capacity Table 4-2 (continued) Summary of equipment and subsystems capacities (p. 2 of 3) 5% Damped Peak Mounting Point Sa Equipment Type C1% = 1.2g C1% = 1.8g C1% > 1.8g Cm = 3.2g Cm = 4.8g Cm > 4.8g (s) (s) yes Transformers (u) (v) (u) (v) yes Battery chargers (w) (w) yes Inverters (w) (w) yes Instrument and control panels and racks (s) (t) (s) (t) yes Temperature sensors No (x) yes Pressure and level sensors No 6 (x) yes Passive electrical power distribution panels, cabinets Notes: a. Boiling water reactor (BWR) piping with suspected intergranular stress corrosion cracking may require evaluation. b. Evaluation not required if supports are designed for combined loading determined by dynamic SSE and double ended guillotine break (DEGB) pipe break analysis. However, plant-specific evaluations are required for NPPs that have eliminated DEGB of the primary system and large branch line loss of coolant accident (LOCA) sources by leak before break analysis. This typically results in removal of most snubbers on the primary system lines and equipment, which may result in reduced seismic margin relative to the capacities provided here. c. Regardless of note (b), evaluation is recommended for pressurized water reactor (PWR) pressurizer supports and BWR reactor vessel and recirculation pump supports. d. Evaluation not required if control rod drive (CRD) housing has lateral seismic support. e. Walkdown of representative piping and ducting systems should be conducted following Section 6 guidance. f. Evaluation recommended for MOVs in piping lines of 2 in. diameter or less. g. Walkdown to ensure that valves do not impact adjacent structures or equipment. h. Margin evaluation only needs to consider anchorage and supports. i. For vessels designed by dynamic analysis or equivalent static analysis enveloping vessel inertial and piping loading, only the anchorage and supports require evaluation. For vessels not meeting these criteria, all potential failure modes require evaluation. j. Evaluation of piping connections is required. Other failure modes do not require evaluation. k. Batteries mounted in braced racks designed for seismic loads or evaluated by dynamic testing do not require evaluation. Rigid spacers between batteries and end restraints are required. Batteries should be tightly supported by side rails. l. Margin review should be conducted for anchorage and attachment of peripheral equipment. Can be done by visual inspection for a peak spectral acceleration of 0.8g or less. m. Margin evaluation required for vertical pumps with unsupported lengths of casing below the flange exceeding 20 ft or pumps with shafts unsupported at their lower end. Note that pressure and level sensor will not fail at spectral accelerations below 0.8g; however, systems engineers should be aware that these sensors may record a change in state due to the earthquake motion. 6 4-14 13633436 Seismic Capacity Table 4-2 (continued) Summary of equipment and subsystems capacities (p. 3 of 3) Notes: (continued) n. o. p. q. r. s. t. u. v. w. x. y. All units supported on vibration isolators require evaluation of anchorage. Evaluation should focus on anchorage and supports. Evaluation required only for potentially large relative displacements between structures or equipment and structures. See Section C.2.19, "Cable Trays and Cabling" for guidance. No evaluation required if supports generally meet the National Electrical Code. Walkdown should be conducted to verify that the instruments are properly attached to the cabinets. Relays, contactors, switches, and breakers must be evaluated for chatter and trip if functionality during strong shaking is required. Anchorage evaluation required. Liquid-filled transformers require evaluation of overpressure safety switches. The transformer coils should be restrained within the cabinet for dry transformers. Solid state units require anchorage checks. Others require evaluation. Insufficient data are available for screening guidelines. Emphasis should be on attachments. Insufficient data to enable recommendations to be made. As an alternative to Table 4-2, improved seismic capacities for eight equipment classes from EPRI 3002011627 [19] are provided in Table 4-3. The same criteria, caveats, and restrictions required to use the capacities in Table 4-2 also apply to Table 4-3, including the need to evaluate anchorage and interactions separately. Table 4-3 Improved seismic capacities based on earthquake experience for eight equipment classes Equipment Class Cm (g) βĈ C1% (g) Control Panels 6.37 0.40 2.53 Engines 5.42 0.41 2.08 Fans 6.54 0.39 2.62 Horizontal Pumps 6.59 0.39 2.65 Inverter and Battery Chargers 5.81 0.40 2.27 Motor Control Centers 6.28 0.40 2.48 Motor Operated-Valves 6.30 0.40 2.49 Medium Voltage Switchgear 5.62 0.41 2.18 4.2.2 Capacities for Structures Table 4-4 is available for simple assessment of the HCLPF capacity of structures based on experience. Appendix C describes the basis for the capacity of each type of structure listed in Table 4-4. This table provides a HCLPF (1% NEP, C1%) capacity expressed in terms of peak spectral acceleration at the ground surface. The fragility analyst must carefully review the load paths to be sure that structures that are evaluated in this manner comply with the caveats and assumptions in the notes of Table 4-4. 4-15 13633436 Seismic Capacity Table 4-4 is generally not used any longer to screen structure failure modes out from either an SOV or CDFM evaluation. It is only available for cases where there is an expedient need for an approximate HCLPF capacity of a structure. For potentially important structures, it is strongly recommended that SOV and CDFM evaluations be conducted via structural analysis of seismic capacities and demands. Table 4-4 Summary of civil structures representative HCLPF (C1%) capacities Type of Structure 5% Damped Peak Ground Sa C1% = 0.8g C1% = 1.2g C1% > 1.2g no (a) (b) Freestanding steel containment (c) (d) (c) (d) yes Containment internal structures (e) (f) yes Shear walls, footings, and containment shield walls (e) (f) yes Diaphragms (e) (g) yes Category I concrete frame structures (e) (f) yes Category I steel frame structures (e) (h) yes Masonry walls yes yes yes Control room ceilings (i) (i) yes Impact between structures no (j) yes Category II structures with safety-related equipment or with potential to fail Category I structures (k) yes yes Dams, levees, dikes yes yes yes Soil failure modes, soil-liquefaction and slope instability (l) (l) (l) Concrete containment (post-tensioned and reinforced) Notes: a. Major penetrations should be evaluated. b. Major and minor penetrations should be evaluated. The concrete containment structure only needs to be evaluated for a 5% damped peak spectral acceleration exceeding 2.0g. c. No evaluation required if base mat is integral part of pressure boundary or steel pressure boundary is keyed to base mat to prevent slipping. d. Mark I tori require evaluation for earthquakes exceeding the design basis. e. Evaluation not required for Category I structures if design was for a SSE of 0.1g or greater. f. Evaluation not required for Category I structures if design was by dynamic analysis for a SSE of 0.lg or greater, and if the structure complies with ACI 318-71 or ACI 349-76 or later editions ductile detailing requirements g. Evaluation not required for Category I structures if design was by dynamic analysis for a SSE of 0.1g or greater, and if the diaphragm complies with ACI 381-71 or ACI 349-76 or later editions ductility detailing requirements, provided the diaphragm seismic loads were explicitly calculated. h. Evaluation not required if structures were designed using dynamic analysis and meets the requirements of AISC, 7th Edition, 1970 or later. i. Inspect for adequacy of bracing or safety wiring. j. Investigation can be limited to potential for electrical malfunction (relay or contactor chatter) and loss of equipment anchorage in immediate vicinity of impact. k. Evaluation not required provided the structure can meet the 1985 UBC Zone 4 requirements. l. Refer to Appendix C to EPRI NP-6041-SLR1 [1] for guidance. 4-16 13633436 Seismic Capacity 4.2.3 Application of Capacity Tables in SPRA It is impractical to perform detailed fragility analysis for every SSC included in a plant systems analysis. Fragility estimates developed using Tables 4-2 and 4-4 are typically an efficient basis for developing representative fragilities. Fragilities based on Tables 4-2 and 4-4 are useful for identifying seismically rugged SSCs, which allows the fragility analyst to reduce the number of more detailed fragilities that must be calculated. Typically, a small number of SSCs dominate the seismic risk of a plant. An effective SPRA strategy, therefore, is to identify the dominant risk contributors and ensure that high quality, realistic fragilities are developed for them. The capacities in Tables 4-2 to 4-4 could result in conservative fragility estimates and, thus, could potentially not be realistic for the SPRA dominant risk contributors. When more specific information is available, it is recommended to perform more detailed fragilities using component-specific data for these dominant risk contributors. Some important considerations have sometimes been overlooked by fragility analysts when developing fragilities using similar methods: • Anchorage capacity must be evaluated and shown to meet or exceed the capacity from Table 4-2 and 4-3. • The SSC must meet all caveats listed in the notes for Table 4-2 or 4-4. • Structure capacities based on Table 4-4 should be supported by additional structural analysis. When the above conditions are not met, more detailed fragility analysis should be conducted for the SSC in question. Identifying the SSCs that meet the Table 4-2 and 4-4 caveats is an important objective of seismic walkdowns performed to support an SPRA, as discussed in Section 6.1. Walkdowns are also an opportunity to identify potential low-capacity anchorage configurations and to categorize similar anchorage configurations among different components. To reduce the number of anchorage calculations that must be performed, the fragility analyst may use generic calculations based on plant-specific design requirements or conservative bounding capacity estimates to ensure anchorage will not govern over the capacities provided in this section. Nuclear structures often have complex load paths and important failure modes can differ, even between similar structures at different plants. While the experience-based capacities in Table 4-2 are considered reasonable approximations of seismic capacity based on the available data, they should not be considered exhaustive or universally conservative for all nuclear structures, even those meeting the listed caveats. Using the experience-based structure capacities can be useful as a rough fragility estimate when expediency is required, but ultimately a structure fragility should be based on more detailed analysis, or the experience-based capacity should be justified by structural analysis taking the structure-specific configuration and characteristics into account. For fragilities based on Table 4-2 or 4-3 (Table 2-4 of EPRI NP-6041-SLR1 [1] or Bayesian updated capacities from EPRI 3002011627 [19], respectively), the median capacity factor is given by a variation of Equation 4-1 with FC = Cm / RRSC = Cm / (CC RRS), where Cm is the median capacity from Table 4-2 or 4-3, RRSC is the median demand as defined in Section 4.1.3 for test-based fragilities, CC is the clipping factor from Section 5.5.3, and RRS is the equipment mounting-point demand due to the reference earthquake.D D7KHFDSDFLWLHVLQ7DEOHVDQGDUHKRUL]RQWDODFFHOHUDWLRQVDQGVKRXOGEHFRPSDUHGWRKRUL]RQWDOGHPDQGVWR GHYHORSWKHFDSDFLW\IDFWRU9HUWLFDOGHPDQGVFDQJHQHUDOO\EHQHJOHFWHGZKHQFDOFXODWLQJHTXLSPHQWIUDJLOLWLHVXVLQJ HDUWKTXDNHH[SHULHQFHH[FHSW ZKHQDQDO\]LQJHTXLSPHQWNQRZQWREHVHQVLWLYHWRYHUWLFDOLQSXW IRUH[DPSOH EDWWHULHVZDOOPRXQWHG0&&V RU ZKHQWKHYHUWLFDOGHPDQGVDUHVLJQLILFDQWO\JUHDWHUWKDQKRUL]RQWDO 4-17 13633436 Seismic Capacity The clipping procedure in Section 5.5.3 will result in a clipped “plateau” region of the RRSC, where the Sa is constant and equal to the clipping factor CC times the peak Sa of the RRS, as shown in Figures 5-15 and 5-16. Outside the plateau region, the RRSC Sa remains identical to the RRS. The value of RRSC used above (in FC = Cm / RRSC) should be taken equal to the Sa of the clipped spectrum at the frequency of the equipment mode that dominates overall equipment response7. Using the Sa at the fundamental equipment frequency is justified because the failure modes represented by Tables 4-2 and 4-3 are governed by the overall equipment response (i.e., not by the response of some subcomponent). The capacities represent “function after” capability only; device chatter (“function during”) must be evaluated separately following the process outlined in Section 6.3. The capability of an equipment item to function after shaking would be compromised only by some permanent deformation or fracture, and therefore, function-after failure modes are caused by seismic-induced stresses. A stress-related failure could hypothetically occur anywhere in the load path of any subcomponent, or in the primary load path of the overall equipment item. For example, the failure could occur in the attachment of a capacitor to a circuit board, a circuit board to a panel, a panel to the cabinet, the cabinet to the structure, or in the primary load resisting members or connections of the cabinet frame. However, there are two sets of rationale for justifying the use of the fundamental frequency for purposes of defining the appropriate seismic response in these specific fragility calculations: 1. Shake table test experience and earthquake experience have demonstrated that the primary load path generally governs stress-related seismic failures. For example, shake table testing has shown that subcomponents can sustain the shake table limiting Sa of 15g (5% damping) for a wide variety of subcomponent mounting configurations (this type of testing is known as “structural integrity testing”). Additionally, the vast majority of function-after failures represented in the SQUG earthquake experience database resulted from inadequate anchorage. The few failures in subcomponent load paths would have been precluded by meeting the criteria and restrictions in Table 4-2, Appendix B, and SAND92 0140 [28] (e.g., requirements that subcomponents be securely attached and not mounted with excessive flexibility). 2. The underlying structural dynamics associated with these function-after failure modes also point to the fundamental mode of the host equipment. Internal subcomponents are generally relatively lightweight, and their individual load paths should therefore not be highly stressed. Supports for exceptionally massive internal components (such as transformer coils, large breakers, or fan motors inside air handling units) require explicit evaluation in Table 4-2, Appendix B, and SSRAP (SAND92 0140 [28]). Subcomponents with frequencies significantly lower than the overall equipment’s fundamental frequency will be excluded as excessively flexible and evaluated separately per these criteria. Seismic demands on higher It is possible that, under certain conditions, the overall equipment response may be governed by a second, third, or higher mode rather than the fundamental mode. This may occur, for example, if the ISRS have significantly greater Sa demands at frequencies above the equipment’s fundamental frequency, and if the higher mode’s mass participation is non-negligible. The fragility analyst should, therefore, review the equipment construction and the seismic input to assess the possibility that overall equipment response may be dominated by a higher mode, and define the seismic input accordingly. 7 4-18 13633436 Seismic Capacity frequency subcomponents will be filtered out by the dynamic response of the overall fundamental mode. Seismic demands on subcomponents with frequencies similar to the overall fundamental mode will be adequately represented by RRSC at the frequency of the equipment mode that dominates overall equipment response. Based on these two justifications, it is recommended that the function-after failure modes represented by Tables 4-2 and 4-3 be evaluated with the seismic demand defined as the Sa of the clipped spectrum at the equipment’s dominant frequency. 4.3 Material Strengths Analysis based capacities are calculated using strength equations and material properties. Strength properties are discussed in this section for concrete and steel, since these are the two most common materials analyzed in NPP SPRAs. Design calculations use high-confidence material strengths such that the design capacity is conservative. Design material strengths are usually specified at about the 95% confidence level. Code or design specified material strengths are generally appropriate for calculating CDFM capacities in the hybrid fragility approach. Material strengths used in the CDFM approach should be sufficiently conservative that there is very low probability that the actual strength is less than used in the analysis. When test data are available, approximately 95% EP strengths should be used to achieve this goal. For some common materials (such as structural steels), it is unlikely that 95% EP strengths from test data will exceed the design level strengths. To calculate median capacities for the SOV fragility approach, material strengths should be increased to median values. Logarithmic standard deviations in the median strengths should be propagated through the fragility evaluation to calculate the logarithmic standard deviation in seismic capacity due to uncertainty in material strength. Median material strengths should be based on plant-specific data, if available. When plant-specific data are not available, median material strength may be estimated from minimum specified strength using typical strength variabilities. 4.3.1 Concrete Material Strength Data from compressive testing of concrete cylinders cast during plant construction are sometimes available to the fragility analyst. These data may be used to determine the median compressive strength and variability at the time of testing (e.g., 28 days). Strength increase with aging should also be included. NUREG/CR-2320 [32] estimated a median concrete aging factor of 1.2 for concrete tested at 28 days. The factor was obtained from Figure 10.10 of Troxell, Davis, and Kelley [33] for specimens that were air-cured and dry at test (the aging curve for the air-cured and dry at test condition is shown here as Figure 4-6). Median aging factors for concrete tested at other ages and conditions may be similarly estimated from Troxell. Consistent with NEI 07-13 [34], the 1.2 aging factor is applicable to concrete members less than 3 ft thick. For members greater than 3 ft thick, a median aging factor of 1.4 is recommended per NEI [34]. In general, guidance is provided here for strength of normal, undegraded (e.g., by alkali-silica reaction) concrete in atmospheric conditions. Additional adjustments may need to be made based on plant-specific testing or condition-specific guidance to quantify the effects of degradation or other abnormal conditions. 4-19 13633436 Seismic Capacity Median in-situ concrete compressive strengths and variabilities may also be determined using data obtained by destructive testing of cores extracted from constructed structures, if available. These data should be corrected for any deviations of the actual core sizes from standard 6 in. diameter by 12 in. high cylinders and potential damage introduced by core extraction following Bartlett and MacGregor [35]. Figure 4-6 Concrete compressive strength increase with time; air-cured, dry at test condition Strength increases due to aging should be conservatively accounted for in CDFM capacity calculations. When available, 28-day or 60-day concrete cylinder test data should be consulted. In cases where these test data show a COV of 0.10 or less, considering typical increases in strength with age over the first several years and material strength variability, it is considered that the median strength after several years is 1.2 times the average 28-day test strength f’c28 with a logarithmic standard deviation of 0.14, or 1.1 times the average 60-day test strength f'c60 with a logarithmic standard deviation of 0.12 (ASCE Working Group [36]). This is consistent with the 1.2 aging factor on 28-day strength for members less than 3 ft thick from NEI 07-13 [34]. For thicker members, the 28-day factor can be increased to 1.4 per NEI [34], and the 60-day factor can be estimated as 1.1/1.2*1.4 = 1.3. Assuming the strength increase due to aging is lognormally distributed, the CDFM strength f’cCDFM with 95% EP can be calculated as follows: COV ≤ 0.10 for Cylinder Tests f f f f where f 1.2 ∗ f 1.1 ∗ f 1.4 ∗ f 1.3 ∗ f and f ∗e . ∗ . ∗e . ∗ . ∗e ∗e . . ∗ . ∗ . 0.95 ∗ f < 3ft thick 1.11 ∗ f > 3 ft thick 0.90 ∗ f 1.07 ∗ f Eq. 4-6 are the average test strengths at 28 and 60 days, respectively. 4-20 13633436 Seismic Capacity As an example, a 2 ft thick concrete member might have a minimum specified 28-day strength of 3,000 psi, and an average test strength of 3,870 psi with a coefficient of variation of 0.095. For this mix, the CDFM strength can be taken as 0.95 * 3,870 = 3,680 psi, which is a significant improvement over the minimum specified 28-day strength. Where the 28-day or 60-day concrete cylinder test data show a COV of 0.14, the strength after several years can be expected to have increased to logarithmic standard deviations of about 0.17 and 0.16 for the 28- and 60-day cylinder test data, respectively (ASCE Working Group [36]). Thus: COV = 0.14 for Cylinder Tests f f f f 1.2 ∗ f 1.1 ∗ f ∗e . ∗ . ∗e . ∗ . ∗e 1.4 ∗ f 1.3 ∗ f ∗e . . ∗ . ∗ . 0.90 ∗ f < 3ft thick 1.06 ∗ f > 3 ft thick 0.85 ∗ f 1.00 ∗ f Eq. 4-7 If plant-specific test data are unavailable, a median concrete compressive strength equal to 1.5 times the minimum specified strength at 28 days and logarithmic standard deviation of 0.17 are recommended for members less than 3 ft thick. The 0.17 logarithmic standard deviation is estimated as the SRSS of a 0.14 COV for cylinder tests and corresponding 0.10 logarithmic standard deviation for the aging factor consistent with Equation 4-7. For thicker members, the median factor may be increased to 1.5*1.4/1.2 = 1.75. These median factors include the increase in strength due to aging, as well as a median estimate of 1.25 for the cylinder test uncertainty, which assumes the minimum-specified strength is at about the 99% EP and a COV of 0.10 on cylinder test per Equation 4-7 (1.25 = exp[2.33*0.10]). In the unlikely event that concrete tensile strengths are required for a fragility evaluation, values in Table 4-5 may be used based on Mirza, Hatzinikolas, and MacGregor [37]. Table 4-5 Concrete tensile strength Stress Median Strength (psi) Logarithmic Standard Deviation Direct Tension 6 .4 f ' c 0.13 Flexural Tension 8 .3 f ' c 0.20 Concrete structures may show strength degradation over time when subjected to ponded water, salt, or high radiation levels. Such degradation is most likely in intake structures, cooling ponds, or reactor support structures. Degradation is usually accompanied by concrete spalling, excessive concrete cracking, or rust stains on the concrete surface. When such conditions are observed, the strength of concrete structures should be reduced below the strength computed using the previously defined material strengths. Such reductions must be developed on a case-by-case basis considering site-specific conditions and should be applied in both SOV and hybrid fragility analyses. 4-21 13633436 Seismic Capacity 4.3.2 Steel Material Strength Plant-specific test data should be used, if available, to directly determine steel material strengths. When plant-specific data are unavailable, a median yield strength and logarithmic standard deviation for A36 steel of 44 ksi and 0.12, respectively, may be used based on data reported by Galambos and Ravindra [38]. A ratio of median to minimum specified yield strengths of 1.1 may be estimated for higher strength steels based on data reported by Galambos and Ravindra [38]. The minimum specified value is considered to have about 95% EP, which results in a logarithmic standard deviation of 0.06. Table 4-6 provides median material strengths and variabilities for common materials. The 0.9 reduction factor for the ultimate tension capacity of A-307 anchor bolts accounts for the increase in stress at the root of the thread and the possibility that the bolt is loaded eccentrically in tension. These effects are already built into the capacities for A-325 and A-490 bolts in the data in Kulak, et al. [39]. The minimum (nominal) specified strengths in Table 4-6 are suitable for use in CDFM calculations for hybrid fragilities. For other structural steels, the minimum yield and ultimate tensile strengths specified in AISC Codes [40, 41] or ASME codes [42] should be used. Even with a small dynamic increase factor (approximately 10% increase), it is unlikely that the 95% exceedance material strength for seismic loads based upon plant specific mill test data will significantly exceed these AISC Code strengths. Table 4-6 Material strengths for common materials Material Strength (ksi) Yield (y) A-36 steel References Ultimate (u) Nominal Median U Nominal Median U 36 44 0.12 58 64 0.06 Galambos and Ravindra [38], NUREG/CR-5270 [43] A-307 36 60 66 0.06 NUREG/CR-5270 [43] A-325 bolt 120 142 0.05 Kulak, et al. [39] A-490 bolt 150 165 0.04 Kulak, et al. [39] Weld *FEXX 1.1FEXX 0.05 Section 4.7.1.2 84 0.07 NUREG/CR-5270 [43] Type 304 Stainless Steel SA240 44 37 0.12 0.13 * FEXX = Minimum code nominal tensile strength for weld material The representative median concrete reinforcement yield strengths and logarithmic standard deviations listed in Table 4-7 may be used if plant-specific data are not available. The median yield strengths are based on review of test data reported by Mirza and MacGregor [45]. The minimum specified values are considered to have 95% EP. 4-22 13633436 Seismic Capacity Table 4-7 Concrete reinforcement yield strength Reinforcement Grade Median Yield Strength (ksi) Logarithmic Standard Deviation Grade 40 48 0.11 Grade 60 66 0.06 For CDFM capacity calculations, 40 ksi and 60 ksi yield strengths should generally be used for Grade 40 and Grade 60 bars, respectively. However, if plant specific mill test data shows a mean capacity at least 15% greater than these minimum strength values and shows a COV less than 0.08, then increased strengths can be justified. For conservatism, no dynamic increase should be included when justifying increased CDFM material strengths for rebar. Strength increases are likely to range from 0% (mean/minimum = 1.15, and COV = 0.08) to 15% for (mean/minimum = 1.25, and COV = 0.04). 4.4 Structure Failure Modes and Capacities When a structure is evaluated by analysis, the evaluation must be plant-specific since structures are generally different from plant to plant. Some examples of the types of structures that are analyzed in SPRAs include:  Reinforced concrete shear walls and diaphragms  Conventionally-reinforced and prestressed containments  Steel frame structures with moment-resistant and/or braced frames  Masonry walls  Field-erected flat-bottom steel storage tanks  Buried structures (e.g., fuel storage tank) Example fragility analyses for a shear wall and flat-bottom tank are given in Appendices O and S, respectively. The examples include fragility calculations following both SOV and hybrid fragility approaches. For the seismic evaluation of buildings and other structures, the analyst needs to perform the following tasks:  Review structure to identify the seismic load path(s)  Identify potential seismic failure modes and order these modes by their relative weakness  Determine capacity of individual failure modes  Evaluate consequences of failure modes The last task requires close coordination with the systems engineers responsible for developing the plant logic model (i.e., event and fault trees). The capacity of structures is important only to the extent they affect systems necessary to prevent or mitigate core damage and radiological release. Hence, structure failure is typically defined by structural damage states that cause failure 4-23 13633436 Seismic Capacity of equipment functions modeled in the SPRA. Also, structure failure may correspond to loss of containment. Structure failure does not necessarily mean building collapse. There have been various structural failure modes that have been found to be important, including shear wall failure, impact between buildings, roof/floor slab failures, and foundation failures. All relevant failure modes of a structure should be identified, and fragilities should be developed for critical failure modes. Depending upon the design documentation available, the structural analyst may extrapolate an ultimate or elastic limit state capacity from the design analysis. In other cases, the analyst may need to conduct a new linear analysis or conduct some degree of non-linear analysis. Usually, this task is achieved using results of linear analysis to determine the demand level at the ultimate capacity for concrete or elastic limit state for steel structures. The key issue in determining the capacity is to focus on the global instability, rather than the local instability of a single element (unless the local instability can affect the function of nearby equipment). In typical design calculations, the focus is on element capacity. To this extent, the design calculations must often be extended to determine the redundant load paths to the point of global instability. This is often done by using simplified non-linear models to approximate an inelastic energy absorption factor, Fμ. On occasion, a more detailed non-linear dynamic analysis may be necessary to determine the redundant load paths and inelastic deformation in a critical structure. In the case of concrete shear walls, the failure mode is often defined in terms of the inter-story deflection (also called drift). The use of a drift limit represents a conservative surrogate for building collapse since the drifts are on the order of only 1% of the story height. In addition, the drift limit is also a surrogate for equipment failure. If SEL equipment is mounted directly on the critical shear walls, then the drift limit may have to be reduced to protect the equipment anchorage. For some situations, a structure may not contain any equipment credited in the SPRA. For this case, there must be a catastrophic failure causing the structure to fall onto an adjacent SEL structure or outside equipment; collapse would have a higher capacity than the failure mode based on a drift limit. Although structure failure is often defined based on a drift limit, drift limits are typically larger than elastic displacements most structures will experience. It may be necessary to evaluate the elastic capacities associated with several different structure failure modes to calculate the governing elastic strength factor, FS. Additional seismic demand beyond the elastic capacity results in nonlinear deformations, eventually exceeding the drift limit and resulting in failure. This additional capacity is accounted for by the inelastic energy absorption factor, which is discussed for structures in Section 4.5. The following sections present strength equations for important structure elements found in nuclear structures. The strength equations are appropriate for calculating elastic capacities for various failure modes and should be used with Equation 4-2 to calculate elastic strength factors, FS. Strength equations are presented for calculating both median and CDFM strength factors. Generally, median capacities of concrete and steel structural components may be based on strength design provisions of ACI 349-13 [46] and ANSI/AISC N690-12 [40], respectively, with median strength reduction factors of 1.0 and median material strengths. The former 4-24 13633436 Seismic Capacity frequently references provisions of ACI 318-08 [47]8 and the latter frequently references provisions of ANSI/AISC 360-10 [41]. CDFM strength capacities may generally be based on the above referenced strength design provisions with the recommended strength reduction factors and design (minimum specified) or 95% EP material strength properties. In some cases, such as for shear strength of low rise concrete shear walls, strength design provisions can be excessively conservative, and for these cases alternative strength equations are recommended for determining both median and CDFM strength factors. 4.4.1 Concrete Shear Wall Strength Equations In-plane strength of shear walls is a predominant mode of resistance in NPP concrete structures. These walls are usually under-reinforced and highly ductile. In an SPRA, it can be assumed that parallel shear walls all attain their ultimate capacities before the story failure mode is reached with the following constraints:  Static equilibrium is maintained.  The floor diaphragms and any collector members have sufficient strength to redistribute the in-plane forces as each shear wall successively reaches its capacity and becomes nonlinear. As discussed previously, the failure mode for structures generally is not catastrophic collapse but rather is defined to be significant inter-story drift (i.e., displacement) which would affect equipment attached to the structure. Limits on inter-story drift are discussed in Section 4.5 in the development of the inelastic energy absorption factor. In determining the strength of a shear wall, the following three failure modes must be investigated:  Diagonal shear cracking  Flexure  Shear friction  Out-of-plane shear In determining the strength of a shear wall, the lowest capacity from these four modes is defined as the strength of the wall. Both shear cracking and flexure failure modes are ductile while shear friction is generally considered to be brittle. If a wall contains openings, then the lowest capacity from these three failure modes is assigned to each pier. Then the wall strength is just the sum of the pier strengths. Note again that static equilibrium must be maintained, which often induces normal forces in the piers, which in turn affect the shear and moment capacities of the piers. An example of this consideration is provided in the sample shear wall fragility calculation in Appendix O. ACI 349-13 [46] is the current code for design of nuclear safety-related concrete structures, and it references provisions of ACI 318-08 [47] extensively. ACI 318-08 [47] provisions are cited in this report as a convenience when they are the same as or applicable to ACI 349-13 [46]. 8 4-25 13633436 Seismic Capacity 4.4.1.1 Diagonal Shear Cracking Diagonal shear cracking strength equations for walls with boundary elements differ from rectangular walls. Boundary elements are regions near the ends of the wall that contain concentrated vertical reinforcement. Intersecting walls at the ends of a shear wall also serve as boundary elements. A rectangular wall has no such intersecting walls or additional reinforcement at its ends. Diagonal shear cracking is a ductile failure mode, and therefore an inelastic energy absorption factor should be developed for shear wall fragilities governed by diagonal shear failure. For multistory walls, the shear capacity should be checked for each individual story; the effective wall height, hw, should be determined as M/V at the base of each story evaluated, where M is the overturning moment and V is the shear. Multiple levels need to be checked when the steel percentage varies up the wall height. When checking the overall shear wall, the area of horizontal reinforcement within intermediate floor slabs within a distance of four times the slab thickness from the wall may be included as part of the horizontal reinforcement of the wall. Shear Walls with Boundary Elements The diagonal shear strength of low-rise shear walls with boundary elements can be based on either the Barda equation [48] as given in ASCE/SEI 43-05 [14], or the equation from Gulec and Whittaker [49]. The Barda equation is applicable to walls with aspect ratios (ratio of effective wall height to length, hw / lw) less than two, and the Gulec and Whittaker equation is applicable for aspect ratios less than one. Experience has shown that the two formulations typically have good agreement for low-rise walls with boundary elements. For low-rise walls with boundary elements (hw / lw ≤ 1.0) that are dominant risk contributors, it is recommended that the capacities from the Barda and Gulec/Whittaker approaches be averaged together to obtain a best estimate. For the SOV fragility approach, the median and 98% NEP capacities from the two approaches can be averaged together, and then the capacity variability may be computed from the median and 98% NEP capacities. Comparison of results from the Barda and Gulec/Whittaker methods are presented in the example shear wall evaluation in Appendix R. ASCE 43-05 / Barda Strength Based on the work by Barda [48], the median strength of low-rise shear walls with boundary elements, Vum, can be represented by the following equations for the diagonal shear cracking failure mode: V ∗d ∗t Eq. 4-8 where: v v v v Eq. 4-9 v 8.3 ∗ f 3.4 ∗ f 4-26 13633436 ∗ h l 0.5 N 4∗l ∗t Eq. 4-10 Seismic Capacity v ρ ∗f 600psi ρ A ∗ρ v = median ultimate shear strength (psi) v = median strength contribution from concrete (psi) v = median strength contribution from steel reinforcement (psi) f = median concrete compressive strength h = height of wall (in.) l = length of wall (in.) t = thickness of wall (in.) N = axial force in wall (lb) f = median steel yield strength (psi) A1, A2 = constants, defined in Equation 4-15 ρ = effective steel reinforcement ratio ρ = vertical steel reinforcement ratio ρ = horizontal steel reinforcement ratio d = distance from extreme compression fiber to center of force of all reinforcement in tension and: A ∗ρ Eq. 4-11 Eq. 4-12 Because of limitations on the data from which Equation 4-8 was derived, se fym should not be taken greater than 600 psi. In Equation 4-8, the term dm is the median distance from the extreme compression fiber to the center of the force from all reinforcement in tension. This term can be determined from a strain compatibility analysis and static equilibrium of the tension and compression forces as is done in a flexure analysis. If such an analysis is not performed, then a reasonable approximation is to assume: d 0.6 ∗ l Eq. 4-13 The contribution of the concrete capacity to the ultimate shear strength of a wall as a function of hw / lw is shown in Figure 4-7 (Figure C4-1 from ASCE/SEI 43-05 [14], with permission from ASCE). Also shown in Figure 4-7 are the test results [48, 50 to 55], and the corresponding ACI 349 concrete strength requirement. The test data included load reversals and varying reinforcement ratios and hw / lw ratios. Ultimately, web crushing generally controlled the failure of the test specimens. Testing was performed with no axial loads, but an increase in shear capacity of [Na / (4 lw tn)] was recommended. When calculating median shear wall capacities, 4-27 13633436 Seismic Capacity Na should be the total axial force in the wall due to normal operating conditions and median seismic demand scaled consistent with the median elastic strength factor. The contribution of the horizontal and vertical reinforcement was determined from test values for the range of 0.5 < hw / lw < 2. Figure 4-7 shows the strength of concrete shear walls calculated by the methods in Section 11.9 of ACI 349-13 [46]. The part of the test data capacities due to reinforcing steel has been removed so that only the concrete capacity is reflected in the data points. When the ACI-349 methods are used, dm is effectively equal to lw as the gross area of the concrete shear wall is used to evaluate the concrete shear force based on Chapter 21 of ACI-349. Therefore, the ACI code curve has been increased in the figure by a factor of 1.67 to make it comparable to the Barda Equation. This corresponds to the case when the default value of dm equal to 0.6 lw is used with the Barda Equation, and effectively lw is equal to dm in the ACI approach. The tests included load reversals and varying reinforcement ratios and hw / lw ratios. Comparing the Barda Equation to 1.67 times the ACI code equation, it is seen that the ACI code severely underestimates the capacity of concrete at low aspect ratios. Figure 4-7 Strength of concrete shear walls 4-28 13633436 Seismic Capacity Based on an evaluation of shear wall test data from many sources, the logarithmic standard deviation for uncertainty of Equation 4-8 was found to be 0.20 (Benjamin and Reed [53]). The minus-one standard deviation concrete capacity contribution can be calculated as follows: v where: ϕ ∗v ϕ therefore, e e v 6.8 ∗ f . 0.8 2.8 ∗ f Eq. 4-14 ∗ h l 0.8 ∗ N 4∗l ∗t 0.5 By substituting Equation 4-14 in place of Equation 4-10 for the concrete contribution to capacity, the fragility analyst can compute the logarithmic standard deviation in seismic capacity for uncertainty in the shear strength equation. The corresponding minus-one standard deviation plot for the concrete strength (not including the axial force term) is also shown in Figure 4-4 (labelled “0.8 x Barda Equation”). CDFM shear wall capacities can be calculated with Equation 4-8 using CDFM values of material strength properties (Section 4.3), rather than the median values indicated in the equation, and by using Equation 4-14 for the strength contribution of concrete. When calculating CDFM shear wall capacities, Na in Equation 4-14 should be the total axial force in the wall due to normal operating conditions plus the 84% NEP axial seismic demand scaled consistent with the CDFM elastic strength factor. These same test data comprise the basis for determining the values of the terms A1 and A2 in Equation 4-12. Based on the results of the evaluation by Benjamin and Reed [53], the terms A1 and A2 are approximated as: For For h l 0.5 For 1.5 0.5 h l h l A 1.5 1 A A 0 h l A 1.5 A A 0 h l 0.5 Eq. 4-15 1 A plot of these equations as a function of hw / lw is shown in Figure 4-8. As seen in this figure, the contribution of the reinforcement is entirely due to the vertical steel for hw / lw values less than 0.5, entirely due to the horizontal steel for hw / lw values greater than 1.5 and a linear interpolation for hw / lw values in between 0.5 and 1.5. 4-29 13633436 Seismic Capacity Figure 4-8 Reinforcement capacity coefficients, A1 and A2 Gulec and Whittaker Strength The following adaptation of “Model Vm1f” developed by Gulec and Whittaker [49] can be used for determining the median peak shear strength of low-rise shear walls with boundary elements. This reference is an update to an MCEER report on this subject [56]. Note that this equation is applicable to low rise shear walls that have a height to length ratio less than one: V f 2.9 ∗ f ∗A 0.43 ∗ F h l 0.11 ∗ F 0.35 ∗ N Eq. 4-16 = Median concrete compressive strength hw = Wall height lw = Wall length beff = Effective flange width equal to the lesser of one-half the wall height minus the web thickness or eight times the flange thickness. Aeff = Wall effective shear area; sum of the area of the web plus the effective flanges area, where the area of an effective flange is the product of the flange thickness and the effective flange width. Fvw = Force carried by vertical reinforcement in the web; product of the area of the vertical reinforcement in the web and the reinforcement yield stress Fbe = Force carried by vertical reinforcement in the boundary element; product of the total area of vertical reinforcement in the boundary element at each end of the wall and the reinforcement yield stress Na = Axial force in wall 4-30 13633436 Seismic Capacity The equation above modifies the equation for Model Vm1f by rounding off the constants and excluding the negative constant assigned to the force carried by the horizontal web reinforcement, which has relatively small contribution to wall strength. Model Vm1f is recommended here, whereas Model Vm1e is preferred by Gulec and Whittaker [49]. The former model expresses the peak shear strength as a function of the square root of the concrete compressive strength, which has traditionally been used to define shear and tensile strengths of concrete. Model Vm1e expresses the peak shear strength as a direct function of the concrete compressive strength. Differences between coefficients of variation for ratios of predicted to measured strengths for Models Vm1e and Vm1f are not significant. Although the authors of the present report have chosen to recommend Model Vm1f here, Model Vm1e is also equally applicable and may be used if preferred by the fragility analyst. From the definition of Aeff, it is observed that dm is effectively equal to lw when Equation 4-16 is used to evaluate the concrete shear force since it includes the entire area of the web. The concrete area used is a major difference in the application of Equations 4-8 and 4-16. Based on an evaluation of shear wall test data from many sources, the logarithmic standard deviation for uncertainty in Equation 4-16 was found to be 0.13 [49]. For CDFM evaluations using the Gulec and Whittaker approach, the HCLPF capacity should be calculated using CDFM material strengths as discussed in Section 4.3. Equation 4-16 should be scaled by a CDFM strength reduction factor ϕCDFM = e-βu = e-0.13 = 0.88 to obtain the 84% EP strength equation. Rectangular Shear Walls Median diagonal shear strengths of rectangular shear walls (i.e., without boundary elements) and walls with aspect ratios greater than 1.0 should be determined following Section 21.9.4.1 of ACI 318-08 [47] with median material strengths and a strength reduction factor of 1.0. CDFM capacities for such walls may be estimated following the code strength equations with the code-specified strength reduction factors and CDFM material strengths as described in Section 4.3. Median strengths and corresponding variabilities for low rise (aspect ratios less than 1.0) rectangular walls may be estimated using the strength equations recommended in MCEER 09-0010 [56]. 4.4.1.2 Flexural Capacity The formulation for the in-plane flexural capacity (flexure about an axis normal to the plane of the wall) follows the basic ultimate strength design provisions for reinforced concrete members subjected to flexure and axial loads as contained in Section 10 of ACI 318-08 [47]. 4-31 13633436 Seismic Capacity An approximate approach for obtaining the flexure capacity of rectangular walls can be developed using Figure 4-9 where it is assumed that all reinforcement has yielded from the tension face to a point equal to twice the distance, am, from the compression face (Benjamin and Reed [53]). For the case of a wall with uniformly distributed reinforcement the median length, am, is calculated as follows: N l ∗t ∗ρ ∗f 0.85 ∗ f ∗ t 2∗t ∗ρ ∗f a Eq. 4-17 where the terms are the same as defined in Section 4.4.1.1. For this case, the median ultimate moment capacity, Mcap,m is: M A , ∗f ∗ d a 2 N ∗ l 2 a 2 Eq. 4-18 where the median steel reinforcing area is calculated as follows: A d l 2 ρ ∗t ∗ l a 2∗a Figure 4-9 Flexural capacity properties 4-32 13633436 Eq. 4-19 Eq. 4-20 Seismic Capacity A similar and equally valid procedure provided in Kennedy, et al. (Report No. 1643.1 [57]) for a wall with uniform reinforcement gives the median ultimate capacity, Mcap,m, as follows: M where: A a , A ∗f N ∗ l 2 ρ ∗l ∗t ∗f A 0.85 ∗ f N ∗t a 2 Eq. 4-21 Eq. 4-22 Eq. 4-23 Equations 4-18 and 4-21 give essentially the same results. Concentrated reinforcement such as embedded steel columns, if present, can be easily included in either of the two formulations given above using basic principles. Once the moment capacity is obtained for a wall section, the equivalent shear capacity can be obtained by dividing the moment capacity by the distance to the inflection point for piers with reverse curvature, or by a distance equal to the moment-to-shear (M / V) ratio obtained from the seismic demand when no reverse curvature is present in the wall section. A strength reduction factor of 0.9 can be applied to Equations 4-18 or 4-21 to obtain strength equations with approximately 84% NEP. These minus-one standard deviation strength equations can be used to calculate the logarithmic standard deviation in seismic capacity for uncertainty in the flexural strength equation. The CDFM flexural capacity of concrete shear walls may be calculated by applying the strength reduction factor of 0.9 and using CDFM material strengths (Section 4.2) in place of the median values indicated in Equations 4-18 and 4-21. 4.4.1.3 Shear Friction Capacity The CDFM shear-friction strength of shear walls may be determined following Section 11.6.4 of ACI 318-08 [47]. The same methods can be followed to calculate median shear friction capacities by using median material properties (including friction coefficient) and a strength reduction factor of 1.0. The alternative formulation noted in Section R11.6.3 of ACI 318-08 [47] may also be used if reinforcement sufficient to develop a normal stress of 200 psi is available. While previous guidance in EPRI TR-103959 [2] permitted shear-friction failure to be disregarded if the diagonal shear capacity exceeds , this approach is no longer considered to be appropriate. 4.4.1.4 Out-of-Plane Shear Capacity One-way, out-of-plane shear strength of reinforced concrete beams, walls, and slabs can be calculated following provisions for shear strength in Chapter 11 of ACI 349-13 [46]. Median shear strengths can be calculated using strength reduction factors of 1.0 with the code provisions. In general, the code provisions with the recommended design strength reduction factors calculate shear strengths with approximately 98% EP and are therefore appropriate for calculating CDFM capacities. 4-33 13633436 Seismic Capacity Research has suggested that the shear strength provisions in ACI 349-13 [46] may calculate shear strength with less than 98% EP for deep members (thicknesses greater than about 15 in.) without shear reinforcement. This affects the strength of reinforced concrete members such as shear walls, which commonly have little or no reinforcement for out of plane shear forces. Research on this subject is ongoing, and the most recent developments should be consulted if out-of-plane shear wall failure is an important failure mode. 4.4.2 Tangential Shear Strength of Cylindrical Concrete Walls The typical governing failure mode considered for cylindrical concrete walls such as containment shells, shield walls, and concrete tanks is tangential shear failure. Flexural failure should be checked, but infrequently governs the seismic capacity of these structures. Test data show substantial ductility for the tangential shear failure mode such that inelastic energy absorption, Fµ, determined for shear walls according to Section 4.5 is easily justified. The tangential shear strength of cylindrical reinforced and prestressed concrete walls can be determined based on an effective shear area, Aeff, which should be defined by: A A ⁄α Eq. 4-24 where Ag is the gross cross section area of the cylindrical wall and  is given by: α α 2.0 2.5 for M V∗d M for V∗d 0.5 Eq. 4-25 1.25 where do is the outside diameter of the cylindrical wall, and M and V are the moment and shear at the most critical location on the wall. Linear interpolation can be used to determine α between these limits. The tangential shear strength of a cylindrical wall may decrease if it is subjected to internal pressure. A considerable amount of testing has been conducted in Japan on scale models of reinforced and prestressed concrete containment structures subjected to internal pressure and lateral cyclic loading. The strength equation developed from these tests (Section 4.4.2.1) includes very little contribution from concrete strength. This may be due to cracking of the test specimens due to internal pressure imposed prior to lateral loading. Pressurized and unpressurized cylindrical walls should be evaluated differently, as outlined in the following sections. 4-34 13633436 Seismic Capacity 4.4.2.1 Pressurized Cylindrical Concrete Walls The tangential shear strength of cylindrical concrete walls that have undergone significant pressurization can be estimated based on scale model tests by Ogaki, et al. [58] and Aoyagi, et al. [59]. The guidance in this section is applicable to walls that have been pressurized (e.g., via pressure testing) such that they have undergone significant cracking resulting in total loss of concrete contribution to shear strength. The median shear capacity for this condition, which is only rarely encountered, can be determined as follows: Vum = vum * Aeff v 0.8 f ρf 21.1 f Eq. 4-26 where both vum and f’cm are in psi units, and (fym)AVER represents the average of the effective reinforcing steel ratios times the reinforcing yield stress in the hoop and meridional directions. The average effective steel ratio is defined by: ρf ρ 2 ρ f σ 2 σ Eq. 4-27 where hp and m are the hoop and meridional reinforcement ratios, respectively; fym is the median yield stress capacity of the reinforcing steel; and h and m are the containment wall hoop and meridional (tension positive) stresses, respectively, resulting from dead load, internal pressure, and seismic. In computing m, the meridional stress from the seismic overturning moment is not included because 1. the average meridional stress around the circumference due to this effect is zero. 2. the overturning moment effect is already included in the test results from which Equations 4-24 through 4-27 are derived. Thermal stresses are not included because they are secondary stresses and do not influence the seismic capacity of a pressurized cylindrical concrete wall. To calculate a median tangential shear capacity for the SOV fragility approach, median material strengths (f’cm and fym) should be used. Strength variability can be calculated by applying a strength reduction factor of ϕ = 0.85 to the median strength equation. The ϕ = 0.85 factor determines a shear capacity with 84% EP, as shown in Figure 4-10, which is reproduced from Ogaki, et al. [58] (with permission and with minor modifications such as variable names and colors). Therefore, the logarithmic standard deviation for uncertainty in the tangential shear strength equation is βU = ln(1/0.85) = 0.16. A CDFM tangential shear strength can be calculated by applying a strength reduction factor of ϕ = 0.85 to Equation 4-26 and using CDFM material strengths (Section 4.2) to calculate vu, rather than median material strengths. Appendix P shows an example CDFM capacity calculation for tangential shear strength of a pressurized cylindrical wall. 4-35 13633436 Seismic Capacity Figure 4-10 Comparison of Japanese scale model test data to predictive formulations 4.4.2.2 Unpressurized Cylindrical Concrete Walls In most cases, cylindrical walls that have not been subjected to significant pressurization (e.g., a crane wall inside a containment internal structure) should be calculated by the strength equations for low-rise shear walls with boundary elements (Equations 4-8 and 4-16). For these equations, the effective wall length of the cylindrical wall, leff, is given by: l A 2t Eq. 4-28 where tn is the cylindrical wall thickness. For higher aspect ratio cylindrical walls, the ACI 318-08 [47] shear wall capacity equations can be used, as is recommended for higher aspect ratio shear walls in Section 4.4.1.1. For cylindrical walls with particularly high steel reinforcement ratios, Equation 4-26 for pressurized cylindrical walls may predict a shear capacity exceeding the ACI 318-08 [47] upper limit. In this case, Equation 4-26 may be used to estimate the shear strength of an unpressurized cylindrical wall. 4-36 13633436 Seismic Capacity 4.4.3 Masonry Walls Masonry wall fragility evaluations should consider both in-plane and out-of-plane failure modes. For in-plane loads, median capacity evaluations can typically be performed using the current design code (e.g., ACI 530/531.1-13 [60]) with median material properties and a strength reduction factor of 1.0. CDFM evaluations can be performed using the same code equations using CDFM material strengths (Section 4.3) and an approximately 84% EP reduction factor on the strength equation. However, since masonry walls in nuclear plants are nearly always non-load bearing, use of such design criteria for out-of-plane response can be unnecessarily conservative. If the stability of the wall can be demonstrated together with retention of adequate anchorage for essential attached piping, conduit, or equipment, then through-wall cracking and large deformations are acceptable for masonry walls in an SPRA (i.e., as long as cracking and deformations do not affect functions modeled in the SPRA). The capacities associated with the stability limit state may be developed by either analysis or a test program for walls with representative geometries and locations within the plant. If analysis is used to develop a fragility for out-of-plane stability, either energy techniques or nonlinear time-history methods are acceptable. For nonlinear time-history analyses, it is recommended that the seismic response of the walls be obtained from the structure response time histories from several actual earthquake records rather than from the response to an artificial time-history record. Loss of stability is indicated from a time-history analysis when the displacement of one or more of the wall segments increases without bound. Normally, this occurs when the displacement of the center of gravity of the segment exceeds about one-half the block width. In addition to stability, verification of the ability of the wall segments to transmit the calculated out-of-plane shear forces, either by friction or dowel action of any imbedded steel reinforcing must be included for walls evaluated by analysis. Provided fully grouted joints exist at the relatively stiff boundaries, "arching" or "bridging" action may also be used in the analysis. Arching may exist either between the floor and ceiling (vertical arching), or between adjacent stiff vertical supports (horizontal arching), or both. An example CDFM evaluation for lightly reinforced non-load bearing masonry block walls is provided in Appendix Q. The procedures in Appendix Q may be adapted to calculate median capacities for the SOV approach by reducing implicit conservatisms. 4.5 Structure Inelastic Energy Absorption It is recognized that the inherent seismic resistance of a well-designed and constructed structure is usually much greater than that expected based on elastic analysis. This occurs largely because nonlinear behavior is mobilized to limit the imposed forces and increase the accompanying deformations. Nonlinear time-history analysis is one approach that can account for the reserve capacity of a structure past elastic strength limits. However, nonlinear time-history analysis involves many complicating considerations beyond the requirements of elastic analysis. Lengthy runtimes and convergence issues with numerical solutions can result in significant allocation of resources to troubleshooting, refinement, and verification of analysis results. Furthermore, care must be taken to establish appropriate failure criteria because equipment in the structure can be adversely affected at nonlinear deformations less than those corresponding to structural collapse. 4-37 13633436 Seismic Capacity An alternate means of accounting for the inelastic energy dissipation of civil structures and equipment at response levels above yield is the use of an inelastic energy absorption factor, Fμ. This approach allows the analyst to perform more simplified linear elastic analyses, and then estimate inelastic energy absorption capability independent of the response analysis. The inelastic energy absorption factor accounts for the additional ground motion input beyond the elastic limit state required to achieve nonlinear displacements that can negatively affect equipment within the structure. 4.5.1 Ductile Failure Modes The inelastic energy absorption factor should only be applied to ductile failure modes. Many failure modes of steel and reinforced concrete structures have some degree of ductility that can be credited in a fragility evaluation. Exceptions include the following9:  pullout or breakout of cast-in-place anchorage  bond failure of reinforcing steel due to inadequate development length  buckling failure modes  shear friction failure of concrete walls  concrete failure in under-reinforced sections  most failure modes of bolted and welded steel connections ACI 318-08 [47] and ANSI/AISC 360-10 [41] typically indicate whether a failure mode is ductile or non-ductile. Most structures have both ductile and non-ductile failure modes. Non-ductile failure modes must be checked when the elastic capacity of a structure is governed by a ductile failure mode, to preclude the possibility of premature brittle failure prior to achieving the increased post-yield strength of the ductile failure mode. As a rule of thumb, it is recommended that the brittle failure mode (Fμ = 1.0) govern unless its HCLPF exceeds the yield strength of the lowest-capacity ductile failure mode by at least 125%. The additional 25% margin accounts for the variability in the yield and brittle capacities. As an example, assume some component has a non-ductile failure mode capacity of 110 kips and a ductile failure mode yield capacity of 100 kips with a computed Fμ of 1.35. For this component, the HCLPF is 110 kips and not 100 kips times 1.35. On the other hand, if the non-ductile capacity had been 130 kips, the HCLPF would be 135 kips. The rule of thumb may not be applicable in many instances, including:  If the two failure modes have significantly different variabilities  If there is significant strain hardening  If the ductile and non-ductile failure modes are governed by two different load paths such that yielding in the ductile failure mode does not limit the marginal increases in load for the non-ductile failure mode While the listed failure modes are traditionally considered non-ductile, some can exhibit appreciable ductility under high-frequency loading. Section 6.4.2 provides guidance for evaluating high-frequency inelastic behavior. 9 4-38 13633436 Seismic Capacity Ultimately, the fragility analyst must consider both ductile and non-ductile failure modes, understand how they interact with each other, and justify the selection of the governing failure mode. In many cases, it may be necessary to develop fragilities for both failure modes if their capacities are similar and it is not straightforward to justify that one governs. Ductile failure modes affected by significant non-seismic load acting in the same direction as the seismic load can be subjected to the effects of ratcheting. Such components include basement walls subject to out-of-plane static earth pressures and floor slabs subjected to gravity loads. The effects of ratcheting on the inelastic energy absorption factor should be included in the fragility evaluation. Eggers and Baig [61] provide an approach that could be used to account for such ratcheting effects. 4.5.2 Inelastic Deformation Limits The maximum inelastic drift in a building story should reflect distortions corresponding to the beginning of strength degradation of the controlling structural element. These distortions would impact equipment in the structure but are unlikely to cause immediate catastrophic collapse. Defining the ultimate limit state as onset of severe strength degradation is expected to provide substantial margin against building collapse. ASCE/SEI 43-05 [14] defines Limit State C as the seismic response of a structure associated with the onset of limited permanent distortion. It is judged that Limit State C response corresponds to deformations that could potentially affect the operability of equipment within a structure. Limit State C is therefore recommended for fragility analysis of critical Seismic Category I structures unless another basis can be justified. Tables 4-8 and 4-9 (developed from Tables 5-2 and 5-3 of ASCE/SEI 43-05 [14] with permission from ASCE) provide Limit State C drift and rotation limits. The 95% EP drift and hinge rotation limits are given in ASCE 43-05 [14], and the median values are estimated to be 1.75 times greater, consistent with Table 4.3 of NUREG/CR-6104 [62]. The drift limits listed in Table 4-8 are the ratio of story displacement to story height (δs / hw). The rotation limits listed in Table 4-9 are given in radians. Table 4-8 Allowable drift limits for Limit State C 95% EP Median 0.010 0.018 6∗ f 0.004 0.007 0.005 0.009 Shear controlled walls, hw / lw  2.0 0.004 0.007 Steel SMRF 0.010 0.018 Steel braced frames (concentric and eccentric): 0.005 0.009 Reinforced concrete special moment resisting frames Reinforced concrete shear wall, in plane: Bending controlled walls, hw / lw  2.0 v v 3∗ f 4-39 13633436 Seismic Capacity Table 4-9 Allowable hinge rotation limits for Limit State C per ASCE/SEI 43-05 [14] 95% EP Median Beams 0.005 0.0088 Columns 0.000 0.000 SMRF reinforced concrete moment frames: SMRF steel moment frames: Beams and columns Pa < 0.2 Pay 0.004 0.007 Columns Pa < 0.5 Pay 0.004 0.007 Columns Pa > 0.5 Pay 0.000 0.000 Roof slabs, floor slabs, beams and walls of reinforced concrete 0.005 0.0088 Slab/wall moment frames: For Tables 4-8 and 4-9: hw = Height of the entire shear wall or segment of the shear wall considered lw = Length of shear wall or segment of shear wall considered in direction of shear force vave = Average shear stress, which is equal to shear divided by the shear area = Concrete compressive strength ℓ = Span length h = Beam depth f Pa = Beam or column axial load Pay = Beam or column elastic axial capacity For fragility analysis by the SOV approach, the median drift limits should be used to evaluate inelastic energy absorption. A composite logarithmic standard deviation of βC = 0.34 for the Limit State C drift limits is conservatively estimated in NUREG/CR-6104 [62]. This composite variability can be broken down into logarithmic standard deviations for randomness and uncertainty of βR = 0.15 and βU = 0.30, respectively. To calculate a CDFM inelastic energy absorption factor, the 95% EP deformation limits should be used. The drift limit for low rise shear walls is based on data from NUREG/CR-6104 [62], which provides statistics on cyclic strength degradation from cyclic tests of 184 low-rise shear walls. The amount of cyclic strength degradation that is likely to occur for a low-rise shear wall is primarily a function of the shear drift to story height ratio, s / hw. It should be noted that s is only the story displacement due to shear. Displacement due to base rotation of the wall and flexural displacements are not included. Also, the s / hw ratio represents the average shear strain over the height hw. Table 4-10 is based on Table 4.3 of NUREG/CR-6104 [62]. 4-40 13633436 Seismic Capacity Table 4-10 Drift limits for low rise shear walls subjected to cyclic loading Fraction of Ultimate Load Retained (%) Median s/hw (%) 100 0.70 90 C ASCE 43-05 Limit State 0.40 0.34 C 1.00 0.50 0.42 - 80 1.25 0.60 0.45 B 70 1.50 0.70 0.46 - 60 1.65 0.70 0.52 - 50 1.80 0.70 0.57 - 95% EP s/hw (%) The median and 95% EP drift limits at 100% load retention are the same as those presented in Table 4-8 for reinforced concrete shear-controlled shear walls. ASCE/SEI 43-05 drift limit for Limit State B is provided for reference. This limit state corresponds to moderate permanent distortion (generally repairable damage). This level of distortion is excessive for safety-related NPP structures that support important equipment or serve as a pressure boundary (containment). Figure 4-11 illustrates shear wall behavior under cyclic loading. It is observed that loading peaks initially increase in load (a, b, c) up to the ultimate strength value, followed by a decrease at larger deformation (d, e). One hundred percent load is retained at deformation c, and at increased deformation, there is cyclic strength degradation at lower values of retained ultimate load. Table 4-10 demonstrates that there is negligible cyclic shear strength degradation when drifts are limited to the 100% retention row in Table 4-10 and the allowable drift limits in Table 4-8. Gulec, Whittaker, and Stojadinovic [63] indicate that the shear strength of low-rise shear walls subjected to cyclic loading exhibits reductions from the peak strength. The strength reduction appears to be more significant for walls with lower aspect ratios. It is demonstrated in above that cyclic degradation does not occur at the drift limits imposed for nuclear safety-related structures. Notwithstanding the deformation limit guidance above, fragility evaluations often involve evaluation of unique conditions and require the analyst to estimate case-specific deformation limits. Additional guidance may be obtained from ASCE/SEI 41-13 [64], in which nonlinear drifts and plastic hinge rotations tend to be reasonable approximations of mean values. 4-41 13633436 Seismic Capacity Figure 4-11 Cyclic shear wall test initial and subsequent loading peaks 4.5.3 System Ductility An estimate of the system ductility ratio (μ) is required to calculate the inelastic energy absorption factor for a structure. The system ductility ratio can be approximated as follows: μ where: ∑Wδ ∑Wδ Eq. 4-29 Wi = Weight of each story, i δTi = Deflection of each story, i, at ultimate capacity corresponding to reaching the nonlinear drift limit at one or more stories δei = Elastic deflection of each story, i, at yield For a single story, Equation 4-29 simplifies down to a story ductility (μs) of: μ where: δ δ Eq. 4-30 δT = Maximum permissible story deflection δy = Elastic story deflection at yield 4-42 13633436 Seismic Capacity For multi-story structures, the system ductility (Equation 4-29) is always less than the story ductility (Equation 4-30), except when the nonlinear distortions are spread equally throughout the structure, which is very unlikely for practical structures. The following equation can be used to estimate the system ductility from the ductility of the governing story: μ 1 F ∗ μ 1 Eq. 4-31 where Fk is a knockdown factor, which will typically range from 0.5 to 0.75 for well-designed structures in which the elastic strength factors for failure at different stories do not vary by more than a factor of about 1.3. For such structures, Equation 4-31 can be used in CDFM analyses with a conservatively estimated Fk of 0.5. Alternatively, a more accurate estimate of system ductility can be obtained by assuming an approximate nonlinear displaced shape for the structure. A slightly conservative estimate of the inelastic deformed shape is obtained by assuming that all the nonlinear inter-story drift is concentrated at the story with the lowest elastic strength factor. For this approximation of the deformed shape, the ultimate story displacements δTi in Equation 4-29 can be calculated as follows for a structure reaching the nonlinear drift limit, δT, at story n: δ δ δ δ for i < n Eq. 4-32 δ for i ≥ n For fragility evaluation by the SOV approach, the maximum permissible nonlinear story deflection (δTi, δT) should be determined based on the median drift and rotation limits in Tables 4-8 and 4-9. To calculate a CDFM system ductility, the 95% EP drift and rotation limits should be used. 4.5.4 Approximate Method of Calculating Inelastic Energy Absorption An approximate method of calculating the inelastic energy absorption factor, known as the Effective Frequency/Effective Damping method, is presented in Section 4.5.4.1. The method is well suited for modeling hysteretic energy dissipation for structural elements such as concrete shear walls that exhibit pinched hysteresis loops. It can be used to calculate the inelastic energy absorption factor for both SOV and hybrid fragility approaches. To calculate a median estimate of Fμ, the method should be followed using a median estimate of system ductility, whereas a CDFM value for Fμ can be calculated by using a system ductility with 95% EP. Section 4.5.4.2 discusses the calculation of logarithmic standard deviations for SOV fragilities. Median inelastic energy absorption factors for structural components with complete hysteresis loops may be determined by methods proposed by Sozen or Iwan as summarized in Section 3.3.1 of NUREG/CR-3805 [26], or in Riddell and Newmark [65]. 4-43 13633436 Seismic Capacity 4.5.4.1 Effective Frequency/Effective Damping Method The Effective Frequency/Effective Damping method based on NUREG/CR-3805 [26]. This method directly accounts for the shape of the input response spectrum along with the shifting of dynamic frequency and increase in effective damping associated with nonlinear structure response. The Effective Frequency / Effective Damping method is recommended for evaluating concrete shear wall failures because it can be adapted to account for the effect of pinched hysteresis loops that are characteristic of this failure mode. Figure 4-12 shows an idealized force deflection diagram for a concrete shear wall. The force Vc corresponds to the capacity of the concrete and Vu corresponds to the capacity of both the concrete and steel. δy is the deflection at yield. Figure 4-12 Idealized force deflection diagram for concrete shear walls The first step is to calculate the ratio of the secant frequency to the elastic frequency, fs/f, which is given by the following equation where the stiffness values K and Ks are defined in Figure 4-12. The frequency ratio depends on the system ductility, μ, discussed in Section 4.5.3. f f K K K K 1 where: Eq. 4-33 s∗ μ μ 1 4-44 13633436 Eq. 4-34 Seismic Capacity In Equation 4-34, the coefficient s defines the ratio f the elastic stiffness to the post-yield stiffness as shown in Figure 4-12. Next, the ratio of the effective frequency to the elastic frequency, fe/f, is calculated where fe is a weighted average of the secant and elastic frequencies. f f 1 A C ∗ 1 where: A A ∗ f f f f 0.85 Eq. 4-35 Eq. 4-36 For strong ground motions with durations greater than one second, CF may be approximated as 2.3. The corresponding effective damping ξe, is obtained by the following equation: f ξ f where: ξ f f = ξ ξ Eq. 4-37 elastic damping for shear wall structure ξh = pinched hysteretic damping, which for strong motion durations longer than one second can be approximated by: = 0.11 ∗ 1 f ⁄f Once fe and ξe are found, then the spectral accelerations Sa(fe, ξe) and Sa(f, ξ) are obtained from the ground input to the building from which the inelastic energy absorption factor, Fµ, is calculated by: F f f f f Sa f, ξ Sa f , ξ Eq. 4-38 The guidance here assumes three strong motion cycles per NUREG/CR-3805 [26]. For situations where a different number of strong motion cycles may be more appropriate, additional guidance can be obtained from NUREG/CR-3805 [26]. 4.5.4.2 Logarithmic Standard Deviations For the SOV approach, logarithmic standard deviations in the seismic capacity should be calculated to account for randomness and uncertainty in the inelastic energy absorption factor. In addition to the effects of randomness and uncertainty in the shear wall drift as given by the logarithmic standard deviations in Table 4-10, it is recommended that an additional R value 4-45 13633436 Seismic Capacity be included to reflect the random scatter of the time-history computed Fµ values versus the predicted values by the Effective Frequency/Effective Damping method. On this basis, the following equation for the additional µ,R is recommended (Report No. 1643.1 [57]): βµ, 0.4 ∗ 0.06 0.03 ∗ F 1 Eq. 4-39 where Fµm is the median inelastic energy absorption factor. In addition, a µ,U value for the uncertainty in the inelastic energy absorption model should be included. µ,U can be estimated by first calculating a composite variability µ,C and then subtracting out µ,R by SRSS. µ,C can be estimated as follows: βµ, F 1 ln Z F Eq. 4-40 where FµZ is the inelastic energy absorption factor with a known EP and corresponding standard normal variable Z. For example, 95% EP inelastic energy absorption factors can be estimated as described in Section 4.5.5. Alternatively, 95% EP inelastic energy absorption factors can be calculated using the Effective Frequency / Effective Damping method following the CDFM criteria in Section 3.4.1. If a 95% EP Fµ is used, then Z = 1.65 in Equation 4-40 in accordance with Table 3-2. 4.5.5 Conservative Representative Inelastic Energy Absorption Factors For structures where an approximate and potentially conservative fragility is sufficient, the analyst may choose to assign a representative inelastic energy absorption factor in lieu of the more rigorous and structure-specific methods outlined above. Representative inelastic energy absorption factors are provided in Table 4-11 (developed from Table 5-1 of ASCE/SEI 43-05 [14], with permission from ASCE). In accordance with ASCE/SEI 43-05, Limit State C corresponds to seismic response with limited permanent distortion. It is judged that Limit State C corresponds to deformations that could potentially affect the operability of equipment within the structure. Per Section 3.4.1, the inelastic energy absorption factor should be defined at 95% EP for a CDFM evaluation. The 95% EP inelastic energy absorption factors in Table 4-11 are obtained from ASCE/SEI 43-05. Corresponding median values are calculated based on Equation 4-41, which is derived by observing that the inelastic energy absorption factor may not be less than 1.0, such that variability is only considered in the inelastic portion of the total capacity (i.e., the portion of Fμ greater than 1.0). The corresponding variability is estimated to be βC = 0.3. These values are generally appropriate for fixed-base structures and are often unconservative for structures with significant soil-structure interaction (SSI) effects. F 1 F , 1 ∗e . 4-46 13633436 ∗ . Eq. 4-41 Seismic Capacity Table 4-11 Inelastic energy absorption factors, Fµ, for Limit State C 95% EP, Fµ,CDFM Median, Fµm Beams 2.5 3.5 Columns* 1.5 1.8 Bending controlled walls, hw/lw  2.0 1.75 2.2 Shear controlled walls, hw/lw  2.0 1.5 1.8 SMRF reinforced concrete moment frames Reinforced concrete shear wall, in plane: SMRF steel moment frames (bending only): Beams and columns* Pa < 0.2 Pay 2.5 3.5 Columns* Pa = 0.3 Pay to 0.5 Pay 1.25 1.4 Columns* Pa > 0.5 Pay 1.0 1.0 Special concentric (bracing members) 2.0 2.6 Ordinary concentric (bracing members) 1.5 1.8 Eccentric; Short link beam, 1.6 Zp/(0.6Aw)  e 2.0 2.6 Eccentric; Long link beam, e  2.6 Zp/(0.6Aw) 2.5 3.5 Chevron bracing 1.5 2.0 2.0 2.6 Steel braced frames: Roof slabs, floor slabs, beams, and walls of reinforced concrete slab/wall moment frames Notes: *Fµ for compression and shear in columns should be unity Aw = Web area of a link beam e = Eccentricity measured along the link beam hw = Height of the entire shear wall or segment of the shear wall considered Pa = Nominal axial load Pay = Axial yield strength Zp = Link beam plastic section modulus ℓ = Span length h = Beam depth lw = Length of shear wall or segment of shear wall considered in direction of shear force The values of inelastic energy absorption in Table 4-11 are conservative for structural systems with nonlinear deformations distributed throughout the structure. The Table 4-11 values may be unconservative for structures that have weak or soft stories and must be reduced for these structures. Table 4-11 values should also be reduced for structures with predominant structural response at a frequency greater than the amplified acceleration region of the input response spectrum. The reductions for soft/weak story and high-frequency response can be computed 4-47 13633436 Seismic Capacity in accordance with Section 5.1.2.1 of ASCE/SEI 43-05 [14]. Reductions calculated following these provisions result in approximately 95% EP values. The 95% EP inelastic energy absorption factors can be increased by Equation 4-41 to estimate conservatively biased median inelastic energy absorption factors. 4.6 Equipment Failure Modes and Capacities 4.6.1 Passive Equipment Typical passive components include:  Reactor pressure vessel  Steam generator (PWR)  Reactor coolant pump (PWR) and recirculation pump (BWR)10  Pressurizer (PWR)  Major vessels (e.g., core flood tank and boron injection tank)  Major heat exchangers  Primary coolant system loop (PWR)  Main steam line inside containment  Other critical vessels, heat exchangers, and distribution systems Seismic capacities for many of these components can be conservatively estimated based on Tables 4-2 and 4-3. If further refinement is necessary (e.g., for dominant risk contributors), additional data may often be obtained from design calculations or seismic qualification reports. Review of the data is often sufficient to judge that the component seismic capacity is governed by failure of supports or anchorage, and it is rarely necessary to use design or qualification data to develop a rigorous capacity for stress related failure modes of passive equipment. Nonetheless, it is important to exercise sound engineering judgement when determining the governing failure mode. All failure modes should be considered unless past analysis or walkdown observations indicate that seismic capacity is obviously governed by supports or anchorage. Support systems for passive components can have a wide variety of configurations. Support system capacities should be calculated following the analytical approach presented in Section 4.1.2. Failure modes of steel support configurations bear many similarities to those of steel structures, and elastic strength factors can generally be calculated following strength provisions of ANSI/AISC N690-12 [40] and ANSI/AISC 360-10 [41]. Median strength factors can be calculated by using median strength reduction factors of 1.0 and median material strength properties in the above referenced design provisions. CDFM strength factors can be developed based on the recommended design strength reduction factors and design (minimum specified) or 95% EP material strengths per Section 3.4.1. For SSC supports designed to ASME code Technically, these pumps are active but trip on a scram signal, so they are not credited as functioning after the earthquake and, therefore, only the pressure boundary and supports are typically evaluated. 10 4-48 13633436 Seismic Capacity requirements, the CDFM capacity would typically be the allowable design stress for Level D Service (support may undergo gross deformations and require repair or replacement but continues to perform its function credited in the SPRA). The median capacities can then be estimated from the code safety factor and using median material properties. Anchorage of passive components can likewise vary. Fragility analysis of anchorage should follow the procedures summarized in Section 4.7. An example fragility analysis for a heat exchanger is given in Appendix T, in which support and anchorage failure modes are evaluated. Another important failure mode for some passive components may be failure of attached distribution systems such as piping or ducting. Attached lines must be capable of accommodating expected seismic displacements of the SSC. In some cases, it may be possible to judge the attached lines sufficiently flexible or the displacements sufficiently small based on walkdown observations. In other cases, more detailed analysis may be necessary. Strength criteria for piping are discussed in Section 4.6.3.1. It is anticipated that most of the component pressure boundaries designed under the ASME Code will meet the requirements for the seismic capacities in Tables 4-2 and 4-3. However, if pressure boundary failure modes of specific components are selected for detailed fragility analysis, the guidance of the current ASME Code [42] for Level D Service can be applied to establish the CDFM strength. The code factors of safety and median material properties can then be used to estimate the median capacity. The minimum ASME code factor of safety is based on not exceeding 0.7 of the specified ultimate tensile strength. Consistent with Section 4.3.2, the median ultimate strength is approximately 1.1 times the specified value; a conservative estimate of ultimate strength factor is, therefore: FScode = 1.1 / 0.7 = 1.57 times the code capacity Eq. 4-42 For cases where the failure mode is ductile, the capacity factor should also include an Fµ factor as described in Section 4.1.2. Methods for estimating Fµ for equipment are outlined in Section 4.8. For instability failure modes, Appendix F of the ASME code limits the load to two-thirds of the calculated buckling capacity. The CDFM instability capacity is taken as the code capacity. As an approximation, the median buckling strength can be estimated as the reciprocal of two-thirds (1.5) if the instability is elastic. This approximation is likely conservative in many cases but is judged reasonable as a first check lacking more detailed case-specific considerations. For plastic buckling, the ratio of the median material yield strength to the code specified yield strength can also be factored into the median buckling strength. Allowable Level D stresses for ASME Class 1, 2, and 3 components are provided in the ASME Code [42]. Other special stress limits and criteria for limit analysis and plastic analysis are contained in Subsections NB, NC, ND, and Appendix F to the ASME B&PV Code [42]. The allowable stresses for Class 1 components are generally higher than for Class 2 and 3 components. The code design philosophy sets this difference on the basis that Class 1 components have more stringent material specifications and fabrication specifications. For loading dominated by seismic events, there should be essentially no difference in the load 4-49 13633436 Seismic Capacity carrying capability of identical components, regardless of their code class. Therefore, for purposes of fragility analysis, the higher Class 1 allowable stresses are permissible if the material is one for which Class 1 allowable stresses are given in the code. 4.6.2 Active Equipment Active equipment includes electrical and control components, pumps, electric motors, engine generators, and valves. Except for large components, the basis for the capacity of many of these items is qualification testing. It is generally impractical in design to perform analyses of many of these components to qualify them for a seismic environment. In the cases of electrical and control components, electric motors, engine generators, and pumps, the anchorage must be considered in addition to functional aspects. Fragility analysis of equipment anchorage is discussed in Section 4.7. Plant-specific qualification test data may be available that can be used in a fragility analysis. Often, the difficultly with this data is that the tests were performed at a level that qualified the equipment to the design basis requirements but did not challenge the failure level. Hence, when fragility curves are developed using qualification data, it is likely that the results will be conservatively biased. Section 4.9 provides guidance for developing equipment capacities from qualification test data. Some early SPRAs used the U.S. Army Corp of Engineers shock test data to develop generic fragility curves for different types of components (NUREG/CR-2405 [66]). The use of these data has received some criticism since the duration of loading is relatively short (about 2.5 sec) compared to seismic input, but the shock level defined by a response spectrum was very high (> 20g). However, this difference in time duration has been reflected in some fragility analyses. The important conclusion of the Corps of Engineers shock testing was that electrical and control components would not survive the high levels of shock and had to be shock-isolated, whereas mechanical components and piping would generally survive the high shock levels as long as the anchorage was robust. An EPRI project for the resolution of NRC USI A-46 developed GERS for various classes of equipment [20, 21]. Section 4.9 provides guidance for developing equipment capacities from GERS. While qualification of electrical components has almost exclusively been done by shake table testing, active mechanical components may have been qualified by analysis. Vertical pumps, for example, have frequently been qualified based on finite element models. Similarly, some active valves have been analyzed to ensure that deformation in the elastic range would not result in binding. Active equipment may be sensitive to plastic deformations or even elastic deformations. If the functional seismic capacity of active equipment cannot be developed from Table 4-2, from earthquake experience methods (Section 4.2.1), or by reference to tests (Section 4.9), then analytical evaluation may be required for the RE. If such an evaluation is undertaken, the limits must be established on a case-by-case basis. As a general guideline, stresses should be limited to the yield stress for membrane loading and to yield times the plastic section shape factor for primary bending. These limits might be applicable to such items as valve yokes that support the operator, or to pump flanges and casings. In some instances, where small clearances are maintained in rotating machinery, there may be displacement or inertia load limits imposed by the vendor. These limits could be exceeded for short term dynamic loading while the component was responding elastically to seismic input. An example might be a large diameter fan with 4-50 13633436 Seismic Capacity a small tolerance between the fan blades and shroud. Rubbing of the blade on the shroud may not constitute a total functional failure, but the limit of seismic demand at a functional failure level is difficult to estimate and justify. Analysis-based qualification reports for pumps and fans sometimes identify excessive displacements of rotating shafts as important failure modes with low capacity. The displacement capacities noted for these failure modes are often very small because they are based on allowable steady-state displacement tolerances. Long-term displacements at the vendor limit level may damage the component, but it is unlikely that seismic displacements exceeding the steady state tolerances will have significant consequences. A review of earthquake experience data (EPRI NP-7498 [30]) has not uncovered any deflection problems with pump assemblies even though the computed displacements between pump impellers and wear rings frequently govern in analysis-based pump qualification. The fragility analyst must use judgment in such cases to determine if the alleged restrictions are truly functional problems or are merely arbitrary design restraints for continued long term operation. Real deformation problems are rare. One exception may be shafts of long vertical pumps that are unsupported along their length. Yielding of the pump column could result in binding of the shaft in its bearings. A potential source of conservatism that is not accounted for in the test-based fragility approach presented in this report concerns the definition of chatter functionality when chatter is the governing failure mode. Standardized relay tests typically use a 2 ms chatter duration (ANSI/IEEE C37.98-1987 [67]) as the definition of failure. In some situations, failure does not occur until a significantly longer chatter time (e.g., 20 ms) occurs. For other components, 3 ms to 4 ms chatter can cause a change of state in a downstream controlled component. The capacity due to chatter is very sensitive to the details of the input time history and the circuitry in which the relay is placed and is difficult to quantify without a significant amount of test data. It is possible that for some components there is a conservative bias if 2 ms is used as the basis for the fragility tests; however, it is difficult to develop a factor of conservatism, and any attempt to generate one would require considerable test effort. 4.6.3 Distribution Systems 4.6.3.1 Piping Piping systems credited in SPRAs are typically seismically robust and are unlikely to be dominant risk contributors. Often, seismic capacities can be developed using Table 4-2 and/or by explicitly estimating and quantifying the conservatism in the design criteria (e.g., the ASME code, material strength, design response analysis). As such, detailed analysis is often unnecessary. However, detailed evaluations may be required if potential vulnerabilities are identified during seismic walkdowns. The known potential vulnerabilities for piping are identified in Table 4-2 and Appendices B and C. They are based largely on earthquake experience and test data, which demonstrate that piping generally does not fail by collapse mechanisms due to seismic inertial loading. Known failures during earthquakes have resulted from either excess anchor displacements that cannot be accommodated by the piping, excessive corrosion of the piping, or use of brittle connections (threaded joints or mechanical couplings). Such cases should be included in the scope of fragility evaluation. 4-51 13633436 Seismic Capacity For critical ASME Class 1 piping that can result in a LOCA, it is sometimes necessary to conduct a fragility evaluation for seismic inertia effects. A piping research program jointly conducted by EPRI and NRC research over several years eventually led to an understanding of the large margin of safety in piping systems subjected to seismic loads. The final documentation and conclusions of the test program (NUREG/CR-5361 [68]) led to changes in the ASME code for piping that were eventually approved by the NRC Code of Federal Regulations in 2007. The change in the ASME code essentially reduced the stress indices applicable to elbows and tees based on test results. The code changes were cast into a probabilistic treatment in a technical paper by Kennedy (PVP 2002-R53 [69]). The approach quantifies conservatism and uncertainty in the piping limit moment, the inelastic deformation beyond the limit moment, and redundancy. The inelastic deformation beyond the limit moment depends on the ratio of the dominant excitation frequency and the dominant piping frequency. Low-frequency input is shown to be significantly more damaging than higher frequency. The methods in the Kennedy paper can be used to demonstrate high capacity of piping for inertial loading. The evaluation of piping for excess anchor displacements can be conducted using simplified elastic-plastic analysis methods. Such methods are presented in EPRI NP-6809 [70]. Loading should consider the effects of dead weight, seismic inertial loading, and anchor displacements. A pseudo-static loading using a factored spectral acceleration loading is proposed in EPRI NP-6809 [70]. The inelastic behavior of the piping is modeled with plastic hinges approximated from piping fitting static and dynamic load tests. The modes of failure of concern are excessive strains or gross buckling. For heavy wall piping, the bounding strains may be compared to the low cycle fatigue curves in the ASME B&PV Code [42]. The calculated strain from the pseudo-static analysis, multiplied by the elastic modulus, E, can be compared to the alternating stress range, Sa, from Figure 1-9 of the Mandatory Appendices to the ASME B&PV Code [42]. Thinner walled piping used in low pressure, high flow systems should be checked for buckling. The applied strain or deformation should not exceed the calculated buckling strain or deformation using conservative (84% EP per Table 3-10) buckling strength equations for CDFM analysis. SOV analyses should use median centered material strengths and buckling equations. The consequence of large displacements may also require examination, principally to ensure that valve operators do not impact hard surfaces or that small stiff branch lines will not be fractured. In some isolated circumstances, the possibility of failure of multiple dead weight pipe supports may be present. For instance, if a long run of large diameter pipe with no lateral support is supported vertically by short threaded rods, several of the rods could fail in low cycle fatigue, causing the unsupported pipe to fail from lack of dead weight support. Low cycle fatigue of threaded rods can be evaluated by the methodology in EPRI NP-7152-D [71] that addresses seismic capacity of threaded rod supports of electrical raceways. The consequences of support failure may be addressed by the simplified inelastic analysis methods developed in NP-6809 [70], or by other suitable means of performing limit or plastic instability analysis. In the example cited, the simplified inelastic analysis reverts to essentially a limit analysis of a continuous beam under dead weight loading. 4-52 13633436 Seismic Capacity Brittle connections in piping systems should be analyzed by ASME B&PV Code [42] methods. Additional data to support evaluations may be obtained from SQURTS shake table testing of mechanical couplings (Farwell & Hendricks [72]). Modern plants do not have brittle connections in safety grade piping. In some older plants, threaded piping has been observed in limited portions of some safety-related systems or appears as flooding issues in fire protection piping. For these cases, a CDFM evaluation may be based on an earlier version of the ASME Code for Class 3 piping that uses stress intensification factors rather than stress indices. Median capacity can be estimated from limited test data on threaded piping or by using generic βC values in Table 3-11 and the hybrid approach. The governing equation is: Pd 4t 0.75i Pp = Operating pressure, psi do = Outside diameter of pipe, in. tnp = Nominal pipe wall thickness, in. MA = Resultant moment on cross section due to weight and other sustained loads, in.-lb MB = Resultant moment loading on cross section due to earthquake inertial loads and steam relief valve (SRV) loads, if applicable, in.-lb S = Section modulus of pipe, in3 (ND-3652) is = Stress intensification factor (Figure ND-3673.2(b)1) Sh = Basic material allowable stress at operating temperature, psi where: M S M 3S Eq. 4-43 Special attention should be directed to components that are constructed with cast iron, which could include piping, valve yokes, or pump casings. If this type of material is found, a conservative analysis assuming brittle behavior should be conducted. The strength of a brittle material should be selected at the 99% EP value. For cast gray iron, a CDFM strength value of 5 ksi tensile stress can be used unless a basis exists for using a higher value. In evaluating brittle components, the effects of SRV induced accelerations for BWRs should be combined with the RE accelerations by SRSS. If pipe support load or nozzle loading is a governing condition in piping reevaluation, the guidance of the ASME B&PV Code should be applied. Alternatively, the AISC code may be used for pipe supports. Pipe supports are not of particular concern unless a support failure can result in excessive nozzle loading on active equipment, excess displacements at valve operators, or failure of multiple supports (unzipping effect). The consequences of support failure may be assessed subjectively without conducting complex analyses or, on the other hand, it may be prudent to demonstrate the integrity of the supports in lieu of assessing the consequences of failure. 4-53 13633436 Seismic Capacity 4.6.3.2 Electrical Raceways Meaningful analytical models of raceways are difficult without test data to determine the equivalent beam properties. Raceways are typically constructed of two channels connected by cross members that form a ladder like structure, or the channels may be connected by perforated metal sheets. If the raceway is oriented horizontally, the section properties about the horizontal axis can be calculated from the properties of the two side channels. The section properties about the vertical axis must either be determined by experiment or by use of a detailed finite element model of the raceway structure. The torsional properties of the raceway are virtually impossible to calculate and should be determined by experiment. Torsional properties are only important in an analytical model if curved tray members are not supported at the curve. If the curved portions are supported, the determination of torsional properties is not of great concern. Analytical models using only the torsional properties of the side rails will vastly under-predict the stiffness and frequency and over-predict the sagging of unsupported curved members. Strengths of raceways have often been determined by static testing of a defined span length in bending and by axial stability testing. Strength of horizontal raceways subjected to vertical load is governed by the side channel strength and may readily be treated analytically. Strength determination of the raceways in lateral or axial loading usually requires testing to define the instability load capacity. Some utilities have sponsored these tests and the stiffness properties and capacities are available (e.g., Linderman and Hadjian [73]). If the test data exist to define strength in each of three loading directions, then an interaction equation may be used to evaluate the acceptability of a particular electrical raceway. Table 4-12 summarizes candidate acceptance criteria, which have been applied to NPP design. In most practical cases, the governing loading will be the moment in the vertical or horizontal plane. The moment capacities in Table 4-12 are based on two-thirds of the test collapse load and are applicable to developing a CDFM capacity. Median capacity can be estimated by using the generic βC values from Table 3-11. Table 4-12 Loading combination and acceptance criteria for electrical raceway Acceptance Criteriaa,b Loading Combination Dw+KµERE M M M M M M E Y ⁄ 1 Notes: a. MUV and MUT are derived from ultimate load tests and are based on two-thirds of the minimum collapse moment. b. YL is two-thirds of the ultimate load capacity. where: Dw EL ERE MD MV MT MUV MUT YL Kµ = = = = = = = = = = Dead weight of tray and contents Axial seismic load in tray Seismic inertial loading Bending moment due to dead weight Seismic bending moment in the vertical plane Seismic bending moment in the transverse plane Allowable moment in the vertical plane Allowable moment in the transverse plane Allowable axial load in tray Ductility reduction factor 4-54 13633436 Seismic Capacity 4.6.3.3 HVAC Ducting HVAC ducting is often designed for seismic loading using AISI code-allowable stresses [74]. This usually results in supports at intervals such that the ducting is seismically rigid. The ducting is usually reinforced with steel angle around the outside to provide resistance to buckling under partial vacuum conditions. The sheet metal thickness is usually controlled by the vacuum or an internal pressure condition, and seismic stress is usually very low. In isolated cases, long unsupported spans of ducting may be found, or cases may be observed where the support integrity during seismic shaking is suspect. In these isolated cases, an evaluation of the ducting capacity may be appropriate. The principal concern for failure of HVAC ducting is support anchorage. This can be evaluated similar to anchorage for other components, as discussed above. Another failure mode for ducting is buckling of the sheet metal from partial vacuum and seismic loading. The buckling may in turn result in tearing of the sheet metal at welds. If it is necessary to evaluate a buckling failure mode, the fragility analyst engineer must determine if a partial vacuum on the ducting during an earthquake is a credible load combination. The vacuum condition usually results from tornados and a simultaneous tornado and earthquake is not considered a credible load combination. The AISI code [74] provides formulae for thin sheet metal structures that are based on allowable stress or the initiation of buckling. The buckling formulae are conservative relative to test data. Several reports (e.g., Kato, et al. [75], Desai, et al. [76], and Stoman [77]) provide results of tests to failure conducted on ducting loaded by bending moment, shear, and pressure. Kato, et al. [75] provides an empirical formula for calculating the buckling moment in rectangular ducting. The supporting test data reveal that the critical buckling moment is dependent only on the duct height in the plane of bending and the duct thickness. The width of the duct in the out of plane direction is not critical. Desai, et al. [76] provides an empirical formula for buckling pressure in a rectangular duct subjected to external pressure. A formula for the effective chord dimension is provided and the failure mode is determined to be corner crippling in the chord. Stoman [77] provides results of post buckling strength tests and a methodology for computing realistic post buckling strength. This methodology can be used for combined pressure loading and duct bending to determine the ultimate capacity. If the post buckling behavior of ducting is considered, it should be rare that a duct would fail due to seismic events with less than 0.8g peak ground spectral acceleration. One caution is that the references cited are based on experiments conducted on welded ducting. Ducting of commercial pocket-lock or similar joints may not be able to exhibit post buckling capacity similar to that demonstrated in Stoman [77]. For these cases, the onset of buckling should be considered the failure threshold unless the fragility analyst has other data to support greater capacity. More sophisticated analytical models may be used and justified by the fragility analyst. Table 4-13 summarizes a candidate acceptance criterion for HVAC ducting based on the above described handbook formula approach. 4-55 13633436 Seismic Capacity Table 4-13 Loading combination and stress limits for HVAC ducting Loading Combination Pp+Dw+ERE Stress Limit σcr where: Dw = Dead weight ERE = Seismic loading including seismic anchor motion effects Pp = Operating pressure acting externally on duct σcr = Critical buckling stress computed for thin sheet simply supported on all edges and subjected to biaxial compressive stresses resulting from Pp, D, and ERE 4.6.4 Sampling Evaluation of Equipment and Subsystems There are some components where plant-wide fragility values can be developed (e.g., distribution systems such as piping, cable trays, HVAC ducting and conduit, as well as valves and small miscellaneous vessels and heat exchangers). For these cases, the capacities should be based on plant-specific information. Because of the variability in the design stress levels relative to the component capacities, there will be larger U values assigned when plant-wide analyses are performed. However, in many cases these components are relatively strong and will not be significant contributors to SCDF. If a component is found to be important, then a componentspecific fragility curve should be developed. Plant-wide fragilities for particular equipment classes may not cover all support or anchorage configurations. Outlier configurations should be identified during seismic walkdown for later assessment. In past SPRAs, plant-wide generic fragility curves were sometimes developed based on knowledge of the code used in the design of a component class for the plant. This allowed the margin between code and the ultimate strength to be determined and included in the estimate of the median capacity. For cases where stress reports are available, the additional margin between the design stress and code allowable can also be reflected in the fragility analysis. Qualification documentation of major components supplied by vendors are typically contained in a single report with appropriate supplements. Architect/Engineer-designed subsystems, such as piping runs, cable trays, conduit, and HVAC ducting, are designed in a production mode by either detailed analysis of each identifiable analytical model, or they may be qualified in a generic manner with some specific analyses being conducted for special supports or unusual conditions. Piping systems are typically designed using detailed analysis, whereas cable trays, HVAC ducts, and conduit are typically designed by generic span spacing rules and use of generic support designs. The equipment and subsystems that are not screened out should be categorized into specific or generic categories according to their similarity and original qualifications and according to how they may be treated in a seismic risk evaluation. For unscreened components placed in the specific category, a fragility estimate should be developed representative of all components in 4-56 13633436 Seismic Capacity this category. For unscreened generic categories of components and subsystems, a sampling methodology should be applied with sufficient sampling to ensure that a representative or bounding fragility is applicable to the entire lot. Sampling criteria are further discussed in Section 6.1.4 and Appendix D. 4.7 Anchorage Failure Modes and Capacities Equipment and distribution systems may be attached to structures by a variety of anchorage systems. Failure modes of the anchorage systems must be considered as part of the equipment fragility analysis. Common anchorage systems include:  Cast-in-place bolts  Post installed anchors  Welds to embedded steel sections  Welds to structural elements or support structures  Bolts to structural members or support structures Appendix T provides an example fragility analysis for a cast-in-place bolt, and Appendix V provides an example for an electrical cabinet anchored with expansion anchors. 4.7.1 Steel Anchorage Failure Modes Median strength equations and variabilities are provided in Table 4-14 for common failure modes of steel anchorage elements. The median equations and variabilities can be used with median material strengths (Section 4.3) for SOV fragility evaluations. For hybrid (CDFM) evaluations, the strength equations should be modified to 84% EP per Section 3.4.1 using a strength reduction factor calculated from the values in Table 4-14. An 84% EP strength reduction factor for ductile failure can be calculated using the following equation: ϕ e Eq. 4-44 , where βEQN,U is the logarithmic standard deviation for uncertainty in the strength equation, given in Table 4-14. Used with CDFM material strength properties (Section 4.3) and a CDFM strength reduction factor, the strength equations in Table 4-14 can be used to calculate CDFM anchorage capacities. 4-57 13633436 Seismic Capacity Table 4-14 Strength capacity equation and uncertainty for common structural elements Median Capacity Logarithmic Standard Deviation for Uncertainty, U Equation Material Fabrication Combined SRSS Bolt Ultimate Tensiona Pum = um As 0.11 0.06 0.05 0.13 Shearb Vum = 0.62 um As 0.06 0.06 0.05 0.10 Longitudinal Directionc Vum = 0.84 um (0.707 t L) 0.11 0.05 0.15 0.19 Transverse Directionc Vum = 1.26 um (0.707 t L) 0.11 0.05 0.15 0.19 bh 4 0.06 0.12 0 0.13 0.06 0.12 0 0.13 Fillet Weld in Shear Plate in Bending Well defined yield pointd Yield Point not well defined M M Pum = Median ultimate tensile force bh 4 σ  3 2σ t = weld leg dimension Vum = Median ultimate shear force L = length of weld Mym = Median yield moment capacity b = width of plate um = Median material strength hp = thickness of plate ym = Median material yield As = Stressed area of bolt (across shank or threads, as appropriate) Notes: a. NUREG/CR-5270 [43], Kulak, et al. [39], and NBS Special Publication 577 [78] b. NUREG/CR-5270 [43], Kulak, et al. [39], and Holmes and Martin [79] c. Section 4.7.1.2 d. NUREG/CR-5270 [43] 4-58 13633436 Seismic Capacity 4.7.1.1 Cast-in-Place Bolts Cast-in-place anchors include headed studs, headed bolts, and hook anchors. Table 4-14 includes strength equations for shear and tensile rupture of steel anchor bolts. EPRI has investigated ductility of anchorage failure modes, however, and found that they exhibit some inelastic energy absorption capability when the dominant loading is in the high-frequency range. Conclusions from this research are summarized in Section 6.4.2. Additionally, it may be possible to justify that tensile failure of a bolt is ductile, provided the bolt has deep embedment, yields in the shank before it ruptures at the threads, is loaded primarily in tension, and is made of low-carbon steel, such as A-307. 4.7.1.2 Welds Figure 4-13 schematically illustrates a fillet weld and is used to define symbols used herein. Over any segment of the weld, the weld may be subjected to longitudinal shearing loads VL, and transverse loads VTX and VTY in the transverse X- and Y-directions, respectively. Figure 4-13 Fillet weld schematic The weld area resisting these applied loads is given by an effective length times the effective throat thickness. In most cases the effective length equals the total fillet weld length, L, and the effective throat thickness equals 0.707 times the weld leg size, t, as shown in Figure 4-13 (where the leg size is equal). The strength equations in Table 4-14 may be used to develop median capacities, using median material strengths. The CDFM weld capacity may always be taken as equal to the AISC-LRFD Limit Load Strengths [80] with the appropriate strength reduction factor, ϕw, or equal to 1.7 times the Allowable Stress Design Strengths [81]. However, both approaches are generally more conservative than necessary for fillet welds, where the effective throat thickness is 0.707t. For this case, a less conservative CDFM capacity may be developed as presented in the following two sections. However, these higher CDFM allowable capacities are only applicable to cases where the effective throat is 0.707t since the weld test data from which these higher allowable strengths were derived had this effective throat thickness. 4-59 13633436 Seismic Capacity The failure of a fillet weld represents essentially a brittle failure mode. The CDFM capacity for this type of brittle failure mode should be defined at about the 99% EP as opposed to the 98% EP recommended for somewhat more ductile failure modes. Per Table 3-10, this higher EP is achieved by defining material strengths, including an allowance for fabrication tolerances, at about the 98% EP as opposed to the 95% probability recommended for more ductile failure modes. Similarly, static capacity equations should be defined at about the 95% EP as opposed to the 84% probability for more ductile failure modes. 4.7.1.2.1 Capacity Under Longitudinal Shear Load Based upon extensive testing of fillet welds under longitudinal shear reported in Fisher, et al. [82], the median shear strength, τwL,m, of the fillet weld can be defined in terms of the median ultimate strength, σum, of the electrode by: τ , 0.84 ∗ σ Eq. 4-45 The logarithmic standard deviation for uncertainty in Equation 4-45 is βEQN,U = 0.11 (Table 4-14). The median ultimate strength is defined in terms of the minimum code nominal tensile strength of the electrode, FEXX, by: σ 1.1 ∗ F Eq. 4-46 The logarithmic standard deviation for material uncertainty in Equation 4-46 is βULT,U = 0.05 (Table 4-14). In addition, a logarithmic standard deviation of βFAB,U = 0.15 due to uncertainty in fabrication tolerances should be combined with material uncertainty per Fisher, et al. [82]. Thus, to achieve 98% EP material strengths, coupled with a 95% EP static capacity equation, the CDFM weld capacity, τwL,CDFM, becomes: τ where: , ϕ ∗f f 0.84 ∗ e % ϕ 1.1 ∗ e % 0.84 ∗ e 1.1 ∗ e ∗F . . ∗ , ∗ , ∗ . ∗ 4-60 13633436 . Eq. 4-47 0.70 . . , . 0.80 Eq. 4-48 Seismic Capacity The material strength reduction factor, ϕwCDFM, and the nominal strength factor, fwCDFM, defined in Equation 4-48 are somewhat more liberal than those specified in AISC-LRFD for the limit strength approach for design. The CDFM longitudinal weld capacity is therefore: V , τ ϕ ∗ 0.707 ∗ t ∗ L , ∗f 0.8 ∗ 0.7 ∗ F ∗F ∗ 0.707 ∗ t ∗ L ∗ 0.707 ∗ t ∗ L Eq. 4-49 ∗ 0.707 ∗ t ∗ L 0.56 ∗ F where t and L are defined in Figure 4-13. The analyst must also limit the shear at the interface of the weld and the base metal. Following AISC Allowable Stress Design (ASD) rules, a conservative estimate of the CDFM interface shear capacity can be obtained by taking 1.7 times the ASD strength (to obtain the ultimate design strength): V, 1.7 ∗ 0.3 ∗ σ , ∗ t ∗ L Eq. 4-50 where σu,B is the minimum specified ultimate strength of the base metal. The limit expressed by Equation 4-50 is likely to be more conservative than necessary and could possibly be relaxed through a detailed study of failure test data. Equation 4-50 will govern over Equation 4-49 when the electrode strength FEXX exceeds the base metal strength by more than a factor of 1.28. For the case of an E70 electrode (FEXX = 70 ksi) or less, and A36 steel base metal (σu,B = 58 ksi), Equation 4-49 will govern for welds oriented longitudinally with respect to the direction of loading. 4.7.1.2.2 Capacity Under Transverse and Combined Shear Loads Based on tests on forty-two welds loaded at seven different loading angles, θ, ranging from 0° (longitudinal) to 90° (transverse), Lesik and Kennedy [83] recommend estimating the ratio of weld strength at an angle θ to longitudinal strength as: . R ⁄ 0.5 ∗ sin θ R ⁄ 0.5 ∗ sin 90° 1.0 Eq. 4-51 where θ is the angle between the applied load axis and the longitudinal axis of the weld. This equation is assumed to be approximately median centered. For a transverse weld (θ = 90°), Equation 4-51 gives a ratio of transverse to longitudinal capacities of: . 1.0 1.5 Eq. 4-52 4-61 13633436 Seismic Capacity For any combination of longitudinal, VL, and transverse VTX and VTY loadings applied to the weld, the vector loading can be obtained by: V V cosθ V V V 0.84 ∗ R ⁄ ∗ F V V Eq. 4-53 applied at an angle, θ, given by: Eq. 4-54 This vector loading can be compared to the median or CDFM capacity: V , 0.56 ∗ R ⁄ ∗ F ∗ 0.707 ∗ t ∗ L ∗ 0.707 ∗ t ∗ L Eq. 4-55 Eq. 4-56 Again, the fragility analyst must also check the vector interface shear between the weld and base metal interface shear capacity VB,CDFM given by Equation 4-50. The maximum interface shear load is given by: V V V Eq. 4-57 where VT is the larger of VTX and VTY. For the case of an E60 electrode (FEXX = 60 ksi) and A36 steel (σu,B = 58 ksi), Equation 4-50 will generally govern when Rθ/L > 1.23, which corresponds to θ > 37°. Again, Equation 4-50 can probably be improved some by further study of failure test data. 4.7.1.3 Plates in Bending The moment capacity for plates in bending is listed with the other anchorage failure modes because plate elements are often loaded in bending in the anchorage load path. For example, electrical cabinets are often mounted to two or more parallel steel angle or channel sections. Unless a stiffer load path is provided perpendicular to the steel sections, the angles or channels must resist lateral forces by local bending. The capacity equations in Table 4-14 are applicable to bending failure modes of plates in other configurations as well. The moment capacity for plates in bending assumes a plastic modulus and an effective stress for non-ferrous materials such as aluminum and stainless steel, which do not have well defined yield points. The effective stress is equal to the sum of two-thirds the ultimate stress and one-third the yield stress, assuming the outside fiber is at the ultimate stress while the middle fiber is at the yield stress, with a linear stress gradient between the two. For material with a well-defined yield point such as A36 steel, it would be unconservative to use this stress relationship because of the long, flat yield plateau. The equations given in Table 4-14 for plate bending reflect this philosophy. 4-62 13633436 Seismic Capacity 4.7.2 Concrete Failure Modes 4.7.2.1 Concrete Breakout of Cast-in-Place Anchors Strengths of cast-in-place anchors controlled by concrete breakout failure may be determined following the concrete capacity design (CCD) method, which is codified in the provisions in Appendix D to ACI 349-13 [46]. The code equations can be modified as described in this section to obtain median strength equations using Fuchs, et al. [84] and NUREG/CR-5563 [85]. CDFM capacities may be calculated following the code provisions with CDFM material strengths. The criteria in Table 3-10 for non-brittle failure modes (i.e., 95% EP material strength and code strength equations) are recommended for concrete anchor breakout failure modes. Concrete anchorage breakout is considered mildly ductile (although an Fµ > 1.0 is typically not justified), so the CDFM criteria for brittle failure modes are not appropriate. Moreover, the ACI basic strength (e.g., Equation 4-58) already includes additional conservatism beyond what is typical of other types of failure modes; therefore, it is considered unnecessary to introduce additional conservatism in the material properties and strength equation to obtain a 99% EP CDFM capacity. The basic concrete breakout strength in tension for anchors in cracked concrete is provided by Equation D-7 from ACI 349-13 [46], included here as Equation 4-58. N k f h. Eq. 4-58 N k f h. Eq. 4-59 where hef is the effective embedment depth, and kc is an empirical coefficient, as defined in ACI 349-13 [46]. For cast-in-headed studs and bolts embedded 11 to 25 in., ACI 349-13 [46] provides Equation D-8 as an alternative, included as Equation 4-59. The kc coefficients provided in ACI 349-13 [46] are 5% fractile values. Mean coefficients for uncracked concrete corresponding to Equations 4-58 and 4-59 are kc = 40 (Fuchs, et al. [84]) and kc = 26.4 (NUREG/CR-5563 [85]), respectively. Median basic strengths may be approximated using the mean coefficients with median material strengths and strength reduction factors of 1.0. The COVs for the ratio of tested to predicted basic strength range from 0.18 to 0.20 (Fuchs, et al. [84] and NUREG/CR-5563 [85]). An additional logarithmic standard deviation of 0.05 should also be included to account for uncertainties such as the shear-tension interaction relationship and the various knockdown factors in ACI 349-13 [46]. The basic strength equations defined in Equations 4-58 and 4-59 should be modified by the reduction factors Ψec,N and Ψed,N from ACI 349-13 [46] to account for eccentricity and edge distance effects. Strengths for anchors in groups and those affected by nearby edges should also be modified by the ratio of the projected area of a 35° rectangular cone following Equations D-4 and D-5 of ACI 349-13 [46]. Factors Ψc,N and Ψcp,N for cracking and post-installed anchors are not applicable because the kc values recommended here are for cast-in-place anchors in uncracked concrete. 4-63 13633436 Seismic Capacity EPRI 3002008099 [86] assesses the median strength equation for single cast-in-place headed anchors considering more recent tests of deeply embedded anchors. The expanded deep anchor dataset includes single anchors up to a depth of 45 in., where “deep anchor” is defined as greater than 7.5 in. For the special case where a single anchor is embedded greater than 7.5 in. and is unobstructed by edge distance or spacing, the following alternate median equation is recommended for the basic concrete tensile strength: N 4.4 f Eq. 4-60 h. where the concrete compressive strength (f’c) used in this equation must not exceed 7,000 psi. The COV for the ratio of tested to predicted basic strength is 0.16 (EPRI 3002008099 [86]). The recommended strength reduction factor to achieve a CDFM capacity is 0.70. The technical basis for the deep single anchor equation recommendation in the EPRI study is summarized in Appendix E. The basic concrete breakout strength in shear for cracked concrete can be calculated following Equation D-23 from ACI 349-13 [46]: V 7 l d . d f c . Eq. 4-61 where le is the load-bearing length of the anchor, da is the anchor diameter, and ca1 is the distance from the center of the anchor shaft to the concrete edge, as defined in ACI 349-13 [46]. Median strength may be obtained for cast-in-place headed studs and headed anchor bolts in uncracked concrete by substituting a value of 13 for the coefficient of 7 in Equation 4-61 (Fuchs, et al. [84]) with median material strengths and strength reduction factors of 1.0. The coefficient of variation for the ratio of test to predicted strength is about 0.17 (Fuchs, et al. [84]). Similar to tension, an additional logarithmic standard deviation of 0.05 is recommended for use in fragility evaluation. 4.7.2.2 Concrete Breakout of Post-Installed Anchors The CCD method should be implemented only for post-installed anchors having a current International Code Council (ICC) evaluation report signifying that the anchors satisfy current acceptance criteria. The evaluation report should be reviewed for any additional requirements or limitations. For these anchors, CDFM capacities can be calculated following the design provisions of ACI 349-13 [46] Appendix D, together with the evaluation report guidance. The median basic concrete breakout strength for uncracked concrete can be calculated using a value of 35 for kc in Equation 4-58; the coefficient of variation for the ratio of tested to predicted strength is 0.23 (Fuchs, et al. [84]). Similar to other concrete failure modes above, an additional logarithmic standard deviation of 0.05 is recommended for use in fragility evaluation. 4.7.2.3 Splitting Failure ACI 349-13 [46] gives guidance on minimum edge distance requirements to preclude splitting for cast-in headed and post-installed anchors. The concrete related failures of hooked bolts evaluated in Meinheit, et al. [87] were characterized by splitting of small test blocks of unreinforced concrete. The hooked bolt test data is insufficient to make general 4-64 13633436 Seismic Capacity recommendations on splitting capacity or minimum edge distances for hooked bolts. Fragility analyst should look at reinforcement across the plane parallel to the tail of a hooked bar to determine if splitting can be excluded as a credible failure mode. If splitting is a credible failure mode, its capacity should be evaluated on a case-by-case basis using the most relevant data and methods available, such as in Meinheit, et al. [87]. 4.7.3 Pullout Failure Modes 4.7.3.1 Post-Installed Anchors Median strengths and associated variability of post-installed anchors may be determined directly from manufacturer test data, or from the extensive testing summarized in EPRI NP-5228-SL [88]. Based on the EPRI NP-5228-SL [88] data, Appendix F provides guidance for developing CDFM capacities and adjusting for the presence of concrete cracks. Guidance in EPRI NP-5228SL [88] should be followed to adjust the capacities for embedment depth, spacing, edge distance, concrete strength, anchor type, and shear-tension interaction. Appendix V provides example calculations using both the SOV and hybrid approaches. 4.7.3.2 Hook Anchors L-bolts and J-bolts are referred to herein as hook anchors. Meinheit, et al. [87] analyzed data on pullout strengths of L-bolts (Figure 4-14) in tension and proposed alternatives to the design strength permitted by ACI 349-13 [46]. The data considered in Meinheit, et al. [87] is re-evaluated in EPRI 3002008099 [86]. Based on the EPRI study, the following equation is recommended for estimating median pullout capacities for fragility calculations: Ppullout = 1200 da3/4 eh hef1/2 f’cm 1/8 (lbs); eh/da  2.0 da = Anchor diameter eh = Hook tail length as defined in Figures 4-14 and 4-15 hef = Effective embedment depth f’cm= Median concrete compressive strength Eq. 4-62 The logarithmic standard deviation associated with the recommended strength equation for pullout is (EPRI 3002008099 [86]): pullout = 0.23 For HCLPF calculations, the CDFM strength reduction factor associated with the recommended strength equation for pullout in tension is (EPRI 3002008099 [86]): pullout = 0.60 The strength reduction factor for pullout is defined at about the 98% EP since the pullout equation is insensitive to material strength (f’cm is raised to the 1/8th power so variations in material strength have a small effect on the anchor strength). When combined with 95% EP material strength, the resulting capacity meets the CDFM performance goal of 99% EP for brittle failures. 4-65 13633436 Seismic Capacity EPRI 3002008099 [86] concludes that the L-bolt strength equations may be used to evaluate the capacities of J-bolts as well, defining hef and eh as shown in Figures 4-14 and 4-15. The basis for the pullout equation recommendation in the EPRI study is summarized in Appendix E. Figure 4-14 L-bolt anchor Figure 4-15 J-bolt anchor 4-66 13633436 Seismic Capacity 4.7.4 Tension-Shear Interaction Equation The following equation is recommended for tension-shear interaction for concrete anchor failure modes based on data reported by Eligehausen, et al. [89]. The shear-tension interaction relationship is appropriate for both median-centered and CDFM calculations, and it includes no intentional conservatism. (V / Vu)ζ + (Pa / Pau)ζ < 1.0 Eq. 4-63 V, Pa = Shear and tension demands, respectively Vu, Pau = Shear and tension strengths, respectively ζ = 2 Steel failure = 1.5 Concrete breakout failure, anchors not affected by an edge = 1.2 Concrete breakout failure, anchors affected by an edge In general, the shear and tension capacities used in the interaction equation should be either for concrete breakout exclusively or steel failure exclusively (e.g., the concrete breakout capacity should not be used for tension while steel is used for shear, or vice versa). Failure modes should not be mixed in the interaction equation. As such, shear-tension interaction need not be considered for pullout since there is no pullout failure mode for shear loading. 4.8 Equipment Inelastic Energy Absorption The inelastic energy absorption factor is applicable to relatively few equipment failure modes since most failure modes for equipment anchorage or supports are non-ductile. Median or 95% EP nonlinear deformations should be determined for application of these methods to SOV or CDFM evaluations, respectively. As a simplifying approximation, inelastic energy absorption factors may be estimated for ductile failure modes of equipment and distribution systems using Table 4-15 (reproduced from Table 8-1 of ASCE/SEI 43-05 [14] with permission from ASCE). Factors are provided for Limit States A, B, and C, any of which may be appropriate for equipment and distribution system failure modes, depending on the configuration and function credited in the systems logic. This is unlike consideration of inelastic energy absorption for structures, where it is judged that Limit State C response corresponds to deformations that could potentially affect the operability of equipment attached within the structure. 4-67 13633436 Seismic Capacity Table 4-15 Equipment and distribution systems inelastic energy absorption factor, Fµ Factor Fµ Limit State A1 Limit State B1 Limit State C1 Vessel 1.50 1.25 1.15 Heat exchanger 1.50 1.25 1.15 Coolers 1.50 1.25 1.15 Chillers 1.50 1.25 1.15 Tanks (vertical) 1.25 1.25 1.15 Tanks (horizontal) 1.50 1.25 1.15 Pumps 1.50 1.25 1.15 Fans 1.50 1.25 1.15 Valves 1.50 1.25 1.15 Dampers Equipment: 1.50 1.25 1.15 2 2.00 1.50 1.25 Glove boxes2 2.00 1.50 1.15 Electrical boards2 2.00 1.50 1.15 Electrical racks2 2.00 1.50 1.15 Electrical cabinets2 2.00 1.50 1.15 Butt joined groove welded pipe 1.75 1.50 1.25 Socket welded pipe 1.50 1.25 1.15 Threaded pipe 1.25 1.15 1.00 Conduit 1.50 1.35 1.25 Instrument tubing 1.50 1.35 1.25 Cable trays 1.50 1.35 1.25 HVAC duct 1.50 1.25 1.15 2.00 1.50 1.25 Filters Distribution systems: Equipment supports2 Notes: 1 Except as discussed in Note 2 below, the allowable behavior limits for passive components are based on the ASME B&PVC, Section III, allowables for Service Level D. It should he noted that ASME B&PVC, Section III, Service Level D allowable stresses range from 1.6 to 2.0σy. 2 These components are normally designed to AISC allowables, which are typically limited to 0.8 to 1.0σy; hence, they are allowed a somewhat higher inelastic energy absorption factor as compared to ASME B&PVC allowables, where allowable stresses can be as high as 2.0σy. 4-68 13633436 Seismic Capacity Limit State D corresponds to essentially elastic behavior and no damage, for which Fµ is unity. Limit State C corresponds to limited permanent distortion and minimal damage. Limit State B corresponds to moderate permanent deformation and generally repairable damage. Limit State A corresponds to large permanent distortion and significant damage but short of complete failure. The 95% EP inelastic energy absorption factors are given in ASCE/SEI 43-05 [14] for each of the Limit States. Median inelastic energy absorption factors can be estimated from the 95% EP values following Equation 4-41 in Section 4.5.5. The inelastic energy absorption factors for Limit States A, B, and C are not applicable to functional equipment failure modes such as stem binding in a valve or bearing clearance in rotating equipment. If the component contains brittle material in the load path or brittle material is used that could affect its credited function, then Fµ values are taken as 1.0. When seismic analysis methods are used to qualify active components (i.e., components that must change state as part of their credited function) during the earthquake, only Limit State D is permitted. Limit State C is permitted for function-after, stress- and strain-related failure modes of active components like electrical cabinets but not for function-during failure modes related to changes of state of chatter-sensitive devices. Pressure-retaining mechanical equipment that must retain its leak-tight integrity is not permitted in Limit State A. Appendix B to ANS 2.26-2004 [91] contains additional guidance that may be used to assist in judging which limit state is appropriate for a given fragility analysis. 4.9 Seismic Capacities Based on Test Test-based capacity factors are calculated following Equation 4-5 per Section 4.1.3. Since TRS from shake table test results represent lower bound equipment capacities, TRS are modified to obtain TRSC for use in Equation 4-5. TRS from both device-based and cabinet-based testing are modified by the clipping (CT), capacity increase (CI), and broad frequency input device capacity factors (FD). TRS from device-based testing are additionally modified by the multi-axis to single-axis conservatism factor, FAX. Median values, logarithmic standard deviations, and values appropriate for calculating CDFM capacities are discussed in Sections 4.9.1 through 4.9.4 for these four factors. An example test-based fragility is given in Appendix X. TRS based on less rigorous testing requirements such as single axis, single frequency sine beat, or sine sweep testing can be used (Figure 4-16), but the need for caution must be emphasized. For device testing, the resulting narrow-band TRS must be clipped to obtain an equivalent broadband random test level that can be compared to the mounting point demand. Testing of this type was considered in EPRI 3002000706 [92]. Sine-beat and sine sweep testing must be conducted with several input motions to span the frequency range of interest. In general, sine sweep testing is not recommended for fragility testing due to the resulting test severity and the number of tests required. Except for line-mounted equipment, sine sweep testing does not reasonably emulate the seismic environment for equipment, and therefore, does not produce the most valuable data to estimate realistic seismic capacity levels. 4-69 13633436 Seismic Capacity Figure 4-16 Typical sine beat and sine sweep time histories Different types of test results represent different levels of conservatism that must be consistently factored into fragility analyses, and caution must be used in interpreting the meaning of different TRS. In particular, care should be taken regarding the location at which a TRS is measured, the directions of shake table excitation, and the frequency content of the shake table motion. For example, data are available for cases where entire electrical cabinets have been tested, and TRS may have been developed from accelerations measured at the base of the cabinet or at specific in-cabinet locations. In other cases, the test data are for electrical devices (e.g., relays or contactors) mounted directly to a shake table. Demand due to the RE, (reference response spectrum, RRS) is typically developed at the equipment attachment point to the ground or structure. When TRS represent the motion experienced by a device mounted inside a cabinet during testing, the RRS must be modified to include the amplification of motion from the floor to the point of attachment of the device to the cabinet. TRS and RRS should only be compared directly when they correspond to seismic motions at the same location. Section 5.5.3.2 provides guidance for estimating cabinet amplification effects. 4.9.1 TRS Clipping Factor Application of clipping factors to TRS should be scrutinized with extra caution by the analyst. Clipping factors were developed for reducing the seismic demand suggested by narrow-banded peaks in RRS (Section 5.5.3.1). Discussion of conservatism in clipping factors must be reversed when they are applied to TRS. A larger clipping factor (i.e., closer to 1.0) will be more conservative for clipping RRS because it results in a larger spectral acceleration demand. Conversely, a larger clipping factor results in a greater prediction of tested capacity, potentially overstating the effective level of testing. Clipping factors should therefore be considered carefully to ensure that TRSC does not significantly overestimate a component’s tested capacity. 4-70 13633436 Seismic Capacity For the CDFM approach, whenever the TRS has broader frequency content (greater bandwidth ratio, B, from Equation 5-17) than the RRS, it is conservative to clip both the TRS and RRS using Equation 5-21. However, if the bandwidth ratio for the TRS is less than for the RRS, it is unconservative to clip both the TRS and the RRS in accordance with Equation 5-21 because this equation is expected to underestimate the clipping factor. For the case of cabinet-based test data, the TRSC is the response spectrum corresponding to the test of the entire cabinet, which may contain devices. In general, TRS are broad-band in shape and do not require clipping. Usually, cabinet tests are conducted using broad-band input or have been corrected and reported as a broad frequency, multi-axis TRS. However, there may be cases where a narrow-band input, such as a series of sine-beat or sine-dwell tests, was used to cover the frequency band of interest. For these situations, the TRS should be clipped. The TRS clipping factor, CT, can be calculated by the same methods of clipping the RRS demand, using Equations 5-21 and 5-22 (Section 5.5.3.1). 4.9.2 Capacity Increase Factor A test response spectrum is usually represented by a constant capacity value over a broad frequency range (i.e., the TRS). This capacity level is a lower bound limit that is set by the response at the resonance frequency of the component being tested. It is unlikely that the ISRS peak from the RE will exactly line up with the capacity spectral acceleration valley. Figure 4-17 shows the more probable case where the frequency at which the real response spectrum fragility curve has a minimum offset from the frequency where the ISRS peaks. Thus, the demand corresponding to the RE can be raised higher than the TRS in determining the capacity factor. Studies to determine how much additional capacity exists have not been performed. However, it is conservatively estimated that the capacity increase factor, CI, has a median value of at least 1.1, with a corresponding CI,U = 0.05. For CDFM capacity calculations, a capacity increase factor of 1.0 should be used. 4-71 13633436 Seismic Capacity Figure 4-17 Realistic demand and capacity response spectra at failure for equipment qualified by testing 4.9.3 Multi-Axis to Single-Axis Conservatism Factor The multi-axis to single axis conservatism factor is applicable to device-based TRS capacities. If the TRS are for multi-axis excitation (as is the case for all the generic device-based TRS capacities defined in EPRI NP-5223 [20], EPRI NP-7147 [21], NUREG/CR-4659 [93], and NUREG/CR-4900/-5470 [94]) and the RRSC is predominately a single axis excitation (as is the case for relays and contactors mounted on panels in cabinets), then the TRS should be increased by a multi-axis to single-axis correction factor, FAX, to remove the unnecessary conservatism. EPRI NP-5223 [20] and SWRI 8608-001 [95] have suggested that FAX equal to 1.2 represents a reasonable and probably slightly conservative multi-axis to single-axis correction factor to be used for cases where this correction is appropriate. The FAX factor of 1.2 is appropriate as a CDFM value and is assumed to be at about the -0.5 probability level. It is also assumed that a FAX value of 1.0 is at the -2.5 level. These assumptions lead to an estimate of the logarithmic standard deviation for uncertainty of: β , 1.20 1.0 2.5 0.5 ln 0.09 4-72 13633436 Eq. 4-64 Seismic Capacity Here, the 1.20 and 1.0 values are found to be two standard deviations apart based on these assumptions. Now knowing the CDFM value and the logarithmic standard deviation, the median value of FAX is found directly to be: F 1.2 ∗ e . ∗ . 1.25 Eq. 4-65 which is consistent with the conservatism assumed for FAX in the CDFM method [1]. The FAX factor is often misunderstood and is meant to be used at the discretion of the analyst to handle situations where the cabinet configuration is such that the cabinet response has a dominant single-axis response motion. As an example, a long lineup of cabinets will often have dominant front-to-back response since the side-to-side motion is suppressed. In the past, the vertical motion was also considered to be negligible. For the case of both base- and top-anchored cabinets or wall-mounted cabinets/components in the high-frequency range, vertical and horizontal high-frequency motion will always be present; thus, it is recommended that the FAX factor be taken as FAX = 1.0 in these cases. For base-mounted cantilever cabinets (without top bracing), the horizontal low-frequency motion is well separated from the vertical high-frequency motion, and the two motions may be considered as independent from each other. If the analyst judges that the horizontal and vertical in-cabinet motions are well separated, then a median FAX = 1.25 is recommended. 4.9.4 Broad Frequency Input Spectrum Device Capacity Factor In general, there is conservatism (bias) and variability in the TRS capacity. The median adjustment factor, FD, depends upon the level of conservatism that is judged to exist in the TRS based on the testing methods that were used. For HCLPF analysis, CDFM adjustment factors were developed using probabilistic techniques discussed in Appendix J. The CDFM factors have been selected to produce about a 99% EP level. Table 4-16 presents a summary of the median factors to apply to broad frequency TRS and the associated logarithmic standard deviations for randomness and uncertainty. Three general TRS sources are covered in Table 4-16:  Test programs for specific classes of components  Relay tests meeting the broadband triaxial testing input motion and contact monitoring requirements given in ANSI/IEEE C37.98-1987 [67]  Qualification test reports The first type consists of capacity parameters that have been developed for specific classes of components and devices. The first three entries in Table 4-16 correspond to test programs carried out for several components, such that failure probabilities corresponding to the test data are relatively well understood. NUREG/CR-4659 [93] and NUREG/CR-4900/-5470 [94] report TRS developed at Brookhaven National Laboratory (BNL) and Lawrence Livermore National Laboratory (LLNL) for electrical components. These TRS are representative HCLPF capacities for the tested equipment classes, and therefore FD for these TRS is 1.0. Median factors and logarithmic standard deviations could be individually determined for the BNL and LLNL TRS based on data in the above referenced reports. However, a median value for FD of 1.75 is reasonable for all TRS obtained from this dataset, as are the logarithmic standard deviations 4-73 13633436 Seismic Capacity listed in Table 4-16. TRS obtained from GERS testing of equipment in EPRI NP-5223 [20] and relays in EPRI NP-7147 [21] are less conservative than the BNL and LLNL TRS. The values for FD and logarithmic standard deviations listed in the second and third rows of Table 4-16 are based on the expert judgement discussed in Appendix J. The second type of test data is represented by TRS that test multiple samples with increasing triaxial motion until the threshold of contact chatter is found. Per ANSI/IEEE Standard C37.98-1987 [67], three relays of the same type may be tested, and the lowest TRS capacity of the three tests is defined to be the TRS of the component type. For each relay tested, the highest test level at which relay chatter did not occur establishes the capacity for that relay since the relay chatters at the next higher test level. Based on an analysis of this procedure with multiple samples, an estimate of the ratio of the median capacity to TRS is given in Appendix J. This is the value of 1.5 given in Table 4-16. This applies only for tests that have three or more sample components of the same item. This variant of testing is most often used by manufacturers who qualify their products. Most qualification efforts, however, consider only testing of a single item in accordance with IEEE Standard 344-1975 [96] (or later editions). The third type of test data is represented by general qualification test data. For this type of data, it is very difficult to obtain fragility parameter values since the tests do not reach a failure level. Judgment is used in EPRI NP-6041-SLR1 [1] (Appendix J) to establish the factors (FD) applied to the test level to obtain HCLPF capacities. Median FD factors are found based on variabilities estimated based on prior testing. The factors given in Table 4-16 depend on the operational requirements (i.e., function during or function after) and the physical results of the test (i.e., anomalies or no anomalies). If structural anomalies are found, such as weld cracking, sheet metal tearing, screw pull out, local permanent cabinet distortion, etc., then the fragility analyst will have to use judgment to estimate how much higher the motion would have to be raised before damage is severe enough to cause the cabinet function to fail. TRS from the sources discussed above are realistic estimates of component capacity at frequencies between about 4 Hz and 20 Hz, but the tests may not have significantly loaded the components in the high-frequency range. The EPRI high-frequency test program (EPRI 3002002997 [23] and EPRI 3002004396 [24]) tested many devices prone to contact chatter with high-frequency shake table input motions. Section 6.4.1 describes how results from these tests should be applied to fragility analysis. Values of FD and logarithmic standard deviations for use with the high-frequency test data are listed in Table 4-16. Selection of FD depends on the results of the high-frequency testing for a component. For component tests where chatter was observed at some input motion level, the median value of FD should be unity. For component tests where the maximum table motion did not cause chatter, the median value of FD should be 1.5. 4-74 13633436 Seismic Capacity Table 4-16 Broad frequency input spectrum device capacity factors Median FD FD,R FD,U CDFM FD HCLPF Capacities (BNL & LLNL) [93, 93] 1.75 0.11 0.23 1.0 GERS – Non relay [20] 1.45 0.11 0.23 0.83 GERS – Relay [21] 1.07 0.09 0.18 0.69 IEEE C37.98-1987 – Relay Fragility [67] 1.5 0.09 0.18 0.96 Qualification Test - Function During 1.4 0.09 0.22 0.84 Function After (no anomalies) 1.95 0.09 0.28 1.06 Function After (anomalies) 1.1-1.65 0.09 0.28 0.6-0.9 1.5 0.09 0.22 0.9 1.0 0.09 0.18 0.64 TRS Data Source High-Frequency Test Program [23, 24] Function Confirmed; Test Table Capacity High-Frequency Test Program [23, 24] Contact Chatter Observed 4.9.5 Additional Test Experience There are ongoing efforts through EPRI to enhance and develop new equipment capacity GERS based upon the results of qualification testing. The SQURTS organization [22] is an EPRI-sponsored group of utilities which has sought to achieve both qualification test standardization and economy by conducting collective (multiple item) shake table tests of replacement equipment for NPPs. The qualification and/or fragility testing results are summarized in a standard test report format and made available through a seismic qualification data library service to all SQURTS utilities. Most of the testing is at the device level such as relays, switches, molded case circuit breakers, transmitters, etc. These data are then analyzed to either enhance existing GERS as originally reported for non-relays and for relays (EPRI NP-5223 [20] and NP-7147 [21]) or develop new GERS for addition to the EPRI GERS reports. New GERS and updates of GERS were developed in EPRI TR-105988-V1 [97] and EPRI TR-105988-V2 [98] and incorporated as addenda to EPRI NP-5223 [20] and NP-7147 [21]. A separate study was performed in EPRI 3002010668 [25] to review SQURTS test data for components typically modeled in SPRAs and summarize the component-specific capacities in a form that is more convenient for fragility calculations. A pilot program was initiated to gather test data from other countries to enhance GERS. Candidate GERS were developed for cabinets, including devices within the cabinets, using the rules for developing GERS for low diversity class equipment. A joint SQUG/USNRC review panel previously ruled that I&C panels and cabinets are a high diversity class; thus, there are as yet no official GERS for this class. The data from the United Kingdom is very useful in a general sense, though, for demonstrating typical damping values and fundamental frequencies. There were two groups of panels. The first group was circa 1980-1985 tested in a biaxial or triaxial mode. The second group was circa 1989 to 1997, all tested triaxially. Fundamental frequencies ranged from 7.5 to 21.4 Hz front to back and 7.8 to 33.7 Hz side to side. Panels in the second 4-75 13633436 Seismic Capacity group tended to be a bit stiffer but there were individual panels in the second group with frequencies near the lower level cited. Damping ratios ranged from 3% to 13%. The lower damping ratios were generally associated with very stiff cabinets. The average of the sixteen cabinets tested was above the 5% damping considered as median damping in the development of fragilities (Section 5.5.2.2). At the OECD/NEA Workshop held in Tokyo (1999), several Japanese papers were presented that summarized high level shake table tests of components conducted on the NUPEC Tadotsu Engineering Laboratory shake table [99]. Many tests are for passive, large scale model structures or equipment that are specific designs. One test of a diesel generator determined, through extrapolation of response measurements, that the crankshaft locating bearing housing would be the governing failure mode when it yielded. In general, these tests are for specific designs and cannot be effectively used to develop generic ruggedness levels for typical U.S. equipment. They do, however, provide additional support for the seismic capacities provided in Table 4-2. NUPEC tests of more typical generic electrical equipment are summarized in Ueki, et al. [100]. From the quoted fundamental frequencies, the equipment tested is considerably stiffer than typical SQUG database equipment, and thus is typically more rugged. The tests were initially conducted as proving tests, and then the shaking level was increased to higher levels with no reported malfunction or damage. The higher-level tests ranged from 3.4g zero period acceleration (ZPA) for metal clad switchgear (minimum side to side fundamental frequency of 22 Hz) to 8.0 g ZPA for an upright panel (minimum side to side fundamental frequency of 27 Hz). These frequencies correspond to the ZPA, so the low-frequency peak of the test response spectra at about 2 Hz has no effect on response. Due to the differences in design, the very stiff construction, and the differences in manufacturers of internal devices, the data are not directly applicable for enhancement of GERS developed for U.S. equipment. The tests do, however, provide further evidence that stiff cabinets and devices within stiff cabinets can have substantial seismic capacities. 4-76 13633436 5 SEISMIC DEMAND 5.1 General As discussed in Sections 3.3.1 and 3.4.1, an SSC’s seismic fragility is calculated as the ratio of capacity over demand (the capacity factor, FC) multiplied by response factors and the RE ground motion parameter (e.g., PGARE). Figure 5-1 identifies the basic elements of the seismic demand evaluation process. This section provides guidance for determining the demand and response factors. Section 4 provides guidance for determining the SSC capacity. Seismic demands are calculated by analyzing the dynamic response of structures and equipment to seismic input. Typically, seismic structure response analysis is first conducted using the RE as seismic input to the structure. Important considerations for RE selection and validation are discussed in Section 5.2. Then, structures are evaluated using structure forces and displacements, and equipment and systems within the structures are evaluated using in-structure seismic response as input. Depending on the fragility approach, either realistic or somewhat conservative seismic demands can be developed from the structure and equipment response analyses. For the SOV fragility approach, median (realistic) seismic demands are calculated using median centered models and analysis parameters. For the hybrid fragility approach, the response factors and variabilities are used to inform the development of 84% NEP responses. Specific methods for calculating median and 84% NEP seismic demands and several related technical topics are presented in Section 5.3. To account for conservatism or unconservatism in the dynamic analysis methods, structure and equipment response factors are applied to the fragility as lognormally distributed random variables FRS and FER. The median values of these random variables are used to calculate the median ground acceleration capacity using Equation 3-16. Variabilities in the response factors are propagated through the seismic capacity analysis to calculate logarithmic standard deviations for the fragility. Guidance is presented in Sections 5.4 and 5.5 for determining median values and variabilities for structure and equipment response factors, respectively. 5-1 13633436 Seismic Demand Figure 5-1 Seismic demand evaluation in the fragility process 5-2 13633436 Seismic Demand 5.2 Reference Earthquake Structure response analyses in SPRAs are typically performed at a single input level and then, as a simplifying approximation, linearly scaled to estimate responses at other levels. To minimize bias introduced by the linear approximation, the input level, or RE, should be carefully selected and subsequently validated. The relationship between structure response and amplitude of seismic input motion is inherently nonlinear across the full range of accelerations considered in an SPRA. SPRA logic models are often quantified for PGAs ranging from 0g to 5g or greater. Due to the nonlinear nature of soil and structure behavior, the response at any given PGA in this range will be governed by a unique set of physical properties. Ideally, structure response analyses would be performed at several different input levels to characterize the nonlinear relationship. In practice, however, the effort required to develop ISRS (as well as assess other non-linearities) at many different input levels is often unnecessary to achieve the objectives of the SPRA (e.g., to identify risk-dominant accident sequences and SSCs). Elastic structure response analysis using a single input level (the RE) has typically been considered adequate to achieve the SPRA objectives. Sensitivity studies can be performed to assess the impact of any potential cliff edge non-linearities (Section 5.2.5) at seismic input levels different from the RE. The following sections define the RE, identify nonlinear effects that should be considered when selecting and using the RE, and provide guidance for selecting the RE to ensure reasonable accuracy in the SPRA results. 5.2.1 Definition of Reference Earthquake The RE is the earthquake selected to represent the fundamental seismic input for calculating seismic response and fragilities. The RE includes defining the spectrum amplitude, the spectrum shape, and the RE location (control point). In addition, the RE influences the soil and structure properties and ground motion characteristics used to develop structure response and, in turn, component fragilities and SPRA risk results. Figure 5-2 relates the concepts of the RE, the seismic hazard, and the SPRA control point – each of which are described in the sections below. In an SPRA, the RE is the UHRS at a specified control point that defines: 1. The level or amplitude of seismic input (PGA or spectral acceleration) used in structure response analyses to develop ISRS, which serve as input to equipment fragility analyses. This level of input determines the stress and strain levels at which the soil and structures are analyzed (e.g., stress and strain levels help determine modeling decisions such as cracked vs. uncracked concrete, material damping, and degraded soil modulus). 2. The response spectrum shape used as seismic input to structure response and fragility analyses. The seismic fragility parameters (e.g., Am and HCLPF) are expressed in terms of a scalar quantity (e.g., PGA and spectral acceleration at a specific frequency) and anchored to the RE response spectrum shape. The response spectrum shape is typically defined by a UHRS or a GMRS, which is derived from UHRS. The UHRS are developed by a probabilistic seismic hazard assessment (PSHA). For estimating the mean risk, it would be most rigorous to use the mean UHRS shape (rather than median, 84% NEP, etc.) (Salmon and Kennedy [101]); therefore, it is recommended that seismic 5-3 13633436 Seismic Demand input to the seismic response analyses be defined by the mean UHRS (or GMRS developed from mean UHRS). Typically, the mean, median, and 84% NEP UHRS shapes are similar such that it usually does not matter which UHRS shape is used. Figure 5-2 Reference earthquake 5.2.2 Nonlinear Effects in Structure Response Several phenomena are responsible for nonlinearity in the relationship between the input motion level and seismic response. The following examples are common nonlinear effects that should be considered when selecting the RE:  Structure properties: Structure degradation with increasing input levels (e.g., concrete cracking, bolt slippage, local yielding) typically reduces structure stiffness and dissipates energy (increased damping). Non-uniform degradation and local failures can also affect load distributions and mode shapes.  Gaps and contact interfaces: Gaps between adjacent buildings and components can close as input levels increase. Impact shock loads can affect ISRS and in-cabinet spectra, stresses, and functional performance (e.g., inducing contact chatter). Interaction between the buildings can also affect global response if significant inertia is transferred across the interface. Relative 5-4 13633436 Seismic Demand displacements between anchor points can take up slack and overload connections (e.g., support failure in commodities crossing building interfaces). Structures and components can slide or uplift from their underlying substrates, which can affect ISRS and equipment response.  Soil properties and soil failure modes: Nonlinearity in soil modulus and damping affects SSI as well as site response. Soil failures such as liquefaction and slope stability are inherently nonlinear and can significantly affect the ISRS and member forces in supported or adjacent structures.  Ground response spectrum shape: The frequency content of the UHRS changes with increasing input level. This is influenced by the magnitude and epicentral distance of the seismic events governing the hazard. In a typical SPRA, several of the above phenomena must be considered simultaneously, and therefore the nonlinear relationship between input and response can be complex. Some effects are relatively simple to predict such as higher structure damping reduces response. Other effects are less straightforward, such as how stiffness degradation or building pounding might affect ISRS shapes, and in turn, equipment response and fragilities. These effects should therefore be considered carefully when selecting the RE and when scaling RE responses to other input levels. 5.2.3 Determination of Reference Earthquake Structure response analyses in an SPRA are typically performed using a single input level and then linearly scaled to estimate responses at other levels. To minimize potential bias introduced by the linear approximation, the input level (i.e. the RE) should be selected carefully and subsequently validated. The recommended approach for selecting an RE is as follows: 1. Estimate the SCDF and SLERF based on the best available information prior to performing the SPRA. This estimate should consider the seismic design criteria, prior SPRA insights (site specific or from similar plants), and the latest site-specific seismic hazard estimate relative to prior hazard estimates. 2. Estimate a plant-level fragility for core damage and large early release. The plant-level fragility is the conditional probability of the damage state as a function of input level (e.g., the SCDF plant-level fragility is the conditional core damage probability (CCDP) as a function of input level). The fragility can be estimated directly based on past evaluations and the latest hazard, or it can be estimated by trial and error by convolving several candidate fragilities within a reasonable range of Am and β values to obtain the predicted SCDF and SLERF values from Step 1. Logarithmic standard deviations (β) for plant level fragilities are typically in the range of 0.3 to 0.5 in past SPRAs. 3. Convolve the plant level fragility or candidate fragilities with the site-specific seismic hazard. The convolution process is typically performed via numerical integration and is described in Appendix C to EPRI 3002000709 [5]. 5-5 13633436 Seismic Demand 4. Inspect the convolution results across the range of input levels considered and use this information to identify the input level that dominates risk. This can be approximated using one or more of the following three measures (Figure 5-3). – The level at which the cumulative risk (SCDF or SLERF) reaches 50% of the total. – The level where the risk density is maximized, defined as the risk contribution normalized to the width of the hazard bin (units are (yr-g)-1). – The level at which the slope of the plant-level fragility curve (also known as the conditional core damage probability, CCDP) is maximized. 3. These three alternative measures should be considered together with the sources of nonlinearity (Section 5.2.2) to decide which RE level would most effectively achieve the SPRA objectives. 5. Select a UHRS with an AEP that is reasonably aligned with the dominant input level. The UHRS selected is the RE. Conventionally, the RE is selected as either the 1E-4 or 1E-5 UHRS. If the dominant input level lies between the 1E-4 and 1E-5 UHRS, then the RE can instead be defined as the GMRS per ASCE/SEI 4-16 [10]. For very low-hazard and/or seismically robust plants, the dominant input level could be closer to the 1E-6 UHRS. If the input levels dominating SCDF and SLERF are significantly different, then a decision must be made whether the accuracy of the SCDF or SLERF results will be more important to the SPRA, and the RE can be selected accordingly. Figure 5-3 Three measures for identifying the dominant seismic input levels 5-6 13633436 Seismic Demand 5.2.4 Application of the Reference Earthquake The RE is used to inform the response analyses and fragility evaluations in an SPRA as follows:  Site response analysis is performed using strain-compatible soil properties to develop foundation input response spectra (FIRS). The soil properties should be compatible with the RE level of input.  Preliminary structure response analyses are performed to determine the structure stress levels, cracking, etc. The structure properties used to develop ISRS should be compatible with the stress levels/damage state associated with the RE level of input. The soil properties used in the SSI analysis should also be compatible with the RE. Section 5.3 elaborates on modeling of structure and soil properties consistent with the RE input level.  Gaps and contact interface effects as described in Section 5.2.2 should be evaluated to quantify their effects on the ISRS and important fragilities. Often, gap and contact interface effects can exhibit sharp nonlinearities (or “cliff-edge” effects) where response changes drastically with a slight increase in input level (e.g., buildings impact and impart shock loads). If cliff-edge effects occur at an input level close to the RE level, then they should be considered explicitly in the development of affected fragilities (e.g., develop nonlinear/ piecewise fragilities, as appropriate). If cliff-edge effects occur at input levels significantly different from the RE, then they may be accounted for with inelastic structural response factors as appropriate, as described in Section 5.5.1.3. 5.2.5 Validation of the Reference Earthquake Selection As initial SPRA results become available, the risk-dominant input level should be evaluated to assess whether it is reasonably aligned with the RE. The initial SCDF/SLERF estimates in Step 1 will necessarily depend on engineering judgment and should be validated and adjusted as necessary as the SPRA progresses. If it is anticipated that the final SPRA results will have significant misalignment between the dominant input level and the RE, then the effect of the misalignment should be evaluated. As an example, a sensitivity study could be performed in which the fragilities in the SPRA are adjusted to approximate how they would change if the RE were changed to align with the dominant input level. Then a decision can be made whether the effort required to adjust the RE and associated structure response analyses would be justified considering the results of the sensitivity study and the potential to significantly impact the SPRA insights (i.e., identification of risk-dominant accident sequences and SSCs). 5.2.6 Reference Earthquake Control Point The control point for the RE defines the location at the site where both the seismic hazard and the seismic fragilities used in the risk quantification are calculated. A consistent control point for the seismic hazard and fragilities is required to accurately calculate the seismic risk. The ground motion is applied at a control point that considers the configuration of the structure and the site soil/rock profile. To minimize bias in the risk quantification, the control point location should be selected where the dominant risk contributors are founded. Since this decision is made early in the SPRA before the dominant risk contributors are identified, judgement and experience are required for this selection. For SPRAs where most of the important structures are surface founded, the control point should be defined the free field ground surface at the site (Figure 5-4). 5-7 13633436 Seismic Demand For sites where the important structures are embedded in soil, it may be desirable to select the control point at the foundation elevation of those structures housing the most important SSCs in the SPRA (Figure 5-5). Figure 5-4 Example reference earthquake control point at the site surface Figure 5-5 Example reference earthquake control point at the foundation of a key structure 5-8 13633436 Seismic Demand 5.2.7 Alternatives to Reference Earthquake Approach The use of UHRS to characterize ground motion spectra has been the state of practice in the industry for many years. Recent developments in seismic hazard technology introduced alternative characterizations of ground motion spectra, e.g., conditional mean spectra (Baker [102]), conditional spectra (Lin, et al. [103]), and scenario spectra (Abrahamson and Al Atik [104]). The earthquake engineering community is exploring methodologies for hazard-consistent ground motion selection and risk computation framework methods built around these alternative spectra definitions. The seismic fragility approaches described in this report can largely be applied independent of the shape of the RE ground motion spectrum used in the seismic response analysis. However, consistency between the seismic hazard, response analysis, fragility evaluation, and risk integration methods are required to achieve reliable risk insights. EPRI 3002008098 [105] piloted an application of a methodology to develop a consistent seismic risk estimate using scenario-based characterization of earthquake ground motion spectra instead of one RE spectrum. A comparison of this methodology to the UHRS-based risk assessment for a case study NPP structure is presented in Talaat, et al. [106]. The fragility concepts provided in this guide can be used to implement this scenario-based methodology with limited adjustments such as keeping the variabilities for the “demand” and “capacity” of an SSC separate during the computation. The pilot implementation of the scenario-based methodology concluded that the required increase in the computational level of effort is significant, while the differences in the estimated seismic risk for the selected case study application were insignificant. An alternative methodology that moves further away from the RE concept and uses a combination of stratified sampling and Monte Carlo simulation was proposed in Huang, et al. [107]. Until a scientific community consensus is reached on an acceptable alternative approach, current practice of defining the RE using the UHRS or GMRS shape is recommended. 5.3 Evaluation of Median and 84th Percentile Seismic Demand To evaluate the probability of failure of structures or equipment, seismic structural responses are commonly needed. Structural response including element forces, story shears, and story drift is commonly needed to evaluate the fragility of building structures. ISRS are commonly needed to evaluate the seismic fragility of structure-supported equipment or components. This section discusses typical activities necessary for calculating seismic demands for fragility analysis, including structure modeling, SSI, ground motion incoherence (GMI), scaling of existing analytical results, deterministic seismic response analysis, and probabilistic seismic response analysis. Three seismic response evaluation methods may be used:  Scale existing design response or other past analyses  Perform new deterministic seismic response analyses  Perform new probabilistic seismic response analyses 5-9 13633436 Seismic Demand Scaling of existing analysis results is an approximate means to estimate median seismic demand. The means of conducting scaling of past analyses are described in Section 5.3.4. In general, if the RE ground motion spectra are significantly different from the previous ground motion from which responses are scaled, or if the structure is founded on a soil site, a new analysis is recommended. Scaled responses are typically generated early in a project to determine dominant risk contributors in a more expedient manner while waiting for new response analyses, which can take a significant amount of time. However, scaling does not provide information on the variability of demand. Generic variability is typically required to evaluate the seismic fragility when a scaling approach is followed. Deterministic seismic response requires more computational effort and provides a reasonable estimate of median seismic response and an estimate of variability in structure seismic response. Probabilistic seismic response requires the most computational effort and provides a good estimate of median seismic response and variability in structure seismic response. The means of performing new deterministic and probabilistic seismic response analyses are described in ASCE 4-98 [108], 4-16 [10], and in Sections 5.3.5 and 5.3.6, respectively. 5.3.1 Structure Modeling The seismic response of a nuclear structure can be determined by preparing a mathematical model of the structure and calculating its response to the prescribed seismic input (i.e., RE). The mass of the structure including self-weight, equipment, distribution systems, and effective live load and the stiffness of its components are typically modeled. To develop seismic structure responses and ISRS, a structural model capable of representing all response quantities of interest at all frequencies of interest is required. Detailed modeling guidance is provided in ASCE/SEI 4-16 [10] and is not repeated here. One consideration in modeling that warrants discussion is the use of lumped mass stick models (LMSM) or detailed finite element models (DFEM). Many of the original models used for the design of nuclear structures were LMSMs. If such models are used for seismic response analyses supporting fragility evaluations, they should be reviewed to determine their adequacy based on current knowledge of seismic behavior. Criteria for review of the adequacy of LMSMs are provided in ASCE/SEI 4-16 [10]. UHRS determined from current PSHAs tend to have more high-frequency content than when nuclear plants were designed. It is important that the LMSM be able to evaluate the response due to amplification at these higher frequencies. In particular, there should be sufficient dynamic degrees of freedom to represent all significant structure modes, and vertical slab flexibility and in-plane diaphragm flexibility should be captured if amplified response is expected. Recommendations are made in Section 6.6 for enhancing existing LMSMs to better capture these structure response features. 5-10 13633436 Seismic Demand 5.3.1.1 Structure Material Properties Material properties for normal weight concrete are typically defined as follows: E = Modulus of elasticity = (psi) f’cmin = Minimum specified concrete compressive strength at 28 days, in psi ν = Poisson’s ratio = 0.17 = Shear modulus = E/[2(1 + ν)] = Unit weight of reinforced concrete = 150 pcf G γ The modulus of elasticity conforms to Section 8.5.1 of ACI 318-08 [47]11. This equation uses the minimum specified 28-day compressive strength, rather than the median strength which is used in fragility evaluation (Section 4.3.1). Section C3.2.1.1 of ASCE/SEI 4-16 [10] provides an alternative equation for concrete having a minimum specified compressive strength greater than 6,000 psi. Section C3.2.1.1 of ASCE/SEI 4-16 [10] recommends the Poisson’s ratio listed above. The unit weight listed above is a representative value for normal weight reinforced concrete. This may not be appropriate for some concrete (e.g., high-density concrete). A representative unit weight of 145 pcf may be used for normal weight unreinforced concrete. Material properties for structural steel are commonly: E = ν = 29,000,000 psi = Poisson’s ratio = 0.30 G = γ Modulus of elasticity Shear modulus = E/[2(1 + ν)] = 11,200,000 psi = Unit weight = 490 pcf 5.3.1.2 Structure Stiffness Structure stiffnesses should be determined following Section 3.3 of ASCE/SEI 4-16 [10]. Best estimate stiffnesses of reinforced concrete components should be determined following 11 See Footnote 8 in Section 4.4. 5-11 13633436 Seismic Demand Table 3-2 of ASCE/SEI 4-16 [10], which is reproduced here as Table 5-1 with permission from ASCE. A reinforced concrete shear wall with a height-to-length ratio equal to or less than 1.5 is typically considered significantly cracked in shear when the average shear stress from an uncracked analysis exceeds 3(f’c)1/2. If the wall height-to-length ratio is equal to or greater than 2.0, the wall cracking strength is 2(f’c)1/2 and the coefficient varies linearly from 3 to 2 for height to length ratios between 1.5 and 2.0. These wall cracking stress limits are taken from Equation 21-7 of ACI 349-13 [46]. A reinforced concrete wall, floor, beam, or column is typically considered cracked in flexure when its flexural stress from an uncracked analysis exceeds 7.5(f’c)1/2. A reinforced concrete diaphragm is typically considered significantly cracked in shear when the average shear stress from an uncracked analysis exceeds 2(f’c)1/2 per Equation 21-9 of ACI 349-13 [46]. Judgment may be exercised when assessing whether cracking is sufficient to warrant stiffness reduction. Localized cracking that does not significantly affect overall structure seismic response and force distribution may not require stiffness reduction. Conversely, stiffness reduction may be appropriate for localized cracking that affects local structure response of significance to SSC fragilities. For seismic response analysis to develop ISRS for equipment seismic fragility evaluation, the best estimate model should represent the extent of cracking due to the RE. For seismic response analysis to calculate structure seismic demands for structure seismic fragility evaluation, the best estimate model should represent the extent of cracking at a ground motion level that initiates structure yielding. More recent testing reported by Rocks, Luna, and Whittaker [109] obtained initial stiffnesses of low aspect ratio reinforced concrete shear walls less than the uncracked stiffnesses recommended by ASCE/SEI 43-05 [10]. This potential difference has not yet been resolved by the industry for application in fragility analysis. Until an industry consensus is reached, current practice as noted above is recommended. 5-12 13633436 Seismic Demand Table 5-1 Effective stiffness of reinforced concrete structural components Structural Element Flexural Rigidity Shear Rigidity Axial Rigidity Nonprestressed bending elements, beams, out-of-plane response of walls, slabs, and diaphragms 0.5EcIg GcAw Prestressed bending elements EcIg GcAw Columns in compression 0.7EcIg GcAw EcAg Columns in tension 0.5EcIg GcAw EsAgs Uncracked EcIg GcAw EcAg Cracked 0.5EcIg 0.5GcAw EcAg In-plane bending and shear of walls and diaphragms where: Ig = gross moment of inertia Aw = web area Ag = gross area of the concrete section Ags = gross area of the reinforcing steel Ec = Modulus of Elasticity of concrete Es = Modulus of Elasticity of steel Gc = Shear modulus of concrete 5.3.1.3 Structure Mass The structure model typically includes the structure mass and the best estimate of non-structural mass likely to be concurrent with a significant seismic event. The masses of significant nonstructural items (e.g., diesel generators, large vessels) may be explicitly modeled as added nodal masses or increased element densities over the item’s footprint. The masses of miscellaneous non-structural commodities (e.g., piping, cable trays) may be represented as uniformly distributed masses assigned to elements modeling floors, roofs, and walls. The best estimates of these masses may be based on field walkdown observations. Section 3.4.2 of ASCE/SEI 4-16 [10] specifies minimum fractions of design live and snow loads to be included as structure mass. These criteria are intended for deterministic design analysis and may be used as guidance for development of models for application to SPRA but are not universally required. Caution should be exercised for equipment laydown areas, which are typically designed for very heavy live loads, and instances in which the design live loads were intended to account for permanent non-structural items already included in the structure mass noted above. 5-13 13633436 Seismic Demand 5.3.1.4 Structure Damping Table 5-6 in Section 5.4.2 lists median and minus-one logarithmic standard deviation structure damping values. Damping values are provided for two levels of structure seismic response: Response Level 1 and Response Level 2. Response Level 1 damping values are applicable to concrete structures which have not cracked significantly, and steel structures whose member demands are less than 50% of their strengths remote from member connections. Response Level 2 damping values are applicable to concrete structures which have cracked significantly, and steel structures whose member demands are between about 50% and 100% of their strengths remote from member connections and/or whose stresses in major load-resisting members are between about 50% and 100% of the yield capacity. For seismic response analysis to develop ISRS for equipment seismic fragility evaluation, the structure should be assigned the median damping value for the applicable response level resulting from the RE. The response level may be based on median structure seismic demands for the best estimate fixed-base or SSI model. Consideration of demands from lower and upper bound stiffness cases is not required. For seismic fragility evaluation of a structure whose inelastic energy absorption factor is explicitly calculated, the seismic response analysis should assign Response Level 2 damping to the best estimate structure model. Response Level 3 damping values recommended by ASCE/SEI 4-16 [10] may be applicable if the evaluation uses conservative representative inelastic energy absorption factors from Section 4.5.5. 5.3.2 Soil-Structure Interaction Nuclear buildings on soil sites may have significant SSI effects. Considerations for SSI include:  Kinematic Interaction: Effects of input reduction with depth, influence of embedment, and effect of ground motion incoherence represented by scattering matrices.  Inertial Interaction: Effects of soil stiffness and radiation damping on structure response for earthquake-strain compatible soil properties represented by impedance matrices. SSI seismic analyses of safety-related structures can be categorized as follows (ASCE/SEI 4-16 [10], DC/COL-ISG-017 [110]):  Surface-founded structures analyzed as a surface-founded structure  Embedded structures analyzed as a surface-founded structure at depth  Embedded structures analyzed as an embedded structure For surface-founded structures, the SSI seismic analysis is most straightforward. The free field ground motion at the ground surface or at an outcrop of competent material near the ground surface is used as the input motion to the SSI analysis. This motion is the RE defined at or near the ground surface that is output from the site PSHA. Some embedded structures can be analyzed as surface-founded because they are surrounded by adjacent buildings in close proximity or have exceedingly soft side soil. In this case, the structure will behave as a surface structure, but the input motion should be appropriate for the embedded foundation level such that the benefit of vertical spatial variation of ground motion is realized. 5-14 13633436 Seismic Demand For an embedded structure analyzed as an embedded structure, the input control motion should be defined as an outcrop motion at the foundation level or FIRS. SSI analysis software may permit the response analysis input motion to be applied at either the foundation level or at the ground surface. In either case, the SSI response analysis input motion must be consistent with the FIRS and the SSI soil profile modeling. ASCE/SEI 4-16 [10] and DC/COL-ISG-017 [110] contain guidance for developing ground motion input for SSI analyses of structures under various embedment conditions. 5.3.3 Ground Motion Incoherence GMI is horizontal spatial variation of ground motion. GMI occurs due to:  Random spatial variation: scattering of waves due to heterogeneous nature of the soil or rock at the locations of interest and along the propagation paths of the incident wave fields  Wave passage effects: systematic spatial variation due to difference in arrival times of seismic waves across a foundation Random spatial variation of ground motion can result in large reductions in foundation motion. Wave passage effects are typically not considered because they tend to produce minimal further reductions and require assignment of an apparent wave velocity that may be controversial and difficult to justify. Coherency functions that express random spatial variation as a function of frequency and separation distance have been developed in EPRI 1014101 [111] and EPRI 1015110 [112]. Coherency functions are available for rock and soil sites as illustrated in Figure 5-6. As shown in the figure:  Incoherence increases with frequency and separation distance.  Incoherence is greater for soil sites than for rock sites. These coherency functions have been implemented in SSI response computer programs as described in ASCE/SEI 4-16 [10]. Important points to note include:  The table for ground motion incoherence reductions in Chapter 3 of EPRI TR-103959 [2] and other references should no longer be used.  Methodology for evaluating GMI in SSI response computer programs and the coherency function for hard rock have been approved by the NRC (DC/COL-ISG-01 [113]). It is recommended that the hard rock coherency function be used for hard rock, soft rock, and most soil sites, and embedded foundations. For SPRA applications, the soil coherency function may be considered for site conditions with soil shear wave velocity between 600 and 950 fps over the top 100 ft beneath the structure foundation. It should be noted that the use of the soil coherency function will be subject to closer regulatory and peer review scrutiny than the use of the hard rock function.  A logarithmic standard deviation should be determined for structure response variability due to incoherence based on comparison of the coherent and incoherent responses (Section 5.4.5.1). 5-15 13633436 Seismic Demand Figure 5-6 Horizontal coherency functions from EPRI 1014101 [111] 5.3.4 Scaling of Existing Analytical Results Scaling of ISRS to account for different ground motions is considered a technically sound approach and has been used in previous SPRAs. Scaling approaches, where appropriate, require less effort than detailed SSI analyses for the new seismic hazard, facilitating the completion of the SPRA effort. Response scaling is based on:  previously developed structure responses (e.g., ISRS, structure forces),  shapes of the previous seismic input spectra (e.g., UHRS, SSE),  shapes of the new RE, and  structural natural frequencies, mode shapes, and participation factors. Example guidance on scaling methods is provided in Section 6.7 and Appendices M and N. Scaling can be used in developing ISRS for those cases where the new RE shape is approximately similar to the spectral shape previously used to generate the ISRS. An example of two response spectra with similar shapes is shown here in Figure 5-7. 5-16 13633436 Seismic Demand Figure 5-7 Example of ground response spectra that are similar Scaling of rock or soil sites will require a rigorous justification that demonstrates the validity of the scaling approach under several conditions:  The shape of the new hazard spectrum is not similar to the previous spectrum. An example of spectra that are not similar is shown in Figure 5-8, where the peak responses of the two spectra have significantly different frequencies.  The amplitudes of the old and new spectra are substantially different, and there is a possibility that they might produce nonlinear responses that would not be adequately estimated by linear scaling  The old analysis from which responses are scaled used obsolete or inaccurate analytical approaches or models These conditions and the effects they may have on response scaling are discussed further in Section 6.7. 5-17 13633436 Seismic Demand Figure 5-8 Example of ground response spectra that are not similar 5.3.5 Deterministic Seismic Response Analyses A deterministic method of calculating structure seismic response is presented in this section. The method presented in this section has been used in past SPRAs to reasonably account for the structure response variabilities discussed in Section 5.4. Alternative deterministic approaches could be developed to calculate seismic demands if the basis for such alternative methods is sufficiently justified. The deterministic approach recommended in this section uses sensitivity studies for several response analysis parameters to estimate the randomness and uncertainty in structure seismic response due to variability in the investigated parameters. In contrast to the probabilistic approach discussed in Section 5.3.6, parameter variations are not randomly selected but are set to selected deterministic values that provide insight into the probability distribution of possible seismic demand quantities. A well implemented deterministic response analysis method can produce results approaching the accuracy of a probabilistic analysis. However, to achieve this level of accuracy, the number of response simulations required by the deterministic method will not be significantly fewer than probabilistic analysis. Despite being less refined for only slight computational savings, a deterministic approach may be preferred by engineers familiar with traditional analysis procedures for structural design. Additionally, the sensitivity study basis of a deterministic methodology provides a set of results that can be more easily verified. Since each simulation changes a single response parameter, gross errors in the analysis may be detected more easily. The deterministic seismic response analysis approach recommended in this section can be adapted to account for the effects of variability in the flowing structure response variables:  Structure frequency  SSI 5-18 13633436 Seismic Demand  GMI  Structure damping  Time-history phasing Soil stiffness and structure frequency typically have the most significant effects on fragility variability because variations of these parameters can affect both shape and amplitude of ISRS. Structure frequency uncertainty is predominantly due to structure stiffness uncertainty, while variations in other parameters such as mass and geometry generally have lesser effects on frequency. Therefore, structure frequency variations are typically modeled as stiffness variations. Soil and structure stiffness cases are designated as follows for the deterministic analysis methodology recommended here: Table 5-2 Deterministic soil and structure stiffness case designations Analysis Case Designation Soil Stiffness Case Structure Stiffness Case BE/BE Best estimate Best estimate LB/BE Lower bound Best estimate UB/BE Upper bound Best estimate BE/LB Best estimate Lower bound BE/UB Best estimate Upper bound The best emstimate (BE) soil profile should use median soil shear modulus and damping values. Since soil stiffness and damping are inversely correlated, the upper bound (UB) soil case should pair plus-one standard deviation soil shear modulus values with minus-one standard deviation material damping values. Similarly, the lower bound (LB) soil profile should pair minus-one standard deviation soil shear modulus values with plus-one standard deviation material damping values. The inverse correlation introduced into the soil damping and stiffness properties is consistent with the guidance for probabilistic analysis in Section 5.3.6. In contrast, structure damping is typically not varied in deterministic response analysis. The UB and LB soil profiles should ideally be developed using site specific COVs for soil shear modulus and damping for each soil layer. If these COVs are not available, a reasonable generic soil shear modulus COV can be selected between 0.5 and 1.0. If a generic variation in soil shear modulus is used, median damping values can be used for all three soil profiles because variability in material damping will minimally affect the structure response relative to the radiation damping variability captured by shifting the shear modulus values. Each of the soil/structure stiffness models should be analyzed for each of the selected earthquake acceleration time-history sets (5.4.4.1). Separate time-history analyses may be performed for each of the directional components of a given set, with the resulting response quantities (e.g., ISRS, peak structure demands) due to the three components combined by the SRSS or 100-40-40 methods permitted by Section 4.2.2 of ASCE/SEI 4-16 [10]. Alternatively, the three directional components may be input simultaneously if they satisfy the statistical independence requirement of Section 2.6.2 of ASCE/SEI 4-16 [10]. 5-19 13633436 Seismic Demand For each of the five soil/structure stiffness models, the median value of a given response parameter (e.g., ISRS, structural element force) with respect to time-history phasing variability is estimated as the average of the responses across the earthquake acceleration time-history sets. The result is one set of response quantities from each of these five soil/structure stiffness analyses. These results are used to estimate median and 84% NEP responses associated with variability in structure and soil properties separately. Then logarithmic standard deviations are calculated separately for uncertainty in soil and structure properties. When the equipment fragility evaluation uses clipped ISRS (e.g., fragility evaluation by earthquake or test experience), median and 84% NEP clipped spectra can be calculated by methods discussed in Section 6.5. 5.3.5.1 Soil Property Variation Median and 84% NEP response quantities considering only variability in soil properties are estimated as follows:  Median response quantities are obtained by averaging the responses from the three variations of soil properties, (BE/BE, LB/BE, and UB/BE). Valleys between peaks of the three averaged ISRS should be filled to obtain realistic median ISRS (Figure 5-9).  84% NEP response quantities are obtained by enveloping the responses from the three cases. Valleys between peaks of the three analysis cases are filled.  The logarithmic standard deviation for structure response due to uncertainty in soil properties is obtained from the median and 84% seismic response quantities as follows: βSSI,U = Logarithmic standard deviation for soil property variability = ln (ZPA84% / ZPAm) using BE/BE, UB/BE, and LB/BE analysis cases ZPAm = Median structure ZPA considering only soil property variation ZPA84% = 84% NEP structure ZPA considering only soil property variation The ZPA comparisons noted above should be made from response analysis results obtained using the BE (median) structure frequencies. Soil property variability is associated exclusively with uncertainty. The method for calculating variability differs for structure and equipment fragilities:  For structure fragilities, the logarithmic standard deviation should be calculated at a range of locations whose inertial responses are significant to seismic demands affecting the structure failure mode of concern. A value representative of variabilities calculated should be selected.  In equipment fragility analyses, spectral accelerations at significant frequencies of equipment response should be compared rather than the ZPAs noted in the equations above. 5-20 13633436 Seismic Demand Figure 5-9 Filling valleys between peaks of deterministic analysis cases 5.3.5.2 Structure Property Variation Structure response analyses are performed for the three structure stiffness cases using the BE soil stiffness: BE/BE, BE/LB, and BE/UB. The UB and LB structure frequencies are typically selected at plus- and minus-one standard deviations from the BE structure frequencies. Median and 84% NEP response quantities considering only variability in structure stiffness are estimated as follows:  Median response quantities are obtained by averaging the responses from these three cases. Valleys between peaks of the three analysis cases are filled.  84% NEP response quantities are obtained by enveloping the responses from the three cases. Valleys between peaks of the three analysis cases are filled.  The logarithmic standard deviation for structure response due to uncertainty in structure stiffness is obtained from the median and 84% seismic response quantities. βfs,U = Logarithmic standard deviation for structure frequency variability = ln (ZPA84% / ZPAm) using BE/BE, BE/LB, and BE/UB analysis cases ZPAm = Median structure ZPA considering only structure property variation ZPA84% = 84% NEP structure ZPA considering only structure property variation 5-21 13633436 Seismic Demand Structure frequency variability is due entirely to uncertainty. As noted in Section 5.3.5.1 for soil property variation, the logarithmic standard deviation for structure property variation should be calculated differently for structure and equipment fragilities. Section 5.3.5.1 details the differences. Current seismic design criteria in ASCE/SEI 4-16 [10] only require analysis using a BE structure model, with peaks of the resulting ISRS broadened by ±15% on frequency. This approach can produce a reasonable estimate of 84% NEP responses for input ground response spectra which have essentially constant spectral accelerations near the significant structure frequencies. This simplified approach should therefore only be used under these special conditions. For input ground spectra whose spectral accelerations vary significantly near the significant structure frequencies, a better approach is to analyze for three structure stiffness cases as considered above. 5.3.5.3 Median and 84% NEP Response The median seismic response quantity for seismic fragility evaluation is the average of: • Median response considering only variability in soil properties, and • Median response considering only variability in structure stiffness. As such, the response quantity obtained for the BE/BE case is effectively assigned twice the weight of the other cases. Similarly, the 84% NEP seismic response quantity for seismic fragility evaluation is the envelope of: • 84% NEP response considering only variability in soil properties, and • 84% NEP response considering only variability in structure stiffness. The overall logarithmic standard deviation for structure response is obtained by combining the logarithmic standard deviations due to soil properties and structure stiffness by SRSS following the SOV approach.b For structures subject to fixed base response analysis and structures with negligible SSI effects, the median and 84% NEP structure ZPAs are obtained from seismic response analyses considering variation in structure stiffness only as described in Section 5.3.5.2. Conversely, if the contribution of structure flexibility to flexibility of the overall soil-structure system is small, a small nominal logarithmic standard deviation may be estimated for structure stiffness variability using judgment. 5.3.5.4 Variability in Other Structure Response Parameters Variability in structure response due to other parameters may be estimated by re-running the SSI analysis for the BE/BE case. For example, to determine the variability in structure response due to uncertainty in structure damping, the BE/BE SSI model is re-analyzed using the 16% NEP structure damping value. The logarithmic standard deviation for structure response due to uncertainty in structure damping is obtained from the response parameters for median structure damping and 16% NEP structure damping. Alternatively, the overall logarithmic standard deviation can be estimated based on the 84% NEP and median responses calculated per the guidance above. Both deterministic methods for estimating 84% NEP response and variability will produce reasonable results. b 5-22 13633436 Seismic Demand Alternatively, if there is another parameter that significantly influences structure response amplitude and variability, it can be treated in the same manner as soil property and structure stiffness following the approach above. The median seismic response is then the average of median responses considering variability in soil properties, variability in structure stiffness, and variability in the third parameter. The overall logarithmic standard deviation for structure response is obtained by combining the logarithmic standard deviations due to soil properties, structure stiffness, and other structure response parameters by SRSS following the SOV fragility approach described in Section 3.3. If multiple parameters are influential, probabilistic response analysis could involve fewer total analyses and may be more economical. 5.3.6 Probabilistic Seismic Response Analyses Probabilistic seismic response analysis is the preferred method to evaluate median seismic response of the structure and of systems and components within the structure along with the variability in that seismic response. This approach explicitly accounts for variability in:  earthquake input ground motion (horizontal and vertical response)  soil properties (shear modulus, material damping)  structure modeling (frequency and damping)  time-history phasing Lower overall variability can be obtained from probabilistic seismic response analyses compared to deterministic seismic response analysis or from the scaling method. Probabilistic seismic analysis involves multiple simulations of response evaluation considering multiple input ground motion time-histories and the distribution of soil shear modulus and damping, and the distribution of the structure’s frequencies and damping. The analysis technique commonly employed is stratified sampling of the probability distributions that model variability in soil, structure, and input motion. The combination of parameters can be determined by an experimental design employing LHS. The LHS approach has the advantage of being able to capture the parameters defining the probability distribution of the response of interest with fewer simulations than the Monte Carlo simulation method. Outputs of these analyses are commonly: probabilistic ISRS; probabilistic seismic forces and moments in structural elements; structure displacements; and story drifts. 5-23 13633436 Seismic Demand The objective of LHS is to evaluate individual factors, Fi, with a median value, Fm, of 1.0 and variability of  that uniformly covers the range of probability from 0 to 1 in N increments. Section 5.5.5.2 of ASCE/SEI 4-16 [10] specifies a minimum value of N = 30 when LHS is used. If the probability distribution is lognormal, LN(Fm, ), then the N samples, Fi, can be formed using the following equation:  i = 1 to N -1 = inverse normal (Gaussian) distribution function rndi = random number between 0 and 1 (different for each i) N = 30 for this example F where: F e Eq. 5-1 Equation 5-1 gives the N values of F for probabilities ranging from 0 to 1 as shown in Figure 5-10. For this example, N equals 30 and 1/N equals 0.033. The median value of structure and soil stiffness and damping are scaled by Fi with the corresponding  to be used in the thirty or more simulations. 1.00 0.90 0.80 Probability 0.70 0.60 0.50 0.40 0.30 0.20 0.10 0.00 ‐1.5 ‐1 ‐0.5 0 0.5 1 1.5 ln (F) F simulation Lognormal Figure 5-10 Thirty scale factors, F, for median of 1.0 and  of 0.35 by Latin hypercube sampling 5-24 13633436 Seismic Demand ASCE/SEI 4-16 [10] and NUREG/CR-2015 [114] describe an approach that uses LHS to assemble parameter combinations for probabilistic SSI analysis. Random variables in the analysis include the structure frequency and damping, soil/rock stiffness and damping, and the input ground motion time histories. In this approach, a median-centered structural model and the median soil/ ock profile are established. Input to the LHS analysis includes the number of simulations, the variability of the structure frequency and damping, the variability of the soil/rock stiffness and damping, and thirty earthquake time series sets. The probability distributions of the structure frequency, structural damping, soil stiffness, and soil damping are defined by scale factors with median values of 1.0 and associated coefficients of variation or logarithmic standard deviations, . Thirty or more SSI response analyses are performed, and statistics are computed for the response quantities of interest. Stiffness and damping properties of the structure are typically considered to be lognormally distributed. Characteristics of their probability distributions are described below:  The cumulative distribution function (CDF) of structural stiffness should be based on the best estimate structural stiffness and COV.  The CDF of structural damping should be based on the best estimate structural damping and COV. The best estimate stiffness and damping should be compatible with the expected stress levels in the structure when subjected to the input motion. Initially, the response stress levels in the structure are unknown. Preliminary analyses should be performed to assess whether uncracked or cracked concrete stiffness is most appropriate. In addition, structural damping should be selected based on the stress level reached in the majority of earthquake-resisting structural elements. Using this approach, structure damping and stiffness variables should be treated as uncorrelated in the sampling. Common coefficients of variation of structural stiffness and damping are 0.30 and 0.35, respectively. These values are based on variability for structure frequency and damping recommended in Section 5.5 of ASCE/SEI 4-16 [10]. These values for variability are based on past seismic fragility evaluations. The statistical soil profile properties should be based on the statistical geotechnical data for the plant site. The soil profiles used for probabilistic SSI should be consistent with the strain-iterated profiles simulating non-linear soil behavior. Using the generated soil data and probability distributions, thirty or more simulated strain-compatible soil profiles should be developed. Section 5.5.3 of ASCE/SEI 4-16 [10] specifies that either a resampling approach or simulation approach may be used to develop the set of N simulated soil profiles (with N ≥ 30). The resampling approach consists of randomly sampling N simulated soil profiles from the strain-compatible soil profiles developed in the probabilistic site response analysis. The statistics of the sampled soil profiles (emphasizing soil shear wave velocity) should be consistent with the total suite of probabilistic site response soil profiles. The simulation approach consists of developing N simulated strain-compatible soil profiles from probability distributions consistent with geotechnical data for the plant site, or with coefficients of variation of the soil properties obtained from the relationship between the median and plus- and minus-one standard deviation values assuming a lognormal distribution. N simulated 5-25 13633436 Seismic Demand scale factors for strain-compatible shear modulus and strain-compatible soil damping can be created for the site using LHS. These scale factors can be applied as constants to layers of the median shear modulus and damping profiles to form N sets that exhibit the desired variability. When using LHS for analyses with two variables, it is typical to form simulation cases as the random combination of the two variables. However, both shear modulus and damping are strain-dependent, with the former decreasing and latter increasing with increased shear strain. Therefore, a general inverse correlation should be maintained between stiffness and damping. For probabilistic seismic response analyses, thirty or more sets of earthquake acceleration time histories compatible with the RE can be used as seismic input. For probabilistic analysis, it is acceptable to use either modified recorded time histories, or, if linear analysis is performed, synthetic time histories with random phasing. Time histories should be developed from the guidance in ASCE/SEI 4-16 [10]. The horizontal component-to-component directional variability represents the randomness in the spectral amplitudes of the two horizontal components relative to the target geomean horizontal UHRS. This random variability is supported by empirical data. Methods are available to generate the ensemble of time histories, including the horizontal component-to-component variability. When this is done, no further modification to the horizontal motions is required. One approach for incorporating horizontal component-to-component variability is discussed in the following paragraph [10]. Variation of the horizontal components with respect to the geomean target response spectrum may be included with a horizontal directionality factor, FH. For each of the N acceleration time series, Horizontal Component 1 is scaled by FH and Horizontal Component 2 is scaled by (1/FH). FH is treated as a lognormally distributed variable with a median value of 1.0 and a logarithmic standard deviation βHDP,R of 0.18 (Section 5.4.1.2). A set of N values of FH can be selected and randomly assigned to the N acceleration time series. The vertical directional variability may be included using an approach similar to that for the horizontal components [10]. A vertical directional factor, FV, is defined. The N vertical acceleration time series are scaled by factor FV. The generation of N random values of FV is based on a median value of 1.0 and a logarithmic standard deviation of 0.25 (Section 5.4.1.3). Figure 5-11 shows an example of acceleration time-histories that have response spectra matching the RE. Figure 5-12 shows an example of the resulting response spectra of the same time histories scaled to include horizontal direction variability. 5-26 13633436 Seismic Demand Figure 5-11 Example response spectra from thirty sets of time histories matching the RE Figure 5-12 Example response spectra from thirty sets of time histories including horizontal direction variability 5-27 13633436 Seismic Demand As an example, the probabilistic approach for seismic response analysis may consist of performing thirty simulations as summarized by the following points:  Use thirty three-component free-field input acceleration time histories matching the RE and including directional variability as described above.  Vary structure stiffness and damping.  Vary soil stiffness and damping.  For all analyses, the structure model should include the best estimate of structure mass and mass of permanently attached non-structural items.  Perform thirty SSI seismic response analyses.  Evaluate response statistics in terms of median and 84th percentile response. Using the stratified sampling and the LHS method, the cumulative probability distribution function of each random variable can be stratified into thirty or more probability bins, in which each bin corresponds to an incremental probability of 1/N (where N equals 30 in this example). A parameter value can be determined for each bin of each random variable. The parameters for a single response simulation can be assigned by randomly selecting a value for each of the base parameters (e.g., structure stiffness, structure damping, soil/rock stiffness, soil/rock damping, and the input ground motion). The full set of response simulations can be assembled by repeating this sampling process, without replacement, thirty times until the values in all probability bins are exhausted. With these data including thirty or more sets of structure stiffness and damping, inversely correlated soil stiffness and damping, and input time histories including directional component variability, thirty seismic response analyses can be performed. An example of resulting ISRS is shown in Figure 5-13. Figure 5-13 Example ISRS from probabilistic seismic response analyses 5-28 13633436 Seismic Demand Randomness and uncertainty in the response variables that are not sampled in the LHS should be included in the fragility calculation by other means. For example, LHS typically does not include any sampling to account for model fidelity (mode shape) uncertainty. This and other variabilities not sampled in LHS can be estimated using the guidance in this report and combined with the other response variabilities by SRSS. Additional probabilistic response analyses are typically performed to separate out the random variability in structure response. Random variability is typically considered to be that due to the earthquake ground motion. Consequently, probabilistic response analyses to determine random variability typically use median SSI models (i.e., median soil profile and structure properties). When the equipment fragility evaluation uses clipped ISRS (e.g., fragility evaluation by earthquake or test experience), the combined variability for structure response and clipping can be determined following one or more of the methods discussed in Section 6.5. 5.4 Response Variables for Structure Fragilities The structure response factor, FRS, as defined by Equations 3-17 through 3-19, is the product of a series of factors for the variables identified in Table 5-3. The logarithmic standard deviations for randomness and uncertainty are the SRSS of applicable logarithmic standard deviations for the structure response variables. If median-centered seismic structure response is determined by either deterministic seismic response analyses as described in Section 5.3.5 or probabilistic seismic response analyses as described in Section 5.3.6, the corresponding median structure response factor is 1.0. The deterministic and probabilistic structure seismic response analyses performed following Sections 5.3.5 and 5.3.6, respectively, result in median and 84% seismic demands. Guidance on estimation of structure response variability for response determined by deterministic seismic response analyses is provided in Sections 5.4.1 to 5.4.6. Guidance on estimation of structure response variability for response determined by probabilistic seismic response analyses is provided in Section 5.4.7. In Sections 5.4.1 to 5.4.6, variabilities are evaluated from computed seismic response following the deterministic approach described in Section 5.3.5. Response quantities are expressed as structure response, R, or ISRS quantities, Sa and ZPA, as determined from the deterministic seismic response analyses. In Section 5.4, fragilities of structures are considered such that certain structure response variabilities for structure fragilities are based on structure ZPAs or spectral accelerations at dominant structure frequencies. For equipment fragilities as addressed in Section 5.5, in-structure spectral accelerations at the median equipment frequency and damping should be used instead. For deterministic seismic response analyses, structure and soil stiffness variabilities are considered by conducting analyses for LB, BE, and UB soil and structure stiffness cases. In the discussion of Sections 5.4.1 to 5.4.6, LB/BE designation for an analysis case means that LB soil stiffness and BE structure stiffness is considered. The designation for these analysis cases is soil stiffness case/structure stiffness case. 5-29 13633436 Seismic Demand Table 5-3 Response variables for structure fragility evaluation Structure Response Category Structure Response Variable Variable Symbol Spectral shape FSA  5.4.1.1 Horizontal direction peak response variability FHDPR  5.4.1.2 Vertical to horizontal (V/H) variability FV  5.4.1.3 Damping Fδs  5.4.2 Frequency Ffs  5.4.3.1 Model fidelity FMs  5.4.3.2 Torsional coupling FTC  5.4.3.3 Time-history FTH   5.4.4.1 Mode combination FMCs  Ground motion incoherence FGMI  5.4.5.1 Soil-structure interaction analysis FSSI  5.4.5.2 Vertical spatial variation FVSV   5.4.5.3 Earthquake component combination FECCs  Ground motion Damping Modeling Structure response phasing Foundation-structure interaction Earthquake component combination Variability βR βU Report Sections 5.4.4.2 5.4.6 5.4.1 Ground Motion As discussed in Section 5.2.3, the RE ground motion is specified to be the GMRS or UHRS at a selected AEP and the associated FIRS. Correction of the structure seismic response for conservatism or unconservatism in the earthquake ground motion is generally unnecessary. Sources of ground motion variability include the following:  Earthquake response spectrum shape  Horizontal direction random variability  Vertical to horizontal ratio (V/H) variability 5.4.1.1 Earthquake Response Spectrum Shape In many early SPRAs, average PGA was used as the ground motion parameter, and the NUREG/CR-0098 [115] median curve was assumed to be the reference response spectrum shape for each horizontal direction. However, it was noted that there was uncertainty in the earthquake signature which resulted in the variability of the smooth response spectrum shape. To account for 5-30 13633436 Seismic Demand variability between (1) the smooth reference response spectrum shape that was assumed in early SPRAs and (2) response spectra shapes more characteristic of natural earthquakes, a spectral shape uncertainty was specified to be included in the structure fragility. In addition, it was noted that, in general, real earthquakes would have spectra different from the assumed smooth reference spectra used in the early SPRAs. Peaks and valleys in real response spectra meant that a future earthquake response spectrum, with the same ground motion parameter, would have spectral ordinates which were either higher or lower than the smooth reference spectrum. This peak and valley variability was due to randomness and was also specified to be included in the structure fragility. Typically, this response spectrum peak and valley variability is included in the development of the seismic hazard estimates. If GMRS or UHRS are used as the RE, the uncertainty in spectral shape is also included in the seismic hazard estimate. Thus, the current recommendation is not to include peak and valley variability or spectral shape uncertainty in fragility estimates since this would result in double counting of the variability in structure response. Modern SPRAs typically use GMRS or UHRS to define the RE. Therefore, the median response spectrum shape variable, FSA, should be 1.0, with no variability for either randomness or uncertainty. The fragility analyst should be aware of the effects of peak and valley variability when reviewing older fragility or CDFM capacity analyses. If an older fragility calculation is updated with the intention of using it in a modern SPRA, it may be necessary to remove peak and variability from the results. Appendix H provides a detailed historical discussion of the issues associated with including peak and valley variability in fragilities. 5.4.1.2 Horizontal Direction Peak Response Variability The horizontal GMRS and FIRS for the RE represent the geomean of the response spectra in the two horizontal directions. Consequently, the magnitude of the ground motion in any arbitrary direction may be higher or lower than the geomean response. This directional variability in the ground motion input leads to variability in the maximum horizontal response of the SSC of interest. The horizontal direction peak response variability accounts for this variability arising from the directional variability in the ground motion input. The horizontal direction peak response variability is all randomness. Watson-Lamprey and Boore [116] report logarithmic standard deviations for the ratio of horizontal spectral acceleration in any arbitrary direction to the geomean spectral acceleration for the two horizontal components. These represent the component-to-component variability in the horizontal earthquake ground motions, and vary from 0.16 to 0.23 over periods between 0 sec and 1 sec. Contribution of horizontal direction peak response variability to structure response variability is dependent on the relative contributions of the two horizontal ground motion components to the seismic demand of interest. Table 5-4 lists applicable median response factors, FHDPRm, for four commonly encountered cases. Development of these values for the four listed cases is presented in Appendix I. The values listed in Table 5-4 are based on a component-to-component variability of 0.18, which is considered appropriate for most nuclear SSCs. In practice, a site-specific determination for the component-to-component variability should be made considering the dominant frequencies of interest for the SSCs considered in the SPRA. 5-31 13633436 Seismic Demand Table 5-5 provides factors appropriate for CDFM evaluations. The development of these factors is also presented in Appendix I. Horizontal direction random variability need not be considered when seismic demand is not strongly influenced by horizontal response of the structure or component. When vertical response dominates the seismic demand, variability in the vertical-to-horizontal ratio of response (Section 5.4.1.3) should be considered. Table 5-4 Median horizontal direction peak response factors and logarithmic standard deviations Case Case Example Median Factor, FHDPRm Logarithmic Standard Deviation, βHDP,R 1 Specific Direction Response Average Direction Response In-plane shear wall response1 1.0 0.18 2 Co-linear Vector Response Average Direction Response Tension response of anchor bolt2 1.06 0.07 3 General Vector Response Average Direction Response Shear response of anchor bolt2 1.10 0.11 4 Axisymmetric Largest Direction Response Average Direction Response Compression in flat bottom tank 1.133 0.13 Notes: 1. 2. 3. In-plane wall shear due primarily to one horizontal ground motion component. Equal anchor bolt tensions or shears resulting from each of the two horizontal ground motion components. Controlling demand is due to the larger of the two horizontal ground motion components. The ratio of this demand to that due to the geomean of the two components is 1.13. Table 5-5 Horizontal direction peak response factors for CDFM Evaluations Case Case CDFM HDPR Factor SSCs at Grade on Rock-supported Structures/Foundations Other SSCs 1 Specific Direction Response Average Direction Response 1.12 1.05 2 Co-linear Vector Response Average Direction Response 1.09 1.07 3 General Vector Response Average Direction Response 1.16 1.12 4 Axisymmetric Largest Direction Response Average Direction Response 1.21 1.16 5-32 13633436 Seismic Demand 5.4.1.3 Vertical Response Variability In many early SPRAs, the vertical input at the ground level was assumed to be two-thirds of the horizontal input. In modern PSHAs, the vertical GMRS or UHRS are generated from the horizontal UHRS by site-specific V/H ratios. A logarithmic standard deviation of 0.25 is estimated for this random variability when site-specific V/H ratios are used. Variability in structure response due to variability in earthquake ground motion is associated exclusively with randomness. The median value of the response factor, FV, is 1.0. The median value of FV should be used to calculate vertical seismic demand for fragilities. Vertical response variability need not be considered when seismic demand is not strongly influenced by vertical response of the structure or component. When horizontal response dominates the seismic demand, variability in the horizontal response (Section 5.4.1.2) should be considered. 5.4.2 Structure Damping Table 5-6 lists median and minus-one logarithmic standard deviation structure damping values. The median damping values are based on Section 3.2.2 of ASCE/SEI 4-16 [10]. The minus-one logarithmic standard deviation damping values generally correspond to a logarithmic standard deviation of about 0.35 on structure damping. The logarithmic standard deviation represents variability in the damping value itself and not variability in response due to variability in damping. Table 5-6 Structure damping values Response Level12 1 2 Structure Type Damping (% of Critical Damping) Median -1σ Welded and friction-bolted steel structures and pre-stressed concrete structures 2 1.5 Bearing-bolted steel structures 4 2.8 Reinforced concrete structures 4 2.8 Welded and friction-bolted steel structures 4 2.8 Bearing-bolted steel structures 7 5 Reinforced concrete structures 7 5 Pre-stressed concrete structures 5 3.5 To calculate median seismic demands for use in the SOV fragility approach, structure response analyses should use the median damping values listed in Table 5-6. The corresponding median response factor for structure damping, Fδs is 1.0. 12 Response levels are defined in ASCE/SEI 4-16 [10] and discussed further in Section 5.3.1.4. 5-33 13633436 Seismic Demand For structures subject to fixed base response analysis and structures with negligible SSI effects, variability in structure response due to variability in structure damping, βδs, may be estimated as follows: βδs = = Logarithmic standard deviation for structure damping variability Eq. 5-2 ln [Sa (ξ-1σ) / Sa (ξm)] where: Sa (ξm) = RE spectral acceleration for median structure damping at the significant structure frequency(ies) Sa (ξ-1σ) = RE spectral acceleration for minus-one logarithmic standard deviation structure damping at the significant structure frequency(ies) Structure damping variability is associated exclusively with uncertainty. If structure seismic response is dominated by a single mode, the damping variability may be based on spectral accelerations at the associated modal frequency. If structure response results from multiple modes, the damping variability may be approximated as a weighted average reflecting relative contributions from these modes. For structures with SSI effects, variability in structure response due to variability in structure damping, βδs, may be estimated as follows: βδs = ln [ZPA (ξ-1σ) / ZPA (ξm)] Eq. 5-3 ZPA (ξm) = Structure ZPA from the SSI analysis using best estimate soil and structure properties ZPA (ξ-1σ) = Structure ZPA from an SSI analysis modified to use the minus-one logarithmic standard deviation structure damping with best estimate soil and structure properties Best estimate soil and structure properties are discussed in Section 5.3.5. The logarithmic standard deviations for variability in structure damping are expected to vary from location-to-location within the structure. A representative value may be selected from a range of locations whose inertial responses are significant to seismic demands on the controlling structural component. To calculate 84% NEP seismic demands for use in the hybrid fragility approach, structure response analyses should use the median damping values listed in Table 5-6, as discussed in Section 3.4.1. 5-34 13633436 Seismic Demand 5.4.3 Structure Modeling 5.4.3.1 Structure Frequency In general, it is expected that the analytical modeling of structures is median-centered without any conservative bias. Considerations for creating median centered structure models are discussed in Section 5.3.1. The primary effect of uncertainty in the material properties used in the structure model is to shift the response frequencies exhibited by the model. A mediancentered model therefore captures median estimates of structure frequencies, and the median value of the structure response factor for uncertainty in structure frequency, Ffs, should be 1.0. The variability of the structure mass term is relatively small compared to the stiffness term. Therefore, uncertainty in structure frequency is generally directly attributable to uncertainty in structure stiffness. Comparisons of calculated and measured periods for various steel and concrete high-rise buildings at small amplitude vibrations are discussed in the ASCE Working Group on Quantification of Uncertainties [36]. Haviland [117] indicates that the COV for the ratio of measured to calculated periods, for steel and concrete building types, is about 0.33. This is also confirmed by results reported in Hadjian, et al. [118] and judgment in Kennedy, et al. [119]. This suggests for NPP-type steel or concrete structures, where detailed analysis and accurate models are used, that the logarithmic standard deviation for frequency is about 0.15 based on shear wall tests to account for construction materials and connections. As models become cruder the value can be up to about 0.35 for approximate models. Note that these β values are for structure frequency itself and not for variability in response due to variability in frequency. The corresponding uncertainty in structure response depends on the RE spectral shape and sensitivity of the structure response to a shift in frequency. One deterministic response analysis approach is recommended in Section 5.3.5, and guidance is provided in that section for calculating the logarithmic standard deviation for uncertainty in structure frequency, βfs,U. The deterministic response analysis method described in Section 5.3.5 captures variability in seismic response due to structure frequency uncertainty by conducting response analysis with three different structure models. If an alternative deterministic response analysis method is used with only a single structure model, variability should still be included to account for uncertainty in structure frequency. This variability should be estimated on a structure-specific basis considering the structure frequencies and the spectral shape of the RE; it is associated exclusively with uncertainty. 5.4.3.2 Model Fidelity In addition to uncertainty in structure frequency, modeling variability should include uncertainty in how well the model captures realistic dynamic response of the structure (i.e., the model fidelity). The degree of additional modeling uncertainty depends on the complexity of the structure and detail of the model. Based on experience and judgment, the logarithmic standard deviation, βMs,U, for additional model fidelity uncertainty is estimated to be in the range from 0.05 to 0.15. The former value is applicable to structures whose responses are dominated by fundamental modes with simple mode shapes, or structures with strong SSI effects whose structure flexibility has small contribution to flexibility of the overall soil-structure system. The latter value is applicable to more complex structures analyzed by simpler models. In all 5-35 13633436 Seismic Demand cases, models should use best estimates of structure configurations and material properties and capture realistic structure behavior. Therefore, the median response factor for structure modeling fidelity, FMs, should be 1.0. This variability is not traditionally included as one of the sampled variables in probabilistic response analysis. As such, it is recommended that it be included in the fragility by other means, such as by SRSS combining a variability determined according to the guidance above with the overall structure response variability obtained by probabilistic response analysis. 5.4.3.3 Torsional Coupling Nuclear safety-related structures are typically analyzed using three-dimensional models that should appropriately capture torsional response. Although containment structures may be analyzed by simple LMSMs, they are essentially axisymmetric structures that should not exhibit significant torsional response. Inclusion of variability due to torsional coupling should be unnecessary for fragility calculations when reasonably detailed structure models are used. For most cases, the median value of the response factor for torsional coupling uncertainty, FTC, should be 1.0. Similarly, 84% seismic demands for CDFM capacity analyses should be calculated using structure models that realistically capture torsional coupling, but additional conservatism need not be introduced for uncertainty in torsional response. It is not advised that LMSMs be used to calculate structure response if they do not appropriately model the relationships between mass and shear centers at the model degrees of freedom. If such a model is used, it may be necessary to use a median response factor, FTC, greater than 1.0 to reflect increased median seismic demand due to torsional effects. In this case, the included logarithmic standard deviation for uncertainty in torsional coupling, βTC should be consistent with the median factor. Since torsion will always increase the peak response except at the center of rigidity, the probability of a factor less than 1.0 should be very small. As a rule of thumb, the 1.0 value should be set at least to the minus-two standard deviation level. For example, if the median factor is judged to be 1.10, then βTC should not be larger than 0.05. 5.4.4 Structure Response Phasing Unique characteristics of individual earthquakes whose ground motions match the same target spectra result in random variations in structural response. This response variability is due to random phasing in the response of the individual structural modes. A time-history analysis, conducted using a different earthquake record but with the same ground motion parameter value (e.g., PGA), will result in different phasing between the Fourier components and hence different peak response. When time-history analysis is used to calculate the seismic demand for a fragility, variability in phasing response can be accounted for by running multiple time histories, as discussed in Section 5.4.4.1. When response spectrum analysis is used to calculate the seismic demand, variability in phasing response can be accounted for by the method used to combine seismic demand contributions of individual structural modes, as discussed in Section 5.4.4.2. 5.4.4.1 Time-History Phasing It is desirable to use at least five sets of earthquake acceleration time histories compatible with the RE as seismic input. It is preferable to use modified recorded time histories when five sets of time histories are used. Recorded time histories should be modified following the guidance in 5-36 13633436 Seismic Demand ASCE/SEI 4-16 [10]. A recommended deterministic method of response analysis using five time-history sets is described in Section 5.3.5. When five sets of time histories are used, median phasing response can be estimated by averaging response quantities from the five analyses. This estimate of median phasing response is realistic with minimal uncertainty, such that the logarithmic standard deviation for uncertainty in the time-history analysis, βTH,U, can be taken as zero, and the median response factor for time-history phasing, FTH, is 1.0. When five time-history sets are used, the logarithmic standard deviation for time-history phasing randomness, βTH,R, can be estimated from ZPAs as follows: βTH,R = Logarithmic standard deviation for time-history variability Eq. 5-4 = (1 / Z) ln(ZPAMAX/ ZPAm) ZPAm = Median ZPA from the five time-history sets ZPAMAX = Maximum ZPA from the five time-history sets assumed to lie at the 90% NEP level Z = Number of logarithmic standard deviations judged to separate the median and maximum ZPAs (Z = 1.282 for median to 90% NEP). For the deterministic methodology discussed in Section 5.3.5, the ZPA comparisons noted above should be made from response analysis results obtained using the BE (median) soil profile and BE structure frequencies. The logarithmic standard deviation should be calculated at a range of locations whose inertial responses are significant to seismic demands affecting the failure mode of concern. A value representative of variabilities calculated may be selected. It is acceptable to use a single input time-history set (consisting of two horizontal components and one vertical component of motion) for deterministic seismic response analyses, although using more time histories will better estimate realistic seismic demands with less variability. It is preferable to use synthetic time histories with random phasing when one set of time histories is used. If a single time history is used, it should be closely matched to the target spectrum, and the power spectral density spectrum must be free of significant gaps in energy near frequencies that are important to risk-significant fragilities. Synthetic time history development and conditioning should be performed in accordance with the criteria in ASCE/SEI 4-16 [10]. Furthermore, if a single time history is used, there is epistemic uncertainty associated with the selected single time-history set’s ability to predict realistic maximum seismic demand for the RE. Although there is uncertainty in the estimate of seismic demand, the estimate is not conservatively or unconservatively biased, and therefore the median response factor for timehistory phasing, FTH, is 1.0. If a single time-history set is used for structure seismic response analysis, logarithmic standard deviations for randomness and uncertainty in the time-history analysis should both be included. Reasonable estimates of the randomness and uncertainty are βTH,R = 0.15 and βTH,U = 0.15, respectively. 5-37 13633436 Seismic Demand 5.4.4.2 Mode Combination Phasing When response spectrum analysis is used to calculate seismic demands, contributions of individual modal responses to the total demand must be combined. Analysis software typically presents the user with several mode combination method options. Acceptable modal combination methods are discussed in Regulatory Guide 1.92 [120] and ASCE/SEI 4-16 [10]. Gupta and Lindley-Yow methods [120, 10] are considered median-centered for modes with both periodic and rigid response components. Other acceptable modal combination methods in Regulatory Guide 1.92 [120] and ASCE/SEI 4-16 [10], including the SRSS method for uncorrelated widely spaced frequencies and algebraic summation of rigid response, may also be considered mediancentered. When these methods are used, the median response factor for mode combination phasing is FMC = 1.0. A reasonable logarithmic standard deviation for randomness in mode combination phasing is MC,R = 0.15 for structures with multiple important modes (Kennedy, et al. [119]). For simple structures, such as a containment building that responds primarily in a single mode, a MC,R value of 0.05 is reasonable. The variability due to mode combination phasing is associated entirely with randomness. The transformation between randomness in the mode combination per se and its effect on response is included in these values. Alternatively, when individual modal contributions to a particular response are known, the absolute sum of the modal values is judged to be two to three standard deviations above the median response. If there are only two modes that contribute to the response, then two standard deviations should be used. If there are several modes contributing, then three standard deviations are appropriate. With this assumption the MC,R value on response can be estimated directly by the following equation: = (1 / Z) [ln(Rmc,abs / R mc,m)] Rmc,abs = Response based on absolute sum of modal contributions Rmc,m = Median response using median-centered modal contribution method Z = Number of standard deviations (i.e., 2 to 3) MC,R Eq. 5-5 where: This calculation would in general have to be performed for each response quantity (e.g., stress, displacement, ISRS) considered for a particular structure. If responses are reported mode-bymode, then this procedure can be used. 5.4.5 Foundation-Structure Interaction The interaction between the structure and the supporting foundation includes consideration of:  GMI  SSI analysis  Vertical spatial variation (VSV) of ground motion 5-38 13633436 Seismic Demand In general, all three foundation considerations affect the response of structures at soil sites, while only GMI has a significant effect at stiff rock sites. Incoherence due to foundation size effects, deconvolution of motion at soil sites, and radiation and damping effects at soil sites reduce the response of structures compared to a fixed-base analysis of surface-supported structures; whereas frequency shifting due to uncertainty in the rock or soil properties may either reduce or increase responses. 5.4.5.1 Ground Motion Incoherence At any instant in time, the input motion at every point under the structure foundation is not the same. For massive rigid foundations common for nuclear structures the overall high-frequency motion is reduced as waves cancel each other across the foundation/soil interface. The reductions referred to here as GMI effects are due to non-vertically propagating shear waves and reflections and refractions causing incoherence as the earthquake waves pass through the underlying heterogeneous geologic media. Ground motion definition spectra, such as typical UHRS spectra, represent the elastic response of an oscillator due to the motion expected at a single point on the horizontal free surface of a half-space media. Actual ground motion, however, has horizontal spatial variation due to wave scattering effects and statistical incoherence of motion in the frequency domain. Considering the motion of two points on the surface with a given horizontal separation distance, measurements have indicated that the two motions can be separated into frequency-dependent in-phase components, or coherent motion, and frequency-dependent components with random phasing, or incoherent motion. A large rigid foundation mat or a rigid multi-cell box-type concrete structure can only achieve coherent motion over the characteristic dimension of its base. The random or incoherent motion has a net zero average over the characteristic dimension of the foundation. Further, observational data indicates that the incoherent portion of the surface ground motion increases in the higher frequency range resulting in reduction in input at higher frequencies for structures with large plan dimension. Ground motion incoherence may be directly accounted for in SSI analysis as described in Section 5.3.4. When GMI is directly accounted for in the response analysis results, the median response factor for GMI, FGMI, is 1.0. The logarithmic standard deviation for uncertainty in GMI, βGMI,U, may be estimated by comparison of structure ZPAs from two SSI analyses, one which includes GMI effects (incoherent SSI analysis) and one which does not (coherent SSI analysis). βGMI,U = (1 / 2.5) ln(ZPACOH / ZPAINC) ZPACOH = Structure ZPA from the coherent SSI analysis ZPAINC = Structure ZPA from the incoherent SSI analysis Eq. 5-6 For the deterministic methodology discussed in Section 5.3.5, the ZPA comparisons noted above should be made from response analysis results obtained using the BE (median) soil profile and BE structure frequencies. 5-39 13633436 Seismic Demand Responses due to the coherent SSI analysis are estimated to be 2.5 logarithmic standard deviations above the responses due to the incoherent SSI analysis. The logarithmic standard deviation should be calculated at a range of locations whose inertial loads contribute to the structure failure mode of concern. A value representative of variabilities calculated should be selected. Ground motion incoherence variability is associated exclusively with uncertainty. 5.4.5.2 Soil Structure Interaction Uncertainty in the median soil properties used in SSI analysis contributes to variability in the structure seismic response. When a rigorous deterministic or probabilistic response analysis methodology is followed, median structure response is calculated without conservative or unconservative bias relative to the soil properties. Therefore, the corresponding median response factor for uncertainty in SSI analysis, FSSI is 1.0. One recommended deterministic response analysis approach is described in Section 5.3.5, and recommendations are made in that section for calculating the logarithmic standard deviation for uncertainty in SSI analysis, βSSI,U. The deterministic response analysis method described in Section 5.3.5 captures variability in seismic response due to soil property uncertainty by conducting SSI analysis with three different soil profile models. If an alternative deterministic response analysis method is used with only a single soil profile model, additional variability should be included to account for uncertainty in SSI modeling and analysis. This variability should be estimated on a structure-specific basis considering the significance of SSI effects on structure response. It is associated exclusively with uncertainty. Probabilistic response analysis, as described in Section 5.3.6, should include soil stiffness and damping as variables in the LHS to capture variability due to uncertainty in SSI analysis. Fixed-base response analysis is realistic for some structures. There is no structure response variability due to uncertainty in the soil properties if fixed-base analysis is justified. Some embedded structures may be approximately analyzed as being surface-founded. Guidance for this modeling decision is provided in Section 5.3.2; if this guidance is followed, then any conservatism introduced by this modeling is small and may be disregarded. 5.4.5.3 Vertical Spatial Variation FIRS constituting seismic input to embedded structures should be developed by current state of the art methods. Response variability due to VSV of ground motion may consequently be excluded. 5.4.6 Earthquake Component Combination Seismic demands on structural components due to three ground motion components should be combined by the SRSS method permitted by ASCE/SEI 4-16 [10], which is considered mediancentered. In some instances, seismic demands on structural components subjected to force interactions (e.g., concurrent axial force and biaxial bending, anchor bolt shear) may be determined by the 100-40-40 method, which is also permitted by ASCE/SEI 4-16 [10]. The 100-40-40 method is slightly conservative in comparison to the SRSS method, particularly for 5-40 13633436 Seismic Demand cases when the responses are not equal. However, the degree of conservatism is small and may be neglected in the fragility evaluation. For either method, the median value of the response factor for earthquake component combination uncertainty is FECCs = 1.0. The 100-40-40 rule requires that 100% of the response in one direction be combined with 40% of the responses from the other two directions. In concept, three analyses are required where 100% of the response is assumed for each direction, one at a time. The combination that gives the highest response is used. Usually the analyst can determine by inspection which direction will control without performing all three calculations. Whether the SRSS or 100-40-40 rule is used, a randomness ECCs,R for response needs to be included in the fragility analysis since the actual response will be higher or lower. In past SPRAs, it has been assumed that the absolute sum of the three directional responses is two to three standard deviations above the median. Similar to Equation 5-5 above for combining modal responses, the logarithmic standard deviation for earthquake component combination randomness, βECCs,R, is given by the following equation: = (1 / Z) [ln(Rabs/Rm)] Rabs = Response based on absolute sum of direction contributions Rm = Median response based on SRSS or 100-40-40 combination of direction contributions Z = Number of standard deviations associated with absolute sum response ECCs,R Eq. 5-7 where: Based on the following assumptions, it is always conservative (overestimates ECCs,R) for the number of standard deviations, Z, in Equation 5-7 to be equal to 2.3 (99% NEP):  Less than approximately 1 in 1,000 chance that the responses from all three earthquake components occur at the same time.  Less than approximately 1 in 100 chance that the two largest responses occur at the same time, whichever controls. However, if the lowest two responses are each at least 20% of the largest, then Z equal to 3.0 can be used. An upper bound value of ECCs,R equal to 0.18 can always be used but may be excessively conservative for cases where the response is primarily from a single direction. A typical value of ECCs,R for building response due to the effects of earthquake component combination is 0.15 (NUREG/CR-1706 [121]). 5.4.7 Structure Response Variability from Probabilistic Analysis A probabilistic approach to structure response analysis can be used as a rigorous method for quantifying several of the response variables discussed in Sections 5.4.1 through 5.4.6. One recommended probabilistic approach used in past SPRAs is discussed in Section 5.3.6. The recommended method uses LHS to run a suite of several response analyses with randomly varied parameters. The probabilistic method discussed in Section 5.3.6 includes a specific set of structure response variables in the LHS. Seismic demands are based on the median structure 5-41 13633436 Seismic Demand response calculated by the probabilistic approach, so the median values of the included response variables should be 1.0. Logarithmic standard deviations calculated from the probabilistic method account for the aggregate variability due to all the variables included in the LHS. Therefore, individual logarithmic standard deviations should not be assigned for the included structure response variables. If some important structure response variables are omitted from the LHS, then it may be necessary to account for additional variability in the seismic response due to the randomness or uncertainty of the omitted variables. In this case, the additional variability may be calculated following the methods discussed in Sections 5.4.1 through 5.4.6 as if the variables were part of a deterministic analysis with care taken not to double count variabilities. Probabilistic seismic response analysis is discussed in Section 5.3.6. The median capacity factor is based on the median structure seismic demand from the probabilistic seismic response analysis (Section 4). The median structure response factor is consequently 1.0. For structure fragility evaluation, the logarithmic standard deviation for response variability is based on the logarithmic standard deviation for the ZPA from ISRS. When all structural response variabilities are considered, the logarithmic standard deviation for response variability, RS,C, is a composite variability, consisting of both randomness and uncertainty. RS,C = Logarithmic standard deviation for structure response variability Eq. 5-8 = ln (ZPA84% / ZPAm) ZPAm = Median structure ZPA from probabilistic analysis simulations that consider all variabilities ZPA84% = 84% NEP structure ZPA from probabilistic analysis simulations that consider all variabilities The logarithmic standard deviation should be calculated at a range of locations whose inertial responses are significant to seismic demands affecting the structure failure mode of concern, and a representative value should be selected. The composite logarithmic standard deviation for structure response is composed of logarithmic standard deviations for randomness and uncertainty as follows: βRS,C RS,R RS,U β2RS,R β2RS,U Eq. 5-9 = Logarithmic standard deviation for randomness of structure response = Logarithmic standard deviation for uncertainty of structure response 5-42 13633436 Seismic Demand Additional probabilistic response analyses are typically performed to separate out the random variability in structure response. Random variability is typically considered to be that due to the earthquake ground motion. Consequently, probabilistic response analyses to determine random variability typically use median SSI models (i.e., median soil profile and structure properties). The logarithmic standard deviation for response variability due to randomness only, RS,R, can be determined in a similar way to RS,C: RS,R = ln (ZPA84%,R / ZPAm,R) ZPAm,R = Median structure ZPA from probabilistic analysis simulations that consider only random variables ZPA84%,R = Eq. 5-10 84% NEP structure ZPA from probabilistic analysis simulations that consider only random variables The uncertainty in structure response may then be determined as follows: βRS,U β2RS,C -β2RS,R Eq. 5-11 5.5 Response Variables for Equipment Fragilities In performing fragility analysis for equipment, variability in structure response, equipment response, and equipment capacity need to be considered. Table 5-7 identifies the basic structure response variables to consider in equipment fragility analysis. The table is very similar to Table 5-3 since equipment fragility evaluation and structure fragility evaluation consider many of the same structure response factors. Section 5.5.1 describes some differences in the methodology for calculating structure response variables in the context of equipment fragility vs. structure fragility evaluation. Table 5-8 identifies the basic equipment response variables for equipment fragility evaluation based on analysis. Section 5.5.2 provides guidance for calculating these equipment response variables. For equipment fragility evaluation based on test, the fragility methodology does not include an equipment response factor (Equation 3-19). Nonetheless, the methodology includes consideration of several concepts related to equipment response such as spectral peak clipping and cabinet amplification. Section 5.5.3 outlines the methods, concepts, and parameters related to equipment response that are considered in equipment fragility evaluation based on test. 5-43 13633436 Seismic Demand Table 5-7 Structure response variables for equipment fragility evaluation Structure Response Category Structure Response Variable Ground motion Variable Symbol Variability βR βU Report Sections Spectral shape FSA  5.4.1.1 Horizontal direction peak response variability FHDPR  5.4.1.2 Vertical to horizontal (V/H) variability FV  5.4.1.3 Damping Damping Fδs  5.4.2 Modeling Frequency Ffs  5.4.3.1 Model fidelity FMs  5.4.3.2 Torsional coupling FTC  5.4.3.3 Time-history FTH   5.4.4.1 Mode combination FMCs  Ground motion incoherence FGMI  5.4.5.1 Soil-structure interaction analysis FSSI  5.4.5.2 Vertical spatial variation FVSV   5.4.5.3 Inelastic structure response FIR   5.5.1.3 Variability Report Sections Structure response phasing Foundation-structure interaction Inelastic structure response 5.4.4.2 Table 5-8 Equipment response variables for equipment fragility evaluation by analysis Equipment Response Category Equipment Response Variable Variable Symbol Qualification method FQM Equipment in-structure spectral shape FSS Equipment damping Equipment damping Equipment modeling Qualification method Equipment mode combination Earthquake component combination 5-44 13633436 βR βU  5.5.2.1  5.5.2.1 Fδe  5.5.2.2 Frequency Ffe  5.5.2.3 Model fidelity FMe  5.5.2.3 Mode combination FMCe  5.5.2.4 Earthquake component combination FECCe  5.5.2.5  Seismic Demand 5.5.1 Structure Response for Equipment Fragilities Table 5-7 lists the structure response variables for equipment fragility evaluation. These variables are appropriate for equipment at elevated locations within a building where there is significant influence from the dynamic response of the structure. For equipment located supported at or near the foundation of rock-founded structures, the contribution of structure response to the equipment demand is due primarily to the ground motion, time-history simulation, and incoherence variables only. At sites where SSI is significant, the other structure response parameters (e.g., damping, frequency, mode shape, mode combination, and SSI) can also be important for equipment supported on building foundations. The structure response variables are essentially the same whether considering structure failure modes (Table 5-3) or equipment failure modes (Table 5-7). However, there are several important differences, which are discussed in this section. 5.5.1.1 Structure Frequency The structure frequency variable has two effects on equipment demands. First, the structure frequency influences the general level of motion. This is due to the amplitude and shape of the ground response spectrum at the median damping of the foundation-structure system. If the structure frequency is different from the median value, then the structure forces and the ISRS will be affected. As a first order approximation, the ISRS are either higher or lower due to the change in the ground spectral acceleration corresponding to the fundamental frequency of the structure. Second, a shift in the structure frequency causes a similar shift in frequency content of the ISRS. Both considerations must be addressed in the equipment fragility analysis. Figure 5-14 shows schematically the effect of a shift in the fundamental frequency of a structure on the corresponding ISRS. Both amplitude and frequency shifting of the ISRS are demonstrated in this figure. The shifted and amplified spectra should be compared to the median spectra at the equipment fundamental frequency to estimate variability due to structure frequency uncertainty. 5-45 13633436 Seismic Demand Figure 5-14 Effects of shift in structure fundamental frequency on in-structure response spectra 5.5.1.2 Earthquake Component Combination The earthquake component combination variable is included in Table 5-8 for equipment response rather than Table 5-7 for structure response. Typically, the best approach in a fragility analysis is to combine the effects from the three seismic input directions in the final response parameter of interest. In this case, the equipment response parameter corresponding to the selected failure mode is of primary importance. Typically, ISRS are the basis for input to the equipment fragility analysis. The most general inputs needed are ISRS in the three perpendicular directions corresponding to the three earthquake components. This means nine sets of response spectra (three directions of response for each earthquake component) are required. However, in most cases there are only three sets of spectra, one set corresponding to each of the three perpendicular earthquake directions. In the more general case where nine sets of spectra are developed, they can be combined by SRSS or 100-40-40 as described for structure failure modes in Section 5.4.6. If the earthquake directions are combined in the structure response analysis (e.g., by simultaneous application during a time-history analysis), then the analyst must take care to avoid double-counting the effects of earthquake component combination in the analysis of structure and equipment responses. 5-46 13633436 Seismic Demand 5.5.1.3 Inelastic Structure Response Factor One additional variable has been added to the structure response list in Table 5-7 as compared to Table 5-3. This variable is the inelastic structure response factor, FIR. In a fragility analysis for structures, inelastic energy absorption is accounted for in the structure capacity. For an equipment fragility, the issue is whether the structure is responding in the nonlinear range at ground motion levels corresponding to equipment failure. If the structure is in the elastic range, then the median value for FIR is unity and the variability is zero. As a structure becomes nonlinear, the frequency of the motion typically shifts downward and the high-frequency spectral response either increases or decreases (NUREG/CR-3805 [26]). Depending on the relationship between the fundamental frequency of the item of equipment and the structure frequencies, the input to the equipment may either increase or decrease as the structure goes nonlinear. This also was observed in the studies reported in Sewell, et al. (John A. Blume Earthquake Engineering Center [122]) where the different parameters that influence ISRS due to inelastic structure response are discussed. Based on NUREG/CR-3805 [26], a composite logarithmic standard deviation of 0.20 was judged to adequately account for the possibility of higher response for high-frequency components at higher elevations if nonlinear structure response is significant. For equipment mounted at or above the structure’s center of gravity (c.g.), variability in seismic demand due to variability in nonlinear structure response can be accounted for by logarithmic standard deviations for randomness and uncertainty of βIR,R = 0.17 and βIR,U = 0.10, respectively. For equipment mounted at the basemat, values of βIR,R and βIR,U equal to 0 can be used since there would be little or no influence from the altered structure response. Linear interpolation of the  values between the c.g. and the basemat can be assumed in the analysis. For lower frequency components, the change due to frequency shifting downward should be addressed on a case-by-case basis. Except in very simple cases, the approximate approach described here will not provide highly reliable estimates of the effects of inelastic structural response. A nonlinear analysis can be performed to develop ISRS directly in lieu of these approximations. Nonlinear analysis is generally not warranted, except in critical cases where the SSC is expected to significantly affect the SPRA results. Therefore, this approximate approach should only be used for failure modes whose capacities are significantly different from the RE. As such, if the RE is aligned well with the dominant input level (Section 5.2), then the approximate approach will not be used for failure modes that dominate risk. 5-47 13633436 Seismic Demand 5.5.1.4 Probabilistic Structure Response Analysis When the equipment fragility evaluation uses unclipped ISRS (e.g., fragility evaluation by analysis), the structure response variability is determined in essentially the same manner as structure fragility evaluation (Section 5.4.7), except that the composite logarithmic standard deviation for structure response is based on spectral accelerations at the significant equipment frequencies. RS,C = = Sam = Sa84% = Composite logarithmic standard deviation for structure response for equipment fragility evaluation ln(Sa84% / Sam) from probabilistic analysis simulations Eq. 5-12 Median spectral acceleration at equipment median frequency and median equipment damping 84% NEP spectral acceleration at equipment median frequency and median equipment damping Logarithmic standard deviations for randomness and uncertainty of structure response should be determined as indicated in Section 5.4.7, except that the logarithmic standard deviation due to randomness in structure response is based on spectral accelerations at the significant equipment frequencies. There may be instances in which the median and 84% NEP peak spectral accelerations occur at slightly different frequencies. When the equipment seismic fragility is based on the median peak spectral acceleration, the structure response variability may be determined using the 84% NEP peak spectral acceleration so long as the frequencies at which these spectral peaks occur are not significantly different. Section 6.5 provides further guidance on determining the structure response variability when the equipment fragility evaluation uses clipped ISRS (e.g., fragility evaluation by testing). 5.5.2 Equipment Response for Fragility Based on Analysis The equipment response factor, FRE (Section 3.3.1), is the ratio of equipment response calculated in the design (or whatever response analysis is being used to estimate equipment response for the current application) to the realistic equipment response; both responses being calculated for the same floor spectra input. FRE is the factor of safety inherent in the computation of equipment response. It depends upon the response characteristics of the equipment and is influenced by some of the variables listed under Equation 3-18. These variables differ according to the seismic qualification procedure. For equipment evaluated by analysis, the important variables that influence response and variability are as follows:  Qualification method  Damping  Modeling – Equipment frequency – Equipment model fidelity (mode shape) 5-48 13633436 Seismic Demand  Equipment response phasing (mode combination)  Earthquake component combination Each of these variables is discussed in the following sections. 5.5.2.1 Qualification Method Fragility analysis can be performed without using results from prior seismic evaluations, in which case the new analysis would identify the critical failure modes for a component using realistic response analysis procedures and material properties. Using this approach, the qualification method median equipment response factor, FQM, is unity. Variability in the new analysis is addressed for each important response variable in Sections 5.5.2.2 to 5.5.2.5, and the variability, βQM,U, is zero. Alternatively, the results of an existing analysis (e.g., for SSE design) can be used as a starting point for a fragility analysis. By knowing the design rules that were used to perform the response analysis, the conservatism in the original analysis can be factored out to produce a median-centered response. The equipment may have been analyzed by dynamic analysis or by using a conservative static coefficient. The design spectra will have been peak-broadened and smoothed and may have been based on very conservative damping. When the component capacity is expressed in terms of a factor times the design input (e.g., SSE PGA of 0.20g) the qualification method median factor is equal to the ratio of the existing analysis response to the estimated median-centered response. For example, in an SSE design, the equivalent static coefficient method may have been used where the peak spectral acceleration was multiplied by a factor of 1.5 to account for multiple modes and applied to the component mass at the c.g. The median qualification method factor should remove the conservative 1.5 factor and any additional conservatism that was introduced to the design by using the peak spectral acceleration. Because of uncertainties in this process of relating the design response to median response, an associated logarithmic standard deviation, βQM,U, needs to be estimated and included in the fragility analysis. Application of any existing equipment analyses (e.g., design, seismic margin assessment, fragility) is presented as follows. As mentioned above, if a new analysis is conducted using the median ISRS for seismic demand, the median qualification method factor is 1.0 and the uncertainty is zero. If the equipment is flexible and was analyzed by dynamic analysis, the median qualification method factor, FQM, is the ratio of the design spectral acceleration at design damping to the median spectral acceleration of the RE ISRS at median damping for the dominant equipment frequency(ies). Median equipment damping values are discussed in Section 5.5.2.2. FQM = SaD (ξD) / Sam (ξm) SaD (ξD) = Design spectral acceleration at design equipment damping for the dominant equipment frequency(ies) Sam (ξm) = Median spectral acceleration at median equipment damping for the dominant equipment frequency(ies) Eq. 5-13 5-49 13633436 Seismic Demand If a static coefficient was used for equipment qualification, the median qualification method factor is the ratio of the static coefficient to the median spectral acceleration at median damping for the dominant equipment frequency(ies). FQM = AD / Sam (ξm) AD = Design static coefficient Eq. 5-14 The uncertainty in the estimated frequency can be included in either the qualification method uncertainty or frequency uncertainty, but not both. Since the frequency estimate is made in the determination of the median qualification factor, inclusion in the former might be preferred. In the case of valves that were evaluated by a static coefficient, the frequency of the piping system in which the valves are located will determine the appropriate median demand. Valves are typically evaluated by static analysis. The specifications vary and are interpreted differently by the valve suppliers. A static load is typically specified in each direction. On earlier NPPs, the ECC design criterion was to combine the worst horizontal response with the vertical response by absolute sum. Later NPPs used the SRSS combination of three earthquake components. The vendors typically used a vector of two or three directions and applied it in the worst direction for the valve. In some cases, a static test was conducted by applying the vector acceleration to the valve operator with the piping at each end of the valve fixed. The qualification procedure for the different vendors needs to be identified to determine the critical load direction and magnitude for the valve qualification and the corresponding median qualification factor. Additional variability in equipment demand can be introduced to an equipment fragility in some cases when it is developed by scaling a design analysis or when a crude scaling approach is used to calculate seismic demand. In these cases, it may be necessary to correct for conservatism or unconservatism associated with the shape of the equipment demand spectra. Example cases where this may be necessary are when equipment demand is developed by scaling design spectra that have been smoothed or broadened, and when a simple scaling approach is used for spectra with dissimilar shapes. Generally, these methods are not recommended and will return crude results. If they are used, however, the additional uncertainty introduced to the fragility analysis should be included. The median value of the equipment response factor for uncertainty in spectral scaling, FSS, and the associated logarithmic standard deviation, βSS,U, should both be estimated by the fragility analyst on a case-by-case basis. Section 6.7.2 provides detailed guidance for estimating equipment response based on prior analyses. 5-50 13633436 Seismic Demand 5.5.2.2 Equipment Damping Recommended median and 84% EP equipment damping values are listed in Table 5-9. Table 5-9 Equipment damping values Equipment Type Median Damping 84% EP Damping Electrical cabinets, mechanical equipment (including horizontal tanks and heat exchangersa) 5% 3.5% Massive, low stressed components 3% 2% Instrument racks 3% 2% Metal flat bottom tanksa (impulsive mode) 5% 3% Piping 5% 3.5% Cable traysb 15% 10% Ducting Welded Companion Angle Pocket lock 4% 7% 10% 3% 5% 7% Notes: a. Damping values for metal tanks and heat exchangers assume some nonlinear behavior e.g., bolt yielding. b. The damping value provided for cable trays assumes there is no significant fireproofing present. Cable trays with fireproofing have lower damping. For equipment fragilities developed from new analysis of seismic capacity and demand, the median spectral acceleration for median equipment damping is used to determine seismic demand. For equipment fragilities developed by scaling design calculations, the median spectral acceleration for median equipment damping is used in determination of the median qualification method factor (Section 5.5.2.1). The median equipment damping factor, Fδe, in both cases is consequently 1.0. The variability in response due to damping probably includes contributions from both randomness and uncertainty; however, it is difficult to determine the exact split, and the results should not be significantly affected if damping variability is assumed to be all uncertainty. The logarithmic standard deviation for uncertainty in equipment damping is determined following an approach similar to structure damping in Section 5.4.2 but using the in-structure spectral acceleration. βδe,U = ln [Sa (ξ-1σ) / Sa (ξm)] Sa (ξm) = Sa (ξ-1σ) = In-structure spectral acceleration for median equipment damping at the significant equipment frequency(ies) In-structure spectral acceleration for minus-one logarithmic standard deviation equipment damping at the significant equipment frequency(ies) Eq. 5-15 5-51 13633436 Seismic Demand 5.5.2.3 Equipment Modeling Equipment modeling factors and variability include equipment frequency and model fidelity. Frequency Variability in equipment response due to uncertainty in equipment frequency, βfe,U, may be estimated as follows: βfe,U = ln (Sa84% / Sam) Sam = Median spectral acceleration for median equipment damping equal to the average spectral acceleration over the frequency range of f1σ. Sa84% = 84% NEP spectral acceleration for median equipment damping equal to the largest spectral acceleration over the frequency range of f1σ. f1σ = Plus- or minus-one logarithmic standard deviation equipment frequency fm = Median equipment frequency βfe,U = Logarithmic standard deviation for equipment frequency Eq. 5-16 For equipment analyzed by new or existing dynamic analysis, the variability in the equipment frequency is estimated. It is judged that the logarithmic standard deviation for equipment frequency is typically between 0.10 and 0.30. The former is applicable to simple equipment analyzed by accurate models, and the latter is applicable to more complex equipment analyzed by simpler models. Alternatively, a more rigorous approach may be used. This more rigorous approach consists of probabilistically varying the frequency about the median frequency value to obtain a distribution of Sa values and fitting a lognormal model to this distribution. For equipment fragilities based on scaling design analysis using a static coefficient, frequency uncertainty should be included in the equipment qualification method uncertainty (Section 5.5.2.1) and not double-counted. Fidelity (Mode Shape) A logarithmic standard deviation for equipment response due to uncertainty in the fidelity of equipment modeling (mode shape) is typically in the range of βMe,U = 0.05 to 0.15. The smaller value is applicable to simple equipment whose response is dominated by a single mode, which should be the case for most components. The larger value is applicable to more complex equipment. This variability should be zero for rigid components. 5.5.2.4 Equipment Response Phasing (Mode Combination) The discussion in Section 5.4.4 for the effects of seismic response phasing is also appropriate for equipment. Most frequently, equipment will be analyzed by response spectrum analysis, and therefore the random variability in the response phasing will be accounted for by the equipment mode combination factor, FMCe, and associated logarithmic standard deviation, βMCe,R. The median value of FMCe should be 1.0 if a median-centered method of mode combination is used to 5-52 13633436 Seismic Demand calculate the equipment demand. If time-history modal superposition analysis is conducted for the equipment, then the above random variability for mode combination is equally applicable to represent the variability of response to different time histories. When the individual equipment modal responses are not available, a MCe,R value ranging from 0.05 to 0.15 can be used. The smaller value is appropriate for most components analyzed by dynamic analysis which have few modes of significance. The larger value is appropriate for piping systems with multiple modes of response. When modal responses are available, the procedure used for structures (discussed in Section 5.4.4.2) can be used to calculate the MCe,R value for equipment response. When equipment seismic demand is calculated by time-history analysis, variability in equipment response phasing should be accounted for by the procedure described for structures in Section 5.4.4.1. 5.5.2.5 Earthquake Component Combination The median ECC factor should be based on the individual component characteristics and using a SRSS or 100-40-40 combination of earthquake directions. If loads such as moments or orthogonal shear forces are combined, the 100-40-40 rule is more appropriate. SRSS combination of moment and shear forces results in a vector and implies that the forces are in phase, which is an incorrect interpretation of the SRSS rule. The SRSS rule is meant to apply to the end item of interest, e.g., stress. As an example, for a vertical tank or heat exchanger with a circular pattern of anchor bolts, the SRSS combination of anchor bolt tensile loads at any location on the circumference for two horizontal directions of earthquake loading will never exceed the anchor bolt tensile load for the maximum horizontal direction. However, for a square anchor bolt pattern on vertical cabinets, the SRSS and 100-40-40 combinations of anchor bolt tensile load can be about 1.4 times higher for two horizontal directions than for one horizontal direction. The ECC specified for design could have been the combination of the worst horizontal response with the vertical response by absolute sum or the combination of the three components by SRSS. When the equipment fragility is developed by scaling the results of design analysis, the median value of the equipment earthquake component combination factor, FECCe should be selected to correct for conservatism or unconservatism in the design approach for component combination. The logarithmic standard deviation in the equipment response due to randomness in ECC, βECCe,R, can be estimated by examining the contribution of each component and applying the guidance in Section 5.4.6 for structures. A conservative upper bound is βECCe,R = 0.18 if all three earthquake components are approximately equal contributors. If only the two horizontal components of earthquake are significant contributors, a logarithmic standard deviation of 0.12 is more reasonable. 5.5.3 Equipment Response for Fragility Based on Testing Test-based capacity factors are calculated following Equation 4-5 (Section 4.1.3). In Equation 4-5, RRSC is the modified spectral acceleration demand that has been clipped. RRSC is compared to the tested spectral acceleration capacity TRSC to calculate the equipment capacity factor. 5-53 13633436 Seismic Demand For cabinet-based test data, the unclipped RRS is equal to the ISRS at the base of the cabinet, and RRSC can be obtained by clipping the RRS. In contrast to cabinet-based TRS, device-based TRS are required if individual electrical components, such as relays, are the source of the test data. For these cases, the RRSC must include amplification (as well as clipping) of the RRS, up through the cabinet to the point of device attachment. To calculate seismic demand for an SOV-based fragility, the RRS should be equal to the median ISRS. To calculate seismic demand for a CDFM seismic capacity, the RRS should be equal to the ISRS with 84% NEP. The factors that modify the RRS in a seismic fragility analysis, and the associated variabilities, are discussed in the following sections. 5.5.3.1 Response Spectra Clipping The input in-structure or in-cabinet reference response spectra (RRS) often have highly amplified, narrow frequency content. Representative in-cabinet RRS are illustrated in Figures 5-15 and 5-16. The spectra are representative of input spectra for relays mounted on a vertical panel with a local panel mode frequency of about 10 Hz mounted within a very stiff cabinet at ground level subjected to a NUREG/CR-0098 [115] median spectrum anchored to 0.3g PGA. The spectra in Figure 5-15 are from a simple 10 Hz single-degree-of-freedom panel model. The RRS in Figure 5-15 is representative of a very stiff cabinet with a single dominant panel mode and is characterized by a narrow highly amplified RRS, which can occur in a cabinet with a single dominant panel mode. The spectrum in Figure 5-16 was developed from a detailed finite element model of the cabinet and mounting panel with 5% cabinet damping and shows lesser peak resonant amplitude and broader frequency content than Figure 5-15, which is nearly always the case when more refined models are used. Figure 5-16 shows an RRS with moderate frequency breadth. However, in both cases, the breadth of frequency content is narrow compared with typical TRS, which are likely to have nearly constant spectral acceleration over a broad frequency range such as 5 to 16 Hz. 5-54 13633436 Seismic Demand Figure 5-15 In-cabinet response spectra for cabinet with single ~10 Hz frequency panel mode Figure 5-16 In-cabinet response spectrum for multiple cabinet modes 5-55 13633436 Seismic Demand Experimental observations (e.g., in EPRI NP-5223 [20] and EPRI NP-7147 [21]) indicate that a narrow frequency input spectrum must be scaled to a higher level than a broad frequency input spectrum to produce relay chatter or structural damage. EPRI NP-5223 [20] states that: The peak values of narrow-band amplified mounting point response cannot be compared directly with the broad-band type of inputs used in multi-axis relay testing which form the basis of relay GERS... For complex devices such as relays, a narrow-band input is judged to be less severe from a fragility standpoint than a broad-band input, due to the absence of multi-mode response (SWRI-6582-002 [123]), variable RMS severity over the bandwidth of test spectra (Kana [124]), and the lack of interaction of nonlinear responses in the narrow-band case. Recent studies (Kana [124], NUREG/CR-5012 [125], NUREG/CR-0088 [126], SWRI 8608-001 [95]) have concluded that a constant correction factor can be applied to narrow-band data to produce an approximately equivalent broad-band result. These conclusions were confirmed for high-frequency motions in EPRI 3002000706 [92] where the results of broad banded triaxial random multi-frequency tests were compared with results of similar tests that included a superimposed narrow-band filtered motion. The filtered multifrequency narrow-band inputs resulted in peak spectral fragility values that were 2.5 to 3 times the spectral fragility values using wide-band multi-frequency inputs. EPRI NP-5223 [20], Kana [124], and Kana and Chen [127] suggest that two corrections should be applied to the narrow frequency high spectral peaks of the RRS to produce a damage-effective RRSC to be used in Equation 4-5. These are a bandwidth correction factor CB and a modal interaction correction factor CMI. Kana [124] and Kana and Chen [127] suggest that equipment malfunction is dependent not only on peak spectral amplitude, but also on the root mean square (RMS) amplitude of the waveform. They provide relationships between the mean ratio of the RMS to peak spectral amplitude as a function of the bandwidth to central frequency ratio, B, as defined in NUREG/CR-5012 [125]. Following NUREG/CR-5012 [125] and Kana and Pomerening [128], the bandwidth to central frequency ratio B is defined as: B ∆f . f Eq. 5-17 where f0.8 is the total frequency range over which spectral amplitudes exceed 80% of the peak spectral amplitude and fc is a central frequency (i.e., frequency at which response spectrum peaks) for the frequencies which exceed 80% of the peak amplitude. Figure 5-17 shows schematically the procedure for obtaining the bandwidth to central frequency ratio, B. Assuming damage is purely dependent on the RMS amplitude of the waveform and is independent of the peak spectral amplitude, Kana [124] and Kana and Chen [127] suggest a relationship between C’B and B, which can be closely approximated by: C’B = 0.32 + 0.4B 5-56 13633436 (0.15 ≤ B ≤ 0.9) Eq. 5-18 Seismic Demand Because Equation 5-18 assumes that damage is purely dependent on RMS amplitude, C’B provides a lower bound (unconservative) estimate of CB. If damages were purely dependent on peak spectral amplitude, then CB would be unity (no correction). In reality, CB lies somewhere between C’B and unity, but probably much closer to C’B than unity. The bandwidth to central frequency ratio B for the 5% cabinet damping spectrum in Figure 5-15 is 0.22 and C’B would be 0.41. Similarly, for Figure 5-16, B equals 0.44 and C’B equals 0.50. Most computed or measured in-cabinet spectra will have bandwidth to central frequency ratios B in the range of 0.15 to 0.6, for which C’B will range from 0.38 to 0.56. ISRS (5% damping) at high elevations within civil structures will also tend to have B ratios in the range of 0.15 to 0.6. For comparison, the 5% damped NUREG/CR-0098 [115] median spectrum for a rock site has a bandwidth to central frequency ratio B of 1.50 which is also representative for broad frequency TRS. Figure 5-17 Example response spectrum clipping For the case of single mode response of the primary supporting structure and a secondary supported component in resonance, NUREG/CR-0088 [126] has suggested a modal interaction correction factor CMI of 0.7. This factor would be appropriate to be applied to the resonant peak at 10 Hz in Figure 5-15 because the supporting cabinet has only a single primary mode. However, it would not be applicable outside of perfect resonance, nor would it be applicable for the in-cabinet spectrum of Figure 5-16 even at 10 Hz. For Figure 5-16 where the response spectrum is broader, CMI probably lies within the range of 0.85 to 1.0. The following equation for CMI is been suggested as a lower bound: CMI = 0.39 + 1.4B ≤ 1.0 Eq. 5-19 To obtain an effective broad-frequency RRSC to be compared with a broad-frequency TRS, the highly amplified peaks of the narrow banded RRS such as those in Figures 5-15 and 5-16 should be clipped at a factor of Cc of the peak value. CC = CB CMI Eq. 5-20 5-57 13633436 Seismic Demand However, the use of Equation 5-20 may result in some double-counting of the benefit of a narrow bandwidth. To avoid this possibility, both CB and CMI should be conservatively estimated. In Appendix J, CDFM clipping factors which considered both CB and CMI have been developed to be used in a HCLPF analysis and are given by the following equation: CC = 0.55 B ≤ 0.2 CC = 0.4 + 0.75B 0.2 ≤ B ≤ 0.8 CC = 1.0 B  0.8 Eq. 5-21 These values are slightly conservative (i.e., at about +0.5 level) to reflect the CDFM philosophy that seeks to define the demand at about the 84% NEP. For the purposes of fragility analysis median equations and logarithmic standard deviations for uncertainty were developed assuming the following constraints:  CDFM equations given by Equation 5-21 are conservative and should be at or above the 0.5 level (this is consistent with the CDFM philosophy).  Full coupling of the lower bound equations for C’B (i.e., Equation 5-18) and CMI (i.e., Equation 5-19) is unconservative and the product of the two equations should be approximately at the -2 level.  Finally, at the +2 level CC should be less than or equal to 1.0. Using these constraints, the following equations were developed for the median value of CC, and logarithmic standard deviation for uncertainty in the clipping factor, Cc,U. Median: Uncertainty: CC = 0.30 + 0.86B B ≤ 0.4 CC = 0.50 + 0.36B B > 0.4 Cc,U = 0.37 - 0.5B B ≤ 0.4 Cc,U = 0.24 - 0.17B B > 0.4 Eq. 5-22 Eq. 5-23 For the spectra shown in Figures 5-15 and 5-16 where the B values for 5% damping are 0.22 and 0.44, respectively; the corresponding CC values are 0.49 and 0.66, respectively; and the corresponding βu values are 0.26 and 0.17, respectively. For illustration, these clipping factors Cc have been applied to the RRS in Figures 5-15 and 5-16 to obtain effective RRSC spectra for comparison with a broad-frequency TRSC. After being clipped, Figure 5-15: Peak RRSC = 1.70g Figure 5-16: Peak RRSC = 1.65g 5-58 13633436 Seismic Demand These clipped peak RRSC represent an effective amplification of 2.66 and 2.58 for Figures 5-15 and 5-16, respectively, over the broad-banded 0.64g peak input spectral acceleration for the applied 0.3g NUREG/CR-0098 median spectrum. This clipping approach may be applied to both narrow-band ISRS to be compared with TRSC appropriate for the base of the cabinet, and to in-cabinet spectra to be compared with the TRSC for a relay or other components mounted within a cabinet. Clipping factors may be conservative when they are calculated for median or 84% NEP ISRS, which account for variability in structure and SSI frequencies and therefore have broader peaks than would occur in a real earthquake. Therefore, it is best to calculate clipping factors for spectra that have not been developed by combining multiple spectra with peaks at different closely spaced frequencies. Recommendations for clipping median and 84% NEP spectra from deterministic and probabilistic response analyses are made in Sections 5.3.5, 5.3.6, and 6.5. 5.5.3.2 Cabinet Amplification Often the analyst does not have an in-cabinet RRS near the location of a critical relay or other device for which test data is available. For these cases, the effective peak RRSC is defined as follows: RRS where: RRS ∗ C ∗ AF Eq. 5-24 RRS = Reference response spectrum demand (peak ISRS due to the RE) CC = Clipping factor for narrow-banded RRS AFC = Cabinet amplification factor In this context, AFC represents an effective cabinet amplification factor. The cabinet response filters and amplifies the floor motion to yield an in-cabinet response spectrum for the component mounting point. Worst-case location (i.e., largest amplification) 5% damped CDFM AFC values were developed for three types of electrical cabinets. Consistent with the determination of the CDFM values, the underlying probabilistic data were used to obtain median AFC values and associated logarithmic standard deviations for randomness and uncertainty. The effective cabinet amplification factors AFC listed in Table 5-10 are provided as representative examples which can be extrapolated with care to other components. Additional studies and recommendations on amplification factors are contained in EPRI NP-7146 SL R1 [129]. Buckets within motor control centers (MCC) in which relays or other components are mounted tend to be small and well attached to the MCC cabinet so that only a small amount of panel amplification is likely. On the other hand, switchgear have large unbraced sheet metal surfaces for which large amplifications are likely. Typically, electrical benchboards and panels associated with main control boards have reasonably stiffly supported panels of moderate unbraced spans located within stiff cabinets so that neither cabinet frequencies nor local panel mode frequencies 5-59 13633436 Seismic Demand are likely to be less than about 13 Hz. For these cases the AFC values for benchboard and panels in Table 5-10 can be used. For other stiff and deep cabinets which have local panel modes with frequencies below about 13 Hz, AFC factors approaching the switchgear case would generally be more appropriate. A generic median value of AFC for vertical response of any cabinet is developed in Appendix C to EPRI 3002004396 [24]. The vertical cabinet amplification factor is valid for both low- and high-frequency ranges. Vertical control cabinet natural frequencies tend to be in the 20 to 30 Hz range and thus have mounting point response in the high-frequency range. Device-based TRS will most often have been developed for approximately equal test motion levels in all three orthogonal directions. A test-based fragility should be calculated for the maximum of horizontal and vertical RRSC values, determined by applying the horizontal and vertical cabinet amplification factors to the clipped horizontal and vertical ISRS. In nearly all cases, effective AFC values from Table 5-10 will result in higher estimated peak RRSC values for most locations within a cabinet than would be obtained by developing a simplified mathematical model of the cabinet to generate an in-cabinet spectrum such as Figures 5-15 and 5-16 and then clipping this spectrum in accordance with Equation 5-22. For example, based on Table 5-10, one would likely estimate an AFC of about 3.3 for a 13 Hz panel in a stiff cabinet, but the clipped RRSC shown in Figures 5-15 and 5-16 would justify an AFC much lower for relays located low in this cabinet. Therefore, a penalty is often paid for using the worst-case location AFC from Table 5-10. Appendix L provides guidance for estimating AFC factors for cabinet positions that have lower expected response. Table 5-10 Cabinet amplification factor, AFC (5% damped – worst-case location) Cabinet Types AFC Median R U CDFM Motor Control Center 2.8 0.10 0.23 3.6 Switchgear (flexible panels) 4.4 0.13 0.37 7.2 Control Room Electrical Benchboards and Panels (with frequency  13 Hz) 3.3 0.11 0.27 4.5 Vertical Cabinet Response 3.0 0.11 0.36 4.7 5.5.3.3 Boundary Conditions Test labs typically mount specimens to the shake table in a rigid manner (welding or high strength bolting). In some cases, the actual field mounting of the equipment is not as rigid as the shake table mounting or vice versa. Boundary conditions can affect the response frequency and can make a difference in the test response versus the as-installed response. The fragility analyst should review the walkdown notes to determine the field conditions of mounting and compare to the described test mounting. If the TRS is broad banded and fairly flat over the credible frequency range of the specimen and its boundary conditions, then minor differences in the as tested frequency and the field mounting frequency should not make any appreciable difference in the equipment response. However, if there is a significant difference in the boundary stiffness, 5-60 13633436 Seismic Demand then the fragility analyst must adjust the effective test response spectra for comparison to the specified response spectra for the RE. An example could be a case where the as installed electrical panel had bolts through flexible flanges and the test lab welded the tested component to a rigid fixture on the table with a rigid load path up through the structural framing of the panel. Moreover, if the as-built boundary conditions are different from the tested boundary conditions, then the natural frequencies reported in the test report may not realistically represent the as-built configuration. Therefore, the fragility analyst must review the test configuration and as-built configuration sufficiently to understand any differences and how they might affect the dynamic response, load path, capacity, etc. 5.5.3.4 Building Response Median equipment seismic demand should be based on median ISRS from the structure seismic response analyses (Section 5.3). The corresponding median structure response factor is 1.0. Structure response variabilities should be determined similar to the approach for structure fragility evaluation (Section 5.4). As noted in Section 5.4, certain structure response variabilities for structure fragilities are based on structure ZPAs. For equipment fragilities, in-structure spectral accelerations at the median equipment frequency and damping should be used instead. The building response factors for other equipment failure modes (i.e., based on analysis) as discussed above are generally the same as for equipment capacities based on testing. In determining the appropriate building response factors and variabilities the analyst needs to judge whether the failure mode is sensitive to one, two, or three directions of input motion. For example, if the failure mode is chatter of a relay mounted on the side of a switchgear cabinet; then it is likely that only one direction of motion contributes to failure. For this case, only the building motion for the corresponding horizontal direction is reflected in the analysis. On the other hand, if the failure mode is structural failure of the cabinet frame it may be determined that two horizontal directions of motion contribute to the failure. Here, factors for both horizontal directions of building motion should be considered. 5-61 13633436 13633436 6 FRAGILITY IMPLEMENTATION TOPICS This section of the report addresses special SPRA implementation topics that support fragility evaluation. The following topics are included: Table 6-1 Outline of implementation topics Section Implementation Topic 6.1 Seismic walkdown criteria 6.2 SSC screening and the use of representative fragilities 6.3 Fragility information unique to relay evaluations 6.4 Considerations for high-frequency motions 6.5 Response spectra clipping 6.6 Structural models for response analysis 6.7 Response analysis scaling methods 6.8 Combining fragilities for multiple failure modes 6.1 Seismic Walkdown The walkdown inspection of essential plant components is particularly emphasized in modern SPRAs. The objectives of the SPRA walkdown are as follows:  Observe and document the current as-built condition of SSCs important to the SPRA, as identified on the SEL.  Screen from further review those SSCs for which the Seismic Review Team (SRT) can judge the capacity meets or exceeds specified screening levels (i.e., seismic capacity at which SSCs are screened from further fragility evaluation; Section 6.2). This focuses the SPRA efforts on those SSCs that are most important and most vulnerable to seismic risk.  Assess whether each SEL SSC satisfies the class-specific requirements of Table 4-2 such that they may be assigned seismic capacities accordingly (i.e., determine whether the caveats in the walkdown Screening Evaluation Sheets (SEWS) are met; Appendices B and C).  Identify dominant failure mode(s) (e.g., functionality, structural integrity, or anchorage failure) of each SEL SSC that is not screened, and identify further information (drawings, design analysis reports, and/or seismic qualification reports) required for their evaluation. 6-1 13633436 Fragility Implementation Topics  Collect key data such as dimensions, materials, and configuration that may be required in future fragility evaluations. This can include specific details (e.g., bolt dimensions) to be used in detailed seismic fragility calculations, as well as general characteristics used to support judgments about seismic capacities as part of developing representative fragilities (Section 6.2).  Assess the similarity of SSCs within each equipment class across parallel trains within a unit, and across similar units, to identify candidates for bounding analysis.  Identify degraded conditions that could potentially affect seismic capacity such as corrosion and concrete cracking.  Identify equipment or structures that are not included in the SEL but whose structural failure may impact nearby SEL SSCs related to seismic spatial interaction (SI), seismic-induced fire, and seismic-induced flooding concerns.  Identify any SSCs that should be added to or removed from the SEL. This requires interaction with the systems modeling engineers.  Observe and document any obvious seismic deficiencies.  Collect information to support judgments concerning statistical correlation of capacity and demand between pairs of SSCs. Additional guidance on treatment of correlation in an SPRA can be obtained from NUREG/CR-7237 [130]. The SSCs on the SEL are reviewed according to the walkdown guidance developed during the conduct of past seismic design verification, SMAs, and SPRAs (SQUG GIP [31], EPRI NP-6041-SLR1 [1], and EPRI 1025286 [131]). The SEL is defined in EPRI 3002000709 [5] and consists of the complete set of SSCs within the seismic initiating sequences that will be considered in the SPRA. Development of the SEL must occur prior to the initiation of the walkdowns. The overall walkdown effort often involves multiple walkdowns for various purposes, such as SEL development, fragility walkdowns, electrical raceway (cable trays and conduit) walkdowns, piping walkdowns, HVAC ducting walkdowns, identification of seismic fire and flood interactions, relay assessment walkdowns, and fragility correlation observations. Many of these walkdowns involving distribution systems (electrical raceways, piping, HVAC ducting, and system interactions) can be conducted on an area survey basis (sometimes referred to as a walk-by). 6.1.1 Past Seismic Walkdown Approaches and Strategies Plant walkdowns have been a fundamental element of several beyond design basis seismic assessment programs for operating nuclear plants over the past thirty years. These programs and the walkdown guidance documents developed include the following:  USI A-46 Issue Resolution (SQUG GIP [31])  IPEEE Program – Seismic Margin Assessment (EPRI NP-6041-SLR1 [1])  NTTF Recommendation 2.3 – Seismic (EPRI 1025286 [131]) 6-2 13633436 Fragility Implementation Topics The A-46 issue was concerned with older operating plants designed and constructed prior to the implementation of more complete equipment qualification procedures (e.g., IEEE 344-1975 [96]). The IPEEE program was focused on demonstrating that all operating plants could be safely shut down following an earthquake exceeding the seismic design basis. The resolution of the Near-Term Task Force (NTTF) issue required each plant to perform a modern PSHA and, for those plants where the resulting seismic hazard exceeded a given threshold, to perform an SPRA. Walkdown guidance is well documented in EPRI NP-6041-SLR1 [1] for the purposes of SMAs. The guidance provided in this section and in Appendices B and C is generally consistent with EPRI NP-6041-SLR1 [1], with some modifications specific to SPRA. One of the key differences between the EPRI NP-6041-SLR1 [1] walkdown guidance and the current SPRA walkdown guidance concerns relays and other control components. EPRI NP-6041-SLR1 [1] assumed that a list of control relays associated with the SEL equipment would be available during the walkdown of the SEL equipment. However, in practice, this seldom occurred in actual SMAs, and the effort to screen equipment with relay GERS or plant qualification documentation was instead typically conducted as a separate deterministic evaluation. For an SPRA, the relay evaluation effort is much larger in scope and requires the estimation of relay fragilities (loss of control function) due to mounting point seismic demand, as opposed to the simpler deterministic screening that is done for an SMA. Therefore, the evaluation of relays or other control components in an SPRA will typically be separate from the walkdown effort. Section 6.3 outlines the relay evaluation process and discusses the requirements and objectives for a specific relay walkdown, when appropriate. 6.1.2 Composition and Qualifications of Seismic Review Team The primary activities in an SPRA walkdown are identified above. These walkdown assessments should be directed by civil, structural, and mechanical engineers who have had considerable experience in earthquake engineering of critical facilities. Typically, there will be two groups of engineers involved in the seismic fragility effort of an SPRA: (1) seismic fragility analysts, who perform the fragility calculations, and (2) the SRT, who perform the walkdown. These two groups are not necessarily mutually exclusive and are often the same engineers. The seismic fragility analysts should perform the seismic fragility evaluation working in close coordination with the SRT. It is expected that they will be civil, structural, mechanical, or electrical engineers with experience in earthquake engineering. The SRT typically consists of three to five members who between them should possess the following qualifications: 1. Knowledge of the failure modes and performance during strong earthquakes of components and structures in heavy industrial process plants and fossil fuel power plants including structures, tanks, piping, process and control equipment, and active electrical components. 2. Knowledge of nuclear design standards and seismic design practices for NPPs including structures, tanks, piping, process and control equipment, and active electrical components. 3. Experience in determining the seismic capacity of electrical contact devices such as relays, contactors, motor starters, and switches. 6-3 13633436 Fragility Implementation Topics 4. Ability to perform fragility/margins-type capability evaluations, including structural/ mechanical analyses of the above-mentioned SSC types. 5. Familiarity with previous SPRA conclusions and systems analysis. 6. Some general knowledge of the plant systems functions. It is not necessary that each member of the team individually have strong capability in all of these areas or strong seismic experience for all of the SSC types that are important to the SPRA. However, among them, at least one member and preferably two members of the SRT should have strong experience in each of the above-mentioned areas so that in the composite, the SRT is strong in all these areas. It may be efficient for the SRT to identify a subgroup to be responsible for relay capacity review since this is a specialty area. The seismic fragility and seismic walkdown teams should strive to make the SPRA efforts highly cost-effective by minimizing purely paper studies, documentation problems, and hypothetical failure scenarios unsubstantiated by experience or expert judgment. These unrealistic problems have often dominated the activities of many seismic studies for the nuclear industry. SPRA work should concentrate on failure modes that have occurred in heavy industrial process plants and fossil fuel power plants in past earthquakes. A cost-effective SPRA requires efficiently estimating seismic capacities based upon historical performance, fragility or high-level qualification testing, and judgment (Section 6.2). Where real failures have occurred, a significant percentage of them have been due to poorly anchored or unanchored equipment, inadequate structural detailing, seismic spatial interactions (SI), or seismic-induced flooding of critical SSCs. A cost-effective SPRA cannot ignore the credible SI failure modes but should not become bogged down into a typical overly detailed nuclear industry SI study. It requires experience to efficiently spot the most critical SI failure modes without becoming overwhelmed in an SI failure mode walkdown study. Efficient screening-out from the SPRA of the rugged SSCs whose capacities greatly exceed other SEL SSCs (Section 6.2) and screening-in of the most critical SI by informed judgment requires a combination of considerable experience and training in earthquake engineering for critical process facilities. The recommended approach to accomplish this screening is to use a qualified and experience SRT. The SRT members are expected to: 1. Become familiar with the seismic design bases for the power plant, especially for those SSCs expected to be most important to the SPRA. This is to be done either by the team members' own efforts or in conjunction with seismic fragility analysts. 2. Take primary responsibility and personally conduct the seismic walkdown of SSCs in the SEL. 3. Screen out from the SPRA all SSCs for which their experience and judgment will justify sufficient ruggedness that they can unequivocally state as a team that they have a fragility greater than the designated screening level (Section 6.2). 4. Specify the failure modes that should be investigated and the type of review to be conducted for SSCs not screened. 6-4 13633436 Fragility Implementation Topics 5. Take responsibility for including in the SPRA all SI items that they judge to be credibly serious enough to warrant investigation. 6. Perform a review function of the seismic fragility evaluations performed by the fragility analysts to ensure they accurately represent the as-built and as-operated configuration of the plant that was observed during the walkdown. The extent of SRT review and participation in the fragility evaluation should be agreed upon at the outset of the assessment effort. It is recommended that at least one SRT member on each walkdown team have at least five years of experience in seismic capacity evaluations and completed the SQUG one-week Walkdown Screening and Seismic Evaluation Training Course or equivalent (i.e., a Seismic Capability Engineer, or SCE). It is also recommended that at least one other engineer have at least two years of seismic capacity experience. The experience and training of the SRT is very important since decisions made during the walkdown propagate through the seismic risk analysis evaluation. It is recommended that the walkdown team include a plant system engineer, operator, or a PRA engineer to answer questions about SSC functional requirements and to determine if SSCs should be added to or deleted from the SEL. The walkdown preparation effort should include coordination of personnel from the plant to escort the SRT, if necessary. The escorts may be operations personnel, shift technical advisors, health physics, or knowledgeable craft personnel who can guide SRT to specific SSCs and who are authorized to open panel doors, access restricted areas, etc. 6.1.3 Pre-Walkdown Preparation Prior to the walkdown, the systems analysts will develop the SEL, which includes the equipment identification number, equipment description, and location of the equipment in the buildings (floors and rooms). Each SSC will be assigned to one of the equipment classes identified in the following list. The classes indicated are based on the SQUG GIP classes, plus several additional classes and modifications, such as the passive mechanical classes introduced by EPRI NP-6041SLR1 [1]. It is possible to add, remove, or modify classes as determined appropriate by the SRT and system analysts as part of the SEL development. The addition of the manual valves class and a generic component class to the EPRI NP-6041-SLR1 [1] list of classes is an example of useful additions that have been made in past SPRA walkdowns. 1. Motor Control Centers 2. Low Voltage Switchgear 3. Medium Voltage Switchgear 4. Batteries and Racks 5. Battery Chargers and Inverters 6. Transformers 7. Control and Instrumentation Panels 8. Instrument Racks 9. Distribution Panels 10. Local Instruments and Temperature Sensors 6-5 13633436 Fragility Implementation Topics 11. Engine Generators 12. Motor Generators 13. Horizontal Pumps 14. Vertical Pumps 15. Air-Operated (Pneumatic) Valves or Dampers 16. Motor-Operated Valves or Dampers 17. Solenoid-Operated Valves 18. Air Compressors 19. Fans 20. Air Handlers 21. Chillers 22. Frame or Skirt Supported Vertical Tanks or Heat Exchangers (also Flat Bottom Tanks) 23. Horizontal Saddle or Cradle Supported Tanks or Heat Exchangers 24. Horizontal Suspended Tanks 25. Buried Tanks 26. Building Penetrations of Underground Utilities 27. Strainers and Filters 28. NSSS Components and Primary Coolant Loops 29. Control Rod Drive Assemblies 30. Building Seismic Gaps 31. Control Room Ceilings 32. Traveling Screens and Sluice Gates 33. Manual Valves or Dampers 34. Generic Components To prepare for the walkdowns, the SRT should review prior walkdown SEWS and evaluations from the IPEEE program or, if applicable, the USI A-46 resolution for each item on the SEL. They should also review component specifications to determine such things as the qualification acceleration level for valves, cable raceway design and HVAC ducting design, and selected seismic qualification reports and general arrangement drawings to become familiar with the plant layout and design basis. Pertinent information can be noted and included on the walkdown datasheets as appropriate to inform the walkdown effort. The prior datasheets and any relevant reference documents (such as IPEEE SEWS and qualification reports) may be compiled into a walkdown data binder, which would be brought to the site for reference during the SPRA walkdown. 6-6 13633436 Fragility Implementation Topics One of the significant benefits of a qualified and experienced SRT is the ability to develop an initial estimate of seismic capacity for SEL SSCs prior to the walkdown. This process can be based on judgement (and possibly, general capacity calculations) that a structure or component has a certain capacity, and that the SRT has high confidence that it will not fail at that specified capacity. This initial capacity estimation can be performed following the experience-based capcity criteria in Section 4.2, which are heavily dependent on the walkdown. During the walkdown of the plant, all initial capacity estimates are reviewed and either confirmed or changed. All SSCs, whether they are assigned an initial capacity estimate or not, are inspected in the field. The initial capacity can help speed up the walkdown process, but the walkdown must confirm any such estimates. The principal benefit of initial estimates is in the organization of the decision-making process before the walkdown. For example, horizontal pumps generally have high capacity, and based on a review of pump specifications, they can be estimated to have a median in-structure Sa capacity of 4.8g, following Table 4-2. This estimate is based on the components having adequate anchorage and is conditional on satisfying the inclusion rules and caveats in Appendices B and C. Then, during the walkdown, the SRT can quickly confirm that a pump and anchorage comply with the drawings and specifications. If the initial work is not performed to assess the design for inclusion rules, caveats, and anchorage capacity, then that effort must be performed during or after the walkdown instead. It is important to recognize that a major part of an SPRA is investigation of equipment anchorage. Tables 4-2 and 4-4 are for the capacity of the SSC itself and do not include consideration of anchorage, which varies from plant to plant. Thus, anchorage must be considered in addition to the guidance given in the capacity tables. One efficient strategy is to perform generic calculations for various typical types of anchorage systems (e.g., cast-in-place anchor bolts, expansion anchors, and welds) for various equipment classes and configurations. Using these generic capacities and the equipment construction drawings, the component anchorage can be estimated in advance, and the construction details verified during the walkdown. Using another strategy, the SRT would carry tables of generic capacities during the walkdown and use them to make bounding assessments in the field to assist in the capacity decisions. Initial estimates of anchorage capacity are entirely up to the SRT and what they believe to be the most efficient way to conduct the walkdown process. After the walkdown process is completed, the SEL SSCs are identified as either meeting or not meeting the criteria of Tables 4-2 and 4-4. This information can then be used as described in Section 6.2 to efficiently estimate seismic fragilities for initial risk quantification, which is used to prioritize any further seismic fragility evaluation effort. The SRT is expected to document the basis for all seismic capacity estimates they have generated and to jointly sign a statement certifying their concurrence with the capacity judgments. With this statement on file, only a minimum amount of documentation of the initial capacity estimate procedure should be required. This minimum documentation should consist of a general description of the basis for the capacity estimates. Section 6.1.6 provides additional guidance for documenting the seismic walkdown. 6-7 13633436 Fragility Implementation Topics Differing levels of expertise for the SRT are permissible. However, the SRT must conscientiously avoid unconservatism in their capacity judgments for any SSC for which they do not have the necessary expertise to make judgments. Once assigned an unconservative capacity estimate, an SSC is likely to not be reviewed further. The SRT members must take full responsibility for this capacity estimation. SSCs should be assigned conservative capacities, or an SSC-specific evaluation should be performed if the SRT’s expertise does not enable them to take this responsibility. 6.1.4 Detailed Walkdowns vs. Walk-Bys The SRT should walkdown or walk-by all SEL components that are reasonably accessible and in non-radioactive or low radioactive environments, unless there exists sufficient previous walkdown information to address the objectives stated above. Alternate methods such as photographs and reliance on design information may be used to address components that are inaccessible or located where there are high radiation dose rates or contamination. For example, many plants have detailed videos of inaccessible areas for operator training purposes that can be used to supplement the SPRA walkdown effort. EPRI NP-6041-SLR1 [1] provides direction for both detailed component inspections and less thorough component inspections, which can be applied to SPRA walkdowns. The SEL can be segregated into groups of similar or identical items, and then a detailed walkdown may be performed on a sample from the group (“lead”) followed by walk-bys on the remaining items in the group to confirm the “lead” sample is representative of the remaining items. The detailed inspection of the lead item can include de-energizing and opening of cabinets or panels. The walk-by can be for identical components in separate trains or similar components, such as valves purchased to the same specification and of similar size. In consultation with the systems analysts and operations personnel, the SRT will select the lead equipment components that will have a detailed walkdown inspection. The remaining components will be initially considered for walk-by inspections. The SRT should consider the following when establishing similarity of a group of components: manufacturer, equipment construction, dimensions, locations, anchorage type, and configurations. The lead-walk-by concept is also applicable between components in separate but similar units. For small, generally rugged SSCs, a walk-by is acceptable, provided no vulnerabilities are identified during the walk-by. The walk-by review should focus on interactions or other obvious vulnerabilities for these items. Section 6.2.1 provides examples of SSC types that are typically considered inherently rugged and additional guidance on criteria for performing a walk-by of such SSCs. General area walkdowns or sampling walk-bys of distribution system such as balance-of-plant (BOP) piping, cable raceways, and HVAC ducting are considered sufficient unless deviations from the design basis or abnormalities are identified. There may be cases when a walk-by is initially planned for a component and, due to concerns identified during the walk-by, the SRT decides to perform a new detailed walkdown. Examples of this could include unanticipated lack of similarity, potential seismic interaction concerns, or a different configuration than prescribed on drawings or specifications. Additional guidance on sampling techniques is provided in Appendix D. 6-8 13633436 Fragility Implementation Topics The SRT can use information from past seismic walkdowns (e.g., USI A-46, IPEEE, NTTF Recommendation 2.3, past SPRAs) such that the new SPRA walkdowns will not have to be as detailed. For components that were previously walked down under prior seismic programs, the SRT should decide if a walk-by is sufficient or a new detailed walkdown inspection is needed. Some issues that the SRT should consider in this determination are:  Has the equipment or part of the equipment or its configuration been modified or replaced since the previous walkdown?  Were the previous seismic walkdowns documented adequately to support the SPRA?  Are there any unresolved discrepancies identified on the old SEWS?  Could there be a potential for degradation (e.g., anchorage corrosion, concrete aging effects) or a new seismic interaction issue introduced since the last walkdown?  Is there a potential that the new RE demands could impact any of the previous judgments on walkdown or screening of components (e.g., new hazard shape may introduce different frequency content)? If there is no change to the equipment item and a minimal potential for degradation, the equipment item could be a candidate for a walk-by provided the previous walkdown documentation (SEWS) is available and no concern was noted. However, the SRT may determine that further walkdowns are warranted. This could be due to the need for further information for the component evaluation, or the identification of a potential discrepancy with the available information. 6.1.5 Component Capacity Estimation As described in Section 4.2 of this report, Tables 2-3 and 2-4 of EPRI NP-6041-SLR1 [1] have historically been used to screen SSCs (excluding equipment anchorage and interactions) in SMAs. For an SPRA, however, the tables are instead used to estimate seismic capacities, which are then compared to site-specific seismic demands to develop plant-specific fragilities. The tables have been updated for SPRA purposes and are provided in this report as Tables 4-2 and 4-4. The SRT should be familiar with the caveats and restrictions associated with these tables, including the checklists in Appendix B, the SSRAP Report (SAND92 0140 [28]), and the historical technical basis for the EPRI NP-6041-SLR1 tables, which is provided in Appendix C. The SRT should also be familiar with the caveats and restriction in the SQUG GIP [31]. The GIP was written for design basis evaluations, so it is not necessary that the caveats be explicitly met; however, the SRT should be aware of the GIP caveats and consider their implications in the fragility evaluation. One of the main objectives of the SPRA walkdown is to evaluate the SEL SSCs against these criteria to enable the fragility analyst to efficiently estimate seismic capacities. Additional guidance for estimating capacities from these tables and from earthquake experience data is provided in Section 4.2 and Section 6.2. An example fragility calculation using such capacities is provided in Appendix Y. 6-9 13633436 Fragility Implementation Topics 6.1.6 Walkdown Documentation Several different forms have been used in the past to document walkdown results. These include SQUG GIP SEWS [31], EPRI NP-6041-SLR1 [1] SEWS; and more recently, NTTF Recommendation 2.3 Seismic Walkdown Checklists (SWCs). As a matter of consistency, the general format of the SEWS provided as an attachment to this report (based on the format suggested in EPRI NP-6041-SLR1 [1]) should be used for new detailed walkdowns. However, as noted in EPRI NP-6041-SLR1, “The exact form of the walkdown data sheets may be varied to suit the SRT” [1]. Therefore, some variation of these forms is acceptable. The important point is that the walkdown forms describe the SSCs considered by the SRT in sufficient detail to arrive at their conclusions, identify concerns that require further detail, and provide as-built information that will be used in fragility calculations. As noted above, the SPRA walkdown guidance concerning relays described in Section 6.3 differs from EPRI NP-6041-SLR1 [1] guidance. The walkdown SEWS that contain relay walkdown sections have been edited to focus on the observation of relay mounting conditions (e.g., relays are mounted securely without any missing mounting hardware or load-path issues). Any EPRI NP-6041-SLR1 [1] sections that require SRT assessment of the potential for relay chatter have removed and should be considered superseded by the relay evaluation guidance in Section 6.3 and elsewhere in this document. Per EPRI NP-6041-SLR1, “For ‘walked by’ items only a general listing needs to be given with a general basis for considering the items to be screened out” [1]. This approach was used, for example, in the Surry SPRA Pilot Plant Review [132]. If the component is similar to another component that is subject to a detailed walkdown (lead component), the walk-by of the similar component can be documented on the SEWS of the lead component. Alternatively, walk-bys may be documented on a similar form developed specifically for walk-bys, or even on SEWS forms. Whatever form is used to document the walkdown observations for both detailed walkdowns and walk-bys, they should include the following:  The basis for which the SRT has judged that the HCLPF capacities are at or above specified levels.  Documentation of any outstanding concerns and to what extent further evaluation is required.  Concurrence of at least two trained and experienced seismic engineers with the content of the forms indicated by signature, initials, or other documentation. During SPRA development, certain components may need to be walked down more than once. This may be to collect additional information needed for fragility calculations or to further investigate an SI issue, for example. For subsequent walkdowns, it is acceptable to capture additional information by annotating the existing walkdown forms or to generate a new sheet that can supplement the existing walkdown form. 6-10 13633436 Fragility Implementation Topics 6.2 Screening and Representative Fragilities Development of detailed fragilities for all SSCs considered in an SPRA is generally neither economical nor necessary. The most important consideration is to ensure that the appropriate risk insights are generated from these fragilities as they are incorporated into an SPRA. As such, inherently rugged components do not require a fragility derivation based on the experience that they have such high seismic capacities that they will never affect the seismic risk (Section 6.2.1). In addition, certain other SSCs with fragilities above a specified capacity screening level may be assigned a fragility equal to the screening level (Section 6.2.2) without being required to develop a detailed fragility characterizing the best estimate of the median and the full uncertainty calculation. For the remaining SSCs that do not screen out, representative fragilities may be developed for use in initial risk quantifications to identify the most important SSCs. Section 6.2.3 outlines one acceptable approach and general criteria for developing representative fragilities. Insights from initial risk quantifications should inform the subsequent strategy for refining fragilities and focus analysis efforts on SSCs that require the most detailed and realistic fragilities. 6.2.1 Screening of Inherently Rugged SSCs Certain SSCs are inherently seismically rugged and consequently have a very low probability of failing due to a seismic event as shown in Figure 6-1. Consistent with long-standing practice in SPRAs, seismic failure of such SSCs need not be included in the PRA logic models since the exclusion of such SSCs does not affect the SCDF, SLERF, or the insights derived from the SPRA. However, these items should be reviewed for abnormalities during the seismic walkdown to ensure they are not susceptible to component-specific unique failure modes such as seismic interaction, e.g., by sampling and / or area-based walk-by as described in Section 6.1.4. Table 6-2 lists SSCs considered inherently rugged. Additional guidance is available in Appendices B and C, EPRI 3002000709 [5], and EPRI TR-104871 [133]. 6-11 13633436 Fragility Implementation Topics Figure 6-1 Capacity based criteria for fragility analysis Table 6-2 Inherently rugged SSCs SSC Comments Manual Valves Manual valves have sufficiently high seismic capacity that they can be screened from the risk quantification. Non-Active Motor-Operated Valves (MOVs) Non-active MOVs that do not change state (e.g., normally open and desired position is to stay open) are considered inherently rugged, but a walk-by should still be performed if they are on small lines (1” and smaller) to confirm that the valve/operator support is adequate for large operators; for non-active MOVs on larger size lines, general area walkdowns, piping walkdowns or a sampling walk-by is typically sufficient. Active MOVs that change state should be included for seismic fragility evaluation. MOVs are also included in the relay chatter evaluation for possible spurious operation due to relay chatter. Non-Active Air-Operated valves (AOVs) Same as Non-Active MOVs. Check Valves Check valves are sufficiently high seismic capacity that they can be screened from the risk quantification. Temperature Elements Temperature elements are small and lightweight and are typically located inside a thermowell within a pipeline. Temperature elements are sufficiently high seismic capacity that they can be screened from the risk quantification. 6-12 13633436 Fragility Implementation Topics Table 6-2 (continued) Inherently rugged SSCs SSC Comments Small, Inline Strainers Small, inline-supported strainers have sufficiently high seismic capacity that they can be screened from the risk quantification. Larger strainers that have their own anchorage or support should be evaluated explicitly. Small Safety and Relief Valves Small, lightweight safety and relief valves on vessels are generally more rugged than the vessels themselves and are therefore considered to be sufficiently high seismic capacity that they can be screened from the risk quantification. Hand Switches Hand switches have sufficiently high seismic capacity that they can be screened from the risk quantification. Passive Dampers Passive dampers that are only required to retain position and are not required to change state have sufficiently high seismic capacity that they can be screened from the risk quantification. 6.2.2 Screening of High-Capacity Components Capacity-based criteria to determine the SSCs for which fragility analyses should be conducted have been developed to provide uniform guidance to analysts performing SPRAs (or margin analyses) and to ensure that proper focus is given to those SSCs that have the potential to be risk-significant. These criteria were developed using a parametric/sensitivity study documented in an NEI White Paper [134]. These criteria establish which SSCs will require explicit calculation of fragility parameters for inclusion in the plant logic models. SSCs with capacities above the screening level calculated using the criteria are not expected to have significant impact on the result of the SPRA analyses, the ranking of accident sequences, or the calculated sequence- or plant-level seismic SCDF or SLERF values. It is noted that a standard practice for SPRA practitioners has been to use insights from logic models to determine the need for detailed fragility calculations and to prioritize SSCs. A preliminary SPRA plant logic model is developed even before the fragility calculation effort begins. Screening or ranking of SSCs from this preliminary SPRA logic model can be done using parametric sensitivity analyses with assumed initial fragilities and ranges of fragility values. Those SSCs that do not contribute significantly to the SCDF of an accident sequence may not need detailed fragility calculations, as long as the initial fragilities are not unconservative (which would cause their risk importance to be underestimated). These SSCs may be retained in the model with a screening level fragility as described below. Other SSCs may be less rugged but would still have sufficient capacity such that their failures would be unlikely to contribute significantly to the SCDF in an SPRA. Screening criteria discussed below are developed for these SSCs. Detailed fragility calculations are not warranted for SSCs that meet these criteria. Figure 6-1 illustrates the use of the screening level concept, which is applicable to the SSCs in the middle box. 6-13 13633436 Fragility Implementation Topics Sensitivity studies were conducted to develop guidance for determining appropriate screening levels (NEI [134]). These sensitivity studies were conducted for sites that had a relatively high seismic risk. Based on these sensitivity studies, the screening fragility of SSCs for a site expected to have relatively high seismic risks should be calculated by convolving the fragility of a single SSC with the site-specific hazard curve such that the SCDF is at most about 5E-7 per year. This can be done with trial and error runs using a quantification code or with a spreadsheet with an assumed composite variability (e.g., βc= 0.4). Because each site will have a different hazard curve, the screening fragility for each SPRA needs to be separately derived. An alternative criterion, equivalent to the above SCDF-based fragility, is to screen SSCs that have a HCLPF above about 2.5 x GMRS. The results of the sensitivity study do not indicate that the screening criteria would be different for soil and rock sites. Even though certain SSCs are recommended not to require the performance of detailed fragility calculations based on their meeting the screening criteria described above, their fragility should ideally be retained in the SPRA logic model. Their capacity can be set equal to the screening level or at a higher capacity level, if calculated, to allow for a more efficient ranking of accident sequences. Additionally, retention of such failures will ensure that future changes or sensitivities that could increase their importance are not overlooked and addresses the potential for a cumulative effect of screened out components. The sensitivity analysis results indicate that the recommended screening fragility derived from an SCDF of 5E-7 is conservative for some seismic risk applications but can also be unconservative for other seismic risk applications. As such, SPRA results should be reviewed to determine whether an SSC modeled at the selected screening level could be identified as a significant contributor to SCDF or to SLERF sequences. If such an SSC is identified, then more detailed fragility calculations should be performed for that SSC and the quantification analysis should be rerun with the new fragility values. Based on results of some early SPRAs, the screening level chosen was often too low and masked the final SCDF results. Consequently, care should be taken to ensure the screening level is not too low, and screening for more seismically active regions (e.g., western United States and higher seismic regions in the central and eastern United States) should correspond to higher HCLPF levels. To implement the capacity-based screening criteria, engineers can review previous calculations and reports (e.g., design basis, IPEEE, USI A-46 analyses, shake-table tests, etc.) to determine and judge if the seismic capacity of an SSC for the new seismic hazard is such that no further calculation of fragility parameters is warranted. It is expected that the use of the above screening methods will reduce the scope of the fragility or margin calculations required in the SPRA, and still meet the objective of identifying and ranking risk-significant SSCs. It is noted that, while the use of the above criteria is optional, engineers should not select a low screening level (such as 0.3g) that was used by some plants during the IPEEEs. The above criteria are expected to result in sufficiently high screening levels to minimize the SCDF contribution stemming from those SSCs whose fragilities were generated based on the selected capacity screening level. Once the screening level is selected, the list of SSCs can be ordered so that the fragilities for the SSCs with the highest SCDF impact are calculated first. 6-14 13633436 Fragility Implementation Topics 6.2.3 Representative Fragilities Overall seismic risk of nuclear power plants tends to be sensitive to a relatively small subset of SSCs from the SEL. The subset is referred to in this report as dominant risk contributors. The quality of an SPRA and reliability of its results and insights are therefore dependent on correctly identifying the dominant risk contributors and characterizing them with realistic fragilities. An approach used in several of the most recent SPRAs included the generation of a set of initial fragilities, referred to as “representative fragilities” in this report. These representative fragilities are intended to provide an efficient method for identifying the dominant contributors to seismic risk (SCDF and SLERF). The representative fragilities are initial estimates provided to the systems analyst for use in an initial risk quantification. Results from the initial quantification are used to identify the most important SSCs and thus focus subsequent fragility evaluation effort. Insights from the initial risk quantification inform the subsequent strategy for calculating and refining fragilities. The systems analysis determines relative contributions of individual SSCs to the overall plant seismic risk. The risk quantification results therefore inform the SPRA team which SSCs require the most detailed fragilities, and fragility analysis efforts can focus on these SSCs. Representative fragilities should be developed using relatively simple and efficient fragility approaches/methods. These simpler methods could include, for example:  Earthquake experience methods  Capacities from Tables 4-2 and 4-4  Scaling fragilities from past SPRAs  Bounding calculations As with all parts of the SPRA, it is preferable that these representative fragilities be as realistic as possible so that an accurate assessment of the dominant risk contributors can be made. However, in many cases, the representative fragilities are conservatively biased to achieve the efficiencies desired. These conservatively biased fragilities serve to mitigate the risk that a more detailed fragility analysis would result in an appreciably lower fragility. The fragility analyst should be able to document the basis for the realism or slight conservatism in the representative fragilities using plant specific insights. If representative fragilities are un-conservative, the risk quantification could fail to identify the corresponding SSCs as the actual dominant contributors, which would lead to erroneous SPRA results. Overly conservative representative fragilities may lead to misidentification of dominant risk contributors in early risk quantifications, which can lead to inefficient use of subsequent fragility refinement effort. After the initial risk quantification, it is good practice to iteratively refine the fragility evaluations for the most important risk contributors using increasingly sophisticated techniques to make them more realistic and plant-specific. For example, iterating the representative fragilities might include refining seismic demands from a more detailed structure response analysis. Appendix H to EPRI 3002000709, Seismic Probabilistic Risk Assessment Implementation Guide (known as the SPRAIG) [5] contains recommended “representative fragilities” for several equipment classes. These representative fragilities originated from early SPRAs published in the literature. Some of these Appendix H representative fragilities have been found to be unconservative with respect to detailed fragilities developed in some recent SPRAs. In general, 6-15 13633436 Fragility Implementation Topics the fragilities in SPRAIG Appendix H can be used in an initial risk quantification to identify dominant contributors if they can be shown to be applicable to the specific plant. Again, the fragility analyst must be able to defend the use of any SPRAIG Appendix H generic version of a representative fragility as being appropriate. In many cases, demonstrating appropriateness for a plant may be difficult due to the limited information available supporting the SPRAIG Appendix H fragilities (e.g., configuration of the SSC, location within the structure, frequency content of the RE). As such, most representative fragilities used as initial fragility estimates should be developed on a plant-specific basis. However, there are some fragilities in SPRAIG Appendix H that are commonly used generically in SPRAs. For example, the loss of offsite power (LOOP) and loss of coolant accident (LOCA) fragilities from SPRAIG Appendix H are conventionally used in SPRAs unless better plant-specific information is available. For small-small LOCA (SSLOCA), Appendix K provides guidance and lessons learned for developing fragilities that are more plant-specific than those provided in SPRAIG Appendix H. Since representative fragilities are likely to be somewhat conservatively biased, the SCDF and SLERF results from the initial quantification should likewise be conservatively biased. Therefore, they should not be considered reliable for any significant risk-informed decision making until the dominant risk contributors are refined to a reasonable degree. The reliability of the initial risk quantification insights (e.g., identification of dominant contributors) is highly sensitive to the completeness and accuracy of the systems model. Since representative fragilities are often developed early in the project, it is likely that the SPRA model may still be under development at the time of the initial quantification. As such, significant judgment and coordination between the systems analyst and fragility analyst is required to ensure insights and fragility refinement decisions based on the initial quantification are reliable and reasonable. Section 6.2.3 outlines the steps involved in one example approach for developing representative fragilities. 6.2.4 Example Approach for Developing Representative Fragilities 6.2.4.1 Selecting Representative Fragility Data Representative fragilities should represent the as-built, as-operated configuration of the plant to the greatest possible degree, while still using relatively simple and efficient fragility approaches. Representative fragility data can be obtained from as-built drawings, design data, previous seismic evaluations, and communication with plant engineers, such that representative fragilities can be developed for the current configurations and conditions of the SEL components. A walkdown is necessary to accurately characterize some failure modes/levels (e.g., seismic interactions, anchorage capacities, degradation such as corrosion or cracking). Recent plant walkdowns could also be used for this purpose if the fragility analyst can justify that the as-built plant has not changed enough to significantly alter the previous walkdown data (Section 6.1). 6-16 13633436 Fragility Implementation Topics 6.2.4.2 Filtering and Screening of the SEL For efficiency, the SEL can be filtered to reduce the number of items that require representative fragilities. The following filters are examples that can be applied:  Items that can be screened from the SEL because they are judged not to impact the SPRA results. This screening is performed by the systems analyst based on their knowledge of the plant logic model.  “Rule of the box” items that can be assigned the representative fragility of the host component. The “rule of the box” is defined in SQUG GIP [31]. One exception to this “rule of the box” is relays (and other types of devices using contacts in the control circuitry). Relay fragilities must be evaluated independent of the cabinets in which they are housed (Section 6.3).  Items identified as inherently rugged (Section 6.2.1). Inherently rugged SSCs have very high capacities relative to other SSCs and therefore will not be contributors to the seismic risk. As such, developing a representative fragility is unnecessary.  Items that have obvious seismic deficiencies or that lack a seismic design basis. These items can require more than the typical level of effort to develop a representative fragility, and they are also more likely to end up being dominant risk contributors based on their lower anticipated fragilities. These items should be considered on a case by case basis (jointly with the systems analyst) to determine whether it is appropriate to move directly to developing a specific, detailed fragility. 6.2.4.3 Developing Seismic Capacities A detailed, plant-specific plan should be developed for developing representative fragilities depending on the available information and resources. The example approach outlined below involves first categorizing SSCs using a capacity ranking system. The rank can then be used to facilitate development of the seismic capacity value of the SSC. The capacity ranks used in the approach outlined below are defined as Rugged, High, Medium, and Low. Depending on plantspecific considerations, it might be more appropriate, for example, to organize the development of representative fragilities around other characteristics such as system (e.g., NSSS), equipment class, basis of capacity (e.g., SSCs qualified by testing or analysis), or previous analyses that are available (e.g., IPEEE or DBE). The approach outlined below has been used successfully on several recent SPRAs performed in response to NTTF Recommendation 2.1. Rugged Rank Equipment expected to be insensitive to reasonable levels of seismic input, and therefore not expected to contribute significantly to seismic risk, are ranked Rugged (see also Section 6.2.1). Items commonly ranked Rugged are listed in Table 6-2. The items must be obviously well anchored and free of interaction concerns. It is anticipated that items ranked Rugged will not require representative fragility assessments because they have very high seismic capacity relative to other SEL items and thus will have negligible contribution to seismic risk. 6-17 13633436 Fragility Implementation Topics High Rank Both the High Rank and the Medium Rank methodology use elements of the seismic capacity approach described in Section 4.2 of this report. This approach consists of estimating the approximate median or HCLPF seismic capacities of SSCs based on Tables 4-2 and 4-4, which originated from EPRI NP-6041-SLR1 [1]. SSCs can be ranked High if they satisfy the applicable seismic capacity criteria described in Section 4.2 for the 1.2g Sa ground motion bin (4.8g median and 1.8g HCLPF in-structure Sa) and have robust anchorage. For example, some valves satisfying the criteria might be ranked High because anchorage is generally not a governing failure mode for valves. Some items ranked High may be governed by anchorage failure, but the anchorage capacities are judged to meet or exceed the 4.8g median / 1.8g HCLPF in-structure Sa capacity. Walkdown teams would need to use engineering judgment during the walkdown to assess whether anchorage is expected to govern the capacity of High ranked items. To validate the walkdown team’s judgments on anchorage capacities, some recent SPRAs have included specific anchorage evaluations for bounding cases selected during or after the walkdown. Medium Rank SSCs ranked Medium satisfy the applicable Section 4.2 walkdown criteria for 1.2g Sa ground motion (4.8g median and 1.8g HCLPF in-structure Sa), but the walkdown team judges that anchorage may govern the seismic fragility. Because they meet the Section 4.2 criteria, their functional HCLPF capacity could be estimated to be at least 4.8g median and 1.8g HCLPF in-structure Sa, but the anchorage capacity may be lower. For example, Medium rank might be assigned to some large mechanical SSCs where the anchorage cannot be justified as having capacities exceeding the 4.8g median and 1.8g HCLPF Sa at the location of the SSC. Medium-ranked items should exhibit no significant degradation, deficiencies, or interaction concerns. Seismic capacities for Medium-ranked SSCs can be based on the seismic design calculations, past beyond design basis seismic evaluations, or new calculations. Representative fragilities for Medium-ranked SSCs should focus on anchorage failure modes, unless the walkdown team observed some other controlling failure mode. If anchorage can be shown to have a capacity exceeding 4.8g median and 1.8g HCLPF in-structure Sa, and there are no other potentially governing failure modes (e.g., interactions), then the rank can be changed to High. If prior evaluations are used to develop the seismic capacity, they should be reviewed for reasonableness and for significant changes in methodology since the time when the prior evaluation was performed (e.g., the ACI 349 anchorage evaluation methodology has evolved significantly since the original design of most U.S. plants). Low Rank Equipment is ranked Low typically because one of the three alternative classifications described above could not be justified. The low ranking typically results from the walkdown team judging that the SSC has a low seismic capacity relative to SSCs in the higher bins due to a seismic interaction that occurs at a relatively low ground motions or because the SSC has not been designed or evaluated for seismic loading. 6-18 13633436 Fragility Implementation Topics 6.2.4.4 Develop Seismic Response and Representative Fragilities Once capacities are established based on the ranking, prior evaluations, bounding calculations, etc., they are compared to demands as described in Sections 3, 4, and 5 to develop the representative fragilities. For efficiency, the representative fragility demands can be estimated on a simplified and/or conservative basis. Simplified approaches typically would involve scaling of past seismic response analyses (Section 6.7), and / or could use the bounding demand for a given floor for all SSCs on that floor. The fragility analyst should be prepared to document and defend these simplified demand approaches. Representative fragilities can be developed using the hybrid or SOV approach and should generally use whichever method is most efficient. Typically, the hybrid approach is the most efficient, but in some circumstances, it may be more efficient to use the SOV approach (e.g., if an SOV fragility calculation is already available from a prior SPRA). The evaluation of several classes of SSCs can be challenging to perform as part of the ranking approach described above. For example, it is not always obvious whether structures, NSSS components, distribution systems, masonry walls, or seismic interaction issues identified during the walkdown can be assigned to one of the ranks. For these SSCs and failure modes that are not addressed by the ranking system, representative fragilities should be developed separately. For structures, Table 4-4 can be used to efficiently develop a representative fragility provided that sufficient information is available to demonstrate the structure satisfies the associated criteria. Structure fragilities developed using Table 4-4 will often be conservative for nuclear power plant type structures. Therefore, it is likely that they will be identified as dominant contributors in the initial quantification and will require refinement in subsequent iterations. To avoid masking the risk insights from the initial quantification, such refinement can be performed before the initial quantification, or higher fragilities could be assumed for the structures, as long as they are revisited and either updated or justified in subsequent iterations. Distribution systems (cable trays, HVAC ducting, piping) can be addressed in the representative fragility evaluation by identifying bounding cases during the walkdown, and then evaluating bounding fragilities for those cases using simplifying and/or conservative approximations. Similarly, masonry walls can be grouped, and bounding evaluations performed to simplify the representative fragility evaluation. If the conservative, bounding fragilities are identified as dominant contributors, then the groups that are bounded by those cases should be broken up, or the fragility sufficiently refined in subsequent iterations. 6.3 Outline of Relay Evaluation As discussed in Section 6.1, the complete relay list is usually not available when the main walkdown takes place. The guidance in Section 6.1 and Appendix B pertaining to relays is limited to ensuring that all hardware in the interior of cabinets is well secured, including relays. This section provides additional guidance on implementing a relay evaluation in an SPRA, including coordination among the walkdown, relay fragility evaluation, and systems analysis tasks such as SEL development and relay chatter evaluation. 6-19 13633436 Fragility Implementation Topics Relays and similar electromechanical devices, such motor starters and switches, are lightweight and can be adequately secured with small screws or clamping mechanisms. Socket-type relays may be held in place by friction in the socket, and their capacity is determined from testing. For purposes of the following discussion, the term “relay” refers to any electromechanical device that can change state when subjected to acceleration13. The relay evaluation is a joint effort between the systems analysis engineers and the SRT. The steps in a detailed relay evaluation are as follows: 1. The SEL is developed by the systems analysis team. Guidance for SEL development is provided in Section 5.1 of EPRI 3002000709 [5]. 2. From the SEL, SSCs that contain relays are identified, typically by the systems analysis team. A complete relay list is developed for SEL SSCs from circuit diagrams to identify those relays and other similar devices that are electromechanical or solid state. Circuit analysis is performed to determine if chatter can cause a malfunction of essential SSCs (trip open, inadvertent actuation, lock out, seal in, etc.). Those relays that are determined not to cause malfunctions are identified as needing only a structural capacity review. Other relays require functional review as well as structural capacity review. Guidance for relay chatter evaluation as described above is provided in Section 5.7 of EPRI 3002000709 [5]. 3. Given the relay list, the fragility analyst determines the functional capacity and structural capacity based on available qualification test data (e.g., GERS [20, 21], the SQURTS Program [22, 25], site-specific test reports). Development of the capacity of relays from test data is discussed in Section 4.9. For those relays that can chatter and lead to malfunction of an SEL SSC, a capacity must be developed to characterize the probability of the relay to fail to function during shaking. For those relays that are not sensitive to chatter, only the capacity after shaking is required. The capacity may be defined relative to the cabinet base TRS or at the input to the individual relay, depending on the test report. 4. For those relays whose capacity is defined at the relay mounting point, cabinet amplification factors, as discussed in Section 5.5.3.2, must be developed using generic factors, such as in Table 5-10, by using acceleration data from specific cabinet tests, or by detailed finite element dynamic analysis of the cabinets. 5. In cases where the amplification factors result in seismic input at the device that is determined to be problematic for the risk analysis, further evaluation and refinement may be required, as discussed in Appendix L. The walkdown evaluation of relays generally follows the procedure described in Section 6.1.4 wherein a lead SSC is thoroughly examined, and the similar SSCs are walked by. This procedure ensures that at least one SSC of a similar group is opened and examined for adequate mounting of devices. Although the similar SSCs may appear to be identical to the lead item in a walk-by, it has often been found that individual relays are placed differently in the cabinets. It is therefore important in a relay evaluation walkdown to confirm that similar cabinets have relays and mounting that are the same as the lead item, if that information is important to the fragility Solid state relays are not strictly included in this definition, but the review outlined herein should nonetheless include the attachment of solid state relays to their enclosure cabinets. 13 6-20 13633436 Fragility Implementation Topics evaluation. This does not necessarily mandate that all cabinets be opened to perform a detailed inspection of each relay. The observations from samples and the judgment of the lead SRT engineer are important to keep the assessment to a manageable level. The actual procedure of a complete relay evaluation may vary depending on the severity of the RE relative to the design basis SSE and the consequences of relay chatter in the risk assessment. Some relay chatter events may not result in significant risk, so the whole relay assessment can take on iterations of systems analysis and more detailed walkdowns and inspection of the individual relays. There are typically thousands of relays in the SEL SSCs, and it is not practical to initially open all SEL electrical and control panels and do a detailed examination of each relay. The detailed examination may best be done only when the consequences of relay chatter are significant. 6.4 Special Considerations for High-Frequency Seismic Demands Seismic accelerations in the 1 to 10 Hz frequency range are generally considered to be the most damaging to SSCs important to SPRAs. For most types of SSCs, accelerations at frequencies above 20 Hz are generally considered to be less damaging than lower-frequency motions because the resulting displacements are inversely proportional to the square of the frequency, which makes the higher-frequency displacements very small. The higher-frequency motion has been prevalent in recent PSHAs for rock sites such as those in the Central and Eastern United States (CEUS). Additionally, mathematical models of stiff NPP structures tend to predict significant amplification of the high-frequency motion, producing ISRS with one or more highly amplified, narrow frequency spectral peaks in the high-frequency range (higher than ~15 Hz). These high-frequency ISRS are generally considered to be unrealistic and/or non-damaging to most NPP equipment. The following subsections describe a variety of evaluation tools and methods focused on treatment of such high-frequency demands and development of high-frequency capacities for specific types of SSCs and failure modes commonly encountered in SPRAs. Section 6.4.1 summarizes the results and salient insights from recent EPRI research on the high-frequency capacity of potentially chatter-sensitive components such as relays and other contactors. The research found that chatter-sensitive devices generally have high-frequency capacities at least as great as their corresponding low-frequency capacities. This guidance provides a procedure for estimating the high-frequency capacity of such devices, which can be compared to high-frequency demands to obtain a seismic fragility. Section 6.4.2 summarizes recommendations from recent EPRI research pertaining to inelastic effects on anchorage. The research demonstrates that the seismic margin of most anchorage configurations is greater when subjected to high-frequency demands as compared to low-frequency demands. The additional margin is quantified by an inelastic capacity factor, Fin, and guidance is provided for calculating the factor under various conditions. 6-21 13633436 Fragility Implementation Topics Section 6.4.3 discusses three general methods used to calculate and interpret high-frequency structure response:  ISRS averaging over several structure model nodes  ISRS averaging over a range of frequencies to account for uncertainty in equipment frequency  Equipment-structure interaction (ESI) Finally, Section 6.4.4 discusses qualitative measures that can be considered in the treatment of high-frequency motions for fragility calculations. 6.4.1 High-Frequency Test Capacities for Fragility Evaluation Equipment items important to safety within operating NPPs have been seismically qualified for the SSE defined for each plant. Active equipment has been qualified by shake table testing to demonstrate function during an SSE event either by testing of the entire equipment item or by separate testing of the functional components of the equipment item. Many equipment items have also been evaluated for an RLE under each plant’s IPEEE Program. The SSE and RLE ground motions, however, do not typically include significant frequency content above about 16 Hz. Therefore, the TRS (typically covering the 4 to16 Hz range) from qualification reports and GERS [20, 21] do not normally provide equipment capacity data in the high-frequency range. EPRI 1015108 [135] summarizes a significant amount of empirical and theoretical evidence, as well as regulatory precedents, that support the conclusion that high-frequency vibratory motions above about 16 Hz are not damaging to the large majority of NPP structures, components, and equipment that have stress- or displacement-based potential failure modes. EPRI NP-7498 [29] concludes that in such cases, the experience-based capacity in the high-frequency range (20 Hz to 40 Hz) can be conservatively estimated by extending the low-frequency spectral bounding value into the high-frequency range to about 40 Hz (Section 4.2.1). An exception to this conclusion is the performance of components subject to electrical functionality failure modes (“contact chatter”). High-frequency excitation of relays and other electrical control and instrumentation devices can potentially cause contact chatter affecting the device output signal. EPRI 1015109 [136] reviewed the devices sensitive to contact chatter, and identified the following list of components likely affected by high-frequency vibratory motion in the 20 to 40 Hz range:  Relays  Contactors  Switches  Switchgear trip mechanisms  Potentiometers  Other devices whose output signal or set-points could be changed by vibration 6-22 13633436 Fragility Implementation Topics The EPRI high-frequency test program (EPRI 3002002997 [23] and 3002004396 [24]) conducted a large volume of shake table tests of components with potential high-frequency vulnerability. The high-frequency test program did not find a unique sensitivity of any control components to high-frequency vibration in the 20 to 40 Hz range. It was demonstrated that contact chatter is initiated at lower spectral levels when low-frequency inputs are used. In all cases where contact chatter occurred in a high-frequency test, contact chatter also occurred in a low-frequency test (4 to 20 Hz) of the same component at an equal or lower input motion level. The tests found no components for which contact chatter occurred in the high-frequency test at an acceleration level lower than in a low-frequency test. Section 5 of EPRI 3002002997 [23] summarizes high-frequency test results from the EPRI high-frequency test program in several tables. A component test spectral acceleration capacity, or TRS, can be developed from the test results in these tables. For many of the tested components, the table acceleration limit was reached with no observed chatter. For these components, the tables in in Section 5 of EPRI 3002002997 [23] list the table acceleration limit, and this value can be used as a lower bound estimate of the component TRS capacity between 20 Hz and 40 Hz. For other components, contact chatter was observed for some test acceleration level. For these components, the tables in Section 5 of EPRI 3002002997 [23] list the highest test acceleration for which no contact chatter occurred (i.e., contact chatter was observed at the subsequent test increment acceleration level). In this case, the component TRS capacity may be estimated midway between the acceleration level of the test in which contact chatter was observed and the acceleration level of the preceding test. For the EPRI high-frequency test program, the acceleration interval between tests was 1.25g, so the TRS capacity between 20 Hz and 40 Hz of components with observed contact chatter can be taken as the value listed in the EPRI 3002002997 [23] tables plus 0.625g, which is half the test acceleration interval. The low-frequency (approximately 4 to 20 Hz) TRS capacity of components may be determined from the results of qualification testing, or from GERS [20, 21] or SQURTS [22] test capacity values. In general, an envelope of the high-frequency and low-frequency TRS may be used to determine the spectral acceleration capacity over the 4 to 40 Hz frequency range, or the two spectra may be used independently for separate evaluations. At a minimum, the low-frequency spectral acceleration may be extended into the high-frequency range, with a spectral plateau roll off at 40 Hz, such as shown in Figure 6-2 for an example component. 6-23 13633436 Fragility Implementation Topics Figure 6-2 Composite test capacity (TRS) for an example component EPRI 3002004396 [24] also provides guidance for conservatively estimating high-frequency structural amplification factors. The factors can be used to estimate 84% NEP in-structure clipped spectral accelerations in the high-frequency (>15 Hz) range to evaluate relays if no better information is available. Factors are provided in the horizontal and vertical directions separately and are based on regression analysis of actual NPP structure responses from past seismic evaluations. The in-structure clipped spectral acceleration is estimated as the product of the amplification factor and the high-frequency peak (>15 Hz) of the input ground motion. 6.4.2 High-Frequency Inelastic Effects on Anchorage Systems Most types of equipment anchors used in NPPs have small deformation capacities. One may thus infer an insignificant benefit in defining anchor failure using deformation capacities (displacement criteria) rather than anchor strengths. While this is true for equipment responding at low frequencies, it is not so for equipment responding at high frequencies. For a given acceleration input level, equipment responding at higher frequencies undergo much smaller displacements than low-frequency equipment. A 5 Hz piece of equipment responding to 5g acceleration input displaces (5g)(32.17 ft/sec2/g)(12 in./ft) / [ (2π)(5 Hz) ]2 = 1.96 in., while a 25 Hz equipment displaces only 0.078 in., which is smaller by a factor of 25. The much smaller equipment displacements at higher frequencies can potentially result in the anchor deformation capacities not being exceeded. Thus, a piece of equipment responding at a high frequency can sustain higher acceleration input levels without failing its anchors. EPRI 3002010665 [137] presents approaches to compute an inelastic capacity increase factor Fin, that quantifies this increase in the input acceleration capacity (i.e., seismic capacity) associated with the anchorage failure mode for equipment responding at higher frequencies. These approaches presented in EPRI 3002010665 [137] can be applied to floor-mounted equipment 6-24 13633436 Fragility Implementation Topics wherein the anchorage is loaded only by seismic loads (e.g., dead load being transferred directly to the floor) and is much stiffer than the equipment (i.e., the anchorage stiffness does not significantly influence the equipment frequency). Section 6.4.2.1 presents the methodology to compute anchorage inelastic capacity increase factors for equipment subjected to seismic input along a single direction. Section 6.4.2.2 extends the methodology to equipment subjected to multi-directional seismic input. 6.4.2.1 Equipment Subjected to Single Direction Seismic Input Step 1: Estimate the elastic frequency f (in the direction of interest) and the elastic damping ξ of the equipment Step 2: Compute the strength factor FS for the equipment anchorage in accordance with methods and approaches presented earlier. Step 3: Compute the system yield displacement δys as: δ F Sa f, ξ 2πf Eq. 6-1 where, Sa(f, ξ) is the input spectral acceleration at elastic frequency f and elastic damping ξ. Step 4: Compute the system inelastic displacement capacity δin (measured at the equipment center of gravity), using the inelastic displacement capacity of the critical anchor element, δin,a. The exact relationship between δin and δin,a depends on the equipment geometry and anchor failure mode of interest. As an example, for equipment anchors failing in direct horizontal shear due to horizontal seismic input, δin = δin,a. For equipment anchors failing in tension due to overturning of equipment subjected to horizontal seismic input, δin = (Hcg/d) δin,a, where Hcg is the height to equipment center of gravity, and d is the distance between the overturning axis and the critical anchor in the direction of seismic input. Tables 6-3 through 6-5 present recommended δin,a values for common anchors found in NPPs. For anchors and failure modes not listed in these tables, test data or published literature may be used to determine δin,a. The quantity δin,a should be based on an elastic perfectly plastic (EPP) fit to the actual force-displacement curve of the critical anchor element. The equivalent EPP fit should retain the elastic stiffness and the peak strength of the true force displacement curve. See Section 4 of EPRI 3002010665 [137] for more details. 6-25 13633436 Fragility Implementation Topics Table 6-3 Inelastic deformation capacity of fillet welds Inelastic Deformation Capacity, δin,a (in.) * Fillet Weld Leg Size (in.) Longitudinal Loading (θ = 0°) Transverse Loading (θ = 90°) Median 95% Exceedance Median 95% Exceedance 3/16 0.024 0.017 0.0071 0.0051 1/4 0.032 0.023 0.0095 0.0069 5/8 0.081 0.058 0.0238 0.0171 3/4 0.097 0.070 0.0286 0.0206 7/8 0.114 0.082 0.0334 0.0240 1 0.130 0.093 0.0381 0.0274 * δin,a = 0.162(θ + 2)-0.32 t, where θ is the angle of loading in degrees, and t is the weld leg size. Table 6-4 Inelastic deformation capacity of anchors failing due to concrete breakout in tension Anchor Inelastic Deformation Capacity Normalized by Embedment Depth Uncracked Concrete Cracked Concrete Median 95% Exceedance Value Median 95% Exceedance Value Cast-in-Place Headed Studs 0.023 0.0028 0.0091 0.0040 Wedge and Sleeve Expansion Anchors 0.030 0.0040 0.017 0.0019 Undercut Anchors 0.022 0.0055 0.016 0.0036 Table 6-5 Inelastic deformation capacity of concrete anchors failing due to concrete breakout in shear Inelastic Deformation Capacity Normalized by Edge Distance (in.) Median 0.0040 95% Exceedance Value 0.0017 6-26 13633436 Fragility Implementation Topics Step 5: Compute the system ductility μ as: μ δ δ δ δ δ 1 δ δ μ Eq. 6-2 where, δu is the system ultimate displacement, i.e., the sum of system yield displacement and the system inelastic displacement capacity, and: For equipment subjected to horizontal seismic input undergoing anchor shear failure (Horizontal Shear Model) 4 ⎧ ⎪ ⎪ ⎪ ⎪10 ⎪ μ Step 6: For equipment subjected to horizontal seismic input undergoing anchor tensile failure due to overturning effects (Horizontal Overturning Model)14 ⎨ ⎪10 ⎪ ⎪ ⎪ ⎪ ⎩25 For weld-anchored equipment subjected to vertical seismic input (Vertical Weld Model) For equipment anchored using steel bolts or concrete anchors being subjected to vertical seismic input (Vertical Anchor Bolt Model) Compute the ratio of secant frequency fs to the elastic frequency f as: f f ⎧ ⎪ ⎪ 1 μ ⎨ 1 ⎪ ⎪ 1 ⎩ 2 If seismic input is along a horizontal direction 1 μ If seismic input is along the vertical direction Eq. 6-3 Does not apply to equipment anchored using welds. For weld-anchored equipment subjected to horizontal seismic input, use the Horizontal Shear Model case irrespective of whether overturning governs or not. 14 6-27 13633436 Fragility Implementation Topics Step 7: Compute the ratio of effective frequency fe to elastic frequency f as: f f A Step 8: B 0.30 ⎧ ⎪ ⎪0.70 Eq. 6-4 Horizontal Shear Model Horizontal Overturning Model Eq. 6-5 ⎨ 0 ⎪ ⎪ ⎩0.60 Vertical Weld Model Vertical Anchor Bolt Model f f 1 B 0.15 ⎧ ⎪ ⎪0.10 Eq. 6-6 Horizontal Shear Model Horizontal Overturning Model Eq. 6-7 ⎨0.50 ⎪ ⎪ ⎩0.50 Vertical Weld Model Vertical Anchor Bolt Model Compute the system effective damping ξe as: ξ Step 10: f f 1 A Compute the system hysteretic damping ξh as: ξ Step 9: 1 f f f f ξ ξ Eq. 6-8 Compute the inelastic capacity increase factor as: F f f f f 6-28 13633436 Sa f, ξ Sa f , ξ Eq. 6-9 Fragility Implementation Topics Logarithmic standard deviations for randomness (βR) and uncertainty (βU) associated with the computed inelastic capacity increase factor are given by: β β 0.40 0.06 0.03 F min 0.20 F ⎧ ⎪ ⎪min 0.25 F ⎪ ⎨ ⎪ ⎪ ⎪ ⎩ 0.15 0.20 1 1 1 . . , 0.20 , 0.25 Eq. 6-10 Horizontal Shear Model Horizontal Overturning Model Eq. 6-11 Vertical Weld Model Vertical Anchor Bolt Model Equations 6-1 through 6-9 can also be used to estimate the anchorage inelastic capacity increase factor for CDFM evaluations. However, a 95% exceedance value for the anchor inelastic deformation capacity should be used instead of the median value to compute the CDFM inelastic capacity increase factor. The fragility analyst should be aware that in certain situations, it may not be appropriate to credit all the available system inelastic displacement capacity (δin). If excessive equipment displacement can lead to impact with adjacent equipment or structural members, then the system inelastic displacement capacity should be limited to a value that would preclude such interaction. Another scenario where some caution should be exercised involves equipment that have essential relays and are anchored using steel bolts or concrete anchors. Accumulation of plastic deformations in the equipment anchor bolts during successive inelastic response cycles as a result of equipment overturning or vertical response may cause gaps to form between the anchor bolt head/nut and the equipment. Due to these gaps, the equipment will be briefly unrestrained in each subsequent cycle, resulting in pounding between the equipment base and the floor supporting the equipment. This could lead to chatter in essential relays. In this case, it may be prudent to not credit any nonlinearity in the equipment anchors. 6.4.2.2 Equipment Subjected to Multi-Directional Seismic Input The method presented in the preceding section applies to equipment subjected to seismic input along a single direction. In a typical equipment seismic fragility evaluation, two orthogonal horizontal seismic components, and one vertical seismic component must be considered acting concurrently. An approach for addressing this general case is presented below. 6-29 13633436 Fragility Implementation Topics Step 1: Compute the anchorage strength factor FS using anchor elastic demands from the two horizontal components (acting along the equipment longitudinal and transverse axes) and the one vertical component. This would typically require the use of an interaction equation to address combined shear and tensile loading of the anchors. Step 2: Using the anchorage strength factor FS, compute independent Fin factors for each combination of anchor demand and seismic input component. Typically, the following Fin factors need to be computed:  Fin associated with the anchor shear demand due to the transverse seismic component (say, FinVT): This Fin is based on the Horizontal Shear Model using the shear inelastic deformation capacity of the anchor and the transverse seismic input.  Fin associated with the anchor shear demand due to the longitudinal seismic component (say, FinVL): This Fin is based on the Horizontal Shear Model using the shear inelastic deformation capacity of the anchor and the longitudinal seismic input.  Fin associated with the anchor tensile demand resulting from rocking due to the transverse seismic component (say, FinPT): This Fin is based on the Horizontal Overturning Model using the tensile inelastic deformation capacity of the anchor and the transverse seismic input.  Fin associated with the anchor tensile demand resulting from rocking due to the longitudinal seismic component (say, FinPL): This Fin is based on the Horizontal Overturning Model using the tensile inelastic deformation capacity of the anchor and the longitudinal seismic input.  Fin associated with the anchor tensile demand due to the vertical seismic component (say, FinPV): This Fin is based on either the Vertical Weld Model or the Vertical Anchor Bolt Model (as the case may apply) using the tensile inelastic deformation capacity of the anchor and the vertical seismic input. Step 3: Reduce the anchor elastic demands with the appropriate Fin factor. For example, the anchor shear demand due to the longitudinal seismic component needs to be reduced by FinVL, shear demand due to the transverse component by FinVT, etc. Step 4: Use the reduced elastic demands to compute a new scale factor to satisfy the failure criteria (e.g., the tension-shear interaction equation); this scale factor is the anchor capacity factor FC, and represents the product of FS and the overall Fμ. Step 5: If required, the overall anchorage Fin can be recovered using the following equation: F F F 6-30 13633436 Eq. 6-12 Fragility Implementation Topics The approach outlined in the above steps suggest that as many as five separate Fin factors may need to be computed to come up with the overall anchorage inelastic capacity increase factor Fin. This would typically be the case for equipment anchor bolts, for which the failure criterion is typically an interaction equation that considers both tensile and shear failure modes. The two horizontal seismic components contribute to the anchor shear demands, while all three seismic components contribute to the anchor tensile demand, resulting in a total of five separate Fin factors that need to be computed in the above approach. In the case of fillet welds, the failure criterion is essentially based on a single failure mode: weld shear failure. Consequently, only three individual Fin factors need to be computed (one for each seismic component), as compared to five for anchor bolts. It is evident that a rigorous application of the above approach requires multiple Fin calculations. A fragility analyst can, upon adequate justification, make suitable simplifications on a case-bycase basis. Typically, the simplification will involve computing Fin factors for only the governing demands. While conservative, the degree of conservatism resulting from such a simplification may not be obvious in every case. 6.4.3 Seismic Response Considerations Three approaches for improving the realism of high-frequency demands are presented in this section. These methods are most helpful when estimating fragilities using analytical methods, where peak clipping techniques are typically not applied. Two of the methods involve spectral averaging techniques for ISRS. The third method involves the consideration of ESI in the calculation of ISRS. 6.4.3.1 Spectral Averaging for In-Structure Response Spectra At high frequencies, the ISRS peaks tend to be localized because the responses are due to local modes. For example, even over a 25 sq ft area, the average peak spectral acceleration can be meaningfully less than that computed for an individual node. Fragility analysts may consider the effects of several nodal ISRS over an effective area of an equipment foundation when computing fragilities. An effective area equal to the footprint of the equipment plus the floor thickness (i.e., projecting 45° through the floor thickness) is considered reasonable. Vertical ISRS can be particularly sensitive to this effect when dominated by local out-of-plane slab modes. Care should be taken to avoid inappropriately masking true in-structure floor motions. For example, averaging the vertical response of a mid-floor node with nodes along the floor-wall interface may not be realistic for a component with a small footprint relative to the slab size. The overall goal is to provide a realistic (rather than conservative) estimate of the input motions for equipment fragility calculations. Higher frequency ISRS can have relatively narrow peaks. In these circumstances, it can be overly conservative to assume that the equipment natural frequency is at the peak of the ISRS. In most cases, it would be more realistic to estimate the equipment natural frequency (in each direction), assume some uncertainty on that estimate of ±10% to 15%, and average the ISRS spectra accelerations over that frequency range. A more sophisticated approach, which would be appropriate, perhaps, for a dominant risk contributor, would involve probabilistic sampling of the spectral accelerations within a frequency range around the best estimate frequency. The sampling should be statistically consistent with the distribution of equipment frequency (i.e., more samples 6-31 13633436 Fragility Implementation Topics around the highest probability frequencies; fewer samples around the tails of the distribution). Statistics can then be performed on the sampled spectral accelerations to obtain a best estimate demand (median) and a logarithmic standard deviation on spectral acceleration due to uncertainty in equipment frequency. 6.4.3.2 Equipment-Structure Interaction Response spectra are typically calculated using a series of zero mass single-degree-of-freedom (SDOF) oscillators at specified frequencies. At resonance, ISRS only correctly estimate the response of equipment that has essentially zero mass relative to the modal mass of the structure for the structural mode that produced the peak spectral acceleration. At higher frequencies, these structure modal masses are generally small and highly localized. Therefore, this assumption of zero equipment mass can lead to conservative response spectra peaks. At an equipment-tostructure modal mass ratio as low as 1%, the coupling effect can sometimes result in a meaningful reduction of the spectral acceleration input to the equipment below the peak spectral acceleration of the ISRS. With a mass ratio of 5%, this reduction can become very significant. Several analytical methods are available to calculate these equipment-structure interaction effects (e.g., Tseng [138] and Gupta [139]). These methods typically require a fair amount of structure and equipment data to compute the effective ISRS. EPRI 3002010666 [140] describes simplified, approximate solutions for estimating coupled ISRS. Statistical values of reduction factors for a simple, representative, 5-DOF system are developed to be considered as conservative estimates for more complex systems. 6.4.4 Qualitative Methods for Considering High-Frequency Motions In May 2016, EPRI hosted a meeting of seismic fragility experts and practitioners to discuss qualitative methods for considering high-frequency responses in a realistic and consistent manner in seismic fragility evaluations. The goals of the meeting were to:  Identify sources of significant potential inaccuracy in the treatment of high-frequency motions in fragility calculations, and  Identify recommended methods that may be helpful in achieving more realistic fragility analyses. As noted in Section 6.4.2, high-frequency accelerations are generally considered non-damaging because spectral displacements are inversely proportional to the square of the spectral frequency; therefore, at higher frequencies, the displacements become relatively small. The consensus judgment among the fragility experts present at the 31 May 2016 EPRI meeting in Charlotte, North Carolina, was that seismic motions above about 20 Hz are generally nondamaging to anchorage and structural failure modes of equipment, including stress-related functional failure modes. Accordingly, the meeting participants agreed that fragility evaluations should focus on spectral demands up to 20 Hz for flexible equipment and ZPA for essentially rigid equipment. For a stiff component with a fundamental frequency above 20 Hz, it would be reasonable to define the seismic input as the lesser of: (1) the Sa at 20 Hz, and (2) the Sa at the equipment fundamental frequency. This method effectively limits the high frequency peaks above 20 Hz to the 20 Hz spectral acceleration, as illustrated in Figure 6-3. 6-32 13633436 Fragility Implementation Topics Figure 6-3 Limiting high-frequency spectral accelerations to 20 Hz spectral ordinate This high-frequency cutoff of 20 Hz may be applied to both structural and anchorage evaluations, as well as to functional fragility evaluations for stress-related functional failure modes. The cutoff is not applicable to active functional failure modes for functions required to be maintained during shaking, such as chatter of electromechanical devices. 6.5 Methods for Spectral Clipping Test-based equipment seismic fragilities can be formulated by comparing broadband TRS to broadband demand spectra (Sections 4.1.3, 4.9, and 5.5.3). Alternatively, as discussed in Section 4.2, broadband capacity spectra from Tables 4-2 and 4-4 can be compared to broadband demand spectra to develop seismic fragilities for equipment that meet the corresponding criteria in Section 4.2 and Appendices B and C. Deterministic and probabilistic ISRS often exhibit highly amplified narrow-band frequency content (i.e., spectral peaks). Clipping factors recommended in Section 5.5.3 are typically used to clip these peaks to obtain broadband demand spectra. Determining a median clipped spectral acceleration demand and variabilities for structure response and clipping is not always straightforward for ISRS developed using the deterministic and probabilistic seismic response analysis approaches discussed in Section 5.3.5 and 5.3.6. The median clipped spectral acceleration and variabilities for structure response and clipping can be determined following one or more of the methods discussed in Sections 6.5.1 and 6.5.2. 6.5.1 Spectral Clipping for Deterministic ISRS Two valid procedures for determining a median clipped spectral acceleration demand and variabilities for structure response and clipping are presented below for ISRS developed from the deterministic seismic response analysis procedure discussed in Section 5.3.5. 6-33 13633436 Fragility Implementation Topics 6.5.1.1 Deterministic Method 1 Median clipped ISRS, 84% NEP clipped ISRS, clipping variability, and composite structure response and clipping variability can be calculated as follows. 1. Calculate median clipping factors individually for ISRS from the five soil/structure property combinations, using Equation 5-22 from Section 5.5.3.1. 2. Apply the clipping factors calculated in Step 1 to the respective spectral peaks to clip the five individual ISRS. 3. The average of the five clipped ISRS calculated in Step 2 is the median clipped ISRS, SaCm. Double weight should be assigned to the clipped BE/BE ISRS in this average. 4. Calculate logarithmic standard deviations individually for ISRS from the five soil/structure property combinations, using Equation 5-23 in Section 5.5.3.1. 5. Select a representative logarithmic standard deviation based on the five logarithmic standard deviations calculated in Step 4, above. 6. Calculate CDFM clipping factors individually for ISRS from the five soil/structure property combinations, using Equation 5-21 from Section 5.5.3.1. 7. Apply the clipping factors calculated in Step 6 to the respective spectral peaks to clip the five individual ISRS. 8. The envelope of the five clipped ISRS calculated in Step 7 is the 84% NEP clipped ISRS, SaC84. 9. The structure response and clipping uncertainty can be determined by comparing median clipped ISRS from Step 3 to 84% NEP clipped ISRS from Step 8: CcRS,U = = Logarithmic standard deviation for structure response and clipping factor uncertainty Eq. 6-13 ln (SaC84 / SaCm) If desired, the structure response variability can be isolated from the clipping factor variability by SRSS subtracting the representative clipping factor uncertainty (Step 5) from the combined uncertainty from Equation 6-12. 6.5.1.2 Deterministic Method 2 Median clipped ISRS, structure response variability, clipping variability, and composite structure response and clipping variability can be calculated as follows. 1. Follow Steps 1 through 3 of Method 1 to determine the median clipped ISRS, SaCm. 2. Envelope the five clipped ISRS to determine the highest clipped ISRS, SaCm84. 6-34 13633436 Fragility Implementation Topics 3. The logarithmic standard deviation due to uncertainty in structure response is equal to the natural log of the ratio of the highest clipped spectral acceleration to the median clipped spectral acceleration at each frequency: RS,U = = Logarithmic standard deviation for structure response uncertainty Eq. 6-14 ln (SaCm84 / SaCm) 4. Follow Steps 6 and 7 of Method 1. 5. Calculate the median of the five clipped ISRS calculated in Step 4 using CDFM clipping factors, SaC84m. 6. The logarithmic standard deviation due to clipping factor uncertainty is equal to the natural log of the ratio of the median of the CDFM-clipped spectral acceleration (Step 5) to the median clipped spectral acceleration (Step 1) at each frequency. Cc,U = = Logarithmic standard deviation for clipping factor uncertainty Eq. 6-15 ln (SaC84m / SaCm) 7. The combined structure response and clipping variability is the SRSS combination of structure response variability (Step 3) and clipping variability (Step 6). CcRS,U = = Logarithmic standard deviation for structure response and clipping factor uncertainty Eq. 6-16 2 (RS,U + Cc,U2)1/2 6.5.2 Spectral Clipping for Probabilistic ISRS Probabilistic seismic response analyses are commonly performed to capture variability in ISRS demand (Section 5.3.6). Four methods are suggested for estimating clipping factor variability and structure response variability from probabilistic ISRS with narrow spectral peaks in Samuelson-Sanford, et al. [141]. There is one rigorous method, which involves independently clipping each of the thirty probabilistic ISRS and calculating structure response and clipping factor variabilities based on statistical analyses of the thirty clipped ISRS. The other three methods are simplified alternatives to the more rigorous method and require less computational effort. Clipping factor and structure response variabilities are functions of different aspects of the probabilistic ISRS: structure response variability is a function of the distribution in probabilistic spectral accelerations and clipping factor variability is a function of the ISRS shapes. The combined variabilities due to clipping factor and structure response for each of the four suggested methods are compared in Samuelson-Sanford, et al. [141]. The simplified methods are denoted Methods 1, 2, and 3 in Samuelson-Sanford, et al. [141] and are considered approximations to the more rigorous method (Method 4). The first two steps in Methods 1 through 3 are the same. The first step is to calculate the median and 84% NEP ISRS using the unclipped ISRS output from the probabilistic seismic response analysis. The second step is to clip the median ISRS by the median clipping factor from Equations 5-17 and 5-22. 6-35 13633436 Fragility Implementation Topics Variabilities for structure response and clipping are calculated differently for each of the three simplified methods:  In Method 1, the composite logarithmic standard deviation for structure response is calculated by comparing the unclipped median and 84% NEP spectral accelerations, and variability in the clipping factor is calculated independently using Equation 5-23.  In Method 2, the clipped 84% NEP ISRS is determined by the CDFM clipping factor from Equation 5-21 and is compared to the median clipped ISRS to determine the combined structure response and clipping factor variability.  In Method 3, the 84% NEP ISRS is clipped by the median clipping factor from Equations 5-17 and 5-22, the clipped 84% NEP ISRS is compared to the median clipped ISRS to determine structure response variability, and clipping factor variability is calculated independently using Equation 5-23. The most rigorous method, Method 4, involves the following steps: 1. The median clipping factor and corresponding variability are determined following Equations 5-17, 5-22, and 5-23 for each ISRS output from the probabilistic seismic response analysis (e.g., 30 ISRS, 60 ISRS). 2. From the median clipping factor and corresponding variability for each of the probabilistic ISRS (e.g., 30, 60), multiple clipping factors are determined, having equally spaced NEPs. 3. The peak spectral acceleration for each of the thirty ISRS are factored by the associated clipping factors, and all resulting clipped spectral accelerations are used to determine the median and 84% NEP values. 4. The combined structure response and clipping factor variability is determined by comparing the clipped median and 84% NEP spectral accelerations. Results from Samuelson-Sanford, et al. [141] are as follows:  It is appropriate to clip the median ISRS by Equations 5-17 and 5-22 and use the lowest combined structure response and clipping variability from either Methods 1 and 2 or Methods 1 and 3.  Using the lesser of Methods 1 and 3 provides a slightly better match to the Method 4 84% NEP clipped spectral accelerations, but can result in an unconservative combined structure response and clipping variability  Using the lesser of Methods 1 and 2 tends to be more conservative than the lesser of Methods 1 and 3. 6.6 Structure Models for Seismic Response Analysis A critical part of SPRAs or SMAs is the development and use of mathematical models of the structures housing equipment being modeled in the SPRA/SMA. From previous design-type analyses, NPPs typically have lumped mass (also referred to as stick models) structural models (LMSMs) to represent the plant structures. The existing structural models used in dynamic analyses to develop seismic responses for the design, licensing, and qualification of plant SSCs (e.g., LMSMs) were reasonably complex for their original intended purpose at the time they 6-36 13633436 Fragility Implementation Topics were developed. These models were used to capture the overall structural frequencies, mode shapes, and seismic responses. Typically, if model complexity was increased, the contribution of the modes identified within the simpler model is decreased, since a fraction of the model mass is shifted from fundamental modes to other local modes. This often resulted in lower spectral peaks for the fundamental modes of the structure but could also lead to new peaks at alternate structural frequencies. Existing structural models (i.e., those used for design basis, USI A-46, or IPEEE studies) could potentially be used in structural dynamic analyses that are performed to support modern SPRAs or SMAs. However, their seismic adequacy should be demonstrated for this purpose. This requires that a review of the existing models be performed by an experienced structural engineer to determine the adequacy of the models for dynamic analysis for application in seismic risk assessments. EPRI 1025287 [18] provides criteria against which structural engineers and peer reviewers should review existing structural models to establish adequacy for SPRAs and SMAs. These criteria are summarized below: 1. The structural models should be able to capture the overall structural responses for both the horizontal and vertical components of ground motion. 2. If there is significant coupling between the horizontal and the vertical responses, one combined structural model should be used for analyzing all three directions of the earthquake. 3. Structural mass (total structural, major components, and appropriate portion of live load) should be lumped so the total mass, as well as the center of gravity, is preserved. Rotational inertia should be included if it affects response in the frequency range of interest. 4. The number of nodal or dynamic degrees of freedom should be sufficient to represent significant structural modes. All modes up to structural natural frequencies of about 20 Hz in all directions should be included. 5. Torsional effects resulting from eccentricities between the center of mass and the center of rigidity should be included. The center of mass and the center of rigidity may not be coincident at all levels, and the torsional rigidity should be computed. 6. The analyst should assess whether a “one-stick” model sufficiently represents the structure. For example, two-stick models could be more appropriate for the analysis of internal and external structures of the containment founded on a common mat. 7. The structural analyst should review whether in-plane floor flexibility (and subsequent amplified seismic response) has been captured appropriately for the purposes of developing accurate seismic response (up to 15 Hz per EPRI 1025287 [18]). More recent research has been conducted to study the structural model fidelity issue in EPRI 3002002804 [142]. This research has shown that, for some structures, the additional complexity of the numerical model may lead to the identification of higher/different modes that may be important for some systems and components. In addition, the effect of in-plane and out-of-plane slab response was determined to be important in calculating the horizontal and vertical structural frequencies, respectively. Overall, the more structurally complex buildings 6-37 13633436 Fragility Implementation Topics were found to require the DFEM while for the simpler structures (axisymmetric containment structures or simple pump structures and diesel structures) well-designed LMSMs were shown to closely match the response from a DFEM. The fragility analyst should be guided by results of EPRI 3002002804 [142] when assessing whether to use LMSM or DFEM models for specific applications. Four key conclusions from the EPRI study [142] are: 1. DFEMs provide the most accurate characterization of seismic response for equipment located within the structure. LMSMs can approximate the seismic response and may exhibit sufficient accuracy depending on the structural configuration and on the intended SPRA/SMA application. 2. Differences in seismic response between LMSMs and DFEMs generally result from differences in the natural frequencies of the equivalent structures, the mass participation ratios at equivalent modes, the spectral shape of the input motion, the shifting in natural frequencies due to the coupling of the structure with the soil, and the inability of the LMSM to capture the out-of-plane and in-plane slab behavior. 3. Structural modelling of the floor slabs (both in-plane and out-of-plane) is typically shown to be the most important element in determining the accuracy of the LMSM seismic response. In-plane and out-of-plane slab flexibility and the resulting amplified seismic response must be carefully considered by a structural analyst to ensure that accurate seismic response is captured up to the frequency range required by the SPRA. 4. LMSMs that assume rigid floor slabs (in-plane and out-of-plane) result in increased stiffness relative to the DFEM results in all three directions because the flexible behavior of slabs is constrained. The increased stiffness of the LMSM was observed in a comparison of the natural frequencies of important structural modes and in the resulting shifting of the fixed-base ISRS peaks. LMSMs that assume diaphragms to be rigid should be reviewed by an experienced structural engineer to ensure that the seismic response is sufficiently accurate for the intended purpose. For LMSMs with diaphragm span-to-depth ratios exceeding 1.0, the analyst should consider adding oscillator enhancements to capture the response. 6.7 Response Analysis Scaling Methods Scaling of design loads from a prior analysis to account for the differences in seismic responses resulting from the RE is permissible under certain circumstances for structural loads, ISRS, and equipment or subsystem responses. Prior to scaling, a review of the structure and equipment models used in design should be conducted to ascertain the adequacy of the existing models to properly predict the response item of interest. For example, if a two-dimensional model was used for the design of a (1) strongly non-symmetric structure with significant expected torsional response characteristics, or (2) a significant structural feature was not appropriately modeled, a new analytical model should be developed. Another example would be a case where a fixed-base analysis was originally conducted for a structure founded on soil. Based on the analysts understanding of the structural dynamics involved with the soil and structure interactions, it would be preferable in some cases to perform a reanalysis. 6-38 13633436 Fragility Implementation Topics The following subsections provide guidance on scaling of seismic demands from prior analyses. Section 6.7.1 provides guidance on scaling structure response analysis results, including structure forces (for input to structure fragility evaluation) and ISRS (for input to equipment fragility evaluation). Section 6.7.2 provides additional guidance for scaling equipment response analyses. For example, such methods are used to estimate component stresses corresponding to RE ISRS using a design stress analysis. 6.7.1 Scaling Structure Seismic Demands As noted in Section 5.3.4, existing structure response analysis may be scaled in some circumstances to obtain new seismic responses corresponding to the RE. In general, if the ground motion spectra from the existing analysis are significantly different from the RE, or if the structures are founded on soil, a new analysis is required. Section 5 provides detailed guidance on performing new SSI analysis to estimate median response and variability. Scaling of existing design response must be justified based on demonstrating adequacy of the existing models, foundation characteristics, and similarity of input response spectra. In most cases where scaling was applied in earlier SPRAs, the assumed median spectral shape was similar in broad band frequency content to design spectra, and scaling was approximately conducted on a mode-by-mode basis. For example, all U.S. plants were designed before the regulatory criteria for soil structure interaction in Revision 2 of the NRC Standard Review Plan (NUREG-0800 [143]) were changed to be more realistic. Some of the newer U.S. plants on soil sites used SSI computer codes in the response analysis, but the previous restrictions on control point for the input motion and limits on radiation damping resulted in very conservative response. Earlier NPP designs used simple soil-spring models that were not capable of capturing the complex behavior of structural response on layered soil sites. For older NPPs on soil sites, it is especially important that the structural response be recomputed. Usually the existing structural model can be used, but the SSI method and modeling must be updated to more modern methods. Scaling can be used to develop structure forces for input to structure fragility evaluation, or to develop ISRS for input to equipment fragility evaluation. These two applications are described in the following two subsections, respectively. 6.7.1.1 Scaling Structure Forces Scaling of existing structural analysis to develop realistic loads for a different ground motion input is much easier than scaling existing ISRS. Scaling of structural loads can be accomplished in many instances with reasonable confidence using the damping and other seismic response parameters described in Section 5 as guidance. The simplest example is a fixed-base (rock foundation) structure designed using either constant modal damping or modal damping ratios developed for a single material damping. For these cases, the mode-by-mode RE loads can easily and accurately be calculated by scaling the spectral accelerations of the individual modes for the new RE ground response spectra corresponding to the RE damping ratios, or: P, P, Sa Sa Eq. 6-17 6-39 13633436 Fragility Implementation Topics where: Pi,j is the seismic load in element i for mode j SajRE is the spectral acceleration from the RE for mode j at RE modal damping SajSSE is the spectral acceleration for the SSE15 for mode j at SSE modal damping. The element load PRE is then determined by appropriate modal combination of Pi,jRE for all modes. As discussed in Section 5.4.4.2, various modal combination methods are discussed in Regulatory Guide 1.92 [120] and ASCE/SEI 4-16 [10]. This scaling approach can only be performed if mode-by-mode structural member loads are available from the previous analysis. If the individual SSE modal responses are not known, a reasonably accurate scaling of the SSE loads can be accomplished following a similar procedure to that above. Modal combination of the loads is performed by scaling the spectral accelerations at the dominant (usually fundamental) frequency of the structure, provided the general shapes of the SSE and RE ground response spectra are similar. However, if the RE ground spectra are much more narrowly peaked than the normally broadband SSE design spectra, it may be necessary to reanalyze the structure for the RE. For simple lumped mass models, if member loads are not provided on a mode-by-mode basis, but the nodal masses, mode shapes, and participation factors are provided, the seismic force from each node for each mode and be computed as: F where: M Γ φ Sa Eq. 6-18 Fij = force at node i for mode j Mi = mass of node i Γj = participation factor for mode j φij = mode shape at node i for mode j Saj = spectral acceleration of mode j at frequency fj The base shear for mode j, Vj, can be calculated as: V M Γ φ Sa Eq. 6-19 For the sake of brevity, “SSE” is used throughout this discussion on scaling to refer to the existing analysis that is being scaled to the RE seismic input. Depending on the application, the existing analysis could be a design analysis using the SSE, an IPEEE analysis using the corresponding RLE, or a previous SPRA analysis using the corresponding RE. “SSE” is used here and throughout the section simply for convenience. 15 6-40 13633436 Fragility Implementation Topics Then the modal base shears may be combined by an appropriate modal combination method as discussed in Section 5.4.4.2. As an example, the SRSS method is shown below: V M Γ φ Sa Eq. 6-20 For soil sites, substantially more uncertainty is introduced by scaling existing analytical results. For structures where the response is predominantly from a single mode (i.e., essentially a SDOF system) and the composite modal damping does not exceed more than about 20% of critical, a similar procedure to that described above for fixed-base structures may be used. However, large increases in the imaginary component of the foundation impedance function (i.e., the geometric damping) can result not only in significant changes in amplitude but also significant frequency variations as well (Tsai [144]). For such cases, it is recommended that a reanalysis be conducted. One major potential difficulty in scaling design analysis results for structures founded on soil is due to the simplifications that have frequently been introduced into the design analysis for SSI effects. Scaling of responses is difficult when substantial simplifications were made in that process. Results of several studies performed to quantify the conservatism introduced by various assumptions can be used to provide guidance as to whether scaling of existing design analyses or conducting new analysis for the SPRA is preferable (Johnson, et al. [145,146], Chen and Johnson [147], and NUREG/CR-4331 [148]). A simple example showing an acceptable process of scaling seismic structural loads (in this case, SRSS shear forces, but other modal combination methods should be considered on a case-bycase basis as discussed in Section 5.4.4.2) in a simple lumped mass model is shown schematically in Figure 6-4. In this example, the shapes of the RE and SSE design ground response spectra are relatively similar, the structure response is assumed to be dominated by the fundamental mode, and the fundamental frequency is assumed not to change significantly for the RE compared to the SSE design analysis (i.e., a rock site or adequate SSI design analysis with negligible soil softening at high strain levels, elastic or only moderate inelastic structure response). If the individual modal responses obtained in design are available, the RE loads can be more accurately determined by scaling on a mode-by-mode basis. However, if only the SRSS loads are known, sufficient accuracy can often be obtained by scaling the SRSS loads as shown in this example. Similar scaling can be applied to other loads (e.g., overturning moments) or other response parameters (e.g., accelerations, displacements). If some shift in fundamental frequency is expected for the RE, but the overall seismic response characteristics are expected to remain similar (e.g., mode shapes remain similar), then the structural loads can be scaled using the ratio of the spectral accelerations for different fundamental frequencies rather than the same frequency as shown in this example. In addition to accounting for the expected increases in structural and geometric damping, credit for parameters such as the incoherence in the input wave motion should be considered for the scaled RE structural loads as applicable. Also, for scaled loads which exceed yield, additional reduction may be appropriate if it can be technically justified. 6-41 13633436 Fragility Implementation Topics Note: 1. The ratio of spectral accelerations at the dominant frequency is likely to be different than the ratio of PGA. This will introduce some degree of either conservatism or unconservatism depending on the shapes of the RE and SSE spectra for higher mode (and hence SRSS) response. 2. The scaled seismic loads as determined above should be further modified as appropriate to account for incoherence and inelastic effects. Figure 6-4 Scaling structural loads 6.7.1.2 Scaling In-Structure Response Spectra Scaling ISRS is, in general, much more complex than scaling structural loads. Often, ISRS for higher equipment damping ratios are required for an SPRA than were developed for the SSE. The effects of the higher equipment damping on the in-structure amplification ratios can usually be estimated reasonably accurately. However, development of different civil structure composite modal damping ratios, and the use of a different shape ground response spectrum may result in 6-42 13633436 Fragility Implementation Topics significant variations in the shapes of the ISRS. Finally, the shapes of the un-broadened ISRS may no longer be easily available so that techniques such as peak shifting rather than peak broadening may be difficult to implement effectively. In many cases, the new ISRS will need to be developed using new analyses rather than by scaling. Guidance has been provided on the amount of conservatism expected in the ISRS from typical assumptions introduced in design SSI analyses (Johnson, et al. [145], Chen and Johnson [147], NUREG/CR-4331 [148], and UCID-20122 [146]). Selection of an approach depends on the amount of information available, the structure configuration, and the level of rigor needed in the results. Two acceptable approaches for scaling ISRS are outlined below.  Simplified approach when only modal frequencies and participation factors are available.  Scaling by random vibration theory (RVT) when modal frequencies, participation factors (Γ) and eigenvectors (φ) are available. The procedure for the simplified scaling approach is briefly outlined below. This method is considered acceptable for rock sites provided the original structure models are adequate and the overall shapes of the SSE and RE ground response spectra are similar. The simplified approach is described in more detail with an example in Appendix M. 1. Evaluate a scale factor as a function of frequency: Scale Factor (frequency) = RE / SSE 2. Use shape of the SSE ISRS and the participation factors to deduce significant modes. 3. Scale the SSE ISRS at each significant mode using the above equation. Apply scaling over a ±15% frequency bandwidth. 4. At frequencies below the first significant mode, the scaled ISRS is transitioned to the SSE ISRS. 5. Between scaled modes, the new RE ISRS is to generally follow the shape of the SSE ISRS. 6. The SSE ISRS ZPA is scaled up by the factor for the first significant mode. From the amplified peak at the highest significant mode frequency out to higher frequencies, the spectra should be transitioned to the scaled ZPA level. The procedure for the RVT approach is briefly described below. The RVT approach is described in more detail with examples in Appendices M and N. 1. Use White Noise (WN) Solution of Cascaded SDOF oscillators from Crandall & Mark [149]. 2. Develop amplification factor, AF, for each modal frequency of the floor oscillator to the structural response at the point of contact from the WN solutions. 3. Evaluate modal floor response as AF  φ (0.8) Sag. The 0.8 constant is the ratio of RVT peak factors from literature (Appendix N). 4. Combine modes and direction components by conventional means to obtain the scaled floor response spectra. 6-43 13633436 Fragility Implementation Topics If the raw (unsmoothed and unbroadened) ISRS are available, it is recommended that they be used for the scaling described herein. Otherwise, broadened ISRS may be scaled as shown in the example shown in Appendix M, and then a correction made to account for the conservatism in the broadening and its effect on equipment fragilities. New response analyses are recommended for the RE in lieu of scaling for the following conditions:  Soil sites with major changes in composite modal damping ratios or increases in the geometric damping  Soi1 or rock sites where the shape of the RE ground response spectra are significantly different from the SSE ground response spectra  Soil or rock sites where significant nonlinear response is expected in the civil structure When ISRS are scaled for the RE, credit may be taken for the reduction in response due to spatial incoherence of the input wave motion if a technical approach for doing so can be justified. However, if significant nonlinear response is expected in the civil structure, increases in the ISRS in the high-frequency range can occur and, in this case, it is recommended that new analyses be conducted to develop the ISRS. Scaling of spectra using a single mode is difficult to justify unless the spectral shape of the RE is similar to that of the original ground spectrum (e.g., SSE), which is rarely the case. If the complete eigensolution parameters are available, existing spectra can be scaled on a mode-bymode basis with reasonable accuracy. However, for soil sites, especially sites with older, more simplified SSI analyses, scaling has little merit and new analysis is recommended. Also, in some cases it has been found that existing models of steel frame structures that respond at very low frequencies do not have a design basis analysis that can be used for mode-by-mode scaling. In these cases, 3D models may have been used, but the design basis response analysis was only carried out to forty or so modes, and the eigensolution was cut off at low frequencies such as 6 to 8 Hz. Thus, scaling of spectra using existing eigensolution parameters may not propagate the high-frequency portion of the RE, which can be important for sites with significant high-frequency content in the hazard, as has been the case for CEUS sites in recent years. Appendix M shows an example of scaling of DBE spectra developed from a simple lumped mass reactor building model subjected to a RG 1.60 spectral shape anchored to 0.05g to develop spectra for a high-frequency UHRS anchored to 0.lg. In this case, the original model was recreated, and the original spectra were verified before the scaling procedure was attempted. Scaling was done by using original eigensolution results and random vibration theory as described in Appendix N and by simplified methods using only the participation factors and scaling at only a few frequencies. 6.7.2 Scaling Seismic Demands for Components and Subsystems It may be cost effective to reevaluate components or subsystems by scaling existing equipment response analyses. This can be done with reasonable accuracy if sufficient detail is provided in the qualification report to separate the seismic response from the total response of the governing load combinations. Separation is not always possible, and in such cases, the scaling must be conservatively biased. If such conservatism is not acceptable for the SSC (e.g., if it is a dominant 6-44 13633436 Fragility Implementation Topics contributor and the conservatism may obscure the risk insights from the SPRA), then a new equipment response analysis may be required. There are several situations which may confront the analyst. Guidance is provided in Table 6-6 for typically encountered situations. Table 6-6 Component seismic demand scaling cases Case Component Existing Analysis Reported Results With Nozzle Loads 1 Flexible component Dynamic analysis Seismic response results separate from normal operating load results No 2 3 Seismic response results not separate from normal operating load results 4 5 Pseudo static seismic analysis or conservative static loading 6 7 8 9 10 Rigid component Static analysis 11 Seismic response results separate from normal operating load results Seismic response results not separate from normal operating load results Seismic response results separate from normal operating load results Seismic response results not separate from normal operating load results 12 Yes No Yes No Yes No Yes No Yes No Yes 13 Flexible or rigid component Combination of testing and analysis with the RRSqual* for tested components derived from a Case 1 scenario N/A No 14 Coupled component and piping model Dynamic analysis Seismic response results separate from normal operating load results No Seismic response results not separate from normal operating load results No 15 *RRSqual is the “required response spectra” specified in the design qualification. It defines the mounting-point response spectrum to which the component must be qualified by testing. 6.7.2.1 Fifteen Response Analysis Scaling Cases Case 1 is a base case that will be described in detail. The other cases are more easily described by referring to appropriate features of Case 1 and by addressing the additional judgements to be made by the analyst for the situation at hand. 6-45 13633436 Fragility Implementation Topics Scaling for Case 1 The component is assumed to be a multiple degree of freedom system, analyzed by the response spectrum method for the SSE response spectrum (or another previous seismic input), and sufficient results of the dynamic analysis are available to determine the frequencies and participation factors of each significant mode. The mode-by-mode responses for each element or node may or may not be available. The preferred situation is one where mode-by-mode responses are available for each element or nodal point in the model. The responses for each mode at selected locations may then be scaled by a factor, Fj, expressed as: F where: Sa , Sa , Eq. 6-21 Saj,RE = Spectral acceleration from the RE ISRS at frequency, j, and at the RE specified damping. Saj,SSE = Spectral acceleration from the SSE ISRS at frequency, j, and at the SSE specified damping. The scaled modal responses are then combined by an appropriate modal combination method as discussed in Section 5.4.4.2. If the response is predominantly in a single mode, the scale factor F can be approximated by direct comparison of the RE spectrum to the SSE spectrum at the fundamental frequency of the component. Alternatively, if frequencies are known but participation factors are not reported, the scale factor may conservatively be estimated by finding the maximum ratio of the RE spectral acceleration to the SSE spectral acceleration in a frequency band judged to dominate the response. Scaling for Case 2 Case 2 is a typical case where an uncoupled dynamic analysis has been conducted for a component to obtain response to the SSE but, the connecting nozzle loads have been specified as pseudo static loads. In some cases, there is a single set of envelope nozzle loads (moments and shears) while in other cases, a breakdown of loads is provided for weight, thermal expansion, and seismic reactions. The specified nozzle loads are rarely the actual calculated loads, and they therefore contain unidentifiable conservatism. In this case, the easier and most conservative method of scaling is to scale the total envelope nozzle load by the maximum ratio of the RE to SSE spectral acceleration in a frequency band judged to contain the most mass participation of the connecting piping system. In the second scenario, only the seismic portion of the load is scaled. Alternatively, results of the final piping analysis may be scaled using Equation 6-20 or by the maximum ratio of the RE/SSE spectral acceleration in a frequency range judged to envelope the range of dominant piping response. 6-46 13633436 Fragility Implementation Topics Results of the seismic induced nozzle loading may then be added to results of the seismic inertial loading by SRSS. An exception is that rigid body modes should be added by algebraic sum and combined by SRSS with modal responses for flexible modes. The combined seismic results are then added to normal operating load results by absolute sum for comparison to strength acceptance criteria. Scaling for Case 3 Case 3 is frequently encountered in review of seismic qualification reports. The desired results have been generated but are not tabulated in the qualification reports. In this case, the analyst has two choices for scaling: (1) contact the vendor or the original analysis organization for the missing intermediate results, or (2) conservatively scale the total results. In the first scenario, the scaling would proceed as described for Case 1. In the second scenario, the total response stress results must be conservatively scaled by the maximum ratio of the RE/SSE spectral acceleration in a frequency range judged to be representative of the predominant mass participation. In many instances, the more conservative approach will suffice. An important consideration for Case 3 scaling is that often small margins are reported for design loadings, but the loads are dominated by normal operating loads. For instance, stresses in pressure boundaries of many components are almost always dominated by pressure loading and are not appreciably affected by seismic loading. Judgment must be exercised on which stresses or loads are seismically critical before scaling. Only those stresses or loads that are significantly affected by seismic loading should be considered for scaling. Scaling for Case 4 Case 4 is a situation where the component seismic inertial response may be at a significantly different frequency than the response of the attached piping. The easiest and most conservative method of RE response prediction is to scale total response to the SSE plus normal operating loads by the maximum ratio of the RE/SSE response spectrum in a frequency range judged to contain the most dominant response of either the attached piping or the component. A second step would be to obtain sufficient information to separate responses from piping reactions from those of inertial loading and conservatively scale these contributions separately for frequency bands that are appropriate for each contributor. A third step would be to obtain a detailed breakdown of piping loading and more detail on the component model so that only the seismic portions of the loading can be scaled. Scaling can then be done on a mode-by-mode basis as specified in Equation 6-20. Scaling for Case 5 Often, vendors have taken a conservative approach to equipment qualification by applying a pseudo static load that envelopes the RE response spectrum. An IEEE 344-1975 [96] (and later editions) requirement for qualification of flexible equipment by static analysis is that the applied static load must be 1.5 times the peak spectral acceleration. This is overly conservative, and a more reasonable approach adapted by EPRI NP-5228-SL [88] is to use 1.0 times the peak spectral acceleration to determine the load on anchorage. Recall that the target for demonstrating a HCLPF by the CDFM method is to compute conservative response and compare it to conservative strength criteria (Section 3.4). The use of peak spectral acceleration as a pseudo static load is excessively conservative, even for CDFM analyses. For instance, Figure 6-5, 6-47 13633436 Fragility Implementation Topics (copied from EPRI NP-6041-SLR1 [1]) shows a cumulative distribution function of the ratio of maximum valve acceleration compared to the peak spectral acceleration of the input spectrum, Avlv/Sapeak, for a sample size of sixty-nine valves in nine piping systems. It is shown in Figure 6-5 that for the sample size examined, there is only about a 3% chance of exceeding the peak spectral acceleration, thus, the use of peak spectral as an equivalent static loading appears to be very conservative and is recommended as a first attempt for scaling response analyses. This may be used for floor or wall mounted equipment, or in-line components such as valves and instrument penetrations. The response to the RE for comparison to the acceptance criteria is: R Sa G R R RT = Total response to the RE plus normal operating loads GSSE = Equivalent static g force used for the SSE qualification SaRE = Peak spectral acceleration from the RE response spectrum RN = Computed load or response to normal operating loads RSSE = Computed load or response to the GSSE loading where: Eq. 6-22 As an alternative, for simple systems that respond in predominantly a single mode, the natural frequency can be calculated and the spectral acceleration from a broadened spectrum corresponding to the fundamental frequency of the component may be used for SaRE. 6-48 13633436 Fragility Implementation Topics Figure 6-5 Cumulative distribution function for the ratio of the maximum valve acceleration vector to the peak spectral acceleration vector (Avlv/Sapeak) Scaling for Case 6 The inertial response portions of the total RE and normal operating loads may be determined using one of the methods described for Case 5. The seismic portion of the nozzle loading may be modified by scaling the RE spectral acceleration to the SSE spectral acceleration at a frequency where the ratio is a maximum. A restriction on this ratio is that the frequency must be reasonably credible for the attached piping. Very low and very high-frequency ranges are usually not major contributors to piping response. The credible frequency range must be determined by the analyst by judgement or by examining the results of the piping analysis. Alternatively, more accurate piping reactions may be determined by scaling the computed SSE response on a mode-by-mode basis using Equation 6-20. Results of the nozzle loading and inertial loading may be combined by SRSS and the combined seismic response added to the normal loading response by absolute sum for comparison to the strength acceptance criteria. 6-49 13633436 Fragility Implementation Topics Scaling for Case 7 Case 7 is similar to Case 5. The total response to the SSE plus normal operating loads may be scaled by the ratio of the RE peak spectral acceleration at RE damping to the pseudo static load, GSSE, used in the SSE. Alternatively, for simple systems that respond in a single mode, the analyst may calculate the fundamental frequency and use the associated RE spectral acceleration in lieu of the peak spectral acceleration. Scaling for Case 8 Scaling for Case 8 should proceed as described for Case 4. The easiest and most conservative method is to scale total response to the SSE plus normal operating loads by the maximum ratio of the RE to SSE spectra in a frequency range judged to produce the maximum response. Alternatively, the analyst may obtain interim results for piping and inertial loading from the vendor and scale these results by the procedures described for Case 6. As a further refinement, the analyst may obtain the calculated piping reactions and scale the SSE portion as described for Case 2. Scaling for Case 9 Case 9 is similar to Case 5 except that the SSE seismic response may be scaled by the ratio of the RE ZPA to the SSE ZPA. Scaled RE responses are added to normal load responses by absolute sum. Scaling for Case 10 For Case 10, the inertial loading portion can be scaled by the ZPA ratios as described for Case 9. The piping reaction loading may be scaled by one of the methods described for Case 2. Seismic responses to nozzle loading and inertial loading may be combined by SRSS and the combined results added to the response to normal operating loads by absolute sum. Scaling for Case 11 In this case, the total response to the RE plus normal operating loads may be scaled by the ratio of the RE ZPA to the SSE ZPA. If this is too conservative, the vendor may be contacted for a load breakdown or a new static analysis may be conducted to separate seismic from normal operating loads. Scaling for Case 12 In this case, the component response is rigid, but the nozzle reactions are governed by flexible piping response. For results that are clearly either a function of nozzle loads, such as flange stress or a function of inertial response, such as displacement of a pump impeller, the scaling may be conducted using one of the procedures previously described for scaling piping response (Case 2) or for scaling rigid body inertial response (Case 9). For regions such as anchor bolts affected by both piping reactions and inertial response, the scaling must either be overly conservative or else more detail on the response to individual loads must be obtained from the vendor or by reanalysis. If scaling is conducted on the total response to normal plus SSE loads resulting from 6-50 13633436 Fragility Implementation Topics both nozzle and inertial loads, the scale factor should be conservatively bounded by the maximum ratio of the RE to SSE spectral acceleration in a frequency range that envelops both the expected dominant response of the attached piping and rigid body response of the component. This may well be too conservative, and a reanalysis may be required. Scaling for Case 13 In this case, scaling must be conducted for both the RRSqual for tested components and for the computed response for analyzed components. First, the analyst can assume that the analyzed component or assembly is floor-mounted and subjected to a defined input motion in the form of a response spectrum or a floor time-history. The response of the analyzed component or assembly to the RE plus normal operating loads may be scaled by any of the methods previously described, depending upon the most applicable case. Tested components are assumed to be mounted on the assembly, which may be flexible or rigid. If the assembly is rigid, the RRSqual is equal to the specified floor spectrum. If the assembly is flexible, the RRSqual is amplified above the floor spectrum. Typically, the RRSqual is specified as a broad banded generic spectrum such as specified in ANSI/IEEE Standard C37.98-1987 [67]. In this case, the peak response of the assembly determines the ZPA of the RRSqual. Peak dynamic response of the assembly may be determined by scaling the SSE response by Equation 6-20 if the dynamic characteristics of the assembly are known, or by taking the maximum ratio of the RE to SSE spectrum for cases where the dynamic characteristics of the assembly are not known. If the maximum RE/SSE spectrum ratio is used, the frequency range considered should be reasonably representative of the frequency characteristics of the assembly. The credible frequency range may be determined by examining the eigensolution results or by judgement. If a specific RRSqual is developed from a time-history analysis (or direct spectra generation approach) of the assembly, the resulting spectrum may also be scaled using Equation 6-20, or alternatively, by the maximum ratio of the RE/SSE spectral acceleration in a credible frequency range of interest. Scaling for Case 14 In some cases, a coupled dynamic analysis of components and piping is conducted. This is typical of primary coolant systems but is rare for the balance of plant systems. If intermediate results of the dynamic analysis are available, the dynamic response can be scaled on a mode-bymode basis using Equation 6-20. Alternatively, individual response parameters may conservatively be scaled by the maximum ratio of the RE spectral acceleration to the SSE spectral acceleration in the frequency range that contains the dominant response. The dominant response frequency range can be determined by examining the mode shapes and participation factors. If more than one mode is a significant contributor to response, the scaling factor should be determined from the maximum ratio of RE spectral acceleration at RE damping to the SSE spectral acceleration at SSE damping over the range of significant modes that contribute to response. 6-51 13633436 Fragility Implementation Topics Scaling for Case 15 In cases where only combined responses to seismic and normal operating loads are reported, the total response must be scaled, or else more details on the analysis must be obtained to separate the seismic response from the normal operating load response. The scale factor for the combined response should be computed from the maximum ratio of the RE spectral accelerations to the SSE spectral acceleration in a frequency range judged to contain the dominant response. 6.7.2.2 Alternatives to Scaling Scaling of existing analysis is usually the most cost-effective method of estimating responses to the RE. However, as pointed out in the previous discussion, scaling may be much too conservative because of the lack of detailed results of the original dynamic analysis, or because overly conservative models were used in the original design. In some instances, the adequacy of the original models to predict seismic response may also be in question. Upon a quick review of the original seismic qualification analysis, an experienced analyst should be able to determine if scaling will be successful, if the original models are acceptable for RE evaluation, or if a reanalysis should be conducted. Often, if the original models are available and judged to be acceptable for RE evaluation, it can be cost effective to use these models and redo the seismic and normal operating load analysis, or engage the original seismic qualification organization to run the existing models for the RE. In many cases, it may be necessary to construct a new equipment response model to compute response to the RE. If new models are constructed, they should be designed to provide accurate results for the areas of concern in the fragility evaluation. Excess detail in non-critical areas is not necessary. For instance, the taper pins used to align pumps with their drive motors are frequently a governing element in conducting seismic analysis of pump assemblies. These pins are affected most significantly by rigid body inertial response of the pump and by the reactions from attached piping. In this case, a very simple static model can be used to transfer nozzle loads and pump rigid body inertial loads to the shear pins. If, on the other hand, the critical area is shaft deflection, a model that properly addresses the dynamic characteristics of the rotating shaft is necessary. Simple models can usually be used to compute reactions at anchor bolts, whereas, a model used to compute the time-history at a particular relay location in an electrical cabinet may be a much more complex finite element model consisting of plates and beams. 6.8 Combining Fragilities for Multiple Failure Modes As noted in Section 3.3.1, if a single SSC has multiple failure modes with similar fragilities such that it is not trivial to judge that one governs over the others, then multiple fragility curves may be developed for that single SSC. The multiple fragilities can be provided to the systems analyst to explicitly include in the systems model. Alternatively, the two fragilities can be combined into a single fragility representing the overall probability of failure for the SSC. An approach is outlined below for combining fragilities of two failure modes that are independent but not mutually exclusive. 6-52 13633436 Fragility Implementation Topics As an example, consider a control cabinet. The fragility parameters may be calculated for the anchorage failure mode and also for its function-after failure mode. The two failure modes are independent but not mutually exclusive. Here, P(A) is the failure probability of event A, P(B) the probability of event B, and P(A ∩ B) is the probability of their intersection (i.e., both events occurring together). The probability that at least one failure will occur is expressed by the union of events A and B or P(A ∪ B) and is calculated using Equation 6-23: P(A ∪ B) = P(A) + P(B) − P(A ∩ B) For independent events, P(A ∩ B) = P(A) x P(B) Therefore, P(A ∪ B) = P(A) + P(B) − P(A) x P(B) A1% Am e-2.33(βc) Eq. 6-23 The approach develops the mean fragility curves for each failure mode (probability vs. PGA), and then calculates the mean curve for at least one failure occurring using Equation 6-22. The combined mean curve may not be lognormal, but an approximate lognormal combined fragility can be approximated from this combined mean curve. From the combined mean curve, the 1% probability gives the new A1% capacity, and the 50% probability gives the new median capacity. From these two values, the composite variability βc can be calculated using Equation 6-24: = Eq. 6-24 βR and βU can then be assigned proportionately, i.e., corresponding to the βR and βU of the dominant failure mode such that their SRSS equals βC. In the above example only two dominant failure modes were considered to occur, which is the case in most fragility evaluations that encompass multiple governing failure modes. However, the above concept can be extended when there are more than two failure modes. As a practical matter, the combined fragility curve will be close to the fragility curve that corresponds to the dominant failure mode (i.e., with the lowest capacity), if the HCLPF capacity of the next governing failure is more than about 20% higher than the dominant failure mode and they have similar variabilities (R, U). Therefore, in such cases, use of the dominant failure mode in the logic model is considered acceptable. Also, use of the dominant failure mode is considered acceptable if the SSC is ranked low in importance. Therefore, this procedure should be used only if the SSC is one of the important risk contributing SSCs in the logic model and the HCLPFs for the governing failure modes are within about 20% of each other (assuming the variabilities are similar). Another option that is considered acceptable would be for the PRA analyst to model both failure modes in the logic model. 6-53 13633436 13633436 7 REFERENCES 1. A Methodology for Assessment of Nuclear Power Plant Seismic Margin, Revision 1. EPRI, Palo Alto, CA: 1991. NP-6041-SLR1. 2. Methodology for Developing Seismic Fragilities. EPRI, Palo Alto, CA: 1994. TR-103959. 3. Seismic Fragility Application Guide. EPRI, Palo Alto, CA: 2002. 1002988. 4. Seismic Fragility Applications Guide Update. EPRI, Palo Alto, CA: 2009. 1019200. 5. Seismic Probabilistic Risk Assessment Implementation Guide. EPRI, Palo Alto, CA: 2013. 3002000709. 6. Alternate Approach, Part 5, Requirements for Seismic Events At-Power PRA. Joint Committee for Nuclear Risk Management, American Society of Mechanical Engineers. Code Case 1 to ASME/ANS RA-Sb-2013. Case JCNRM-1. 2017. 7. Methodology for Probabilistic Risk Assessment of Seismic Margin Evaluations. EPRI, Palo Alto, CA: 2001. 1003121. 8. Methodology and Case Study for Use of Seismic Margin Assessments in Quantitative Risk-Informed Decision Making: A Revision to EPRI Report 1003121. EPRI, Palo Alto, CA: 2004. 1009648. 9. U.S. Nuclear Regulatory Commission. Interim Staff Guidance on Implementation of a Probabilistic Risk Assessment-Based Seismic Margin Analysis for New Reactors. Washington, D.C. 2009. ISG DC/COL-ISG-020. 10. Seismic Analysis of Safety Related Nuclear Structures and Commentary, American Society of Civil Engineers, Reston, VA: 2017. ASCE/SEI Standard 4-16. 11. J. R. Benjamin and C. A. Cornell. Probability, Statistics and Decision for Civil Engineers. McGraw-Hill Book Co., New York, NY, 1970. 12. U.S. Nuclear Regulatory Commission, Design Response Spectra for Seismic Design of Nuclear Power Plants, Revision 2, Washington, D.C. 2014. Regulatory Guide 1.60. 13. R. P. Kennedy, “Overview of Methods for Seismic PRA and Margin Assessments Including Recent Innovations,” Proceedings of the OECD-NEA Workshop on Seismic Risk, Tokyo, Japan (August 1999). 14. Seismic Design Criteria for Structures, Systems and Components in Nuclear Facilities, American Society of Civil Engineers, Reston, VA: 2005. ASCE/SEI Standard 43-05. 15. U.S. Nuclear Regulatory Commission, An Approach to the Quantification of Seismic Margins in Nuclear Power Plants, Washington, D.C. 1985. NUREG-4334. 7-1 13633436 References 16. U.S. Nuclear Regulatory Commission, Recommendations to the Nuclear Regulatory Commission on Trial Guidelines for Seismic Margin Reviews of Nuclear Power Plants. Washington, D.C. 1986. NUREG/CR-4482. 17. U.S. Nuclear Regulatory Commission, An Approach to the Quantification of Seismic Margins in Nuclear Power Plants: The Importance of BWR Plant Systems and Functions to Seismic Margins. Washington, D.C. 1988. NUREG-5076. 18. Seismic Evaluation Guidance, Screening, Prioritization, and Implementation Details (SPID) for the Resolution of Fukushima Near-Term Task Force Recommendation 2.1: Seismic, EPRI, Palo Alto, CA: 2013. 1025287. 19. Updated Equipment Seismic Capacities from Experience Data for Use in Fragility Calculations. EPRI, Palo Alto, CA. 3002011627. 20. Generic Seismic Ruggedness of Power Plant Equipment, Revision 1. ERRI, Palo Alto, CA: 1991. NP-5223. 21. Seismic Ruggedness of Relays. EPRI, Palo Alto, CA: 1991. NP-7147. 22. Seismic Qualification Reporting and Testing Standardization (SQURTS) Test Report Database v2.0, EPRI, Palo Alto, CA: 2009. 1019309. 23. High Frequency Program: High Frequency Testing Summary. EPRI. Palo Alto, CA: 2014. 3002002997. 24. High Frequency Program: Application Guidance for Functional Confirmation and Fragility Evaluation. EPRI, Palo Alto, CA: 2015. 3002004396. 25. Review and Compilation of SQURTS Test Data for Use in Seismic Fragility Evaluations, EPRI, Palo Alto, CA. 3002010668. 26. U.S. Nuclear Regulatory Commission, Engineering Characterization of Ground Motion –Task 1, Effects of Characteristics of Free-Field Motion on Structural Response, Washington, D.C. 1984. NUREG/CR-3805. 27. U.S. Nuclear Regulatory Commission. Verification of Seismic Adequacy of Mechanical and Electrical Equipment in Operating Reactors, Unresolved Safety Issue (USI) A-46 (Generic Letter 87-03). Washington, D.C. 27 February 1987. 28. Use of Seismic Experience and Test Data to Show Ruggedness of Equipment in Nuclear Power Plants, Part I. Sandia National Laboratories, Albuquerque, NM: 1991. SAND92-0140. 29. Industry Approach to Seismic Severe Accident Policy Implementation, EPRI, Palo Alto, CA: 1991. NP-7498. 30. Summary of the Seismic Adequacy of Twenty Classes of Equipment Required for the Safe Shutdown of Nuclear Plants. EPRI, Palo Alto CA: 1994. NP-7149D. 31. Generic Implementation Procedure (GIP) for Seismic Verification of Nuclear Plant Equipment, Revision 2, Seismic Qualification Utility Group, 1992. 32. U.S. Nuclear Regulatory Commission, Seismic Structural Fragility Investigation for the Zion Nuclear Power Plant, Seismic Safety Margins Research Program (Phase 1). Washington, D.C. 1981. NUREG/CR-2320. 7-2 13633436 References 33. G. E. Troxell, H. E. Davis, and J. W. Kelly, Composition and Properties of Concrete, Second Edition, McGraw-Hill Book Company, New York, NY, 1968. 34. Methodology for Performing Aircraft Impact Assessments for New Plant Designs, Revision 7, Nuclear Energy Institute, Washington, D.C. 2009. NEI 07-13. 35. Equivalent Specified Concrete Strength from Core Test Data, Concrete International, American Concrete Institute, Farmington Hills, MI: 1995. 36. Working Group on Quantification of Uncertainties. Uncertainty and Conservatism in the Seismic Analysis and Design of Nuclear Facilities. American Society of Civil Engineers, 1986. 37. S. A. Mirza, M. Hatzinikolas, and J. G. MacGregor, “Statistical Descriptions of the Strength of Concrete,” Journal of the Structural Division, American Society of Civil Engineers (1979). 38. T. V. Galambos and M. K. Ravindra, “Properties of Steel for Use in LRFD,” Journal of the Structural Division, American Society of Civil Engineers (1978). 39. G. K. Kulak, J. W. Fisher, and J. H. A. Struik. Guide to Design Criteria for Bolted and Riveted Joints. John Wiley & Sons, New York, NY 1987. 40. Specification for Safety-Related Steel Structures for Nuclear Facilities, American Institute of Steel Construction, Chicago, IL: 2012. ANSI/AISC N690-12. 41. Specification for Structural Steel Buildings, American Institute of Steel Construction, Chicago, IL: 2010. ANSI/AISC 360-10. 42. Boiler and Pressure Vessel Code, Section II, Materials and Section III, Division 1, Rules for Construction of Nuclear Power Plant Components, American Society of Mechanical Engineers, NY. 2007. 43. U.S. Nuclear Regulatory Commission. Assessment of Seismic Margin Calculation Methods. Washington, D.C. 1989. NUREG/CR-5270. 44. Risk Methodology for Geologic Disposal of Radioactive Waste: Small Sample Sensitivity Analysis Technicques for Computer Models, with an Application to Risk Assessment. Sandia Labs, Albuquerque, NM: 1980. NUREG/CR-1397. 45. S. A. Mirza and J. G. MacGregor, “Variability of Mechanical Properties of Reinforcing Bars,” Journal of the Structural Division, American Society of Civil Engineers (1979). 46. Code Requirements for Nuclear Safety-Related Concrete Structures (ACI 349-13) and Commentary, American Concrete Institute, Farmington Hills, MI: 2013. ACI 349-13. 47. Building Code Requirements for Structural Concrete (ACI 318-08) and Commentary (ACI 318R-08), American Concrete Institute, Farmington Hills, MI: 2008. ACI 318-08. 48. F. Barda, J. M. Hanson, and W. G. Corley. "Shear Strength of Low-Rise Walls with Boundary Elements," ACI Symposium on Reinforced Concrete Structures in Seismic Zones. American Concrete Institute, Detroit, MI (1976). 49. C. K. Gulec and A. S. Whittaker, “Empirical Equations for Peak Shear Strength of Low Aspect Ratio Reinforced Concrete Walls,” ACI Structural Journal, American Concrete Institute (2011). 7-3 13633436 References 50. T. Shiga, A. Shibata and J. Tabahashi. "Experimental Study on Dynamic Properties of Reinforced Concrete Shear Walls," 5th World Conference on Earthquake Engineering. Rome, Italy (1973). 51. A. E. Cardenas, et al., "Design Provisions for Shear Walls," ACI Journal. Vol 70, No. 3 (1973). 52. R. G. Oesterle, et al. Earthquake Resistant Structural Walls - Tests of Isolated Walls Phase II. Construction Technology Laboratories (Division of PCA), Skokie, IL, 1979. 53. Recommended Evaluation Criteria for Diablo Canyon Nuclear Power Plant Auxiliary Building Walls and Diaphragms. Jack R. Benjamin and Associates, Inc., Mountain View, CA: 1983. 54. Jack R. Benjamin and Harry A. Williams. Investigation of Shear Walls, Part 6: Continued Experimental and Mathematical Studies of Reinforced Concrete Walled Bents Under Static Shear Loading. Dept. of Civil Engineering, Stanford University, 1954. 55. Harry A. Williams and Jack R. Benjamin. Investigation of Shear Walls: Part 3, Experimental and Mathematical Studies of the Behavior of Plain and Reinforced Concrete Walled Bents under Static Shear Loading. Dept. of Civil Engineering, Stanford University, 1953. 56. C. V. Gulec and A. S. Whittaker, “Performance-Based Assessment and Design of Squat Reinforced Concrete Shear Walls,” MCEER-09-0010, University of Buffalo (September 2009). 57. Probabilistic Evaluation of the Diablo Canyon Turbine Building Seismic Capacity Using Nonlinear Time History Analyses. Pacific Gas & Electric Company: 1988. 1643.1. 58. Y. Ogaki, et al., “Shear Strengths Test of Prestressed Concrete Containment Vessels,” Paper J4/3, Sixth International Conference of Structural Mechanics in Reactor Technology, Paris, France (1981). 59. Y. Aoyagi, et al., “Strength and Deformational Characteristics of Orthogonally Reinforced Concrete Containment Models Subjected to Lateral Forces,” Paper J4/4, Sixth International Conference of Structural Mechanics in Reactor Technology, Paris, France (1981). 60. Building Code Requirements and Specification for Masonry Structures and Companion Commentaries, American Concrete Institute. 2013. ACI 530/530.1-13. 61. D. W. Eggers and I. Baig, “Significance of Ratcheting in Seismic Analyses,” Paper 358, Division V Transactions, SMiRT-23, Manchester, UK (August 2015). 62. U.S. Nuclear Regulatory Commission, Shear Wall Ultimate Drift Limits. Washington, D.C. 1994. NUREG/CR-6104. 63. C. K. Gulec, A. S. Whittaker, and B. Stojadinovic, “Peak Shear Strength of Squat Reinforced Concrete Walls with Boundary Barbells or Flanges,” ACI Structural Journal, American Concrete Institute (2009). 64. Seismic Evaluation and Retrofit of Existing Buildings, American Society of Civil Engineers, Reston, VA: 2013. ASCE/SEI 41-13. 7-4 13633436 References 65. R. Riddell and N. M. Newmark, Statistical Analysis of the Response of Nonlinear Systems Subjected to Earthquakes, University of Illinois, Champaign-Urbana, IL 1979. 66. Subsystem Fragility, Seismic Safety Margins Research Program (Phase I), Lawrence Livermore National Laboratory, Livermore, CA: 1981. NUREG/CR-2405 (UCRL-15407). 67. IEEE Standard Seismic Testing of Relays, Institute of Electrical and Electronics Engineers, 1991 (reaff 1999). ANSI/IEEE C37.98-1987. 68. U.S. Nuclear Regulatory Commission, Seismic Analysis of Piping, Washington, D.C. 1998. NUREG/CR-5361. 69. R. P. Kennedy, “Using Component Test Data to Assist in Establishing Code Criteria to Achieve the Desired Seismic Capacity Margin for Piping,” ASME Pressure Vessels and Piping Conference, Codes and Standards, PVP 2002-R53, PVP Vol. 439, 2002. 70. A Simplified Inelastic Seismic Analysis Method for Piping Systems. EPRI, Palo Alto, CA: 1990. NP-6809. 71. Seismic Evaluation of Rod Hanger Supports for Electrical Raceway Systems. EPRI, Palo Alto, CA: 1991. NP-7152-D. 72. Farwell & Hendricks, Seismic Testing Report for Piping Assembly, Revision 1, prepared for EPRI/SQURTS. 1995, Report No. 50093.8. 73. R. B. Linderman and A. R. Hadjian. "Development of Bechtels Electric Raceway Systems Test Programs," Proceedings of the American Power Conference, Vol. 43 (1981). 74. Specification for the Design of Cold-Formed Steel Structural Members. American Iron and Steel Institute, 1986. 75. T. Kato, et al., "Limit Strength of Rectangular Air Ventilation Ducts Under Seismic Design Conditions." Transactions of the 10th International Conference on Structural Mechanics in Reactor Technology. pp. 775-780 (1989). 76. S. C. Desai, S. H. Stoman and D. Marano, "Structural Design of Seismic Category I HVAC Ducts," Transactions of the 10th International Conference on Structural Mechanics in Reactor Technology. pp. 781-786 (1989). 77. Sayed H. Stoman. "Application of Post-Buckling Theory to HVAC Ducts." Transactions of the 10th International Conference on Structural Mechanics in Reactor Technology. pp. 799-804 (1989). 78. U.S. Department of Commerce / National Bureau of Standards, Development of a Probability Based Load Criterion for American National Standard A58. Washginton, D.C. 1980. NBS Special Publication 577. 79. M. Holmes and L.H. Martin, Analysis and Design of Structural Connections: Reinforced Concrete and Steel, John Wiley & Sons, New York, NY, 1983. 80. AISC Manual of Steel Construction: Load and Resisstance Factor Design, First Edition, American Institute of Steel Construction, 1987. 7-5 13633436 References 81. AISC Manual of Steel Construction: Allowable Stress Design, Ninth Edition, American Institute of Steel Construction, 1989. 82. J. W. Fisher, et al., "Load and Resistance Factor Design Criteria for Connections." Journal of Structural Division, Vol. 104, ST9, pp. 1427-1441 (1978). 83. Dale F. Lesik and D. J. Laurie Kennedy. Ultimate Strength of Eccentrically Loaded Fillet Welded Connections, Structural Engineering Report 159, University of Alberta Department of Civil & Environmental Engineering, Edmonton, Alberta, Canada, May 1988. 84. W. Fuchs, R. Eligehausen, and J. E. Breen, “Concrete Capacity Design (CCD) Approach for Fastening to Concrete,” ACI Structural Journal, American Concrete Institute (1995). 85. U.S. Nuclear Regulatory Commission. A Technical Basis for Revision to Anchorage Criteria. Washington, D.C. 1999. NUREG/CR-5563. 86. Seismic Fragility Strength Equation Recommendations for Embedded Anchors. EPRI, Palo Alto, CA: 2016. 3002008099. 87. D. F. Meinheit, A. E. N. Osborn, and M. R. Krueger, Pullout Strength of L-Bolt Anchors—Revisiting Design Equations, American Concrete Institute, Farmington Hills, MI, 2014. SP-296. 88. Seismic Verification of Nuclear Plant Equipment Anchorage, Vol. 1: Development of Anchorage Guidelines, Rev. 1. EPRI, Palo Alto, CA: 1991. NP-5228. 89. R. Eligehausen, R. Mallee, and J. F. Silva, Anchorage in Concrete Construction, Ernst & Sohn, Berlin, Germany, 2006. 90. Diverse and Flexible Coping Strategies (FLEX) Implementation Guide. Appendix H. Revision 4. Nuclear Energy Institute, Washington D.C.: 2016. NEI 12-06. 91. Categorization of Nuclear Facility Structures, Systems, and Components for Seismic Design, American Nuclear Society, 2107. ANS 2.26-2004. 92. High Frequency Program: Phase 1 Seismic Test Summary. EPRI, Palo Alto, CA: 2013. 3002000706. 93. Seismic Fragility of Nuclear Power Plant Components (Phases I, II, and III) Vols. 1, 2 and 3. Brookhaven National Laboratory, June 1986, Dec. 1987 and Dec. 1988. NUREG/CR-4659. 94. Component Fragility Research Program. Phase I, and Phase II. Lawrence Livermore National Laboratory, Livermore, CA: Dec. 1986 and June 1989. NUREG/CR-4900, NUREG/CR-5470. 95. A Framework for Qualification of Equipment by Safety Margin Methodology. EG&G, ID: 1985. SWRI 8608-001. 96. IEEE Recommended Practices for Seismic Qualification of Class 1E Equipment for Nuclear Power Generating Stations. Institute of Electrical and Electronics Engineers, Piscataway, NJ. 1975. IEEE Standard 344-1975. 97. GERS Formulated Using Data from the SQURTS Program, Volume 1. EPRI, Palo Alto, CA: 1996. TR-105988-V1. 7-6 13633436 References 98. GERS Formulated Using Data from the SQURTS Program, Volume 2. EPRI, Palo Alto, CA: 1999. TR-105988-V2. 99. Proceedings of the OECD/NEA Workshop on Seismic Risk. Organization for Economic Co-operation and Development/Nuclear Energy Agency, Committee on the Safety of Nuclear Installations PWG3 and PWG4. Tokyo, Japan: 1999. NEA/CSNI/R(99)28. 100. T. Ueki, T. Sueki, Y. Kitada, H. Niwa and M. Fujii, ''High Acceleration Level Vibration Tests for Electric Components," Proceedings of OECD/NEA Workshop on Seismic Risk, Tokyo, Japan (August 1999). 101. M. W. Salmon, and R. P. Kennedy, “Seismic Response Levels for CDFM Approach for Estimating Seismic Fragility,” 9th Nuclear Plants Current Issues Symposium: Moving Forward, North Carolina State University (December 2014). 102. J. W. Baker, “Conditional Mean Spectrum: Tool for Ground-Motion Selection,” Journal of Structural Engineering, Vol. 137, No. 3, pp. 322–331 (2011). 103. T. Lin, S. C. Harmsen, J. W. Baker,N. Luco, “Conditional Spectrum Computation Incorporating Multiple Causal Earthquakes and Ground-Motion Prediction Models,” Bulletin of the Seismological Society of America. Vol. 103, No. 2A. pp. 1103–1116. (2013) 104. N. A. Abrahamson and L. Al Atik, “Scenario Spectra for Design Ground Motions and Risk Calculation,” 9th U.S. National and 10th Canadian Conference on Earthquake Engineering, Toronto (2010). 105. Development and Application of a New Seismic PRA Methodology for Determining Seismic Fragilities Using Scenario Earthquakes. EPRI. Palo, Alto, CA: 2016. 3002008098. 106. M. M. Talaat, “A Case Study of Scenario Earthquake-based Risk Assessment for Nuclear Power Plants,” Paper 373, Division V Transactions, SMiRT-23, Manchester, UK (August 2015). 107. Y.N. Huang, A. S. Whittaker, and N. Luco “A Probabilistic Seismic Risk Assessment Procedure for Nuclear Power Plants: (I) Methodology,” Nuclear Engineering and Design, Vol. 241, No. 9, pp. 3996-4003 (2011). 108. Seismic Analysis of Safety Related Nuclear Structures and Commentary, American Society of Civil Engineers, Reston, VA: 1998. ASCE Standard 4-98. 109. J. F. Rocks, B. N. Luna, and A. S. Whittaker, “Seismic Response of Low Aspect Ratio Reinforced Concrete Shear Walls,” Transactions of the 21st Conference on Structural Mechanics in Reactor Technology, New Delhi, India (2011). 110. U.S. Nuclear Regulatory Commission, Office of New Reactors, Interim Staff Guidance on Ensuring Hazard-Consistent Seismic Input for Site Response and Soil Structure Interaction Analyses DC/COL-ISG-017. Washington, D.C. 2009. NRC-2009-0380. 111. Program on Technology Innovation: Spatial Coherency Models for Soil Structure Interaction. EPRI, Palo Alto, CA: 2006. 1014101. 7-7 13633436 References 112. Program on Technology Innovation: Effects of Spatial Incoherence on Seismic Ground Motions. EPRI, Palo Alto, CA: 2007. 1015110. 113. U.S. Nuclear Regulatory Commission. Interim Staff Guidance on Seismic Issues Associated with High-Frequency Ground Motion in Design Certification and Combined License Applications. Bethesda, MD: 2008. Revised and confirmed 9 January 2009. DC/COL-ISG-01. 114. SMACS – Seismic Methodology Analysis Chain with Statistics, Volume 9, Lawrence Livermore National Laboratory, Livermore, CA: 1981. NUREG/CR-2015 (UCRL-53021). 115. U.S. Nuclear Regulatory Commission. Development of Criteria for Seismic Review of Selected Nuclear Power Plants. Washington, D.C. 1978. NUREG/CR-0098. 116. J. Watson-Lamprey and D. Boore, “Beyond SaGMRotI: Conversion to SCArb and SaMaxRot,” Bulletin of the Seismological Society of America, Vol. 97, No. 5, pp 15111524 (2007). 117. R. Haviland. A Study of the Uncertainties in the Fundamental Translational Periods and Damping Values for Real Buildings. Massachusetts Institute of Technology, Boston, MA 1976. 118. A. H. Hadjian, et al., "Variability in Engineering Aspects of Structural Modeling," Proceedings, 6th World Conference on Earthquake Engineering, New Delhi, India (January 1977). 119. R. P. Kennedy, et al., "Probabilistic Seismic Safety Study of an Existing Nuclear Power Plant," Nuclear Engineering and Design, Vol. 59, No. 2, pp. 315-338 (1980). 120. U.S. Nuclear Regulatory Commission, Combining Modal Responses and Spatial Components in Seismic Response Analysis, Revision 1. Washington D.C. 1976. Regulatory Guide 1.92. 121. U.S. Nuclear Regulatory Commission, Seismic Safety Margins Research Program (Phase I), Subsystem Response Review. Washington, D.C. 1981. NUREG/CR-1706. 122. A Study of Factors Influencing Floor Response Spectra in Nonlinear Multi-Degree-ofFreedom Structures. The John A. Blume Earthquake Engineering Center, 1986. 82. 123. Correlation of Methodologies for Seismic Qualification Test of Nuclear Plant Equipment. Prepared for the U.S. Nuclear Regulatory Commission by Southwest Research Institute, San Antonio, TX: 1983. SWRI-6582-002. 124. D. D. Kana. "Use of Amplification Factors for Developing Equipment Base Seismic Capacity for Relays." letter report to P. Y. Chen, U.S. Nuclear Regulatory Commission, February 28, 1989. 125. Similarity Principle for Equipment Qualification by Experience. Southwest Research Institute, San Antonio, TX: 1988. NUREG/CR-5012. 7-8 13633436 References 126. D. D. Kana and D. J. Pomerening. "Determination of Modal Interaction Correction for Narrow-Band Fragility Data." Transactions of the 9th International Conference on Structural Mechanics in Reactor Technology, JK Panel Session (NUREG/CR-0088) (July 1987). 127. D. D. Kana and P. Y Chen. "Dynamic Amplification Factors for Seismic Evaluation of Devices Mounted in Equipment." 11th Structural Mechanics in Reactor Technology Conference, Tokyo, Japan (August 1991). 128. D. D. Kana and D. J. Pomerening. "Determination of Waveform Similarity from Seismic Response Spectra." Transactions of the 10th on Structural Mechanics in Reactor Technology Conference, Vol. K-1, pp. 55-60, Anaheim, CA (August 1989). 129. Guidelines for Development of In-Cabinet Seismic Demand for Devices Mounted in Electrical Cabinets. EPRI, Palo Alto, CA: 1995. NP-7146 SL R1. 130. U.S. Nuclear Regulatory Commission. Correlation of Seismic Performance in Similar SSCs (Structures, Systems, and Components), Office of Nuclear Regulatory Research, Washington, D.C. 2017. NUREG/CR-7237. 131. Seismic Walkdown Guidance for Resolution of Fukushima Near-Term Task Force Recommendation 2.3: Seismic, EPRI, Palo Alto, CA: 2012. 1025286. 132. Surry SPRA Pilot Plant Review. EPRI, Palo Alto, CA. 1020756. 133. Generic Seismic Technical Evaluations of Replacement Items (GSTERI) for Nuclear Power Plants. EPRI, Palo Alto, CA: 1995. TR-104871. 134. Nuclear Energy Institute (K. Keithline) Letter to NRC (D. Skeen), White Paper Supporting Seismic Evaluation Guidance, Criterion for Capacity-Based Selection of Structures, Systems and Components for Fragility Analyses in a Seismic Risk-based Evaluation, Project Code 689, Washington, D.C. November 28, 2012. 135. Program on Technology Innovation: The Effects of High-Frequency Ground Motion on Structures, Components, and Equipment in Nuclear Power Plants. EPRI, Palo Alto, CA: 2007. 1015108. 136. Program on Technology Innovation: Seismic Screening of Components Sensitive to HighFrequency Vibratory Motions. EPRI, Palo Alto, CA: 2007. 1015109. 137. High Frequency Seismic Inelastic Effects on Equipment Anchorage. EPRI, Palo Alto, CA: 2017. 3002010665. 138. W. S. Tseng, “Equipment Response Spectra including Equipment-Structure Interaction Effects”, Proceedings of the 1989 ASME Pressure Vessels and Piping Conference, PVP Vol. 155, pp. 21 29. Honolulu, HI (1989). 139. A. J. Gupta, Response Spectrum Method in Seismic Analysis and Design of Structures, CRC Press Inc., Boca Raton, FL, 1992. 140. Coupled Analysis of Primary-Secondary System to Generate Floor Response Spectra, Quantifying Reduction Factors for Coupled In-Structure Response Spectra Amplitudes, EPRI, Palo Alto, CA: 2017. 3002010666. 7-9 13633436 References 141. Samuelson-Sanford, C. B., et al., “Structure Response and Clipping Factor Variabilities using Probabilistic In-Structure Response Spectra for Functional Seismic Fragility Evaluation of Equipment,” Proceedings of the ASME 2015 Pressure Vessels & Piping Conference, PVP2015-45660, Boston, MA (July 2015). 142. Assessment of Lumped Mass and Finite Element Structural Models for Seismic Analysis Applications. EPRI, Palo Alto, CA: 2014. 3002002804. 143. U.S. Nuclear Regulatory Commission, Standard Review Plan, Revision 2. Washington, D.C. 1989. NUREG-0800. 144. N. C. Tsai, “Modal Damping for Soil-Structure Interaction,” Journal of the Engineering Mechanics Division, American Society of Civil Engineers, April 1974. 145. J. J. Johnson, O. R. Maslenikov, and E. C. Schewe, “SSI Response of a Typical Shear Wall Structure,” Paper K619, Proceedings of the Eighth SMiRT Conference, Brussels, Belgium (1985). 146. SSI Response of a Typical Shear Wall Structure, Vols. 1 and 2, Lawrence Livermore National Laboratory, Livermore, CA: 1984. UCID-20122. 147. J. C. Chen and C. Johnson, “Influence of the Local Site Condition on Seismic Response of a PWR-Containment Building,” Paper K6/8, Proceedings of the Eighth SMiRT Conference, Brussels, Belgium (1985). 148. Simplified Seismic Probabilistic Risk Assessment Procedures and Limitations, Lawrence Livermore National Laboratory, Livermore, CA: 1985. NUREG/CR-4331 (UCID20468). 149. S. H. Crandall and W. D. Mark, Random Vibration in Mechanical Systems, Academic Press, New York, NY, 1963. 7-10 13633436 A ENGLISH TO SI UNIT CONVERSION The evaluations and examples in this report are in imperial units. This appendix provides the conversions applicable for this report and can be used to provide for converting between units. Physical Quantity Length English Unit SI Unit 1 in. 2.54 cm 1 ft 0.3048 m 1 sq in. 6.452 cm2 1 sq ft 0.0929 m2 1 cu in. 16.3871 cm3 1 cu ft 0.0283 m3 Mass 1 lb 0.4536 kg Force 1 pound (force) 4.448 N (kg·m/s2) 1 kip = 1,000 lbs 4.448 kN 1 psf (pounds per square foot) 47.8803 Pa (N/m2) 1 psi (pounds per square inch) 6.89476 kPa 1 ksf (kip per square foot) 47.88 kPa 1 ksi (kip per square inch) 6.89476 MPa Density 1 pcf (lb/ft3) 16.01846 kg/m3 Velocity 1 in/sec 0.0254 m/s 1 ft/sec 0.3048 m/s 1 ft/s2 0.3048 m/s2 1g 9.807 m/s2 1 in-lb 0.11298 N·m 1 lb-ft 1.36 N·m 1 kip-ft 1.3558 kN·m Area Volume Pressure and Stress Acceleration Moment of force; torque A-1 13633436 13633436 B WALKDOWN GUIDANCE Section 6.1 describes, in general terms, the salient features of the preparatory work and conduct of the seismic capability walkdown of plant components. During the walkdowns, the seismic review team (SRT) is to make judgements on seismic capacity of the structures, systems, and components (SSCs) on the seismic equipment list (SEL). These SRT capacity decisions are aided by the guidelines in Table 4-2 (based on Table 2-4 of EPRI NP-6041-SLR1 [B-1]). The SRT should also be familiar with and consider the guidance and caveats offered by the Senior Seismic Review and Advisory Panel (SSRAP, SAND92 0140 [B-2]). In addition, the SRT must assess the potential for seismic spatial systems interactions (SI). This appendix consolidates the caveats of Table 4-2 and those from SSRAP, along with potential SI conditions to be considered, into checklists. For convenience, example walkdown data sheets are also provided for various classes of equipment in digital, PDF format as attachments to this report. These sheets allow walkdown preparatory information to be entered, provide a summary of caveats, and contain space for notes and sketches. Data sheets of this type have been found to be very useful during walkdowns. The data sheets provide a neat, compact record of pertinent design information, walkdown observations, and capacity-related judgments. While the exact form of these sheets is not mandatory, there is a need to document the walkdown (Section 6.1.6), and the data sheets provide a convenient format for this documentation. The responsibility for capacity-based judgments developed during the plant walkdown rests entirely with the SRT. The screening and evaluation worksheets (SEWS) provided in this appendix for the walkdown team will assist the SRT in this effort. These forms have been purposely abbreviated to provide an efficient means for documenting what the SRT finds in the field. This gives the maximum room for judgement by the SRT, but the SEWS are organized to remind the SRT of the various issues that they should consider. For example, on each SEWS, topic words which correspond to the checklist items are specified. In the spirit of the responsibility given to the SRT, the actual areas that the SRT must check off are kept to a minimum. It is preferred that the SRT spend its time looking at the components to identify any potential issues rather than being required to make repetitive entries on the sheets. B.1 Walkdown Checklists This section contains suggested checklists that the SRT should consider for each of the components reviewed during their walkdown. The equipment classes identified in Section 6.1 are in some cases grouped together in the checklists and SEWS in this appendix for convenience. The original source of these checklists is EPRI NP-6041-SLR1 [B-1]; however, there are modifications incorporated to tailor the checklists for the conduct of an SPRA walkdown. The guidelines of Table 4-2 assume that the concerns noted here are generally absent. The SRT, B-1 13633436 Walkdown Guidance however, is the final judge on whether the components meet the capacity criteria, or to what extent further assessment is required to make that determination. These checklists have been summarized on the example component specific walkdown data sheets (SEWS) in the attached forms. Where it is noted to check anchorage, the guidance given in Section 4.7 and Appendices E and F, as well as the examples in Appendices T and V, should be used. EPRI NP-5228 [B-3] also provides general information on anchor bolts. Of particular concern in examining anchorage is whether units mounted on grout pads have their anchor bolts extending into the base concrete floor. The anchorage criteria are not intended to be a quality assurance check requiring torqueing of bolts, etc. Often, experience and engineering judgement are sufficient to conclude with high confidence that anchorage does not govern the seismic fragility, and this may be performed as part of the walkdown. However, such judgments must be defendable, and detailed evaluation of bounding cases can be helpful to avoid detailed checks of all anchorage. Electrical panels are typically opened during seismic probabilistic risk assessment (SPRA) walkdowns to review internal anchorage and internal load paths. The utility should coordinate the walkdowns with work control, maintenance, and operations to allow the SRT to open and view electrical panel internals. Cabinets may be grouped by similarity in advance of the walkdown to minimize the number of cabinets that are required to be opened. For cabinet groups in which the lead item cannot be opened during the walkdown, an alternate item should be sought, or the review may be accomplished by other means such as review of the documented results of prior walkdown programs. The historical seismic margin assessment (SMA) walkdown guidance in EPRI NP-6041-SLR1 [B-1] sought to address electrical sub-components and assemblies that contain acceleration sensitive devices such as relays, motor starters, switches, etc., during the equipment walkdown. For an SPRA, however, the functional assessment of such devices is accomplished in a separate evaluation procedure as outlined in Section 6.3. Typically, only the physical mounting configuration of relays and other control devices are observed and reviewed for proper mounting during an SPRA walkdown. Sometimes, subsequent relay-specific walkdowns are performed as needed to collect information for refinement of important seismic fragilities. B.1.1 Motor Control Centers and Low and Medium Voltage Switchgear Units 1. Evaluation of cabinets selected for sampling a. Check mounting tabs or rolled flanges for excessive flexibility. b. Check that internal device mountings are not excessively flexible, and that they appear seismically rugged and properly attached to cabinet. c. Estimate tributary weight of external enclosures. Tributary weights should be less than about 100 lbs per bay. d. Check adequacy of seismic load paths to anchor points. e. Check for excessively large cutouts in the lower half of cabinets. SSRAP cutout limits for motor control centers (MCCs) are about 6 in. wide and 12 in. high. Switchgear cutouts should be generally limited to 30% of panel width with the cutout height limited to about 60% of panel width. B-2 13633436 Walkdown Guidance f. Check whether cabinets appear to be excessively flexible. g. Check that general cabinet equipment configuration is similar to the National Electrical Manufacturers Association (NEMA) standards for MCCs and ANSI C37.20 standards for switchgear. h. Check that all doors are secured by latches or fasteners. i. Verify that motor starter panel units are not mounted on masonry block walls. 2. Relay evaluation a. Spot check to confirm that any relays present are properly mounted. b. Check whether adjacent sections, or other cabinets, that are close enough together to impact, are bolted together. c. Functionality of relays is a separate evaluation per Section 6.3. 3. Anchorage evaluation a. Observe and note the number, type, condition, and size of anchor bolts, plug welds, or fillet welds. b. Check anchor spacing, free-edge distance, and concrete condition. c. Check that all specified anchor bolts, plug welds, or fillet welds per the design drawings are present. Note any non-uniformity in installation of anchorage, grout/concrete pad, and condition of nearby concrete. d. Verify that nuts are present and apparently tight on all bolts, and/or that bolts are apparently tight in expansion anchors. A torque test is not required unless the SRT suspects a bolt/nut to be loose. e. Where visible, spot check that gap under the base is less than 1/4 in. for bolted anchorages. f. Check that anchorage appears to be relatively stiff, and that there is no excessive prying action on anchors. g. Determine whether excessive flexibility exists between anchorage tie down location and cabinet walls. 4. Systems interactions a. Conduct a general area review for systems interactions. b. Check external cables and conduits connected to equipment for adequate flexibility to accommodate any relative movement. c. Determine if adjacent units are bolted together or if there is adequate gap between units and adjacent structure or equipment (i.e., cabinets will not deflect and impact). d. Check that adjacent cabinets are free from impact due to deflection or failure of nearby equipment or structures. e. Check that soft targets on cabinets are free from impact by nearby equipment or structures that could fail and fall. B-3 13633436 Walkdown Guidance f. Check if there is potential of collapse of adjacent structures or walls, overhead equipment, or distribution systems that might grossly impact equipment. g. Check that area is free of masonry block walls. h. Confirm that no potential flooding sources exist that could flood or cascade onto sensitive equipment. B.1.2 Batteries and Racks 1. Batteries evaluation a. Check if battery plates are of lead-antimony construction. b. Batteries should be restrained in all horizontal directions. Check that batteries are completely restrained by the rack framework and/or shimmed to be closely fitting to end and side rails. c. Check that spacers between individual batteries are not made of soft, crushable open cell foam and fill at least two-thirds of vertical space between batteries. d. Check adequacy of strength and stiffness of side rails. 2. Racks evaluation a. Check adequacy of the lateral load resistance system (including connections) of the racks. b. Check whether adjacent racks, close enough together to impact, are adequately secured. c. Check adequacy of wood racks. 3. Anchorage evaluation a. Observe and note the number, type, condition, and size of anchor bolts, plug welds, or fillet welds. b. Check anchor spacing, free-edge distance, and concrete condition. c. Check that all specified anchor bolts, plug welds, or fillet welds per the design drawings are present. Note any non-uniformity in installation of anchorage, grout/concrete pad, and condition of nearby concrete. d. Verify that nuts are present and apparently tight on all bolts, and/or that bolts are apparently tight in expansion anchors. A torque test is not required unless the SRT suspects a bolt/nut to be loose. e. Where visible, spot check that gap under the base is less than 1/4 in. for bolted anchorages. f. Check that anchorage appears to be relatively stiff, and that there is no excessive prying action on anchors. B-4 13633436 Walkdown Guidance 4. Systems interactions a. Conduct a general area review for systems interactions. b. Check attached cables for adequate flexibility to accommodate relative movement. c. Check if there is potential of collapse of adjacent structures or walls, overhead equipment, or distribution systems that might grossly impact and short out batteries. d. Check that area is free of masonry block walls. e. Confirm that no potential flooding sources exist that could flood or cascade onto batteries. B.1.3 Battery Chargers and Inverters 1. Evaluation of cabinets selected for sampling a. Check that battery chargers or inverters are solid state devices. No guidance is provided for older technologies (e.g., vacuum tubes). b. For floor-mounted units, check that transformers are near the base and securely attached to the cabinet or the base assembly; otherwise, check adequacy of seismic load paths. c. For wall-mounted units, check that transformer supports and bracing provide adequate seismic load paths to the rear cabinet wall. d. Check adequacy of lateral load paths through base of cabinet, particularly around cutouts. e. Check adequacy of base assemblies to resist lateral forces. f. Check that all doors are secured by latches or fasteners. 2. Relay evaluation a. Spot check to confirm that any relays present are properly mounted. b. Check whether adjacent sections, or other cabinets, that are close enough together to impact, are bolted together. c. Functionality of relays is a separate evaluation per Section 6.3. 3. Anchorage evaluation a. Observe and note the number, type, condition, and size of anchor bolts, plug welds, or fillet welds. b. Check anchor spacing, free-edge distance, and concrete condition. c. Check that all specified anchor bolts, plug welds, or fillet welds per the design drawings are present. Note any non-uniformity in installation of anchorage, grout/concrete pad, and condition of nearby concrete. d. Verify that nuts are present and apparently tight on all bolts, and/or that bolts are apparently tight in expansion anchors. A torque test is not required unless the SRT suspects a bolt/nut to be loose. e. Where visible, spot check that gap under the base is less than 1/4 in. for bolted anchorages. B-5 13633436 Walkdown Guidance f. Check that anchorage appears to be relatively stiff, and that there is no excessive prying action on anchors. g. Check that stiffeners are provided for base assembly structural members subject to weak axis bending. 4. Systems interactions a. Conduct a general area review for systems interactions. b. Check connecting cables for adequate flexibility to accommodate seismic displacement. c. Check that soft targets on cabinets are free from impact by nearby equipment or structures that could fall and fail. d. Check if there is potential of collapse of adjacent structures or walls, overhead equipment, or distribution systems that might grossly impact equipment. e. Check that area is free of masonry block walls. f. Confirm that no potential flooding sources exist that could flood or cascade onto sensitive equipment. B.1.4 Transformers 1. Evaluation of cabinets selected for sampling a. Check attachments of components (coolers, etc.). b. Check transformer coils of floor-mounted dry- and oil-type units for adequate restraints to limit motion between the coil assembly and surrounding cabinet. c. Check that transformer coils attachments in wall-mounted units appear seismically rugged and properly anchored to enclosure near enclosure support surface. d. Check that all doors are secured by latches or fasteners. 2. Relay evaluation a. List any devices, such as sudden pressure switches, that could trip transformers. b. Check whether mounted control cabinets, which may have vibration isolation, are restrained to prevent impact. c. Functionality of relays is a separate evaluation per Section 6.3. 3. Anchorage evaluation a. Observe and note the number, type, condition, and size of anchor bolts, plug welds, or fillet welds. b. Check anchor spacing, free-edge distance, and concrete condition. c. Check that all specified anchor bolts, plug welds, or fillet welds per the design drawings are present. Note any non-uniformity in installation of anchorage, grout/concrete pad, and condition of nearby concrete. B-6 13633436 Walkdown Guidance d. Verify that nuts are present and apparently tight on all bolts, and/or that bolts are apparently tight in expansion anchors. A torque test is not required unless the SRT suspects a bolt/nut to be loose. e. Where visible, spot check that gap under the base is less than 1/4 in. for bolted anchorages. f. Check that anchorage appears to be relatively stiff, and that there is no excessive prying action on anchors. g. Check that light base assemblies are stiffened to accommodate weak axis bending. 4. Systems interactions a. Conduct a general area review for systems interactions. b. Check attached cables connected to transformers for adequate flexibility to accommodate seismic displacement. c. Check that soft targets on cabinets are free from impact by nearby equipment or structures that could fall and fail. d. Determine if adjacent switchgear panels are bolted to the transformer enclosure or there is adequate gap between units and adjacent structure or equipment (i.e., cabinets will not deflect and impact). e. Check if there is potential of collapse of adjacent structures or walls, overhead equipment, or distribution systems that might grossly impact transformers. f. Check that area is free of masonry block walls. g. Confirm that no potential flooding sources exist that could flood or cascade onto sensitive equipment. B.1.5 Control and Instrumentation Panels 1. Evaluation of cabinets selected for sampling a. Check mounting tabs or rolled flanges for excessive flexibility. b. Spot check that internal devices are mounted according to manufacturer's specifications. c. Check that internal device mountings are not excessively flexible, and that they appear seismically rugged and properly attached to cabinet. d. Check adequacy of seismic load paths. e. Check for excessively large cutouts in the lower half of cabinets. Cutouts are limited to about 6 in. wide and 12 in. high (see Motor Control Centers). f. Check whether cabinets appear excessively flexible. g. Check that general cabinet equipment configuration is similar to NEMA standards. h. Check that all doors are secured by latches or fasteners. i. Check that control components within pull-out drawers and circuit boards on slides are restrained to prevent unplugging. B-7 13633436 Walkdown Guidance 2. Relay evaluation a. Spot check to confirm that any relays present are properly mounted. b. Check whether adjacent sections, or other cabinets, that are close enough together to impact, are bolted together. c. Functionality of relays is a separate evaluation per Section 6.3. 3. Anchorage evaluation a. Observe and note the number, type, condition, and size of anchor bolts, plug welds, or fillet welds. b. Check anchor spacing, free-edge distance, and concrete condition. c. Check that all specified anchor bolts, plug welds, or fillet welds per the design drawings are present. Note any non-uniformity in installation of anchorage, grout/concrete pad, and condition of nearby concrete. d. Verify that nuts are present and apparently tight on all bolts, and/or that bolts are apparently tight in expansion anchors. A torque test is not required unless the SRT suspects a bolt/nut to be loose. e. Where visible, spot check that gap under the base is less than 1/4 in. for bolted anchorages. f. Check that anchorage appears to be relatively stiff, and that there is no excessive prying action on anchors. g. Determine whether excessive flexibility exists between anchorage tie down locations and cabinet walls. 4. Systems interactions a. Conduct a general area review for systems interactions. b. Check attached lines connected to equipment for adequate flexibility to accommodate relative movement. c. Determine if adjacent panels are bolted together or if there is adequate gap between units and adjacent structure or equipment (i.e., cabinets will not deflect and impact). d. Check that soft targets on cabinets are free from impact by nearby equipment or structures that could fail and fall. e. Check if there is potential of collapse of adjacent structures or walls, overhead equipment, or distribution systems that might grossly impact equipment. f. Check that area is free of masonry block walls. g. Confirm that no potential flooding sources exist that could flood or cascade onto sensitive equipment. B-8 13633436 Walkdown Guidance B.1.6 Instrument Racks 1. Evaluation of racks selected for sampling a. Check that attached device mountings are not excessively flexible, and that they appear seismically rugged and properly attached to the rack structure. b. Check adequacy of the lateral load resistance system (including connections). 2. Relay evaluation a. Spot check to confirm that any relays present are properly mounted. b. Check whether adjacent racks, or other cabinets, that are close enough together to impact are bolted together. c. Functionality of relays is a separate evaluation per Section 6.3. 3. Anchorage evaluation a. Observe and note the number, type, condition, and size of anchor bolts, plug welds, or fillet welds. b. Check anchor spacing, free-edge distance, and concrete condition. c. Check that all specified anchor bolts, plug welds, or fillet welds per the design drawings are present. Note any non-uniformity in installation of anchorage, grout/concrete pad, and condition of nearby concrete. d. Verify that nuts are present and apparently tight on all bolts, and/or that bolts are apparently tight in expansion anchors. A torque test is not required unless the SRT suspects a bolt/nut to be loose. e. Where visible, spot check that gap under the base is less than 1/4 in. for bolted anchorages. f. Check that anchorage appears to be relatively stiff, and that there is no excessive prying action on anchors. 4. Systems interactions a. Conduct a general area review for systems interactions. b. Check electrical and pneumatic lines attached to the racks for adequate flexibility to accommodate seismic displacement. c. Check that soft targets on racks are free from impact by nearby equipment or structures that could fail and fall. d. Check if there is potential of collapse of adjacent structures or walls, overhead equipment, or distribution systems that might grossly impact racks. e. Check that area is free of masonry block walls. f. Confirm that no potential flooding sources exist that could flood or cascade onto sensitive equipment. B-9 13633436 Walkdown Guidance B.1.7 Distribution Panels 1. Evaluation of cabinets selected for sampling a. Check that internal device mountings are not excessively flexible, and that they appear seismically rugged and properly attached to cabinet. b. Check whether floor-mounted panels appear excessively flexible. c. Wall- or floor- mounted enclosures should be similar to NEMA standards. d. Check that all doors are secured by latches or fasteners. e. Verify that panel units are not mounted on masonry block walls. 2. Relay evaluation a. Spot check to confirm that any relays present are properly mounted. b. Check whether adjacent sections, or other cabinets, that are close enough together to impact, are bolted together. c. Functionality of relays is a separate evaluation per Section 6.3. 3. Anchorage evaluation a. Observe and note the number, type, condition, and size of anchor bolts, plug welds, or fillet welds. b. Check anchor spacing, free-edge distance, and concrete condition. c. Check that all specified anchor bolts, plug welds, or fillet welds per the design drawings are present. Note any non-uniformity in installation of anchorage, grout/concrete pad, and condition of nearby concrete. d. Verify that nuts are present and apparently tight on all bolts, and/or that bolts are apparently tight in expansion anchors. A torque test is not required unless the SRT suspects a bolt/nut to be loose. e. Where visible, spot check that gap under the base is less than 1/4 in. for bolted anchorages. f. Check that anchorage appears to be relatively stiff, and that there is no excessive prying action on anchors. 4. Systems interactions a. Conduct a general area review for systems interactions. b. Check external lines connected to equipment for adequate flexibility to accommodate relative movement. c. Determine if adjacent cabinets are bolted together or if there is adequate gap between cabinets and adjacent structure or equipment. d. Check that soft targets on cabinets are free from impact by nearby equipment or structures that could fail and fall. B-10 13633436 Walkdown Guidance e. Check if there is potential of collapse of adjacent structures or walls, overhead equipment, or distribution systems that might grossly impact equipment. f. Check that area is free of masonry block walls. g. Confirm that no potential flooding sources exist that could flood or cascade onto sensitive equipment. B.1.8 Local Instruments and Sensors 1. Local instrument/sensor evaluation a. Check adequacy of the attachments. b. Check that there is no concern for excessive differential displacement between mountings of connection heads and mountings of temperature sensors. 2. Systems interactions a. Conduct a general area review for systems interactions. b. Check attached wire, cabling, and associated distribution for adequate flexibility to accommodate relative movement. c. Check that soft targets on devices are free from impact by nearby equipment or structures that could fail and fall. d. Check if there is potential of collapse of adjacent structures or walls, overhead equipment, or distribution systems that might grossly impact devices. e. Check that area is free of masonry block walls. f. Confirm that no potential flooding sources exist that could flood or cascade onto devices. B.1.9 Engine Generators 1. Engine-generator unit and appurtenances evaluation a. Check that engine and generator are attached to a common stiff skid or structural assembly. b. For engines and generators that are mounted separately on vibration isolators, check that flexible couplings between engine and generator are used, and check manufacturer’s misalignment limits for couplings. c. Check adequacy of the lateral load resistant system of the structural assembly (including connections). d. Check for potential of relative motion of anchor points for non-flexible interconnecting fuel, lube oil, and water cooling lines. e. Verify that appurtenances are supported with stiff members. f. Check attachments to engine or skid for weak seismic load paths. g. Where assemblies are mounted on vibration isolators, check for adequate strength lateral stops on isolators, or for adequate lateral strength and stiffness of isolators and use of ductile materials. Verify that there are no cast iron parts potentially subject to impact. B-11 13633436 Walkdown Guidance 2. Ancillary equipment (non-skid or non-common base mounting) evaluation a. Check adequacy of foundations and anchorages of essential components for engine start and operation. b. Check interconnecting subsystems such as pipe, conduit, and cable tray for flexibility to accommodate motion of their anchor points. 3. Relay evaluation a. Spot check to confirm that any relays present are properly mounted. b. Spot check to confirm that any relays and other control components (pressure switches, etc.) present are properly mounted. c. Check whether mounted control cabinets, which may have vibration isolation, are restrained to prevent impact. d. Functionality of relays is a separate evaluation per Section 6.3. 4. Anchorage evaluation a. Observe and note the number, type, condition, and size of anchor bolts, plug welds, or fillet welds. b. Check anchor spacing, free-edge distance, and concrete condition. c. Check that all specified anchor bolts, plug welds, or fillet welds per the design drawings are present. Note any non-uniformity in installation of anchorage, grout/concrete pad, and condition of nearby concrete. d. Verify that nuts are present and apparently tight on all bolts, and/or that bolts are apparently tight in expansion anchors. A torque test is not required unless the SRT suspects a bolt/nut to be loose. e. Where visible, spot check that gap under the base is less than 1/4 in. for bolted anchorages. f. Check that anchorage appears to be relatively stiff, and that there is no excessive prying action on anchors. 5. Systems interactions a. Conduct a general area review for systems interactions. b. Check connected tubing, piping, and conduits for adequate flexibility to accommodate relative movement. c. Check that soft targets on the engine and ancillary equipment are free from impact by nearby equipment or structures that could fail and fall. d. Check if there is potential of collapse of adjacent structures or walls, overhead equipment, or distribution systems that might grossly impact equipment. e. Check that area is free of masonry block walls. f. Confirm that no potential flooding sources exist that could flood or cascade onto sensitive equipment. B-12 13633436 Walkdown Guidance B.1.10 Motor Generators 1. Motor-Generator unit and appurtenances evaluation a. Check that motor and generator are attached to a common stiff skid or structural assembly. b. Check adequacy of the lateral load resistant system of the structural assembly (including connections). c. Check for potential of relative motion of anchor points for non-flexible interconnecting fuel, lube oil, and water cooling lines. d. Verify that appurtenances are supported with stiff members. e. Check attachments to motor-generator or skid for weak seismic load paths. f. Where assemblies are mounted on vibration isolators, check for adequate strength lateral stops on isolators, or for adequate lateral strength and stiffness of isolators and use of ductile materials. Verify that there are no cast iron parts potentially subject to impact. 2. Anchorage evaluation a. Observe and note the number, type, condition, and size of anchor bolts, plug welds, or fillet welds. b. Check anchor spacing, free-edge distance, and concrete condition. c. Check that all specified anchor bolts, plug welds, or fillet welds per the design drawings are present. Note any non-uniformity in installation of anchorage, grout/concrete pad, and condition of nearby concrete. d. Verify that nuts are present and apparently tight on all bolts, and/or that bolts are apparently tight in expansion anchors. A torque test is not required unless the SRT suspects a bolt/nut to be loose. e. Where visible, spot check that gap under the base is less than 1/4 in. for bolted anchorages. f. Check that anchorage appears to be relatively stiff, and that there is no excessive prying action on anchors. 3. Systems interactions a. Conduct a general area review for systems interactions. b. Check connected lines and conduits for adequate flexibility to accommodate relative movement. c. Check that soft targets on the motor and ancillary equipment are free from impact by nearby equipment or structures that could fail and fall. B-13 13633436 Walkdown Guidance d. Check if there is potential of collapse of adjacent structures or walls, overhead equipment, or distribution systems that might grossly impact equipment. e. Check that area is free of masonry block walls. f. Confirm that no potential flooding sources exist that could flood or cascade onto sensitive equipment. B.1.11 Horizontal Pumps 1. Pump evaluation a. Check that driver and pump are attached to a common stiff skid or structural assembly. b. Check adequacy of the lateral load resistant system of the structural assembly (including connections). c. Check that shaft is thrust-restrained in both axial directions. d. Where units are mounted on vibration isolators, check for adequate strength lateral stops on isolators, or for adequate lateral strength and stiffness of isolators and ductile materials. Verify that there are no cast iron parts potentially subject to impact. e. Check that there is no concern for excessive nozzle loadings resulting from large diameter connecting piping and reduced size nozzles, gross pipe motion, or differential displacement and prying about a rigid pipe support close to the pump. f. Check for adjacent relatively massive, unsupported or lightly supported, in-line components or long unsupported pipe spans. 2. Anchorage evaluation a. Observe and note the number, type, condition, and size of anchor bolts, plug welds, or fillet welds. b. Check anchor spacing, free-edge distance, and concrete condition. c. Check that all specified anchor bolts, plug welds, or fillet welds per the design drawings are present. Note any non-uniformity in installation of anchorage, grout/concrete pad, and condition of nearby concrete. d. Verify that nuts are present and apparently tight on all bolts, and/or that bolts are apparently tight in expansion anchors. A torque test is not required unless the SRT suspects a bolt/nut to be loose. e. Where visible, spot check that gap under the base is less than 1/4 in. for bolted anchorages. f. Check that anchorage appears to be relatively stiff, and that there is no excessive prying action on anchors. 3. Systems interactions a. Conduct a general area review for systems interactions. b. Check attached lines for adequate flexibility to accommodate relative movement. B-14 13633436 Walkdown Guidance c. Check that soft targets on pumps are free from impact by nearby equipment or structures that could fail and fall. d. Check if there is potential of collapse of adjacent structures or walls, overhead equipment, or distribution systems that might grossly impact pumps. e. Check that area is free of masonry block walls. f. Confirm that no potential flooding sources exist that could flood or cascade onto sensitive equipment. B.1.12 Vertical Pumps 1. Pump evaluation a. Check baseplate for excessive flexibility. b. Check that equipment is free of intermediate flexible base. c. Check that shaft is thrust-restrained in both axial directions. d. Check that impeller drive shaft is supported within the casing. e. Verify that the unsupported length of vertical casing cantilevered below base plate of pump does not exceed 20 ft. Lengths over 20 ft are allowed if they are supported below pump base plate such that they are less flexible than a 20 ft cantilever. f. Check that there is no concern for damage to pump resulting from differential structural motion between pump mounting flange and casing supports. g. Check that there is no concern for excessive nozzle loadings resulting from gross pipe motion, or differential displacement and prying about a rigid pipe support close to the pump. h. Check for adjacent relatively massive, unsupported or lightly supported, in-line components or long unsupported pipe spans. 2. Anchorage evaluation a. Observe and note the number, type, condition, and size of anchor bolts, plug welds, or fillet welds. b. Check anchor spacing, free-edge distance, and concrete condition. c. Check that all specified anchor bolts, plug welds, or fillet welds per the design drawings are present. Note any non-uniformity in installation of anchorage, grout/concrete pad, and condition of nearby concrete. d. Verify that nuts are present and apparently tight on all bolts, and/or that bolts are apparently tight in expansion anchors. A torque test is not required unless the SRT suspects a bolt/nut to be loose. e. Where visible, spot check that gap under the base is less than 1/4 in. for bolted anchorages. f. Check that anchorage appears to be relatively stiff, and that there is no excessive prying action on anchors. B-15 13633436 Walkdown Guidance 3. Systems interactions a. Conduct a general area review for systems interactions. b. Check attached lines for adequate flexibility to accommodate relative movement. c. Check that soft targets on pumps are free from impact by nearby equipment or structures that could fail and fall. d. Check if there is potential of collapse of adjacent structures or walls, overhead equipment, or distribution systems that might grossly impact pumps. e. Check that area is free of masonry block walls. f. Confirm that no potential flooding sources exist that could flood or cascade onto sensitive equipment. B.1.13 Air- or Fluid-Operated Valves (Diaphragm or Piston Type) or Dampers 1. Valve evaluation a. Verify valve is mounted on pipe of 1 in. diameter or greater. b. Verify that valve body, bonnet, yoke, or operator supports are not made of cast iron. c. Verify that distance from pipe centerline to top of operator is either (1) 45 in. or less when the pipe is less than or equal to 4 in. in diameter or (2) 60 in. or less when the pipe is greater than 4 in. in diameter (See SSRAP Guidelines in SAND92 0140 [B-2] shown in Figures B-1 and B-2 of this appendix). The SRT should exercise judgment in cases where the operator slightly exceeds the criteria limits. d. Verify that either (1) operator and yoke are supported by pipe and not braced to or supported by the structure or (2) valve operator and pipe adjacent to valve are both braced to a common structure. e. For valves that are fail safe, evaluation of the air supply is not required. 2. Systems interactions a. Conduct a general area review for systems interactions. b. Check attached tubing, piping, and conduits for sufficient flexibility. c. Check that soft targets on valves are free from impact by nearby equipment or structures that could fail and fall. d. Check if there is potential of collapse of adjacent structures or walls, overhead equipment, or distribution systems that might grossly impact valves. e. Check that area is free of masonry block walls. f. Confirm that no potential flooding sources exist that could flood or cascade onto sensitive equipment. B-16 13633436 Walkdown Guidance Figure B-1 Limits of experience data for air-operated diaphragm valves and piston-operated valves of light-weight construction Figure B-2 Limits of experience data for motor-operated valves, substantial piston-operated valves, and solenoid valves B-17 13633436 Walkdown Guidance B.1.14 Motor-Operated Valves or Dampers 1. Valve evaluation a. Verify valve is mounted on pipe of 1 in. diameter or greater. b. Verify that valve body, bonnet, yoke, or operator supports are not made of cast iron. c. Verify that valve is within weight and eccentricity limits as given in the SSRAP Guidelines (SAND92 0140 [B-2]) and tabulated below (Table B-1) and as shown in Figure B-2 of this appendix. The SRT should exercise judgement in cases where the operator slightly exceeds the criteria limits. d. Verify that either (1) operator and yoke are supported by pipe and neither is braced to or supported by the structure or (2) valve operator and pipe adjacent to valve are both braced to a common structure. 2. Systems interactions a. Conduct a general area review for systems interactions. b. Check attached tubing, piping, and conduits for sufficient flexibility. For valves that do not have to change state, electrical supply does not require evaluation. c. Check that soft targets on valves are free from impact by nearby equipment or structures that could fail and fall. d. Check if there is potential of collapse of adjacent structures or walls, overhead equipment, or distribution systems that might grossly impact valves. e. Check that area is free of masonry block walls. f. Confirm that no potential flooding sources exist that could flood or cascade onto sensitive equipment. Table B-1 SSRAP guidelines for valve weight and eccentricity limits Pipe Diameter Distance Pipe Centerline to Top of Motor Actuator Max. Actuator Weight (approximately) > 14 in. 100 in. 750 lbs 8 in. to 14 in. 80 in. 750 lbs 6 in. to 8 in. 60 in. 400 lbs 4 in. to 6 in. 40 in. 200 lbs 2 in. to 4 in. 30 in. 100 lbs 1 in. to 2 in. 25 in. 75 lbs B-18 13633436 Walkdown Guidance B.1.15 Solenoid-Operated Valves 1. Valve evaluation a. Verify that valve body, bonnet, yoke, or operator supports are not made of cast iron. b. If the valve is mounted on a line at least 1 in. in diameter, verify that distance from pipe centerline to top of operator is within the guidelines shown in Figure B-2 of this appendix. c. Verify that either (1) operator and yoke are supported by pipe and neither is braced to or supported by the structure or (2) valve operator and pipe adjacent to valve are both braced to a common structure. 2. Systems interactions a. Conduct a general area review for systems interactions. b. Check attached tubing, piping, and conduits for sufficient flexibility. c. Check that soft targets on valves are free from impact by nearby equipment or structures that could fail and fall. d. Check if there is potential of collapse of adjacent structures or walls, overhead equipment, or distribution systems that might grossly impact valves. e. Check that area is free of masonry block walls. f. Confirm that no potential flooding sources exist that could flood or cascade onto sensitive equipment. B.1.16 Air Compressors 1. Compressor evaluation a. Check that motor and compressor are rigidly connected to a common stiff base. b. Check that shaft is thrust-restrained in both axial directions for larger units. c. Where units are mounted on vibration isolators, check for adequate strength lateral stops on isolators, or for adequate lateral strength and stiffness of isolators and use of ductile materials. Verify that there are no cast iron parts potentially subject to impact. d. Check that there is no concern for excessive nozzle loadings resulting from gross pipe motion or differential displacement and prying about a rigid pipe support close to the compressor. e. Check for adjacent relatively massive, unsupported or lightly supported, in-line components or long unsupported pipe spans. 2. Relay evaluation a. Spot check to confirm that any relays present are properly mounted. b. Check whether mounted control cabinets, which may have vibration isolation, are restrained to prevent impact. c. Functionality of relays is a separate evaluation per Section 6.3. B-19 13633436 Walkdown Guidance 3. Anchorage evaluation a. Observe and note the number, type, condition, and size of anchor bolts, plug welds, or fillet welds. b. Check anchor spacing, free-edge distance, and concrete condition. c. Check that all specified anchor bolts, plug welds, or fillet welds per the design drawings are present. Note any non-uniformity in installation of anchorage, grout/concrete pad, and condition of nearby concrete. d. Verify that nuts are present and apparently tight on all bolts, and/or that bolts are apparently tight in expansion anchors. A torque test is not required unless the SRT suspects a bolt/nut to be loose. e. Where visible, spot check that gap under the base is less than 1/4 in. for bolted anchorages. f. Check that anchorage appears to be relatively stiff, and that there is no excessive prying action on anchors. 4. Systems interactions a. Conduct a general area review for systems interactions. b. Check connected piping for adequate flexibility to accommodate relative movement. c. Check that soft targets on compressors are free from impact by nearby equipment or structures that could fail and fall. d. Check that air lines are free from impact by nearby equipment or structures that could fail and fall. e. Check if there is potential of collapse of adjacent structures or walls, overhead equipment, or distribution systems that might grossly impact compressors. f. Check that area is free of masonry block walls. g. Confirm that no potential flooding sources exist that could flood or cascade onto sensitive equipment. B.1.17 Fans and Air Handlers 1. Fan and air handler evaluation a. Check that drive motor and fan are connected to a stiff common base when they are connected by a shaft. b. Check that long shafts are supported at both ends. c. Check that there is no concern for damage by impact to fan blades resulting from excessive distortion of the fan shroud or duct. d. Check that internal device mountings (e.g., heat exchanger coils) appear seismically adequate. e. Where units are mounted on vibration isolators, check for adequate stiffness or seismic stops to limit uplift and lateral movement. B-20 13633436 Walkdown Guidance f. Check that internal piping is sufficiently flexible to accommodate differential motions between heat exchanger and outer enclosure. g. Check that all doors are secured by latches or fasteners. h. Check that loads on connecting piping that is distributed to heat exchanger tubing will not overstress heat exchanger tubing. 2. Relay evaluation a. Spot check to confirm that any relays present are properly mounted. b. Check whether mounted control cabinets, which may have vibration isolation, are restrained to prevent impact. c. Functionality of relays is a separate evaluation per Section 6.3. 3. Anchorage evaluation a. Observe and note the number, type, condition, and size of anchor bolts, plug welds, or fillet welds. b. Check anchor spacing, free-edge distance, and concrete condition. c. Check that all specified anchor bolts, plug welds, or fillet welds per the design drawings are present. Note any non-uniformity in installation of anchorage, grout/concrete pad, and condition of nearby concrete. d. Verify that nuts are present and apparently tight on all bolts, and/or that bolts are apparently tight in expansion anchors. A torque test is not required unless the SRT suspects a bolt/nut to be loose. e. Where visible, spot check that gap under the base is less than 1/4 in. for bolted anchorages. f. Check that anchorage appears to be relatively stiff, and that there is no excessive prying action on anchors. 4. Systems interactions a. Conduct a general area review for systems interactions. b. Check piping and conduits connected to equipment for adequate flexibility to accommodate relative movement. c. Check that soft targets on equipment are free from impact by nearby equipment or structures that could fail and fall. d. Check if there is potential of collapse of adjacent structures or walls, overhead equipment, or distribution systems that might grossly impact equipment. e. Check that area is free of masonry block walls. f. Confirm that no potential flooding sources exist that could flood or cascade onto sensitive equipment. B-21 13633436 Walkdown Guidance B.1.18 Chillers 1. Chiller unit electrical and control panels evaluation a. Check mounting tabs or rolled flanges for excessive flexibility. b. Check that internal device mountings are not excessively flexible, and that they appear seismically rugged and properly attached to cabinet. c. Estimate tributary weight of external attached enclosures. Tributary weights should be less than about 100 lbs per bay. d. Check adequacy of seismic load paths. e. Check for excessively large cutouts in the lower half of any cabinets. SSRAP cutout limits are about 6 in. wide and 12 in. high. f. Estimate whether cabinets appear to be excessively flexible. g. Check that general cabinet configuration is similar to NEMA standards. h. Check that all doors are secured by latches or fasteners. i. Verify that any associated motor starter panel units are not mounted on block walls. 2. Motor-Compressor unit evaluation a. Check that motor and compressor are attached to a common stiff skid or structural assembly. b. Check adequacy of the lateral load resistant system of the structural assembly (including connections). c. Check that rotating shaft is thrust-restrained in both axial directions. d. Where units are mounted on vibration isolators, check for adequate strength lateral stops on isolators or for adequate lateral strength and stiffness of isolators and use of ductile materials. Verify that there are no cast iron parts potentially subject to impact. e. Check that there is no concern for excessive nozzle loadings resulting from gross pipe motion or differential displacement and prying about a rigid pipe support near the compressor. f. Check for adjacent relatively massive unsupported or lightly supported in-line components or long unsupported pipe spans. 3. Tank/heat exchanger evaluation a. Check adequacy of connection of tank/heat exchanger to saddle or cradle, by such means as straps, welds, lugs, etc. b. Check adequacy of saddle or cradle in weak axis bending. c. Check tank/heat exchanger for threaded pipe connections. d. For one horizontal tank mounted over another, verify adequacy of saddle supports for horizontal effects. e. Verify there are isolation valves on nonessential lines such as drain and fill lines. B-22 13633436 Walkdown Guidance 4. Relay evaluation a. Spot check to confirm that any relays present are properly mounted. b. Check whether mounted control cabinets, which may have vibration isolation, are restrained to prevent impact. c. Functionality of relays is a separate evaluation per Section 6.3. 5. Anchorage evaluation a. Observe and note the number, type, condition, and size of anchor bolts, plug welds, or fillet welds. b. Check anchor spacing, free-edge distance, and concrete condition. c. Check that all specified anchor bolts, plug welds, or fillet welds per the design drawings are present. Note any non-uniformity in installation of anchorage, grout/concrete pad, and condition of nearby concrete. d. Verify that nuts are present and apparently tight on all bolts, and/or that bolts are apparently tight in expansion anchors. A torque test is not required unless the SRT suspects a bolt/nut to be loose. e. Where visible, spot check that gap under the base is less than 1/4 in. for bolted anchorages. f. Check that anchorage appears to be relatively stiff, and that there is no excessive prying action on anchors. 6. Systems interactions a. Conduct a general area review for systems interactions. b. Check external cables and conduits connected to equipment for adequate flexibility to accommodate relative movement. c. Check that soft targets on chillers are free from impact by nearby equipment or structures that could fail and fall. d. Check if there is potential of collapse of adjacent structures or walls, overhead equipment, or distribution systems that might grossly impact chillers. e. Check that area is free of masonry block walls. f. Confirm that no potential flooding sources exist that could flood or cascade onto sensitive equipment. B-23 13633436 Walkdown Guidance B.1.19 Frame or Skirt Supported Vertical Tanks and Heat Exchangers (also Flat Bottom Tanks) 1. Tank/heat exchanger evaluation a. For flat bottom metal fluid storage tank, verify validity of tank property information collected in the preparatory phase. b. For flat bottom metal fluid storage tank, check that chairs appear seismically rugged. c. Verify adequacy of connection of vessel to frame or skirt. d. Check overall appearance of support systems for obvious weak links. e. Check adequacy of lateral support for tall vertical tanks. f. For tank supported at more than one floor, check that tank can withstand expected story drift in the structure. g. Verify there are isolation valves on nonessential lines such as drain and fill lines. h. Check attached piping for threaded joints. 2. Anchorage evaluation a. Observe and note the number, type, condition, and size of anchor bolts, plug welds, or fillet welds. b. Check anchor spacing, free-edge distance, and concrete condition. c. Check that all specified anchor bolts, plug welds, or fillet welds per the design drawings are present. Note any non-uniformity in installation of anchorage, grout/concrete pad, and condition of nearby concrete. d. Verify that nuts are present and apparently tight on all bolts, and/or that bolts are apparently tight in expansion anchors. A torque test is not required unless the SRT suspects a bolt/nut to be loose. e. Where visible, spot check that gap under the base is less than 1/4 in. for bolted anchorages. f. Check that anchorage appears to be relatively stiff, and that there is no excessive prying action on anchors. 3. Systems interactions a. Conduct a general area review for systems interactions. b. Check attached piping for adequate flexibility to accommodate relative movement. c. Check that soft targets on tanks/heat exchangers are free from impact by nearby equipment or structures that could fail and fall. d. Check if there is potential of collapse of adjacent structures or walls, overhead equipment, or distribution systems that might grossly impact tanks/heat exchangers. e. Check that area is free of masonry block walls. B-24 13633436 Walkdown Guidance B.1.20 Horizontal Saddle or Cradle Supported Tanks or Heat Exchangers 1. Tank/heat exchanger evaluation a. Check adequacy of connection of tank to saddle or cradle, by such means as straps, welds, lugs, etc. b. Check adequacy of saddle or cradle in weak axis bending. c. Check adequacy of anchorages of saddle or cradle to structure. d. Check tank for threaded pipe connections. e. Verify there are isolation valves on nonessential lines such as drain and fill lines. 2. Anchorage evaluation a. Observe and note the number, type, condition, and size of anchor bolts, plug welds, or fillet welds. b. Check anchor spacing, free-edge distance, and concrete condition. c. Check that all specified anchor bolts, plug welds, or fillet welds per the design drawings are present. Note any non-uniformity in installation of anchorage, grout/concrete pad, and condition of nearby concrete. d. Verify that nuts are present and apparently tight on all bolts, and/or that bolts are apparently tight in expansion anchors. A torque test is not required unless the SRT suspects a bolt/nut to be loose. e. Where visible, spot check that gap under the base is less than 1/4 in. for bolted anchorages. f. Check that anchorage appears to be relatively stiff, and that there is no excessive prying action on anchors. 3. Systems interactions a. Conduct a general area review for system interactions. b. Check attached piping for adequate flexibility to accommodate seismic motion of tank. c. Check that soft targets on tanks/heat exchangers are free from impact by nearby equipment or structures that could fail and fall. d. Check if there is potential of collapse of adjacent structures or walls, overhead equipment, or distribution systems that might grossly impact tanks/heat exchangers. e. Check that area is free of masonry block walls. B-25 13633436 Walkdown Guidance B.1.21 Horizontal Suspended Tanks 1. Tank evaluation a. Check adequacy of welded or bolted hanger to tank connection. b. Check adequacy of welded or bolted hanger to structural steel connection. c. Check adequacy of lateral support (sway braces or stops). d. Check tank for threaded or mechanical pipe connections. e. Verify there are isolation valves on nonessential lines such as drain and fill lines. 2. Anchorage evaluation a. Observe and note the number, type, condition, and size of anchor bolts, plug welds, or fillet welds. b. Check anchor spacing, free-edge distance, and concrete condition. c. Check that all specified anchor bolts, plug welds, or fillet welds per the design drawings are present. d. Note any non-uniformity in installation of anchorage, grout/concrete pad, and condition of nearby concrete. e. Verify that nuts are present and apparently tight on all bolts, and/or that bolts are apparently tight in expansion anchors. A torque test is not required unless the SRT suspects a bolt/nut to be loose. f. Where visible, spot check that gap under the base is less than 1/4-in. for bolted anchorages. g. Check that anchorage appears to be relatively stiff, and that there is no excessive prying action on anchors. 3. Systems interactions a. Conduct a general area review for systems interactions. b. Check attached piping for adequate flexibility to accommodate seismic motion of tank. c. Check that soft targets on tanks are free from impact by nearby equipment or structures which could fail and fall. d. Check if there is potential of collapse of adjacent structures or walls, overhead equipment, or distribution systems which might grossly impact tanks. e. Check that area is free of masonry block walls. B.1.22 Buried Tanks 1. Valve pit evaluation a. Check that there are no signs of structural distress in valve pit walls. b. Check connections of pipe and sensor lines to the tank that enter the valve pit from the ground for adequate flexibility. B-26 13633436 Walkdown Guidance c. Verify that long fill and vent lines have adequate seismic supports at top. d. Verify that the pit cover lip is adequately sized to accommodate seismic motions without the possibility of the cover falling into the pit. 2. Systems interactions a. Conduct a general area review to verify that there is no potential for interactions that could negatively affect the tank or its connections. b. Check attached piping for adequate flexibility to accommodate seismic motion of tank. c. Check if there is potential of collapse of adjacent structures or walls, overhead equipment, or distribution systems that might grossly impact equipment. B.1.23 Building Penetrations of Underground Utilities 1. Structure a. Check for free space around penetrating utilities, such as pipes, conduits and duct banks, to accommodate seismic motions of the buildings. 2. Utility a. Check for flexible details near the penetration. b. Stiff supports located near a penetration may be a concern. B.1.24 Strainers and Filters Use the appropriate procedures suggested for either horizontal or vertical tanks. B.1.25 NSSS Components and Primary Coolant Loops 1. Branch piping and sensor lines evaluation a. Check for stiff routing details that may be vulnerable to large relative seismic motions, such as short, straight segments with rigid supports. b. Check for adequate lateral and vertical seismic supports on all major components. c. Check for non-ductile failure modes of the supports (buckling, weld connections, etc.). d. Verify adequacy of joints at embedment plates. 2. Anchorage evaluation a. Check anchor spacing, free-edge distance, and concrete condition. b. Check that all specified anchor bolts, plug welds, or fillet welds per the design drawings are present. c. Note any non-uniformity in installation of anchorage, grout/concrete pad, and condition of nearby concrete. d. Verify that nuts are present and apparently tight on all bolts and/or that bolts are apparently tight in expansion anchors. A torque test is not required unless the SRT suspects a bolt/nut to be loose. B-27 13633436 Walkdown Guidance e. Where visible, spot check that gap under the base is less than 1/4 in. for bolted anchorages. f. Check that anchorage appears to be relatively stiff, and that there is no excessive prying action on anchors. 3. Systems interactions a. Conduct a general area review for systems interactions. b. Check lines connected to components for adequate flexibility to accommodate relative movement. c. Check for possibility of vessel or pump potential motion impacting more lightly braced or supported equipment. d. Check that soft targets on components are free from impact by nearby equipment or structures that could fail and fall. e. Check if there is potential of collapse of adjacent structures or walls, overhead equipment, or distribution systems that might grossly impact equipment. f. Check that area is free of masonry block walls. g. Confirm that no potential flooding sources exist which could flood or cascade on to sensitive equipment. B.1.26 Control Rod Drive Assemblies The control rod drive (CRD) mechanism assemblies for pressurized water reactors drop by gravity during a plant scram and require no external components to function. For boiling water reactors (BWRs), the hydraulic control units (HCUs) may or may not be important to the scram function. Their importance should be determined by the systems and/or plant operation engineers. 1. Check for lateral support of the CRD housings. a. For BWR CRDs, check the potential for crimping of scram discharge lines from II/I or proximity. This should be a virtually impossible condition to occur. b. For BWR HCUs, check mounting of HCUs. B.1.27 Building Seismic Gaps 1. Structures a. Check, where possible, at the top and bottom of gapped structures for gap conformance to the drawings. b. Subsystems spanning gaps c. Check containment penetration room areas or other building-to-building interface areas for adequate subsystem flexibility to accommodate the relative building seismic motions. B-28 13633436 Walkdown Guidance B.1.28 Control Room Ceilings 1. Inspect for adequate lateral bracing or tie-backs to prevent reflective panels or light fixtures from falling on operators. a. Check area above lightweight ceiling units for heavy equipment that might fall. B.1.29 Traveling Screens and Sluice Gates 1. Traveling screen/sluice gate evaluation a. Check for adequacy of the overall stability of the structures. b. Check for adequate lateral and vertical seismic supports. c. Check for non-ductile failure modes of the supports (buckling, weld connections, etc.). 2. Anchorage evaluation a. Check anchor spacing, free-edge distance, and concrete condition. b. Check that all specified anchor bolts, plug welds, or fillet welds per the design drawings are present. Note any non-uniformity in installation of anchorage, grout/concrete pad, and condition of nearby concrete. c. Verify that nuts are present and apparently tight on all bolts, and/or that bolts are apparently tight in expansion anchors. A torque test is not required unless the SRT suspects a bolt/nut to be loose. d. Where visible, spot check that gap under the base is less than 1/4 in. for bolted anchorages. e. Check that anchorage appears to be relatively stiff, and that there is no excessive prying action on anchors. 3. Systems interactions a. Conduct a general area review for systems interactions. b. Check that soft targets on structures are free from impact by nearby equipment or structures that could fail and fall. c. Check if there is potential of collapse of adjacent structures or walls, overhead equipment, or distribution systems that might grossly impact structures. d. Check that area is free of masonry block walls. B-29 13633436 Walkdown Guidance B.1.30 Manual Valves or Dampers Manual valves are often included on an SEL since, in an SPRA, the capability of plant operators to reconfigure piping system flows is considered. While such valves are considered passive, the movement of the piping during an earthquake may lead to system interactions that could result in impact and valve damage that could impair manual operation of the valve. 1. Valve evaluation a. Verify that the valve operating handle or wheel has sufficient clearance from adjacent structures or walls, anchored equipment, other piping runs, and associated supports to preclude any impact. 2. Systems interactions a. Conduct a general area review for systems interactions. b. Check general piping configuration for excessive flexibility. c. Check that soft targets on valves (valve stems) are free from impact by nearby equipment or structures that could fail and fall. d. Check if there is potential of collapse of adjacent structures or walls, overhead equipment, or distribution systems that might grossly impact valves. e. Check that area is free of masonry block walls. B.1.31 Generic Components There are many miscellaneous plant components such as strainers, filters, building penetrations, masonry walls, and control room ceilings, etc., that can be identified for inclusion on the SEL by the PRA engineers. To aid the SRT in tracking these miscellaneous items that have been identified, a generic or blank form is provided in the digital PDF format attachment file. This form has the basic description, evaluation, relay mounting, anchorage, system interaction, and general note sections that can be used for documenting the walkdown observations of the SRT. The SRT may prefer to adapt this for items that occur frequently in a given plant. B.2 Area Walkdown Reviews Many general areas of a plant can be identified by the systems analysis team as operator access pathways. The SRT should review these pathways for seismic interaction effects that could impede access to equipment or other areas requiring operator actions following an earthquake. Distribution systems (electrical, HVAC, piping, etc.) are typically supported overhead, and require review along access pathways. Such systems also serve important functions in the SPRA. These systems are best observed by dividing the plant layout into general areas, which are then reviewed by the SRT on a walk-by basis. Documentation can be accomplished by using the generic SEWS form referenced to plant areas identified on layout drawings. Example checklists are provided below for electrical distribution systems, balance-of-plant piping, and HVAC ducting. B-30 13633436 Walkdown Guidance B.2.1 Electrical Conduit and Cable Tray Raceways 1. Conduit a. Check for the use of malleable clamps with back strap. The support capacity for these clamps is from friction developed from the strap bolt; thus, capacity is limited. 2. Cable tray raceway a. Check to see if the trays are overfilled. b. Check adequacy of connection of trays to supports. c. Check cable tautness in regions of anticipated large motion. 3. Anchorages and supports a. Visually examine anchor bolt number and size on a sampling basis. b. Check support configuration for lateral stiffness to limit excessive lateral motions. c. Check spacing of supports for vendor or code requirements. d. Check adequacy of support connection to base plate. 4. Masonry block walls a. Identify any block walls supporting cable tray and conduit. B.2.2 Balance-of-Plant Piping The SRT is advised to review Section 10.1 of DOE Standard DOE/EH-0545 [B-4] for further guidance. 1. Safety-related piping, including fire protection piping (pressure boundary integrity is credited in SPRA model). a. Ensure that ductile materials are used. b. Identify if threaded joints or mechanical couplings are used. Check for brittle connections, socket welds, and brittle cast iron piping. c. Check that vertical support spacing is in general compliance with design criteria. d. Identify if threaded rod hangers are used. e. Observe if stiff branch and flexible headers are present. f. Ensure that differential building motion can be accommodated. For systems spanning seismic gaps between buildings and for buried pipe entering building penetrations, check for expansion joints or flexible loops of pipe. g. Ensure that piping can accommodate anchor motion of flexible equipment. h. Observe if lateral support spacing is in general compliance with design criteria. i. Identify if long axial runs are adequately supported. j. Identify if any falling or proximity systems interactions are present. k. Check for adequate support on long vertical risers (tight U-bolts, lugs, etc.). B-31 13633436 Walkdown Guidance l. Check design and apparent adequacy of horizontal and vertical supports, including anchorage (supports sliding off, weak anchorage, load path, etc.). m. Check that piping with flexible joints (bellows) are adequately supported near joint. n. Look for signs of degradation such as leakage and/or excessive erosion or corrosion. o. Check long, flexible pipe runs for the possibility of valve operator systems interactions. p. Review the physical arrangement of the pipe and anchorage layout with the intent of identifying details that could be potential concerns when seismic and normal operating loads are combined, i.e., is there any potential for buckling or fracture of stiff sections subjected to thermal expansion loadings and seismic loading, or for support or anchor point overload. 2. Non-safety piping (systems interaction, spray, and flooding sources) a. Identify if piping is a flood or spray source. b. Identify if piping is a falling or proximity systems interaction source. c. Identify targets. d. For piping that is a flood, spray, or spatial interaction source, identify vulnerabilities as described for safety-related piping. B.2.3 HVAC Ducting The SRT is advised to review Section 10.4 of DOE Standard DOE/EH-0545 [B-4] for further guidance on HVAC ducting evaluation. 1. Rectangular and round ducting for which flow integrity is required. a. Verify that duct material, stiffeners, and joints meet Sheet Metal and Air Conditioning Contractors’ National Association (SMACNA) standards [B-5, B-6, B-7]. b. Determine if vertical support spacing is in general compliance with SMACNA or plant design criteria. c. Determine if horizontal support spacing is in general compliance with plant design criteria. d. Identify any heavy in-line components and their support system (e.g., fans, dampers, filters). e. Identify if threaded rod hangers are used for vertical support. f. Identify if threaded rod hangers have sufficient length to accommodate lateral seismic motion. g. Identify any apparent vulnerability of anchorage of rod hangers (beam clamps, inserts in overhead, etc.). h. Determine the apparent adequacy of horizontal and axial supports, including anchorage. i. Determine if floor supports may become unstable with large lateral duct motion. j. Determine the apparent adequacy of supports for vertical risers. B-32 13633436 Walkdown Guidance k. Identify if branch runs have adequate flexibility to accommodate seismic displacements of main run. l. Identify any issues of differential building motion. m. Determine if ducting is adequately supported near flexible joints. n. Identify any sources of falling interaction that could damage ducting. 2. Rectangular and round ducting for which only position retention is required (e.g., systems interaction sources) a. Determine if ducting is a falling or proximity hazard. b. Identify systems interaction targets. c. If ducting is an interaction source, check support vulnerabilities as described above. B.3 Seismic Spatial Systems Interactions As discussed in Section 5 of EPRI NP-6041-SLR1 [B-1], systems interactions are typically grouped into proximity, II/I, and spray and flooding. Proximity refers to the potentially adverse effect from the seismic motion of one component or structural element into another. II/I refers to the potential for failure of a seismic Category II component and its subsequent effect on a required Category I component. Spray and flooding may result from failure of either Category II or I components. The following are some guidelines on the types of conditions that might be encountered in a walkdown. These conditions are not exhaustive but are intended to support the SRT in making reasonable judgements as to the credibility of observed potential systems interactions. B.3.1 Proximity Proximity is only a concern for "soft" targets on essential components. Examples of "soft" targets of concern are: 1. Valve stems 2. Valve motor operators 3. Instrumentation and its tubing 4. Small pipe and tubing (< 1 in.) 5. Exposed belts, chains, or couplings on motors 6. Glass or ceramic components 7. Cable and wire terminations 8. Dials and gauges 9. Victaulic, threaded, or other mechanically coupled piping systems 10. Batteries 11. Exposed electrical circuits, switches, and relays 12. Fan shrouds or dampers that must change positions B-33 13633436 Walkdown Guidance Soft targets may be impacted as a result of relative motion between adjacent components or structures and components. Equipment and subsystems on the SEL should be visually examined for adequate free space adjacent to other equipment or structural members to eliminate the possibility of seismically induced damaging impacts. To evaluate whether any potential impact could be damaging, an assessment of the damageable items must first be made. For instance, the sheet metal of cabinets may become dented, but a visual check can be made to show that adequate free space exists within the cabinet to preclude damage to devices. The internal devices may see a larger shock than they normally would if the intervening impacted structure was not present. Another example is a valve stem or valve motor operator that could be impacted by a hung light fixture, but due to the relatively small mass of the light fixture, the impact is judged to be not potentially damaging. The following guidelines are suggested to eliminate from consideration the situations of potential equipment/equipment and structure/equipment seismic interaction: 1. Only the motion of equipment with "soft" targets need be of concern. "Hard" targets, such as pipes and tanks, should remain functional and structurally sound regardless of possible interaction. However, passive items such as a lube oil filter on a large electric motor could be located within the swinging arc radius of a flexible rod hung cable tray raceway. In this way, if the filter is within both the radius of the hanger and the anticipated "gap" of lateral translation, then it would be subjected to the forces of impact, which might result in cracking and subsequent leakage. Cabinets and panels can usually be classified as "hard" targets except for surfaces with instrumentation, gauges, and/or switches on them. 2. Large amplitude displacements from seismically induced motions of Category I or Category II piping or components may present SI concerns. For instance, "soft" targets may be impacted by the larger pipe motions due to: (1) one or more failed supports in a given segment; or (2) use of threaded rod or trapeze hangers with no lateral restraint of the pipe, provided that the pipe has an unobstructed path of motion. Bounds on the amplitude of pipe motion can be estimated from the applicable floor spectrum and system frequency from Equation B-1. Sd ≈ SaRRS� ω2 Eq. B-1 where: Sd is the displacement response (in.). SaRRS is the spectral acceleration from the applicable required response spectrum (RRS) in in./sec2 at the lowest fundamental frequency of the system, and ω is the lowest circular frequency of the system. 3. Generally, for equipment and subsystems with fundamental frequencies exceeding 5 Hz that have engineered anchorages and supports, the following conservative criteria can be used to estimate an adequate proximity gap space between structures and equipment: a. 1 in. for up to 40 ft above plant grade b. 2 in. for over 40 ft above plant grade c. Equipment to equipment proximity gaps should be double the above values. For equipment that is essentially rigid, such as pumps, motors, and pressure vessels that have nearly rigid anchorages, the gap guidelines may be reduced by a factor of two. These gap criteria are not intended to be applied to subsystems sharing the same support, such as B-34 13633436 Walkdown Guidance multiple conduits on a unistrut support segment bolted to a wall. The criteria are intended to aid the SRT for identifying the potential interaction of systems during walkdowns. These rules of thumb are associated with the capacity levels in Table 4-2. If a capacity greater than those in Table 4-2 are used for an SSC, then the criteria above are not applicable and should be adjusted to accommodate increased potential relative displacements associated with higher seismic input levels. d. Unbraced equipment and subsystems that are hung by threaded rods can, depending on the suspension length and seismic input, experience amplitudes of motion of a foot or more. 4. Non-"soft" equipment and subsystems that appear to be excessively flexible in their support (less than about 6 Hz to 10 Hz depending on the energy peak of the RE) may need to be evaluated if it is judged that sufficient energy exists to cause damage, such as severing of cables in a conduit impacted by adjacent piping. These types of failures could only occur if the impact point on the structure is a corner or knife edge or if the impacted object is not ductile, and large velocities of response are anticipated. In general, subsystems will not be able to develop the necessary velocities to produce damaging results because they will "rattle" together, thus dissipating the energy. An exception is the case where the flexible oscillator is massive and the impact point is vulnerable. 5. Commonly shared supports, brackets, or embedments will not excite subsystems, either similar or dissimilar, into damaging one or the other regardless of spacing or size differences. This will eliminate from consideration, for example, two or more conduits that are attached to the same unistrut fixture and do not satisfy the minimum gap space requirements. 6. Small bore piping or sensor lines running out of larger flexible pipes or vessels subject to large seismic motions can potentially fail if there is insufficient flexibility either in loops or supports to accommodate the responses. B.3.2 II/I Interactions Possible II/I interaction situations that are of concern to the essential components are defined as follows: 1. The postulated missile is a relatively large piece of equipment such as a space heater, vessel, tank, or large bore pipe. Ricocheting or secondary impacts and "smart" missiles that go around corners are not considered credible sources for damage to critical components. Judgement of the SRT must be used in each situation. 2. The target or area of possible impact on the critical component or subsystem must be classified as being "soft" to be of any concern. 3. Relatively lightweight and non-rigid components that could possibly fall, such as light fixtures, are not considered to damage non-"soft" critical components regardless of the falling height. B-35 13633436 Walkdown Guidance 4. Large bore piping hung by threaded rods or other potentially weak supports may damage a non-"soft" critical piece of equipment provided that the free-fall path is unobstructed, and the free-fall height is "large." If intervening subsystems or structures are present, only the appurtenances that are judged to be "soft" need to be visually examined for the possibility of a direct hit by the falling pipe segment. 5. Welded non-seismic piping should not be considered to sever and fall provided that the anchor points, such as wall penetrations, pumps and tanks, do not fail. Past SI design practices in the nuclear industry have been to assume that non-seismic piping will sever during the earthquake and "rain" down. Intermediate pipe supports may fail but ductile steel (not cast iron) pipes should not be considered to fall unless multiple support failures are possible in very long runs of pipe in open areas, such as can be found in turbine bays. 6. Pipe penetrations through concrete or reinforced masonry walls can be considered effective pipe support points with the pipe resting on the bottom of the penetration. 7. Visual examination of the areas around non-seismic or unreinforced non-load bearing masonry block walls for critical equipment and subsystems should be conducted. The non-seismic or unreinforced masonry block walls may not have sufficient capacity to maintain structural soundness. Thus, they should conservatively be assumed to fail by collapsing downwards over a region of about one-half of the wall height. Alternatively, they may be analytically evaluated to demonstrate that they will not fail prior to equipment fragility levels. Essential equipment and subsystems that are not shielded or removed from the collapse path of the block walls must be evaluated for the impact. Independently supported major welded steel piping systems (equal to or greater than about 12 in.) without in-line devices are likely immune to the effects of a collapsing standard 8 in. thick masonry block wall. 8. A block wall collapse may not be a concern for a particular component or "soft" target if intervening structures or components are judged to provide adequate shielding or protection from impact. B.3.3 Spray and Flooding Effects of possible ruptured vessels or piping systems that could spray, flood, or cascade onto essential equipment should be considered. Of particular concern is threaded fire protection piping with long unsupported spans. If adequate seismic supports are present or there are isolation valves near the tanks or charging sources, flooding may not be a real concern. Numerous failures have been observed in past earthquakes resulting from sprinkler head impact. Less frequent but commonly observed failures have occurred due to flexible headers and stiff branch pipes, non-ductile mechanical couplings, seismic anchor motion, and failed supports. The presence of floor drains that empty into other rooms or passageways with follow-on flooding considerations should also be checked. The potential for exposure of electrical and instrumentation cables to acidic solutions is also of concern. B-36 13633436 Walkdown Guidance If a potential flooding source is identified, such as from the failure of a tank support for a non-seismic tank, the following should be considered before a concern requiring analytical evaluation is noted: 1. Check to see if the plant layout or room layout is such that the flooded water level could rise high enough to short-out electrical devices or components or restrict access of required plant personnel. 2. Check to see if the ruptured pipe or tank has the volume capacity and discharge flow rate to flood the area. 3. Check for drainage paths out of the affected area. Determine if the drainage paths can remove the water at a rate comparable to the rupture discharge rate. 4. Check for valves and flow constrictors that would limit or inhibit the discharge flow rate to thereby accommodate the drainage paths. 5. If the discharge is coming from a high-energy system, it will first flash to steam. Depending on the closeness of the essential electrical components and their need for prolonged service following the postulated earthquake, the steamy environment may or may not be acceptable. B.4 Walkdown Data Sheets The attached digital SEWS forms are provided for the SRT’s convenience to document their walkdown observations. SEWS forms are provided for the following equipment classes: • Motor Control Centers and Low and Medium Voltage Switchgear • Batteries and Racks • Battery Chargers and Inverters • Transformers • Control and Instrumentation Panels • Instrument Racks • Distribution Panels • Local Instruments and Sensors • Engine Generators • Motor Generators • Horizontal Pumps • Vertical Pumps • Air- or Fluid-Operated Valves or Dampers • Motor-Operated Valves or Dampers • Solenoid-Operated Valves • Air Compressors B-37 13633436 Walkdown Guidance • Fans and Air Handlers • Chillers • Vertical Tanks or Heat Exchangers • Horizontal Tanks or Heat Exchangers • Traveling Screens and Sluice Gates • Manual Valves or Dampers • Generic Components Part A of the sheets contains prompts and spaces for pertinent component identification and location information; Parts B through E contain a checklist of observations to be made and potential concerns. The general caveats noted in the guidelines of Table 4-2 and as noted by the SSRAP (SAND92 0140 [B-2]) are included in the sheets. Space is provided to record notes on observed concerns or potential systems interactions. The exact form of the walkdown data sheets may be varied to suit the SRT. Experience gained in plant walkdowns suggests that a single summary sheet for each component to be observed is most convenient. The check-off items and prompts make the recording of walkdown results most convenient, as it is often very difficult to carry background information and write on notepads, etc., when in restricted or contaminated areas. It is suggested that the SRT copy the corresponding checklists for the group of items being evaluated during a given walkdown segment for reference during the walkdown. There are two blanks for dated signatures for at least two SRT members to indicate that they both concur on the findings and conclusions noted on the sheets. The SEWS forms or similar forms should be used to document the walkdown findings and observations for full scope walkdowns. It is noted that the SRT is free to adapt the format of the SEWS forms to enhance the presentation of walkdown results. Each SEWS should indicate the SRT’s assessment as to whether the component satisfies the Table 4-2 caveat checklists for the associated equipment class, whether relays are present and properly mounted (if applicable), whether the anchorage appears to be adequate, and whether any potential spatial systems interactions exist. The entries in the SEWS forms are to be interpreted as follows: • “Yes” means the specific criteria are met. • “No” means the specific criteria are not met. • “Unknown” means it cannot be determined whether the criteria are met at the time of walkdown. This response is also used to indicate that additional information or evaluation is required. • “N/A” means not applicable. The specific criteria are not applicable for the item under review. For example, relay evaluation is not applicable for electrical distribution panels where it can be determined that no relays or contactors exist. B-38 13633436 Walkdown Guidance B.5 References B-1 A Methodology for Assessment of Nuclear Power Plant Seismic Margin, Revision 1. EPRI, Palo Alto, CA: 1991. NP-6041-SLR1. B-2 Use of Seismic Experience and Test Data to Show Ruggedness of Equipment in Nuclear Power Plants, Part I. Sandia National Laboratories, Albuquerque, NM: 1991. SAND92-0140. B-3 “Seismic Verification of Nuclear Plant Equipment Anchorage, Vol. 1,” Development of Anchorage Guidelines, Revision 1. EPRI, Palo Alto, CA: 1991, NP-5228. B-4 Department of Energy, Seismic Evaluation Procedure for Equipment in USDOE Facilities, Washington D.C. 1997. DOE/EH-0545. B-5 HVAC Duct Construction Standard, Metal and Flexible, Sheet Metal and Air Conditioning Contractors’ National Association, Vienna, VA: 1985. B-6 Rectangular Industrial Duct Construction Standards, Sheet Metal and Air Conditioning Contractors’ National Association, Vienna, VA: 1988. B-7 Round Industrial Duct Construction Standards, Sheet Metal and Air Conditioning Contractors’ National Association, Vienna, VA: 1989. B-39 13633436 13633436 C WALKDOWN CRITERIA: BASIS FOR SEISMIC CAPACITY GUIDELINES FOR STRUCTURES, EQUIPMENT, AND SUBSYSTEMS C.1 General Discussion Seismic capacity guidelines are presented for various equipment classes in Section 4.2 and are summarized in Tables 4-2 and 4-3. These tables are based on Tables 2-3 and 2-4 of EPRI NP-6041-SLR1 [C-1], which are in turn based heavily on the recommendations of the Expert Panel on the Quantification of Seismic Margins in NUREG/CR-4334 [C-2]. These seismic capacity recommendations were developed based on a detailed assessment of a wide variety of available seismic capacity information, including the following: • Seismic fragilities from several seismic probabilistic risk assessment (SPRA) studies tabulated and discussed in NUREG/CR-4334 [C-2] • Earthquake experience data collected as part of the Seismic Qualification Utility Group (SQUG) research efforts • Seismic qualification test data • Generic Equipment Ruggedness Spectra (GERS) gathered by EPRI • Combined judgments and experience of the Expert Panel on the Quantification of Seismic Margins [C-2] The purpose of this appendix is to: • Summarize the historical basis for both the Expert Panel Screening Guidelines (Table 5-1 of NUREG/CR-4334 [C-2]) and the resulting seismic capacity guidelines contained in Tables 2-3 and 2-4 of EPRI NP-6041-SLR1 [C-1]. • Describe the additional data beyond that contained in NUREG/CR-4334 [C-2] that support the seismic capacity conclusions documented in Tables 4-2 and 4-4. The information documented in this appendix is largely obtained directly from Appendix A to EPRI NP-6041-SLR1 [C-1]. It provides a detailed description of the information that formed the basis for the seismic capacity levels summarized in Tables 4-2 and 4-4 of this report. As such, this appendix is an important reference for the fragility analyst to understand and properly apply the seismic capacity levels as part of an SPRA or seismic margin assessment (SMA). The technical content remains essentially unchanged from its source except for (1) minor editorial changes and (2) notifications to the reader in situations where additional relevant material is available that post-dates the completion of EPRI NP-6041-SLR1 [C-1]. C-1 13633436 Walkdown Criteria: Basis for Seismic Capacity Guidelines for Structures, Equipment, and Subsystems The additional seismic capacity data discussed in this appendix consists primarily of earthquake experience data, seismic qualification data, aging effects test data, probabilistic risk assessment (PRA) fragility estimates, and fragility data from the Safeguards shock test program (NUREG/CR-2405 [C-3]). Much of this data gathering was an ongoing effort at the time of publication of the original Appendix A to EPRI NP-6041-SLR1, and the discussions reflect the information available during the time frame that appendix was originally prepared (fall of 1985 through 1986). The additional data were reviewed at that time to compare to recommendations made by the Expert Panel on the Quantification of Seismic Margins (the “Panel”), who wrote NUREG/CR-4334. Statements attributed to the “Panel” throughout this appendix were also supported by the authors of EPRI NP-6041-SLR1. The objective of the additional data review was to determine if there were any potentially weak links not addressed in the “Panel” report (NUREG/CR-4334 [C-2]). The following topics are discussed in this appendix: Table C-1 Topics discussed in Appendix C Section Topic C.2 Background and Discussion of Capacity Guidelines C.3 Earthquake Experience Data C.4 Seismic Qualification Data C.5 Aging Effects C.6 Probabilistic Risk Assessment Fragilities C.7 Fragility Data from SAFEGUARD Program C.8 Electrical Cable Raceways C.9 Piping Systems C.2 Background and Discussion of Capacity Guidelines The following discussion of capacity guidelines presents the “Panel” recommendations. In cases where the authors of EPRI NP-6041-SLR1 [C-1] Appendix A had alternate or supplemental recommendations, such recommendations and their bases are discussed. Additional categories of components and subsystems were added to the guidelines where supplemental data were available to support these additions at the time EPRI NP-6041-SLR1 was written. C-2 13633436 Walkdown Criteria: Basis for Seismic Capacity Guidelines for Structures, Equipment, and Subsystems C.2.1 Reactor Containment Structures C.2.1.1 Primary Containment There are three major types of construction employed for containment structures: • reinforced concrete • post-tension reinforced concrete • steel vessels The reinforced and post-tension concrete containments employ steel liners to provide a leak-tight boundary, but the primary pressure and seismic force resistance is derived from the tensile, shear, and flexural strength of the concrete and reinforcing steel. Steel containment vessels have concrete shield structures surrounding them except for some of the very early plants, which have spherical steel containments without a concrete shield. Internal to the containment structure are steel and reinforced concrete structures providing support for the primary coolant system, internal structural elements, and other functional and non-functional components, including cranes. Internal structures also provide shielding from radiation. Boiling water reactors (BWRs) with Mark II and Mark III containments have internal structural elements that separate a drywell region from a pool of water (wetwell) used to condense steam in the event of a pipe break or safety relief valve discharge. Mark I containments have their suppression pool external to the drywell in the form of a steel torus. There is an inherent seismic resistance of concrete containments resulting from the heavy wall construction and heavy reinforcing required to resist pressure from a design basis accident. The “Panel” estimated that for this type containment, the high confidence of low probability of failure (HCLPF) capacity is greater than 0.8g peak ground acceleration (PGA). Furthermore, the Panel concluded that major equipment penetrations (e.g., containment hatch and personnel airlocks) have large margins above the safe shutdown earthquake (SSE) level. However, there is very little data available to the “Panel” to judge how much the HCLPF exceeds 0.3g PGA. Thus, the recommended HCLPF capacity is limited to 0.3g. For small electrical penetrations protected with gas packing, survey work has found that qualification tests demonstrate the capacity of these types of penetrations exceed 2.0g (local) peak acceleration. Since electrical penetrations are located generally below grade or slightly above grade and will generally experience little dynamic amplification, the HCLPF capacity is greater than 0.5g PGA. For potential failures of penetrating piping caused by large relative displacements resulting from rocking or sliding, see the discussion on piping. In addition, the possibility of impact with adjacent structures or of soils failures beneath the containment should be screened. The “Panel” did not make judgments concerning the failure capacities of BWR Mark I containments, freestanding steel containments, or the ice-condenser support portion of pressurized water reactor (PWR) containments. However, as part of seismic margin effort in developing EPRI NP-6041-SLR1 [C-1], SPRA results on three example steel containments were reviewed. In these cases, the steel containment was estimated to be more seismic-resistant than the surrounding reinforced concrete shield structures. One of the steel containments was from an earlier plant, and its weak link was the lack of positive attachment of the containment to the C-3 13633436 Walkdown Criteria: Basis for Seismic Capacity Guidelines for Structures, Equipment, and Subsystems basemat. The containment vessel itself had a very high seismic capacity. Although there were only three examples of seismic ruggedness of steel containments with concrete shield structures in the available SPRA database, those examined indicated that modern plants with steel containment have HCLPFs of at least 0.5g PGA. Exceptions might be earlier spherical steel containment design plants. It is herein recommended that modern steel containments designed for a combined loading of design basis accident pressure plus SSE, with a dynamic analysis conducted for the SSE, be characterized with a HCLPF of at least 0.5g PGA. The concrete outer shield vessels should be evaluated similarly to shear walls as described in the following subsection. Steel containments and their outer shield vessels not qualified for the SSE by a dynamic seismic analysis in combination with design basis accident pressure loading should be reevaluated for earthquakes greater than the original design basis. There was only one case of a Mark I torus in the available SPRAs when EPRI NP-6041-SLR1 [C-1] was published, and although the capacity was high, there was insufficient basis to draw any general conclusions. Most Mark I designs are relatively old. It would be expected, however, that the resolution of new dynamic load issues on Mark I containments has resulted in the torus, its supports, and internals being capable of withstanding loads greatly in excess of the SSE. It is suggested, however, that until this is demonstrated, Mark I tori be explicitly evaluated for beyond design basis earthquakes. C.2.1.2 Internal Structures Internal steel and concrete structures in containments are generally very seismic resistant. This arises from conservatively specified design loads and load combinations. Typically, loss of coolant accident (LOCA) loads have been combined with SSE and other normal-plus-accident conditions. The structures must support all attached equipment subjected to pipe break jet forces combined with SSE. For a margin study or SPRA, large LOCA loads are typically not considered to be coincident with the seismic loading, and the seismic resistance of internal structures is expected to be very large. A review of the available SPRAs at the time of EPRI NP-6041-SLR1 [C-1] revealed that containment internal structures designed to modern codes for LOCA plus SSE loading had HCLPFs exceeding 0.5g PGA. Concrete internal structures should be evaluated by the same criteria as applicable to shear walls. C.2.2 Category I Concrete Structures Designed for Seismic Loads C.2.2.1 Shear Walls and Footings The “Panel” concluded that the HCLPF capacity for all nuclear power plant Category I, primarily concrete shear wall structures, is at least 0.3g PGA. For the Category I structures that comply with the requirements of either the ACI 318-71 [C-4] or ACI 349-76 [C-5] or later building codes and are designed for an SSE of at least 0.1g PGA, as long as they do not have any special problems as discussed below, the HCLPF capacity is at least 0.5g PGA. The HCLPFs given above for Category I concrete shear wall structures are based on the assumption that the structures will respond in a ductile manner. Certain details found in some nuclear power plants are brittle and thereby limit the capacity past the elastic level. For example, the common wall between the auxiliary and turbine buildings at the Zion plant was constructed C-4 13633436 Walkdown Criteria: Basis for Seismic Capacity Guidelines for Structures, Equipment, and Subsystems of reinforced concrete with an embedded steel frame. In the utility-sponsored SPRA, it was assumed that the shear studs that transfer shear forces between concrete panels are brittle and have little ductile capacity, although some investigations suggest that this assumption is overly conservative. The HCLPF capacity for this failure mode was calculated, based on the PRA results, to be 0.35g PGA. Another example, also from Zion, is the crib house roof, which has large openings over the service water pumps that disrupt the continuity of the structural slab. Other examples include large openings in floor diaphragms that are not adequately reinforced or reinforcement bars that are not sufficiently embedded to prevent a bond failure before the yield capacity of the steel is reached. The “Panel” concluded that for earthquakes less than 0.3g PGA, it is very unlikely that nonductile details would be a problem. However, for earthquakes greater than 0.3g PGA, potential structural problems should be investigated. To demonstrate a HCLPF greater than 0.3g PGA, the construction drawings and design criteria should be carefully reviewed. Simplified analyses conducted to determine if potential non-ductile problems exist that would require specific evaluation may be justified. The authors of EPRI NP-6041-SLR1 [C-1] agreed in general with the “Panel's” judgment. There is, however, a concern that structures in some of the earlier power plants did not have an adequate design basis to apply the “Panel” recommendations across the board. Some review of additional SPRAs indicates that there must be a minimum design basis for lateral load resistance in order to apply the “Panel's” recommendation. Table 2-3 of EPRI NP-6041-SLR1 [C-1] therefore stipulates that there must be a minimum design basis of 0.1g PGA to demonstrate a HCLPF of at least 0.3g PGA. In addition, between 0.3g and 0.5g, the criteria require that the design be based on dynamic analysis. This modification to the “Panel's” recommendation should have no effect on almost all of the existing nuclear power plant structures. C.2.2.2 Diaphragms (Includes Roofs) In the design of many nuclear power plants, the seismic design of roof and floor diaphragms has not received the same level of attention as have the shear walls of the structures. This is particularly true for structures designed on the basis of single stick lumped-mass dynamic models where the seismic diaphragm loads are not directly calculated from the lumped-mass model. Major cutouts for hatches or for pipe and electrical chases may also pose special problems for diaphragms. Since more equipment tends to be anchored to the diaphragm compared to the shear walls, moderate amounts of damage may be more critical for the diaphragms compared to the same amount of damage in a wall. The experience in evaluation of diaphragms in SPRAs suggests that special attention should be devoted to diaphragms. Diaphragms of Category I structures designed for an SSE of 0.1g PGA or greater may be characterized with a HCLPF of at least 0.5g PGA provided that: 1. The diaphragm loads were developed using dynamic analysis methods 2. They comply with the ductility detailing requirements of ACI 318-71 [C-4] or ACI 349-76 [C-5] or later editions C-5 13633436 Walkdown Criteria: Basis for Seismic Capacity Guidelines for Structures, Equipment, and Subsystems Category I concrete diaphragms that do not comply with the above ductility detailing or which did not have loads explicitly calculated using dynamic analysis should be explicitly evaluated to demonstrate a HCLPF exceeding 0.3g. If there was no design for lateral load, evaluation should be conducted to demonstrate HCLPFs exceeding the original design basis. C.2.2.3 Steel and Concrete Frame Construction The “Panel” did not address steel frame construction. Most framed structures are in Category II buildings but in some plants may house safety-related equipment. A review of the calculations for steel and concrete framed structures in the SPRA database suggested that Category I framed structures designed by dynamic analysis and meeting American Institute of Steel Construction (AISC) or American Concrete Institute (ACI) codes of 1971 or later can be characterized with a HCLPF of at least 0.3g PGA. Other Category I and Category II framed structures housing safetyrelated equipment should be explicitly evaluated to demonstrate HCLPFs exceeding the original design basis. Such a review of steel structures should concentrate on structural detailing at connections. If it can be shown that the structure complies with the general seismic provisions of the 1985 Uniform Building Code (UBC) [C-6] for Zone 4, a reevaluation is unnecessary to demonstrate a HCLPF of 0.3g PGA or less. C.2.3 Non-Category I Structures In some plants, non-Category I structures have been used to house essential safety-related equipment. For these structures and other Category I structures that were not designed or qualified by a dynamic seismic analysis, a small percentage may have sufficiently low capacities that a HCLPF of 0.3g cannot be assumed without an explicit evaluation of the structure. The necessary level of review will depend on both the details of the structure and the seismic demand. If the shear wall and diaphragm structure is capable of meeting the 1985 UBC Zone 4 detailing and lateral load capacity requirements, no further review is required to demonstrate HCLPFs up to 0.3g PGA. If brittle connections are discovered during the review, a detailed capacity review is recommended. Large cutouts in diaphragms that have not been seismically detailed should be reviewed. C.2.4 Masonry (Block) Walls Many of the earlier power plants had unreinforced or lightly reinforced masonry non-loadbearing walls constructed for fire protection or other purposes around safety-related equipment. The “Panel” recommended that unreinforced or lightly reinforced walls be evaluated in a margin review. In response to Nuclear Regulatory Commission (NRC) IE Bulletin 80-11 [C-7], most of these masonry walls were shown to be capable of withstanding the SSE by either testing or analysis using arching and rigid body rocking (energy) methods or were strengthened by the addition of external reinforcing and bracing to meet design codes. For unreinforced or lightly reinforced masonry walls that were qualified using arching or rigid body analysis methods, the degree of capacity beyond the SSE may be limited. It is therefore recommended that masonry walls near safety-related equipment that were qualified using arching or rigid body analysis methods be investigated if a HCLPF exceeding the SSE is required. Walls that were externally reinforced to withstand an SSE of at least 0.1g using rolled steel sections anchored to floor and ceiling, with through-wall bolts to plates, can be characterized with a HCLPF of at least 0.3g. C-6 13633436 Walkdown Criteria: Basis for Seismic Capacity Guidelines for Structures, Equipment, and Subsystems C.2.5 Control Room Ceilings Hung ceilings, typical of the types installed in nuclear power plants, have failed at moderate accelerations in commercial buildings and fossil fuel plants during past earthquakes. Generally, nuclear power plant ceilings are better braced than typical commercial buildings. In addition to the ceilings per se, equipment above the ceilings could also fail, fall through the ceiling and injure the operators below, or possibly cause damage to the control equipment. For example, heavy transite light-reflecting panels found above the ceiling in the Indian Point nuclear power plant control rooms were determined to be capable of sliding off their supports and falling through the ceiling to the floor at moderate accelerations. These conditions were discovered at the time of the SPRA, and the panels were secured. The “Panel” concluded that the HCLPF capacity for control room ceilings is at least 0.3g PGA. However, this is predicated on an inspection by an experienced engineer who verifies that the ceilings are adequately braced and that equipment and other objects above the ceiling are properly anchored. For HCLPFs greater than 0.3g PGA, an explicit evaluation should be conducted. The principal focus of the analysis should be the ceiling lateral bracing system and the support system for the equipment and other objects located in the space above the ceiling. C.2.6 Impact Between Structures Structure-to-structure impact may become important for earthquakes significantly above the SSE, particularly for soil sites. Structures are conservatively designed with rattle space sufficient to preclude impact at the SSE level, but there are no set standards for margins above the SSE. Substantial impact is unlikely below 0.3g PGA for structures designed by dynamic analysis and founded on rock sites. In one SPRA reviewed for a rock site, impact between a non-Category I turbine building and a control building occurs at less than 0.3g. This causes a concern with control equipment operability. Thus, contrary to the “Panel” recommendation, a recommendation is made in Table 2-3 of EPRI NP-6041-SLR1 [C-1] to evaluate effects of impact on electrical equipment for any level of earthquake, regardless of the medium upon which the building is founded. The potential for impact should be considered for all earthquake levels above the design basis. In most cases, impact is not a serious problem, but given the potential for impact, the consequences should be addressed. For impacts at earthquake levels below 0.5g PGA, the potential for electrical equipment malfunction and local structural damage causing loss of equipment anchorage should be examined. Above 0.5g, the potential for more severe structural damage should be evaluated. C.2.7 Other Structure Failure Modes Failure of an upstream dam was found to be a major contributor in the first SPRA developed for one nuclear plant. Because dams often are not designed for the same high structural capacity as required for nuclear power plant components, a HCLPF capacity for dams, levees, and dikes cannot be assumed a priori. Thus, for any earthquake level that exceeds the design basis, the HCLPF capacity for any dams, levees, or dikes that could fail and affect a plant should be evaluated. Soil-related failure modes including liquefaction and slope instability should be addressed as well. C-7 13633436 Walkdown Criteria: Basis for Seismic Capacity Guidelines for Structures, Equipment, and Subsystems C.2.8 NSSS Primary Coolant System and Supports For PWRs manufactured by Westinghouse, Combustion Engineering, and Babcock and Wilcox, the primary coolant system consists of a reactor vessel, steam generators, primary coolant pumps, connecting piping, and in some cases isolation valves in the primary coolant piping. In addition, there is a pressurizer connected to the primary coolant loop by a surge line. For BWRs manufactured by General Electric Company, the primary coolant system consists of a reactor vessel, recirculation loops with recirculation pumps and valves, main steam piping from the reactor vessel to the first isolation valve, and feedwater piping from the reactor vessel to the first isolation valve. These systems are of heavy wall construction and are designed for high pressure combined with seismic and, for most plants, pipe break loadings. The supports provided are similarly designed. In most instances, the dominant design loading is not seismic, and very large margins exist for seismic-plus-normal operation loading. The “Panel” suggested that, as determined in SPRA analyses, the HCLPFs of the supports for reactor pressure vessels, reactor coolant pumps, and PWR steam generators and pressurizers, are at least 0.5g PGA. Recirculation pumps for BWR plants have been estimated to have HCLPFs below 0.5g PGA in several SPRAs. The “Panel” called for no review of nuclear steam supply system (NSSS) supports to assign a HCLPF of 0.3g or less and stated that to demonstrate HCLPFs of 0.3g to 0.5g, evaluation should be conducted only for BWR recirculation pumps. However, the text suggested some review for all NSSS supports to demonstrate HCLPFs greater than 0.3g. Based upon a review of the results from twenty SPRAs plus other studies, EPRI NP-6041-SLR1 [C-1] suggests that a review be performed for PWR pressurizer supports and BWR reactor vessel and recirculation pump supports to demonstrate HCLPFs of 0.3g to 0.5g. It is recognized that this recommendation is likely to be very conservative, but such conservatism is judged to be warranted because of the importance of these supports. EPRI is conducting a study to provide additional information relevant to seismic fragility analysis of a variety of PWR NSSS components (NSSS primary components, reactor internals, fuel, etc.). This project consists of a series of workshops with NSSS vendors to review their experience in seismic design and beyond-design-basis analysis and testing. When this project is completed, an EPRI report will be issued to provide the fragility analyst with additional insights such as: • Governing failure modes for specific NSSS components • Failure capacities for selected failure modes • Relative ranking of loads/stresses based on experience between seismic, deadweight, thermal, pressure and LOCA conditions C-8 13633436 Walkdown Criteria: Basis for Seismic Capacity Guidelines for Structures, Equipment, and Subsystems C.2.9 Reactor Internals The failure of reactor internals will affect the insertion of the control rods and may prevent the shutdown of the reactor. Either failure of the annular plate that laterally supports the shroud or yielding or buckling of the shroud-support cylinder will cause distortion of the reactor core. The design of the reactor internals is performed by NSSS suppliers, and information concerning the stress states for various loading conditions is proprietary and usually very difficult to obtain. The “Panel” concluded that the HCLPF capacities are probably larger than 0.3g PGA since the internals are generally designed for an envelope of various severe loading conditions. However, because of a general lack of available detailed information, no HCLPF capacities were given by the “Panel” for reactor internals. C.2.10 Control Rod Drives Control rod drive (CRD) units are designed to be failsafe so that on loss of power or control they will automatically scram the plant. The principal concern is whether excessive deformations can occur that would preclude successful insertion of the control rods. Limited test data and analytical studies on scram capability during seismic events have been reviewed in support of SPRA fragility development. These data have formulated the bases for PRA fragility descriptions. On PWRs, the control rods are oriented vertically on the top head of the reactor vessel. Scram is accomplished by releasing the rods and allowing them to fall by gravity into the core. On BWRs, the rods are driven from the bottom of the vessel by hydraulic pressure from the hydraulic control units or, alternatively, by the pressure in the reactor vessel. For both PWRs and BWRs, the CRD housings and CRD assemblies cantilever vertically outward from the reactor vessel head and are potentially sensitive to lateral seismic loading. In many plants, the housings have lateral supports. The requirement for support is definitely dictated by seismic loading. It is believed that the "Panel's" recommendation that the HCLPF is at least equal to 0.3g was based upon these lateral supports being present. It is recommended that if no lateral support is present, a review should be conducted to demonstrate a HCLPF exceeding the SSE design basis. Hydraulic control units (HCUs) and CRD piping for BWRs are part of the CRD system. Although these items are designed as Category I components, it is not clear that their failures can preclude a scram. A break in the CRD hydraulic piping does not preclude a scram. The only possible piping failure mode to preclude scram is complete crimping or collapse of the CRD discharge piping. This is not considered credible and should not be a point of concern in SMAs or SPRAs. The HCUs provide an initial boost to control rod insertion but are not required to achieve a scram unless the reactor vessel pressure is too low. There are no known failure modes of HCUs that could suppress a scram; thus, performance or structural integrity of HCUs should not be of concern in seismic margin studies unless the systems engineers state the contrary. C-9 13633436 Walkdown Criteria: Basis for Seismic Capacity Guidelines for Structures, Equipment, and Subsystems C.2.11 Piping The “Panel” concluded that, in general, piping systems in nuclear power plants have HCLPF capacities greater than 0.5g PGA. However, certain construction details have led to past earthquake damage in industrial facilities. Examples of potential piping failure modes include the following: • Valve failure caused by impact resulting from large displacements of flexible pipes • Pipe failure caused by large displacement of inadequately anchored equipment (e.g., tanks) • Failure of small, stiff pipes attached to large, flexible pipes • Failure of piping between buildings as a result of large relative displacement caused by rocking or sliding of the buildings • Failure of brittle connections (i.e., threaded pipe), eroded or corroded piping, and brittle cast iron piping • Leakage from mechanical (e.g., Victaulic) couplings due to excessive rotations at the joints All these failure modes are related to displacement effects in contrast to inertia-induced stresses. Experience from past earthquakes in industrial facilities indicates that piping is rugged and can resist earthquakes of at least 0.5g PGA, which is the limit of the experience data (NUREG-1061 [C-8]). This was also confirmed by testing (NUREG/CR-5023 [C-9]) and by piping analyses using the methodology developed in the Seismic Safety Margins Research Program (SSMRP) (NUREG/CR-2405 [C-3]). SPRA calculations also support this conclusion. In SPRAs where representative, plant-specific piping fragility values are developed, they have always been conservative relative to data in NUREG/CR-5023 [C-9], but even using conservative fragility descriptions, piping has typically not been a dominant contributor to risk. Experience has also shown that even if piping supports fail, failure of piping does not necessarily follow. Again, failure of piping is primarily caused by large relative displacements rather than inertial effects. In order to verify the HCLPF capacity of piping, a plant walkdown must be conducted by engineers experienced in earthquake engineering and failure analysis. To demonstrate a HCLPF of at least 0.3g PGA, a careful inspection of typical safety-related piping runs that are accessible should provide a reasonable sample to verify that no problems exist. Piping sections between buildings should be carefully investigated. The level of effort for this task should be minimal. To demonstrate HCLPFs between 0.3g and 0.5g, additional complete inspection of all runs in two or three safety-related piping systems should be conducted to provide confidence that no low-capacity piping failure modes exist. The total effort required for this level of inspection is also minimal. Finally, to demonstrate a HCLPF above 0.5g PGA, a more detailed evaluation should be conducted. As part of the evaluation, a walkdown by experienced engineers of all runs of all safety-related piping systems should be conducted. The evaluation of a piping system should consider the number of segments and supports and the probabilistic dependence between their failures. C-10 13633436 Walkdown Criteria: Basis for Seismic Capacity Guidelines for Structures, Equipment, and Subsystems The above-mentioned walkdown should concentrate on: • Verifying anchorage of equipment to which piping is attached. • Performing a walkdown and piping isometric review to look for: – Non-ductile joints – Long runs of pipe with weak supports where multiple support failure could cause excess pipe motion – Inadequate piping flexibility of small branch lines to accommodate main pipe run displacements • Review of the potential for soil settlement to cause excess motions in piping. • Verifying adequate separation between valve operators and adjacent structures or equipment. Some limited analyses may be necessary to evaluate potentially vulnerable conditions observed in a walkdown or to compute support reactions on potentially vulnerable supports identified in a walkdown. Emphasis in selecting analyses should be on ensuring that support failures will not occur that would result in complete loss of support over long runs of pipe, and that excessive loading will not result on nozzles of active equipment. Credit should be taken for support provided at wall penetrations in determining the overall potential excessive pipe length. Displacements should be bounded to ensure that valve operators do not impact adjacent structures in equipment and that sufficient flexibility between adjacent structures exists. C.2.12 Valves Valves in nuclear power plants can be categorized as passive valves (e.g., check valves), motoroperated valves, air-operated valves, and hydraulic-operated valves. The “Panel” stated that the experience in past earthquakes in fossil fuel power plants and other industrial facilities indicates that there has been no damage for earthquakes up to 0.5g PGA, except for one air-operated valve that failed in the 1979 Imperial Valley earthquake. The damage was caused by impact against a column caused by large displacement of flexible pipe (see discussion above for piping). Since then, several similar additional valve failures have been reported. In SPRAs, the estimated median capacities for valves are generally high. In few cases, the HCLPF values are less than 0.5g PGA; however, these values are based on conservative assumptions. Review of qualification test data for motor operators for valves indicates that the lowest capacity is 20g to 40g, 5% damped spectral acceleration. This capacity is for the operator per se and does not include the capacity of the operator and yoke assembly. However, both the earthquake experience data and the capacities generated in SPRA analysis reflect potential failure of the yoke between the valve and operator. Analysis performed with the use of the methodology developed in the SSMRP confirms that valves have high capacities. Finally, data from the U.S. Corps of Engineers shock tests indicate high capacities for valves [C-3]. Median spectral acceleration capacities above 30g have been found. Except for motor-operated valves on small pipes subjected to earthquakes above 0.3g PGA, the “Panel” concluded that a HCLPF capacity for valves of at least 0.5g can be assigned if a plant walkdown of the piping systems is conducted. In addition to the concerns expressed for piping, the engineer should also look for cases where the operator is anchored to the structure but the C-11 13633436 Walkdown Criteria: Basis for Seismic Capacity Guidelines for Structures, Equipment, and Subsystems valve or piping immediately adjacent to the valve is not anchored. Again, the concern is large piping inertia loads (restrained displacements) that may severely strain the yoke between the valve and operator and cause binding of the operator stem or leakage past the stem seals. It is believed the above recommendations from the “Panel” may not apply for valves mounted at high elevations above grade if the 5% damped floor horizontal spectral acceleration off of which the piping is supported exceeds 2g. This caution concerning use of the “Panel” recommendations for cases in which high floor spectral acceleration occurs has been added to a number of the components in Table 2-4 of EPRI NP-6041-SLR1 [C-1] when it is judged to be of possible concern. C.2.13 Heat Exchangers From the SPRA fragility estimates, it is concluded that the lowest capacity failure modes are from anchorage or component supports. In all cases, nozzles, vessel walls, and tube bundles had capacity significantly in excess of the governing failure mode. This is typical of pressure vesseltype equipment. The supports and anchorage design are dominated by seismic loading and may fail in a brittle mode while pressure boundary designs are controlled by a combination of pressure, seismic and piping reactions, and are almost always ductile. Furthermore, earthquake experience data on pressurized tanks have shown that any failures are associated with anchorage and not the pressure boundaries. Consequently, to assign a HCLPF less than 0.3g PGA, only the anchorage and supports need be evaluated. For heat exchangers that have been designed by dynamic analysis, or by a static coefficient method that results in loading that envelops inertial and nozzle loading, only the anchorage and supports require evaluation to assign a HCLPF between 0.3g and 0.5g PGA. For equipment not meeting these criteria or to assign a HCLPF exceeding 0.5g PGA, all failure modes must be assessed. Active components of heat exchangers, such as fans and controls, should be evaluated by their respective criteria. C.2.14 Tanks C.2.14.1 Atmospheric Storage Tanks Historically, some flat-bottom atmospheric storage tanks have suffered significant damage in strong motion earthquakes. Analysis of flat-bottom storage tanks in fourteen nuclear power plants, whose tanks were originally designed for seismic events, has resulted in a wide range of margins beyond the SSE. Therefore, no generic conclusions can be reached for these tanks. Based upon the historical performance of flat-bottom tanks and the analytical database, it is concluded that all flat-bottom storage tanks identified as potentially important to the SPRA be explicitly evaluated for earthquakes greater than the SSE. This effort should concentrate on tank anchorage. C.2.14.2 Pressure Vessels The capacity criteria should be the same as for heat exchangers (Section C.2.13). C-12 13633436 Walkdown Criteria: Basis for Seismic Capacity Guidelines for Structures, Equipment, and Subsystems C.2.14.3 Buried Tanks Buried tanks are not particularly vulnerable to seismic damage. Damage may occur at piping connections if there is large motion of the soil surrounding the buried pipe relative to the tanks. The tank designs are usually not controlled by seismic loading. For this reason, at earthquake levels less than 0.5g PGA, the “Panel” recommended that only piping connections need to be evaluated for the possibility of large relative displacements of the surrounding soil. To assign a HCLPF of 0.5g or greater, the buried tanks should be evaluated explicitly. C.2.15 Batteries and Racks In the past, the battery racks in older nuclear power plants were often found to be weak and not securely anchored to the supporting structure. Many of the racks in older plants have subsequently been strengthened, while racks in new plants that have been designed for the SSE are generally rugged. HCLPFs of racks as determined in SPRAs have been estimated to be as low as 0.3g PGA. The “Panel” concluded that an inspection by an experienced engineer can be used to determine whether battery racks need further evaluation to assign a HCLPF up to 0.5g PGA. The principal concerns are the sturdiness of the racks, anchorage of the racks to the supporting structure, and adequacy of spacers between the batteries and shims at the ends of the battery rows. Also important is the potential failure of space heaters, hanging lights, or block wall enclosures that could fall and impact the batteries. To demonstrate a HCLPF greater than 0.5g PGA, the HCLPF capacity should be calculated for battery racks explicitly and not just assessed by inspection. C.2.16 Diesel Generators Diesel generators per se have not been found to be low-capacity components. The generators in nuclear power plants are similar to generators found in ships and trains. However, the peripheral equipment required for the diesel generators to operate can have low capacities. Although many diesel generator systems have survived earthquakes of 0.5g PGA, the peripherals in fossil fuel plants do not appear to be as elaborate as in nuclear power plants. These support equipment items include diesel oil day tanks, control cabinets, accumulators, compressors and motors, lube-oil coolers, fuel oil transfer pumps, heat exchangers, heating and venting equipment, etc. The SPRA fragility calculations reviewed before publication of EPRI NP-6041-SLR1 [C-1] indicates that the HCLPF capacity for these support equipment items is often greater than 0.39g PGA. Again, the failure modes of concern are primarily attachments of components and anchorage of equipment. It is important during the walkdown of the plant that the anchorage of all the safety-related components associated with the diesel generators is inspected and its adequacy visually verified. The “Panel” concluded that diesel generators and their supporting equipment have HCLPF capacities of at least 0.3g PGA. An inspection should be conducted to verify that the equipment is properly anchored. An exception, which must be evaluated, is the shock-mounted diesel generator. Although this situation had not been encountered in nuclear power plants by any of the “Panel” members, it is possible that it may exist. The HCLPF capacities for all shockmounted equipment in a nuclear power plant should be evaluated explicitly for earthquakes exceeding the SSE. C-13 13633436 Walkdown Criteria: Basis for Seismic Capacity Guidelines for Structures, Equipment, and Subsystems To demonstrate HCLPFs between 0.3g and 0.5g PGA, an explicit evaluation should be conducted focusing on the anchorage and support of peripherals. To assign a HCLPF greater than 0.5g PGA, both the capacities of the diesel generator per se and the supporting equipment should be evaluated. C.2.17 Pumps Except for the case of service water pumps with long cantilevered casings, pumps have been shown to have high capacities. For horizontal pumps, where the failure mode is assumed to be failure of the drive shaft, the HCLPF capacities calculated in SPRAs have been less than 0.5g PGA. However, the “Panel” concluded that this failure mode is conservative, and that shaft bending and pump failure would not occur during or immediately after an earthquake. There is evidence that pumps wear faster after earthquakes, but these pumps have operated satisfactorily during and following a seismic event. Experience data indicate that many pumps have survived earthquakes without damage for 0.5g PGA. Because of the vibrations and stresses which occur for normal operations, pumps have inherent capacity to resist earthquakes. The “Panel” concluded that all pumps have HCLPF capacities of at least 0.3g PGA. For horizontal pumps and vertical pumps with shafts supported at their ends and with casings supported laterally at least every 20 ft, the HCLPF capacities are at least 0.5g PGA. In addition, vertical pumps with shafts and casings less than 20 ft in length where the shafts have not been laterally supported at their ends have survived earthquakes up to 0.5g PGA without damage. Between 0.3g and 0.5g PGA, an explicit evaluation is required to determine the HCLPF capacity for vertical pumps with shafts and casings that do not comply with the support requirements given above. For all pumps, an explicit evaluation is required to assign a HCLPF capacity greater than 0.5g PGA. C.2.18 HVAC Systems HVAC systems are vital support systems to some equipment in confined spaces. HVAC ducting for control rooms and switchgear rooms typically originates high in the control or auxiliary building structures where ground motion may be highly amplified. Ducting for cooling pump rooms and diesel generators is at much lower elevations, often below grade for ECCS pump rooms. Review of design specifications and review of ducting design for several plants leads to the following general conclusions on ducting itself: • The ducting wall thickness is often governed by tornado-induced vacuum conditions. Seismic-induced stresses are rarely a significant design loading in plants where ducting supports have been designed for seismic events. In the absence of design condition vacuum, the ducts are highly resistant to buckling from seismic loading. • Design practice of all plants studied was to provide supports at intervals that would result in the ducting being essentially rigid in flexure. This limits the amplified response of ducting systems. There may be earlier plants with rod-hung ducting that would result in low fundamental frequencies. C-14 13633436 Walkdown Criteria: Basis for Seismic Capacity Guidelines for Structures, Equipment, and Subsystems • Ducting supports are significantly overdesigned for seismic loads. Their weak link is expected to be concrete expansion anchor attachments to the building structures. • Dampers and turning vanes have not shown to be a weak link in ducting systems except possibly for fusable links used for fire protection. • Dampers are usually designed to move into a failsafe position upon loss of electrical power or air to the operators. Reviews of damage reports for major earthquakes have not indicated ducting to be a problem in itself. The only HVAC-related problems were associated with loss of anchorage of fans and blowers and possibly fan blade misalignment resulting in rubbing and banging after the earthquake. For these reasons, the “Panel” concluded that the dominant failure modes for HVAC systems are anchor bolt and support failures. From the results of SPRAs, the HCLPF capacities for fans and cooler units are larger than 0.3g PGA. The HCLPF capacities for ducting are estimated to exceed 0.5g PGA. Normally, ducting failure is not explicitly included in SPRAs because of its high capacity. In some SPRAs, low capacities have been found for fan shaft bending and binding. This failure mode is not believed to have HCLPFs less than 0.5g PGA. Although bending and subsequent rubbing may occur, the fans will operate during and immediately after the earthquake. This latter conclusion of the “Panel” has been subsequently confirmed by earthquake experience data collected and analyzes from subsequent to the publication of EPRI NP-6041-SLR1 [C-1]. The “Panel” concluded all components in HVAC systems have HCLPF capacities of at least 0.3g PGA. An inspection should be performed to verify that the equipment is properly anchored. The presence of shock-mounted HVAC equipment is an exception that must be evaluated. This situation is common in nuclear power plants and must be systematically investigated during the plant walkdown. For earthquakes between 0.3g and 0.5g PGA selected for screening, the HCLPF capacity should be evaluated. The analysis should focus on fan and cooler unit equipment supports and anchorage systems. For ducting that spans between buildings, potential failure due to large relative displacements should be evaluated. To assign HCLPFs greater than 0.5g PGA, an evaluation should be performed for all potential failure modes that could lead to failure of the fans, cooler units, and ducting. C.2.19 Cable Trays and Cabling There have been few failures of cable trays and supports in past earthquakes for ground motions up to 0.5g PGA. Extensive tests performed on cable trays have shown that high capacities exist. Cable trays in nuclear power plants have been constructed in the past differently from design drawings and calculations. Therefore, a sampling walkdown of cable tray raceways is necessary to assess their as-built seismic capacity. According to the “Panel,” the principal failure modes of concern include failure of taut cables due to large relative displacement (e.g., relative motions between buildings), severing of cables caused by sharp edges at the ends of cable trays, and failure of welds, particularly at connections between cable tray supports and anchor plates. C-15 13633436 Walkdown Criteria: Basis for Seismic Capacity Guidelines for Structures, Equipment, and Subsystems The authors of EPRI NP-6041-SLR1 [C-1] took exception to some of these “Panel” recommendations. Cable trays with sufficiently sharp edges at the ends of the trays had not been observed by the NP-6041 authors during plant walkdown or noted in reviews of earthquake experience data and test data and do not appear to be a sufficiently credible concern to warrant the inspection effort necessary to look for such concerns. Second, the “Panel” members stated they were not aware of any test data or earthquake experience data that would justify a particular concern with the failure of welds at the connection between cable tray supports and anchor points. In fact, the available test results would indicate that failure modes were always in unistrut clips or in threaded rods. The “Panel” concluded that cable trays have HCLPF capacities of at least 0.3g PGA. During the plant walkdown, example cable trays should be inspected to verify that they are adequately supported. Based upon the test data summarized in this appendix, no explicit capacity evaluation should be necessary for cable tray raceways supported by braced trapeze struts to assign HCLPFs below 0.5g. For rod-hung, braced and unbraced cantilever, and unbraced trapeze struts, an explicit capacity evaluation should be performed on representative cable raceway systems to demonstrate HCLPFs greater than 0.3g. Analytical methodology and acceptance criteria are summarized in EPRI NP-7152-D [C-10], NP-7150 [C-11], and NP-7151 [C-12]. The evaluations should concentrate on the following: • Rod-Hung Trays. A fatigue analysis in accordance with the criteria in EPRI NP-7152-D [C-10] should be conducted for a limited number of bounding cases selected in a plant walkdown. • Braced Cantilever Struts. Anchorage and brace buckling checks should be made for a limited number of bounding cases selected in a plant walkdown (EPRI NP-7150 [C-11]). • Unbraced Cantilever and Trapeze Struts. Anchorage checks should be made on a limited number of bounding cases selected in a plant walkdown (EPRI NP-7150 [C-11]). Bounding cases would be those with multi-tier configuration and heavy cable fills. Short threaded rods should be more vulnerable than longer rods due to their greater ductility demand for a given displacement, whereas unbraced cantilever and trapeze assemblies of longer length result in a greater demand on anchorage. C.2.20 Electrical Conduit The “Panel” did not make recommendations on HCLPF levels for electrical conduit. The authors of EPRI NP-6041-SLR1 [C-1] performed several walkdowns of nuclear power plants and found that electrical conduit is generally well supported and appears seismically rugged. The “Panel’s” experience is that rigid metal conduit assembled by threaded joints that is supported in accordance with the National Electrical Code requirements is quite stiff and capable of withstanding earthquakes well in excess of the design bases. Surveys of earthquake damage have not indicated that electrical conduit is vulnerable for seismic events up to 0.5g. Tests of conduit in Linderman and Hadjian [C-13] and Koss [C-14] indicate that rigid metal conduit and electrical metal conduit (EMC) meeting the requirements of the National Electrical Code can withstand vibration motion corresponding to a broad banded spectrum anchored to 3.0g zero period acceleration (ZPA) without failure. Therefore, unless a walkdown indicates a general lack of adequate conduit support, no evaluation is required to C-16 13633436 Walkdown Criteria: Basis for Seismic Capacity Guidelines for Structures, Equipment, and Subsystems assign a HCLPF less than 0.3g PGA. If the conduit is supported in general accordance with the National Electrical Code requirements, an evaluation should not be required to assign HCLPFs between 0.3g and 0.5g PGA. To demonstrate HCLPFs above 0.5g PGA, conduit and supports should be evaluated on a sampling basis. C.2.21 Active Electrical Equipment Active electrical equipment includes switchgear, motor control centers (MCCs), inverters, battery chargers, instrumentation racks, load sequencers, control system cabinets, and other cabinets that contain electrical sensors, switches, or control instruments. Potential failure modes include relay chatter, breaker trip, or structural failure. The important problem of relay chatter and breaker trip cannot be addressed by walkdown. Only the potential for structural failure of the electrical components or the cabinet to which they are attached is considered in this discussion. In past earthquakes that were surveyed by SQUG and reviewed by the Senior Seismic Review and Advisory Panel (SSRAP, SAND92 0140 [C-15]), it was found that active electrical equipment can survive ground accelerations up to 0.5g PGA provided that the cabinets and instruments are properly anchored (EPRI NP-7150 [C-11]). The HCLPF capacities calculated in SPRAs are typically larger than 0.4g PGA. Results from qualification tests and the U.S. Corps of Engineers shock tests (NUREG/CR-2405 [C-3]) indicate that the electrical components are as strong as the supporting cabinets. The “Panel” concluded that active electrical equipment has HCLPF capacities of at least 0.3g PGA. During the plant walkdown, the cabinets should be inspected to verify that the cabinets or racks are securely anchored to the floor and the instruments are rigidly attached. To assign a HCLPF between 0.3g and 0.5g PGA, an evaluation should be conducted. The focus of the evaluation should be the cabinet anchorage and attachment of the instruments. To demonstrate a HCLPF greater than 0.5g PGA, a complete evaluation, including potential failure of the cabinets or individual instruments, in addition to the anchorage system, should be conducted. C.2.22 Other Electrical Components Generally, the same anchorage review recommendations as for the active electrical components apply. Specific recommendations are covered by the footnotes of Table 2-4 in EPRI NP-6041-SLR1 [C-1]. C.3 Earthquake Experience Data SQUG sponsored an activity to collect and evaluate data from actual seismic events. This was a continuing program when EPRI NP-6041-SLR1 [C-1] was originally published, and it was anticipated that the results would be particularly useful to demonstrate the seismic resistance of certain generic classes of equipment. C-17 13633436 Walkdown Criteria: Basis for Seismic Capacity Guidelines for Structures, Equipment, and Subsystems SSRAP (SAND92 0140 [C-15]) performed an extensive review of the SQUG database, including an additional category of equipment, and formulated recommendations for minimum thresholds of survival for eight classes of equipment. The eight classes of equipment included: • MCCs • Low-voltage (480-V) switchgear • Metal-clad (2.4-4kV) switchgear • Unit substation and transformers • Motor-operated valves • Air-operated valves • Horizontal pumps and motors • Vertical pumps and motors SSRAP concluded after their review that: 1. Equipment installed in nuclear power plants is generally similar to, and at least as rugged as, that installed in conventional power plants. 2. This equipment, when properly anchored, and with some reservations, have an inherent seismic ruggedness and a demonstrated capability to withstand significant seismic motion without structural damage. 3. For this equipment, functionality after the strong shaking has ended has also been demonstrated, but the absence of relay chatter during strong shaking has not been demonstrated. SSRAP further recommended bounding spectra that represent lower bound seismic ground motion for which survivability of the eight categories of equipment has been conclusively demonstrated. In many cases, actual capacities are likely to be much greater than these lower bound spectra. If the specified ground motion spectra are enveloped by the SSRAP bounding spectra, no qualification is considered necessary provided that certain qualifying conditions are met. SSRAP subsequently reviewed seismic experience data for additional classes of equipment and specified a single bounding spectrum in [C-15] to represent a seismic survivability level for the twenty classes of equipment identified in EPRI NP-7149-D [C-16]. The recommended bounding spectrum is shown in Figure C-1. The bounding spectrum is intended for comparison to design spectra and is applicable to equipment mounted in structures no more than 40 ft above grade. For equipment mounted greater than 40 ft above grade, the applicable 5% damped floor spectra may be compared to 1.5 times the bounding spectra. Alternatively, 1.5 times the bounding spectrum may be compared to floor spectra at any elevation. Specific restrictions and bounds on component size, weight, stiffness, eccentricity, etc., were detailed for each of the twenty-one classes of components in SSRAP (SAND92 0140 [C-15]). C-18 13633436 Walkdown Criteria: Basis for Seismic Capacity Guidelines for Structures, Equipment, and Subsystems Use of the SQUG/SSRAP bounding spectrum applies to ruggedness of the equipment and does not cover anchorage of the equipment nor operability of equipment during the shaking (i.e., relay chatter). The latest SSRAP recommendations, based upon further review of experience data, are compatible with the guidelines of NUREG/CR-4334 [C-2] and those recommended in Table 2-4 of EPRI NP-6041-SLR1 [C-1]. Figure C-1 Seismic motion bounding spectra horizontal ground motion (SAND92 0140 [C-15]) The SQUG program identified twenty-one classes of equipment typically required for a safe shutdown. They concentrated on active electrical and mechanical equipment and passive electrical equipment. For purposes of an SMA or SPRA, additional classes of active and passive mechanical equipment must also be included. Table C-1 lists the twenty-one classes of equipment identified by SQUG plus additional classes of passive mechanical equipment that must be demonstrated to survive a beyond design basis earthquake. These additional classes of equipment have not been the subject of experience data collection. However, a lack of evidence of seismic vulnerability in major earthquakes leads to the belief that these classes of equipment are also very rugged, the exception being flat bottom storage tanks. C-19 13633436 Walkdown Criteria: Basis for Seismic Capacity Guidelines for Structures, Equipment, and Subsystems Table C-2 Equipment categories for seismic margin studies Equipment Categories for SQUG Program 1 Motor control centers 8 Motor-operated valves 15 Battery Racks 2 Low-voltage switchgear 9 Fans 16 Battery chargers & invertors 3 Medium voltage, metal-clad switchgear 10 Air handlers 17 Engine generators 4 Transformers 11 Chillers 18 Automatic transfer switches 5 Horizontal pumps 12 Air compressors 19 Instrument racks 6 Vertical pumps 13 Motor generators 20 Temperature sensors 7 Pneumatic-operated valves 14 Distribution panels 21 Control & instrumentation cabinets Additional Categories for Seismic Margin Studies Control rod drives Piping Reactor internals NSSS Electrical raceways & conduit HVAC ducting BOP Heat Exchangers Reactor internals Steam generators Reactor vessel Liquid/liquid Traveling screens & sluice gates Liquid/air Tanks Air/air Flat-bottom Buried Other C.4 Seismic Qualification Data EPRI collected and summarized equipment qualification test data as described in EPRI NP-5223 [C-17]. The original pilot study concentrated on the following classes of equipment: • Batteries on racks* • Battery chargers* • Inverters* • Electrical distribution panels* • MCCs* • Switchgear C-20 13633436 Walkdown Criteria: Basis for Seismic Capacity Guidelines for Structures, Equipment, and Subsystems • Switches* • Transformers* • Transmitters* • Automatic transfer switches • Control panels • Instrument rack components • Air-operated valves* • Solenoid-operated valves* • Safety relief valves • Motor operators* • Electrical penetration assemblies • Relays (several subclasses)* GERS were developed for the classes of equipment identified with an asterisk. These GERS define conservative response spectra that envelop achieved test levels but are below any test level for which a malfunction has been recorded. Unlike the SQUG bounding spectra, the GERS are only applicable to the base of the component and are to be compared directly to the reference response spectrum (RRS) at any equipment location. This was a continuing program at the time EPRI NP-6041-SLR1 [C-1] was originally authored. The latest guidance for use of GERS in fragility evaluations is provided in Section 4.9 of this report. For active equipment, two GERS were developed: one for operability and one for survivability. The operability GERS define the level of response that equipment can withstand and remain operational during the seismic event. The failure modes for operability are typically relay and contactor chatter or trip-out. The survivability GERS define the level of response that equipment can withstand and perform their intended function after the earthquake. Figures C-2 and C-3 show survivability and operability GERS for battery chargers. GERS for other components are shown in EPRI NP-5223 [C-17], as are the inclusion rules for use of GERS. The GERS are intended to be used in the same manner as a test response spectrum (TRS) in that they provide high confidence of survival of the equipment if the RRS is enveloped by the GERS. Statistical confidence bounds were not developed from the test data. The approach is an engineering approach where the GERS are enveloped by the highest achieved tests level and substantially below the lowest threshold of failure. In most cases, the definition of failure is conservative in that the so-called failures are functional anomalies rather than total functional failure or destruction. The use of GERS complements the guidelines in Table 2-4 of EPRI NP-6041-SLR1 [C-1]; there are no results from the GERS development that are contrary to those guidelines. Section 4.9.5 provides additional information on updates and further development of GERS after their initial publication. C-21 13633436 Walkdown Criteria: Basis for Seismic Capacity Guidelines for Structures, Equipment, and Subsystems Figure C-2 Comparison of GERS with ruggedness TRS data: operability for battery chargers (EPRI NP-5223 [C-17]) C-22 13633436 Walkdown Criteria: Basis for Seismic Capacity Guidelines for Structures, Equipment, and Subsystems Figure C-3 Comparison of GERS with TRS data: failure for battery chargers (EPRI NP-5223 [C-17]) C.5 Aging Effects Degradation of seismic resistance with time is a concern of the SMA and SPRA processes. If deterministic acceptance criteria are used to demonstrate a HCLPF capacity, such criteria must ensure with high confidence that the end of life seismic resistance exceeds the applied loading. The earthquake experience database discussed in this appendix has a unique advantage in that the equipment was naturally aged, in many cases more than twenty years. Although aging effects were not specifically addressed, there was no evidence of detrimental aging effects on equipment function, although excessive corrosion was cited in a few instances to result in failure of piping systems. Artificially aged, naturally aged, and unaged equipment form the database for development of the GERS discussed in this appendix. There is evidence of degradation of seismic resistance in batteries due to natural aging (NUREG/CR-3923 [C-18], -4095 [C-19], -4096 [C-20], and -4097 [C-21]). However, these effects have been included in the recommended GERS for batteries. A series of aged and unaged electrical components were tested to determine if there is any appreciable degradation in seismic resistance due to aging (EPRI NP-5024 [C-22]). C-23 13633436 Walkdown Criteria: Basis for Seismic Capacity Guidelines for Structures, Equipment, and Subsystems The devices tested in EPRI NP-5024 [C-22] were hypothesized to be age-sensitive due either to their materials of construction or required cyclic operation. Only devices that are normally qualified for a mild environment were included. Mild environment includes moderate amounts of radiation and normal plant operating temperatures. LOCA effects in containment were not considered. Sufficient tests were conducted in EPRI NP-5024 [C-22] so that any strong correlations between unaged and aged malfunctions could be determined. A few types of electrical components experienced a statistically significant degradation due to aging while most were not significantly affected by aging. In some cases, malfunction occurred with such a scatter band in both the aged and unaged condition that no statistically significant correlation was demonstrated. Table C-3 lists the types of devices and the number of aged and unaged specimens tested. Seismic testing was conducted in two phases. In the first phase, devices were subjected to biaxial random input. Cabinets in which the devices were mounted did not exceed approximately 200 lbs. In the second phase, triaxial random input motion was used, and the test cabinets were much larger. A generic response spectrum was used as the basis for seismic motion input in each of the phases. Table C-3 Devices tested Device No. of Total Quantity Mfgrs. / Types Capacitors, Aluminum Electrolytic 280 6 140 Capacitors, Metalized Polycarbonate 100 4 Capacitors, Mylar 50 Capacitors, Paper Unaged Naturally Aged Artificially Aged 12-yr 50-yr 0 20 120 50 0 0 50 2 25 0 0 25 150 3 45 0 30 75 Capacitors, Polyester 100 2 50 0 0 50 Circuit Breakers, Molded Case 23 3 6 5 6 6 Connectors for P.C. Boards 16 2 8 0 0 8 Contactors (Motor Starters) 7 1 2 1 2 2 Control Station Assemblies 6 1 2 0 2 2 Electronics, ICs 82 8 32 0 0 50 Electronic P.C. Boards 16 4 8 0 0 8 Electronics, Resistors (for ICs and Capacitors) 943 1 743 0 0 200 Electronics, SCRs 45 1 15 0 15 15 C-24 13633436 Walkdown Criteria: Basis for Seismic Capacity Guidelines for Structures, Equipment, and Subsystems Table C-3 (continued) Devices tested Device No. of Total Quantity Mfgrs. / Types Unaged Electronic Alarms 4 2 1 Fuse Blocks, Gas-filled Polyester 4 1 Fuse Blocks, Phenolic 60 Fuse Blocks, Polycarbonate Naturally Aged Artificially Aged 12-yr 50-yr 2 0 1 2 0 0 2 1 20 0 10 30 20 1 5 0 5 10 Fuse Blocks, Melamine 20 1 10 0 0 10 Fuse Blocks, X Laminate 20 1 10 0 0 10 Fuses, Ceramic, Slo-Blow 40 1 20 0 0 20 Fuses, Glass 20 1 10 0 0 10 Fuses, Glass Melamine 20 1 10 0 0 10 Fuses, Glass, Slo-Blow 20 1 10 0 0 10 Fuses, Dual Element Fibre 20 1 10 0 0 10 Fuses, Dual Element Fiberglass 20 1 10 0 0 10 Fuses, Dual Element, Slo-Blow 20 1 10 0 0 10 Fuses, Melamine 20 1 10 0 0 10 I.C. Sockets 82 16 32 0 0 50 Inductors 26 5 12 2 0 12 Lamps 15 1 4 3 4 4 Lamp Sockets 15 1 4 3 4 4 Limit Switches 6 2 1 3 0 2 Meters 9 4 1 6 0 2 Motors 4 2 1 2 0 1 Power Supplies 3 2 1 1 0 1 Pressure Switches (Assembly) 18 3 8 0 7 3 Pressure Switches, Snap Acting 30 3 13 0 12 5 Pressure Transmitters 6 5 1 4 0 1 RTD 6 4 1 2 0 3 Relays 59 5 22 5 17 15 Rotary Switches 10 2 2 4 2 2 C-25 13633436 Walkdown Criteria: Basis for Seismic Capacity Guidelines for Structures, Equipment, and Subsystems Table C-3 (continued) Devices tested Device No. of Total Quantity Mfgrs. / Types Unaged Solenoid Valves 7 3 1 Switches, Snap Acting 25 3 Terminal Blocks, DAP 20 Terminal Blocks, Glass Filled Phenolic Naturally Aged Artificially Aged 12-yr 50-yr 5 0 1 11 0 7 7 1 10 0 0 10 70 1 30 0 10 30 Terminal Blocks, G.P. Phenolic 30 1 7 10 6 7 Terminal Blocks, Melamine 48 1 24 0 12 12 Terminal Blocks, Nylon 20 1 10 0 0 10 Terminal Blocks, Nylon 6.6 56 1 28 0 14 14 Terminal Blocks, Polypropylene 12 1 4 0 4 4 Time Delay Relays 16 8 2 10 2 2 Transformers, Filament 8 2 2 2 2 2 Transformers, Instrument 6 3 3 0 2 1 Wire PVC 22 AWG 300 ft 1 150 ft 0 0 150 ft Totals 2,733 135 1,499 70 195 969 Source: EPRI NP-5024 [C-22] Prior to testing, devices were grouped into two categories: those hypothesized to have no correlation between seismic resistance and aging, and those hypothesized to have correlation. For those devices hypothesized to have no correlation, either no malfunctions occurred or a statistically insignificant number of malfunctions occurred in both aged and unaged devices so that the no correlation hypothesis was accepted. For devices hypothesized to have a correlation between aging and seismic resistance, it was concluded that no statistical evidence could be produced that aging affects the past-seismic performance. Only the following devices were observed to have a performance difference between aged and unaged components during high levels of seismic excitation:  Pressure switches  Rotary switches  Limit switches The performance difference in all cases was contact chatter. Contact chatter during a seismic event does not usually result in a detrimental response and must be examined on a case-by-case basis. This is discussed in more detail in Section 6.3. C-26 13633436 Walkdown Criteria: Basis for Seismic Capacity Guidelines for Structures, Equipment, and Subsystems Based on the results of this comprehensive test program and the lack of any aging correlation in the earthquake experience data, it is suggested that aging in mild environments does not significantly degrade seismic resistance. C.6 Probabilistic Risk Assessment Fragilities At the time EPRI NP-6041-SLR1 [C-1] was published, the SPRA fragility estimates available on U.S. plants in the open literature were summarized in NUREG/CR-4334 [C-2] and used by the “Panel” in making its screening recommendations. In addition, the “Panel” was aware of several unpublished studies that contributed to the recommendations. Since passive mechanical equipment is normally qualified by analysis and failure modes can be assessed by analytical means, the analytically derived fragility estimates from these summaries can serve as a basis of estimating seismic ruggedness for such equipment. In addition, an extensive series of probabilistic studies were conducted for NRC on the probability of pipe failure in the reactor coolant loops of almost all PWRs in the United States (NUREG/CR-3660 Vols. 2 [C-23] and 3 [C-24], -3663 Vols. 2 [C-25] and 3 [C-26], and -4290 Vols. 1 [C-27] and 2 [C-28]). In these studies, directly induced guillotine break due to crack growth and fracture and indirectly induced guillotine break due to failure of vessel or pump supports were studied. Pressurizers and pressurizer surge lines were not included in the studies. The directly induced, double-ended guillotine break (DEGB) studies were conducted by using the probabilistic fracture mechanics computer code PRAISE (NUREG/CR-2189 [C-29]). Detailed PRAISE analyses were conducted for bounding cases of Westinghouse and Combustion Engineering (CE) plants. Stress histories for loadings produced by pressure, thermal expansion, thermal transients, and seismic events were applied in the studies to track the growth of cracks and to determine at which point the cracks would become unstable during a seismic event. The seismic event was defined probabilistically by a family of hazard curves (Figure C-4); thus, the results were presented as probability of pipe break. The Westinghouse plants have austenitic stainless steel piping while the CE plants have stainless steel clad carbon steel piping. For both plant types and both material types, the probability of DEGB was extremely low. The hazard curves used were generic and derived from hazard studies of six sites dispersed over the Eastern and Midwestern United States. The hazard curves were developed in support of utility-sponsored SPRAs. The hazard curves were normalized to the SSE so that stresses from the SSE could be scaled directly in the PRAISE analysis. From the results of these studies, it can be concluded that the primary coolant loops of all Westinghouse and CE plants included in the study should not require evaluation to assign HCLPFs of 0.5g PGA and less. Babcock and Wilcox (B&W) primary coolant piping stresses and materials were compared to Westinghouse and CE conditions (NUREG/CR-4290 Vol. 1 [C-27]), and based upon the comparison, similar conclusions should result for B&W plants. C-27 13633436 Walkdown Criteria: Basis for Seismic Capacity Guidelines for Structures, Equipment, and Subsystems Figure C-4 Generic hazard curves (NUREG/CR-3660, Vol. 3 [C-24]) When EPRI NP-6041-SLR1 [C-1] was published, a pilot study was being conducted on BWR piping at Lawrence Livermore National Laboratory. Personal communication with the researchers indicated that, in the absence of intergranular stress corrosion cracking (IGSCC), results are similar to those of the PWR studies. In the presence of IGSCC, the failure probability is greatly increased, although the steady state loadings tend to govern the failure rate due to the low frequency of occurrence of seismic events. The General Electric (GE) BWR primary coolant systems piping should be treated on a case-by-case basis until a new standard is established. In the absence of IGSCC, BWR primary coolant piping should not require evaluation to demonstrate HCLPF levels up to 0.5g. If the potential for IGSCC is present, the potential for pipe break should be considered explicitly. Studies conducted for the probability of indirectly induced primary coolant system pipe break concentrated on supports for the primary coolant system vessels and pumps. It was postulated that a support failure could result in DEGB. Results of studies on PWRs have been documented in the NUREG reports cited above. For all plants studied, it was determined that the probability of support failure and consequent DEGB was extremely low. There were a few of the earlier Westinghouse plants that were not included in the study, and the conclusions apply only to the C-28 13633436 Walkdown Criteria: Basis for Seismic Capacity Guidelines for Structures, Equipment, and Subsystems participating plants. Plant names were not identified (NUREG/CR-3660 Vol. 3 [C-24]), but the participating utilities that provided the information will be able to identify themselves as being included or excluded. The CE and B&W plants are specifically named (NUREG/CR-3663 Vol. 3 [C-26] and -4290 Vol. 2 [C-28]). A pilot study of Brunswick, a GE plant, was conducted with conclusions similar to those for PWRs (NUREG/CR-4792 [C-30]). Other BWR primary coolant system supports have been studied in utility-sponsored SPRAs. The only credible seismic-induced failure modes determined for BWR systems were those for the reactor pressure vessel (RPV) supports and the recirculation pump supports. The RPVs of GE plants are skirt-supported and most have an upper stabilizer. In order for RPV support failure to cause DEGB, both the skirt support and the upper stabilizer must fail. Typically, the skirt will yield first, increasing the loading on the upper stabilizer. When the upper stabilizer fails, the skirt cannot carry the overturning moment, and failure of piping connected to the RPV is assumed to occur. From the pilot DEGB study on Brunswick and a review of fragility derivations for six other BWRs, it is concluded that the reactor vessel support system has a HCLPF of at least 0.3g PGA. This conclusion is contingent upon the RPV support loading being developed from dynamic analyses and being designed for combined SSE-plus-steam or recirculation line pipe break loading. Recirculation pump supports are not included in the indirect DEGB study (NUREG/CR-4792 [C-30]). From knowledge gained in SPRAs, there is strong evidence to indicate that HCLPFs of recirculation pump supports are at least 0.3g PGA. A condition on this conclusion is that the loads must have been developed by dynamic analysis of the recirculation system. Pressurizer fragilities developed from plant-specific SPRAs were reviewed. The governing failure modes have most often been the pressurizer supports. In one exception, the heater support plate was identified as the lowest capacity element. Heater support plate failure should not be considered a credible failure for SMA or SPRA studies since it should not result in a breach of the pressure boundary and the heaters are not necessary to achieve a safe shutdown. Pressurizers are of heavy wall construction, and the pressure boundary design is almost totally dominated by pressure loading. The support design is dominated by a combination of pipe break and seismic loading. The SPRA results reviewed are consistent with data for other portions of PWR NSSS systems. For plants that have had their pressurizer support loads determined by a dynamic analysis and for which the supports are designed to resist combined SSE and pipe break loading, the pressurizer may be assigned a HCLPF capacity of at least 0.3g PGA. For plants not meeting the criteria, an explicit evaluation should be performed and its scope should be limited to the pressurizer supports. C.7 Fragility Data from SAFEGUARD Program A comprehensive testing program was undertaken by the U.S. Army Corps of Engineers (referred to as the SAFEGUARD program) to demonstrate acceptable reliability of power and process equipment installed in a hardened radar installation. The results have been summarized in NUREG/CR-2405 [C-3]. In that program, off-the-shelf equipment was procured rather than procuring specially engineered equipment qualified for shock and vibration environments. The C-29 13633436 Walkdown Criteria: Basis for Seismic Capacity Guidelines for Structures, Equipment, and Subsystems equipment was very similar to equipment installed in nuclear power plants. Consequently, the test performance of SAFEGUARD equipment should be indicative of balance-of-plant nuclear power plant equipment installed in plants prior to the more stringent qualification requirements specified in IEEE 344-1975. At the time of procurement, most manufacturers of commercial equipment were unsure of ultimate shock and vibration capacity of their products and did not have experience in qualification for shock and earthquake environments. Procurement specifications that contained severe shock environments would have resulted in prohibitive cost and delay in the SAFEGUARD program. It was therefore decided to conduct selected fragility and shock environment qualification tests on generic equipment and develop the reliability of untested equipment by a pseudo-probabilistic methodology. Some 400 component and system tests were conducted in support of the qualification of some 30,000 critical items in the SAFEGUARD installation. Initially in the SAFEGUARD program, fragility testing was conducted for selected equipment items. This proved to be very costly, and further testing was restricted to go/no-go qualification testing. It was found from the initial fragility tests that properly anchored mechanical equipment would usually survive the specified shock when hard-mounted, but that electrical equipment required shock mounting. The resulting database is predominantly shock test results of equipment for which no permanent functional failure occurred. In many of the tests, however, some structural damage was observed, and in many of the electrical and control equipment tests, electrical malfunctions occurred that were only temporary or intermittent. These data are not directly applicable to development of GERS due to the short duration of the complex waveforms shock input. They do, however, provide insight on the ability of equipment to withstand dynamic loading. The data summarized here reinforce and supplement the observations and conclusions developed in the SQUG program and the development of GERS. C.7.1 Shock Environment The SAFEGUARD program shock test environments were defined as undamped in-structure response spectra. The spectra were not typical of earthquake spectra in that the shock spectra emphasized the high frequency, high spectral acceleration regions typical of blast loading and contained very little response to frequencies below about 5 Hz. Figure C-5 is a typical shock test spectrum for hard-mounted equipment. Figure C-6 is typical for shock-mounted electrical equipment. C-30 13633436 Walkdown Criteria: Basis for Seismic Capacity Guidelines for Structures, Equipment, and Subsystems Figure C-5 Typical hard-mounted spectrum for mechanical equipment, horizontal spectrum C-31 13633436 Walkdown Criteria: Basis for Seismic Capacity Guidelines for Structures, Equipment, and Subsystems Figure C-6 Typical shock-mounted spectrum for electrical equipment The terminology "shock tests" was used in the SAFEGUARD program to describe a complex time history input of 2 to 5 sec duration. The tests were not, as might be reasoned from the title, single shock pulse inputs. The input typically consisted of several superimposed sine beats that would result in the required response spectrum. Tests were predominantly uniaxial, but several biaxial tests with independent random motion in one horizontal and the vertical axes were also conducted. The SAFEGUARD program undamped test spectra were compared to damped spectra in order to derive a scale factor for converting undamped spectral accelerations to damped spectral accelerations. A typical multiple sine beat input was run through a response spectrum generation program and a comparison made of damped and undamped spectra. Figure C-7 compares 0%, 2%, and 5% damped spectra from a typical complex waveform input. The 5% damped spectral accelerations were typically about two-thirds of the undamped spectral accelerations. Five percent damping has been used as a reference damping level in commercial SPRAs and is the reference damping level for GERS; thus, 5% damped shock spectra can be used in direct comparison. Actual damping was not measured in the equipment tested. C-32 13633436 Walkdown Criteria: Basis for Seismic Capacity Guidelines for Structures, Equipment, and Subsystems Figure C-7 Synthesized shock waveform responses for varied damping (NUREG/CR-2405 [C-3]) C.7.2 Applicable of Shock Test Data The shock spectra differ from earthquake-induced floor spectra in that they are rich in frequency content between about 5 to 500 Hz while earthquake in-structure spectra normally peak in the 2 to 10 Hz range with the peaks being fairly narrow. The shock spectra are felt to have the greatest applicability for equipment that fail either functionally or structurally in a non-ductile mode (i.e., relay chatter and brittle fractures of device attachments). The survivability level may be optimistic for ductile failures due to the lower energy content in the short duration shocks. The high-frequency content of the shock spectra is not considered to bias the survivability. It was generally observed during the shock test program that the lower frequency content of the shock spectra was the most significant contributor to malfunctions and certainly to structural failures. There is no positive way to separate out frequency effects from the test data since almost all tests were conducted with broadband shock spectra typical of Figures C-5 and C-6. A few fragility tests were, however, conducted at lower frequency input that demonstrated that electrical malfunction problems with relays and switchgear were due primarily to lower frequency input. The shock test data are not particularly applicable to equipment whose fundamental frequency is below 5 Hz. Fortunately, most equipment items of concern have fundamental frequencies considerably above 5 Hz, and the shock test data are felt to be a good indicator of seismic resistance for non-ductile failure modes. C-33 13633436 Walkdown Criteria: Basis for Seismic Capacity Guidelines for Structures, Equipment, and Subsystems C.7.3 Fragility Results of Shock Tests C.7.3.1 Mechanical and Passive Electrical Equipment The SAFEGUARD shock test data were previously reviewed during the SSMRP and were used to formulate fragility descriptions for selected classes of equipment. Table C-3 (obtained from NUREG/CR-2405 [C-3]) summarizes the fragility description for selected classes of equipment. These fragility descriptions were derived using the Corps of Engineers Pseudo-Probabilistic Methodology, also described in NUREG/CR-2405. Fragilities in Table C-4 are presented in terms of 5% damped spectral acceleration. The spectral acceleration capacity is applicable to frequencies above 5 Hz. The capacities are generally high and reinforce conclusions from the SQUG and GERS programs. The data that formulate Table C-4 are sparse; the mean, median, and uncertainties are the products of a pseudoprobabilistic methodology used in the Corps of Engineers Program, and the results cannot be compared directly to GERS or SQUG/SSRAP bounding spectra. There is also the question of limited energy content in the shock spectra. For these reasons, the SAFEGUARD data will generally be more optimistic than the GERS bounding spectra, and one would be concerned if the SAFEGUARD results were less than the GERS bounding spectra. However, batteries are the only component for which the SAFEGUARD data in Table C-4 appear to be close to the GERS. The initial batteries tested in the SAFEGUARD program had a lower capacity than currently shown by GERS. The battery racks were subsequently modified and the battery case material changed to increase capacity. The updated configuration withstood 11g undamped horizontal and vertical shock spectra with no damage. Currently, recommended GERS are for batteries in seismic racks. Thus, the SAFEGUARD data do not compromise the recommended GERS. Table C-4 Fragility descriptions developed from Corps of Engineers methodology Generic Category Mean Spectral Acceleration, Sa (g) Standard Deviation, σ (g) Median Spectral Acceleration, Sa (g) Logarithmic Standard Deviation, β Large Hydraulic and Air Operated Valves 35.8 10.7 34.7 0.308 Large Check and Spring Relief Valves 39.8 12.0 38.5 0.311 Small Misc. Valves 39.8 12.0 38.5 0.311 Batteries 4.25 0.65 4.19 0.155 Transformers 10.8 2.25 10.7 0.210 Local Instruments 39.1 12.1 37.8 0.320 Air Conditioning and Air Handling Units (Structural Failure) 9.7 2.29 9.5 0.241 Air Conditioning and Air Handling Units (Fan Failure) 22.4 5.20 22.0 0.24 Pumps and Compressors 26.6 5.53 26.2 0.21 Source: NUREG/CR-2405 [C-3] C-34 13633436 Walkdown Criteria: Basis for Seismic Capacity Guidelines for Structures, Equipment, and Subsystems Of the over 400 systems and components tested, very little retrofit was required to survive the required shock test levels. Table C-5 summarizes the extent of retrofit required. Failures noted in the table are consistent with observations of equipment damage in earthquakes and reinforce that emphasis should be placed on anchorage and electrical function. Table C-5 Summary of required retrofit to survive shock environment Items Requiring Retrofits Description of Failure Recommended Retrofit 1. Axial Flow Fans Broken support structure welds Re-weld 2. HSCW 40 Chiller Broken support structure welds Add gussets 3. Antenna Washdown System Inadequate pipe support Strengthen pipe and paint with a reflective paint 4. Tank - Hold Down Anchor bolts insufficient Add anchor bolts 5. Shock Isolation Platforms Insufficient rattle space & overload isolators Increase rattle-space and replace isolators 6. RLOB Engine Air Filter Filter failed in test 1. Remove filter or 2. Ruggedize filter or 3. Add by-pass valves 7. Electrical Components Contact chatter resulting in loss of critical function 1. Rewire to prevent elec. loss and/or 2. Replace with more rugged devices 8. Light Fixtures Deficient fixtures and tube loss Strengthen fixture and provide locking device for tubes 9. Station Battery System Deficient battery rack and cases Strengthen the battery rack and use different material for battery cases Source: EPRI NP-6041-SLR1 [C-1] C.7.3.2 Active Electrical and Electro-Mechanical Equipment Active electrical equipment frequently experienced anomaly during the testing program but rarely suffered failures that would result in inoperability after the shock. Initially, much screening was done of relays to determine their operability limits during a shock. The results on relays were widely varied. Table C-6 (obtained from NUREG/CR-2405 [C-3]) provides fragility descriptions for electrical and control equipment that contained relays, switches and contactors. The fragilities are referenced to 5% damped spectral acceleration at the cabinet base and are a consolidation of switchgear, MCCs, control panels, relay racks, panel boards, etc. This is very broad treatment of electrical equipment fragility, and it is useful to examine the raw data by component type, manufacturer, and model to compare more directly to GERS. C-35 13633436 Walkdown Criteria: Basis for Seismic Capacity Guidelines for Structures, Equipment, and Subsystems Table C-6 Fragility descriptions by failure mode for electrical and control equipment Failure Mode Mean Acceleration Standard Deviation, σ Median Acceleration Logarithmic Standard Deviation, β Chatter 4.72g 4.00g 2.074g 1.46 Trip 10.86g 7.34g 7.97g 0.774 Structural 15.0g 11.9g 14.6g 0.800 Source: NUREG/CR-2405 [C-3] Table C-7 lists test results of some initial screening tests on protective relays for 5 kV and 15 kV switchgear. The relays were subjected to single frequency, single axis, sine beat tests of five cycles per beat. The lowest capacity in any axis is tabulated in Table C-7. In this case, the capacity is the peak input acceleration from the sine beat tests. In three of the ten tests, a maximum input of 4.0g was achieved without malfunction. Note that the 4.0g was horizontal input. The relays survived 10g vertical without malfunction. Seven of the ten specimens tested experienced chatter at 1.0g or less peak input. The 5% damped spectral acceleration for the sine beat input is 5.5 times the peak input acceleration; thus, the relays tested survived 5% damped spectral accelerations of from 1.5g to 22.0g. Relay malfunctions are very sensitive to frequency input, the orientation, and the electrical state. Figures C-8 and C-9 show typical behavior between the energized and de-energized state for two orientations. Table C-7 Fragility descriptions by failure mode for electrical and control equipment Item Manufacturer Type Lowest Functional Fragility Level (Peak Input in g) Notes 1. General Electric 12CFVB11A3A 0.27 Front/Back 2. General Electric Type HFA 1.0 De-energized, Vertical 3. Electro Switch 7808D, Type LOR-24 4.0 No Malfunction 4. Westinghouse 606B028Al2, Type AR 4.0 No Malfunction 5. Westinghouse 1875290, Type AR 1.0 Vertical 6. Westinghouse 606B504A10, Type LC-2 1.0 Side/Side 7. Westinghouse 290B346A09, Type HU 1.0 Normal Polarity 8. Westinghouse 290B481A09, Type KLF 0.62 ICS Contacts Active 9. General Electric 12SAM11C22A 4.0 No Malfunction 10. General Electric 12PVD11C11A 0.47 Vertical Notes: 1. No permanent damage to render relays inoperable after shock tests. Minor damage included broken wire on Item 2 and broken reset spring on Item 3. 2. Test input was single axis, single frequency sine beat, five cycles per beat. C-36 13633436 Walkdown Criteria: Basis for Seismic Capacity Guidelines for Structures, Equipment, and Subsystems Figure C-8 Specimen performance General Electric HFA relay Y axis vert C-37 13633436 Walkdown Criteria: Basis for Seismic Capacity Guidelines for Structures, Equipment, and Subsystems Figure C-9 Specimen performance General Electric HFA relay Z axis F-B Table C-8 shows results of shock tests conducted on twenty-three electrical components, of which seventeen were relays. The initial tests were single frequency, single axis, sine beat tests in each of three axes. The smoothed envelope of the achieved test levels without malfunction defined a functionality spectrum. The items were then subjected to a random motion biaxial input motion whose 5% damped spectrum would match that of the achieved sine beat test 5% damped spectrum. Figure C-10 shows a typical achieved input with corresponding 0.5% and 5% damped spectra. Note that the specified level reached its maximum of 10g at 20 Hz. Below 20 Hz, the input at the malfunction level was variable. Most malfunction levels indicated in Table C-8 occurred at less than 20 Hz. C-38 13633436 Walkdown Criteria: Basis for Seismic Capacity Guidelines for Structures, Equipment, and Subsystems Table C-8 Electrical component fragility test Item Type Manufacturer Model Sine Beat Sine Beat Notes 1. Control Ward-Leonard 4471-210-11, Type HR 0.9g 70% Vertical 2. Overload Relay Square D SEO-8, B2, 65 10.0g* 100% All Axes 3. Control Relay Square D Type HO-20 1.3g 100% Vertical 4. Control Relay Westinghouse AR420A 3.4g 100% F-B 5. Control Relay General Electric CR120C38922 10.0g* 80% S-S 6. Control Relay Allen Bradley 700-N200-AL 8.0g 85% F-B 7. Overload Relay Allen Bradley 815-BOV16 2.9g 65% S-S 8. Overload Relay Allen Bradley 815-BOV16-N40 5.7g 90% S-S 9. Overload Relay Allen Bradley 815-EOV16 2.0g 70% S-S 10. Overload Relay Square D SEO-8, B19.5 10.0g* 100% All Axes 11. Overload Relay Square 0 SEO-15, CC156 10.0g* 100% All Axes 12. Overload Relay Ward Leonard 5990-1301, Cata2 4.0g 60% Vertical 13. Overload Relay Ward Leonard 5990-1301, CatB23 7.0g 90% Vertical 14. Protective Relay Westinghouse 290B481A09, Type KLF 10.0g 100% All Axes 15. Protective Relay Westinghouse 290B346A09, Type HV 2.1g 70% Vertical 16. Auxiliary Relay Westinghouse 289B360A15, Type MG-6 1.4g 70% All Axes 17. Control Relay Allen Bradley 700NM200-A1 10.0g 85% Horz. Axis 18. Air Circuit Breaker Westinghouse Unknown 4.2g 70% Horz. Axis 19. Panel Board (Breakers) Westinghouse RK32890 10.0g* 95% Horz. Axis 20. Field Circuit Breaker General Electric 224A351-104B6 10.0g* 100% All Axes 21. Molded Case Breakers Westinghouse EHB3070LT 10.0g* 100% All Axes 22. Molded Case Breakers Westinghouse FB3125 10.0g* 95% Horizontal 23. Switch-indicating Contactor General Electric 12SAM11C22A 1.6g 65% Vertical C-39 13633436 Walkdown Criteria: Basis for Seismic Capacity Guidelines for Structures, Equipment, and Subsystems Figure C-10 Typical shock input and response level for electrical devices Table C-8 shows some interesting comparisons between single axis, single frequency tests, and complex waveform biaxial tests. None of these complex waveform capacities fell below 60% of the weak axis capacity determined by single axis, single frequency testing. There was one instance where only 40% was achieved, but the 40% was applied to a stronger axis and was not the controlling acceleration limit. C-40 13633436 Walkdown Criteria: Basis for Seismic Capacity Guidelines for Structures, Equipment, and Subsystems Devices of the type in Table C-8 would be expected to have very little multi-axial coupling, and the reduction in capacity from biaxial multi-frequency input is judged to be primarily from the multi-frequency input. When comparing TRS or GERS to RRS where the TRS or GERS do not completely envelope the RRS, the non-enveloped region must be sufficiently away from the component resonant frequency to ensure that the non-enveloped input frequency range has very little influence on the component response. Electrical and electro-mechanical assemblies corresponding to generic categories in Table C-2 were tested to their malfunction level in the SAFEGUARD Program. Tables C-9 through C-12 list results for the following categories: • Motor Control Centers Table C-9 • Low-Voltage Switchgear Table C-10 • Medium-Voltage Switchgear Table C-11 • Distribution Panels Table C-12 The tables list the equipment description, highest functional level of input operability and highest achieved test level without impairing post-shock operation (survivability). The tests were both uniaxial and biaxial and capacities are listed in accordance with the test axes. Table C-9 Motor control centers Description Undamped Spectral Acceleration Test Type Operability for Three Orthogonal Axes X, Y, and Z Survivability Hatch Mfg., Model E87MC Wt. = 2146 pounds Z – 8g X – 2g Y – 2g 15g 15g 15g Uniaxial Hatch Mfg., Model E52MC Wt. = 2231 pounds Z – 8g X – 2g Y – 2g 15g 15g 15g Uniaxial Hatch Mfg., Model E06MC-1 Wt. = 1470 pounds (left half) Z – 8g X – 12g Y – 12g 12g 12g 12g Uniaxial Hatch Mfg., Model E0614MC-2 Wt. = 1522 pounds (right half) Z – 1.5g X – 1.5g Y – 2.5g 12g 12g 12g Uniaxial Hatch, Model E87MC Wt. = 2146 pounds Z – 5.0g X – 2.5g Y – 2.5g 12g 12g 6g* Uniaxial C-41 13633436 Walkdown Criteria: Basis for Seismic Capacity Guidelines for Structures, Equipment, and Subsystems Table C-9 (continued) Motor control centers Description Undamped Spectral Acceleration Test Type Operability Survivability Hatch, Model 89MC Wt. = 2377 pounds Z – 12g X – 5g Y – 5g 12g 12g 12g Uniaxial Hatch, Model E52MC Wt. = 2231 pounds Z – 12g X – 3g Y – 3g 25g 25g 25g Uniaxial Westinghouse Electrical, Type W Wt. = 550 pounds Z < 25g X – 10g Y – 10g 25g*** 10g 10g Uniaxial Westinghouse, ITC E05SS Wt. = 1820 pounds X-Z – 8g Y-Z – 8g 8g 8g Biaxial Westinghouse, ITC E12SS Wt. = 722 pounds X-Z – 6g Y-Z < 2g** 8g 8g Biaxial Notes: *Column buckling but no loss of function. **Lower test level not conducted to determine function level. ***Severe structural damage but no loss of function. Table C-10 Switchgear – low voltage Description Undamped Spectral Acceleration (5-30Hz) Test Type Operability Survivability Unit Substation Westinghouse Electrical Model E05SS-13 Wt. = 4771 pounds X-Z – 4g Y-Z – 6g 8g 8g Biaxial Unit Substation Westinghouse Electrical ITC 2755 Wt. = 4949 pounds X-Z – 1.5g Y-Z < 1.75g* 8g 8g Biaxial Unit Substation Westinghouse Electrical ITC 2955 Wt. = 7200 pounds Y-Z – 2.5g X-Z – 8g 12g 12g Biaxial Notes: *Lower test level not conducted to determine function level. C-42 13633436 Walkdown Criteria: Basis for Seismic Capacity Guidelines for Structures, Equipment, and Subsystems Table C-11 Switchgear – medium voltage Description Undamped Spectral Acceleration (5-30Hz) Test Type Operability Survivability ITE Corp., 5HK75 Wt. = 1800 pounds X < 1.5g Y < 1.5g Z – 1.5g 1 - 8g (ramp) 1 - 8g (ramp) 1 - 8g (ramp) Uniaxial ITE Corp., 5HK350 Wt. = 1400 pounds X < 0.5 - 3g (ramp) Y – 0.5 - 2g (ramp) Z – 1 - 4g (ramp) 5g 5g 5g Uniaxial ITE Corp., 5HK500 Wt. = 3500 pounds X < 0.5 - 2g (ramp) Y < 0.5 - 2g (ramp) Z – 0.5 - 2g (ramp) 5g 5g 5g Uniaxial General Electric, TCE01GD Generator Neutral Breaker Wt. = 2300 pounds X < 0.5 - 1.5g (ramp) Y < 0.5 - 1.5g (ramp) Z – 0.5 - 1.5g (ramp) 1 - 8g (ramp) 1 - 8g (ramp) 1 - 8g (ramp) Uniaxial X - Z – 2g Y - Z – 6g 8g 8g Biaxial Unit Substation Westinghouse ITC E0455 Table C-12 Distribution panels Description Undamped Spectral Acceleration (5-30Hz) Test Type Operability Survivability ITC E11PD Circuit Breakers Wt. = 85 pounds X-Y < 17g* Z-Y < 17g* 17g 17g Biaxial ITC E07PP Circuit Breakers with Protection Relays Wt. = 112 pounds X-Y < 17g* Z-Y 17g 20g 20g Biaxial ITC E09PP Circuit Breakers with Protection Relays Wt. = 393 pounds X-Z 20g Z-Y < 17g* 20g 20g Biaxial ITC E11PP Automatic Transfer Switch Wt. = 355 pounds X-Y – 20g Z-Y – 20g 20g 20g Biaxial ITC E26PL Circuit Breakers and Filters Wt. = 835 pounds X-Y – 20g Z-Y – 20g 20g 20g Biaxial C-43 13633436 Walkdown Criteria: Basis for Seismic Capacity Guidelines for Structures, Equipment, and Subsystems Table C-12 (continued) Distribution panels Description Undamped Spectral Acceleration (5-30Hz) Test Type Operability Survivability ITC E34PD Air Circuit Breakers & Electrical Panel Wt. = 644 pounds X-Y – 17g* Z-Y – 17g* 17g 17g Biaxial ITC E02PP Circuit Breakers & Protective Relay Wt. = 141 pounds X-Y – 17g Z-Y – 17g 17g 17g Biaxial ITC E84PD Breakers with Protective Relays Wt. = 452 pounds X-Y – 17g* Z-Y – 20g 20g 20g Biaxial Notes: *Lower shock level not applied. C.7.3.3 Motor Control Centers The test data show chatter-type malfunction at undamped spectral accelerations down to about 1.5g. This would correspond to about 1.0g spectral acceleration at 5% damping. GERS show slightly higher capacity for MCCs (EPRI NP-5223 [C-17]). Some of the relays used in the SAFEGUARD MCC tests may be weaker than those used in the GERS database. From Table C-8, the survivability level is at least 6g undamped spectral acceleration (equivalent to about 4g at 5% damping) and almost always much greater. For the limiting case of a 6g undamped survivability level, structural damage was noted but there was no loss of function. GERS indicate a limit of about 4g's spectral acceleration at 5% damping. This is comparable to the shock test results. If chatter of contactors or protective relays can be demonstrated to be inconsequential, then the only issue of concern is that of survivability. Survivability will most likely be governed by anchorage and not the capacity of devices. C.7.3.4 Low-Voltage Switchgear There are only three test articles in Table C-10. The operability limit is as low as 1.5g undamped spectral acceleration (about 1.0g at 5% damping), while the survivability limit exceeds 8g undamped spectral acceleration. C.7.3.5 Medium-Voltage Switchgear Table C-11 lists functional and survivability levels of medium-voltage switchgear tested in the SAFEGUARD program. In many of these tests, a flat shock spectrum was not used. The shock levels reported in Table C-11 reflect the range of acceleration input between 5 Hz and 30 Hz. Higher accelerations were achieved at higher frequency and these higher input, high frequency levels may have caused the anomaly rather than the acceleration levels in the range of cabinet C-44 13633436 Walkdown Criteria: Basis for Seismic Capacity Guidelines for Structures, Equipment, and Subsystems fundamental frequencies. Figure C-11 is a typical shock spectrum applied to medium-voltage switchgear. In most cases, the anomaly noted at the lowest acceleration were protective relay chatter without switchgear trip, but at higher accelerations, the switchgear sometimes tripped as a result of relay chatter. The lowest functional levels are lower than GERS from Figure C-10 in the lower frequency range. Since the most sensitive frequency of the protective relays cannot be determined from the test data, specific conclusions cannot be drawn from the comparison. Figure C-11 Typical shock spectrum for medium voltage switchgear C.7.3.6 Distribution Panels The generic category of distribution panels covers a broad range of components. In Table C-12, there are eight distribution panels that contain circuit breakers of different types, some with and some without protective relays. Only one level of testing was conducted; thus, in those cases where anomalies were noted, the functional level was not determined. The anomalies noted were either relay chatter or breaker contact chatter. No trips were recorded. C-45 13633436 Walkdown Criteria: Basis for Seismic Capacity Guidelines for Structures, Equipment, and Subsystems These data can best be used to confirm that the survivability level of distribution panel breakers and structures is quite high. The data are insufficient to formulate any conclusions regarding functional fragility levels. It is apparent, though, that breaker trip due to inertial effects is not likely at any credible levels of spectral acceleration that might be experienced. SAFEGUARD test data for other generic categories listed in Table C-3 were reviewed. The data were sparse, but the trend was consistent with that noted previously. Any components that contain relays or contactors where intermittent chatter can cause an unacceptable loss of function must be reviewed. No instances were noted in any mechanical or electro-mechanical components or devices to indicate weak links requiring detailed fragility review. The other categories reviewed include: • Transformers up to 13.8 KV • Control Panels with Relays and Switches • Motor Generators • Instrument Racks • Battery Chargers • Air Compressors • Air Handlers C.8 Electrical Cable Raceways Cable trays and supports are typically designed for seismic loading on a generic basis using very conservative criteria. Typically, maximum span spacings are specified, and upper bound tributary weights of the spans are lumped onto the supports. The support reactions and tray accelerations are approximately bounded by estimating a system frequency and applying the corresponding spectral acceleration to the lumped tributary mass at each support. Damping used in the design process is typically very much lower than observed by test. As a result, the raceways on modern plants are relatively stiff and overdesigned for strength. Earlier plant designs did not specifically provide seismic supports for cable raceways, and many of the earlier systems are quite flexible. Several test programs have been conducted to demonstrate the seismic resistance of the earlier designs, as well as more modern designs. The results of the test programs demonstrate a seismic resistance of electrical raceways well beyond analytical predictions. C.8.1 Tests of Modern Commercial Raceways and Conduit Bechtel Corporation managed a comprehensive program to test an assorted variety of commercially-available cable trays and cable tray support systems, as summarized in Linderman and Hadjian [C-13]. The types of trays tested included ladder-type of steel and aluminum manufactured by three firms, punch-bottom-type, and trough-type. Most of the trays tested were 24 in. wide and 4 in. deep. Eight-foot spans with cable fills of 0 to 50 lbs/ft in one to five tier configurations were tested. They were tested on rigid supports and on trapeze supports. C-46 13633436 Walkdown Criteria: Basis for Seismic Capacity Guidelines for Structures, Equipment, and Subsystems Two support systems were tested. They consisted of 5/8 in. diameter all-thread rods and struts. Additional low-cycle fatigue tests were conducted on strut connections. The rod-hung systems experienced significantly lower fragility levels than the strut-hung systems; thus, emphasis was placed on the strut systems with no conclusions being drawn for the rod-hung systems. In addition, electrical conduit systems were tested. The conduit was rigid metal conduit (equivalent to Schedule 40 pipe) and thinner wall EMC. Sizes were 3/4 in., 2 in., and 4 in. The conduits were filled with the maximum normal fill of cable allowed by the National Electrical Code. Conduits were tested on rigid supports, trapeze supports, and in wall-mount configurations. Standard hold down clamps and straps were used, and the support spacing corresponded to the National Electrical Code. The input motion for the raceways and conduit was generated by applying ground motion time histories to a hypothetical structure that had the same resonant frequencies as the test specimens. Test results for trapeze-hung cable trays showed about 7% damping for unfilled trays and from 15% to 50% damping for trays with 20 to 50 lbs/ft cable fill. Damping increased with input motion level. Koss [C-14] shows the measured damping from tests of braced strut systems. Several interesting conclusions were drawn from the test results. The most important conclusion was that all the strut-supported systems, whether braced or unbraced, would survive input levels to 3g ZPA. Damage was noted at these levels of input, but the systems stayed intact and remained functional. Low-cycle fatigue of the strut hanger system is the limiting factor. Other interesting observations from the test results are: 1. System flexibility is usually governed by the anchor point details. Complete fixity cannot be assumed. 2. Only the damping and mass characteristics of the cables have a strong influence on response characteristics of the system. 3. Cantilever side loading trays have higher damping than the traditional trapeze-hanger systems. 4. Parameters found not to have significant influence in tray systems dynamics are: – Splice plate and its location – Mix of cable size – Presence of cable ties – Type of tray and manufacturer 5. Cable tray strength is dependent upon the type of splice, but the capacity of splices tested was sufficiently high to withstand the maximum input motion achieved. Tests of conduit systems indicated that damping is one-third to one-half that for cable trays. The only noticeable distress observed in conduit tests was for a vertical strut simulating a wall mounting. The conduit clamp slipped down the strut. With the addition of a twist nut, square washer, and bolt beneath the conduit clamp, the clamps would resist the limit of the test machine (about 15g). Tests conducted of cable raceways and conduit indicated that conduit runs between raceways and junction boxes can resist large relative displacements. C-47 13633436 Walkdown Criteria: Basis for Seismic Capacity Guidelines for Structures, Equipment, and Subsystems Based upon the extensive series of tests conducted, it is concluded that cable raceway systems hung by strut-type systems have HCLPFs of at least 0.5g PGA. Electrical conduits supported in accordance with the National Electrical Code also have HCLPFs of at least 0.5g PGA. A plant walkdown of electrical cable raceway and conduit systems should concentrate on flexibility of conduit runs between electrical trays and junction boxes or any non-standard brittle detail of raceway supports. C.8.2 Rod Hung Raceways EPRI conducted a study of the performance of rod hung raceways (EPRI NP-7152-D [C-10]) and developed an analytical approach used to develop seismic evaluation guidelines for rod hanger trapeze support of electrical raceway systems. The seismic evaluation method focuses on supports with short, fixed-end threaded rod hangers. The analytical approach concentrates on the low-cycle fatigue life of the threaded rods subject to high strain seismic loading. Criteria for the fatigue capacity of rods are based on available test data. Seismic demand is defined in terms of bounding response spectra. Time history analyses, response cycle counting, and fatigue usage factor calculations are used to establish acceptable rod hanger support parametric combinations for in-plant screening evaluations. Additional studies are presented that were performed to validate various aspects of the simplified approach used in the calculations. C.9 Piping Systems Much attention has been paid to seismic design requirements for piping systems. Historically, the general belief is that the nuclear piping design practice has been very conservative. The cost of detailed piping analysis, pipe support design, support installation, and maintenance prompted analytical and experimental studies and compilations of historical performance. Experimental studies (ANCO [C-31]) on an unbranched and branched piping system indicated little distress up to the limits of the shake table. The highest elastically computed stress levels in the piping system were approximately four times the ASME Code Level D stress limits for Class 2 piping (the limit that is applied to normal plus SSE loading). One of the two test piping systems was transferred to another laboratory and successfully withstood the equivalent of five operating basis earthquakes and nine SSEs, as well as nearly a 30g sinusoidal test (NUREG/CR-5023 [C-9]). Other testing programs in the United States, Japan, and Germany reached similar conclusions. Results of these programs are briefly summarized in NUREG-1061 [C-8]. A comprehensive testing program sponsored by EPRI of individual pipe fittings showed very high damping of piping elbows cycled into the inelastic range and only moderate strains at pseudo-elastic stress levels grossly exceeding the ASME Code allowables (EPRI TR-102792 [C-32]). At the time EPRI NP-6041-SLR1 [C-1] was written, these experimental results were considered conclusive that piping systems designed to regulatory requirements had a very high resistance to seismic loading, and it was judged that piping HCLPFs were at least about four times the SSE. C-48 13633436 Walkdown Criteria: Basis for Seismic Capacity Guidelines for Structures, Equipment, and Subsystems There are many plants with piping systems designed to varying degrees of rigor for earthquakes and some of the very early plants with no specific design for earthquake. The historical performance of piping systems in past earthquakes can provide valuable insight on inherent piping ruggedness and potential weak points. NUREG-1061 [C-8] summarizes the performance of above ground industrial piping in the following eleven earthquakes: • Kern County – 1952 • Alaska – 1964 • San Fernando – 1971 • Managua – 1972 • Ferndale – 1975 • Miyagi-Ken-Oki – 1978 • Schwabische-Alb – 1978 • Imperial Valley – 1979 • Eureka – 1980 • Coalinga – 1983 • Hawaii – 1983 Although there are reported failures of piping in past earthquakes, it is pointed out that there are no known instances where seismic inertial loading was the cause of failure unless the piping contained weak joints or was badly corroded. The most common types of failure occur from the following causes: • Weak points are present due to brittle materials, excessive corrosion, faulty welding, pipe threads, and mechanical couplings. • Failure of equipment anchorage results in excess displacement demands on connecting piping. • Soil settlement or excess building motion results in excess displacement demands on connecting piping. • Insufficient flexibility of branch lines coupled with large motions of main runs of pipe results in excess displacement demands on branch piping. • To a lesser extent, multiple pipe support failures have resulted in pipe breaks. • Valve failures have been noted due to impact of the operator on an adjacent structure. C-49 13633436 Walkdown Criteria: Basis for Seismic Capacity Guidelines for Structures, Equipment, and Subsystems It can be deduced that a seismic fragility evaluation should concentrate on the above types of failures and not on dynamic piping analysis to demonstrate code stress compliance. The above types of failures can be evaluated by: • Reviewing anchorage of equipment to which piping is attached. • Performing a walkdown and piping isometric review to look for: – Non-ductile joints. – Long runs of pipe with weak supports where multiple support failure could cause excess pipe motion. – Inadequate piping flexibility between structures and equipment to accommodate seismic motion. – Inadequate flexibility of small branch lines to accommodate main pipe run displacements. • Review of the potential for soil settlement to cause excess motions in piping. • Verifying adequate separation between valve operators and adjacent structures or equipment. For piping systems designed by dynamic analysis for a. SSE of at least 0.10g or an equivalent static analysis of 0.2g or greater, the HCLPF may be estimated to be 0.5g PGA. A review of piping and instrumentation diagrams, piping isometric drawings, and a walkdown of selected runs should be performed to look for potential weak links as described above. For piping systems with no specific provisions for seismic support, a more detailed review of isometrics and a more detailed walkdown should be conducted to identify and then evaluate potential weak links. Some limited analyses may be necessary to evaluate potentially vulnerable conditions observed in a walkdown. Emphasis in selecting analyses should ensure that support failure(s) will not occur (resulting in complete loss of support over long runs of pipe), and that excessive loading will not result on nozzles of active equipment. Displacements can be bounded to ensure that valve operators do not impact adjacent structures in equipment, and that sufficient flexibility between adjacent structures exists. C.10 References C-1 A Methodology for Assessment of Nuclear Power Plant Seismic Margin (Revision 1). EPRI, Palo Alto, CA: 1991. NP-6041-SLR1. C-2 U.S. Nuclear Regulatory Commission. An Approach to the Quantification of Seismic Margins in Nuclear Power Plants, Lawrence Livermore National Laboratory, Livermore, CA: 1985. NUREG/CR-4334 (UCID-20444). C-3 U.S. Nuclear Regulatory Commission. Seismic Safety Margin Research Program, Phase 1, Subsystem Fragility. Washington, D.C. 1982. NUREG/CR-2405. C-4 Building Code Requirements for Reinforced Concrete (ACI 318-71), American Concrete Institute, Farmington Hills, MI: 1971. ACI 318-71. C-5 Code Requirements for Nuclear Safety Related Concrete Structures (ACI 349-76); and, Commentary on Code Requirements for Nuclear Safety Related Concrete Structures (ACI 349-76), American Concrete Institute, Farmington Hills, MI: 1976. ACI 349-76. C-50 13633436 Walkdown Criteria: Basis for Seismic Capacity Guidelines for Structures, Equipment, and Subsystems C-6 International Conference of Building Officials, 1985 Uniform Building Code, Whittier, CA 1985. C-7 U.S. Nuclear Regulatory Commission. IE Bulletin 80-11: Masonry Wall Design, Washington, D.C. 1980. C-8 U.S. Nuclear Regulatory Commission. Summary and Evaluation of Historical Strong-Motion Earthquake Seismic Response and Damage to Above-Ground Industrial Piping, Addendum to NUREG-1061, Vol. 2. Washington, D.C. 1985. C-9 U.S. Nuclear Regulatory Commission. High-Level Seismic Response and Failure Prediction Methods for Piping. Washington, D.C. 1988. NUREG/CR-5023. C-10 Seismic Evaluation of Rod Hanger Supports for Electrical Raceway Systems. EPRI, Palo Alto, CA: 1991. NP-7152-D. C-11 Raceway Experience Data Summary. EPRI, Palo Alto, CA: 1991. NP-7150. C-12 Cable Tray and Conduit System Seismic Evaluation Guidelines, EPRI, Palo Alto, CA: 1991. NP-7151. C-13 R. B. Linderman and A.H. Hadjian, "Development of Bechtel's Electrical Raceway System Test Program," Proceedings of the American Power Conference, Vol. 43 (1981). C-14 P. Koss, "Seismic Testing of Electrical Cable Tray Support Systems," Proceedings of Structural Engineers of California Conference, San Diego, CA (September 1979). C-15 Use of Seismic Experience and Test Data to Show Ruggedness of Equipment in Nuclear Power Plants, Part I. Sandia National Laboratories, Albuquerque, NM: 1991. SAND92-0140. C-16 Summary of the Seismic Adequacy of Twenty Classes of Equipment Required for the Safe Shutdown of Nuclear Plants, EPRI, Palo Alto, CA: 1991. NP-7149-D. C-17 Generic Seismic Ruggedness of Power Plant Equipment Rev. 1. EPRI, Palo Alto, CA: 1991. NP-5223. C-18 U.S. Nuclear Regulatory Commission. Test Series 1: Seismic Fragility Tests of Naturally-Aged Class 1E Gould NCX-2250 Battery Cells. Washington, D.C. 1984. NUREG/CR-3923. C-19 U.S. Nuclear Regulatory Commission. Test Series 2: Seismic Fragility Tests of NaturallyAged Class lE Exide FHC-19 Battery Cells. Washington, D.C. 1985. NUREG/CR-4095. C-20 U.S. Nuclear Regulatory Commission. Test Series 3: Seismic Fragility Tests of NaturallyAged Class lE C&D LCU-13 Battery Cells. Washington, D.C. 1985. NUREG/CR-4096. C-21 U.S. Nuclear Regulatory Commission. Test Series 4: Seismic Fragility Tests of NaturallyAged Exide EMP-13 Battery Cells. Washington, D.C. 1985. NUREG/CR-4097. C-22 Seismic Ruggedness of Aged Electrical Components. EPRI, Palo Alto, CA: 1987, NP-5024. C-51 13633436 Walkdown Criteria: Basis for Seismic Capacity Guidelines for Structures, Equipment, and Subsystems C-23 U.S. Nuclear Regulatory Commission. Probability of Pipe Failure in the Reactor Coolant Loops of Westinghouse PWR Plants, Vol. 2, Pipe Failure Induced by Crack Growth, Load Combination Program, Vol. 2. Washington, D.C. 1984. NUREG/CR-3660. C-24 U.S. Nuclear Regulatory Commission. Probability of Pipe Failure in the Reactor Coolant Loop of Westinghouse PWR Plants, Vol. 3, Guillotine Break Indirectly-Induced by Earthquakes, Vol. 3. Washington, D.C. 1985. NUREG/CR-3660. C-25 U.S. Nuclear Regulatory Commission. Probability of Pipe Failure in the Reactor Coolant Loops of Combustion Engineering PWR Plants, Vol. 2, Pipe Failure Induced by Crack Growth, Vol. 2. Washington, D.C. 1984. NUREG/CR-3663. C-26 U.S. Nuclear Regulatory Commission. Probability of Pipe Failure in the Reactor Coolant Loops of Combustion Engineering PWR Plants, Volume 3, Double-Ended Guillotine Break Indirectly-Induced by Earthquakes, Vol. 3. Washington, D.C. 1985. NUREG/CR-3363. C-27 U.S. Nuclear Regulatory Commission. Probability of Pipe Failure in the Reactor Coolant Loop of Babcock and Wilcox PWR Plants, Vol. 1, Pipe Failure Induced by Crack Growth, Vol. 1. Washington, D.C. 1985. NUREG/CR-4290. C-28 U.S. Nuclear Regulatory Commission. Probability of Pipe Failure in the Reactor Coolant Loops of Babcock and Wilcox PWR Plants, Vol. 2, Guillotine Break Indirectly-Induced by Earthquakes, Vol. 2. Washington, D.C. 1985. NUREG/CR-4290. C-29 U.S. Nuclear Regulatory Commission. Probability of Pipe Fracture in the Primary Coolant Loop of a PWR Plant, Volume 9, PRAISE Computer Code User's Manual, Load Combination Program, Project 1, Final Report, Vol. 9. Washington, D.C. 1981. NUREG/CR-2189. C-30 U.S. Nuclear Regulatory Commission. Probability of Failure in BWR Reactor Coolant Piping, Guillotine Break Indirectly-Induced by Earthquakes. Washington, D.C. 1986. NUREG/CR-4792. C-31 Laboratory Studies: Dynamic Response of Prototypical Piping Systems, Final Report. ANCO Engineers, Inc.: 1984. Report 1182.13. C-32 Piping and Fitting Dynamic Reliability Program, EPRI, Palo Alto, CA: 1994. TR-102792. C-52 13633436 D WALKDOWN CRITERIA: SAMPLING GUIDELINES D.1 Introduction For seismic margin assessments (SMAs) and seismic probabilistic risk assessments (SPRAs), rigorous statistically based sampling criteria are neither practical nor desirable. The SMA and SPRA procedures and guidelines are heavily reliant on the judgement of highly experienced engineers, and criteria for sampling should likewise be modeled around the judgement of those experienced engineers. This appendix, therefore, focuses on providing general guidelines to address the sampling issues that must be confronted in an SMA or SPRA. Sampling is particularly applicable to walkdown and fragility evaluation of groups of structures, systems, and components (SSCs) in which there is a great deal of redundancy or similarity within the group. Issues that influence the sampling process include: • Redundancy provided by multi-train systems • Similarity in design and location of redundant trains • Treatment of single failures • Access to components during walkdowns • Seismic interaction potential, including fire and internal flood sources The age of existing nuclear power plants and the extent of post start up reevaluations and documentation vary considerably and influence the approach to addressing the above-stated issues. For instance, sampling is technically valid for identical or similar components if there is evidence that the components are manufactured and installed in a consistent manner. On the other hand, the resolution of potential interaction questions does not lend itself well to sampling. In some instances, access is severely limited by radioactive environments, and limited sampling is the only practical method of conducting a walkdown. In cases of restricted sampling, redundancy, single failure, and consequences of failure become much more important issues. For major components on the seismic equipment list, sampling may not be as cost beneficial as for the distribution systems installed in bulk. The complexity of the fluid, pneumatic, electrical, instrumentation, and HVAC distribution systems make sampling a highly desirable feature of the SMA and SPRA processes. The following guidelines are provided for the seismic review team (SRT) and the seismic fragility engineers. Due to the unlimited variety of situations that may be encountered in nuclear power plants, the guidelines are general and must be interpreted by highly experienced engineers for application to the specific plant being assessed. An important point to remember is that the SMA and SPRA processes do not constitute quality assurance verifications. They are conditional upon the assumptions that the design, fabrication, and installation meet regulatory and industry standards for the safe shutdown earthquake (SSE) event. The emphasis is therefore on whether D-1 13633436 Walkdown Criteria: Sampling Guidelines properly installed equipment capable of withstanding the SSE will function during and after beyond-design-basis earthquakes, rather than on verifying by statistical sampling that expansion anchors, welds, etc., are properly installed, inspected, etc. D.2 Capacity Table Sampling The procedures outlined in Section 4.2 are formulated for developing seismic capacities for categories of equipment and structures. Certain caveats or inclusion rules require satisfaction by either a plant walkdown for equipment or by drawing reviews for structures or equipment. If equipment in the plant is purchased and installed to similar codes and standards, then the SRT may develop lower bound conservative capacities for classes of equipment based on the criteria outlined in Section 4.2. The evaluation sample size in this case is one for each equipment class. However, the walkdown verification will require sample sizes greater than one. In some instances, the SSCs may be unique in design, construction, or installation detail. These unique SSCs should be evaluated individually by examining the drawings to determine the specific design and installation features. While structure capacities may be evaluated approximately using the procedures in Section 4.2, there is a requirement to review the drawings and analysis models for details that might indicate seismic vulnerabilities. If the drawing and structural analysis reviews show consistent good practice in design detail and analysis, then it should not be necessary to review more than a small sample of the details of connections, reinforcement bar placement, construction joints, etc., to make defendable judgments on seismic capacity based on the criteria in Section 4.2. The depth of sampling should be justified by the reviewer. Commodities installed in bulk (such as piping, cable trays, HVAC ducting, electrical conduit, and instrument lines) can usually be evaluated as a group, based on a limited sample, subject to walkdown verification of inclusion rules. If design and installation practice are consistent, judgement may be based upon a review of general specifications and drawings for a single run of each class (i.e., a sample size of one per class). If review of the general specifications and drawings indicates significant differences in design and installation practice (e.g., because of changes in design criteria during the plant construction), then the sample size of one per class may have to be increased to cover the combinations of design and construction practice employed. An example might be the case of cable trays that are supported by unbraced threaded rods, by unbraced trapeze struts, and by braced trapeze struts. There are clearly three different classes of support, which require three different sets of evaluation criteria (sample of three). Structures, components, and subsystems installed in bulk should be grouped by equipment/ structure categories and by other design features or design standards. The sample size may then be rationally determined by examining the groupings. For instance, for the category of valves, there may be several groupings by valve types, installed elevation in the plant, and original design requirements. As an example, Table D-1 shows how active valves could be subdivided into several subcategories by valve type, elevation in the plant, and initial design criteria (design code and method of analysis). In this example, the number of groupings (sample size) is eight. One decision with associated inclusion rules is made for the eight combinations of valve type, valve location, and design code. Depending upon the judgement of the engineer and the capacity guidelines provided elsewhere in this report, the engineer may elect to consolidate the categories and reduce the sample size. For example, if the screening level is very low (Section 6.2), the D-2 13633436 Walkdown Criteria: Sampling Guidelines analyst might conclude that all valves at elevations less than 40 ft above grade can be evaluated as one category regardless of size or design code. The analyst might elect to look at only some extreme examples of motor-operated valves at high elevations with no seismic qualifications. If the extreme examples have sufficiently high capacity such that they do not contribute significantly to seismic risk, then all other combinations should be satisfactory, subject to a walkdown. Table D-1 Example of categorizing active valves for capacity evaluation Valve Type Elevation above Grade* Seismic Qualification Method Design Code Motor-operated valve > 40 ft Analysis 1971 ASME None 1968 B31.1 Analysis 1971 ASME None 1968 B31.1 < 40 ft > 40 ft < 40 ft Air-operated valve > 40 ft < 40 ft > 40 ft * Elevation guidelines from SSRAP (SAND92 0140 [D-1]) D.3 Walkdown Sampling In most nuclear power plants, safety-related systems have redundant trains with identical or very similar components. The general philosophy in the walkdown process is to conduct a walkdown of a high percentage of all components and electrical and fluid distribution systems for purposes of evaluating potential for interaction from II/I, proximity, flood, or seismic-induced fire. For the purposes of seismic interaction, the terminology "walk by" is used to denote that a detailed "inspection" of each component in the system is not necessary, but only that the potential for major interaction can be identified or ruled out by a surveillance of the general area. The detailed inspection of anchorage, attachment of appurtenances, and mounting of electrical and electronic devices in cabinets is only required on a sample of one for each "like'' component. For example, there may be twenty motor control centers to walkdown. If the specifications and a walkdown sampling show that all motor control centers are anchored in the same way, then only one anchorage system needs to be examined in detail. However, all twenty should be walked by to look for the remote possibility of seismic induced damage due to interactions. Where identical components are used in redundant trains, only one of the two or more components needs to be examined in detail for purposes of satisfying inclusion rules and anchorage criteria. However, both trains should have a walk by to satisfy the SRT that there are no credible seismic interactions. An example would be the diesel generator units. There may be five engine generators for a two-reactor system plant, where one unit per reactor system is required to survive. Only one engine generator unit needs to be examined in detail, but all units should have a walk by to ensure that there are no outliers in the installation, and that there is no potential for interaction. The key question is, if there is a potential for failure, is it common to all D-3 13633436 Walkdown Criteria: Sampling Guidelines trains? The secondary issue is, can one train fail, and if so, is the reliability of the surviving train sufficiently high to not be concerned with loss of one train? While the 100% walk by is a desired goal, it may be impractical in highly radioactive areas, and reliability / probability arguments are a viable alternative. In walking down piping, electrical, and HVAC distribution systems, a 100% walk by of one of the trains should be conducted to look for outliers. These systems are generally very seismically robust except for such outliers. The 100% walk by of these systems does not imply a 100% inspection of all support details since loss of a single support is likely not to be a serious problem. The intent is to do general area reviews to look for exceptions to the installation practice and to examine the potential for fires, floods, and physical impact from adjacent components or structural elements. A 100% walk by of both trains of redundant systems is desirable but may not be absolutely necessary. The rationale for a single train walkdown is that both trains are identical or similar; therefore, the integrity of both trains is validated by a walkdown of one train, except for the interaction issue. Unless there is evidence of general problems associated with interaction, a valid argument for not conducting a 100% walkdown of both trains or even for all of a single train is that "the probability of an interaction-induced failure of both trains is extremely low, and the combined probability of an interaction-induced failure of one train coupled with random failure or maintenance induced unavailability of the other train is also extremely low." In an SPRA, these kinds of decisions about whether one or both trains are required and how they are modeled are made by the systems analyst. Therefore, the walkdown team should work closely with the systems analyst to determine an appropriate sampling strategy for distribution systems. On newer plants where separation and interactions have been incorporated into the design process, a much smaller sample can be justified. The emphasis on interaction sampling during a walkdown is to demonstrate good design and housekeeping practice. The SRT should be concerned principally with verifying that any major outliers that could cause fires, floods, or failure are identified and explicitly evaluated. In highly radioactive environments, a 100% walkdown of one train may not be practical, and alternate arguments must be made for sampling. First, it should not be necessary to walkdown major structural elements such as steam generator and primary coolant pump supports. They can be assessed by reviews of the drawings and calculations. The principal concerns in containment are the potential for a small pipe break in the primary coolant system, the integrity of the essential instrument lines, and the integrity of the service water and component cooling water systems. Experience in walking down a non-contaminated containment indicates that it would not be practical to do a 100% walkdown of all branch connections to the primary coolant system, all component cooling water and service water systems, and all high-pressure instrument lines. Appendix K provides specific guidance for evaluating a fragility for small-small loss of coolant accident induced by failure of small bore piping and tubing inside containment. There are usually more than two redundant instrument taps for each essential reading. A small walkdown sampling of instrument lines requires an argument that there are no credible common cause seismic-induced failure modes of the instrument lines. Walkdown experience in an uncontaminated plant indicates that the only potential failure mode for instrument lines is an interaction-induced impact from non-seismic piping, emergency lights, loud speakers, etc. Due to the field installation routing of instrument lines and of non-seismic piping and components, there should not be a credible common cause failure mode for instrument lines (i.e., a single D-4 13633436 Walkdown Criteria: Sampling Guidelines interaction source will not fail all lines), and a zero walkdown sampling may be acceptable. Systems and operations engineering must verify the redundancy of the instrumentation to support this zero sampling. The only requirement for instrument line walkdown may be in a localized area where the lines are collected to penetrate containment. Here, a seismic-induced missile could potentially break off all lines, and this potential should be reviewed by a "quick look." Ultimately, some entrance into containment will be required to examine the essential active valves in the emergency core cooling system and others. The most practical method is to walkdown only the essential components during maintenance or in-service inspection (ISI) of that component. This prevents excess radiation exposure but may stretch out the completion of an SMA or SPRA for several years. Here is a case where practical arguments should be made that if the components in one redundant train are free of vulnerabilities, the probability of a random failure coupled with the probability of a beyond-design basis earthquake is so low that only one train needs to be examined; such judgments should be made by the systems analyst and supported by the walkdown observations as needed. Valves in containment that must isolate essential from non-essential component cooling water and service water should ideally have a 100% walk by unless the integrity of the non-essential systems they supply can be demonstrated. The walk by is principally to confirm that the valves will not become inoperable from an interaction condition. Caveats on valves can be satisfied by review of vendor drawings, and integrity of the valves can be demonstrated by analysis. Since the potential for valve damage due to interaction is extremely low, the 100% walk by should justifiably be conducted at the time of valve maintenance or during ISI near the valve. The only valves where interaction is of concern are active valves identified by the systems analysts as necessary to be operable to accomplish the safe shutdown. Thus, there are not many in containment to ultimately walk by. D.4 Sampling Analyses Two types of seismic analysis may be required during an SMA or SPRA. Specific structural elements or specific components may require an analysis to verify their structural integrity or function. These are plant-specific analyses and, for SSCs that are not screened, the general rule is to conduct the evaluation for each component designation. If there are redundant components of identical or very similar design, then the analysis can be conducted for the installation location that has the highest demand as long as the fragility that is developed is not a dominant contributor to seismic risk. Judgement of the SRT or seismic fragility analysts may be used to argue on a relative basis that analysis of one component is representative or bounding for others. For instance, anchorage checks might be made for an electrical cabinet, Cabinet A, with 7/16 in. anchor bolts for which large margins are demonstrated. Then a similar Cabinet B with 7/16 in. or larger diameter anchor bolts should not require an analysis on the basis that anchorage capacity of Cabinet B is approximately equal to or greater than Cabinet A, which had a large margin demonstrated by analysis. However, if Cabinet B has smaller anchor bolts or is vastly dissimilar to Cabinet A, then Cabinet B should also be evaluated analytically. For fluid and electrical distribution systems installed in bulk, if analyses are required to demonstrate margin, such analyses should initially be bounding analyses for worst case situations selected during the walkdowns. For instance, the weakest-appearing support system with the greatest demand should be evaluated first. If its fragility is sufficiently high that it does D-5 13633436 Walkdown Criteria: Sampling Guidelines not contribute to seismic risk, then all other portions of the system should be assumed to be adequate. If the worst case is important to risk, then additional analyses should be conducted for the next stronger portion or next lower demand until a threshold of demand and capacity is identified which will not significantly contribute to risk and beyond which (either lower demand or stranger support system) further analysis is not required. The selection of these bounding cases requires skill on the part of the SRT. Most of these systems are complex and contain redundant load paths. Thus, the bounding case may not be initially obvious, even to experienced engineers, and more than one sampling analysis may be required. Masonry block walls are another example where a bounding demand may be applied to a typical or lower bound capacity wall. If the analysis demonstrates negligible contribution to risk, then the sample of one is adequate to conclude all such walls in the plant need not be analyzed further. D.5 References D-1 Use of Seismic Experience and Test Data to Show Ruggedness of Equipment in Nuclear Power Plants, Part I. Sandia National Laboratories, Albuquerque, NM: 1991. SAND92 0140. D-6 13633436 E FRAGILITY METHODS: BACKGROUND ON RECOMMENDATIONS FOR HOOK ANCHORS AND DEEPLY EMBEDDED ANCHORS E.1 Background The governing failure modes for many nuclear plant structures, systems, and components are their anchorage. Larger and heavier components are typically anchored by embedded anchors (cast-in-place (CIP) bolts). ACI 349-13 [E-1] and ACI 318-14 [E-2] contain methods to develop the capacity for these CIP anchors, some of which result in significantly reduced capacities when compared to earlier versions of these codes, particularly for larger embedment lengths. These reduced seismic capacities are judged to be overly conservative in many instances. EPRI initiated a task to conduct research on the validity of using existing code strength equations as part of seismic probabilistic risk assessment and seismic margin assessment applications (EPRI 3002008099 [E-3]). Three types of embedded anchors are included as part of the EPRI task related to the seismic fragility and conservative deterministic failure margin (CDFM) strength equations: L-bolts, J-bolts, and headed bolts (Figure E-1). The goal of this task was to research available test data for moderate/deeply embedded anchors and to assess whether more realistic seismic capacity criteria could be justified for use in high confidence of low probability of failure (HCLPF) calculations and for seismic fragilities. This appendix summarizes two of the main conclusions from the EPRI study: recommendations for a pullout equation for L- and J-bolts, and a recommendation for the concrete breakout equation for CIP headed bolts and studs in uncracked concrete free from spacing and edge distance effects. Sections 4.7.1 and 4.7.2 in the main body of this report provide recommended strength criteria for traditional CIP anchors with steel and concrete breakout failures that include spacing and edge effects. The EPRI study recommends using an equation with a linear relationship to embedment depth for hooked bolt concrete breakout. Since the publication of the EPRI study, the test data used to develop this equation was discovered to more closely resemble splitting failure of a small specimen. Some discussion on splitting failure of hooked bolts is included in Section 4.7.2.3 of the main body of this report. For concrete breakout of hooked bolts, the analyst is directed to follow the guidance for CIP anchors given in Section 4.7.2.1. E-1 13633436 Fragility Methods: Background on Recommendations for Hook Anchors and Deeply Embedded Anchors (a) (b) (c) Figure E-1 Embedded anchor types: (a) headed bolt; (b) L-bolt; (c) J-bolt E.2 L-Bolts The purpose of this section is to recommend a median pullout strength equation for L-bolts. Additionally, a strength reduction factor is recommended consistent with the CDFM method. E.2.1 Test Data In 2014, Meinheit, Osborn, and Krueger revisited the ACI 318 hooked bolt pullout equation in ACI Special Publication SP-296-2 [E-4]. The test data is summarized in Table 1 of Meinheit, et al. [E-4]. Ninety-seven L-bolt tests in total were compiled. Pullout failure was observed in sixty of these tests. Five of the pullout failure test specimens were wrapped in Teflon to isolate the effects of bearing. Concrete related failures were observed in seventeen of the ninety-seven tests. Steel failure was observed in fourteen tests, and nut strip failure was observed in two tests. The failure modes for four tests were listed as unknown in Meinheit, et al. [E-4]. These four University of Texas tests were later confirmed to be concrete-related failures. E.2.2 Pullout Failure Prediction Equations Based on multiple linear regression analyses of the fifty-five pullout failure tests (excluding the Teflon wrapped test), Meinheit, et al. [E-4] proposed the following mean pullout equations: Ppullout = 9500eh da [lbf] 1 1 Ppullout = 1600d2a h2ef fc′ 4 [lbf] 3 4 1 2 1 Ppullout = 1200da eh hef fc′ 8 [lbf] Ppullout = 2.20fc′ da eh + 0.08fc′ πda hef [lbf] E-2 13633436 Eq. E-1 Eq. E-2 Eq. E-3 Eq. E-4 Fragility Methods: Background on Recommendations for Hook Anchors and Deeply Embedded Anchors Where: eh = Distance from inner face of hook bolt shaft to furthest tip of hook da = Bolt diameter hef = Effective embedment f’c = Concrete compressive strength Figures 4-14 and 4-15 in the main body of this report illustrate eh, da, and hef. Meinheit, et al. [E-4] reports the mean test/predicted ratios (RT/P), standard deviation, and coefficient of variation for these four equations against the fifty-five tests with observed pullout failure. Meinheit, et al. [E-4] recommends the bearing and the bond/bearing equations (Equations E-1 or E-3) instead of the existing ACI 318 hooked bolt pullout equation because the ACI equation is too conservative since it does not include the contribution from bond/friction. Pullout capacity is not clearly dominated by either bond or bearing but is a combination of both. It is concluded that although adhesive bond is lost prior to the initiation of concrete crushing, bond/friction forces are developed due to the transverse force on the leg extension and at the bump that forms at the L-bolt elbow when it is straightened out. For this reason, the recommended pullout strength equation should account for bond/friction as well as bearing. E.2.3 Pullout Failure Prediction Equation Recommendation According to Meinheit, et al. [E-4], the mean RT/P ratio for Equation E-3 applied to the fifty-five observed pullout failure tests is 1.002, with a standard deviation of 0.193. Equation E-3 is an empirical relationship and is considered a valid candidate for the recommended pullout strength even though it is in a form that does not provide physical insight as to which component governs (bearing or bond/friction). It is also counterintuitive because the concrete strength exponent indicates this variable is not as significant as expected for a concrete bearing related failure. However, it was demonstrated that Equation E-3 is the most statistically accurate equation of the four proposed. Equation E-3 also has an embedment variable that allows for a determination of the required depth to preclude pullout failure. Therefore, the EPRI study [E-3] recommends that Equation E-3 be used for fragility applications. The following median equation was evaluated for use in fragility calculations by testing the assumption that the data is lognormally distributed. 3 4 1 2 1 Ppullout = 1200da eh hef fc′ 8 [lbf] The following limitations on the pullout median strength equations were also recommended. eh > 2.0 da Before the equation was evaluated, the references used to compile the L-bolt test data were reviewed to gather additional understanding of the failure modes observed. The review resulted in a reclassification of four of the previously defined pullout failures to steel failures. After exclusion of the five Teflon tests and the reclassified steel failures, the number of pullout failures E-3 13633436 Fragility Methods: Background on Recommendations for Hook Anchors and Deeply Embedded Anchors was reduced to fifty-one tests. With the dataset of fifty-one, the recommended equation was used to predict the capacity. The natural log of each of the RT/P ratios was then calculated. Then the median RT/P ratio was calculated using the mean of the natural logs of the ratios. The final statistics are summarized in Table E-1. Table E-1 Statistics comparing tested to predicted pullout strengths Predicted Failure Mode Number of Tests Mean Standard Deviation Mean of ln(RT/P) Median = exp(mean(ln (RT/P))) Logarithmic Standard Deviation 51 1.09 0.274 0.061 1.06 0.234 Pullout E.2.4 Recommended Strength Reduction Factor The CDFM approach is aimed at estimating the mean 1% probability of failure. To achieve this goal, the component strength should be aimed at the 98% exceedance probability (EP) for ductile failures and greater than the 99% EP for brittle failures. The material strengths are generally defined by code specified material strengths (less than 5% non-exceedance probability (NEP)). To achieve the strength goals (98 or 99% EP) with the 5% NEP material strengths, the strength equation is defined by: PCDFM = ϕ Pcm where ϕ is the strength reduction factor and Pcm is the median tensile capacity. To achieve the CDFM strength goals for the pullout failure mode, ϕ should be defined at 98% EP because of the large variability in test results and the mild sensitivity to conservatism in the code specified concrete strength. Thus: ϕpullout = e−2.05βpullout where βpullout is the logarithmic standard deviation for uncertainty in the pullout strength equation. Based on the logarithmic standard deviation from Table E-1, the computed ϕ factor is: ϕpullout = 0.6 It was demonstrated in EPRI 3002008099 [E-3] that this strength reduction factor predicts strengths less than all the test data. The EPRI study also confirmed that the pullout test data is reasonably well represented by a lognormal distribution. E.2.5 Conclusion The following median L-bolt pullout equation is recommended for fragility calculations: 3 1 1 4 Ppullout = 1200da eh h2ef fc′ 8 E-4 13633436 [lbf] eh > 2.0 da Eq. E-5 Fragility Methods: Background on Recommendations for Hook Anchors and Deeply Embedded Anchors The logarithmic standard deviation associated with the recommended strength equation for pullout is: βpullout = 0.23 The corresponding CDFM strength reduction factor recommended for pullout is: ϕpullout = 0.6 The pullout equation recommended here should be used in lieu of equations developed in EPRI NP-5228 [E-5], Generic Implementation Procedure Appendix C [E-6], and ACI 318-14 [E-2] because these methods can be excessively conservative. E.3 J-Bolts The purpose of this section is to recommend a median and CDFM level pullout strength equation for J-bolts. The EPRI research for J-bolt test data did not produce results from the available literature. Since J-bolt anchors are less prevalent in practice, they are understandably less investigated in the laboratory compared to L-bolts, headed bolts, and headed studs. Lacking sufficient J-bolt test data, separate mean capacity equations could not be developed. However, based on the similarities between J-bolts and L-bolts, it was judged that L-bolt equations should be considered for J-bolts as well. J-bolts have a “double elbow” and a legextension beyond the second elbow, such that they are more likely to develop larger bearing and bond/friction forces than L-bolts. In fact, a phenomenon referred as the “rope-effect” is expected as the J-bolt hook tightens like a noose around the concrete as tension is applied to the bolt. Therefore, the L-bolt equations were judged to represent the lower bound capacity of J-bolts with an equivalent leg length. Per the EPRI study [E-3], it is recommended that the L-bolt pullout strength equation may be used to evaluate the capacities of J-bolts when hef and eh are defined as shown in Figure E-2. To support the conclusion that the L-bolt pullout equation is conservatively applicable to J-bolts, several smooth 180° (semicircular or J-shaped) hooks were examined since they are similar to the J-bolts found in equipment anchorage. In 1928, Mylrea published “The Carrying Capacity of Semicircular Hooks” [E-7]. The paper examined a series of smooth reinforcing bars with 180° hooks of various sizes, in unconfined and confined conditions; confinement was provided by spiral transverse reinforcement. Based on this examination of 180° hooks with the L-bolt pullout equation and the equivalent leg length, it was concluded that using the L-bolt equation for J-bolts is conservative. The recommended median and HCLPF pullout strength equations for J-bolts are thus defined as in Section E.2.5. E-5 13633436 Fragility Methods: Background on Recommendations for Hook Anchors and Deeply Embedded Anchors Figure E-2 J-bolt anchor to concrete E.4 Deeply Embedded Headed Bolts and Studs A median tensile concrete breakout strength equation is recommended herein for the special case of deeply embedded studs and bolts in uncracked concrete unaffected by nearby edges or neighboring anchors. Additionally, a strength reduction factor is recommended consistent with the CDFM method. For the purposes of the EPRI study [E-3], deeply embedded was defined as having an embedment of 7.5 in. (191 mm) or greater. This is consistent with the definition of “deep” in NUREG/CR-5563 [E-8] (7.4 in.;188 mm). E.4.1 Test Data The available literature reporting tension tests for deeply embedded headed bolts is relatively limited. Most deep headed bolt tests have been conducted on single anchors; group tests or tests near an edge are sparse or non-existent. The EPRI study [E-3] was able to assemble a total of 102 deeply embedded bolt tests. Seventy-seven of these tests were collected under an earlier anchor capacity study documented in NUREG/CR-5563 [E-8]. Twenty-five more recent deep anchor tests were reviewed in the EPRI study, totaling 102 tests. Early equations for deeply embedded anchors codified in ACI 318 were limited to 21 in. (533 mm), which represented the limits of the research at the time the deep anchor equation was introduced into ACI. The largest group of the more recent tests comprises fourteen tests performed in Korea in 2007 (Lee, et al. [E-9]). The Korean tests extended the deep anchor dataset beyond 21 in. to 45 in. of embedment. E-6 13633436 Fragility Methods: Background on Recommendations for Hook Anchors and Deeply Embedded Anchors E.4.2 Concrete Breakout Strength Equations The NUREG/CR-5563[E-8] strength equation was used to check for reasonableness of fit to the complete dataset compiled for the 102 tests for concrete breakout failure. The existing headed bolt mean equation for deeply embedded anchors in uncracked concrete from NUREG/CR-5563 is: ⁄ Nc.NUREG = 26.4�fc′ h5ef 3 [lbf] The reasonableness of the data fit was determined by developing the variance from the actual ultimate test load reported to the predicted failure load using the above NUREG/CR-5563 equation. The goal of the reasonableness review is to develop a median ratio of tested to predicted load RT/P approximately equal to 1.0 and the lowest logarithmic standard deviation as possible, given the range of the data. The statistical data review using the NUREG/CR-5563 equation for the 102 tests produced the following: • Median RT/P Ratio • Logarithmic Standard Deviation 0.181 1.09 The median RT/P ratio was not as close to 1.0 as would be desired for an optimum data fit. This was likely due to the new deep anchor samples having been added to the dataset of deep anchors, which were not available when the NUREG equation was developed. Error plots (residuals) are often used to assess the fit of the data and to assess whether the spread of the data is stochastic (random), or if the data spread has a bias that needs correcting. Error plots for tested ultimate loads to predicted loads ratios (RT/P) versus concrete strength and embedment depth for the NUREG/CR-5563 strength equation revealed that there is conservatism in the equation and the exponent on the compressive strength is skewed toward higher strength concrete. Since the NUREG/CR-5563 strength equation produces a biased prediction of the expanded data, a regression analysis of the 102 tests was performed examining the two key independent variables for breakout strength: the concrete compressive strength and the embedment depth. E.4.3 Developing a Strength Equation An equation of the following form was used to fit the data with regression analysis using parameters, α1 , α2 , and α3 . α α Pcm = α1 ∗ f ′ c 2 ∗ hef3 Eq. E-6 The dataset contained 102 tests with the two independent variables ranging from: • • Embedment depth: 7.48 < hef < 45 in. Concrete compressive strength: 2349 < f ′ c < 12,040 psi E-7 13633436 Fragility Methods: Background on Recommendations for Hook Anchors and Deeply Embedded Anchors The first iteration of regression analysis continued to demonstrate bias in the high concrete compressive strength range. To address this bias, the tests with concrete compressive strength greater than 7,000 psi were omitted from the second iteration of regression analysis. Based on the second regression analysis iteration, the EPRI study recommended the following median equation: Pcm = 3 ′4 4.4 ∗ f cm ∗ h1.6 ef The proposed deeply embedded anchor equation applies at all concrete strengths; however, the median concrete compressive strength used to compute a strength for a fragility application should not exceed 7,000 psi. It was necessary to examine this equation over the full dataset of 102 tests by limiting the concrete compressive strength used in the equation to 7,000 psi. The resulting statistics for lognormally distributed data are: • Median RT/P Ratio • Logarithmic Standard Deviation 0.16 1.00 The error plots for concrete strength and embedment depth were once again checked for bias, and it was confirmed that the proposed equation with limits on the concrete compressive strength provided a reasonable fit with no substantial bias. It was concluded that the proposed deeply embedded anchor equation provides a best estimate of the ultimate tension load on single anchors. E.4.4 Recommended Strength Reduction Factor For concrete breakout failure modes, the strength reduction factor should be defined at the 98% EP because of the relatively large variability of this brittle failure mode. Thus: ϕconc = e−2.05βconc where βconc is the logarithmic standard deviation for the concrete breakout failure mode equal to 0.16. The computed ϕconc factor is: ϕconc = 0.7 The CDFM concrete breakout capacity is calculated with the 98th percentile equation and the 95% exceedance material strength. The CDFM concrete breakout capacity equation for embedded anchors in uncracked concrete is defined as: 3 PcCDFM = ϕconc 4.4 ∗ f ′ 4cCDFM ∗ h1.6 ef E-8 13633436 Eq. E-7 Fragility Methods: Background on Recommendations for Hook Anchors and Deeply Embedded Anchors E.4.5 Conclusion The following median strength equation is recommended for concrete breakout of deeply embedded anchors: 3 Pcm = 4.4 ∗ f ′ 4cm ∗ h1.6 ef Eq. E-8 where the concrete compressive strength used in the equation does not exceed 7,000 psi. The logarithmic standard deviation associated with the recommended strength equation is: βconc = 0.16 The corresponding CDFM strength reduction factor recommended is: ϕconc = 0.7 E.6 References [E-1] Code Requirements for Nuclear Safety-Related Concrete Structures (ACI 349-13) and Commentary, American Concrete Institute, Farmington Hills, MI: 2013. ACI 349-13. [E-2] Building Code Requirements for Structural Concrete (ACI 318-14) and Commentary (ACI 318R-14), American Concrete Institute, Farmington Hills, MI: 2014. ACI 318-14. [E-3] Seismic Fragility Strength Equation Recommendations for Embedded Anchors, EPRI, Palo Alto, CA: 2016. 3002008099. [E-4] D. F. Meinheit, A. E. N. Osborn, and M. R. Krueger, "Pullout Strength of L-Bolt Anchors - Revisiting Design Equations," Symposium Honoring James O. Jirsa's Contributions in Structural Concrete: A Time to Reflect, ACI SP-296CD, Dallas, TX (Spring 2012). [E-5] Seismic Verification of Nuclear Plant Equipment Anchorage, Vol. 1: Development of Anchorage Guidelines, Revision 1, EPRI, Palo Alto, CA: 1991. NP-5228. [E-6] Generic Implementation Procedure (GIP) for Seismic Verification of Nuclear Plant Equipment, Revision 2, Appendix C, Anchorage Data, Seismic Qualification Utility Group, 1991. [E-7] T. D. Mylrea, “The Carrying Capacity of Semicircular Hooks,” Proceedings, American Concrete Institute, Vol. 24, pp. 240-263 (1928). [E-8] Division of Engineering Technology, Office of Nuclear Regulatory Research, A Technical Basis for Revision to Anchorage Criteria, U.S. Nuclear Regulatory Commission, Washington, D.C. 1999. NUREG/CR-5563. [E-9] N. H. Lee, S. K. Kim, C. J. Bang, and K. R. Park, “Tensile-Headed Anchors with Large Diameter and Deep Embedment in Concrete,” ACI Structural Journal, Vol. 104, No. 4, pp. 479-486 (2007). E-9 13633436 13633436 F FRAGILITY METHODS: CDFM CAPACITY CRITERIA FOR EXPANSION ANCHORS F.1 Introduction The capacity, C, of expansion anchor bolts in concrete is normally defined by: C = Mean Ultimate Capacity / FS Eq. F-1 where FS is a safety factor used to achieve the desired degree of conservatism. As an expansion anchor approaches its ultimate capacity, tension pullout and shear distortions of the bolt/concrete exceed at least half the bolt diameter. Although these distortions are not sufficiently large to justify including an inelastic energy absorption capability Fµ > 1.0 in the conservative deterministic failure margin (CDFM) evaluation of anchor bolts, some inelastic energy absorption does occur. Thus, it is considered appropriate to define the CDFM capacity CCDFM at about the 98% exceedance probability to achieve a high confidence of low probability of failure. Hence, the factor of safety FS should be set at a level consistent with about a 2% probability of failure. The mean ultimate capacity to be used in Equation F-1 may be obtained from references such as the manufacturer's catalog ICBO ultimate capacities or EPRI NP-5228-SL [F-1]. The mean ultimate capacity must include any appropriate reductions for concrete strength, bolt spacing, and edge distances as discussed in EPRI NP-5228-SL [F-1]. The factor FS does not cover these issues. F.2 Factor of Safety for Uncracked Concrete Expansion bolt failure data reasonably fits a normal distribution (i.e., equal probability of capacities lying at a certain percentage either below or above the mean). Thus, to achieve about a 2% failure probability: FS = [1 – 2.05(COV)]-1 Eq. F-2 where COV is the coefficient of variation of failure capacities. The expansion bolt failure data summarized in EPRI NP-5228-SL [F-1] may be used to estimate the coefficient of variation (COV). The COV will be estimated in three ways. First, the COV is estimated from: COV1 = Standard Deviation / Mean Eq. F-3 F-1 13633436 Fragility Methods: CDFM Capacity Criteria for Expansion Anchors where both the standard deviation and mean are simply statistical parameters of the raw data. Equation F-3 provides the rigorous definition for COV but does not provide any basis for accepting that the data is normally distributed, or that the properties of a normal distribution may be used together with this COV to estimate probabilities of failure in the 1% to 4% region of interest. To make these later assessments, COV2 and COV3 will be back-computed from the reported failure probabilities PF of (Mean / 2) and (Mean / 3) data, respectively, using an assumed normal distribution. These three estimates of COV are given in Table F-1 separately for shell type and non-shell type bolts for tension and shear. Note the similarity between COV1, COV2, and COV3 for all cases in Table F-1 and thus the reasonableness of approximating this data by a normal distribution and using Equation F-2 to estimate FS. Also note there is no significant difference between the COV for shell and non-shell type bolts. Therefore, these bolt types can be lumped together and a single COV used for both types. However, also note that the COV for shear are consistently lower than for tension failures. A COV of 0.28 is recommended for tension failures, and 0.245 for shear failures. Thus, for uncracked concrete: CDFM FS = 2.4 (tension) Eq. F-4 2.0 (shear) Table F-1 Estimated coefficients of variation for expansion bolts in uncracked concrete Loading Bolt Type Mean/2 COV1 Mean/3 Eq. F-3 Tension Shear PF Backcomputed COV2 PF Backcomputed COV3 Non-Shell 0.27 3.8% 0.28 0.8% 0.28 Shell 0.28 4.2% 0.29 1.0% 0.29 Non-Shell 0.20 1.3% 0.22 0.6% 0.26 Shell 0.26 2.3% 0.25 0.0% 0.25 Recommended COV 0.28 0.245 F.3 Influence of Small Concrete Cracks on Capacity As shown in Figures 2.9, 2.10, and 2.12 of EPRI NP-5228-SL [F-1], small concrete cracks extending the full depth of the expansion bolt and in the near proximity of the bolt may significantly reduce the bolt capacity in tension. When such cracks are present, the CDFM FS = 2.4 for tension given in Equation F-4 is inadequate to provide a 98% exceedance probability tensile capacity and must be increased. However, small cracks should not significantly influence the shear capacity, so that the CDFM FS = 2.0 for shear is still appropriate even when small cracks are present. For purposes of the following discussion, the following crack size definitions will be used: Hairline Crack 0 to about 0.01 in. (0.25 mm) Small Crack about 0.01 in. to about 0.03 in. (0.75 mm) F-2 13633436 Fragility Methods: CDFM Capacity Criteria for Expansion Anchors In addition, small surface cracks that do not extend into the concrete at least half the bolt depth are not expected to reduce the bolt tensile capacity and are considered to be non-cracks as far as selecting an appropriate FS for tension is concerned. The analyst will have to exercise judgement when deciding whether any observed cracks is in the proximity of a bolt and whether it is a non-crack, hairline crack, or small-crack by the above definition. For painted concrete surfaces, the walkdown team should keep in mind that hairline or small cracks that existed prior to painting will not be observed but may still be present. Also, due to the presence of steel anchorage plates, the concrete in the immediate proximity of an expansion bolt often cannot be observed, and the decision concerning the possibility of various size cracks in the near vicinity will have to be based on observing concrete at some distance from the expansion bolt. Table F-2 provides recommended CDFM FS to be used under various concrete conditions. A discussion on the derivation of this table follows. The analyst should decide which condition in this table is most applicable and use the corresponding FS in Equation F-1 to determine the CDFM capacity CCDFM. Unless evidence exists to the contrary, it is recommended that the single bolt hairline crack unlikely FS = 3.0 be used for tensile (pullout) capacities. When two or more bolts share the applied load, the FS may be somewhat reduced as shown in Table F-2. However, this two-or-more bolt FS should only be used when the load can be redistributed from a bolt to an adjacent bolt if the first bolt begins to fail. As used in Table F-2, the word "unlikely" corresponds to about a 20 to 40% probability of a crack exiting within the immediate proximity of a bolt and extending the full bolt depth. The word "likely" is intended to correspond to a 40 to 100% probability. The FS values are intended to provide about a 2% failure probability for crack probabilities midway within these ranges and a failure probability less than about 3% at the highest crack probability within each of these two ranges. Table F-2 Recommended expansion bolt safety factors to be used in CDFM evaluations Shear: FS = 2.0 Tension: FS Concrete Condition Single Bolt Two or More Bolts No cracks 2.4 2.4 Hairline Crack Unlikely 3.0 2.8 Hairline Crack Likely, Small Crack Unlikely 3.6 3.2 Small Crack Likely 4.0 3.6 Values of FS are not provided in Table F-2 for cases of cracks larger than about 0.03 in. extending the full bolt depth in the proximity of a bolt. It is conservatively recommended that a large crack be treated as a free concrete edge and the edge distance reduction from EPRI NP-5228-SL [F-1] be used to define a reduced mean ultimate capacity for both tension and shear and then use the uncracked concrete FS of Equation F-2 to define CCDFM. F-3 13633436 Fragility Methods: CDFM Capacity Criteria for Expansion Anchors To derive Table F-2, certain assumptions had to be made. These assumptions are: 1. In uncracked concrete, bolt tensile capacities are normally distributed with a COV = 0.28. 2. In uncracked concrete, capacities of multiple bolts are dependent, so that the COV of a bolt group is also 0.28, rather than reducing as would be the case for independent capacity. This assumption means that if any bolt in a group has less than mean capacity, then all other bolts in the group have an identical less than mean capacity. This assumption is conservative but is also likely to be more realistic than the assumption of independence. 3. Crack width size is uniformly distributed over the following ranges: Hairline 0 to 0.01 in. Small 0.01 in. to 0.03 in. 4. Based upon Assumption 3 and Figures 2.9, 2.10, and 2.12 of EPRI NP-5228-SL [F-1], the capacity reduction factors FR for hairline and small cracks are estimated to have the probability distributions given in Table F-3. 5. For two bolts, the capacity reduction factor for each bolt is independent of the reduction factor for the other bolt. The probability distribution also given in Table F-3 for the combined reduction factor for two bolts is then developed from this assumption of independence and the probability distribution given Table F-3 for one bolt. This two-bolt capacity reduction factor probability distribution function was then used

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