PEER Performance-Based Earthquake
Engineering Methodology:
Content Damage and Operability Aspects
By the UC Science Building Testbed Committee
Pacific Earthquake Engineering Research Center
University of California, Berkeley
July 18, 2002
Development Schedule
CC: Comartin
FF: Fillipou
GF: Fenves
GGD: Deierlein
GP: Pardoen
JE: Ellwood
JLB: Beck
KAP: Porter
KM: Mosalam
MCC: Comerio
NM: Makris
RM: Macoun
RZ: Zerbe
SEC: Chang
TH: Hutchinson
WTH: Holmes
Schedule
Section
1. Introduction
1.1 Background
1.2 Objectives
1.3 Scope
2. Building Description
2.1 Summary description
2.2 Geotechnical properties
2.3 Structural properties
2.4 Architectural features
2.5 MEP
2.6 Contents
3. Components to be tested
4. Seismic Hazard Analysis
4.1 Conventional free-field
hazard analysis
4.2 Hazard, improved IM
5. EDPs
5.1 Analytical modeling of
soil-foundation-structure
system
5.2 Validation of analytical
models
5.3 Prediction of EDPs
Responsible
Due
Done
GGD, MCC
MCC, KAP, GGD
MCC, KAP, GGD
5/02/02
5/02/02
5/02/02
MCC, WTH
KAP, PS
KM
MCC
MCC, WTH
MCC, WTH
KAP w/MCC
10/02
Outline 1/17/02, draft ?
Outline 1/17/02, draft ?
4/02-5/02
4/02
4/02
4/02
5/02 to be revised 12/02
5/02
5/02
4/15/02
PS, KAP
5/02
5/02/02
NM
?
KM, FF (not in this Outline 5/02, Draft 10/02
testbed?)
KM, FF
Outline 5/02, Draft 10/02
KM, CAC, JLB,
FF
Outline 1/02, Draft 10/02,
Final 4/03
ii
5/07/02
5/07/02
7/10/02
5/03
5/07/02
5/07/02
7/10/02
7/10/02
Section
Responsible
6. Damage analysis
6.1 Testing of
nonstructural
components
TH, GP
NM, TH, GP
6.2 Damage estimation
7. Loss analysis
7.1 DV/DM
relationships for
important components
7.2 Application of loss
(and downtime)
estimation methodology
7.3 Propagation of
uncertainties from IM to
DV
8. Relation to current
approaches
8.1 Current Practice
TH, GP, NM,
GF
KAP, JLB
KAP, JLB
Due
Select & describe components &
limit states 3/15/02 (WTH, TH,
NM); outline, testing schedule,
5/02; final draft 10/03
Outline 5/02, damage estimates,
partial draft (TH, GP, NM),
OpenSEES equipment model
10/02 (GF),
Quantify & disseminate by
7/15/02, report draft by 8/15/02,
final draft by 10/1/02
Outline by 5/02, itemize elements
to be considered by 5/15/02, final
report 5/03
CAC, JLB,
BE, RZ, SEC
????
CAC outline 1/17/02, CAC, JLB
identify sources of uncertainty by
4/1/02, CAC, BE, RZ, SEC
quantify impacts on DV by 7/02,
CAC, BE, RZ, SEC final report
by 10/02
WTH, CC
Assessment by 6/02, draft report
by 7/02
CC: Comparison w/ FEMA 356
by 10/02; WTH: Critique of
PEER methodology by 12/02
?
8.2 Assessment of PEER WTH, CC
Methodology
9. Societal issues and impact JE, RM, RZ,
SEC???
9.1 Stakeholders defined
and issues described
9.2 Engineers vs.
occupants attitude
toward loss and contents
damage, downtime
9.3 DVs
Done
iii
Outlined
6/02. Some
text inserted
6/02.
Table of Contents
1. Introduction ............................................................................................................................... 1
1.1 Background ...................................................................................................................... 1
1.2 Objectives ........................................................................................................................ 2
1.3 Scope ................................................................................................................................ 3
2. Description ................................................................................................................................ 6
2.1 Summary Description ...................................................................................................... 6
2.2 Geotechnical Properties ................................................................................................... 7
2.3 Structural Properties......................................................................................................... 8
2.4 Building Conditions ....................................................................................................... 12
2.5 Mechanical Equipment .................................................................................................. 29
2.6 Contents: Inventory of Scientific Equipment ................................................................ 31
2.7 Identification of critical factors affecting inventory: life safety, chemical hazard,
importance, and value ................................................................................................................... 56
2.8 Implications of using critical factors to target retrofits .................................................. 58
2.9 Prior anchorage .............................................................................................................. 59
2.10 Summary ........................................................................................................................ 61
3. Components of Methodology to be Tested ............................................................................. 63
4. Seismic Hazard Analysis ........................................................................................................ 64
4.1 Conventional Free-Field Hazard Analysis ..................................................................... 64
4.2 Free-Field Hazard Analysis and Record Selection Based on “Improved IMs” ............. 77
5. Engineering Demand Parameters ............................................................................................ 79
5.1 Structural modeling ........................................................................................................ 79
5.2 Validation of Analytical Models .................................................................................... 83
5.3 Prediction of EDPs ......................................................................................................... 83
6. Damage Analysis .................................................................................................................. 123
6.1 Testing of Nonstructural Components ......................................................................... 123
6.2 Damage Estimation ...................................................................................................... 123
7. Loss Analysis ........................................................................................................................ 125
7.1 Decision Framework .................................................................................................... 125
7.2 Formulation of Loss-Estimation Methodology............................................................ 127
7.2.1
Definition of Operational Units. ......................................................................... 127
7.2.2
Evaluation of the operational decision variable, DVO ........................................ 128
7.2.3
Evaluation of the Life-safety Decision Variable, DVL ....................................... 131
7.3 Mitigation Decision-Making Methodology ................................................................. 132
7.4 Application of Loss-Estimation Methodology............................................................. 134
7.4.1
Major Contributors to Loss ................................................................................. 138
7.4.2
Simplifications .................................................................................................... 138
7.5 Propagation of Uncertainties from IM to DV .............................................................. 138
8. Relation to Current Practice .................................................................................................. 140
iv
8.1 Current Practice of Engineering Evaluation ................................................................ 140
8.2 Engineering Assessment of the PEER PBEE Methodology ........................................ 140
9. Societal Issues and Impact .................................................................................................... 141
9.1 Stakeholders defined and issues described .................................................................. 141
9.2 Engineers vs. Occupants attitude toward loss and contents damage, downtime ......... 141
9.3 Decision Variables that matter ..................................................................................... 141
10. References ............................................................................................................................. 142
Appendix A. Four methods ......................................................................................................... 147
Appendix B. Engineering Demand Parameters .......................................................................... 148
Displacement measures ......................................................................................................... 148
Velocity measures ................................................................................................................. 148
Acceleration measures .......................................................................................................... 148
Structural-deformation measures .......................................................................................... 148
Structural-force measures ..................................................................................................... 149
Additional notation ............................................................................................................... 149
v
Index of Figures
Figure 1-1. Overview of PEER analysis methodology .................................................................. 4
Figure 2-1. Structural plan view of UCS building .......................................................................... 9
Figure 2-2. Structural elevation view of frame 8 and cross sections of the shear wall ................ 10
Figure 2-3. UC Science Building .................................................................................................. 14
Figure 2-4. Architectural floor plans, basement to 6th floor ........................................................ 15
Figure 2-5. Building sections ........................................................................................................ 16
Figure 2-6. Basement floor plan and space use ............................................................................ 17
Figure 2-7. First-floor plan and space use .................................................................................... 18
Figure 2-8. Second-floor plan and space use ................................................................................ 19
Figure 2-9. Third-floor plan and space use ................................................................................... 20
Figure 2-10. Fourth-floor plan and space use ............................................................................... 21
Figure 2-11. Fifth-floor plan and space use .................................................................................. 22
Figure 2-12. Sixth-floor plan and space use ................................................................................. 23
Figure 2-13. Net and gross space use in the building ................................................................... 24
Figure 2-14. Diagram of structural system ................................................................................... 25
Figure 2-15. Some mechanical systems ........................................................................................ 26
Figure 2-16. Sample interior conditions ....................................................................................... 27
Figure 2-17. Sample interior and exterior conditions ................................................................... 28
Figure 2-18. Typical laboratory layouts........................................................................................ 32
Figure 2-19. Sample laboratory #1 floor plan ............................................................................... 35
Figure 2-20. Sample laboratory #1 floor plan, cont. ..................................................................... 36
Figure 2-21. Sample laboratory #1 relationship between lab, core, and animal space ................. 37
Figure 2-22. Sample laboratory #1 three-dimensional diagram with photos................................ 38
Figure 2-23. Sample laboratory #1 three-dimensional diagram with photos (continued) ............ 39
Figure 2-24. Sample laboratory #1, examples of critical items .................................................... 40
Figure 2-26. Sample laboratory #2, floor plan .............................................................................. 42
vi
Figure 2-27. Sample laboratory #2 floor plan (cont.) ................................................................... 43
Figure 2-28. Sample laboratory #2, relationship between lab, core, and animal space ................ 44
Figure 2-29. Sample laboratory #2, three-dimensional diagram with photos............................... 45
Figure 2-30. Sample laboratory #2, three-dimensional diagram with photos (cont.) ................... 46
Figure 2-30. Sample laboratory #2, examples of critical items .................................................... 47
Figure 2-32. Sample laboratory #2, critical items......................................................................... 48
Figure 4-1. Soil Profile at K-net Site Kofu (TTR007). ................................................................ 67
Figure 4-2. Soil Profile at Kik-net Site Hino (TTRH02). ............................................................ 68
Figure 4-3. Variability in the ground motions of each set of ten scaled recordings for the
longitudinal and transverse components for each of three ground motion levels................. 72
Figure 4-4. Variability in the ground motions of each set of ten scaled recordings for the vertical
component for each of three ground motion levels. ............................................................. 73
Figure 4-5. Comparison of the longitudinal and transverse response spectra averaged over the
ten scaled recordings for the 50% in 50 year ground motion level. ..................................... 75
Figure 4-6. Comparison of the longitudinal and transverse response spectra averaged over the
ten scaled recordings for the 10% in 50 year ground motion level. ..................................... 76
Figure 4-7. Comparison of the longitudinal and transverse response spectra averaged over the
ten scaled recordings for the 2% in 50 year ground motion level. ....................................... 77
Figure 5-1: OpenSees model of UCS building ............................................................................. 80
Figure 5-2: Modeling of shear walls using beam-column elements and rigid elements .............. 81
Figure 5-3: Discretization of the element monitoring sections ..................................................... 82
Figure 5-4: Description of ENT material to simulate soil behavior in OpenSees ........................ 82
Figure 5-5: Spring forces in soil springs (top) and Roof displacement (bottom) due to 50% in 50
years Coyote Lake earthquake recorded at Gilroy #6 (full gravity load is applied) ............. 84
Figure 5-6: Spring forces in soil springs due to 50% in 50 years Coyote Lake earthquake
recorded at Gilroy #6 (only 50% of the gravity load is applied) .......................................... 85
Figure 5-7: Relative displacements of Roof (top), Level 4 (middle), and Level 1 (bottom) due to
50% in 50 years, Coyote Lake, Coyote Lake Dam abutment earthquake ............................ 89
Figure 5-8: : Relative accelerations of Roof (top), Level 4 (middle), and Level 1 (bottom) due to
50% in 50 years, Coyote Lake, Coyote Lake Dam abutment earthquake ............................ 90
vii
Figure 5-9: Absolute displacement (top) and absolute acceleration (bottom) of Roof due to 50%
in 50 years, Coyote Lake, Coyote Lake Dam abutment earthquake ..................................... 91
Figure 5-10: Relative displacements of Roof (top), Level 4 (middle), and Level 1 (bottom) due to
50% in 50 years, Coyote Lake, Gilroy #6 earthquake .......................................................... 92
Figure 5-11: Relative accelerations of Roof (top), Level 4 (middle), and Level 1 (bottom) due to
50% in 50 years, Coyote Lake, Gilroy #6 earthquake .......................................................... 93
Figure 5-12: Absolute displacement (top) and absolute acceleration (bottom) of Roof due to 50%
in 50 years, Coyote Lake, Gilroy #6 earthquake .................................................................. 94
Figure 5-13: Relative displacements of Roof (top), Level 4 (middle), and Level 1 (bottom) due to
50% in 50 years, Livermore, Fagundes Ranch earthquake ................................................... 95
Figure 5-14: Relative accelerations of Roof (top), Level 4 (middle), and Level 1 (bottom) due to
50% in 50 years, Livermore, Fagundes Ranch earthquake ................................................... 96
Figure 5-15: Absolute displacement (top) and absolute acceleration (bottom) of Roof due to 50%
in 50 years, Livermore, Fagundes Ranch earthquake ........................................................... 97
Figure 5-16: Relative displacements of Roof (top), Level 4 (middle), and Level 1 (bottom) due to
50% in 50 years, Livermore, Morgan Territory Park earthquake ......................................... 98
Figure 5-17: Relative accelerations of Roof (top), Level 4 (middle), and Level 1 (bottom) due to
50% in 50 years, Livermore, Morgan Territory Park earthquake ......................................... 99
Figure 5-18: Absolute displacement (top) and absolute acceleration (bottom) of Roof due to 50%
in 50 years, Livermore, Morgan Territory Park earthquake ............................................... 100
Figure 5-19: Relative displacements of Roof (top), Level 4 (middle), and Level 1 (bottom) due to
50% in 50 years, Morgan Hill, Anderson Dam Downstream earthquake .......................... 101
Figure 5-20: Relative accelerations of Roof (top), Level 4 (middle), and Level 1 (bottom) due to
50% in 50 years, Morgan Hill, Anderson Dam Downstream earthquake .......................... 102
Figure 5-21: Absolute displacement (top) and absolute acceleration (bottom) of Roof due to 50%
in 50 years, Morgan Hill, Anderson Dam Downstream earthquake ................................... 103
Figure 5-22: Relative displacements of Roof (top), Level 4 (middle), and Level 1 (bottom) due to
50% in 50 years, Parkfield, Array #5 earthquake ............................................................... 104
Figure 5-23: Relative accelerations of Roof (top), Level 4 (middle), and Level 1 (bottom) due to
50% in 50 years, Parkfield, Array #5 earthquake ............................................................... 105
viii
Figure 5-24: Absolute displacement (top) and absolute acceleration (bottom) of Roof due to 50%
in 50 years, Parkfield, Array #5 earthquake ....................................................................... 106
Figure 5-25: Relative displacements of Roof (top), Level 4 (middle), and Level 1 (bottom) due to
50% in 50 years, Parkfield, Array #8 earthquake ............................................................... 107
Figure 5-26: Relative accelerations of Roof (top), Level 4 (middle), and Level 1 (bottom) due to
50% in 50 years, Parkfield, Array #8 earthquake ............................................................... 108
Figure 5-27: Absolute displacement (top) and absolute acceleration (bottom) of Roof due to 50%
in 50 years, Parkfield, Array #8 earthquake ....................................................................... 109
Figure 5-28: Relative displacements of Roof (top), Level 4 (middle), and Level 1 (bottom) due to
50% in 50 years, Parkfield, Temblor earthquake ................................................................ 110
Figure 5-29: Relative accelerations of Roof (top), Level 4 (middle), and Level 1 (bottom) due to
50% in 50 years, Parkfield, Temblor earthquake ................................................................ 111
Figure 5-30: Absolute displacement (top) and absolute acceleration (bottom) of Roof due to 50%
in 50 years, Parkfield, Temblor earthquake ........................................................................ 112
Figure 5-31: Relative displacements of Roof (top), Level 4 (middle), and Level 1 (bottom) due to
10% in 50 years, Tottori, Kofu earthquake ......................................................................... 113
Figure 5-32: Relative accelerations of Roof (top), Level 4 (middle), and Level 1 (bottom) due to
10% in 50 years, Tottori, Kofu earthquake ......................................................................... 114
Figure 5-33: Absolute displacement (top) and absolute acceleration (bottom) of Roof due to 10%
in 50 years, Tottori, Kofu earthquake ................................................................................. 115
Figure 5-34: Relative displacements of Roof (top), Level 4 (middle), and Level 1 (bottom) due to
2% in 50 years, Tottori, Kofu earthquake ........................................................................... 116
Figure 5-35: Relative accelerations of Roof (top), Level 4 (middle), and Level 1 (bottom) due to
2% in 50 years, Tottori, Kofu earthquake ........................................................................... 117
Figure 5-36: Absolute displacement (top) and absolute acceleration (bottom) of Roof due to 2%
in 50 years, Tottori, Kofu earthquake ................................................................................. 118
Figure 7-1. Mitigation effectiveness chart. ................................................................................ 133
ix
Index of Tables
Table 2-1. Probability of at least one M6.7 event by 2030 ............................................................. 8
Table 2-2: Geometrical properties and the reinforcement schedule of the interior shear wall ..... 11
Table 2-3: Geometrical properties and the reinforcement schedule of the exterior shear wall .... 11
Table 2-4: Coupling beam reinforcement schedule ...................................................................... 12
Table 2-5. Common types of furniture and equipment in the laboratories. ................................. 34
Table 2-6. Value-group designations ........................................................................................... 50
Table 2-7. Life-safety priority levels assigned to furniture and equipment .................................. 51
Table 2-8. Chemical hazard conditions noted in the laboratories ................................................. 53
Table 2-9. Importance measures for equipment and materials in laboratories. ........................... 55
Table 2-10. Data categories for the furniture and equipment inventory ...................................... 57
Table 2-11. Equipment with prior retrofits .................................................................................. 60
Table 4-1. Site uniform hazard spectra, 5% damping, Sa at 0.45 seconds. .................................. 64
Table 4-2. Time histories representing 50% exceedance probability of Sa in 50 years. ............... 66
Table 4-3. Time histories representing 10% and 2% exceedance probability of Sa in 50 years. .. 66
Table 5-1: Summary of 50% in 50 years ground accelerations used for analyses ....................... 86
Table 5-2: Summary of 10% and 2% in 50 years ground accelerations used for analyses .......... 87
Table 5-3: Ground records that induced numerical problem in the nonlinear time-history analyses
............................................................................................................................................... 88
Table 5-4: Various maximum responses of each floor level subjected to different earthquake
records with 50% probability of occurance in 50 years. ..................................................... 119
Table 5-5: Various maximum responses of each floor level subjected to Tottori, Kofu earthquake
records with 10% and 2% probabilities of occurance in 50 years. ..................................... 122
Table 7-1. Inventory of critical components in MC laboratory. ................................................ 136
Table 7-2. Inventory of life-safety-level-D components in ML laboratory. .............................. 136
Table 7-3. Quantity of Equipment in ML Laboratory by Life-Safety Hazard........................... 137
Table 7-4. Quantity of Equipment in ML Laboratory by Life-Safety Hazard and Equipment
Description. ......................................................................................................................... 137
x
1. Introduction
Keith A. Porter, California Institute of Technology, Pasadena, CA
1.1
Background
Three structural design paradigms. Structural design comprises the selection of
structural, nonstructural, and geotechnical systems, and their materials and configuration, with
the goal of constructing a building, bridge, or other structure that will be safe and economical
under foreseeable circumstances. Historically, structural engineers have used allowable-stress
design (ASD) and load-and-resistance-factor design (LRFD), which focus on individual
structural elements and connections, and seek to ensure that none will experience loads or
deformation greater than it is capable of withstanding. An emerging approach, called
performance-based design (PBD), seeks to ensure that a designed facility as a whole will
perform in some predictable way, in terms of safety and functionality. Seismic aspects of PBD
are referred to as performance-based earthquake engineering (PBEE). PBEE therefore considers
the seismic reliability of the elements and connections, but also directly addresses the facility's
earthquake performance from the viewpoint of facility users, owners, and other stakeholders.
SEAOC, FEMA, and ASCE PBEE efforts. The PEER Center is not alone in developing
PBEE. The Structural Engineers Association of California (SEAOC) created an early sketch of
the objectives and methodologies of PBEE, in its Vision 2000 document (Office of Emergency
Services, 1995) and Conceptual Framework for Performance-Based Seismic Design (Structural
Engineers Association of California, 1999). SEAOC’s approach addresses performance in terms
of a continuum from operability, to life safety, to resistance to collapse, under four discrete levels
of seismic excitation. The Federal Emergency Management Agency (FEMA) and the American
Society of Civil Engineers (ASCE) build upon these documents in their prestandard,
ASCE/FEMA 356 (Federal Emergency Management Agency, 2000), which expresses
performance in four discrete levels though on much the same terms at four slightly different
hazard levels.
1
PEER's PBEE effort. PEER is producing an analysis methodology and a design
methodology. (Design encompasses the selection of systems, materials, and components, along
with the estimation of performance.) The combined methodology will address seismic
performance in terms of damage-repair cost and loss-of-use duration, as well as operability, lifesafety, and collapse potential. The methodology will detail how one can estimate future
performance in probabilistic terms, such as via probability distributions on repair costs and lossof-use duration on an annualized or lifetime basis as well as at discrete hazard levels.
Thus, the PEER methodology will be the first PBEE approach to provide economic and
probabilistic information. One important implication of this innovation is that it will be the first
PBEE methodology to inform the single most-common seismic evaluation performed in the
seismic regions of the United States: the estimation of probable maximum loss (PML). PEER’s
PBEE methodology will improve upon this fairly simplistic metric of seismic risk, to provide
more information about the downstream benefits both of seismic retrofit for existing buildings,
and of new design to higher performance levels.
1.2
Objectives
Purpose of the testbed project. PEER's analysis methodology is currently in
development. The testbed project seeks to synthesize disparate university research products of
PEER's first five years into a coherent methodology and to demonstrate and exercise that
methodology on six real facilities: two buildings (of which this report treats one), two bridges, a
campus of buildings, and a network of highway bridges.
Engineering practitioners involved in the testbed project compare the new PEER
methodology with current practice, to identify strengths and development needs relative to other
approaches. This comparison will help to guide our research and ensure that it meets practitioner
expectations and capabilities, and that the PEER methodology contributes materially to the value
practitioners can offer facility stakeholders.
Focus for the UC Science Building testbed. PEER researchers working on this facility
are focusing on issues relevant to newer institutional or industrial buildings for which the
primary hazard is seismic shaking, and the primary peril is damage to contents such as laboratory
equipment, and the consequent loss of use. This study both develops the theoretical basis of the
methodology, and illustrates it using the demonstration building. Later study may examine the
2
building under what-if (retrofitted) conditions, using it to test the desirability of various retrofit
techniques.
Other aspects of the PEER analysis methodology, such as estimating structural and
architectural damage, collapse potential, and repair duration, are the focus of the Van Nuys
testbed. The interested reader is referred to Van Nuys testbed Committee (in progress).
1.3
Scope
Overview. The performance evaluation presented here is performed for a single, real
facility, considering regional faults and their seismicity, site soils, the foundation and structural
system, the architectural features of the facility, its contents and scientific equipment, and
possibly its mechanical, electrical, and plumbing (MEP) components as well. The study
evaluates the seismic hazard (including creation of a set of ground-motion time histories at three
hazard levels), engineering demand (deformations, accelerations, and member forces), contents
damage, and the potential for operational failure of the laboratories it houses. We treat how
these performance metrics are used in real-world risk-management decision-making. We
explicitly address origins and propagation of uncertainty at each step of the analysis.
The PEER analysis methodology is summarized in Figure 1-1. As shown in the figure,
once the facility has been thoroughly described, the methodology embodies four stages: hazard
analysis (the study of how frequently earthquakes occur and how strongly they affect a site),
structural analysis (here, the study of how earthquake motion induces forces and deformations in
the structure), damage analysis (the relationship between structural response and physical
damage), and loss analysis (the relationship between damage and the final measures of
performance). The next section summarizes the aspects of this methodology that are examined
within the present study.
3
Facility
info
Hazard analysis
Struct'l analysis
Damage analysis
Loss analysis
g[IM|O,D]
p[EDP|IM]
p[DM|EDP]
p[DV|DM]
O, D
g[IM]
p[EDP]
p[DM]
p[DV]
O: Location
D: Design
IM: intensity
measure
EDP: engineering
demand param.
DM: damage
measure
DV: decision
variable
Decisionmaking
Select
O, D
Figure 1-1. Overview of PEER analysis methodology
Intensity measures. Seismic intensity will be measured initially in terms of damped
elastic spectral acceleration response at the building’s small-amplitude fundamental period (Sa).
PEER researchers will also test alternative intensity measures (IM). Our objective is to identify
an IM that is more strongly correlated with performance, and whose occurrence rates can be
readily calculated. That is, the new IM should reduce uncertainty on facility performance,
conditioned on hazard level. We illustrate the calculation of probability (or occurrence rate)
p[IM], and a methodology for selecting and scaling ground motions with a desired IM. It would
desirable to create a probabilistic model of detailed ground motion as a function of IM, i.e.,
p[GM|IM], but for the present, we treat as equiprobable a set of historic ground-motions
recorded at similar sites with approximately similar hazard conditions.
Engineering demand parameters. PEER researchers will attempt to identify a limited
set of engineering demand parameters (EDP) that are indicative of overall structural response, for
use in simplifying design. It is hoped that a single parameter (or perhaps a small set) such as
peak transient drift at the top of the structure, will correlate strongly enough with performance
that structural designers will not need to explicitly evaluate damage and loss, but merely
demonstrate that EDP is less than some allowable level, associated with the desired level of
performance. We will elucidate and illustrate a methodology for calculating the conditional
probability p[EDP|GM, IM], and given this and p[GM|IM], the probability p[EDP|IM]. One can
convolve p[EDP|IM] with p[IM] to produce p[EDP], as illustrated in Figure 1-1, or carry along
conditioning on IM until the end of the process, depending on how one wishes to express
performance.
4
Damage measures. PEER researchers will create or compile fragility functions for the
major damageable contents of the building. Fragility functions give the probability of a facility
component reaching or exceeding an undesirable performance level, as a function of excitation.
PEER researchers will categorize the building contents in a limited, clearly defined taxonomic
system; define relevant physical damage measures (DM) for each category; and create fragility
functions for each damage state, p[DM|EDP]. Given this and p[EDP], we will elucidate and
illustrate the calculation of p[DM]. Again, conditioning on IM can be carried though the
process, so the product of the damage analysis can also by p[DM|IM].
Decision variables. These decision variables (DV) measure overall facility performance
in terms most relevant to facility stakeholders. For the building owner considered here, DV is
most likely to include the operational failure of the scientific laboratories housed in the building.
This study elucidates and illustrates a methodology for calculating p[DV|DM] and, given p[DM],
the calculation of p[DV]. If one retains conditioning on IM, the product of this stage is
expressed as p[DM|IM], which represents the generic case of a seismic vulnerability function. It
can measure performance at discrete hazard levels, as in the ASCE/FEMA methodology. One
can then convolve with IM to produce p[DV], which can measure per-event, per-year, or lifetime
performance, depending on how hazard is expressed.
Decision-making implications. While financial decision-making is not a primary focus
of PEER’s effort, we recognize that to define and estimate DV correctly, we must understand
how the DV is used in financial practice. This study therefore examines the decision-making
practices of typical stakeholders of such a building, and illustrates how the DV estimates
produced here could inform an owner’s risk-management decisions.
Uncertainty. We identify the major sources of uncertainty in p[DV], quantifying the
contribution at each step from IM, GM, EDP, and DM to DV, considering propagation and
correlation. We identify the sources of uncertainty that are most significant in this situation, and
those that can be neglected. Of the major contributors, we identify opportunities for reducing
uncertainty by additional data-gathering or by changes in modeling. In other situations, such as
an older commercial building, a building on a site with significant potential for ground failure, or
a bridge, different sources of uncertainty may be more important. The larger PEER effort will
seek to categorize a variety of such situations and identify important sources of uncertainty in
each.
5
2. Description
Mary C. Comerio, Tae-Hyung Lee, Khalid M. Mosalam, University of California, Berkeley
Paul Somerville, URS Corporation, Pasadena, CA
2.1
Summary Description
The UC Science Building studied for this testbed is a modern reinforced-concrete spaceframe building completed in 1988 to provide high-technology research laboratories for
organismal biology. The building is 203,800 square feet overall, with 122,000 assignable (net
useable) square feet of research laboratories, animal facilities, offices and related support spaces.
The building is six stories plus a basement, and is rectangular in plan with overall dimensions of
approximately 306 feet in the longitudinal direction (oriented N16.5W) and 105 feet in the
transverse direction. The basement is contained within the periphery of the building. The single
level below grade avoids problems of a high water table and the costly underpinning of an
adjacent building.
The vertical load-carrying system consists of a complete reinforced-concrete space frame.
The floor structure is a waffle slab on every level and is composed of a 4-½ inch thick reinforced
concrete slab supported on 20-inch deep joists in each direction. The waffle slab is supported by
reinforced-concrete girders, which in turn are supported by reinforced-concrete columns. The
typical bay spacing is 20’-0” in the longitudinal direction and 22’-10” in the transverse direction.
The foundations consist of a 38-inch deep continuous mat foundation.
The building was designed to meet the 1982 Uniform Building Code (International
Conference of Building Officials, 1982), and is classified as C2 Building Type 9—Concrete
Shear Wall (Both Directions). The structure was evaluated in 1997 as part of a campus effort to
estimate the seismic response of and potential damage to campus buildings. In an earthquake
with a 50% probability of exceedance in 50 years, the building was ranked Operational, at level 8
on the 10-level scale of performance as outlined in Vision 2000 (Office of Emergency Services,
1995). In this scenario, the building is expected to have minor cracking in exterior pier and
6
spandrel elements, as well as minor cracking in coupling beams in transverse shearwalls. In an
earthquake with 10% probability of exceedance in 50 years, the building was ranked
Operational, at level 7. In this scenario, the building might have significant repairable cracking
in coupling beams and exterior piers, spandrels, and end framing, as well as minor repairable
cracking in the waffle slabs. In a very rare earthquake, one with 10% exceedance probability in
100 years, the building was ranked Life-Safe, at level 6. In this scenario, fracture of coupling
beams is possible, and major cracking in shear walls, waffle slabs, and end framing, but collapse
is prevented. The building was rated “good” in the UC rating system and was not considered to
be in need of any structural retrofits (University of California, Berkeley, 1997).
This testbed building was built as part of a larger campus plan to upgrade research and
teaching facilities in the biological sciences. This building provides laboratory space for more
than 40 faculty members. It is designed with a central core of mechanical rooms, circulation,
and shared storage and equipment rooms. A loop circulation plan connects the eight to ten
laboratories on the east and west sides of the building. Offices are within the laboratories. These
are designed in a modular format so that a laboratory/office space can expand or contract by
adding or removing a module along the corridor. Although the building was planned with all
laboratories in a standard configuration, the laboratories undergo regular remodels to
accommodate new research techniques and equipment. Two floors are dedicated to animal
facilities. Overall, 82% of the net area is dedicated to laboratory and animal facilities. The
remainder of the space is for offices, administration space, conference rooms, stockrooms, and
other support facilities.
2.2
Geotechnical Properties
Site conditions. The site conditions at the UC Berkeley campus are summarized by
Geomatrix Consultants (2000). The UC Science Building is located at a site consisting of stiff
soil of thickness in the range of 6 to 16 meters, with an estimated average of about 12 meters,
above Franciscan bedrock. No seismic-velocity profiles are available. The Franciscan rocks
underlying the central campus are assumed to be not pervasively sheared, and to have a shear
wave velocity of about 0.9 km/sec. Older alluvium overlies the Franciscan rocks at the site. The
alluvium typically comprises very stiff sandy clay, with average standard penetration resistance
values of 50 or greater, and estimated shear wave velocity of about 0.37 km/sec. The site is thus
classified as NEHRP category Sc.
7
Nearby faults, earthquake history. The Hayward Fault traverses the UC Berkeley
campus, with a trace within 2900 ft (900 m) of the testbed building. The Hayward Fault is
active, with an average slip rate of 9 mm/yr. The latest rupture of its southern segment (Fremont
to somewhere between San Leandro and Berkeley) occurred on 21 Oct 1868, producing a M7
earthquake. Trenching data suggest that the southern segment has an average earthquake
recurrence interval of at most 370 years (Kelson et al., 2000). The northern section (to Pinole)
appears not to have ruptured during the written history of the area, i.e., not for at least 220 years
(Hayward Fault Paleoearthquake Group, 1999). It is believed capable of producing a M7 event
with an average recurrence interval of no more than 710 years, and possibly less than 270 years.
The Working Group on California Earthquake Probabilities (1999) estimates a 17%
probability of an event at least M6.7 on the Southern Hayward by 2030; 16% on the Northern
Hayward Fault. Other faults that could cause damaging earthquakes include the San Andreas (30
km distant, M ≤ 8.0), Calaveras (20 km, M ≤ 7.2), Concord-Green Valley (22 km, M ≤ 6.8), Mt
Diablo Thrust (16 km, M ≤ 6.7), Greenville (30 km, M ≤ 7.2), Rodgers Creek (32 km, M ≤ 7.1),
and San Gregorio (36 km, M ≤ 7.5). Table 2-1 summarizes the Working Group’s estimated
probabilities of earthquakes M ≥ 6.7 in the San Francisco Bay Area by 2030.
Table 2-1. Probability of at least one M6.7 event by 2030
Fault
Probability
Hayward/Rodgers Creek
San Andreas
Calaveras
San Gregorio
Concord/Green Valley
Greenville
Mt. Diablo
2.3
32%
21%
18%
10%
6%
6%
4%
Structural Properties
General. The gravity load-carrying system of the UC Science Building consists of a
reinforced concrete space frame, as shown in Figure 2-1 which includes the global geometry and
span dimensions. The lateral force-resisting system consists of coupled shear walls in the
transverse direction (approximately normal to the Hayward fault) and perforated shear walls in
the longitudinal direction. The floors consist of waffle slab systems with solid parts acting as
8
integral beams between the columns. The building foundation consists of mat foundation with
38" thickness.
203'-0"
N
20'-9"
3@20'=60'
20'-9" 20'-9"
3@20'=60'
20'-9"
A
19'-9" 22'-10" 19'-4" 22'-10" 19'-9"
104'-6"
16o 33'
B
D
E
G
H
3
4
5
6
7
8
9
10
11
12
13
101'-6"
Figure 2-1. Structural plan view of UCS building
The modeling of the UCS building is conducted on two levels. In the first, twodimensional analysis is performed to investigate the seismic response of the middle frame
(labeled 8 in Figure 2-1). The second analysis will consider three-dimensional modeling of the
entire UCS building under multi-directional ground motion. The discussion in the subsequent
sections pertains to the two-dimensional modeling configuration.
Geometrical Properties. Figure 2-2 presents the structural elevation view of frame 8 (as
identified in Figure 1) of the UCS building and indicates the story heights and the different
labeling of the building levels. All interior columns of the UCS building are square with
dimensions 24" with transverse reinforcement in the form of #4@8" closed ties. The longitudinal
reinforcing bars of the interior columns vary with the levels of the building; 12#11 are used for
the columns between the foundation level and level 1, 12#10 are used for the columns between
levels 1 and 3, and 8#8 are used for the columns between levels 3 and the roof. The cross
sections of the shear walls are shown in Figure 2-2 where all the geometrical properties and
9
reinforcement schedules of the interior (between axes D and E) and exterior (between axes A and
D and E and H) walls are summarized in Table 2-2. and Table 2-3, respectively. The coupling
beams between the shear walls are 48" wide and 241/2" deep for all levels with the reinforcement
schedule given in Table 2-4.. In addition to the reinforcement in Table 2-4., the coupling beams
have transverse reinforcement #5@6" (6 branches) in the form of three sets of closed stirrups.
A
B
D
E
G
H
20'-5"
Roof
13'-6"
Level 6
13'-6"
Level 5
13'-6"
110'-11"
Level 4
13'-6"
Level 3
13'-6"
Level 2
18'-6"
Level 1
19'-9"
14'-10"
8'
19'-4"
8'
14'-10"
19'-9"
104'-6"
Figure 2-2. Structural elevation view of frame 8 and cross sections of the shear wall
10
Table 2-2. Geometrical properties and the reinforcement schedule of the interior shear wall
b1
b1
t
24"
WC1
WC1
21'-4"
Column WC1
Wall
b1 (in.) Long. reinf. Trans. Reinf. t (in.) Reinf.*
6th story
5th story
4th story
3rd story
2nd story
1st story
Basement
24
24
24
24
24
33
33
8#8
8#8
8#8
8#8
8#8
12#9
14#11
#4@8"
#4@8"
#4@8"
#4@8"
#4@8"
#4@4"
#4@4"
14
14
14
14
16
18
18
#5@6"
#5@6"
#6@6"
#6@6"
#7@6"
#7@6"
#7@6"
* Reinforcements in both of the horizontal and vertical directions
Table 2-3. Geometrical properties and the reinforcement schedule of the exterior shear wall
b2
b3
t
b4
t
WC2
WC3
19'-9"
6th story
5th story
4th story
3rd story
2nd story
1st story
Basement
t
WC2 24"
15'-10"
Column
depth (in.)
b3
b4
WC2
b2
t
WC3
15'-10"
WC2
WC2
19'-9"
WC3
Wall
b2
b3
b4
Long.
reinf.
Trans.
reinf.
Long.
reinf.
Trans.
reinf.
t
(in.)
Reinf.*
25
25
31
37
44
49
49
24
24
24
24
24
30
30
24
24
29
25
42
47
47
8#8
8#8
12#8
12#9
16#10
22#10
26#10
#4@8"
#4@8"
#4@8"
#4@8"
#4@8"
#4@4"
#4@4"
8#8
8#8
8#8
8#8
8#8
12#9
12#9
#4@8"
#4@8"
#4@8"
#4@8"
#4@8"
#4@4"
#4@4"
14
14
14
14
16
18
18
#5@6"
#5@6"
#6@6"
#6@6"
#7@6"
#7@6"
#7@6"
* Reinforcements in both of the horizontal and vertical directions
11
Table 2-4.: Coupling beam reinforcement schedule
4.5"
Bar type "a"
Top & Bottom
Bar type "b"
24.5"
20"
48"
6th story
5th story
4th story
3rd story
2nd story
1st story
Basement
Type “a”
Type “b”
9#10
9#10
10#11
10#11
11#11
10#11
10#11
3#7
3#7
3#8
3#8
3#8
3#8
3#8
Material Properties. According to the design specifications, the concrete of the shear
walls and the coupling beams has nominal 28-day compressive strength of f c '  5 ksi . On the
other hand, the concrete for the interior columns and the waffle slab systems has nominal
strength of f c '  3 ksi . The reinforcing steel is scheduled as ASTM A-615 Grade 40 for #4 and
smaller bars and Grade 60 for #5 and larger bars.
2.4
Building Conditions
Architectural Features: The UC Science Building studied for this research is a modern
concrete building completed in 1988 to provide high technology research laboratories for
organismal biology. The building is 203,800 square feet overall, with 122,000 assignable (net
useable) square feet of research laboratories, animal facilities, offices and related support spaces.
The building is six stories plus a basement, and is rectangular in plan with overall dimensions of
approximately 306 feet in the longitudinal (north-south) direction and 105 feet in the transverse
12
(east-west) direction. The basement is contained within the periphery of the building. The
single level below grade avoids problems of a high water table and the costly underpinning of an
adjacent building.
This building was built as part of a larger campus plan to upgrade research and teaching
facilities in the biological sciences. This building provides laboratory space for more than 40
faculty members. The building is designed with a central core of mechanical rooms, circulation,
and shared storage and equipment rooms. A loop circulation plan connects the eight to ten
laboratories on the east and west sides of the building. An internal corridor provides a secondary
circulation system within the laboratories. Research offices are situated within the laboratories.
The laboratories are designed in a modular format so that a laboratory or office space
may expand or contract by adding or removing a module along the corridor. Although the
building was planned with all laboratories in a standard configuration, the laboratories undergo
regular remodels to accommodate new research techniques and equipment. Two secure floors—
the basement and the sixth floor—are dedicated to animal facilities. A total of 82% of the net
area is used for laboratory and animal facilities. The remainder of the space is for offices,
administration space, conference rooms, stockrooms, and other support facilities. Figure 2-3
through Figure 2-17 provide a graphic description of the building in plan and section, including
exterior and interior finishes, structural and mechanical systems.
The building’s exterior is simple, with cast-in-place concrete panels, with a light
sandblast finish. The windows have a painted extruded aluminum frame with solar grey glass.
The rooftop mechanical penthouse is set back from the walls. Ceramic roof tiles are used as a
mechanical screen, but the roof is made of a built-up bituminous roofing system with layers of
asphalt and fiberglass felt, covered with black gravel.
Inside the building uses steel-stud (3-5/8” x 25 gauge metal) and gypsum partition walls
to divide laboratories. Typically ceilings are open with exposed mechanical piping in the
laboratories. Some offices contain acoustical drop-ceilings, and the corridors have a metal-grid
hanging ceiling to cover mechanical equipment. Floors are either vinyl tile or exposed concrete.
The floors are not impermeable to toxic spills.
13
Figure 2-3. UC Science Building
14
Figure 2-4. Architectural floor plans, basement to 6th floor
15
Figure 2-5. Building sections
16
Figure 2-6. Basement floor plan and space use
17
Figure 2-7. First-floor plan and space use
18
Figure 2-8. Second-floor plan and space use
19
Figure 2-9. Third-floor plan and space use
20
Figure 2-10. Fourth-floor plan and space use
21
Figure 2-11. Fifth-floor plan and space use
22
Figure 2-12. Sixth-floor plan and space use
23
Figure 2-13. Net and gross space use in the building
24
Figure 2-14. Diagram of structural system
25
Figure 2-15. Some mechanical systems
26
Figure 2-16. Sample interior conditions
27
Figure 2-17. Sample interior and exterior conditions
Structural Features: The vertical load carrying system consists of a reinforced concrete
frame. The floor structure is a waffle slab on every level and is composed of a 4 ½ inch thick
concrete slab supported on 20 inch deep joists in each direction. The waffle slab is supported by
concrete girders which in turn are supported by concrete columns. The typical bay spacing in
28
20’-0” in the longitudinal direction and 22’-10” in the transverse direction. The foundations
consist of a 38 inch deep continuous mat foundation.
The building was designed to meet the 1982 Uniform Building Code, and is classified as
C2 Building Type 9—Concrete Shear Wall. The structure was evaluated in 1997 as part of a
campus effort to predict the seismic response and potential damage to campus buildings. In a
moderate earthquake, defined as an earthquake with a 50% chance of exceedance in 50 years, the
building was ranked Operational, at level 8 on the 10 level scale of performance as outlined by
the Structural Engineers Association of California in Vision 2000 (Hamburger et al., 1995). In
this scenario, the building is expected to have minor cracking in exterior pier and spandrel
elements, as well as minor cracking in coupling beams in transverse walls. In a magnitude 7.0
earthquake on the Hayward fault, the building was ranked Operational, at level 7 on the 10 level
scale. In this scenario, the building might have significant repairable cracking in coupling beams
and exterior piers, spandrels, and end framing, as well as minor repairable cracking in the waffle
slabs. In a very rare earthquake, a magnitude 7.25 on the Hayward fault, the building was ranked
Life-Safe, at level 6. In this scenario, there could be possible fracture of coupling beams and
major cracking in shear walls, waffle slabs, and end framing, but collapse is prevented. The
building was rated “good” in the UC rating system and was not considered to be in need of any
structural retrofits (UCB, 1997).
2.5
Mechanical Equipment
Light fixtures are florescent, suspended and modular. The mechanical systems are
sophisticated to allow for specialized air changes and temperature controls in certain research
settings and animal holding areas. Separate systems for de-ionized water, and other chemicals
are designed into the mechanical services for laboratories. All laboratories have emergency
eyewashes, showers and fume hoods.
HVAC: The building is air conditioned, with separate air handling systems and fans for
lobbies, conference rooms, and offices; laboratories, and animal holding rooms. All are designed
to meet CEC Title 24 requirements. Animal rooms have an independent collected exhaust
system with pre-filters at each room inlet. Laboratories with hoods have a manifold exhaust
system with vertical riser shafts, and negative pressure is maintained. Special purpose hoods
have independent exhausts, as do glass-washing and cage cleaning rooms. Two water-cooled
29
chillers provide for cooling. Steam is taken from the existing central plant, but new steam-to-hot
water heat exchangers are in the building.
Electrical System: Service to the building is provided at 12.47 KV. Three phase
transformers to bring the power down to 480/277V are on the roof. Additional transformation
down is accomplished on each floor. One 600W generator is on the ground floor outside to
supply 277/480V emergency power to critical loads, however, there is concern that this system is
not monitored and is overloaded.
A 12-in-wide cable tray system runs on each side of the building, supported on a utility
trapeze. Utility drops to each lab bench are made through conduit. The building has a multizone, combination detection and alarm, Class B, two-wire fire alarm system. Smoke detectors
are in elevator lobbies, equipment rooms, and HVAC ducts. Manual pull stations, water flow
switches, horns and bells are connected to a central control panel. The main building and
laboratories are tied to the university central alarm system, while local alarm systems are used in
basement animal rooms.
Seismic Performance of Systems: Although not the main target of this study, the
traditional nonstructural systems of the building, such as mechanical, electrical, and plumbing,
also have an important influence on post-earthquake usability of the building. A visual survey of
these systems was performed by the consulting engineers in February 2002 to determine if they
were, in general, installed in accordance to seismic requirements of the building code. The
purpose of this evaluation was to determine if any severe seismic deficiencies existed that would
override any consideration of performance of the laboratory contents.
The engineering survey (conducted by Rutherford and Chekene) covered the normal
systems associated with initial construction of a laboratory building. They can be categorized as
follows:

Ducts and piping, including HVAC, plumbing, and chemical, both in functional spaces and
in mechanical rooms.

Rooftop mechanical equipment, including chillers.

Floor mounted mechanical equipment, including HVAC and other mechanical.

Floor mounted electrical equipment, including cabinets and transformers.

Tanks, including single and multiple compressed gases and water tanks.

Suspended equipment, including HVAC and electrical.
30
The engineer’s evaluation revealed that the building systems feature an unusually high
level of compliance with code seismic anchorage and bracing requirements. In fact, the level of
anchorage and bracing of nonstructural systems is more complete than what is considered
average for this vintage of building, and low damage levels can be expected, at least in moderate
shaking. However, in general, the seismic bracing installed for the larger pipe systems is judged
relatively ineffective, and could lead to more than expected damage to those systems, as well as a
greater chance of “water damage” to contents. The building walk-through also indicated that the
emergency generator housed in a separate small building near the Southeast corner of the
building was apparently installed after the building was complete and was not provided adequate
seismic protection. Until retrofitted, power from this generator should not be counted on after
moderate to strong shaking.
2.6
Contents: Inventory of Scientific Equipment
The building contents are typical of a wet laboratory: lab benches with storage shelving
above, and very densely packed equipment. The laboratories were designed using three modular
plans for the arrangement of laboratory benches, sinks, storage, and office space (see Figure
2-18). Each of these provides a standard configuration of parallel laboratory benches against or
between walls. Those set against a wall have cabinets or shelves above the bench, attached to
the wall. Heavy fixed equipment, such as a fume hood, is typically located against the wall. The
benches within the open space are designed as a back-to-back set of laboratory benches with a
sink or other shared feature at the end, and open shelves built on a Unistrut system above.
Research offices are separated from the main laboratory space by partitions and typically
accessed from the internal corridor. This modular laboratory design seems to work well in the
biological sciences where the research depends on a conventional arrangement of bench-top
equipment, microscopes, and computers combined with refrigerators and freezers for storage of
samples.
31
Figure 2-18. Typical laboratory layouts
There are approximately 10,500 items of furniture (lab benches, wall shelves, desk units,
etc.) and equipment (tanks, cylinders, microscopes, computers, and other bench-top equipment,
32
as well as heavy equipment such as refrigerators, freezers, incubators, fume hoods, etc.) Fortyfour percent of the contents can be classified as furniture and 56% is equipment.
Although there may be many different types of microscopes, roto-baths, freezers, etc.,
there are only about 15 different types of furniture and 95 different categories of equipment in
the building. The top five most numerous furniture types, and the top fifteen most numerous
equipment types are shown in Table 2-5. It is interesting to note that if all the standard types of
computer equipment (CPUs, monitors, printers, fax and copy machines) are added together,
these represent some 1300 items (12% of the total and 22% of the equipment). Refrigerators and
freezers, together comprise 4.5% of the total and 8% of the equipment, followed by centrifuges
and microscopes, each representing about 3% of the total contents and 5% of the equipment.
33
Table 2-5. Common types of furniture and equipment in the laboratories.
Furniture type
Number of items
Shelving unit
Workbench
Cabinet
Desk
File cabinet
Other
Total furniture
2,022
674
614
553
385
352
4,600
Equipment type
Number of items
Monitor
CPU
Refrigerator
Centrifuge
Microscope
Equipment rack
Mixer
Printer
Water bath
Power supply
Incubator
Gas cylinder
Freezer
Fume hood
Stirrer
Other
Total equipment
557
544
349
319
279
273
266
212
141
139
131
122
119
104
102
2,243
5,900
Each laboratory was documented in drawings and in a database during the spring and
summer of 2001. The plans and equipment lists of two sample laboratories are described in
Figure 2-19 through Figure 2-30, with addition detail provided in Table 2-6 and Table 2-7. The
detailed information presented in this report represents a snapshot in time. Equipment may have
been added or changed. Some laboratories may have moved since then. However, the goal of
the research—to understand the issues in a nonstructural retrofit of a laboratory building—is not
dependant on an exact representation of each laboratory, but on the aggregate understanding of
the patterns of equipment use and the typical conditions in laboratory buildings.
34
Figure 2-19. Sample laboratory #1 floor plan
35
Figure 2-20. Sample laboratory #1 floor plan, cont.
36
Figure 2-21. Sample laboratory #1 relationship between lab, core, and animal space
37
Figure 2-22. Sample laboratory #1 three-dimensional diagram with photos
38
Figure 2-23. Sample laboratory #1 three-dimensional diagram with photos (continued)
39
Figure 2-24. Sample laboratory #1, examples of critical items
40
Table 2-6. Sample laboratory #1, critical items.
Room
Sub
Key
Equipment
341
341
341
343
343
343
343
343
343
343
343
343
343
345
345
345
345
345
345
345
345
345
345
C
C
C
C
A
A
A
B
P
WS-1-2
I
K
M
N
C
G
J
K
L
M
B
E
E
M
N
WB-2
WS-3
WS-3
WS-4
WS-4
Low Temp Incubator
Fume Hood
Open Shelving
CPU
Monitor
CPU
Monitor
Incubator
Refrigerator
Incubator
Freezer
Centrifuge
Refrigerator
Refrigerator
Fume Hood
Fume Hood
Refrigerator
Refrigerator
Work Bench
Open Shelving
Open Shelving
Open Shelving
Open Shelving
Life safety
Value
Importance
B
C
A/SL
B
B
B
B
C
D*
D
D
D
D
D
C
C
D
D
A
A/SL
A/SL
A/SL
A/SL
1
2
1
3
1
3
1
1
1
1
2
3
1
1
2
2
1
2
1
1
1
1
1
Y
Chem. hazard
CH/A
CH/A
Y
Y
Y
Y
Y
Y
Y
CH/A
CH/A
CH/A
CH/A
CH/A
CH/A
CH/A
Note: Items designated as life safety, valuable, important, and chemical-hazard are 14% of local
laboratory contents. (Critical items may also be located in related spaces.)
* Only life-safety category D is shown in Figure 21.
41
Figure 2-25. Sample laboratory #2, floor plan
42
Figure 2-26. Sample laboratory #2 floor plan (cont.)
43
Figure 2-27. Sample laboratory #2, relationship between lab, core, and animal space
44
Figure 2-28. Sample laboratory #2, three-dimensional diagram with photos
45
Figure 2-29. Sample laboratory #2, three-dimensional diagram with photos (cont.)
46
Figure 2-30. Sample laboratory #2, examples of critical items
47
Figure 2-31. Sample laboratory #2, critical items
48
Table 2-7. Sample laboratory #2, critical items
Room
Sub
Key
Equipment
Life Safety
Value
Importance
261
261
261
261
261
261
261
261
261
265
265
265
265
265
269/271
269/271
244
B
B
B
C
C
Core
I
N
Q
F
O
O
E
F
OS 1-5
A
D
E
F
R
B
C
H
D*
C
D
B
C
C
D
C
A/SL
C
C
D
D
C
D
D
C
5
6
1
1
2
2
2
1
1
4
2
2
2
2
1
1
2
244
Core
J
C
2
Y
244
Core
K
C
2
Y
244
244
244
244
248
248
248
248
248
248
26
26
690
690
690
690
690
690
Core
Core
Core
Core
Core
Core
Core
Core
Core
Core
Basemt.
Basemt.
Basemt.
Basemt.
Basemt.
Basemt.
Basemt.
Basemt.
I
L
B
C
G
B
C
E
K
L
B
F-H
A-C
A-C
A-C
A-E
A-B
A-B
Con Focal Microscope
DNA Sequencer
Cyrotone
Cabinet
Fume Hood
Fume Hood
Freezer
Gas Cylinder
Open Shelving
Centrifuge
Freezer –20
Refrigerator
Refrigerator
Fume Hood
Refrigerator
Refrigerator
BioCabinet/
Fume Hood
BioCabinet/
Fume Hood
BioCabinet/
Fume Hood
Freezer
Incubator
Incubator
Centrifuge
Freezer
Freezer
Freezer
Freezer
Water Tank
Water Tank
Racks
Racks
Racks
Racks
Racks
Racks
Racks
Racks
D
D
D
D
C
D
D
D
D
D
B
B
C
C
C
C
C
C
2
2
2
2
2
2
2
2
1
1
1
1
1
1
1
1
1
1
Chem haz
CH/A
CH/A
CH/A
CH/A
CH/A
Y
CH/A
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Y
Note: items designated as life safety, valuable, important, and chemical hazard are 13% of local
lab contents. Critical items in related spaces are included below.
Value: The database listing each item was assembled by drawing and photographing
each laboratory in order to document the equipment’s location within the laboratory. The type of
equipment was noted as well as the manufacturer, model number, size, and estimated weight.
Using the campus equipment purchase records the value of each item was coded on a 1 to 7 scale
49
as outlined in Table 2-8. This categorization allowed the data to be sorted by ranges of value,
rather than exact purchase prices.
Table 2-8. Value-group designations
Designation
0
1
2
3
4
5
6
7
Range of value
Room Empty
Zero to $5,000
$5,000 to $10,000
$10,000 to $20,000
$20,000 to $50,000
$50,000 to $100,000
$100,000 to $250,000
$250,000 to $1,000,000
Average cost per item
$0
$3,000
$7,500
$15,000
$35,000
$75,000
$175,000
$400,000
The total value of the equipment in the building is about $21 million. This represents all
scheduled equipment costing over $1,500 (BETS, 2001). Other equipment (valued less than
$1,500) could add another 10% to the total value. Ninety percent of the items are valued
between $2,000 and $5,000 (see Figure 29). The majority of these are the bench-top
microscopes, stirrers, mixers, and other small equipment. The remaining 10% of the equipment
range in value from $10,000 to $1 million. There are only 3 confocal microscopes in the
building—valued at $500,000 each—serving unique research needs. Since completing the
inventory, however, three laser tables with visualization computers, valued at $1.2 million, have
been purchased by researchers.
[Figure 29 near here]
Life Safety: Two assessments were made to evaluate the degree to which each item
represented a life-safety hazard. The first evaluated direct life safety, that is, risk of injury from
the impact of a moving/falling object. Life safety can be threatened by heavy objects falling or
tipping directly onto occupants, or by sliding or tipping into a position to block egress from a
work area. The second assessment was on indirect life safety issues, that is, from the release of
hazardous materials, either directly by broken containment, or by two or more released materials
combining to create a hazardous substance or fire.
The first assessment of life safety hazards was done by Rutherford and Chekene,
consulting engineers. Each item in the database was coded as a potential falling hazard. The
categories described in Table 6 are aimed at prevention of serious injury. Being struck by a 20
50
pound object falling from 5 feet or more from the floor clearly could cause a death, but is more
likely to cause a serious injury. The break-point of 20 pounds is somewhat arbitrary, but based
on the State of California’s code governing hospital construction.
The matrix in Table 2-9 demonstrates how the life safety priority and the risk will
increase from the upper left to the lower right. The locations that qualified as low, medium, or
high risk were defined for consistent application. For example, a low risk item might be floormounted with a low aspect ratio, while a high risk item could be directly overhead. Note that the
weight cutoffs are arbitrary and must be set by judgment. Those shown here are weights used for
similar priority settings in building codes.
Table 2-9. Life-safety priority levels assigned to furniture and equipment
Location
Weight
< 20 pounds
20-400 pounds
> 400 pounds
Low
Medium
High
A
B
C
B
C
C
C
C
D
Importance levels A through D in Table 2-9 are defined as follows:
A:
No specific anchorage requirement; low priority.
B:
Anchorage using a standard commercially available product, installed by users or
maintenance staff; moderate priority
C:
Anchorage using a standardized conceptual detail, customized by trained staff or
professionals for the particular condition; high priority
D:
Anchorage designed by professionals for the specific situation; highest priority
For the assessment of indirect life safety hazards, a specialist from the campus office of
Environment, Health and Safety (EH&S) visited each laboratory and noted potential associated
chemical and biological hazards. This review was focused on conditions which could be
hazardous in the event of an earthquake, separate from the regular EH&S inspections conducted
to enforce basic safety standards. In the review undertaken for this study, associated chemical
hazards were noted when hazardous materials could cause contamination, fire, release of
51
poisonous gasses, or other life-threatening conditions. Table 2-10 provides list of the conditions
cited. Overall there were 333 conditions cited. These were coded as to whether the remediation
was administrative (e.g. moving the substance to a safer location) or whether some retrofit was
required.
52
Table 2-10. Chemical hazard conditions noted in the laboratories
Code
Description
2C Secondary
containment
required
A/B Acids stored
with bases
CI No chemical
inventory
Explanation
Liquids greater than 1 gallon in size must have a chemically compatible
secondary container that could prevent a potential spill from spreading to
other chemicals or to the environment.
Acids and bases could mix with a violent reaction and/or a release of
poisonous gas.
Federal, state, and local laws require that all hazardous materials
(including all compressed gases) must be registered in a chemical
inventory. The EH&S Chemical Inventory database is the UC Berkeley
repository of this information which is essential for appropriate
emergency response actions.
Hazardous chemicals used or stored in any machine or device that could
potentially spill during an earthquake due to the device rupturing or
falling. Secure the chemicals or device to prevent a spill.
Flammable liquids should be secured and/or secondarily contained to
avoid the potential for them falling or spilling near an ignition source
(including electrical equipment).
Oxidizers will ignite flammables (sometimes explosively) if they are
mixed.
CP Chemical
process spill
potential
FL Flammable
liquids may
spill/ignite
F/O Flammables
stored with
oxidizers
GC Gas cylinder not Gas cylinders must be secured with double chains or non-combustible
secured
straps to prevent them from falling and rupturing. If a compressed gas
cylinder valve breaks off, the cylinder could "torpedo" with a high force.
HiC Corrosives
Corrosives could damage eyes and cause blindness if spilled. Store
above eye-level corrosives below eye-level.
HiR Reactives stored Reactive chemicals can ignite or explode if shocked by a fall (or if
high above
heated while confined). Store reactives in a secure, low-to-ground
ground
location to minimize the potential fall force.
HT Highly toxic
Highly toxic chemicals may be fatally poisonous if spilled. Minimize
chemical spill
the spill potential for highly toxic chemicals by storing them in a secure,
potential
low-to-ground location.
OC Open container All hazardous chemical containers (including waste collection bottles)
must be closed when not actively in use.
Seg Chemicals not Store chemicals segregated by hazard characteristics so that
segregated by
incompatible chemicals are separated and will not mix. Do not store
hazard
incompatible chemicals alphabetically.
WR Water reactive Water reactive chemicals can react violently or explosively with water or
near water
other aqueous chemical solutions. Store these chemicals away from
source
sources of water, including water pipes and fire sprinklers.
53
In the database, each item was coded as a life-safety priority, A, B, C, or D, or as a
chemical hazard requiring administrative attention (Ch-A) or requiring an actual retrofit (Ch-R).
The engineers also noted the items which had a shelf lip, because so many of the life safety
issues were related to items on shelves. This size is not a function of any seismic anchorage
requirements in the building code. The typical shelf lip height derives from life-safety
requirements normally enforced by the fire marshal to protect against fire hazards (LBNL, 2000).
In the UC Science Building, there are four types of items typically found on the shelves:
glassware, chemicals, equipment and books. Although we did not inventory these, observation
by the research team and building occupants suggest that the shelf contents are equally divided
among these four groups.
Figure 30 provides the number and percent of items in each life safety category, as well
as the number and percent of items in each category which are related to shelf lips. While more
than one third (36%) of the items are categorized C, D, or Ch, only 4% are a function of
inadequate shelf lips.
[Figure 30 near here.]
Importance: As the surveys of the laboratories were conducted, the study team spoke
with researchers in the laboratories, to get an understanding of the kind of work they did. These
conversations led to a more formal survey of research faculty and/or their lab managers to
ascertain which of the items in their laboratories were critical to their research. The survey
provided examples of importance measures (see Table 2-11), and asked researchers to list the
equipment, data, animals, and storage systems that were critical to their ability to work.
Responses were received from more than 50% of the laboratories. For those that did not respond
after repeated requests, we used the pre-existing list of items to be checked in an emergency
situation (on file with the building manager) as a guide to what was considered important in that
lab. Animals which have been genetically designed and bred, or those whose conditions would
be difficult to replicate were also designated as important. Further, all shared equipment in the
building core was designated as important because it serves numerous laboratories. Overall,
about 500 items are rated as critical to continuing research. Of these, about 30% are genetically
designed animals, 20% are refrigerators and freezers containing fragile cell lines, 15% are
54
microscopes, and 15% are computers (referred to as CPUs in the survey) where current data is
stored.
Table 2-11. Importance measures for equipment and materials in laboratories.
Measure
Equipment replacement cost
Equipment replacement time (weeks, months)
Data or material replacement cost
Data or material replacement time (weeks, months)
Irreplaceability
Interruption sensitivity (can tolerate none, or very little)
Loss of research benefits (income, salutary applications)
Related hazards that may occasion long clean-up periods (chemicals, biohazard)
55
2.7
Identification of critical factors affecting inventory: life safety, chemical
hazard, importance, and value
Together, the detailed drawings documenting the equipment in each laboratory and the
database provide a mechanism for understanding the number and types of equipment as well as
the issues involved in planning for the seismic retrofit of laboratory contents. Table 2-12
provides a complete list of all the categories of data about each item. Several factors appear to
be critical to the ongoing function of a research laboratory. These are importance, value, life
safety, and associated chemical hazards.
Any item designated important by the researcher is essential to continued research—
whether it is an animal or a cell line that took years to develop or whether it is customized
equipment. Similarly, high value equipment may require a long lead time for purchase, or may
require specialized equipment funding not always available to researchers. Life safety
designations C or D imply real hazards to the occupants of the laboratories. Likewise, chemical
hazards affect not only the occupants, but also the larger community. Equally important, a
chemical spill could add months or years to a building being out of service after an earthquake
(even if the building has no damage) as a result of the time needed for clean-up.
56
Table 2-12. Data categories for the furniture and equipment inventory
Data category
Lab name
Room number
Sub-number
Equipment key (to drawings)
Equipment name
Equipment manufacturer*
Equipment model number*
Equipment information*
Weight (estimate if greater than 50 pounds)
Life safety hazard code
Chemical hazard (yes/no)**
Estimated value (by category)
Importance (yes/no)
Retrofit attempt (yes/no)
Quantity
*
Included when available
** If chemical hazard is noted, additional data includes: finding number,
location, lab name, date, finding code, and a detailed description of the
conditions.
Only 1,287 items (about 10%) are tagged as important, chemical hazard, and life safety
category D. With life safety category C, the total goes to 3,993 items. The high-value category
was found to be a subset of those designated important. There are only 65 items in the building
valued greater than $20,000. Thus, the combination of important, chemical hazard, life-safety
hazard C and D, and value category 4 through 7, puts the number of items that could be
considered critical to operations at 40% of the total contents in the building (see Figure 32).
Thus, 40% of the contents are tools and specimens that are critical to research, valuable and hard
to replace, a threat to life safety, or some combination. If this subset of items were to be
seismically anchored, the overall benefit to limiting downtime would be significant. These
should become a first priority in any plan to retrofit contents. Although it may be ideal to
consider anchoring every item in a laboratory, it may not be practical or cost effective.
[Figure 32 near here.]
The research team was initially surprised by the fact that 83% of the equipment in the
building had a replacement cost of less than $10,000. However, the majority of bench-top
57
equipment in biological research is small, and lab staff and students need many more ordinary
microscopes and mixers than they need high-tech optics.
Although we have powerful examples of devastating losses to laboratory contents in past
earthquakes, such as the loss of the Chemistry Building at Cal State Northridge in 1994, there is
no statistical data on contents losses from past earthquakes. Ideally, we would like to develop a
cost/benefit calculation to make the case for contents retrofitting, but there is no fragility
information available to do such analysis. Preliminary results from shake table tests of bench-top
equipment suggest that the earthquake motions are amplified one to two times at the bench, and
that unanchored objects will slide into other equipment or off the bench (Hutchinson, 2003). The
tests on heavy equipment suggest that tall refrigerators and freezers will slide between 12 and 18
inches and may overturn if one of the legs buckles (Makris, 2003).
2.8
Implications of using critical factors to target retrofits
In evaluating the kind of equipment and furnishings that populate the laboratories of the
UC Science Building, the three categories of critical factors—important, valuable, and a lifesafety concern—are the obvious first priority for a retrofit program. This applies not only to this
building, but also to any other science laboratory. It would be possible for any researcher to
identify the critical items in his or her laboratory in terms of their importance to the research,
their value, or the length of time needed to replace a unique item. This listing could be combined
with an assessment of potential life safety hazards to create a first priority retrofit list. Other
items could be added as the laboratory users deemed necessary.
The obvious response to the threat of damage from earthquakes is to provide restraint for
all contents in the laboratory environment. There are two primary reasons why this may not
always be necessary or appropriate: 1) cost and, 2) the potential effects of seismic restraint on the
function of the element or the lab as a whole. Restraining a portable bench-top instrument, even
with a quick-release system to facilitate changes in location, may reduce efficiency and may not
be used by staff. Similarly, providing a docking station for wheeled equipment may take up
space and inhibit movement in the room.
58
A preliminary estimate of the cost of providing seismic protection for every item of a
typical laboratory ranges from $10 to $16 per square foot of laboratory space plus a percentage
for contractor overhead and profit (Comerio and Stallmeyer, 2001). Given cost and functionality
concerns, it is prudent to prioritize contents with respect to their potential to cause losses. It is
recommended here that life-safety issues be considered first, then importance, and value third,
although any order could be used to evaluate the contents of a laboratory.
2.9
Prior anchorage
In the case-study building the research team observed a number of existing non-structural
seismic restraints on furnishings and equipment. Most of these were funded by the QuakeBracing Assistance Program (Q-Brace), which allowed individual units to reinforce bookshelves,
file cabinets, and other heavy equipment that could pose a life safety risk during an earthquake.
The number of items with existing restraints was documented and evaluated by Rutherford and
Chekene. Most of the existing non-structural seismic restraints fell into the following three
categories:
1. Refrigerators, incubators, racks, and other large and heavy equipment had been attached
to walls, strongbacks, or each other with chains. Manual latches were also added to some
refrigerators or cabinets to prevent doors from opening.
2. Lips, elastic cords, or metal plates had been added to some cabinets or open shelves in
order to prevent chemicals, lab samples, or books from falling. Some floor mounted
bookcases and cabinets had been attached directly to shear walls or partitions with
screws, nails, or bolts.
3. Commercial fabric tethers had been attached with adhesive to some computers,
microscopes, microwave ovens, and other small items to secure them to desks or shelves.
See Table 2-13.
59
Table 2-13. Equipment with prior retrofits
Name
Quantity Retrofit
Environmental chamber
Low temp. incubator
Freezer
Dna sequencer
Liquid tank
Gas cylinder
Biological safety cabinet
Refrigerator
Incubator
Bookcase
Gravity convection incubator
Ice maker
Cryogenic container
Electronic rack
Shelving unit
Cabinet
Cpu
Monitor
Other
TOTAL
2
13
119
6
9
122
56
349
131
181
13
8
36
60
234
614
486
499
2
6
48
2
3
30
12
70
21
28
2
1
4
3
10
23
14
10
27
316
Two concerns are raised by the number of prior retrofits in the building. First, is the
effectiveness of the existing attachments and second is the cost if these restraints need to be
redone. In sum, the engineers questioned the effectiveness of the restraint cables attached to
most heavy equipment. They were concerned with the adequacy of the connection and the
effectiveness of the partitions to serve as an adequate restraint. They were similarly concerned
about the effectiveness of many shelf lips to restrain objects with higher centers of gravity. The
fabric tethers were not always installed correctly, and the adhesives used my not perform well
over time.
It would be very difficult to estimate the adequacy of the existing anchors without
detailed testing of the specific conditions. In the PEER shake table tests of heavy equipment
(Makris, 2003) refrigerators and freezers were attached with chains to the partition wall in a
subset of the tests. Preliminary results indicate that the restraints were able to reduce
displacements, but the anchors pulled loose from the wall. Based on the tests and engineering
60
calculations, it is our judgment that the existing anchors are not well detailed and should
eventually be replaced with the kinds of details suggested in this report.
2.10 Summary
The analysis of the contents of the UC Science Building brings out a number of issues
that were not evident in the review of individual laboratories. First, while laboratory space is
more than eighty percent of the net useable area, the laboratories are only about half the overall
gross square footage of the building. Thus, the valuable contents are concentrated in about 50%
of the building area. Second, the laboratory contents are almost equally divided between
furnishings and equipment. Shelving units, computers, and heavy equipment such are
refrigerators, freezers, and centrifuges comprise the majority of the items in the building. Third,
items of critical importance to researchers are the refrigerators and freezers containing biological
samples, the cages and racks housing animals, and the computers where current research data is
stored.
When considering the potential threat of damage from earthquakes, the first concern is
the life safety of the building occupants. A second concern is the protection of data and ongoing
experiments. A third concern is the protection of valuable or hard-to-get equipment. Taken
together, these concerns suggest that is possible to prioritize any building’s contents with respect
to their potential to cause losses. In the UC Science Building, heavy equipment such as
refrigerators and freezers are top priority for seismic anchoring because they are a life safety
hazard, they contain critical contents, and there are many located throughout the building.
Equipment racks, animal cage racks, and other heavy equipment are similar in hazard level,
importance, and number. Equally significant is the size of the shelf lips. Shelving units are the
single largest category of all the building contents. Those that contain chemicals and glassware
can represent a serious hazard, and the anchorage of the shelf itself and the restraint of the
contents are a key issue.
Based on the observations of the number and type of items in the UC Science Building, it
seems appropriate to develop an evaluation system that will result in a priority rating system for
all contents based on life safety first, importance, second, and dollar value, third. Although
considerable judgment will be required by the users to place the contents of their laboratories
61
into one or more priority levels, the systematic approach developed here will assist the process.
In the UC Science Building, we found that only about 40% of the contents required anchorage if
these criteria were applied.
REFERENCES
62
3. Components of Methodology to be Tested
Mary C. Comerio, University of California, Berkeley
Case Specific Summary of Methodology

Global methodology (by reference – presumes that a methodology paper will be
available)

Components applicable to testbed

Major challenges
Deliverables:


Draft of chapter by April 15, 2002
Authors: Comerio, Mosalam, Fillipou, Makris, Hutchison, Ellwood
63
4. Seismic Hazard Analysis
Paul Somerville, URS Corporation, Pasadena, CA
4.1
Conventional Free-Field Hazard Analysis
Uniform hazard spectra. Uniform hazard spectra for the site (Table 1) were generated
for the UC Berkeley Seismic Guidelines Project by URS (2000). They were calculated for rock
site conditions using the average of the following ground motion models:

Abrahamson and Silva (1997). Rock and shallow soil (up to 20 meters) over rock

Idriss (1991, 1994). Rock

Sadigh et al. (1997). Rock within about 1 meter of the surface; often weathered rock.
Of these three relations, the Abrahamson and Silva model is most compatible with the
site conditions at the UC Science Building site.
The URS uniform hazard spectra have not been adopted, and will probably be revised to
incorporate the new USGS Working Group hazard model that was released in November 2001.
To avoid the dissemination of spectra that have not been adopted and will probably be revised,
the spectra are not provided in this report aside from the 0.45 sec spectral acceleration given in
Table 4-1. If there is a need for investigators to see the spectra, they should contact Paul
Somerville.
Table 4-1. Site uniform hazard spectra, 5% damping, Sa at 0.45 seconds.
Hazard Level
Sa at 0.45 sec M mode R mode
50% in 50 years
0.710
5.5 – 6.0
1 km
10% in 50 years
1.625
6.5 – 7.0
1 km
2% in 50 years
2.740
6.5 – 7.0
1 km
64
Deaggregation of the hazard. The deaggregation of the hazard at a period of 0.3 seconds
is given in Table 1. At all three hazard levels, the hazard is dominated by earthquakes on the
Hayward fault, which is located about 1 km east of the site. The Hayward fault is a strike-slip
fault that has the potential to generate earthquakes having magnitudes as large as 7. For the 50%
in 50 year hazard level, the largest contributions come from earthquakes in the magnitude range
of 5.5 to 6.0. For both the 10% in 50 year and 2% in 50 year levels, the largest contributions
come from magnitudes in the range of 6.5 to 7.0. The higher ground motions for the 2% in 50
year probability level reflect not larger magnitudes (the maximum magnitude earthquake on the
Hayward fault is 7.0), but higher ground motion levels for the same magnitude (larger number of
standard deviations above the mean).
Process of selecting ground-motion recordings. The recordings listed in Tables 2 and 3
were selected to satisfy to the extent possible the magnitude and distance combinations listed in
Table 1 for strike-slip earthquakes on SC sites. In general, it was not easy to satisfy these
requirements, and none of the sets of time histories is larger than the minimum requirement of
ten. It was not possible to satisfy the distance requirement exactly, but all of the selected
recordings are within about 10 km of the fault. In all but a few cases, the recordings are from
sites that are classified as SC, but in general these site classifications are not based on shear wave
velocity measurements. If there were a much larger set of recordings to choose from, it is likely
that the sets of selected recordings would have less variability than the sets that are provided.
Time histories. The time histories used to represent 50% exceedance probability of Sa at
this site in 50 years are listed in Table 4-2. Three of the recordings are from sites that are
classified as SD. No attempt was made to adjust these recordings for SC site conditions. Two of
the recordings are from the abutment of the Coyote Lake dam.
The time histories used to represent 10% and 2% exceedance probability of Sa at this site
in 50 years are listed in Table 4-3. The same set of time histories is used to generate the two sets.
This is justified in part by the fact that the magnitude – distance combinations that dominate the
hazard in each case are the same (Table 4-1). However, this ignores the fact that the 2%-in-50year time histories should be drawn from larger ground motion recordings than the 10%-in-50
year time histories. The use of different scaling factors largely but not completely obviates this
shortcoming.
65
Table 4-2. Time histories representing 50% exceedance probability of Sa in 50 years.
Dist
(km)
Site
Coyote Lake Dam abutment
Gilroy #6
4.0
1.2
C
C
1.395 Liu & Helmberger
0.999 (1983)
6.0
Temblor
Array #5
Array #8
4.4
3.7
8.0
C
D
D
1.143 Cloud & Perez
0.978 (1967)
2.302
Livermore
27 Jan 1980
5.5
Fagundes Ranch
Morgan Territory Park
4.1
8.1
D
C
1.644 Boatwright &
2.958 Boore (1983)
Morgan Hill
24 Apr 1984
6.2
Coyote Lake Dam abutment
Anderson Dam Downstream
Halls Valley
0.1
4.5
2.5
C
C
C
0.673 Hartzell & Heaton
0.572 (1986)
1.362
Earthquake
Mw
Station
Coyote Lake
8 Jun 1979
5.7
Parkfield
27 Jun 1966
Scale Reference
Table 4-3. Time histories representing 10% and 2% exceedance probability of Sa in 50 years.
Earthquake
Mw
Station
Dist Site
(km)
Scale,
10/50
Scale,
2/50
Reference
Loma Prieta
17 Oct 1989
7.0
Los Gatos
Presentation Center
Saratoga Aloha Ave
Corralitos
Gavilan College
Gilroy historic
3.5
C
1.016
1.713
Wald et al.
(1991)
8.3
3.4
9.5
?
C
C
C
C
2.653
1.394
2.097
2.319
4.473
2.350
3.535
3.910
Kobe, Japan
17 Jan 1995
6.9
Kobe JMA
0.5
C
0.912
1.537
Wald
(1996)
Tottori, Japan
6 Oct 2000
6.6
Kofu
Hino
10.0
1.0
C
C
1.039
0.827
1.751
1.395
K-net
Kik-net
Erzincan Turkey
13 Mar 1992
6.7
Erzincan
1.8
C*
2.455
4.139
EERI
(1993)
There is a remarkable sparsity of appropriate recordings on rock from strike-slip
California earthquakes in the magnitude range of 6.5 to 7. The recording that would nominally
appear to be the best representations of a Hayward fault earthquake is the recording of the Kobe
earthquake. However, the rheology of the faults that produced the Kobe earthquake may be quite
different from that of the Hayward fault, which has been described by Bergmann et al. (2000).
66
The Kofu recording of the Tottori earthquake was obtained at a K-net site whose soil and
seismic wave velocity profiles are known to bedrock at a depth of 10 km (Figure 4-1). The Hino
recording of the Tottori earthquake was obtained at a Kik-net site whose soil and seismic wave
velocity profiles are known to a depth of 100 meters (Figure 4-2). The Hino site consists of 10
meters of sand and gravel overlying weathered granite. The spectral peak at a period of about 0.7
second is interpreted as indicating strong non-linear effects. The ground motion level at the Kofu
site was apparently not high enough to cause similar nonlinear effects at Kofu, whose soil also
has higher shear wave velocity.
Figure 4-1. Soil Profile at K-net Site Kofu (TTR007)
67
Figure 4-2. Soil Profile at Kik-net Site Hino (TTRH02)
68
The Erzincan recording of the Erzincan earthquake was recorded on deep alluvium
(EERI, 1993). It was spectrally modified to represent a rock site recording. The target spectrum
for the spectral matching was obtained by scaling the recorded spectrum by the ratio of rock to
soil in the Abrahamson and Silva (1997) ground-motion relations. The resulting response
spectrum is very compatible with the uniform hazard spectrum. The rheology of the Anatolia
fault on which the Erzincan earthquake occurred is considered to be potentially quite compatible
with that of the Hayward fault. The Lexington Dam record was obtained on the rock abutment of
Lexington Dam. Using this recording as a representation of the input ground motions at the base
of the dam, several investigators have successfully modeled the recordings from the crest of the
dam (Mejia et al., 1992; Makdisi et al., 1994), implying that the abutment recording is not
severely contaminated by dam interaction effects.
Near-fault rupture directivity effects in the ground-motion recordings. The selected
ground-motion time histories were all recorded sufficiently close to the fault to contain rupture
directivity effects, although not all of the recordings are as close as the UC Science Building is to
the Hayward fault. In strike-slip earthquakes, forward rupture directivity (propagation of rupture
horizontally towards the recording station) produces a pulse of intermediate or long period
ground motion whose particle motion is orientated in the direction normal to the strike of the
fault (Somerville et al., 1997; Somerville, 1998; Somerville et al., 2000). This pulse is
manifested by a response spectrum that is larger on the fault-normal component than on the
fault-parallel component at periods longer than about 0.5 seconds. There are indications that the
period of the pulse may increase with magnitude (Somerville, 2000). If the earthquake ruptures
away from the recording station, then rupture directivity effects are less pronounced. Some of the
selected recordings contain strong forward rupture directivity pulses, and others do not.
Near the UC Berkeley campus, the Hayward fault has a strike of N 34 W. The
longitudinal axis of the UC Science Building has an azimuth of N 16.5 W. The longitudinal axis
is thus oriented 17.5 degrees clockwise from the fault strike, and the transverse axis is oriented
17.5 degrees clockwise from the fault normal direction. This rotation means that the two
components lie about 40% of the way between the fault normal and fault parallel orientation, in
which they are expected to be maximally different, and a rotation 45 degrees off fault strike, in
which they are expected to be maximally similar.
69
All of the recorded time histories were rotated to the strike normal and strike parallel
directions, and then rotated clockwise by 17.5 degrees to produce the longitudinal and transverse
components. Generally, if the recording contains forward rupture directivity effects, its
transverse component is expected to be larger than its longitudinal component for peak velocity
and peak displacement, and for spectral accelerations having periods longer than about 0.5
seconds. This expectation is generally borne out in the recordings.
Site effects in the ground-motion recordings. The shallow, stiff soil conditions at the
site have the potential of causing strong resonances in the ground motions. Some of the
recordings contain resonances at periods shorter than 0.45 seconds that may be attributable to
such effects. Many of the recordings have response spectral amplitudes that are larger than the
uniform hazard spectrum at periods longer than 0.45 seconds. In many cases, these may be
attributable to forward rupture directivity effects.
In near-fault recordings on soil sites, it may be difficult to separate site response effects
from rupture directivity effects. As shown by Rodriguez-Marek (2000), the effect of the soil
layer is generally to increase both the peak velocity and the period relative to the input rock
motion. The amount of the increase depends on the level of the input motion, and the thickness
and physical properties of the soil layer. The soil layer may thus generate effects that resemble
those of near fault rupture directivity.
Scaling and variability of the ground-motion recordings. For each set of recordings, a
scaling factor was found by taking the lognormal average of the two horizontal components at a
period of 0.45 seconds, and dividing it into the uniform hazard spectrum. This scaling factor was
then applied to all three components of the recording. This scaling procedure preserves the
relative scaling between the three components of the recording. Consequently, the transverse
component is larger than the longitudinal component at longer periods for many of the
recordings, because of forward rupture directivity effects.
The variability in the ground motion recordings for each component for each ground
motion level is shown in Figure 4-3 and Figure 4-4 for the horizontal and vertical components,
respectively. These figures show the median and plus and minus one standard deviation level for
each set of ten recordings. As pointed out above, the variability may be artificially large, because
the relatively small number of suitable recordings made it difficult to select recordings that
faithfully represent the earthquake magnitudes, distances and site conditions that pertain to the
70
site. The variability is not zero at 0.45 seconds for the horizontal components because the scaling
was based on the average of the two horizontal components. For the 50%-in-50-year time
histories, the largest variability occurs at periods less than 0.45 seconds due to variability in
shallow soil response. For the 10%-in-50-year and 2%-in-50 year time histories, there is large
variability in the transverse (approximately fault normal) component at periods longer than 0.45
seconds due to variability in forward rupture directivity effects, which are present in some
recordings and absent in others.
71
Figure 4-3. Variability in the ground motions of each set of ten scaled recordings for the
longitudinal and transverse components for each of three ground motion levels
72
Figure 4-4. Variability in the ground motions of each set of ten scaled recordings for the vertical
component for each of three ground motion levels
73
Comparison of scaled recording spectra with the uniform hazard spectra. Figure 4-5,
and Figure 4-6 show the longitudinal and transverse response spectra averaged over the ten
recordings for the three ground-motion levels. For all three ground-motion levels, the average
response spectra of the recordings are lower than the uniform hazard response spectra at periods
shorter than 0.45 seconds. This is expected, because the uniform hazard spectra were defined for
rock site conditions, while the recordings are mostly from sites characterized by shallow soil
over rock. The discrepancy is larger for the 10%-in-50-year and 2%-in-50-year response spectra
than for the 50%-in-50 year response spectra. The uniform hazard spectra peak at a period of
about 0.2 seconds, while the recording response spectra peak at a period of about 0.3 to 0.35
seconds. The average longitudinal and transverse response spectra for the ten 50 % in 50 year
time histories are very similar to each other at periods longer than 0.45 seconds, where they
exceed the uniform hazard spectrum.
The average transverse response spectrum is consistently larger than the average
longitudinal response spectrum at periods longer than about 0.6 seconds for both the 10% in 50
year and 2% in 50 year time histories. This difference is presumably attributable to rupture
directivity effects. In the period range of 0.6 to 1.4 seconds, the uniform hazard spectrum lies
between the average transverse and longitudinal components. For periods longer than 1.4
seconds, the average transverse response spectrum is similar to the uniform hazard spectrum, but
the longitudinal response spectrum is significantly lower.
74
Figure 4-5. Comparison of the longitudinal and transverse response spectra averaged over the
ten scaled recordings for the 50% in 50 year ground motion level
75
Figure 4-6. Comparison of the longitudinal and transverse response spectra averaged over the
ten scaled recordings for the 10% in 50 year ground motion level
76
Figure 4-7. Comparison of the longitudinal and transverse response spectra averaged over the
ten scaled recordings for the 2% in 50 year ground motion level
4.2
Free-Field Hazard Analysis and Record Selection Based on “Improved IMs”
Discussion of IM hazard curves
Deliverables: Discussion of “ IM”s for UCS: Makris
77
78
5. Engineering Demand Parameters
Tae-Hyung Lee and Khalid M. Mosalam, University of California, Berkeley
5.1
Structural modeling



Outline of section by May 2002
Draft section by October 2002
Author: Mosalam
General. The computational model of the UCS building is developed using the modeling
capabilities of the software framework of OpenSees. The complete model of the UCS building in
OpenSees is illustrated in Figure 5-1. In this section, description of this modeling is presented
together with a list of the adopted assumptions and the limitations of the modeling process.
79
Beam-column element
node 53
node 28
Rigid element
node 7
Spring element
for soil modeling
y
x
Element 81
Element 89
Hinged support
Rollered support
Figure 5-1. OpenSees model of UCS building
Assumptions and Limitations. The current model of OpenSees focuses on modeling
frame 8 of the UCS building, as identified in Figure 2-1. This model is based on the following
assumptions:

Two-dimensional idealization of the selected frame is considered.

Linear elastic shear force-deformation relationship is chosen for all the used elements in
the model relying on the fact that shear failure will not occur prior to flexure failure.

Reinforcing bars are assumed fully bonded to the surrounding concrete.

The analyzed frame has a tributary area having 101'-6" width, as shown in Figure 2-1.
80
Modeling Shear Wall Elements. All shear wall elements are modeled using one
dimensional beam elements aligned with the centerline of the actual shear wall. For proper
idealization of the geometry, the node at the shear wall centerline and the node at the boundary
of the shear wall (representing one end of a coupling beam) are connected using rigid elements.
This approach of idealizing shear walls is illustrated in Figure 5-2.
Beam-column element
Shear wall
Beam
Column
Rigid element
Figure 5-2. Modeling of shear walls using beam-column elements and rigid elements
Modeling Beam Elements. All elements in the UCS building model are based on
flexibility formulation of beam elements (nonlinearBeamColumn). Each beam element has
two nodes where each node has three degrees of freedom (two translations and one rotation). The
beam element has four monitoring sections with fiber element discretization, as shown in Figure
5-3. In this discretization, distinction is made between the constitutive modeling of the
reinforcing bars, unconfined concrete, and confined concrete. For the reinforcement, a bilinear
stress-strain relationship is used. As for the concrete, the modified Kent-Park stress-strain (with
zero tensile strength) relationships are used.
81
Monitoring sections
y
x
Concrete fiber
Steel fiber
y
z
z
Section
Element
Figure 5-3. Discretization of the element monitoring sections
Boundary Conditions. Flexible supports are used at the foundation level in the vertical
direction using truss elements. These elements represent soil having a modulus of subgrade
reaction of 200 lb/in3. The tributary width of these truss elements included the width of the shear
wall and twice the thickness of the mat foundation. To simulate the characteristic of soil
behavior, ENT (Elastic and No Tension) material in OpenSees material library is adopted. An
element with ENT material has elastic properties in compression and zero tensile strength as
shown in Figure 5-4.
Stress
Modulus of
subgrade reaction
Compression
Deformation
Tension
Figure 5-4. Description of ENT material to simulate soil behavior in OpenSees
82
5.2
Validation of Analytical Models

Validation through component tests (Mosalam, Fillipou) (by October 2002)

Relation to contents testing
Deliverables:



Outline of section by May, 2002
Final report by October 2003
Authors: Mosalam, Fillipou
5.3







1.
2.
3.
4.
5.







Prediction of EDPs
Relevant EDPs for damage assessment, including structural, architectural, MEP, and content
subsystems (Holmes, Mosalam. If this means identification of the EDPs relevant to
nonstructural damage, shouldn’t authors be Holmes, Makris, Pardoen, & Hutchinson?)
Predictions of EDPs from non-deteriorating and deteriorating models (e.g., structure specific
descriptions of EDP/IM, and site specific EDP hazard curves) (Mosalam)
Propagation of uncertainties (this ties in with Section 4.2) (Cornell, and Beck???)
Assessment of adequacy of selected EDPs for determination of $ losses and downtime
(Cornell and Beck???)
Sensitivities? (Der Kiureghian, Conte – not officially on team)
Prediction by means of simplified engineering approaches (Krawinkler???) (Beck?)
Simplifying structural analysis. Requires (1 or 2) and 3:
A “perfect” ground motion GM* exists such that EDP[GM*] = E[EDP[GM]], i.e., a single
structural analysis is required using GM* to estimate mean response, for this hazard level,
category of structure, etc., OR
A “perfect” secondary intensity measure IM* exists such one can select or generate a GM*
with features {IM, IM*}, wit the same features as in (1), AND
A common correlation matrix V[EDP] exists for this class of structures.
If [(1 or 2) and 3], then many sample vectors of EDP can be simulated based on a few
structural analyses.
Research underway or needed to answer 1, 2, and 3
Deliverables:
Outline of section by January 17, 2002 (Cornell borrow from Van Nuys)
List of EDPs and their representation (in the context of EDP/DM/DV evaluation process, i.e.,
central value, measure of dispersion, etc.) to researchers by March 15, 2002 (Mosalam)
Comprehensive EDP/IM data and EDP hazard curves (or other relevant representations) on
web site by August 15, 2002 (Cornell, Mosalam, Fillipou??)
Assessment of adequacy of selected EDPs by December 15, 2002 ( Cornell and ??)
Partial draft by October 1, 2002
Final report by April 2003
Authors: Mosalam, Cornell, Fillipou, and (Der Kiureghian & Conte?)
83
Figure 5-5 shows time histories of spring forces in Element 81 and Element 89 and
horizontal displacement at node 53 due to one of the 50% in 50 years earthquakes recorded at
Gilroy #6 station, Coyote Lake. Element 81 and Element 89 represent soil spring elements at
both ends of the building in Figure 5-1 (Element 81 on the left and Element 89 on the right).
Node 53 is located at the center of the roof, as shown in Figure 5-1. In the vertical axis of the
upper plot in Figure 5-5, negative values represent compression. The gravity load is observed to
be large enough to keep soil springs under compression for the most of the time of the analysis.
Figure 5-6 shows time histories of spring forces in Element 81 and Element 89 due to the same
earthquake but in this case, only half of the total gravity load is applied to observe the behavior
of the soil spring, especially in the tension regime. One can clearly observe, in the tension regime
(positive in the vertical axis), the spring force is zero, while the spring provides the required
resistance in the compression regime.
1000
Spring force, kips
0
-1000
-2000
-3000
-4000
-5000
elem 81
elem 89
-6000
-7000
0
2
4
6
8
10
12
14
8
10
12
14
Time, sec.
3.0
Displacement, in.
2.0
1.0
0.0
-1.0
-2.0
-3.0
-4.0
0
2
4
6
Time, sec
Figure 5-5. Spring forces in soil springs (top) and Roof displacement (bottom) due to 50% in 50
years Coyote Lake earthquake recorded at Gilroy #6 (full gravity load is applied)
84
1000
Spring force, kips
0
-1000
-2000
-3000
elem 81
elem 89
-4000
-5000
0
2
4
6
8
10
12
14
Time, sec.
Figure 5-6. Spring forces in soil springs due to 50% in 50 years Coyote Lake earthquake
recorded at Gilroy #6 (only 50% of the gravity load is applied)
Mass Idealization and Gravity Load. The dead load accounted for the self-weight of the
waffle slab system and the supporting elements, i.e. shear walls and columns. The assumed unit
weight of the concrete is 145 pcf. The computed dead load is 183 psf. Moreover, 25 psf
representing building contents are included as a superimposed dead load. The live load of 100
pcf is assumed according to the original design of the building. The mass of the UCS building is
modeled using lumped masses at the nodes. Nodal masses are directly computed from the dead
load including the superimposed dead load.
Damping Idealization. The damping characteristics of the UCS building is modeled
using mass and stiffness proportional damping with 5% of critical damping for modes 1 and 2.
These modes are estimated from the eigen solution using the initial elastic stiffness matrix as
0.64 and 0.28 seconds.
Solution Strategy. Newmark  -method is used as the time integrator with coefficients
  0.50 and   0.25 . In general, a time step of 1/10 the ground motion time interval is used,
which implied a time step in the range of 0.0005 to 0.001 seconds. The modified NewtonRaphson solution algorithm is utilized for solving the nonlinear system of equilibrium equations.
Ground Motion. Ground acceleration records selected for analyses can be categorized
by the hazard level: 50%, 10%, and 2% probability of occurrence in 50 years. 10 ground
acceleration records in transverse direction per each hazard level were selected because the
frame in 2-D modeling stands in fault-normal direction. Additional two ground acceleration
85
records in longitudinal direction were also considered in analyses for the purpose of the future
shake table tests of the building contents by UCI researchers. The peak ground accelerations and
statistics of ground accelerations selected for analyses are summarized in Table 5-1 and Table
5-2.
Table 5-1. Summary of 50% in 50 years ground accelerations used for analyses
Earthquake
Station
Coyote Lake Coyote Lake Dam abutment
8 Jun 1979
Gilroy #6
Parkfield
27 Jun 1966
Livermore
27 Jan 1980
PGA
(g)
0.386
0.474
Temblor
0.393
Array #5
0.394
Array #8
0.564
Fagundes Ranch
0.386
Morgan Territory Park
0.749
Coyote Lake Dam abutment
0.641
Morgan Hill Anderson Dam
24 Apr 1984 Downstream
Halls Valley
0.257
0.360
Mean (COV*)
*: Coefficient of variation
86
0.460 (32.3%)
Table 5-2. Summary of 10% and 2% in 50 years ground accelerations used for analyses
Station
10% PGA
(g)
2% PGA
(g)
Los Gatos Presentation Center
0.649
1.094
Saratoga Aloha Ave
0.854
1.441
Corralitos
0.529
0.892
Gavilan College
0.664
1.119
Gilroy historic
0.675
1.137
Lexington Dam abutment
(transverse)
0.875
1.475
Lexington Dam abutment
(longitudinal)
0.837
1.412
Kobe, Japan
17 Jan 1995
Kobe JMA (transverse)
0.777
1.310
Kobe JMA (longitudinal)
0.439
0.740
Tottori, Japan
6 Oct 2000
Kofu
0.686
1.157
Hino
0.743
1.253
Erzincan
1.482
2.498
Earthquake
Loma Prieta
17 Oct 1989
Erzincan, Turkey
13 Mar 1992
Mean* (COV*)
0.793 (33.1%) 1.338 (33.1%)
* Statistics of ground accelerations in transverse direction only
Results: Time Histories. The presented results consist of time histories for the floor midpoint displacement and acceleration. These time histories are given as relative to the ground (for
estimation of the structural response) and also as absolute values (for the purpose of the future
shake table tests of the building contents by UCB and UCI researchers). Some of the ground
accelerations induced a numerical problem during the incremental-iterative nonlinear analysis.
These records are listed in Table 5-3 where their resulting time histories are not presented here.
87
Table 5-3. Ground records that induced numerical problem in the nonlinear time-history analyses
Earthquake
Morgan Hill
Station
Coyote Lake Dam Abutment
Halls Valley
Hazard level
50 % in 50 yrs
Los Gatos Presentation Center
Saratoga Aloha Ave
Corralitos
Gavilan College
Loma Prieta
Gilroy historic
Lexington Dam abutment
(transverse)
Lexington Dam abutment
(longitudinal)
Kobe, Japan
Tottori, Japan
Kobe JMA (transverse)
Kobe JMA (longitudinal)
Hino
Erzincan, Turkey Erzincan
88
10 % and 2 %
in 50 yrs
4.0
Displacement, in.
3.0
2.0
1.0
0.0
-1.0
-2.0
-3.0
-4.0
0
5
10
15
20
25
30
20
25
30
20
25
30
Time, sec
4.0
Displacement, in.
3.0
2.0
1.0
0.0
-1.0
-2.0
-3.0
-4.0
0
5
10
15
Time, sec
4.0
Displacement, in.
3.0
2.0
1.0
0.0
-1.0
-2.0
-3.0
-4.0
0
5
10
15
Time, sec
Figure 5-7. Relative displacements of Roof (top), Level 4 (middle), and Level 1 (bottom) due to
50% in 50 years, Coyote Lake, Coyote Lake Dam abutment earthquake
89
Acceleration, g
1.2
1.0
0.8
0.6
0.4
0.2
0.0
-0.2
-0.4
-0.6
-0.8
-1.0
0
5
10
15
20
25
30
20
25
30
20
25
30
Acceleration, g
Time, sec
1.2
1.0
0.8
0.6
0.4
0.2
0.0
-0.2
-0.4
-0.6
-0.8
-1.0
0
5
10
15
Acceleration, g
Time, sec
1.2
1.0
0.8
0.6
0.4
0.2
0.0
-0.2
-0.4
-0.6
-0.8
-1.0
0
5
10
15
Time, sec
Figure 5-8. Relative accelerations of Roof (top), Level 4 (middle), and Level 1 (bottom) due to
50% in 50 years, Coyote Lake, Coyote Lake Dam abutment earthquake
90
4.0
Displacement, in.
3.0
2.0
1.0
0.0
-1.0
-2.0
-3.0
-4.0
0
5
10
15
20
25
30
20
25
30
Acceleration, g
Time, sec
1.2
1.0
0.8
0.6
0.4
0.2
0.0
-0.2
-0.4
-0.6
-0.8
-1.0
0
5
10
15
Time, sec
Figure 5-9. Absolute displacement (top) and absolute acceleration (bottom) of Roof due to 50%
in 50 years, Coyote Lake, Coyote Lake Dam abutment earthquake
91
3.0
Displacement, in.
2.0
1.0
0.0
-1.0
-2.0
-3.0
-4.0
-5.0
-6.0
0
5
10
15
20
25
30
20
25
30
20
25
30
Time, sec
3.0
Displacement, in.
2.0
1.0
0.0
-1.0
-2.0
-3.0
-4.0
-5.0
-6.0
0
5
10
15
Time, sec
3.0
Displacement, in.
2.0
1.0
0.0
-1.0
-2.0
-3.0
-4.0
-5.0
-6.0
0
5
10
15
Time, sec
Figure 5-10. Relative displacements of Roof (top), Level 4 (middle), and Level 1 (bottom) due to
50% in 50 years, Coyote Lake, Gilroy #6 earthquake
92
1.2
Acceleration, g
0.8
0.4
0.0
-0.4
-0.8
-1.2
0
5
10
15
20
25
30
20
25
30
20
25
30
Time, sec
1.2
Acceleration, g
0.8
0.4
0.0
-0.4
-0.8
-1.2
0
5
10
15
Time, sec
1.2
Acceleration, g
0.8
0.4
0.0
-0.4
-0.8
-1.2
0
5
10
15
Time, sec
Figure 5-11. Relative accelerations of Roof (top), Level 4 (middle), and Level 1 (bottom) due to
50% in 50 years, Coyote Lake, Gilroy #6 earthquake
93
3.0
Displacement, in.
2.0
1.0
0.0
-1.0
-2.0
-3.0
-4.0
-5.0
-6.0
0
5
10
15
20
25
30
20
25
30
Time, sec
1.2
Acceleration, g
0.8
0.4
0.0
-0.4
-0.8
-1.2
0
5
10
15
Time, sec
Figure 5-12. Absolute displacement (top) and absolute acceleration (bottom) of Roof due to 50%
in 50 years, Coyote Lake, Gilroy #6 earthquake
94
1.0
0.8
Displacement, in.
0.6
0.4
0.2
0.0
-0.2
-0.4
-0.6
-0.8
-1.0
0
2
4
6
8
10
12
14
16
18
20
12
14
16
18
20
12
14
16
18
20
Displacement, in.
Time, sec
1.0
0.8
0.6
0.4
0.2
0.0
-0.2
-0.4
-0.6
-0.8
-1.0
0
2
4
6
8
10
Displacement, in.
Time, sec
1.0
0.8
0.6
0.4
0.2
0.0
-0.2
-0.4
-0.6
-0.8
-1.0
0
2
4
6
8
10
Time, sec
Figure 5-13. Relative displacements of Roof (top), Level 4 (middle), and Level 1 (bottom) due to
50% in 50 years, Livermore, Fagundes Ranch earthquake
95
Acceleration, g
0.8
0.4
0.0
-0.4
-0.8
0
2
4
6
8
10
12
14
16
18
20
12
14
16
18
20
12
14
16
18
20
Time, sec
Acceleration, g
0.8
0.4
0.0
-0.4
-0.8
0
2
4
6
8
10
Time, sec
Acceleration, g
0.8
0.4
0.0
-0.4
-0.8
0
2
4
6
8
10
Time, sec
Figure 5-14. Relative accelerations of Roof (top), Level 4 (middle), and Level 1 (bottom) due to
50% in 50 years, Livermore, Fagundes Ranch earthquake
96
Displacement, in.
1.0
0.8
0.6
0.4
0.2
0.0
-0.2
-0.4
-0.6
-0.8
-1.0
0
2
4
6
8
10
12
14
16
18
20
12
14
16
18
20
Time, sec
Acceleration, g
0.8
0.4
0.0
-0.4
-0.8
0
2
4
6
8
10
Time, sec
Figure 5-15. Absolute displacement (top) and absolute acceleration (bottom) of Roof due to 50%
in 50 years, Livermore, Fagundes Ranch earthquake
97
4.0
Displacement, in.
3.0
2.0
1.0
0.0
-1.0
-2.0
-3.0
0
5
10
15
20
25
15
20
25
15
20
25
Time, sec
4.0
Displacement, in.
3.0
2.0
1.0
0.0
-1.0
-2.0
-3.0
0
5
10
Time, sec
4.0
Displacement, in.
3.0
2.0
1.0
0.0
-1.0
-2.0
-3.0
0
5
10
Time, sec
Figure 5-16. Relative displacements of Roof (top), Level 4 (middle), and Level 1 (bottom) due to
50% in 50 years, Livermore, Morgan Territory Park earthquake
98
1.6
Acceleration, g
1.2
0.8
0.4
0.0
-0.4
-0.8
-1.2
0
5
10
15
20
25
15
20
25
15
20
25
Time, sec
1.6
Acceleration, g
1.2
0.8
0.4
0.0
-0.4
-0.8
-1.2
0
5
10
Time, sec
1.6
Acceleration, g
1.2
0.8
0.4
0.0
-0.4
-0.8
-1.2
0
5
10
Time, sec
Figure 5-17. Relative accelerations of Roof (top), Level 4 (middle), and Level 1 (bottom) due to
50% in 50 years, Livermore, Morgan Territory Park earthquake
99
4.0
Displacement, in.
3.0
2.0
1.0
0.0
-1.0
-2.0
-3.0
0
5
10
15
20
25
15
20
25
Time, sec
1.6
Acceleration, g
1.2
0.8
0.4
0.0
-0.4
-0.8
-1.2
0
5
10
Time, sec
Figure 5-18. Absolute displacement (top) and absolute acceleration (bottom) of Roof due to 50%
in 50 years, Livermore, Morgan Territory Park earthquake
100
2.5
Displacement, in.
2.0
1.5
1.0
0.5
0.0
-0.5
-1.0
-1.5
0
5
10
15
20
25
30
20
25
30
20
25
30
Time, sec
2.5
Displacement, in.
2.0
1.5
1.0
0.5
0.0
-0.5
-1.0
-1.5
0
5
10
15
Time, sec
2.5
Displacement, in.
2.0
1.5
1.0
0.5
0.0
-0.5
-1.0
-1.5
0
5
10
15
Time, sec
Figure 5-19. Relative displacements of Roof (top), Level 4 (middle), and Level 1 (bottom) due to
50% in 50 years, Morgan Hill, Anderson Dam Downstream earthquake
101
0.6
Acceleration, g
0.4
0.2
0.0
-0.2
-0.4
-0.6
-0.8
0
5
10
15
20
25
30
20
25
30
20
25
30
Time, sec
0.6
Acceleration, g
0.4
0.2
0.0
-0.2
-0.4
-0.6
-0.8
0
5
10
15
Time, sec
0.6
Acceleration, g
0.4
0.2
0.0
-0.2
-0.4
-0.6
-0.8
0
5
10
15
Time, sec
Figure 5-20. Relative accelerations of Roof (top), Level 4 (middle), and Level 1 (bottom) due to
50% in 50 years, Morgan Hill, Anderson Dam Downstream earthquake
102
2.5
Displacement, in.
2.0
1.5
1.0
0.5
0.0
-0.5
-1.0
-1.5
0
5
10
15
20
25
30
20
25
30
Time, sec
0.6
Acceleration, g
0.4
0.2
0.0
-0.2
-0.4
-0.6
-0.8
0
5
10
15
Time, sec
Figure 5-21. Absolute displacement (top) and absolute acceleration (bottom) of Roof due to 50%
in 50 years, Morgan Hill, Anderson Dam Downstream earthquake
103
3.0
Displacement, in.
2.0
1.0
0.0
-1.0
-2.0
-3.0
0
5
10
15
20
25
30
35
40
45
30
35
40
45
30
35
40
45
Time, sec
3.0
Displacement, in.
2.0
1.0
0.0
-1.0
-2.0
-3.0
0
5
10
15
20
25
Time, sec
3.0
Displacement, in.
2.0
1.0
0.0
-1.0
-2.0
-3.0
0
5
10
15
20
25
Time, sec
Figure 5-22. Relative displacements of Roof (top), Level 4 (middle), and Level 1 (bottom) due to
50% in 50 years, Parkfield, Array #5 earthquake
104
0.6
Acceleration, g
0.4
0.2
0.0
-0.2
-0.4
-0.6
-0.8
0
5
10
15
20
25
30
35
40
45
30
35
40
45
30
35
40
45
Time, sec
0.6
Acceleration, g
0.4
0.2
0.0
-0.2
-0.4
-0.6
-0.8
0
5
10
15
20
25
Time, sec
0.6
Acceleration, g
0.4
0.2
0.0
-0.2
-0.4
-0.6
-0.8
0
5
10
15
20
25
Time, sec
Figure 5-23. Relative accelerations of Roof (top), Level 4 (middle), and Level 1 (bottom) due to
50% in 50 years, Parkfield, Array #5 earthquake
105
3.0
Displacement, in.
2.0
1.0
0.0
-1.0
-2.0
-3.0
0
5
10
15
20
25
30
35
40
45
30
35
40
45
Time, sec
0.6
Acceleration, g
0.4
0.2
0.0
-0.2
-0.4
-0.6
-0.8
0
5
10
15
20
25
Time, sec
Figure 5-24. Absolute displacement (top) and absolute acceleration (bottom) of Roof due to 50%
in 50 years, Parkfield, Array #5 earthquake
106
5.0
Displacement, in.
4.0
3.0
2.0
1.0
0.0
-1.0
-2.0
-3.0
-4.0
0
5
10
15
20
25
30
20
25
30
20
25
30
Time, sec
5.0
Displacement, in.
4.0
3.0
2.0
1.0
0.0
-1.0
-2.0
-3.0
-4.0
0
5
10
15
Time, sec
5.0
Displacement, in.
4.0
3.0
2.0
1.0
0.0
-1.0
-2.0
-3.0
-4.0
0
5
10
15
Time, sec
Figure 5-25. Relative displacements of Roof (top), Level 4 (middle), and Level 1 (bottom) due to
50% in 50 years, Parkfield, Array #8 earthquake
107
1.5
Acceleration, g
1.0
0.5
0.0
-0.5
-1.0
-1.5
0
5
10
15
20
25
30
20
25
30
20
25
30
Time, sec
1.5
Acceleration, g
1.0
0.5
0.0
-0.5
-1.0
-1.5
0
5
10
15
Time, sec
1.5
Acceleration, g
1.0
0.5
0.0
-0.5
-1.0
-1.5
0
5
10
15
Time, sec
Figure 5-26. Relative accelerations of Roof (top), Level 4 (middle), and Level 1 (bottom) due to
50% in 50 years, Parkfield, Array #8 earthquake
108
5.0
Displacement, in.
4.0
3.0
2.0
1.0
0.0
-1.0
-2.0
-3.0
-4.0
0
5
10
15
20
25
30
20
25
30
Time, sec
1.5
Acceleration, g
1.0
0.5
0.0
-0.5
-1.0
-1.5
0
5
10
15
Time, sec
Figure 5-27. Absolute displacement (top) and absolute acceleration (bottom) of Roof due to 50%
in 50 years, Parkfield, Array #8 earthquake
109
1.5
Displacement, in.
1.0
0.5
0.0
-0.5
-1.0
-1.5
-2.0
-2.5
-3.0
0
5
10
15
20
25
30
35
40
25
30
35
40
25
30
35
40
Displacement, in.
Time, sec
2.0
1.5
1.0
0.5
0.0
-0.5
-1.0
-1.5
-2.0
-2.5
-3.0
0
5
10
15
20
Displacement, in.
Time, sec
2.0
1.5
1.0
0.5
0.0
-0.5
-1.0
-1.5
-2.0
-2.5
-3.0
0
5
10
15
20
Time, sec
Figure 5-28. Relative displacements of Roof (top), Level 4 (middle), and Level 1 (bottom) due to
50% in 50 years, Parkfield, Temblor earthquake
110
Acceleration, g
1.0
0.8
0.6
0.4
0.2
0.0
-0.2
-0.4
-0.6
-0.8
-1.0
0
5
10
15
20
25
30
35
40
25
30
35
40
25
30
35
40
Acceleration, g
Time, sec
1.0
0.8
0.6
0.4
0.2
0.0
-0.2
-0.4
-0.6
-0.8
-1.0
0
5
10
15
20
Acceleration, g
Time, sec
1.0
0.8
0.6
0.4
0.2
0.0
-0.2
-0.4
-0.6
-0.8
-1.0
0
5
10
15
20
Time, sec
Figure 5-29. Relative accelerations of Roof (top), Level 4 (middle), and Level 1 (bottom) due to
50% in 50 years, Parkfield, Temblor earthquake
111
Displacement, in.
2.0
1.5
1.0
0.5
0.0
-0.5
-1.0
-1.5
-2.0
-2.5
-3.0
0
5
10
15
20
25
30
35
40
25
30
35
40
Acceleration, g
Time, sec
1.0
0.8
0.6
0.4
0.2
0.0
-0.2
-0.4
-0.6
-0.8
-1.0
0
5
10
15
20
Time, sec
Figure 5-30. Absolute displacement (top) and absolute acceleration (bottom) of roof due to 50%
in 50 years, Parkfield, Temblor earthquake
112
3.0
Displacement, in.
2.0
1.0
0.0
-1.0
-2.0
-3.0
0
5
10
15
20
25
30
35
40
25
30
35
40
25
30
35
40
Time, sec
3.0
Displacement, in.
2.0
1.0
0.0
-1.0
-2.0
-3.0
0
5
10
15
20
Time, sec
3.0
Displacement, in.
2.0
1.0
0.0
-1.0
-2.0
-3.0
0
5
10
15
20
Time, sec
Figure 5-31. Relative displacements of roof (top), level 4 (middle), and level 1 (bottom) due to
10% in 50 years, Tottori, Kofu earthquake
113
1.2
Acceleration, g
0.8
0.4
0.0
-0.4
-0.8
-1.2
0
5
10
15
20
25
30
35
40
25
30
35
40
25
30
35
40
Time, sec
1.2
Acceleration, g
0.8
0.4
0.0
-0.4
-0.8
-1.2
0
5
10
15
20
Time, sec
1.2
Acceleration, g
0.8
0.4
0.0
-0.4
-0.8
-1.2
0
5
10
15
20
Time, sec
Figure 5-32. Relative accelerations of roof (top), level 4 (middle), and level 1 (bottom) due to
10% in 50 years, Tottori, Kofu earthquake
114
3.0
Displacement, in.
2.0
1.0
0.0
-1.0
-2.0
-3.0
0
5
10
15
20
25
30
35
40
25
30
35
40
Time, sec
1.2
Acceleration, g
0.8
0.4
0.0
-0.4
-0.8
-1.2
0
5
10
15
20
Time, sec
Figure 5-33. Absolute displacement (top) and absolute acceleration (bottom) of roof due to 10%
in 50 years, Tottori, Kofu earthquake
115
5.0
Displacement, in.
4.0
3.0
2.0
1.0
0.0
-1.0
-2.0
-3.0
0
5
10
15
20
25
30
35
40
25
30
35
40
25
30
35
40
Time, sec
5.0
Displacement, in.
4.0
3.0
2.0
1.0
0.0
-1.0
-2.0
-3.0
0
5
10
15
20
Time, sec
5.0
Displacement, in.
4.0
3.0
2.0
1.0
0.0
-1.0
-2.0
-3.0
0
5
10
15
20
Time, sec
Figure 5-34. Relative displacements of roof (top), level 4 (middle), and level 1 (bottom) due to
2% in 50 years, Tottori, Kofu earthquake
116
2.0
1.5
Acceleration, g
1.0
0.5
0.0
-0.5
-1.0
-1.5
-2.0
-2.5
0
5
10
15
20
25
30
35
40
25
30
35
40
25
30
35
40
Time, sec
2.0
1.5
Acceleration, g
1.0
0.5
0.0
-0.5
-1.0
-1.5
-2.0
-2.5
0
5
10
15
20
Time, sec
2.0
1.5
Acceleration, g
1.0
0.5
0.0
-0.5
-1.0
-1.5
-2.0
-2.5
0
5
10
15
20
Time, sec
Figure 5-35. Relative accelerations of roof (top), level 4 (middle), and level 1 (bottom) due to
2% in 50 years, Tottori, Kofu earthquake
117
5.0
Displacement, in.
4.0
3.0
2.0
1.0
0.0
-1.0
-2.0
-3.0
0
5
10
15
20
25
30
35
40
25
30
35
40
Time, sec
2.0
1.5
Acceleration, g
1.0
0.5
0.0
-0.5
-1.0
-1.5
-2.0
-2.5
0
5
10
15
20
Time, sec
Figure 5-36. Absolute displacement (top) and absolute acceleration (bottom) of roof due to 2% in
50 years, Tottori, Kofu earthquake
Extreme Values. Extreme values for displacement and accelerations are also given in a
tabulated form in Table 5-4 and Table 5-5. Note that these values are not necessarily taking place
at the same point in time. They are provided for the sake of the shake table test preparations of
the building contents by the UCB and UCI researchers.
118
Table 5-4. Various maximum responses of each floor level subjected to different earthquake
records with 50% probability of occurance in 50 years
Level
Coyote
Lake,
Coyote
Lake
Dam
Abutment
drel
dabs
arel
aabs
drel
Coyote
Lake,
Gilroy #6
dabs
arel
aabs
drel
Parkfield,
Temblor
dabs
arel
aabs
+
+
+
+
+
+
+
+
+
+
+
+
-
1
2
3
4
5
6
R
0.55
0.55
1.06
1.40
0.27
0.28
0.33
0.22
0.35
0.51
2.16
3.13
0.19
0.20
0.48
0.29
0.20
0.19
1.63
2.16
0.12
0.13
0.25
0.33
0.94
0.95
1.29
1.45
0.35
0.38
0.30
0.23
0.65
0.96
2.26
3.46
0.34
0.35
0.52
0.29
0.35
0.33
1.69
2.16
0.19
0.23
0.21
0.28
1.33
1.34
1.61
1.60
0.49
0.49
0.32
0.30
0.98
1.45
2.38
3.84
0.47
0.45
0.57
0.36
0.52
0.47
1.75
2.19
0.24
0.32
0.25
0.20
1.70
1.73
1.98
1.85
0.62
0.62
0.38
0.42
1.32
1.95
2.51
4.28
0.60
0.53
0.61
0.43
0.68
0.61
1.81
2.24
0.35
0.42
0.26
0.20
2.06
2.12
2.33
2.15
0.76
0.67
0.45
0.49
1.66
2.46
2.63
4.74
0.73
0.68
0.66
0.50
0.85
0.74
1.86
2.32
0.47
0.52
0.23
0.22
2.42
2.51
2.69
2.47
0.89
0.73
0.56
0.60
2.04
3.00
2.76
5.24
0.84
0.95
0.74
0.78
1.03
0.88
1.92
2.40
0.61
0.62
0.25
0.31
2.81
2.95
3.08
2.86
1.01
0.82
0.69
0.64
2.53
3.62
2.91
5.81
0.96
1.04
0.95
0.90
1.23
1.03
1.97
2.51
0.80
0.72
0.40
0.39
dabs = absolute displacement, in.
drel = relative displacement, in.
aabs = absolute acceleration, g
arel = relative acceleration, g
119
Table 5-4 (cont.). Various maximum responses of each floor level subjected to different
earthquake records with 50% probability of occurance in 50 years
Level
drel
Parkfield,
Array #5
dabs
arel
aabs
drel
Parkfield,
Array #8
dabs
arel
aabs
drel
Livermore,
Fagundes
Ranch
dabs
arel
aabs
+
+
+
+
+
+
+
+
+
+
+
+
-
1
2
3
4
5
6
R
0.24
0.25
2.12
1.44
0.10
0.14
0.33
0.27
0.32
0.38
3.35
3.15
0.29
0.23
0.61
0.55
0.18
0.17
0.36
0.32
0.16
0.14
0.37
0.36
0.42
0.45
2.24
1.57
0.17
0.26
0.28
0.23
0.59
0.70
3.42
3.12
0.45
0.40
0.68
0.63
0.31
0.30
0.36
0.42
0.26
0.22
0.35
0.35
0.61
0.66
2.36
1.72
0.22
0.38
0.21
0.25
0.87
1.04
3.53
3.14
0.58
0.55
0.70
0.65
0.43
0.43
0.49
0.54
0.34
0.27
0.29
0.34
0.81
0.86
2.48
1.87
0.28
0.50
0.23
0.28
1.14
1.39
3.74
3.19
0.70
0.68
0.70
0.70
0.55
0.55
0.61
0.66
0.42
0.31
0.17
0.28
1.00
1.06
2.60
2.02
0.37
0.60
0.27
0.34
1.41
1.73
3.94
3.27
0.91
0.80
0.67
0.65
0.68
0.67
0.73
0.78
0.49
0.37
0.19
0.23
1.19
1.27
2.71
2.17
0.47
0.69
0.31
0.36
1.68
2.09
4.14
3.36
1.15
0.89
0.71
0.62
0.80
0.79
0.85
0.89
0.55
0.53
0.21
0.21
1.41
1.49
2.84
2.38
0.58
0.76
0.42
0.43
2.00
2.51
4.39
3.67
1.43
1.01
0.99
0.93
0.94
0.92
0.99
1.02
0.61
0.78
0.29
0.46
dabs = absolute displacement, in.
drel = relative displacement, in.
aabs = absolute acceleration, g
arel = relative acceleration, g
120
Table 5-4 (cont.). Various maximum responses of each floor level subjected to different
earthquake records with 50% probability of occurance in 50 years
Level
drel
Livermore,
Morgan
Territory
Park
dabs
arel
aabs
drel
Morgan
Hill,
Anderson
Dam
Downstream
dabs
arel
aabs
+
+
+
+
+
+
+
+
-
1
2
3
4
5
6
R
0.52
0.49
1.61
0.84
0.37
0.30
0.75
0.79
0.23
0.23
1.22
0.84
0.11
0.13
0.19
0.12
0.88
0.83
1.88
0.98
0.53
0.43
0.72
0.91
0.40
0.40
1.33
0.93
0.17
0.21
0.14
0.17
1.21
1.15
2.12
1.22
0.64
0.45
0.71
0.89
0.56
0.56
1.46
1.03
0.23
0.28
0.16
0.20
1.52
1.46
2.34
1.45
0.77
0.49
0.66
0.79
0.72
0.72
1.60
1.11
0.29
0.35
0.19
0.24
1.82
1.75
2.54
1.67
0.88
0.56
0.63
0.59
0.88
0.88
1.74
1.20
0.33
0.45
0.23
0.26
2.12
2.04
2.75
1.88
1.14
0.77
0.58
0.48
1.04
1.04
1.88
1.29
0.36
0.54
0.26
0.30
2.46
2.36
3.09
2.12
1.49
1.15
0.81
0.81
1.22
1.21
2.02
1.38
0.43
0.65
0.32
0.39
dabs = absolute displacement, in.
drel = relative displacement, in.
aabs = absolute acceleration, g
arel = relative acceleration, g
121
Table 5-5. Various maximum responses of each floor level subjected to Tottori, Kofu earthquake
records with 10% and 2% probabilities of occurance in 50 years
Level
drel
Tottori,
Kofu 10%
in 50 yrs
dabs
arel
aabs
drel
Tottori,
Kofu 2% in
50 yrs
dabs
arel
aabs
+
+
+
+
+
+
+
+
-
1
2
3
4
5
6
R
0.25
0.28
2.41
1.43
0.29
0.29
0.68
0.69
0.47
0.46
4.04
2.40
0.56
0.59
1.35
1.28
0.46
0.50
2.40
1.42
0.49
0.47
0.71
0.74
0.82
0.82
4.01
2.40
0.79
0.93
1.33
1.21
0.68
0.73
2.44
1.42
0.66
0.66
0.69
0.65
1.17
1.18
4.10
2.40
0.96
1.19
1.35
1.00
0.90
0.97
2.53
1.43
0.79
0.82
0.65
0.53
1.52
1.57
4.24
2.42
1.07
1.34
1.14
0.78
1.12
1.22
2.62
1.44
0.86
0.93
0.58
0.49
1.89
1.96
4.38
2.43
1.22
1.48
0.83
0.74
1.35
1.49
2.70
1.60
0.91
1.03
0.50
0.54
2.28
2.38
4.52
2.46
1.44
1.74
0.79
0.87
1.59
1.84
2.79
1.87
1.10
1.14
0.77
0.69
2.80
2.93
4.67
2.61
1.88
2.06
1.23
1.09
dabs = absolute displacement, in.
drel = relative displacement, in.
aabs = absolute acceleration, g
arel = relative acceleration, g
122
6. Damage Analysis
6.1
Testing of Nonstructural Components

Performance of furniture/benchtops/shelves and equipment and contents of
shelves (Hutchinson, Pardoen) [This is DM|EDP]

Performance testing of heavy equipment (Makris)
Deliverables:

Select and describe components and limit states by March 15 (Holmes,
Hutchinson, Makris)

Outline section by May 2002

Schedule of testing program May 2002

Plan for delivery of Preliminary data to Holmes May 2002

Final Report October 2003

Authors: Makris, Hutchinson, Pardoen
6.2
Damage Estimation
123





Models for equipment damage, p[DM|EDP] (Hutchinson, Pardoen, Makris). The DM refers
to a limit state that requires remedial action (e.g., replacement of a gypsum board wall), and
the DM/EDP relationships may be viewed as “fragility” curves
Estimation of equipment damage p[DM] (Hutchinson, Pardoen, Makris)
Prediction of hazmat (??)
Propagation of uncertainties (Cornell, and ??)
Prediction by means of simplified engineering approaches (???)
Deliverables:







Outline of section by May, 2002
Damage predictions by October 1, 2002
Partial draft by October 2002
OpenSees model for equipment damage & by October 1, 2002 (Fenves?)
Local collapse prediction and consequences by April 2003 (??)
Final report by October 2003
Authors: Mosalam, Fillipou, Cornell, etc.
124
7. Loss Analysis
Keith A. Porter, James L. Beck, and Rustem V. Shaikhutdinov, California Institute of
Technology, Pasadena, CA
Mary C. Comerio, University of California, Berkeley
7.1
Decision Framework
PEER has posed PBEE as a tool for assessing uncertain future seismic performance
(parameterized via decision variables) as a function of design and seismic hazard. The question
to be addressed at this point then is how to measure performance. To answer this question, it is
useful to step back and consider the context in which performance is assessed.
It is helpful, when considering how to measure performance, to think about the situation
in a facility immediately after an earthquake has occurred. Imagine the facility in question.
Picture some physical damage to the facility and its contents. Possibly there have been
casualties, and the facility’s operability has been impacted. You are picturing the seismic
performance of the facility. How would the performance be measured? Imagine a set of
decision-makers walking around, trying to summarize the earthquake impacts in the facility, so
they can decide what needs doing. How exactly will they measure the performance? First, let us
identify the decision-makers.
Decision-makers and performance metrics. There are a number decisions associated
with the seismic performance of the UCS building. Potential graduate students will decide
whether to attend the University in the light of earthquake damage. Graduate research associates
might be thinking about whether they can complete their research in light of the damage, and
may be considering transferring to another institution. Faculty investigators are likewise
determining, first, whether everyone is safe, second, whether there are hazardous conditions in
the lab, and third, the status of their experiments: which can continue, and which will need to be
restarted. University administrators are thinking about how to depict the damage to top
administrators, alumni, the Regents, and the public. Which decision-makers shall we consider?
125
Probably the most reasonable approach is to look at the situation from the viewpoint of
the faculty researchers. They are the ones responsible for their graduate students, responsible to
the research sponsors who fund the research, and to the administration for the safety of their
laboratories. We shall therefore consider the faculty in the facility as the decision-makers, and
address the facility’s seismic performance from their viewpoint, i.e., in terms of life-safety and
post-earthquake operability.
Alternatives. Now let us step back to present day, before the earthquake has occurred.
We know that the performance metrics we care about are the future life-safety and future
operability of the lab spaces. We will estimate how likely it is that a future earthquake will
impact life safety, and how likely it is that a future earthquake will cause the operational failure
of a particular investigator’s laboratory space.
We want to estimate these probabilities for at least two alternatives: (a) do-nothing, i.e.,
leave the facility as it is, and (b) mitigate the risk. Available risk-mitigation alternatives
typically include various combinations of retrofit measures, the addition of redundancy through
backup equipment, emergency-response training to use human resources to minimize negative
consequences, and possibly other approaches. This dauntingly wide array of options can be
considerably narrowed by recalling that the objective for the present study is to assess structural
approaches to risk management, as opposed to process-oriented approaches. Thus we can ignore
emergency training alternatives. Furthermore, as the present study focuses on equipment and
contents, and as the addition of redundant equipment and contents implies a process-oriented
approach, we ignore these alternatives as well, as valuable as they may be.
We therefore limit ourselves to engineering approaches for dealing with equipment and
content damage, which typically employ anchorage, bracing, and in some cases the addition of
flexibility. Common retrofit measures for equipment have been extensively cataloged; see for
example [>>ref the FEMA yellow book on equipment<<]. The costs of these mitigation
measures are readily estimated. The question then is what effect they have on uncertain future
seismic performance, i.e., on the decision variables.
Decision variables. In the PEER framework, the seismic performance of a facility is
parameterized via the decision variable, or DV. There are a variety of ways to parameterize the
seismic performance of a facility. PEER has selected as general measures of interest: casualties
(number deaths and injuries, or the event that life-threatening damage occurs), dollar losses
126
associated with repair costs or loss of income, and loss of use, measured in terms of restoration
time or the binary event that restoration time exceeds some intolerable level. In the present case,
the facility owner is primarily concerned with threats to life safety and the potential for
unacceptable downtime. We have therefore selected two provisional DVs, to be reviewed by the
stakeholders:
DVO
The probability that, during a planning period T, a given operational unit of the
facility (defined here as the facility space, equipment, and contents required by an
individual faculty researcher) experiences damage that renders it inoperative for
an unacceptable period of time; and
DVL
The probability that, during a planning period T, a given operational unit of the
facility experiences life-threatening damage, either by the sliding or overturning
of large objects that could cause trauma or block egress, or by the release of
hazardous material.
Note that DVO can be evaluated without the analyst needing to know what an
unacceptable downtime is, if the facility owner can identify DMs that imply unacceptable
downtime, and if the analyst can estimate the DMs. This is the case here.
Either DV can be evaluated for a given scenario event, a given level of excitation, or on a
per-annum basis. For the present, we will evaluate the DVs at the three hazard levels discussed
in previous chapters, and determine by discussions with the decision-makers which of these
levels appears to be most relevant. The following text presents a methodology for evaluating
these DVs.
7.2
7.2.1
Formulation of Loss-Estimation Methodology
Definition of Operational Units.
Let the facility be comprised of a set of Nm distinct operational units. An operational unit
comprises a set of facility components that serve some distinct function of interest. In the case of
a commercial building, an operational unit could be a rental suite, a floor, or the entire building.
In an industrial setting, an operational unit could be a building and all its equipment and contents
that perform a distinct industrial process.
In the present application, the operational units are defined as all of the laboratory space,
structural, nonstructural, and particular equipment and contents serving a particular investigator.
127
The building spaces comprising an operational unit need not be contiguous and need not be
delineated by particular rooms or suites of rooms, but can include both dedicated suites and
portions of the central core and basement serving a particular investigator. The loss analysis will
be performed on an investigator-by-investigator basis. It must begin at the level of particular
components serving the operational unit.
7.2.2
Evaluation of the operational decision variable, DVO
Equipment operational fragility. Let P[DO,i,m | EDP] denote the probability that a
component i (located in operational unit m) will be rendered inoperative when subjected to
engineering demand parameter EDP. This is the operational fragility of the component, which
can be determined via laboratory testing, from theoretical considerations, by engineering
judgment, or some combination of these.
Operational-unit fragility function. In the present context, a potentially large number of
components i in a given operational unit m will be excited by a given event E, which produces a
value of EDP for each component. We wish to consider system performance at the level of the
event E. Furthermore, for operational performance, we are only concerned with those
components i that the faculty investigator considers critical to his or her operation, i.e., those
components, which, if they were damaged, would cause an unacceptable disruption in the
processes performed in that operational unit. Let these be referred to as operationally critical
components. Let P[DO,i,m | E] therefore denote the probability that operationally critical
component i in operational unit m will be rendered inoperative given the occurrence of event E.
If the EDP resulting from an event E is completely determined by structural analysis, then we
can substitute:
P[DO,i,m | E] = P[DO,i | EDP(E)]
(7-1)
and simply bear in mind that each event E is associated with a set of EDPs that can be input to
component fragility functions to determine P[DO,i | EDP(E)] and thus P[DO,i,m | E].
Let NO,m represent the number of operationally critical components in operational area m.
Let P[FO,m | E] represent the probability of operational failure in operational unit m, given event
E. If the damage to component i is conditionally independent of that of component j  i, then
128
PFO ,m | E   1   1  PDO ,i ,m | E 
NO , m
(7-2)
i 1
which is an expression of DVO for event E. Note that the set {P[DO,i,m | E]} comprises the
damage measure for operational performance in event E, produced by the damage analysis.
If furthermore a set of events {E} = {E1, E2, … ENE} are considered equiprobable, as in
the case of NE independent ground motions for a single level of shaking severity, then
PFO ,m
1
| E 
NE
1

NE
 PF
NE
O ,m
e 1
| E
 NO ,m

1   1  PDO ,i ,m | E e 



e 1 
i 1

NE
(7-3)
which is an expression of DV1 for the set of events {E}, such as for a given hazard level.
Here, hazard level refers to a value of the intensity measure IM = im corresponding to a
given mean exceedance frequency, i.e., a given mean number of events per year G with IM ≥ im.
The hazard curve is defined as the mean exceedance frequency (events per year) as a function of
intensity IM.
We are now ready to define an operational fragility function. Let {E}im denote an
equiprobable set of events corresponding to a given hazard level im. Let P[FO,m | im] denote the
probability of operational failure of operational area m, conditioned on the occurrence of an
event with IM = im. The functional relationship between P[FO,m | im] and im is the operational
fragility function for an operational unit. If for every particular level im we can select a set of
events {E}im, then we can estimate the operational-unit fragility function as
P[FO,m | im] ≈ P[FO,m | {E}im]
(7-4)
Thus, one can estimate the probability that an operational unit will experience operational
failure as a function of the intensity level, IM.
Probability of operational failure per year, or during planning period t. With the
operational fragility function thus defined, we can turn to the evaluation of DVO independent of
intensity level, i.e., on an annualized basis or during a planning period t. Let earthquakes be
modeled as independent events with Poisson arrival rates determined by the negative first
derivative of the hazard curve. Let G(im) denote the hazard curve, and let the occurrence rate
density at a particular value of IM be defined as
129
g im   
dG
dIM
(7-5)
im
which gives an occurrence rate per unit of IM.
Let Q[FO,m] denote the mean frequency of operational failures of operational area m, and
let P[FO,m] denote the annual operational failure probability (i.e., the probability that at least one
event will cause operational failure) of operational area m. Then
QFO ,m  

 PF
O ,m
| im g im dim
(7-6)
im IM 0
and
PFO ,m   1  exp  QFO ,m 
(7-7)
where IM0 denotes a threshold intensity level that can cause operational failure (convenient
because of the high frequency of negligible events). Note that Q[FO,m] ≥ P[FO,m], because of the
probability that two or more events will occur in a year. For small occurrence frequencies,
P[FO,m] ≈ Q[FO,m].
Because it may be convenient to evaluate Q[FO,m] numerically, it is worthwhile to
consider another form of the seismic hazard. Let n(im) denote the mean annual number of events
of intensity im ± im/2. For small im, n(im) is approximated by
n(im) ≈ -g(im)im
(7-8)
Furthermore, if the hazard curve G(im) can be locally approximated as a log-linear
function of IM, i.e.,
G(im) ≈ exp(a*im + b)
(7-9)
where a and b are constants near IM = im. Then n(im) can be approximated as
n(im) ≈ -dG/dim*im = -aG(im)im
(7-10)
for im = im0, im0 + im, im0 + 2im, … immax where im is some small increment in IM, immax is
some upper-bound value of IM at which the hazard curve can be reasonably truncated, and a is
evaluated numerically from the hazard curve at each value of im. Frankel and Leyendecker
(2001) offer hazard curves with the warning that exceedance frequencies less than 10-4 should be
used with caution, so immax ≈ G-1(10-4) is a reasonable truncation point.
130
Finally, the mean operational failure rate of operational area m can be approximated by
QFO ,m  
 PF
immax
imim0
O ,m
| im nim 
(7-11)
and the annual operational failure probability P[FO,m] can be evaluated as shown above.
Assuming Poisson arrivals of failure events, one can estimate the failure probability during a
planning period t as
PFO ,m,t  1  exp QFO ,m t 
(7-12)
Evaluation of DVO. It remains to be determined whether DVO is defined as the
probability of operational failure of an operational unit for a given hazard level, on an annualized
basis, or during a particular planning period. If the first, then DVO is given by Equation 7-4. If
the second, then DVO is given by Equation 7-11. If the last, then DVO is given by Equation 7-12.
7.2.3
Evaluation of the Life-safety Decision Variable, DVL
Analogous to operational failure, let P[DL,i,m | EDP] denote the probability that a
component i (located in operational unit m) will cause a life-safety failure when subjected to
engineering demand parameter EDP. Only certain types of components can cause a life-safety
failure. We will not attempt to define the set of components capable of causing life-safety
failure, but will rather list some categories of life-safety equipment. A variety of life-safety
equipment components are listed in Porter et al. (1993). Categories of life-safety components
include:

Large, heavy objects, which if overturned could cause life-threatening trauma to a facility
user

Objects, which overturned, could release hazardous materials

Objects whose damage could result in electrical shock to facility users, such as switches
in electrical substations

Equipment on whose continued operation human lives depend, such as medical apparatus
in hospitals

Telecommunications equipment in telephone central offices that handle emergency (911)
calls

Fire-detection, fire-alarm, or fire-suppression equipment
131
With these categories in mind, let P[DL,i,m | EDP] denote the probability that a component
i (located in operational unit m) will be cause a life-safety failure when subjected to engineering
demand parameter EDP. This is the life-safety fragility of the component, which can be
determined via laboratory testing, from theoretical considerations, by engineering judgment, or
some combination of these. Given the set of components in a facility that can cause life-safety
failure, and given their life-safety fragility functions, one can evaluate DVL of an operational unit
i in the same way DVO was evaluated in the previous report section.
7.3
Mitigation Decision-Making Methodology
First, for simplicity let us assume that each damageable facility component has one best
choice for mitigation, such as anchorage or bracing. Let us also assume that the cost of each
mitigation measure is readily estimated, and that testing will allow us to estimate the failure
probability for each component without and with mitigation. If this is the case, then using the
foregoing methodology we can estimate the failure probability (either operational failure or lifesafety failure) of each operational area in either a scenario event or on an annualized basis. The
following discussion assumes the latter, but it can be readily restated on a scenario basis.
Let the reduction in annual failure probability for an operational area m associated with
mitigating a particular component i be denoted by P[Fm,i], and the cost to mitigate component i
be denoted by Ci. Then let us define i  P[Fm,i]/Ci, reflecting bang-for-the-buck mitigation
effectiveness. Let the mitigation measures be sorted in decreasing order of , and let P[Fm,j!]
denote the failure probability associated with mitigating all of the j most cost-effective measures,
and let Cj! indicate the cumulative cost of these mitigation measures. Then a plot of failure
probability P[Fm,j!] versus cumulative retrofit cost Cj! might look schematically like Figure 7-1.
132
1
Failure probability
Failure probability
1
Do nothing
0.1
Retrofit 1 item
0.01
Retrofit 2 items
etc.
0.001
0.0001
Resource-controlled
0.1
Efficiency-controlled
0.01
Probability controlled
0.001
0.0001
0
10
20
30
40
0
Cumulative retrofit cost, $000
10
20
30
40
Cumulative retrofit cost, $000
Figure 7-1. Mitigation effectiveness chart
The curves in the left-hand and right-hand figures are the same. They reflect a
hypothetical operational area with 25 mitigation measures available, perhaps the anchorage or
bracing of each of 25 pieces of equipment or contents. Each dot represents one particular
mitigation measure. Consider for the moment only the left-hand figure.
If nothing is done, the failure probability in any given year is approximately 0.08. If all
the items are retrofitted, the failure probability can be reduced by more than two orders of
magnitude, to 0.0003, but not to zero, reflecting a system with at least some inherent fragility.
Observe that the retrofit of the first item reduces the failure probability most dramatically
per dollar invested. Mathematically, the measure’s efficiency is reflected in the slope of the line
between the do-nothing alternative—the “zeroth” dot at (x, y) = (0, 0.08) —and the first
measure, at ($625, 0.16). Observe also that the bulk of the possible mitigation is achieved by
mitigating four of the twenty-five possible items. After the sixth or seventh item, little advantage
is gained through the additional mitigation measures.
How could such a figure be used in make retrofit decisions? The question is particularly
important if the length of the x-axis represents a large amount of money—say tens or hundreds of
thousands of dollars for an individual lab—and the do-nothing alternative represents an
unacceptably high failure probability.
133
There are several ways the decision-maker could proceed. Each procedure starts with the
question of whether the do-nothing alternative exceeds some tolerable failure probability. If not,
no more need be done. Otherwise, consider three available methods illustrated in the right-hand
side of Figure 7-1.
Probability control. One straightforward approach is to identify a tolerable failure
probability y and then gather enough resources to mitigate enough items to reduce the failure
probability to y, and then stop. Let this be called the probability-controlled approach, as it
essentially draws a horizontal line on the chart at a level of tolerable failure probability, and does
all the mitigation measures that fall above that line. In the illustration, if the tolerable probability
were 0.001, or 1 in 1000, then at least the first four measures should be undertaken, at a cost of
approximately $7,300.
Resource control. Another approach that seems likely in an institutional setting is to
allocate a certain amount of money x for the operational area and do all the mitigation that that
amount will buy. This can be called the resource-controlled approach. If for example only
$5,000 were available, then the decision-maker should perform the first three measures. If these
measures do not reduce the failure probability to a tolerable level, the decision-maker must hope
to gather more resources in the future.
Efficiency control. A third approach—probably too elaborate to be practical—is to
choose a minimum tolerable bang-for-the-buck efficiency, and select all the mitigation measures
with that efficiency or greater. On the chart, this would mean performing all measures whose
slopes are steeper than the minimum efficiency.
7.4
Application of Loss-Estimation Methodology
Prototypical laboratories. The methodology is illustrated here for several prototypical
laboratories in the facility. A laboratory is defined here as all of the facility space, equipment
and contents belonging to a particular investigator. It can therefore include multiple spaces in
the building, including equipment and specimens in shared spaces such as the basement, 6th
floor, and core.
The prototypes were selected to represent the 10th, 50th, 90th, and 100th percentiles of
number of components per lab in each of two categories: components that are deemed critical for
134
operations by the investigator, and components that are rated D for life safety on an A-D (best to
worst) scale. Let the laboratories with the 10th, 50th, etc. quantities of critical components be
denoted as LC, MC, HC, and WC, respectively, for low-critical, medium-critical, high-critical,
and worst-critical. Similarly, let the laboratories with the 10th, 50th, etc. quantities of life-safety
level-D components be denoted y LL, ML, HL, and WL, respectively. Bear in mind that these
notations refer to the quantity of components available to be damaged, not an evaluation of the
likelihood of the failure. The former is a measure of exposure; the latter, of risk. We begin with
a loss analysis of the MC and ML laboratories.
Description of the MC and ML laboratory. The MC and ML laboratory contains nine
components that are deemed critical and eight that are rated D on an A-to-D scale of life-safety
hazard. The critical components appear in three suites of the 3rd floor, and include four
incubators, a freezer, two computers (or the data thereon), and two monitors, which in the view
of the investigator would cause unacceptable delays in research if any were to be damaged. An
inventory of these components is shown in Table 7-1. (It is questionable whether a monitor
really is critical, since it can be readily replaced, but for the time being, the list will stand as
assessed by the investigator.)
The life-safety-level-D components also all appear in the 3rd floor. These components,
listed in Table 7-2, include five refrigerators, an incubator, a freezer, and a centrifuge. Two
components (the incubator and the freezer) appear in both lists. The ML laboratory contains a
total of 192 pieces of equipment, with quantities by life-safety rating shown in Table 7-3.
Further detail is provided in Table 7-4.
135
Table 7-1. Inventory of critical components in MC laboratory
Room
Key
Equipment Manufacture Life
Name
Safety
341c
B
341c
343a
H
I
Low Temp.
Incubator
Incubator
Computer
343a
K
Monitor
343a
M
Computer
343a
N
Monitor
343
343
343
C
J
K
Incubator
Incubator
Freezer
VWR
Scientific
Precision
Silicon
Graphics
Silicon
Graphics
Silicon
Graphics
Silicon
Graphics
Percival
Coldspot
Critical
Chem Quantity Retrofit
Hazard
Cost
Equip
Value
Retrofit
Attempt
B
Y
N
1
$50
$3,000
N
B
B
Y
Y
N
N
1
1
$50 $3,000
$50 $15,000
N
N
B
Y
N
1
$50
$3,000
N
B
Y
N
1
$50 $15,000
N
B
Y
N
1
$50
$3,000
N
C
D
D
Y
Y
Y
N
N
N
1
1
1
$150
$2,200
$1,480
$3,000
$3,000
$7,500
N
N
N
Table 7-2. Inventory of life-safety-level-D components in ML laboratory
Room
Key
Equipment Manufacture Life
Name
Safety
Critical
343
343
G
J
Refrigerator Kenmore
Incubator Percival
D
D
N
Y
N
N
1
1
$1,480
$2,200
$3,000
$3,000
N
N
343
K
Freezer
Coldspot
D
Y
N
1
$1,480
$7,500
N
343
L
Centrifuge
Du
Pont/Sorvall
Instruments
D
N
N
1
$860 $15,000
N
343
M
Refrigerator Kenmore
D
N
N
1
$1,480
$3,000
N
345
B
Refrigerator Philco
D
N
N
1
$1,480
$3,000
Y
345
345
M
N
Refrigerator Kenmore
Refrigerator Fisher
Scientific
D
D
N
N
N
N
1
1
$1,480
$1,480
$3,000
$7,500
Y
Y
136
Chem Quantity Retrofit
Hazard
Cost
Equip
Value
Retrofit
Attempt
Table 7-3. Quantity of equipment in ml laboratory by life-safety hazard
Life Safety Quantity
D
C
B
A
8
42
80
68
Table 7-4. Quantity of equipment in ML laboratory by life-safety hazard and equipment
description
LS Equipment Name
D Refrigerator
D Freezer
D Incubator
D Centrifuge
C Bookcase
C Centrifuge
C 5-drawer File Cabinet
C Water Bath
C Fume Hood
C Microscope Apparatus
C Printer
C Incubator
C File Cabinet
C Microscope
C Gyrotory Water Bath Incubator
C Orbital Shaker
C Thermal Cycler
C Power Supply
C Peltier Thermal Cycler
C Shaking Water Bath
C Orbit Shaker
C Rotator
C Low Temp. Incubator
C Electronic Equipment
B Desk
LS: Life-safety hazard
Qty: quantity
Qty
LS Equipment Name
Qty
5
1
1
1
5
5
4
4
3
2
2
2
2
2
2
1
1
1
1
1
1
1
1
1
16
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
B
A
A
A
A
7
7
6
5
4
4
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
45
12
6
4
137
Computer
Mixer
Microscope
Stirrer
Dry Bath
Cabinet
Refrigerator
Cryogenic Container
Microwave
Balance
Slide Projector
Shelving
Scanner
Computer Equipment
Pneumatic Table
pH Meter
Low Temp. Incubator
Light Box
Incubator
Computer + Monitor
Printer
Open Shelving
Work Bench
Cabinet
Computer
Operability Loss Analysis. As noted above, if any of the critical components is damaged,
the MC laboratory experiences operational failure. The values of P[DO,i,m | E] are provided in the
damage analysis. [Remaining text awaiting preliminary damage analysis.]
7.4.1
Major Contributors to Loss
[Present the mitigation effectives charts for the prototype labs, identifying the
components that contribute most strongly to operational and life-safety failure.]
7.4.2
Simplifications
[Can the (DM/EDP + DV/DM) detour be avoided by providing cost functions that
directly relate EDP to DV? Recast the fragility functions for the prototypical labs as
P[FO,m|EDP], which can then be reused for similar facilities.]
Deliverables:




Outline Section by May, 2002
Itemize (quantity and location of) structural, architectural, MEP, and content
components/subsystems that will be considered in application by May 15, 2002
Final report by end of May 2003
Author: Comerio with all
7.5
Propagation of Uncertainties from IM to DV

Identify and quantify all sources of uncertainties. Here is a preliminary list for
considerations:
138




Occurrence of earthquakes in space and time
Earthquake magnitude
Attenuation from source to site
Inherent randomness of ground motion time histories
 Effects of geotech. geometric and material properties on ground motions
 Effects of geotech. geometric and material properties on SFSI
 Structural geometric and material properties
 Modeling uncertainties at component and system levels
• Construction uncertainties (human errors)
 Consequences of limit state exceedance (life safety, $ losses, downtime)
 Economic assumptions (discount rate, etc.)
 Recovery rates (availability of finances, state of economy in region)

What are the important sources of uncertainties?
Deliverables:




Outline of section by January 17, 2002 (Cornell from Van Nuys)
Identification of all important sources of uncertainty, by April 1, 2002 (Cornell, and Beck?)
Quantification and impact on DV by July 2002 (Cornell, Ellwood, w/Zerbe/Chang)
Final report by October 1, 2002 (Cornell, Ellwood w/Zerbe/Chang)
139
8. Relation to Current Practice
8.1
Current Practice of Engineering Evaluation


How would an engineering office evaluate performance of the UC Science
building?
What are the options and tool available for an engineering evaluation?
Deliverables:


An assessment of the options and tools available to engineering offices, by June 2002
(Holmes, Comartin)
Report by July 2002
8.2
Engineering Assessment of the PEER PBEE Methodology



How to relate the FEMA 356 evaluation to the PEER PBEE evaluation
From a practicing engineer’s perspective, what are the best parameters to
describe performance at various levels?
What needs to be done to implement the PEER PBEE methodology in
engineering practice?
Deliverables:


A comparison between the FEMA 356 and PEER PBEE performance evaluations, by
October 2002 (Comartin)
A critique of the PEER PBEE methodology, and suggestions how to overcome impediments
to implementation of the methodology, by December 2002 (Holmes)
140
9. Societal Issues and Impact
9.1
Stakeholders defined and issues described
9.2
Engineers vs. Occupants attitude toward loss and contents damage, downtime
9.3
Decision Variables that matter
Section to be filled out with help of Ellwood, Macoun, and Zerbe/Chang
141
10. References
Abrahamson, N.A. and W.J. Silva, 1997, “Empirical response spectral attenuation relations for
shallow crustal earthquakes,” Seismological Research Letters 68, 94-127.
Berkeley Equipment Tracking System (BETS), 2001, BETS Database, Materiel Management,
Business Services, University of California, Berkeley.
Boatwright, J, and D.M. Boore, 1982, “Analysis of the ground accelerations radiated from the
1980 Livermore Valley earthquakes for directivity and dynamic source characteristics,”
Bulletin of the Seismological Society of America, 72 (6), 1843-1865
Building Seismic Safety Council (BSSC), 1998, 1997 Edition NEHRP Recommended Provisions
for Seismic Regulations for New Buildings and Other Structures, FEMA 303, Federal
Emergency Management Agency, Washington DC.
Burgmann, R., D. Schmidt, R.M. Nadeau, M. d’Alessio, E. Fielding, D. Manaker, T.V.
McEvilly, and M.H. Murray, 2000, “Earthquake potential along the Northern Hayward
Fault, California,” Science 289, 1178-1182.
Chang, S., and A. Falit-Baiamonte, 2002, Disaster Vulnerability of Businesses in the 2001
Nisqually Earthquake, Pre-publication Draft, University of Washington, Seattle, WA.
Cloud, W.K. and V. Perez, 1967, “Accelerograms – Parkfield earthquake,” Bulletin of the
Seismological Society of America, 57, 1179-1192.
Comerio, M.C. and J.C. Stallmeyer, 2002, Nonstructural Loss Estimation: The UC Berkeley
Case Study, Pub. #2002-01, Pacific Earthquake Engineering Research Center, Berkeley,
CA.
Comerio, M.C., 2000, The Economic Benefits of a Disaster Resistant University. IURD WP
#2000-02 University of California, Berkeley, CA, http://wwwiurd.ced.berkeley.edu/pub/abstract_WP200002.htm
Comerio, M.C., 2003, Seismic Protection of Laboratory Contents. IURD WP #2003-02
University of California, Berkeley, CA, http://www-iurd.ced.berkeley.edu/pub/
142
Earthquake Engineering Research Institute, 1993, “Erzincan, Turkey Earthquake of March 13,
1992: Reconnaissance Report, Chapter 2 – Geology and Geotechnical Effects,”
Earthquake Spectra, Supplement to Volume 9, Oakland, CA
Federal Emergency Management Agency (FEMA), 2003, The Disaster Resistant University
Guide, Washington, DC, (forthcoming)
Filiatrault, A. and C. Christopoulos, 2002, Guidelines, Specifications, and Seismic Performance
Characterization of Nonstructural Building Components and Equipment, PEER Report
2002/05, Pacific Earthquake Engineering Research Center, Berkeley, CA, 102 pp.
Geomatrix Consultants, 2000, Geologic hazards investigation, Central campus, University of
California, Berkeley, California, Appendix One, report prepared for The Economic
Benefits of a Disaster Resistant University.
Hamburger, R.E., A.B. Court, and J.R. Soulages, 1995, “Vision 2000: A Framework for
Performance Based Engineering of Buildings,” Proceedings of SEAOC Annual
Convention, Indian Wells, California.
Hartzell, S. H. and T. H. Heaton, 1986, “Rupture history of the 1984 Morgan Hill, California,
earthquake from the inversion of strong motion records,” Bulletin of the Seismological
Society of America, 76, 649- 674.
Hayward Fault Paleoearthquake Group (HPEG), 1999, Timing of Paleoearthquakes on the
Northern Hayward Fault–Preliminary Evidence in El Cerrito, California, Open-File
Report 99-318, Online version 1.0, U.S. Geological Survey, Menlo Park, CA,
http://geopubs.wr.usgs.gov/open-file/of99-318/
Holmes, W.T., and M.C. Comerio, 2003, Implementation Manual for the Seismic Protection of
Laboratory Contents, (PEER report forthcoming), Pacific Earthquake Engineering
Research Center, University of California, Berkeley, CA.
Idriss, I.M., 1991, Procedures for Selecting Earthquake Ground Motions at Rock Sites, Report to
NIST.
International Conference of Building Officials (ICBO), 1997, Uniform Building Code, Whittier,
CA.
International Conference of Building Officials, 1982, Uniform Building Code, Whittier, CA
Kelson, K.I, R.D. Koehler, R.C. Witter, A.D. Barron, A.C. Sojourner, M.R. Fite, J.N. Baldwin,
and W.R. Lettis, 2000, Earthquake History of the Southern Hayward Fault, San
143
Francisco Bay Area, California, Award Number 99-HQ-GR-0102, U.S. Geological
Survey, Menlo Park, CA, http://erp-web.er.usgs.gov/reports/annsum/vol42/nc/G0102.pdf,
23 pp.
KikNet website: www.kik.bosai.go.jp
K-Net website: www.k-net.bosai.go.jp
Lawrence Berkeley National Laboratory (LBNL), 2000, “Chapter 23: Seismic Safety,” Health
and Safety Manual, Publication 3000, Berkeley, CA.
Liu, H. L. and D. V. Helmberger, 1983, “The near-source ground motion of the 6 August 1979
Coyote Lake, California, earthquake,” Bulletin of the Seismological Society of America,
73, 201-218.
Makdisi, F., C.-Y. Chang, Z.-L. Wang, and C.-M. Mok, 1994, Analysis of the Recorded
Response of Lexington Dam During Various Levels of Ground Shaking; Data Utilization
Report CSMIP/94/03.
Mejia, L., J. Sun, S. Salah-Mars, Y. Moriwaki and M. Bekai, 1992, “Nonlinear dynamic
response analysis of Lexington Dam,” Proceedings of the CSMIP 1992 Conference,
Sacramento, May 22, 10-1 to 10-14.
Mezaros, J., 2001, Post-Nisqually Earthquake Survey of Losses and Lessons 2001 [cited 2002].
http://peer.berkeley.edu/news/2001spring/nisqually.html.
Office of Emergency Services, 1995, Vision 2000: Performance-Based Seismic Engineering of
Buildings, prepared by Structural Engineers Association of California, Sacramento, CA
Office of the Vice-Provost, 2000, Strategic Plan for Loss Reduction and Risk Management.
University of California, Berkeley, http://wwwiurd.ced.berkeley.edu/pub/abstract_WP200003.htm
Porter, K.A., 2002, “Life-Safety Risk Criteria in Seismic Decisions,” Acceptable Risk Processes:
Lifelines and Natural Hazards, Monograph No. 21, C.E. Taylor and E. VanMarcke, eds.,
American Society of Civil Engineers, Technical Council for Lifeline Earthquake
Engineering, Reston, VA, www.its.caltech.edu/~keithp/publications.htm.
Porter, K.A., G.S. Johnson, M.M. Zadeh, C.R. Scawthorn, and S.J. Eder, 1993, Seismic
Vulnerability of Equipment in Critical Facilities: Life-Safety and Operational
Consequences, NCEER-93-0022, Multidisciplinary Center for Earthquake Engineering
Research, State University of New York, Buffalo, NY, 364 pp.
144
Rodriguez-Marek, A., 2000, Near Fault Seismic Site Response, Ph.D. Thesis, Civil Engineering,
University of California, Berkeley, 451 pp.
Sadigh, K., Chang, C.Y., Egan, J.A., Makdisi, F., Youngs, R.R., 1997, “Attenuation relationships
for shallow crustal earthquakes based on California strong motion data,” Seismological
Research Letters, 68 (1), January.
Somerville, P.G., 1998, “Development of an improved representation of near fault ground
motions,” Proceedings of the SMIP98 Seminar on Utilization of Strong Ground Motion
Data, 1-20.
Somerville, P.G., 2000, “Magnitude scaling of near fault ground motions,” Earthquake
Engineering and Engineering Seismology, 2, 15-24.
Somerville, P.G., A. Pitarka and N. Collins, 2001, Ground Motion Maps that Account for Site
Effects, Basin Effects, Duration of Shaking and Rupture Directivity Effects in the San
Francisco Bay Area, Final Report to USGS, Award No. 99-HQ-GR-0030.
Somerville, P.G., H. Krawinkler and B. Alavi, 2000, Development of Improved Ground Motion
Representation and Design Procedures for Near-Fault Ground Motions, Final Report to
CSMIP Data Utilization Program, Contract No. 1097-601.
Somerville, P.G., K. Irikura, R. Graves, S. Sawada, D. Wald, N. Abrahamson, Iwasaki, T.
Kagawa, N. Smith and A. Kowada, 1999, “Characterizing earthquake slip models for the
prediction of strong ground motion,” Seismological Research Letters,70, 59-80.
Somerville, P.G., N.F. Smith, R.W. Graves, and N.A. Abrahamson, 1997, “Modification of
empirical strong ground motion attenuation relations to include the amplitude and
duration effects of rupture directivity,” Seismological Research Letters 68, 199-222.
Structural Engineers Association of California, 1999, Recommended Lateral Force Requirements
and Commentary, Sacramento, CA, 440 pp.
University of California, Berkeley, 1997, Preliminary Seismic Evaluation, Planning, Design and
Construction
URS Corporation, 2000, Probabilistic Ground-Motion Analysis for the Central Campus, Draft
report prepared for the U.C. Berkeley Seismic Guidelines Project, June 8, 2000.
Van Nuys Testbed Committee, in progress, PEER Performance-Based Earthquake Engineering
Methodology: Structural and Architectural Aspects, Pacific Earthquake Engineering
Research Center, Richmond, CA
145
Wald, D. J., D. V. Helmberger and T.H. Heaton, 1991, “Rupture model of the 1989 Loma Prieta
earthquake from the inversion of strong motion and broadband teleseismic data,” Bulletin
of the Seismological Society of America, 81, 1540-1572.
Wald, D.J., 1996, “Slip history of the 1995 Kobe, Japan, Earthquake determined from Strong
Motion, Teleseismic, and Geodetic data,” J. Physics of the Earth, 44, 489-503
Working Group on California Earthquake Probabilities, 1999, Earthquake Probabilities in the
San Francisco Bay Region: 2000 to 2030 - a Summary of Findings. U.S. Geological
Survey Open File Report 99-517.
146
Appendix A. Four methods
147
Appendix B. Engineering Demand Parameters
Under the PEER framework, structural response is parameterized one or more
engineering demand parameters, or EDPs. We herein use the following EDPs and notation.
Displacement measures
Directional peak transient interstory drift ratio. PTDi,x = Maxt(|di,x(t) – dj,x(t)|)/(hi – hj)
Peak torsional drift PRDi,j = Maxt(|qi,z(t) – qj,z(t)|)
Directional peak relative displacement. PRDi,j = Maxt(|di,x(t) – dj,x(t)|)
Directional peak displacement. PDi,x = Maxt(|di,x(t)|)
Velocity measures
Directional peak diaphragm velocity. PDVi,x = Maxt(|Vi,x(t)|)
Directionless peak diaphragm velocity. PDVi = Maxt(|V2i,x(t) + V2i,y(t)|)0.5
Acceleration measures
Directional peak diaphragm acceleration. PDAi,x = Maxt(|Ai,x(t)|)
Directionless peak horizontal diaphragm acceleration. PDAi = Maxt(|A2i,x(t) + A2i,y(t)|)0.5
Peak acceleration ratio. PARz,x,i = Maxt(|Ai,z(t)/Ai,x(t)|)
Structural-deformation measures
Peak plastic hinge rotation. PHRm,i,x = Maxt(|m,i,x(t)|). (Krawinkler believes this must be
more clearly defined.)
Peak positive curvature. PPCm,i,x = Max(Maxt(m,i,x(t)), 0)
Peak negative curvature. PNCm,i,x = Min(Mint(m,i,x(t)), 0)
Positive curvature ductility. PCDm,i,x = PPCm,i,x/m,i,x,y+
Negative curvature ductility. NCDm,i,x = PNCm,i,x/m,i,x,yMember chord rotation. MCRi,j,x = Maxt(rotation of the member whose ends are at nodes
i and j parallel to a constant local axis x that is perpendicular to the vector from i
to j at time t0)
148
Structural-force measures
Directional peak force. PFm,i,x = Maxt(|Fm,i,x|)
Peak principal tensile stress. PTSm,i
Additional notation
| | = absolute value of the term between the bars. If the term is a vector, its magnitude.
Ai,x(t) = absolute acceleration of node i parallel to direction x at time t
Ai,x(t) = absolute acceleration of node i parallel to direction x at time t
Ai,y(t) = absolute acceleration of node i parallel to direction y at time t
di,x(t) = absolute displacement of node i parallel to direction x at time t.
Fm,i,x = internal force in member m at node i parallel to direction x
hi = height above datum of node i
hj = height above datum of node j
i = reference node
j = reference node ≠ i (for PTD, would be on a diaphragm, one floor below node i)
m = index referring to a member
Max( ) = maximum of two or more values in parentheses
Maxt( ) = maximum over time t of the value in parentheses
Min( ) = minimum of two or more values in parentheses
qi,z(t) = rotation of node i parallel to vector z (i.e., about vertical axis) at time t, in rads
qj,z(t) = rotation of node j (one floor below node i) parallel to vector z at time t, in rads
T = some reference time such as the end of strong motion
t0 = some reference time such as the start of strong motion
t = time during motion such that t0 ≤ t ≤ T
Vi,x(t) = absolute velocity of node i parallel to direction x at time t
x, y, z = constant unit vectors; depending on context, may be parallel to global or local
axes, and may be translational or rotational.
m,i.x(t) = curvature in member m at node i parallel to direction x at time t
m,i.x,y- = negative yield curvature in member m at node i parallel to direction x (a
constant).
149
m,i.x,y+ = positive yield curvature in member m at node i parallel to direction x (a
constant).
m.i,x(t) = plastic hinge rotation, radians, in member m at node i parallel to direction x at
time t
150