D 2.12
DELIVERABLE
PROJECT INFORMATION
Project Title:
Acronym:
Project N°:
Call N°:
Project start:
Duration:
Systemic Seismic Vulnerability and Risk Analysis for
Buildings, Lifeline Networks and Infrastructures Safety Gain
SYNER-G
244061
FP7-ENV-2009-1
01 November 2009
36 months
DELIVERABLE INFORMATION
Deliverable Title:
Date of issue:
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Reviewer:
D2.12 – Efficient Intensity Measures for Components
Within a Number of Infrastructures
30 April 2011
WP2 Development of a Methodology to Evaluate Systemic
Vulnerability
University of Pavia
Norwegian Geotechnical Institute
REVISION: Final
Project Coordinator: Prof. Kyriazis Pitilakis
Institution: Aristotle University of Thessaloniki
e-mail: kpitilak@civil.auth.gr
fax: + 30 2310 995619
telephone: + 30 2310 995693
Abstract
The characterisation of strong ground motion is a crucial element of analyses of seismic risk
for isolated structures and lifeline networks. Many measures of the strength of ground motion
(intensity measures) have been developed. Each intensity measure may describe different
characteristics of the motion, some of which may be more adverse for the structure or
system under consideration. The use of a particular intensity measure (IM) in seismic risk
analysis should be guided by the extent to which the measure corresponds to damage to
local elements of a system or the global system itself. Optimum intensity measures are
defined in terms of effectiveness, efficiency, sufficiency, robustness and computability. A
detailed review of studies into the optimality of different intensity measures for specific
structural systems shows that the most efficient intensity measures are those that relate
directly to the structure under consideration. For each system considered in the lifeline
analysis, preliminary recommendations are made as to the most appropriate IM to use in
fragility and vulnerability models. These recommendations are guided on the basis of current
state-of-the-art in the relevant fragility models, in addition to consideration of the physical
response of elements within the system. For buildings, building aggregates and structures,
most current fragility models are defined in terms of spectral acceleration at the fundamental
period of the structure (Sa[T0]), whilst non-structural and/or mechanical elements are more
sensitive to peak ground acceleration (PGA). Within a lifeline analysis, however, structural
failure may also occur due permanent ground deformation (e.g. slope displacements,
liquefaction etc.), which may also correlate to energy and duration-based IMs. Definition of
the strong motion input for system analysis will likely need to consider multiple IMs in order
to implement vulnerability analyses in the most efficient manner.
Keywords: Strong Ground Motion, Intensity Measures, Fragility, Efficiency
i
Acknowledgments
The research leading to these results has received funding from the European Community's
Seventh Framework Programme [FP7/2007-2013] under grant agreement n° 244061
iii
Deliverable Contributors
University of Pavia Graeme Weatherill
Helen Crowley
Rui Pinho
v
Table of Contents
Table of Contents
Abstract ...................................................................................................................................... i
Acknowledgments ................................................................................................................... iii
Deliverable Contributors .......................................................................................................... v
Table of Contents .................................................................................................................... vii
List of Figures .......................................................................................................................... xi
List of Tables .......................................................................................................................... xiii
1
Introduction ....................................................................................................................... 1
2
Seismic Fragility Analysis ................................................................................................ 5
3
Defining Optimum Intensity Measures ............................................................................ 7
4
3.1
CONTEXT .................................................................................................................. 7
3.2
PRACTICALITY AND SUFFICIENCY ......................................................................... 8
3.3
EFFECTIVENESS AND EFFICIENCY ....................................................................... 9
3.4
ROBUSTNESS......................................................................................................... 11
3.5
PROFICIENCY ......................................................................................................... 11
3.6
COMPUTABILITY .................................................................................................... 12
Summary of Studies to Define Optimum Intensity Measures ...................................... 13
4.1
CABAÑAS ET AL. (1997) ......................................................................................... 13
4.2
SHOME ET AL. (1998) ............................................................................................. 13
4.3
CORDOVA ET AL. (2000) ........................................................................................ 13
4.4
ELENAS (2000) ........................................................................................................ 13
4.5
MACKIE AND STOJADINOVICH (2003; 2005) ........................................................ 14
4.6
GIOVENALE ET AL. (2004)...................................................................................... 14
4.7
BAKER AND CORNELL (2005)................................................................................ 15
4.8
VAMVATSIKOS AND CORNELL (2005) .................................................................. 15
4.9
TOTHONG AND CORNELL (2006), TOTHONG AND LUCO (2007) AND
TOTHONG AND CORNELL (2008) .......................................................................... 15
4.10 LUCO AND CORNELL (2007) .................................................................................. 16
4.11 RIDDELL (2007) ....................................................................................................... 16
4.12 TSELENTIS AND DANCIU (2008)............................................................................ 16
4.13 BRADLEY ET AL. (2008) ......................................................................................... 17
4.14 PADGETT ET AL. (2008) ......................................................................................... 17
vii
Efficient Intensity Measures for Multiple Systems and Infrastructures
4.15 MEHANNY (2009) .................................................................................................... 18
4.16 YANG ET AL. (2009) ................................................................................................ 18
5
6
Suitable Intensity Measures for Different Infrastructure Systems .............................. 19
5.1
SUMMARY OF THE NEEDS FOR SUITABLE IMS .................................................. 19
5.2
PERMANENT GROUND DEFORMATION ............................................................... 19
5.3
TRANSIENT GROUND STRAINS ............................................................................ 21
Recommendations for Intensity Measures to be Used in Lifeline Analysis................ 22
6.1
BUILDINGS .............................................................................................................. 22
6.2
TRANSPORTATION NETWORKS AND BRIDGES .................................................. 23
6.3
6.4
6.5
6.6
6.7
7
6.2.1
Roadways and Railway Tracks ..................................................................... 23
6.2.2
Tunnels ........................................................................................................ 23
6.2.3
Bridges ......................................................................................................... 24
WATER AND WASTE SYSTEMS ............................................................................ 25
6.3.1
Extraction and Treatment ............................................................................. 25
6.3.2
Pipelines and Distribution ............................................................................. 25
6.3.3
Storage ........................................................................................................ 26
ELECTRICAL SYSTEMS ......................................................................................... 26
6.4.1
Distribution ................................................................................................... 26
6.4.2
Generation ................................................................................................... 26
GAS AND OIL SYSTEMS ........................................................................................ 27
6.5.1
Pipelines....................................................................................................... 27
6.5.2
Components ................................................................................................. 27
6.5.3
Storage Tanks .............................................................................................. 28
HARBOUR SYSTEMS ............................................................................................. 28
6.6.1
Waterfront Structures ................................................................................... 28
6.6.2
Cargo Handling and Storage Components ................................................... 29
6.6.3
Fuel Facilities ............................................................................................... 29
OTHER FACILITIES (HOSPITALS, COMMUNICATION, AIRPORT AND NONSTRUCTURAL ELEMENTS ..................................................................................... 29
6.7.1
Non-Structural Elements .............................................................................. 29
6.7.2
Hospitals ...................................................................................................... 30
6.7.3
Communications........................................................................................... 30
6.7.4
Airports ......................................................................................................... 30
Conclusive Remarks ....................................................................................................... 76
References .............................................................................................................................. 79
viii
Table of Contents
Appendix A .............................................................................................................................. 96
A
Strong Motion Intensity Measures for Application to Fragility Analysis of
Buildings and Lifelines ................................................................................................... 96
A.1 PEAK GROUND ACCELERATION .......................................................................... 96
A.2 PEAK GROUND VELOCITY AND DISPLACEMENT................................................ 97
A.3 PEAK GROUND MOTION RATIOS.......................................................................... 98
A.4 ENERGY DEPENDENT PARAMETERS .................................................................. 99
A.4.1
Root Mean Square Acceleration ................................................................... 99
A.4.2
Arias Intensity ............................................................................................... 99
A.5 STRONG MOTION DURATION ............................................................................. 100
A.6 CUMULATIVE ABSOLUTE VELOCITY .................................................................. 103
A.7 COMPOUND METRICS ......................................................................................... 103
A.8 EFFECTIVE NUMBER OF CYCLES OF MOTION ................................................. 104
A.9 RESPONSE SPECTRA.......................................................................................... 105
A.10 SPECTRUM INTENSITY........................................................................................ 106
A.11 EFFECTIVE PEAK ACCELERATION AND VELOCITY .......................................... 106
A.12 ELASTIC INPUT ENERGY ..................................................................................... 107
A.13 INELASTIC AND STRUCTURE-SPECIFIC MEASURES OF INTENSITY .............. 108
ix
List of Figures
List of Figures
Fig. 2.1 Idealised fragility curves adopted from HAZUS (NIBS, 2004) ................................... 5
Fig. 3.1 Comparison of an insufficient (a, b) intensity measure [Sa(T0)] and a sufficient (c, d)
intensity measure [IM1E&2E] (adapted from Luco and Cornell, 2007). .................. 9
Fig. 3.2 Visualisation of efficiency and effectiveness – adapted from Padgett et al. (2008) . 10
xi
List of Tables
List of Tables
Table 6.1 Fragility Studies for Lifeline Systems and Components ...................................... 32
Table 7.1 Recommended IMs for Different Systems .......................................................... 77
xiii
Introduction
1
Introduction
A crucial step when analysing the seismic vulnerability of different lifeline systems, is to
make the connection between the seismic hazard and damage to the systems under
consideration. For an effective and accurate analysis these connections should be as strong
as possible. Estimates of damage, be it in terms of physical effects on a structure or system,
or in terms of the economic cost of losses and repair, should show a clear correlation with
the strength of ground motion to which a system is subjected. Statistical correlation, from
both empirical and numerically simulated analyses, should be also be qualified by a clear
understanding of the underlying physics.
Over the past four decades a wide variety of physical metrics have been developed, from
which, the strength of ground motion can be characterized. Collectively, these metrics are
referred to throughout as ―Intensity Measures‖ (IMs). These refer to physical properties of
the waveform, or in some cases the response of a simplified system subjected to the wave
motion, from which key properties (e.g. strength, duration, energy) of the strong motion can
be determined. These intensity measures are not to be confused with macroseismic intensity
measures, which are derived from mostly qualitative assessments of damage rendered onto
a discrete numerical scale. Macroseismic intensity scales have a wide range of applications
and can be found in some fragility analyses both in the past and present. Their use in
detailed engineering-based assessments of fragility and loss is limited, however, and they
shall not be considered in any detail here except as an example of legacy application in
seismic fragility assessments.
The characteristics of ground motions that influence the seismic performance and integrity of
structures are the intensity, frequency content, and duration of the motions. Each of these
characteristics of the ground motion at a given site is influenced by the nature of the fault
rupture process, the travel path followed by the resulting seismic waves as they propagate
from the ruptured fault to the site, and the ―site effects‖ including the effects of local soil
conditions, basin effects and topography. These factors can modify, considerably, the
ground motion characteristics form one site to another, and from one seismotectonic region
to another. The intensity of the shaking has been most commonly represented using the
peak ground acceleration; however, the use of this single parameter is a misleading and
incomplete basis for representing the overall destructive energy of the ground motion and its
effect on the response of the structures. More descriptive parameters for this purpose are
the root-mean-square acceleration or the spectral amplitudes of the motions over the range
of periods that are important to the structure. The frequency content of the ground motion
can be always characterized by a Fourier spectrum, but more commonly, by response
spectra. The duration of the ground shaking is particularly important for structures that will
undergo inelastic deformations when subjected to strong ground shaking. The inelastic
response and potential for damage to structures is strongly dependent on the number of
cycles of strong shaking that will be induced during the earthquake.
Earthquake ground motions are usually described by means of one or several of the
following parameters or functions:
o
Peak Ground Acceleration - horizontal (PGAH). and vertical (PGAV)
o
Peak Ground Velocity - horizontal (PGVH). and vertical (PGVV)
1
Efficient Intensity Measures for Multiple Systems and Infrastructures
o
Peak Ground Displacement (PGD).
o
Acceleration time histories.
o
Acceleration, Velocity and Displacement Response Spectrum SA(T, ξ) for a suitable
range of periods. (normally <10 s but recently up to 20 s as well especially for the
displacement spectra)
o
Transient ground strains
o
Arias Intensity
o
Fourier Spectrum
o
Fundamental period of the ground motion (it is related to the site effects as well)
o
Duration (Bracketed Duration, Significant Duration).
o
Equivalent number of uniform cycles, Neq.
In case of slope movement, fault crossing and liquefaction induced phenomena (lateral
spreading and subsidence), the Permanent Ground Deformations (displacements, PGD) total and differential - are the key parameters.
An abundance of literature is available to give clear definitions of many of these parameters,
including their calculation and the physical interpretation (e.g. Kramer, 1996). For reference,
a brief description of many of these quantities can be found in Appendix A of this report. The
list of IMs contained within Appendix A is by no means an exhaustive account of every
ground motion measure found in the scientific literature. It does, however, describe the IMs
used in the vast majority of practical applications of seismic hazard and risk analysis. Some
other IMs are introduced by certain references, and where brief description of the IM is
necessary this may be found in the main body of this report.
This report has several key aims that are intended to guide the selection and application of
the optimum parameters for input into seismic fragility analyses of different lifeline systems.
The first aim is to identify and outline the criteria by which the suitability of a given IM for
seismic fragility analysis is assessed. This will take into consideration the statistical
correlations between a given IM and engineering demand, as well as practical issues in
integrating the IM into a seismic risk assessment. A review of several key studies on this
particular issue can be found in the next section.
The second aim of this report is to review the current literature to identify the IMs that are
most suitable, and most widely used, in current seismic fragility analysis. A large number of
fragility studies for different systems have been published in scientific and technical
literature. An extensive, though by no means exhaustive, list of relevant publications is
reviewed here. Most of these publications have produced clear functions to describe the
fragility of the system under consideration. These may include empirical functions derived
from observations of lifeline performance during recent earthquakes, numerical simulations
of system performance using observed or synthetic records of ground motion, or via
nonlinear static analysis. A summary of each publication is given in Table 6.1. The summary
includes the lifeline system and element considered, the IM used in the fragility results, the
engineering demand parameter or damage index, and key details regarding the context,
methodology and number and type of damage states used.
2
Introduction
The lifeline systems considered here are:
1. Buildings – Unreinforced Masonry (URM), Reinforceed Concrete (RC), Steel and
Wood
2. Transportation networks – Roads, Bridges, Tunnels, Railway
3. Water systems and components
4. Electrical systems and components
5. Gas and Oil systems and components
6. Ports and Harbours
7. Miscellaneous – Hospitals, Non-structural elements, Telecommunications, Airports
For each lifeline system discussion is presented regarding the range of IMs used, and a
provisional recommendation of appropriate IMs for each system is made. The
recommendation reflects the author’s judgment, which takes into consideration the emerging
trends in the reviewed literature, the necessary input for analytical methods and the
practicality of implementing the IM within the hazard component of the seismic vulnerability
analysis. It is intended that the literature review reflect the state of the art in seismic fragility
analysis, and that this will form a coherent and appropriate basis for the lifeline analyses
undertaken within SYNER-G.
3
Seismic Fragility Analysis
2
Seismic Fragility Analysis
A full derivation of the fragility functions, both empirical and analytical, is beyond the scope
of this work, although several publications cited offer a pertinent summary (e.g. Shinozuka et
al., 2007b; 2007c). For most structures and systems identified as a point structure (not a
linear structure such as a pipeline), fragility functions assume the form:


 log IM IM 

PDP  DPdsi  | IM   




(2.1)
where, DP is the demand parameter or index, IM the median value of the IM for a given
damage state (dsi), β the log-standard deviation of the fragility curve and Φ indicates the
normal cumulative distribution function. For a set of assumed damage states a typical
fragility curve may resemble Fig. 2.1.
Fig. 2.1 Idealised fragility curves adopted from HAZUS (NIBS, 2004)
As is expected from the assumption of a cumulative lognormal distribution, the shape of the
fragility curve is controlled by the median and the log standard deviation. The latter of which
determines the slope of the curve, indicating the overall rate of increase in probability of
exceeding a particular damage state for a higher IM. For fragility curves defines via observed
earthquake damage, or by numerical analysis of a structure type, it may be necessary to
provide additional constraint upon the functions to ensure that the curves for different
damage states do not intersect (i.e. the probability of reaching a higher damage state being
greater than the probability of reaching a lower damage state). The interpretation of the
damage state may differ in accordance with the typology of the structure or system.
5
Defining Optimum Intensity Measures
3
Defining Optimum Intensity Measures
3.1
CONTEXT
The selection of an intensity measure for assessment of seismic risk to a given structure
requires careful consideration of the effectiveness (used in the general sense here but given
a specific definition later on) that the IM has in predicting the extent of damage arising from
seismic motion. Several concepts and quantities are commonly used to assist in identifying
the optimum intensity measure for the required purpose. These are defined as practicality,
effectiveness, efficiency, sufficiency and robustness (Cornell, 2002; Mackie and
Stojadinovich, 2003; 2005). A further concept, proficiency, was introduced by Padgett et al.
(2008), which represents an effective composite of efficiency and practicality.
The qualities for defining optimal IMs discussed here derive from the conceptual framework
introduced in FEMA-350 as a basis for performance based design. This is intended to
describe the probability (typically annual, but other durations may be considered) of a
structure exceeding a given limit state at a designated site. The probability is determined
from the annual frequency of exceedence of a given limit state (λ[LS]) (Cornell and
Krawinkler, 2000; Luco and Cornell, 2007). This is done via the use of both a structural
demand measure and an intensity measure:
LS   
DM , IM
GLS | DM  | dGDM | IM  | dIM 
(3.1)
where G[LS|DM] indicates the probability of exceeding limit state LS, conditional upon the
value of the structural demand measure, G[DM|IM] indicates the conditional probability of
exceeding the demand measure DM given knowledge of IM. Finally λ[IM] indicates the
probability of exceeding a given IM; the expected output of the probabilistic seismic hazard
analysis.
The concept introduced in Eq. (3.1) is extended by Krawinkler (2002) to include the concept
of the decision variable (DV) and the engineering demand parameter (EDP). The decision
variable may assume the form of a quantitative value (e.g. annual loss) rather than
specifically a damage limit state as given previously. The definition of the damage measure
in this formulation generally refers to the level or state of damage (e.g. non-structural,
collapse etc). This alteration indicates a dependence on the engineering demand parameter,
which refers to a quantitative measure of demand on a structure (e.g. inter-story drift).
DV   
DM , EDP , IM
GDV | DM dGDM | EDPdGEDP | IM dIM 
The remaining terms and the conditional probabilities are the same as those in Eq. (3.1).
7
(3.2)
Efficient Intensity Measures for Multiple Systems and Infrastructures
The conceptual framework described by Eq. (3.1) and Eq. (3.2) illustrate the need to define
IMs that can be readily integrated into PSHA (λ[IM]), and that show strong correlation with
damage to the structure. The conditional probabilities indicate the loss of information
associated with using IMs that show poor correlation with damage.
The definitions of optimal intensity measures given previously may give the impression that
there exists a universal optimum IM, i.e. one that satisfies all these conditions for every
structure type under any feasible response to seismic motion. Whilst it may not be possible
to say for certain whether such an IM exists, the current state of knowledge would indicate
otherwise. The performance of an IM in predicting structural damage may be highly
dependent on both the structure in question as well as the conditions of seismic motion
(Riddell, 2007). There may still be circumstances under which an otherwise effective
structure-specific long-period IM is less effective than other IMs more closely associated with
shorter period motion. One example of this may be in near-fault regions where directivity
effects may result in pulse-like ground motions. These will have a greater impact on shorter
period motion than on longer period motion, and very little impact on duration dependent
IMs.
3.2
PRACTICALITY AND SUFFICIENCY
Practicality refers to the recognition that the IM has some direct correlation to known
engineering quantities, and that it ―makes engineering sense‖ (Mackie and Stojadinivich,
2005; Mehanny, 2009). The practicality of an IM may be verified analytically via
quantification of the dependence of the structural response on the physical properties of the
IM (e.g. energy, response of fundamental and higher modes etc). It may also be verified
numerically by interpretation of the response of the structure under non-linear analysis using
existing time histories.
Sufficiency describes the extent to which the IM is statistically independent of ground motion
characteristics such as magnitude and distance (Padgett et al., 2008). A sufficient IM is one
that renders the structural demand measure conditionally independent of the earthquake
scenario. This term is more complex and is often at odds with the need for computability of
the IM. Sufficiency may be quantified via statistical analysis of the response of a structure for
a given set of records. This point is well-illustrated in Luco and Cornell (2007), who
demonstrate the difference between a sufficient IM and an insufficient one (Fig. 3.1). The
sufficient IM (IM1E&2E in Fig. 3.1) provides a robust correlation with the demand parameter
when using records from moderate event (M ≤ 6.5) or records from large (M > 6.5) events. In
the example illustrated in Fig. 3.1, the peak interstory drift angle for a 20 story reinforced
concrete structure is taken as the EDP, and Sa(T0) is shown to be insufficient with respect to
earthquake magnitude. In both cases the regression parameters and the uncertainty remain
stable. For the insufficient IM the variability (σ) is similar, yet the gradient of the regression
line of the residuals changes significantly with respect to magnitude. Sufficiency is
determined by the statistical significance of the trend of residuals (typically p-value) from the
regression between the engineering parameters and magnitude, distance or other scenario
dependent feature of the record. Those IMs that result in little significance (high p-value) are
considered to be the most sufficient.
8
Defining Optimum Intensity Measures
Fig. 3.1 Comparison of an insufficient (a, b) intensity measure [Sa(T0)] and a sufficient
(c, d) intensity measure [IM1E&2E] (adapted from Luco and Cornell, 2007). Further
explanation is found in the text.
3.3
EFFECTIVENESS AND EFFICIENCY
The effectiveness of an IM is determined by its ability to evaluate Eq. (3.2) in closed form
(Mackie and Stojadinovich, 2003), so that the mean annual frequency of a given decision
variable exceeding a given limiting value (Mehanny, 2009) can be determined analytically.
This requires that the demand model can assume the form:
EDP  aIM 
b
(3.3)
which transforms into logEDP  loga   b logIM  to allow for constants a and b to be
estimated by linear regression in log-log space (e.g. Fig. 3.2). This form is usually required
for inclusion into probabilistic analysis of the annual frequency for which a given demand
level is exceeded.
9
Efficient Intensity Measures for Multiple Systems and Infrastructures
Fig. 3.2 Visualisation of efficiency and effectiveness – adapted from Padgett et al.
(2008)
The most widely used quantitative measure from which an optimal IM can be obtained is
efficiency. This refers to the total variability of an engineering demand parameter for a given
IM (Mackie and Stojadinovich, 2003; 2005). Efficiency is visualized by the dispersion of the
residuals for the model given by Eq. (3.3) (Fig. 3.2). It is quantified by the standard deviation
of the logarithm of the residuals of the demand model, which we refer to here as β, and is
calculated by:
 logEDP   logEDˆ P 
n

2
i
i 1
n  df
ˆP 
where ED
1 n
 EDPi
n i 1
(3.4)
The primary advantage of an efficient IM is that it should require fewer numerical analyses to
achieve a desired level of confidence in the response of the EDP (Mackie and Stojadinovich,
2005). This does, however, raise the issue of epistemic uncertainty in the model. In the initial
estimation of effectiveness it is necessary to consider whether the number of records used to
determine efficiency is sufficient to estimate the true dispersion with a high degree of
confidence. For inefficient IMs it is assumed that the aleatory variability will dominate the
overall uncertainty, but this may not be the case for highly efficient IMs. The effect of
epistemic uncertainty may be overcome by introducing an epistemic uncertainty term (σe)
and defining total efficiency (βT) as the root sum of squares of the two terms:
 T   2   e2
The epistemic uncertainty may be given by expert judgment or via simulation
10
(3.5)
Defining Optimum Intensity Measures
3.4
ROBUSTNESS
Robustness describes the efficiency trends of an IM-EDP pair across different structures,
and therefore different fundamental period ranges (Mackie and Stojadinovich, 2005;
Mehenny, 2009). This addresses the issue raised earlier in attempting to identify universally
optimum IMs. For example, PGA may be a relatively effective and efficient measure of
damage to short-period or brittle structures, but becomes progressively less effective for
structures sensitive to longer period vibration. Conversely, energy-dependent IMs or IMs
associated with longer period motion may be effective for larger structures and allow for
ductility, but are not effective for smaller brittle structures.
A simple first-order method for quantifying robustness is to determine the stability of the
efficiency over a range of fundamental periods (T). A robust IM should satisfy the condition:
 EDP|IM
T
0
(3.6)
where βEDP|IM is the conditional dispersion of an EDP for a given IM (Mehanny, 2009).
Another form of robustness that may also be a desirable property for an IM is that of scaling
robustness (Tothong and Luco, 2007). This described the property that records scaled to a
value of the IM result in unbiased structural responses compared to the analogous
responses from as-recorded (unscaled) ground motions. This is usually determined by
analysis of the statistical dependence of an EDP on the scaling factor applied to a given
record. Much like sufficiency this can be quantified by the p-value of a regression of EDP on
the scaling factor in log-log space. A high p-value indicates a weaker dependence on scaling
factor and therefore a greater scaling robustness.
3.5
PROFICIENCY
This measure of IM quality is introduced by Padgett et al. (2008) as an effective composite of
practicality and efficiency. It is derived from the conditional probability of engineering
demand exceeding a given demand level, denoted here simply by d. Following the
assumption of that dispersion is lognormal the conditional probability is given by:
 log d   log EDP  

PEDP  d | IM   1  



(3.7)
Substituting Eq. (3.3) into Eq. (3.7) gives:
11
Efficient Intensity Measures for Multiple Systems and Infrastructures
log d   log a  

 log IM  

b

PEDP  d | IM   





b


(3.8)
The proficiency (ζ) is therefore defined by:
 

(3.9)
b
This indicates that a more proficient IM has a lower modified dispersion, which is an
indication of the uncertainty introduced into the analysis by use of a particular IM (Padgett et
al., 2008).
3.6
COMPUTABILITY
The computability of the intensity measure is an important consideration, especially when
considering damage to spatially distributed structures. Complex measures of seismic
intensity, or metrics that require accurate characterization of the physical properties of a
structure, may have a limited application in loss models of the type considered here.
Furthermore, probabilistic loss models are reliant on characterization of the intensity from the
hazard model, or at the very least the hazard scenario. Except in cases where stochastic
simulation of ground motion can be applied, most models utilize predictive ground motion
attenuation equations. The vast majority of these models consider only a small number of
measures, namely PGA and spectral acceleration. Empirical ground motion models for other
IMs such as PGV, spectral velocity and displacement and energy-based intensity (e.g. Arias
Intensity, Cumulative Absolute Velocity, Housner Intensity etc.) are increasing in number but
are not yet as well established. Basing spatial loss models on IMs of greater complexity than
those listed requires development of new predictive attenuation models, which have not
undergone the extensive analysis and testing of those considered here.
12
Summary of Studies to Define Optimum Intensity Measures
4
Summary of Studies to Define Optimum
Intensity Measures
4.1
CABAÑAS ET AL. (1997)
This study analyses the effectiveness of CAV and Arias Intensity (for different filtering bands)
by calculating the correlation with MSK Intensity. These show good positive correlations with
local intensity and damage level (as defined in the MSK scale) to type A structures.
Correlations were less clear for type B and C structures.
4.2
SHOME ET AL. (1998)
Whilst the focus of this paper is primarily on scaling of ground motion histories, some
consideration is given to nonlinear response of structures. The paper demonstrates the use
of spectral acceleration at the fundamental period of the elastic structure (Sa(T1)) as a more
effective and efficient IM than PGA.
4.3
CORDOVA ET AL. (2000)
In this study a metric is introduced to take into account ―period-softening‖ of a structure due
to inelastic response. The metric represents the ratio of the spectral acceleration at the
fundamental period of the inelastic structure (Tf) to that of T1, the fundamental period of the
elastic structure:
S a*  S a T1 RSa
where
RSa  S a T f
 S T 
a
(4.1)
1
The ratio of Tf/T1 and the parameter α are determined by optimization. This is done by
considering three reinforced concrete structures and one steel space frame and identifying
the combination of α and Tf/T1 that maximizes the efficiency of the IM given in equation 4.1
in predicting inter-story drift ratio. A ratio of 2 and an α value of 0.5 emerge as appropriate
values for general use, although the ratio is generally stable in the range 2 ≤ T f/T1 ≤ 3.
4.4
ELENAS (2000)
Whilst not specifically a study on the efficiency of a selection of IMs, Elenas (2000)
investigates the correlation between many common scalar IMs and damage to a 9-story RC
frame structure designed to Eurocode. Notionally this is a first-order approximation of the
effectiveness of the IM in predicting damage to the structure. Damage is measured using the
13
Efficient Intensity Measures for Multiple Systems and Infrastructures
Park and Ang (1985) and the DiPasquale and Cakmak (1989) indices. Overall spectral
acceleration and input seismic energy showed the strongest correlation [effectiveness] with
damage, whilst PGV, PGD and Arias intensity also demonstrated good correlation.
4.5
MACKIE AND STOJADINOVICH (2003; 2005)
The first of these two studies aims to identify optimum IMs (and non-optimal IMs) for
highway bridge structures, which are representative of typical California highway
overpasses. A wide range of IMs and EDPs are considered in the analysis, although results
are not presented for every combination. They concluded that the spectral quantities at the
fundamental period of the structure, such as spectral acceleration, velocity and
displacements, produce better results than do peak ground motion quantities, such as peak
ground acceleration, velocity and displacement. This result is consistent with similar studies
(Wen et al., 2003; Hwang et al., 2001). Spectral displacements (elastic) were found to be the
most efficient and effective, whilst Arias Intensity and PGV were less efficient. A difficulty
arises due to the ambiguity in fundamental period when the transverse and longitudinal
directions are considered. Although Sd remains the most efficient parameter, Arias Intensity
may also be considered an optimal structure-independent IM for highway bridges, despite
the decreased efficiency. Analysis is also undertaken for a vector IM [SdT1, SdT1/SdT2]. The
results also found, however, that the efficiency of the spectral IMs was also sensitive to the
design parameters used in the structural model.
A wider ensemble of IMs are analysed for optimality in the 2005 study. Here the IMs are
divided into three classes: I) IMs that can be taken directly from the strong motion record, 2)
IMs taken from records with a SDOF system used as a filter (including class I IMs and
spectral IMs), 3) class I and 2 IMs applied to records filtered by a) two-degree of freedom
structural filter and b) a bandpass filter. 23 EDPs, corresponding to both local elements
within the bridge structure and the global response of the structure itself, are tested for 134
IMs. First mode spectral quantities (Sa(T1), Sv(T1) and Sd(T1)) were identified as being
optimal, taking into account practicality, whilst the class III IMs (generated using a bandpass
filter) were the mode efficient. CAD and PGV were found to be efficient structureindependent IMs.
4.6
GIOVENALE ET AL. (2004)
The analyses presented in this paper demonstrate the efficiency of given IMs via the use of
Incremental Dynamic Analysis (Vamvatsikos and Cornell, 2002). Records are scaled by
different methods, as introduced in Shome et al. (1998). Sa(T1) is shown to be a more
efficient IM than PGA for a SDOF structure. The IM introduced by Cordova et al. (2000) is
also tested and shows a poorer performance than previously assumed. It is suggested,
however, that the regression approach introduced in this analysis may not be appropriate for
an IM such as Sa*, which is efficient for only a narrow range of damage measure values.
14
Summary of Studies to Define Optimum Intensity Measures
4.7
BAKER AND CORNELL (2005)
This study demonstrates one of the most comprehensive investigations into the use of vector
IMs in predicting structural collapse. The preferred vector is [Sa(T1), ε], where ε is the
number of standard deviations above or below the median, which shows greater significance
than M or R in predicting structural collapse. The vector IM is tested on a seven-story RC
frame building, designed to 1960’s Californian standards. The results show a reduction in the
number of predicted structural collapses when the vector is used compared to the scalar IM.
This demonstrates an improved sufficiency in the use of Sa.
4.8
VAMVATSIKOS AND CORNELL (2005)
A wider range of elastic and inelastic IMs are considered in this study. Three structures are
considered: a 5 story steel chevron braced frame (T1 = 1.8 s), a 9-story steel momentresisting frame with fracturing connections (T1 = 2.4 s) and a 20-story steel moment-resisting
frame with ductile connections (T1 = 4 s) – all based on Los Angeles building stock. This
particular study differs slightly from those previously as it considers the efficiency of IMs at
predicting damage for each different limit states, rather than estimating the efficiency across
all limit states. This approach elucidates the differences in efficiency of an IM when higher
modes and inelastic responses are taken into account. Analysis of the building response
indicates that for buildings with negligible higher mode contributions the spectral acceleration
at an optimum period greater than that of the first elastic mode is most efficient. For taller
buildings with higher mode effects the efficiency varies considerably with period for greater
damage states, and spectral acceleration at any single period may result in poorer efficiency.
Analyses of vector IMs using two or three spectral values shows an improvement in
efficiency for structures with significant higher modes. Finally a more continuous vector IM is
introduced, which is designed to take into account the variation in T1:
te
 S  ,5% 
ln S ac ,i T1 ,5%        ln  a
d   i
ts


S
T
,
5
%
 a 1

(4.2)
where α is the regression intercept, β(τ) the regression coefficient function and εi the
normally distributed errors and ts and te the lower and upper periods of interest.
4.9
TOTHONG AND CORNELL (2006), TOTHONG AND LUCO (2007) AND
TOTHONG AND CORNELL (2008)
In these extensive investigations the authors investigate the use of Sa(T1) (hereafter referred
to simply as Sa), IM1I (applied via the spectral displacement SdI) and IM1Iand2E in predicting
damage to 16 different frame structures under 40 ground motion histories. Structural
response is determined via incremental dynamic analysis. These results find that Sa is
insufficient for most structures, whilst SdI satisfies most of the optimum IM conditions for firstperiod dominated structures, and IM1Iand2E performs better for higher-mode structures. They
15
Efficient Intensity Measures for Multiple Systems and Infrastructures
also find that SdI outperforms the [Sa, ε] vector IM for pulse-like (near source) ground
motions. In addition to the analysis of optimum IMs, empirical attenuation models are also
presented for SdI and IM1Iand2E.
4.10
LUCO AND CORNELL (2007)
This study introduces several new IMs intended to capture the impact of inelasticity at the 1st
mode (IM1I), 1st and 2nd mode effects of an elastic structure (IM1Eand2E) and inelasticity in the
first mode combined with an elastic 2nd mode (IM1Iand2E) – see Appendix for full definition.
Using nonlinear analysis of 3-, 9- and 20-story steel moment-resisting frame buildings
(designed according to the 1994 Uniform Building Code) these IMs are compared with Sa(T1)
(related here via the proxy Sd) in their ability to predict peak inter-story drift angle. A detailed
set of results is given in the paper, but shall be summarized here. Sa(T1) is generally shown
to be inefficient and insufficient (in terms of magnitude) for all structures considered. For the
20-story building IM1Eand2E is shown to be relatively efficient and sufficient compared to Sa(T1)
and IM1Iand2E, but is less so for the 3- and 9- story buildings. Not all the results are robust
across all structure types and for near-source ground motions. Generally IM1Iand2E is shown
to be most efficient and sufficient, except in the case of 20-story structures where it is
insufficient with respect to distance. The general consensus of these results is that the more
advanced IMs should be preferable to Sa(T1).
4.11
RIDDELL (2007)
Correlations between a wide variety of IMs and damage are presented for three elastic and
inelastic SDOF systems. The fundamental periods of each of the systems were 0.2 s, 1 s
and 5 s, assumed to relate to the acceleration, velocity and displacement parts of the
spectra respectively. 90 earthquake records are used, and damage measured via spectral
accelerations and energy input, for elastic systems, and maximum deformation and
hysteretic energy (per unit mass), for inelastic systems. The correlations indicate both the
effectiveness and the efficiency of the IMs for each damage parameter. It is found that PGA,
PGV and PGD correlate strongly with elastic and inelastic response, for the 0.2 s
(acceleration), 1 s (velocity) and 5 s (displacement) regions respectively. Housner Intensity
(SI) also correlates strongly with damage to structures with fundamental periods in the
velocity part of the spectrum, and Fajfar’s Index (If) also performs well. For inelastic systems,
where damage is measured by hysteretic energy, Arias intensity shows a stronger
correlation to damage for acceleration sensitive structures than PGA, whilst S I displays a
consistently stronger correlation to velocity sensitive structures than PGV. No IM, however,
correlates well for all the structures across the spectrum.
4.12
TSELENTIS AND DANCIU (2008)
This investigation pursues a different route to determine which of a small numbers of IMs
(PGA, PGV, Ia and CAV) correlate most strongly to damage as determined via Modified
Mercalli Intensity (IMM). Whilst discussion of effectiveness, efficiency and sufficiency is not
explicitly given in the paper, the regressions do provide this information, or at least a firstorder approximation. It should be recognized, however, that IMM is not dependent on a single
16
Summary of Studies to Define Optimum Intensity Measures
structure, and hence the correlations account for different structures types and different
degrees of damage. MMI is related to the logarithm of the IM via the linear relation:
I MM  b0  b1 log10 IM   
(4.3)
The linear regressions are weighted to allow for the varying number of observations at each
intensity level. The results indicate that b1 (an analogue for effectiveness) is greatest for log
(CAV), but that β is smallest (i.e. most efficient) for log (PGA). Analysis of the residuals for
linear trends, a first-order approximation to sufficiency but not a direct analogue, indicates
PGA residuals show the weakest correlation with magnitude, but Ia the weakest correlation
with respect to epicentral distance. However, when regressions are performed taking into
account magnitude, distance and site condition, the differences in β are negligible for all the
IMs. It should be emphasized that the use of IMM does not allow for direct comparison of
these results with those of Luco and Cornell (2001) and Tothong and Luco (2007).
4.13
BRADLEY ET AL. (2008)
The focus of this study is on the efficiency of IMs in modeling the seismic response of pile
foundations. Comparison is made between foundations in liquefiable and non-liquefiable
soils. The structural model is that of a rigid pile embedded in a two layer soil deposit, with a
SDOF superstructure. Peak pile head displacement is adopted as a global EDP. Using finite
element analysis under 40 ground motions, SI is shown to be the most efficient IM for piles
with short (T0 = 0.8s) and long (T0 = 1.8s) fundamental periods. It is also shown to be
distance and magnitude sufficient. PGV is also shown to be reasonably efficient and
distance-sufficient, albeit less so for piles with shorter fundamental periods. SI is also shown
to be most efficient on liquefiable soils too. It is noticeable that SI and PGV correspond to
properties of the ground velocity, which is believed to be due to its capabilities in predicting
peak free-field soil displacements that cause kinematic induced loads on the pile foundation.
4.14
PADGETT ET AL. (2008)
This study represents a different approach to the others in that the focus is not on buildings
or idealized SDOF systems, but on a portfolio of multi-span simply-supported (MSSS)
highway bridge structures. The implications of the results of this study as they pertain to
lifeline loss modeling are discussed later on in this report. The bridge structures used in the
portfolio are multi-span simply-supported steel girder bridges, typical of southeastern and
central United States. The geometric and the design parameters vary across the portfolio,
which consists of 48 bridge samples. Fundamental periods range from 0.16 s to 0.34 s. For
many different EDPs PGA proved to be the most efficient and proficient IM, whilst Sa (0.2 s),
Sa (1.0 s) and Sa(gm) (spectral acceleration at a period equivalent to the geometric mean of
the fundamental period in the longitudinal and transverse directions) also performed well.
Sufficiency analyses of the parameters showed more variability as many IMs were
conditional upon magnitude. PGA is shown to be the most sufficient for synthetic ground
motions, whilst CAV was consistently sufficient for many EDPs when recorded ground
17
Efficient Intensity Measures for Multiple Systems and Infrastructures
motions were used. Overall, however, PGA was a consistently proficient parameter. The
performance of PGA over Sa as an optimum highlights the impact of additional uncertainties
when considering a portfolio of structures. This may, in part, be accounted for by the nonlinear response of structures under excitation as fundamental periods change due to
degradation of the structure under sustained loading. The consideration of longitudinal and
transverse fundamental periods, and the differences in the softening of the structures under
strong motion, is not unique to bridge design and may be found elsewhere in lifeline analysis
4.15
MEHANNY (2009)
This study presents a modification of the IM introduced by Cordova et al. (2000) (Eq. (4.1)),
whereby the relative weighting of the lengthened period T f is assumed equal to that of the
elastic fundamental period T1 – as illustrated by α = 0.5. The modification relaxes the
assumption of equal weighting thus:
IM SR  S a T1 
Sa

R  T1

(4.4a)
IM CR  S a T1 
Sa

R  T1

(4.4b)
1
1
3


The efficiency and robustness of these IMs are compared with Eq. (4.1) and Sa(T1) for a
range of idealized SDOF systems, with fundamental periods between 0.2 s and 3.0 s. Both a
bilinear constitutive model and a modified Clough model are compared, both with and
without cyclic degradation. Across all the constitutive models, and for different values of R,
the IMs given in Eqs. (4.4a) and (4.4b) are shown to be more efficient and robust than the
other IMs considered. It should be recognized, however, that the analysis is undertaken for
single mode structures and that the influence of higher mode MDOF systems has not been
taken into consideration.
4.16
YANG ET AL. (2009)
This study builds upon that of Riddell (2007) by focusing on near-source strong motion
records from the Chi-Chi and Northridge earthquakes. The same EDPs are considered and
correlations undertaken in a similar manner to that of Riddell (2007). The correlations
illustrate the influence of impulsive motions on the determination of optimum IMs. The results
are consistent with those of Riddell (2007) in that acceleration, velocity and displacement
based IMs perform better for short, intermediate and long period structures respectively. It is
also shown that for acceleration based IMs, correlations with EDPs of short periods SDOF
systems are improved with the inclusion of pulse-like motions. The differences are less
significant for longer period systems.
18
Suitable Intensity Measures for Different Infrastructure Systems
5
Suitable Intensity Measures for Different
Infrastructure Systems
5.1
SUMMARY OF THE NEEDS FOR SUITABLE IMS
Seismic hazard, when input into vulnerability analysis and risk assessment of lifelines, must
be specified according to the precise needs for the particular lifeline components and
networks, as well as the models used to describe vulnerability and fragility curves or
relationships. Moreover due to the large spatial extent of lifeline systems, the hazard
assessment should be able to describe the spatial variability of ground motion, considering
incoherent ground motion and local soil conditions. Consequently, macroseismic intensity
descriptors, which have been used in past approaches (e.g. ATC 1985) are not adequate.
For linear lifeline systems like pipelines it has been shown that peak ground velocity is better
correlated to the observed damages, and thus the vulnerability assessment should be based
on ground velocity estimates. An alternative approach may be the use of ground strains
(longitudinal and transversal) or/and differential ground displacements, which are directly
correlated to the ground velocity. For other lifeline components it may be peak ground
acceleration (i.e. buildings, tanks, waterfront structures). Of course, permanent ground
deformation (i.e. for embankments, roadways, railways and in certain cases for buildings as
well) is also a key parameter.
It is interesting to note that although most of the recent fragility work for buildings is
undertaken using spectral quantities, PGA remains a common intensity measure for input
into bridge fragility functions. The prevalence of PGA as the input IM, in favour of spectral
values is in part due to the challenges associated with the definition of the fundamental
period of a bridge system. When the bridge types have different fundamental periods, the
fragility comparisons must be done at a specific ground motion. Also to use the fragility
curves in a risk assessment program it is imperative that the fundamental period of the
structure be known. In addition to the challenges of implementation, some in the
transportation arena assert that there is very little difference in the transportation network
loss calculations as well as the dispersion of the results when the use of PGA and Sa is
compared (after Nielson, 2003).
5.2
PERMANENT GROUND DEFORMATION
Whilst not necessarily an IM in the sense considered thus far, or in the sense of those
presented in Appendix A, permanent ground deformation is an essential consideration for
any analysis of lifeline vulnerability. To distinguish this term from Peak Ground Displacement
(PGD), permanent ground deformation will be indicated by the abbreviation PGDf for the
remainder of this report. PGDf refers to the displacement or failure of ground resulting from
co-seismic effects, be it strong shaking or direct rupture, and remains after the transient
loading of the earthquake is removed. Whilst the PGDf may usually be measured in metres
or centimetres (or inches in some regions) it can be attributable to a wide variety of
19
Efficient Intensity Measures for Multiple Systems and Infrastructures
phenomena. This includes liquefaction (both lateral spreading and ground settlement), coseismic landsliding and surface fault rupture.
Although some empirical models exist that correlate PGDf with a hazard scenario (e.g.
magnitude and distance), assessment of PGDf cannot usually be undertaken in the same
manner as that of other IMs. Given the uncertainty in geotechnical conditions necessary for
ground failure to occur, it is more common to relate a conditional probability of PGD f
exceeding a given level, to a more common IM description of the ground shaking. A
conceptually simple framework for this is developed in HAZUS (NIBS, 2004), which may
form the basis for analysis of PGDf on such a scale such as that needed for this project. In
the case of liquefaction, most conditional relations utilize PGA as the preferred IM. However,
other IMs, in particular those related to duration or equivalent number of uniform cycles, may
be more efficient. A detailed analysis of optimum IMs for liquefaction assessment has been
undertaken by Kramer and Mitchell (2006), who identify CAV5 (see Appendix A) as the
optimum IM for liquefaction assessment. This develops an earlier analysis by Kayen and
Mitchell (1997) who use Arias Intensity as an IM for predicting the liquefaction potential of a
soil column. Bradley et al. (2008) analyze the optimality of 19 different IMs for use in
predicting pile response on both liquefiable and non-liquefiable soils, for which they find that
velocity spectrum [Housner] intensity (SI) is both efficient and sufficient as a predictor of
damage
For coseismic slope displacement the HAZUS methodology expressed PGDf as a function of
both PGA and number of equivalent cycles of motion (NIBS, 2004), the latter of which is
derived using an empirical relation to moment magnitude. Other analyses of the relation
between landsliding and accelerometric ordinates suggest Arias Intensity as the preferred
IM, in combination with a parameter, or parameters, describing the threshold acceleration or
horizontal coefficient of friction (Carro et al. 2003; Jibson, 2007; Wang et al., 2008).
Investigation of the optimality of different IMs for predicting slope displacements has been
undertaken by Travasarou (2003), and summarized in Bray and Travasarou (2007). This
suggests that Housner Intensity (SI) is a reasonably efficient period-independent parameter,
whilst Arias Intensity was generally more efficient for a weak slope and smaller block mass.
They also suggest, however, that Sa(1.5Ts) (where Ts is the fundamental period of the
sliding block mass) was the most efficient and robust across a range of periods.
Surface fault rupture is, perhaps, a more conceptually straightforward ordinate of PGDf to
determine, as it is constrained directly by the seismic source, i.e. path and site effects need
not be considered. The most common approach, and that implemented in HAZUS (NIBS,
2004), is to use empirical relations between maximum displacement and magnitude (e.g.
Wells and Coppersmith, 2004) to define PGDf. This usually requires certain constraints, such
as displacement tending to zero at the ends of the fault. There is considerable uncertainty,
however, in the location of the maximum displacement along the fault. Probabilistic
approaches to surface rupture modeling are proposed by Youngs et al. (2003) and
Todorovska et al. (2007), which aim to incorporate the variability in occurrence and location
of surface rupture into a hazard analysis approach that is compatible with that for ground
shaking. Intensity measures have little use for this purpose, as it is necessary to define a
suitable scaling relation, and in many cases controlling earthquake scenarios.
20
Suitable Intensity Measures for Different Infrastructure Systems
5.3
TRANSIENT GROUND STRAINS
In addition to PGDf, many lifeline structures (most notably buried pipelines) respond
adversely to the strains induced in the ground under seismic motion. Under ideal conditions
transient ground strain (typically referred to as ε but referred to here as εtr to avoid confusion
with ε defined elsewhere) would be measured directly via strainmetres within the structure of
interest. In practice it can be derived from strong motion data, given certain assumptions
regarding the nature of the medium of propagation. A commonly used measure of peak
ground strain (εtr) is derived from the solution of the one-dimensional wave equation
(Newmark, 1967):
 tr 
PGV
CS
(5.1)
Where, for short source-site distances, Cs is apparent S-wave propagation velocity in the
direction of the longitudinal axis of the structure, and for long distances the phase velocity of
the surface waves. This relation gives rise to the common use of PGV as a predictor of the
damage to underground pipes. It is demonstrated by O’Rourke and Deyoe (2004) that
relation of pipeline damage to strain, via peak particle velocity, is consistent with damage
estimated only via PGDf. Further investigation of the transient strain determined via dense
seismic networks demonstrates the variability in Cs, and in doing so present empirical
relations between PGS and the ground motion ordinates PGV and PGA.
21
Efficient Intensity Measures for Multiple Systems and Infrastructures
6
Recommendations for Intensity Measures to
be Used in Lifeline Analysis
6.1
BUILDINGS
The review of IMs for different structural types (masonry, reinforced concrete, steel frame
and wood/timber) indicates that whilst different IMs display precedent for use in development
of fragility functions, there is convergence toward a standard (Table 6.1a). The choice of IM
may also depend on the method used in the analysis of building vulnerability. It is evident
that for most regular structures and buildings where most of the mass participates in the first
mode that spectral acceleration (Sa) and/or spectral displacement (Sd) are the preferred IMs.
Where the capacity spectrum method is used, and the performance of a structure is
determined by the yielding and ultimate capacity, the full spectrum is essential. Furthermore
damping reduction factors also need to be defined clearly.
The selected studies shown in Table 6.1 are taken mostly from the last ten to fifteen years.
Prior to this the application of macroseismic measures of seismic intensity, and the use of
damage probability matrices, was more widespread. The adoption of nonlinear numerical
techniques gave rise to a wider variety of numerical and analytical means of developing
fragility functions. This is visible in the near uniform adoption of Sa and Sd for studies
conducted in the last five years.
There is little evidence to suggest that a certain IM is anymore widely used for a given
building type than any other. For some fragility curves PGA is preferred over S a, although
there is no clear preference for PGA over Sa for a particular building type. Some fragility
analyses of RC structures have used PGV as the input IM. This may be due to the
prevalence of mid-rise buildings (3- to 6-stories) within a county’s building stock, whose
fundamental periods (both elastic and inelastic) may lie in the velocity dominant portion of
the elastic response spectrum. The natural corollary to this is to assume that damage to
short period brittle structures, which may be more sensitive to acceleration, would correlate
nearly as well with PGA as Sa, and hence could be modelled via PGA to the same extent.
Low rise URM buildings (pre-code or early code) would be the most obvious example of this,
yet there is no obvious preference for PGA over Sa for these buildings than for any other
structure type.
As has been discussed earlier in the report, there are different considerations when
analysing a population of structures and an individual structure. Arguably the most important
implication of this is when considering the use of inelastic IMs or IMs that reflect the
influence of higher modes of a structure. Whilst they are shown to satisfy most of the criteria
for optimality, particularly efficiency and sufficiency, they require constraint of mechanical
parameters to an extent that may be unrealistic when considering loss scenarios for large
cities. Diversity of building stock in terms of material, age, code, quality of construction,
quality of material, irregularity in plan etc., all increase the uncertainty in the risk analysis.
22
Recommendations for Intensity Measures to be Used in Lifeline Analysis
The consideration of practicality therefore leads to the conclusion that the preferred IMs for
use in building loss assessment are Sa, Sd, PGA and PGV. These four IMs are used in all
but a few studies in building vulnerability. Existing predictive attenuation models are
available, in Europe, for all of these IMs, and methods for scaling time histories, particularly
those for Sa and PGA, are well-established. Furthermore, empirical relations to allow for
rescaling of the spectra for different damping ratios are also widely recognised for these IMs.
Where it may be necessary to consider inelastic ground motions, attenuation models are
available, though not abundant. An inelastic modification of the Campbell and Bozorgnia
(2008) ground motion prediction equation has recently been published by Bozorgnia et al.
(2010). This gives spectral ordinates for the 5 % damped case with different values of
ductility. Alternatively, Tothong and Cornell (2006) present another empirical model to scale
elastic spectral ordinates (Sa) to inelastic ordinates (IM1I) and even combined higher mode
ordinates (IM1Iand2E). These would suggest that inelastic IMs may be incorporated into loss
analysis in the future, even if not a direct objective in the present study.
6.2
TRANSPORTATION NETWORKS AND BRIDGES
There are many separate elements within the roadway network that are vulnerable to
earthquakes. There is, however, a significant bias in the volume of research directed toward
bridges, which along with tunnels, represent the elements of the system with the highest
consequences of failure and longest restoration times. It can be, and often is, presumed that
for the purposes of seismic fragility analysis there is no typological difference between
bridges and tunnels used for roadways, and those used for railways. Where multi-lifeline
analyses are undertaken this assumption is often prevalent, and shall remain so here.
Differences do emerge in the consideration of the road surface and railway track, and
fragility curves or damage definitions differ for these two elements. Before addressing issues
in the selection of IMs for analysis the seismic fragility of bridges, we shall consider the IMs
for the other components. The HAZUS methodology (NIBS, 2004) outlines the other key
elements of the roadway network, which include the road surface and tunnels.
6.2.1
Roadways and Railway Tracks
Damage to the road surface or railway track is generally considered to be only susceptible to
ground deformation, mostly liquefaction, settlement and landsliding. Elements related to the
strength of shaking, e.g. electrical traffic signals, may be considered separately as electrical
components. It naturally follows, therefore, that the IMs used for road surface fragility are
similar to those for pipelines, i.e. PGDf and PGV. As damage to the road surface may usually
come from ground settlement, it is logical to consider the use of IMs that show correlation to
PGDf (e.g. CAV, Ia), in addition to direct analysis of offset resulting from fault rupture.
6.2.2
Tunnels
From an engineering perspective, understanding the seismic response of tunnels represents
a challenge of a different nature from that of other elements of the road network. Hashash et
al. (2001) summarize several key observations from tunnel damage caused by significant
seismic events. These observations include: i) underground structures suffer appreciably
less damage [in response to strong shaking] than surface structures, ii) reported damage
23
Efficient Intensity Measures for Multiple Systems and Infrastructures
decreases with increasing overburden depth, iii) underground facilities in soils suffer more
damage than those constructed in rock, iv) damage may be related to PGA and/or PGV and
also duration (as longer durations may result in fatigue failure) and v) ground motion may be
amplified upon incidence with a tunnel if wavelengths are between one and four times the
tunnel diameter. Tunnel structures, particularly those of greater length, are complicated
further by the spatial variability in the ground motion to which they may be subjected.
One result of these observations is that identification of simple scalar or vector IMs that are
most appropriate for tunnel systems is not a straightforward matter. This also means that
despite a significant quantity of literature on the topic of tunnel response and design
(Hashash et al., 2001 [and references within], 2005; Pakbaz and Yareevand, 2005; Ding et
al., 2006; Anastasopoulos et al., 2008; Balideh et al., 2009; Park et al., 2009a) there are
comparatively few fragility studies. In most of the examples listed the tunnel response is
analysed using numerical simulation or FEM, but the studies do not extend to a probabilistic
fragility analysis.
Arguably the most comprehensive seismic fragility study on tunnels is found in the ALA
Guidelines (ALA, 2001b), derived from work by Eidinger, (1999) for water systems, which
also forms a basis for the HAZUS methodology (NIBS, 2004). The distinction between cut
and cover tunnels and bored tunnels is particularly important for roadway network. These
studies both use PGA and PGDf as the fragility parameter; however if is also foreseeable
that PGV could also be considered as a possible IM, at least for empirical fragility studies.
6.2.3
Bridges
There is a wide body of literature relating to fragility investigations of bridge structures. As
has already been noted, however, the most common IM used is PGA. This is in contrast to
the predominance of Sa and Sd (and inelastic spectral parameters), which have become
more standard IMs for building fragility. From a conceptual perspective, bridges may be
considered an example of a spatially distributed, irregular structure. Both single bridges and
bridge portfolios display enormous heterogeneity in terms of column type and depth, soilstructure interaction and skewness. Identification of the elastic fundamental period of the
structure, and its subsequent alteration under inelastic response, is a more complicated and
uncertain process compared to regular RC or masonry structures. Consequently, numerical
simulations, including spatial coherent ground motion, are a widely used tool for their
analysis. Capacity spectrum methods are sometimes used, but show a poorer correlation
with numerical time history fragility analysis when higher damage states are considered
(Shinozuka et al., 2000). The adoption of capacity spectrum methods for bridge design has,
not become as widespread as for building design. This may, in part, account for the
persistence in the use of PGA rather than spectral ordinates.
The extensive investigation of IMs for bridge analysis undertaken by Mackie and
Stojadinovich (2005) may provide the greatest insight into the use of particular IMs for bridge
vulnerability analysis. This study indicated that that whilst Sa(T1) was preferable to PGA for
use as an IM, it was neither the most efficient nor the most robust IM for bridge structures
with a wide range of fundamental periods. It was found that the PGD from an inelastic SDOF
filter displayed an improvement in efficiency, and that the efficiency of many of the standard
IMs could be improved by first applying a 2DOF or bandpass filter around the fundamental
period of the structure. The implications of the Mackie and Stojadinovich (2005) study are
far-reaching and would imply that a wide range of IMs could be considered for the analysis
24
Recommendations for Intensity Measures to be Used in Lifeline Analysis
of fragility to a bridge structure. The practicality of implementing such IMs, and their
consistency with the HAZUS methodology for analysing risk to lifelines, may require much
more detailed consideration. It should be noted that other more structure-independent and
practical IMs were also more efficient and robust than PGA, these included PGV, CAV and
Ia, all of which are feasible to implement in an lifeline analysis, It should also be noted that
other studies (e.g. Karim and Yamazaki, 2003; Kim and Feng, 2003) have also considered
efficiency for IMs such as Housner Intensity (SI) and averaged Sa and Sv over a given period
range. Whilst some predictive attenuation models are available for these IMs, they are rare.
Nevertheless their implementation within a lifeline analysis could be feasible.
For bridges, ATC initially proposed to use the Modified Mercalli Intensity Scale as the
descriptive intensity measure (ATC, 1985). This descriptor was later modified using
intensity measures used in FEMA’s loss assessment program HAZUS (FEMA, 1997): The
peak ground acceleration (PGA) and the permanent ground deformation (PGDf). The latest
version of HAZUS has switched to the use of spectral acceleration at a period of one second
(Sa 1.0s) and PGDf. So there is a continuous re-consideration and upgrade, and it may be
anticipated that further progress in fragility assessment for bridges will likely require more
complex inputs including inelastic and vector intensity measures.
6.3
WATER AND WASTE SYSTEMS
The vast majority of the literature reviewed develops fragility curves for water systems in
terms of PGA, PGV and PGDf. Clearly the IM will depend on the component under
consideration, and in this sense guidance in the use of an IM should take into account the
context of the application. For shaking hazard, the water system should be divided into
separate areas: facilities for extraction and treatment; pipelines and distribution; storage.
6.3.1
Extraction and Treatment
In widespread use for fragility analysis at the point of water extraction and treatment is PGA.
In this area failure of a lifeline system may be attributed to mechanical failure of machine
components. Generally this is more sensitive to higher frequency motion, for which PGA acts
as a practical proxy. For assessment of failure on a spatial scale, and given uncertainties on
the fundamental response of each component of the system, PGA is the logical approach.
Where the analysis may be extended to consider structural risk of the facilities for extraction
and treatment (e.g. pumping station) it may be more appropriate to use IMs consistent with
structural analysis undertaken for buildings. These would logically include Sa(T1), Sd(T1) and
inelastic IMs where available.
6.3.2
Pipelines and Distribution
The majority of empirically developed fragility analyses for seismic risk to pipelines have
defined seismic action in terms of PGV (for strong shaking) and PGDf, with some older
models using PGA. The use of PGV allows for the consideration of transient strain
(O’Rourke and Deyoe, 2004), which is shown to be a more efficient predictor of pipeline
damage. For shaking hazard, the use of PGV is recommended. For PGDf the same
considerations described in section 5.2 still apply.
25
Efficient Intensity Measures for Multiple Systems and Infrastructures
6.3.3
Storage
For tanks and other forms of storage the most common IM for the fragility curves is PGA. For
storage tanks, the approach implemented by the American Lifelines Alliance (2001a,b) offers
the clearest insight and the widest amount of data. For on-ground level tanks PGA would
appear to serve as an appropriate IM for most material types. It should be noted, however,
that the response of above-ground steel tanks and water towers to shaking may be more
efficiently predicted via spectral acceleration and displacement, and may be approximated
as a SDOF structure. Consequently it is also recommended that Sa, Sd and IM1I (or IMCBP) be
considered for this purpose too and more discussion of this can be found for gas and oil
systems. For buried tanks it is also necessary to consider PGDf, which may be predicted
using an appropriate IM.
6.4
ELECTRICAL SYSTEMS
As is the trend when considering utility systems, the choice of IM depends on the
components under consideration. Failure of a substation is attributable to damage to a
proportion of the elements in the circuit. Each of these elements is sufficiently small as to
respond adversely high frequency and impulsive motion. Therefore PGA or high frequency
spectral acceleration would be the optimal IM for consideration here. It should also be noted
that the use of porcelain in the components, and the dense interconnectivity of the circuitry
would is likely to result in failure of the substation shortly after the initiation of inelastic motion
of any element.
6.4.1
Distribution
For electrical distribution a similar approach may be taken as for water distribution. Where
electrical circuits are included within buried pipes, PGV and transient strain are needed to
optimally predict the failure of pipes. Similarly, PGDf will also be necessary for the prediction
of pipe damage due to ground failure.
6.4.2
Generation
Electrical generation facilities present a more complicated picture, and failure of the
generating plant may be attributable to a wide variety of phenomena. This is before
consideration of issues relevant to a particular form of power generation (e.g. nuclear
reactors, tidal barrages etc). Generally the seismic response of machinery and electrical
components may correlate most strongly to PGA and high frequency motion, in the same
manner as for substations.
Damage to the building structure of the electrical generation facility may be characterised in
the same fashion as for buildings of high importance or high consequence of failure. At the
extreme end of this approach are nuclear reactors and hydroelectrical generation systems,
both of which require special consideration under any loss analysis scheme. In many other
cases electrical generation facilities may assume a complex structural form, for which elastic
IMs (PGA, Sa(T1) etc) are inefficient. The NIBS (2004) characterisation of ―small‖ and
―medium/large‖ generation facilities may be useful in this analysis. It would provide a firstorder delineation of the generation facilities whose response may be adequately
26
Recommendations for Intensity Measures to be Used in Lifeline Analysis
characterised by first mode, and those facilities for which higher modes may be of
importance. The recommendations, therefore, are that IMs for fragility analysis of the
electrical generation facilities be selected using similar criteria as those for high importance
buildings and structures. Likely IMs therefore include Sa(T1), IM1I, IM1Iand2E and IMCBP.
6.5
GAS AND OIL SYSTEMS
There are many common elements between gas and oil systems and water transportation
systems, not least within the pipelines. Indeed, many of the empirical fragility studies based
on observed earthquake data do not necessarily make distinctions. It should be recognised,
however, that in terms of loss and vulnerability studies direct equivalence between the two
systems may not be advised, even after taking into account the differences in consequence
of failure. Nevertheless, the derivation of fragility functions for both gas/oil and water
pipelines relies on many of the same underlying principles i.e. longitudinal and transverse
responses to transient strains and permanent deformations.
6.5.1
Pipelines
In common with water pipes, fragility functions for gas pipelines are generally derived from
PGV (for transient strains and empirical studies) and PGDf (for permanent displacements).
Several studies have used PGA and sometimes even SI, although these tend to be only
used for empirical analyses. One particular metric is of interest, however, and that is
PGV2/PGA (Pineda-Porras and Ordaz, 2007). Dimensionally this metric corresponds to
displacement, and when modified by a correction factor is shown to be an effective proxy for
peak ground displacement (PGD). As this particular IM is a simple function of two common
quantities, it can be readily implemented in seismic risk analyses, subject to determination of
an appropriate region- or system-specific correction factor.
6.5.2
Components
For many of the other elements of the gas/oil network (storage, production and pumping
plants) the most common IM remains PGA, with PGDf used in cases where some
components are commonly subsurface. Where the element of the network may have a large
number of acceleration-sensitive components, as may be the case for extraction and
pumping facilities, downtime and repair may be closely related to PGA (or high frequency
spectral acceleration). For these elements PGA may remain the most practical and effective
IM for input into fragility studies. However, it could well be pertinent to distinguish between
structural damage to the given facilities and non-structural/component damage. Convolution
of structural (displacement sensitive) and non-structural (mostly acceleration sensitive)
failures into a single definition of damage state may obscure important distinctions in the
fragility of systems such as these. In particular, highly acceleration-sensitive elements such
as electrical and telecommunication components and machinery may exhibit substantial
damage whilst the response of the structure remains essentially elastic. Such a distinction is
given in the HAZUS methodology, which treats fragility for the structures housing the
components in same manner as that of buildings (ordinary or high importance). These
issues are particularly important for critical facilities.
27
Efficient Intensity Measures for Multiple Systems and Infrastructures
6.5.3
Storage Tanks
Gas and oil storage tanks are the final elements in the system that require specific
consideration. Investigation of the response of tanks (O’Rourke and So, 2000; Iervolino et
al., 2004; Berahman and Benhamfar, 2007) indicates that fragility is affected by many
factors, including the geometry, the anchoring and the volume of content. There does
appear, however, to be a lack of agreement between the demand parameter or damage
index used. Qualitative damage states are used in some cases, particularly empirical
studies, whilst analytical fragility studies may determine damage (or consequence) in terms
of fluid release or in terms of stresses in the tank roof or sides. The preferred IM in most of
these cases is PGA, and PGDf where some elements are buried.
Despite the paucity of applications of nonlinear static procedures to determine the seismic
response of tanks, it is not clear why such an approach should not be attempted. There are
considerable uncertainties that need to be taken into consideration, which further complicate
the seismic response of tanks. In particular, the elastic fundamental period (and the degree
of damping) of a tank is conditional upon the volume of the tank’s contents, which may vary,
almost randomly, across a field of identical tanks at any given time, or within one tank over a
period of time. The difficulties in application of nonlinear static procedures may account for
the persistence of the use of PGA as the preferred IM. Nevertheless, it may be of interest to
consider such application, for which spectral IMs (Sa and Sd) may also be necessary.
6.6
HARBOUR SYSTEMS
Harbour systems represent an important and complex environment where failure of the
system can result in severe and prolonged economic loss for a region. For practical analysis,
the system can be divided into three elements: waterfront structures, cargo handling and
storage, and fuel facilities. Vulnerability analyses of the whole system tend to rely on event
tree or fault tree models to determine the cost of inoperation following an earthquake. The
1995 Hyogoken-Nanbu earthquake and its damage to the port of Kobe, Japan, resulted in
more than $US 5.5 billion in direct losses, and an additional US $ 6 billion economic loss
within the initial 9 months (Na and Shinozuka, 2009). More than 15 years on from the
earthquake the port has not returned to its pre-1995 operational level.
6.6.1
Waterfront Structures
These are a crucial component of the port system as the serve the purpose of allowing
embarkation and disembarkation, and loading and unloading, of ships in the port. Failure of
these structures will most likely render the port functionless until full repair. They also
provide a significant engineering challenge as they are constructed on saturated soils of
limited cohesion. Settlement of the foundations beneath these structures via liquefaction is a
primary cause of failure of the waterfront. In most of the fragility analyses reviewed the input
was given mostly in the form of PGA and PGDf, and damage defined in terms of seaward
displacement or rotation angle of the quay wall.
28
Recommendations for Intensity Measures to be Used in Lifeline Analysis
6.6.2
Cargo Handling and Storage Components
The extent to which failure of these elements affects the operation of the port, and the
duration of restoration, may depend heavily on the configuration of each port. Cargo
handling equipment may be particularly vulnerable to both strong shaking and ground
deformation. For ports where cargo movement is undertaken via rail systems, failure of
these elements, usually associated with failure of the wharf structure, will further reduce the
operation of the report, thus increasing restoration time. Fragility curves for these elements
also rely on PGA and PGDf.
6.6.3
Fuel Facilities
Fuel facilities are lifeline components that are common to harbour systems, railway networks
and airports. These may in some cases consist of both above ground and below ground
storage, as well as pumping and distribution components. The response of these elements
may depend on the degree of anchoring, which is clearly addressed within the HAZUS
methodology. A further distinction is also made between fuel facilities with and without
backup power. The post-earthquake functionality of fuel facilities will depend on damage to
sub-components (storage, electricity, pipelines and mechanical equipment); hence fragility
curves may be derived via fault tree analysis (NIBS, 2004). Many of the sub-components
may be considered acceleration-sensitive structures, so existing fragility curves have largely
considered PGA as an input parameter. The notable exception to this is buried storage
tanks and pipelines, for which PGDf may also be required.
6.7
OTHER FACILITIES (HOSPITALS, COMMUNICATION, AIRPORT AND
NON-STRUCTURAL ELEMENTS
There are several other elements within a lifeline system that have not yet been explicitly
addressed. In many of these cases the function of these systems is conditionally dependent
on the function of their respective sub-systems (usually water and electricity). The
conditional dependence on the sub-systems will, in most cases, result in full-system fragility
curves using an IM that is consistent with most or all of the respective sub-systems. For
critical facilities the aggregation of structural and non-structural fragility is important in
assessing the performance of a given lifeline following earthquakes.
6.7.1
Non-Structural Elements
The most distinguishing feature of many of critical facilities that distinguishes them from
―ordinary‖ buildings is their substantial dependence on the performance of non-structural
elements. The definition of non-structural elements can include architectural partitions,
ceilings and piping systems, in addition to mechanical and electrical equipment. In the case
of the latter the sliding block displacement fragility models developed by Lopez-Garcia and
Soong (2003a, b) may have widespread applications in many types of critical facility. These
fragility modes, and indeed many others for non-structural elements, are dependent upon
PGA or peak floor acceleration (PFA). The former may be taken directly from the record,
whilst the latter may depend on the structural response of the building and can be derived
analytically for a well-modelled structure. A comprehensive set of fragility parameters for
typical non-structural buildings elements has recently been produced by Eidinger (2009),
29
Efficient Intensity Measures for Multiple Systems and Infrastructures
which forms the basis of the FEMA Cost-Benefit calculations. With the exception of nonstructural utility pipelines (for which PGV and PGDf are preferred) all the non-structural
element fragilities use PGA or PFA as the direct input. It is therefore likely that PGA will
remain a necessary input for loss estimation as non-structural fragilities are generally reliant
on this parameter.
6.7.2
Hospitals
Arguably the clearest illustration of the previous point can be found in the fragility of hospitals
and healthcare systems. In the case of the former the hospital [system] fragility is
determined via fault or event tree analysis of the fragilities of its essential subsystems. These
sub-systems include water, electricity, HVAC (heating, ventilation and air conditioning),
suspended ceilings and medical monitors and equipment, including backups to all these
systems. It can be seen from Table 6.1g that for almost all of the sub-systems the main IM
used in fragility studies is PGA. Empirical models may sometimes be used to relate the
expected non-structural damage to a given inter-story drift level for each floor. Such
analyses would require considerable knowledge of the functionality of the hospital, which is
unlikely to be feasible for performance analyses of hospitals on a metropolitan scale.
Modelling the fragility of healthcare systems presents a more complex task due to the
analysis of interconnected elements. Such analyses will be the focus of future work within
SYNER-G. It is likely, however, that potential IMs for this analysis will include PGA, PGV, Sa
and Sd.
6.7.3
Communications
Communications systems may share similar properties to those of electrical systems, and
hence the modelling approach may be the same. The components of a communication
system generally include central offices and broadcasting stations, transmission lines and
cabling (NIBS, 2004). Within the HAZUS methodology only central offices and broadcasting
systems are considered, as it is suggested that transmission lines and cabling may carry
sufficient slack to withstand strong shaking and moderate ground displacement. This
assumption may depend on the region under consideration, and it should be recognised that
this may not be valid for regions of densely packed optical fibre cable. Whilst it is not explicit
in the HAZUS methodology, it may be necessary for the fragility of transmission lines to be
determined using PGDf as an input. For central offices, communication facilities consist of
switching equipment. These are themselves acceleration-sensitive and dependent on the
operation of the power supply. The most likely IM to be used, and that used in HAZUS, is
PGA.
6.7.4
Airports
Airport facilities, much like railway facilities, represent another system for which different
elements may be analysed separately, despite their clear interaction for operation of the
system. Once again HAZUS offers an insight into some of the important components. These
generally correspond to three groups: runway, buildings (control tower, terminal, hangar etc.)
and fuel/maintenance. For runways the input for fragility is naturally PGDf and is defined in a
similar manner to road surface. The fragility of buildings may be analysed as for general
buildings, in which case Sa, Sd and inelastic IMs may be necessary, especially given that
30
Recommendations for Intensity Measures to be Used in Lifeline Analysis
terminal structures and hangers may not always be regular in plan. For fuel facilities the
most likely IM is PGA, although PGDf may be a necessary input where fuel storage is below
ground. Again, the fragility analysis of storage tanks may be applied here.
31
Efficient Intensity Measures for Multiple Systems and Infrastructures
Table 6.1 Fragility Studies for Lifeline Systems and Components
a) Buildings
Elements
at Risk
Reference
Intensity
Measure
Demand Parameter or
Damage Index
Comments
Masonry
Lang (2002)
Sd
Top displacement
o Extensive investigation for URM and RC buildings.
o 6 Damage states and curves defined for separate classes
(low rise URM, mid-rise URM and mixed URM-RC).
o Based on Basel building stock
Penelis et al.
(2002)
Sd
Yield and Ultimate
Displacement
NIBS (2004)
Sd;
Displacement Ductility
equivalent
PGA for
components
o 5 Damage states.
o 5 HAZUS Damage classes: ds1 (none), ds2 (slight), ds3
(moderate), ds4 (extensive), ds5 (complete).
o Separate curves for ―high code‖, ―moderate code‖, ―low code‖
and pre-code.
o Capacity Spectrum Method (CSM) used.
Milutinovic
and
Trendafiloski
(2003)
RISK-UE
32
Sd
EMS Damage Scale (LM1);
Park and Ang Damage
Index (LM2), Yield
Displacement. Ultimate
ductility. Drift Ratio.
o Two approaches: LM1 – damage matrices (EMS damage
grades), LM2 – capacity spectrum method and non-linear
dynamic analysis.
o Fragility curves for many URM typologies using different
analysis procedures.
Recommendations for Intensity Measures to be Used in Lifeline Analysis
Kostov et al.
(2004)
Sd
As RISK-UE approach
o As RISK-UE approach - 5 damage states.
o Application to Sofia.
o Curves for modern URM and historical buildings.
Faccioli et al.
(2004)
Sd
As RISK-UE approach
Pitilakis et al.
(2004)
Sd; PGA
Pasquale et
al. (2005)
IMCS
MSK Defined Damage
Intensity
o Vulnerability
matrices.
D’Ayala
(2005)
Sa (Mean
Response);
Sd
EMS Damage Scale;
Displacement Ductility
o Two approaches compared:
displacement- based (Sd).
o As RISK-UE approach.
o Application to Catania.
As RISK-UE approach
o As RISK-UE approach.
o Application to Thessaloniki.
curves
derived
from
damage
force-based
probability
(Sa)
and
o Five damage states (EMS) compared.
o Data from Istanbul.
Barbat et al.
(2006)
Sd
Yield Displacement;
Displacement Ductility
o Curves for Low-, Mid-, and High-Rise URM buildings in
Barcelona.
o 5 Damage states: none, slight, moderate, extensive and
complete
Kappos et al.
(2006)
PGA; Sd
Roof displacement – Yield
and Ultimate
o 6 Damage states.
o Comparison of empirical curves with fragility analysis.
o Separate curves for brick URM and stone URM.
33
Efficient Intensity Measures for Multiple Systems and Infrastructures
Lagomarsino
and
Giovinazzi
(2006)
IEMS; PGA
Yield and Ultimate
Displacement
o Fragility curves not given.
o Comparison of macroseismic and analytical fragility models
for many different URM typologies.
o Based on EC8 design
Lagomarsino
(2006)
Sd
Yield displacement
o 5 damage states considered.
o Monumental Buildings.
o Capacity spectrum method used
Gueguen et
al. (2007)
IEMS
Barbat et al.
(2008)
Sd
EMS Building Damage
o Macroseismic based loss model for Grenoble.
o Damage probability matrices used.
Yield and Ultimate
Displacement
o 5 Damage states defined.
o Three URM classes (Low-, Mid- and High-Rise).
o Curves derived from Barcelona Building Stock.
Borzi et al.
(2008b)
PGA
Average Drift
o Fragility curves derived via SP-BELA for masonry structures.
o Separate curves defined for low quality stone, high quality
stone, brick with low void percentage and brick with high void
percentage.
o Separate curves for 2, 3, 4 and 5 stories.
o Three damage states considered.
Columbi et al.
(2008)
Sd
Yield Displacement
o Three limit states considered.
o Empirical vulnerability curves for Italian earthquake data.
o SP-BELA analysis
34
Recommendations for Intensity Measures to be Used in Lifeline Analysis
Erberik
(2008)
PGA
Base Shear
o Three damage
severe/collapse.
states
–
insignificant,
moderate
and
o Curves for Turkish masonry, based on No. of Stories,
material, regularity in plan and wall length/opening criteria.
Park et al.
2009b)
Sa
Maximum drift ratio (inplane and out-of-plane
walls)
o HAZUS damage states.
o Low-rise URM based on CEUS earthquake and stock.
o Two families of curves defined based on connection of inplane walls.
Ruiz-Garcia
and Negrete
(2009)
Sd
Rota (2008);
Rota et al.
(2010)
PGA
Reinforced Kappos et al.
Concrete
(1998)
Drift ratio
o Two damage states defined by extent of cracking.
o Low rise URM typical of Latin America
Top Displacement
o Four damage states considered.
o Stochastic analysis of uncertainty on building parameters.
IMM
Repair cost to buildings
o No fragility curves – damage probability matrices (DPM) used.
o Application to Thessaloniki RC frame structures.
o DPM only given for Mid-Rise (4 – 7 story) concrete.
Yamaguchi
and
Yamazaki
(2000)
PGV
Song et al.
(2000)
Sa
Cost parameter – property
tax reduction
o Empirical vulnerability curves based on data from Kobe
earthquake.
o Four categories of RC construction considered (according to
construction date).
Inter-story drift angle, roof
displacement angle
35
o FEM of two RC frame structures built to 1980’s California
design code.
Efficient Intensity Measures for Multiple Systems and Infrastructures
Dymiotis et al. PGA; Sa
(2000)
Yield rotation; critical interstory drift.
o Regular 10-story RC frame considered.
DumovaJoanoska
(2000)
Park and Ang damage
index
o Non-linear analysis of RC frame structures using synthetic
earthquakes scaled to IMM.
IMM
o Two limit states: ultimate and serviceability, as defined by
Eurocode 8.
o Analysis for < 10 and > 10 story RC structures.
o 5 Damage states considered.
o Based on Skopje building stock.
Sasani et al.
(2001)
Sd
Sasani et al.
(2002)
Significant
PGA
Top displacement
o Displacement-based analysis for 15-story RC structural wall.
o Fragility estimates given for case with uncertainties and case
without.
Maximum base shear
demand.
o Application of inelastic dynamic analysis to RC structural wall.
o Time histories based on near source motions.
o Fragility curves given for mean and uncertainty, plus shear
failure and flexural failure.
Lang (2002)
Sd
Top Displacement
o See Lang (2002) - Masonry Buildings.
Penelis et al.
(2002)
PGA; Sd
As for masonry
o See Penelis et al. (2002) – Masonry Buildings
Franchin et
al. (2003)
Sa
Ultimate strength
o Response surface procedure applied to 6-story RC frame
structure.
o Curves for FORM and SORM analysis.
36
Recommendations for Intensity Measures to be Used in Lifeline Analysis
Masi (2003)
Normalised base shear;
Inter-story drift; ductility
demand
o Four-story gravity load designed RC frame (different degrees
of infilling).
o Nonlinear time history analysis (artificial accelerograms and
Umbria-Marche sequence).
o DPMs produced for six damage states.
Rossetto and
Elnashai
(2003)
Sd; Sa; PGA
Homogenised RC damage
scale, DIHRC (function of
maximum inter-story drift)
o New damage scale introduced for European RC stock.
Milutinovic
and
Trendafiloski
(2003)
Sd; IMM
As for masonry structures
o As RISK-UE
Ayoub et al.
(2004)
Sa
Ductility; Strength reduction
factor
o Fragility curves given for frames undergoing degradation with
strong shaking.
o Fragility curves derived from empirical data for six damage
states. Correlation of DIHRC to other damage scales also
given.
o Incremental Dynamic Analysis used, and curves presented for
different degrees of degradation and for different models.
De Stefano et
al. (2004)
PGA
Inter-story Drift
o Non-linear dynamic analysis of 8-story RC frame structure
designed to Eurocode 8.
o Four limit states considered.
o Comparison of curves with and without P-Δ effects.
Kostov et al.
(2004);
Faccioli et al.
(2004)
As RISK-UE
o As RISK-UE
37
Efficient Intensity Measures for Multiple Systems and Infrastructures
Erberik and
Elnashai
(2004)
Sd
Schotanus et
al. (2004)
Sa
Dimova and
Negro (2005)
PGA
Rossetto and
Elnashai
(2005)
Sd
Inter-story Drift
o Four limit states considered for medium rise 5 story RC flat
slab structures, based on US code design.
o Fragility curves derived from inelastic dynamic analysis.
Response surface
o Application of response surface method to 3D RC structure.
o Separate curves given for different directions of loading.
Maximum inter-story drift
and DIHRC; Park and Ang
Index
o Experimental fragility curves for 1-story RC structure.
DIHRC
o Fragility curves for 3-story RC in-filled frame structure –
designed to 1982 Italian Code.
o Four damage grades defined.
o Derived from inelastic dynamic analysis.
o 6 damage grades considered.
Akkar et al.
(2006)
PGV
Drift ratio
o RC frame structures based on Istanbul building stock.
o 32 sample buildings considered, classified into 4 groups by
height.
o Three damage states considered.
Dimova and
Negro (2006)
PGA
DIHRC; Inter-story drift
o Comparison of fragility curves for 1-story RC frame, based on
construction quality.
o Five damage states considered.
Kirçil and
Polat (2006)
Sd
Inter-story drift ratio.
o Fragility curves for mid-rise RC buildings designed to 1975
Turkish code.
o Nonlinear dynamic analyses performed
reinforcement grade allowed to vary.
38
with
steel
Recommendations for Intensity Measures to be Used in Lifeline Analysis
Kwon and
Elnashai
(2006)
PGA
Inter-story drift
o Fragility curves for three story moment resisting RC frame
structure, CEUS design.
o Curves for strong motion on ―lowland‖ and ―upland‖ soil, for
three damage states.
o Comparison for time histories with low, intermediate and high
a/v ratios.
Ramamoorthy Sa
et al. (2006)
Inter-story drift
o Fragility curves for two-story gravity designed RC structures,
close to CEUS standard.
o Three damage states considered.
o Comparison of curves with some retrofitting.
Ellingwood et
al. (2007)
Sa
Maximum inter-story drift
angle
o Fragility curves for 3- and 6-story gravity load design RC
frames, typical of CEUS construction.
o Nonlinear time history analysis on synthetic ground motions.
o Three damage states considered, corresponding to NEHRP
2003 limit states.
Goulet et al.
(2007)
Sa (1.0 s)
Heuste and
Bai (2007)
Sa; Sd; PGA
Roof drift ratio (for precollapse); maximum interstory drift ratio
o Fragility curve for 4-story RC structure designed to IBC 2003.
Maximum inter-story drift
o Fragility curves for 5-story RC flat slab office building, typical
of CEUS. Three limit states considered.
o Nonlinear dynamic analysis for pre-collapse response, IDA for
collapse response.
o Comparison of retrofit schemes and summary of comparable
analyses.
39
Efficient Intensity Measures for Multiple Systems and Infrastructures
Jeong and
Elnashai
(2007)
PGA
Spatial damage index; Park
and Ang Damage Index;
o Fragility analyses for torsionally imbalanced RC frame
structures.
o Three limit states considered.
o Three story 2 × 2 bay RC frame structure used.
Beker and
Erberik
(2008)
PGV
Maximum inter-story drift
ratio
o Fragility curves for three classes of Turkish Low- and MidRise frames (Poor, Typical and Superior).
o Three damage states use (Immediate Occupancy, Life Safety
and Collapse prevention).
o Modelled using linear hysteretic analysis.
Borzi et al.
(2008a)
PGA
Inter-story (chord) rotation
o Fragility curves for 2, 3, 4, 5, 6, and 8 story RC frames,
characteristic of Italian typology.
o Curves derived by SP-BELA, with four limit states considered.
o Comparison with DBELA beam- and column-sway curves.
Columbi et al.
(2008)
Sd
Spectral Displacement
o Empirical fragility curves defined for RC and mixed RCmasonry from Italian earthquake damage data.
o Comparison of empirical curves with analytical curves derived
by DBELA and SP-BELA.
o Three limit states considered.
Erberik
(2008)
40
PGV
Softening Index (for
serviceability LS) , spectral
displacement and drift ratio
o Four Turkish RC classes considered: low and high rise, bare
frame and in-filled.
o Comparison of nonlinear time history derived curves with
empirical data from the Izmit and Duzce earthquakes.
Recommendations for Intensity Measures to be Used in Lifeline Analysis
Güneyisi and
Altay (2008)
PGA; Sa; Sd
Inter-story drift ratio.
o Fragility curve for 12-story RC frame office building (circa
1975 Turkish code).
o Comparison of different degrees of viscous damping. Four
damage states considered.
o Nonlinear time history analysis using 240 synthetic motions.
Lagaros
(2008)
PGA
Maximum inter-story drift
o Fragility curve for 4-story RC buildings designed to meet
current Greek codes, with and without infill.
Polese et al.
(2008)
Sd
Inter-story drift ratio
o Based on Naples building stock, three RC classes considered
(1 – 3 storys; 4 – 7 stories; > 7 stories).
o Four damage states considered.
Ramamoorthy Sa
et al. (2008)
Peak inter-story drift (%)
o Fragility curves for regular plan, gravity load designed, low(1-, 2-, and 3-story) and mid-rise (6- and 10-story) RC
concrete – typical of CEUS design.
o Three limit states considered (IO, LS, CP), and curves given
for first yield and plastic mechanism initiation.
Bai et al.
(2009)
Sa
Inter-story drift (%)
o Probabilistic method for assessing structural damage to
CEUS structures (5-story RC flat slab; steel moment-resisting
frame and 2-story URM).
o Four damage states considered.
o Curves given with uncertainty bands.
41
Efficient Intensity Measures for Multiple Systems and Infrastructures
Ji et al.
(2009)
PGA; Sa
(0.2 s); Sa
(1.0 s)
Peak Inter-story drift (%);
Inter-story pure translation
(%)
o 54 story dual core wall high-rise RC structure modelled.
o Three limit states considered.
o Numerical time history analysis used – records split into three
categories (near and large M; near and small M; far and large
M).
Buratti et al.
(2010)
Sa
Column strength; concrete
strain
o Application of response surface method to three story RC
frame structure.
Celik and
Ellingwood
(2010)
Sa
Peak inter-story drift
o FEM analysis of 3-, 6- and 9-story gravity load designed RC
structures typical of CEUS stock.
o Three limit states considered (IO, LS, CP).
o Fragility curves given for each structure and each limit state
including confidence bands
Steel
Song and
Ellingwood
(1999)
Sa
Maximum inter-story drift
angle; Roof drift angle
o Reliability and fragility analysis of four steel moment resisting
frames (SMRF) with welded connections designed to 1994
Uniform Building Code.
o Four limit states considered and curves presented for
degraded and bilinear models, and for recorded and
simulated ground motion.
Dimova and
Elenas (2002)
Sa, Sv, S a ,
S v ,SI,
PGA, PGV
42
Story drifts; maximum
moment; axial force of
bracings; Local Damage
Index
o Fragility curves for four types of 4-story steel frame structure.
o Comparison of multiple IMs to test correlation with EDP.
o Fragility curves given for failure in each structure using
different EDPs, and for 2nd-story failure using different IMs.
Recommendations for Intensity Measures to be Used in Lifeline Analysis
Curadelli and
Riera (2004)
PGA
Peak inter-story drift (and
inter-story drift vector)
o Comparison of fragility curves with and without energy
dissipation device.
o Two structures considered: 10-story steel frame (designed to
UBC 1997) and 6-story RC frame.
Kinali and
Ellingwood
(2007)
Sa
Inter-story drift angle
o Fragility curves for 3-, 4- and 6-story steel frames designed to
1993 National Building Code, 1948 San Francisco code and
1991 Standard Building Code respectively.
o Three limit states considered (IO, SD [structural damage],
CP).
Lagaros and
Fragiadakis
(2007)
Vector IM;
Sa
Maximum inter-story drift
o Application of neural network approach to fragility analysis for
a 10-story steel moment resisting frame.
o Ground motion input from various vectors of ≤16 different IMs.
o Five damage states considered and curves presented for
―optimum‖, ―good‖, ―bad‖ and ―full‖ vector of IMs.
Bermudez et
al. (2008)
Sd
Yield and ultimate
displacement
o Fragility curves for 4-story curved plan steel building designed
to 1998 Columbian Code.
o Capacity spectrum method used. HAZUS damage state
definition used. Separate curves for each damage state for
braced frame and for moment-resisting frames.
Kazantzi et al. Sa
(2008a)
Maximum inter-story drift
o Fragility curves derived for 5-story mid-rise steel frame
designed to EC8 standard.
o Time-history analysis undertaken using European records.
o Two limit states considered (Life safety, collapse prevention),
and curves defined for finite and unlimited joint ductility.
43
Efficient Intensity Measures for Multiple Systems and Infrastructures
Kazantzi et al. Sa (2%
(2008b)
damped)
Roof drift angle; inter-story
drift angle.
o Fragility curves for 3-story steel framed structure designed to
UBC 1994.
o Three limit states considered (IO, LS, CP) and fragility curves
presented separately using roof drift and inter-story drift.
Li and
Ellingwood
(2008)
Sa
Maximum inter-story drift
ratio
o Fragility curves for 9- and 20-story steel moment resisting
frame buildings – designed to 1994 UBC.
o Three limit states considered (IO, LS, CP).
o Comparison of acceptable workmanship (21 % of total
connections suffer early fracture) and marginal workmanship
(58 %).
Timber/
Wood
Ellingwood
and Kinali
(2009)
Sa
Maximum inter-story drift
angle
Filatroult and
Folz (2002)
Sd
Maximum Top
Displacement
o Performance of wooden frame shear wall analysed – fragility
curves not given – for UBC 1997 design.
Rosowsky
(2002)
PGA
Peak shear-wall
displacement
o Structural performance (not fragility curve) of wood framed
walls.
o Fragility analysis for 2- and 4-story partially restrained
moment frames and a 6-story cross braced frame.
o Fragility curves for three damage states (IO, LS, CP).
o Two limit states considered (IO and LS).
o Performance curves given for different configurations of wall.
Ellingwood et
al. (2004)
Sa
Peak shear-wall
displacement
o Fragility functions developed from Rosowsky (2002) structural
performance data.
o LS and IO limit states defined in terms of peak transient drift, ,
and with different R factors for LS state.
44
Recommendations for Intensity Measures to be Used in Lifeline Analysis
Horie et al.
(2004)
PGV
Collapse
o Empirical fragility functions derived from Kobe earthquake
damage.
o Curves given for each era of woodframe construction, for
collapse only.
Kim and
Rosowsky
(2005)
Sa
Kim et al.
(2006)
Sa
Peak shear-wall
displacement
o Fragility curves derived for wooden shear-wall designed to
UBC 1997 standards, typical for California.
o Three limit states considered (IO, LS and CP), with curves
given for limit states, nailing schedules and R factors.
Peak shear-wall
displacement
o Fragility curves given for wooden shear-walls under different
degrees of biological degradation of the fasteners.
o Three limit states considered (IO, LS, and CP).
o Curves for each limit states considering different fastener
degradation times and configurations.
Lee and
Rosowsky
(2006)
Sa
Li and
Ellingwood
(2007)
Sa
Pang et al.
(2007)
Sa
Roof drift; inter-story drift
o Fragility surface derived for wood frame structures under
combined snow and earthquake loads.
o Curve parameters for 1-story and 2-story structures and for
three limit states (IO, LS and CP) under different snow loads.
Peak shear-wall drift
o Fragility curves presented for three types of shear-wall: solid,
openings and garage door.
o Three limit states considered (IO, LS and CP).
Peak shear-wall
displacement
o Fragility curves derived for wooden shear-walls using
evolutionary parameter hysteretic model.
o Two limit states (IO and LS) considered; curves only for IO.
45
Efficient Intensity Measures for Multiple Systems and Infrastructures
Gencturk et
al. (2008)
PGA; Sd
Yield and Ultimate Strength
o Fragility curves for population of woodframe buildings using a
modified CSM method, which incorporates non-linear dynamic
analysis.
o Five damage states considered.
Onishi and
Hayashi
(2008)
S v 1 3s 
Collapse
o Empirical fragility curves for the collapse of wooden houses,
derived from damage distribution from Kobe earthquake.
o Curves presented for increasing age of building.
o Correlations between velocity definition tested – strongest
correlation between average Sv over 1 to 3 s (5 % damped)
period (near analogue for SI).
Pang et al.
(2009)
Sa
Peak drift ratio
o Fragility analysis for six wooden frame structure
configurations (1- and 2- stories, with and without cripple wall)
typical of Memphis.
o Three limit states considered (Operational, IO and LS) as well
as for splitting and wall uplift.
Pei and van
de Lindt
(2009)
46
Sa
Peak drift ratio
o Loss model (including fragility analysis) for two structures (1story and 2-story) with different floor plans.
o Curve for the collapse limit state shown, derived using time
history analysis from California earthquake records.
Recommendations for Intensity Measures to be Used in Lifeline Analysis
b) Transportation Systems
Elements
at Risk
Reference
Intensity
Measure
Bridges
Basoz and
PGA
Kiremidjian
(1997, 1998);
Demand Parameter/
Damage Index
Observed Damage
o Empirical fragility curves derived from Loma Prieta and Northridge
data.
o Most bridges considered are multiple span concrete box girder
highway bridges
Basöz et al.
(1999)
Tanaka et al.
(2000)
Comments
o Five damage states considered (none, minor, moderate, major,
collapse).
PGA (IMM)
Observed Damage
o Empirical fragility curves derived from damage data from Kobe
earthquake for highway bridges.
o Separate curves for RC bridges and Steel bridges for both
―collapse‖ and ―major‖ damage state.
Yamazaki et
al. (2000)
PGA;
PGV
Damage Rank
(qualitative)
o Empirical fragility curves derived from damage data highway
bridge damage from Kobe earthquake.
Hwang et al.
(2001)
Sa; PGA
Displacement ductility
ratio
o Analytical fragility curves for CEUS (Memphis) bridges (4-span
continuous concrete deck, supported by concrete column bents)
using artificial time histories.
o 5 damage states considered (HAZUS).
47
Efficient Intensity Measures for Multiple Systems and Infrastructures
Karim and
Yamazaki
(2001)
PGA;
PGV
Park and Ang Damage
Index
o Analytical and dynamic fragility curves for RC bridge piers
designed to Japan Code standards.
o Bridge model is 40 m by 10 m, with a pier height of 8.5 m and
cross section area of 4 m by 1.5 m.
o Five damage states (None, slight, moderate, extensive, complete).
o Curves for 1964 and 1998 codes and for different sets of
earthquake records.
Gardoni et
al. (2002)
Sa
Drift Demand;
Normalised shear
demand
o Fragility curves derived for RC Californian bridges designed to
Caltrans criteria.
o Separate curves for failure in shear, failure in deformation and
failure of the system.
o Different curves for different formulations of bridge bent.
Codermatz
et al. (2003)
PGA
-
o Fragility curve for class ―B‖ bridge (continuous bridges < 150 m
continuous span) based on Risk Management Solutions (1996 –
Unseen) methodology.
Karim and
Yamazaki
(2003)
PGA;
PGV; SI
Park and Ang Damage
Index
o Comparison of Karim and Yamazaki (2001) fragility method with
simplified method based on overstrength ratio.
o 30 bridges considered: 4 RC bridge piers and two RC bridge
structures, built to 1964, 1980, 1990 and 1995 Japanese code
standard
o 4 damage states considered (slight, moderate, extensive and
complete).
o Comparison of isolated and non-isolated system.
48
Recommendations for Intensity Measures to be Used in Lifeline Analysis
Kim and
Feng (2003)
PGA,
PGV, Sa,
Sv, SI
Ductility Demand
o Analytical fragility curves for 7 structures representing typical
California RC highway bridges with lengths between 34 m and 500
m, using spatially coherent synthetic time histories.
o Four damage states considered (―at least minor‖, ―at least
moderate‖, ―at least major‖, ―collapse‖).
o Curves for cases with and without spatial variation, for each
damage states and for each listed IM.
Mackie and
23 IMs
Stojadinovich tested; Sa
(2003)
21 Different EDPs
tested;
Longitudinal Drift Ratio
o Large scale comparison of IM-EDP combinations for the optimal
model.
Sharma and
Mandar
(2003)
Maximum Displacement
o Fragility analysis for timber-pile bridge bent.
Sa
o Fragility curves not given.
o Responses tested on Shaketable and using nonlinear time history
analysis.
o Fragility curves given for moderate and slight damage states.
Choi et al.
(2004)
PGA
Column curvature
ductility; deformation
o Fragility analyses for four types of bridge typical of CEUS. HAZUS
damage states used.
o Fragility curves given for components (column, fixed bearing and
expansion bearing).
o Lower and upper bound curves for system damage to each bridge
type for each damage state.
49
Efficient Intensity Measures for Multiple Systems and Infrastructures
Kim and
Shinozuka
(2004)
PGA
Ductility Demand
o Comparison of fragility curves for bridges with and without steel
column jacketing.
o Two sample bridges (34 m and 242 m) used for nonlinear tie
history analysis. Five damage states (none, slight, moderate,
extensive, complete).
o Curves for each damage state, before and after retrofit.
Nateghi and
Shahsavar
(2004)
PGA;
PGV
NIBS (2004)
Sa (1.0s);
PGDf
Inelastic Displacement
Ductility Ratio; Park and
Ang damage index
o Fragility curves derived from nonlinear time history analysis for
pre-stressed concrete bridge.
-
o Fragility curves derived by Basoz and Mander (1999).
o Five damage states considered (none, slight, moderate, extensive
and complete).
o Five damage states (HAZUS).
o Medians given for 28 bridge classes (with dispersion fixed at 0.6)
for Sa (1.0 s) and PGDf.
Lupoi et al.
(2005)
PGA
Curvature Ductility
o Fragility analysis for different configurations of three cantilever pier
bridge under spatially variable ground motions.
o Curves given for different configurations of varying soil type under
the abutments.
Mackie and
134 IMs
Stojadinovich tested.
(2005)
Sa; CAD
23 EDPs tested;
Drift ratio; displacement
ductility
o Extensive update of Macke and Stojadinovich (2003), considering
a wider range of IM-EDP combinations.
o Fragility curves and surfaces given for Drift Ratio-Sa, Drift RatioCAD, for 1.5 % drift ratio limit state.
o Sensitivity to span/height ratio and column to superstructure width
tested, and uncertainty bounds given for curves.
50
Recommendations for Intensity Measures to be Used in Lifeline Analysis
Kappos et al.
(2006)
PGA
Ductility ratio; shear
deformation of bridge
beams
o Fragility curves derived for two different bridge types in Northern
Greece using both capacity spectrum and nonlinear time history
analysis.
o Four damage states considered (minor, moderate, major and
collapse) with curves given for each damage state in the
longitudinal and transverse direction for each bridge example.
Karacostas
et al. (2006)
PGA
Drift ratio
o Fragility analysis undertaken for the Polymylos bridge (Greece).
o Comparison of response under loading suggested in Greek Code,
and under time histories from Greek earthquakes.
o Four damage states considered (minor, moderate, extensive,
collapse) and curves given for both transverse and longitudinal
direction.
Mackie and
Sa
Stojadinovich
(2006)
Tangential drift ratio
o Fragility analysis for PEER testbed bridges – two configurations
considered.
o Curves given for some configurations of bridge at the 2.5% drift
limit states.
o Curves also given for one configuration at the spalling, buckling
and failure limit states.
Banerjee and PGA
Shinozuka
(2007)
Rotational ductility
demand
o Analysis undertaken using nonlinear static procedure (CSM
converted to rotations at column ends) for example 242 m span
Californian bridge.
o Five damage states considered (none, slight, moderate, extensive
complete), and curves given for each damage state in the
longitudinal and transverse directions.
51
Efficient Intensity Measures for Multiple Systems and Infrastructures
Nielson and
Des Roches
(2007a)
PGA
8 EDPs tested: column
curvature ductility most
efficient for PGA.
o Component level nonlinear time history analysis for 8
configurations of multi-span simply supported concrete girder
bridge (typical CEUS).
o Four damage states (slight, moderate, extensive and complete)
with fragility parameters given for each component (columns,
bearings and abutments) and for the system for each damage
state.
Nielson and
Des Roches
(2007b)
PGA
Sharma et al. Sa
(2007)
Depends on component
(column ductility,
component deformation)
o Nonlinear time history analysis for 8 configurations of bridges
typical of CEUS.
Drift Ratio
o Capacity spectrum method applied to determine fragility for timber
bridges.
o Four damage states considered (As Nielson and DesRoches,
2007a) and fragility curves given for components and system (with
uncertainty) for each damage state.
o 5 damage states considered (none, minor, moderate, extensive,
complete).
o Curves given for braced timber pile bents (longitudinal and
transverse), and for foundation failure.
Shinozuka et
al. (2007b,c)
PGA; Sa
Observed Data, Column
rotational demand
o Extensive comparison of empirical (Northridge) and analytical
methods for derivation of fragility curves.
o Mostly based on California designs, with ground motions typical of
the Los Angeles region.
o HAZUS damage states adopted.
o Many curves compared for each different analysis method,
damage state, retrofit strategy etc.
52
Recommendations for Intensity Measures to be Used in Lifeline Analysis
Banarjee and PGA
Shinozuka
(2008)
Rotational ductility
demand
Kashighandi
et al. (2008)
Curvature ductility
PGDf
o Comparison of analytical fragility analysis for three configurations
of RC bridges with empirical fragility curves for California bridges.
o Five damage states considered, and analytical technique
optimised for agreement with empirical curves.
o Fragility analysis for bridges under ground deformation and
liquefaction.
o Monte Carlo analysis of bridge structure parameters, with
configuration consistent with 1971 Californian Code.
o Four damage states given in terms of curvature ductility.
Padgett and
DesRoches
(2008)
Zhang et al.
(2008a,b)
PGA
PGA;
PGDf
Column curvature
ductility; bearing
deformation; abutment
deformation
o Fragility analysis for bridge configurations given in Nielson and
DesRoches (2007), curves given for retrofitted components with
different retrofit methods.
Section ductility, shear
strain
o Nonlinear time history analysis for 6 bridge configurations
(California type) under strong shaking and liquefaction-induced
lateral spreading.
o Four damage classes (slight, moderate, extensive and complete),
with parameters given for each component and each class.
o Four damage states, with each damage state defined by
composite of section ductility and shear strain.
o Fragility curves given for each model at each damage state for
PGA and PGDf
53
Efficient Intensity Measures for Multiple Systems and Infrastructures
Zhang and
Huo (2008,
2009)
PGA
Section ductility, bearing
shear strain
o Nonlinear time history analysis used to derived fragility curves for
both isolated and non-isolated bridge (Mendocino Crossing,
California).
o Four damage states considered (slight, moderate, extensive,
collapse), with different curves depending on type of isolation
(column, pier, bearing)
Zhong et al.
(2008, 2009)
Sa;
Deformation demand;
PGV/PGA shear demand
o Vectorial fragility analysis for two column RC bridge (I-880
viaduct), incorporating interaction of columns.
o Only one damage state is considered (failure), but fragility
surfaces defined for different modes of failure on different
columns.
Choe et al.
(2009)
Sa
Shear demand
o Fragility curves for RC concrete bridge (to current Caltrans
standard) in a tidal zone, taking into account corrosion.
Moschonas
et al. (2009)
PGA
Bridge-deck
displacement; bearing
shear deformation
o Classification and capacity spectrum analysis of 11 common
Greek bridge types.
o Five damage states
extensive, complete).
considered
(none,
minor,
moderate,
o Longitudinal and transverse fragility curves given for each bridge
and each damage state.
o Comparison of code input and time-histories from Greek
earthquakes.
54
Recommendations for Intensity Measures to be Used in Lifeline Analysis
Tunnels
ALA
(2001a,b)
PGA;
PGDf
Damage State
o Parameters of fragility curves given for water tunnels (see water
systems).
o Parameters given for bored tunnels and cut and cover tunnels, for
both poor/average and good quality construction.
o Two damage states used (three considered), with additional
curves for the possibility of landslide debris closing the portal.
NIBS (2004)
PGA;
PGDf
Damage State
o Five damage states considered (none, slight, moderate, extensive
and complete), but parameters given for only 2 when using PGA
(minor and moderate), and three when using PGDf
(slight/moderate, extensive, complete).
o Two tunnel types considered: bored/drilled and cut and cover.
Argyroudis et
al. (2007)
PGA
Pitilakis et al.
(2007)
PGA
-
o Analytical fragility analysis for shallow tunnels in alluvial deposits.
o Fragility curves given for different soil classes.
LESSLOSS
Ratio of developing
moment to moment
resistance of tunnel
lining.
o Tunnel response modelled via FEM.
o Four damage states considered (None, Minor,
Extensive).
Moderate,
o Fragility curves given for circular or rectangular shapes, and for
different soil classifications.
Roads
NIBS (2004)
PGDf
Damage State
o Fragility parameters given only for PGDf.
o Three damage states considered: slight/minor (slight offset),
moderate (offset several inches) and extensive/complete (offset
several feet).
o Separate parameters for major roads and urban road.
55
Efficient Intensity Measures for Multiple Systems and Infrastructures
Maruyama et
al. (2008)
PGV, IJMA
Damages per kilometre
o Empirical fragility curves derived using data from 2003 Northern
Miyagi and 2003 Tokachi-Oki earthquakes.
o Most damages analysed due to embankment failure.
o PGV and JMA determined for gird cells via empirical attenuation
models and kriging.
o Separate curves for major and minor damage using both PGV and
JMA intensity
Sakai et al.
(2010)
PGV
Road damage ratio
o Empirical correlations between road damage ratio (ratio of
damaged roads in a grid cell to total number of roads in a grid cell)
and PGV (also spatial PGV gradient).
o Stronger correlation to PGV than to PGV gradient.
Railway
Tracks
NIBS (2004)
PGDf
Damage State
o As for roads
Railyway
System
Facilities
NIBS (2004)
PGA;
PGDf
Damage State
o Fragility curves given for fuel facilities (in terms of PGA and PGDf)
and dispatch facilities (in terms of PGA).
o Five damage states considered (HAZUS).
o Separate curves given for facilities with and without anchored
components and with and without backup power.
56
Recommendations for Intensity Measures to be Used in Lifeline Analysis
c) Water Systems
Elements at
Risk
Reference
Water
Source
(Wells)
NIBS (2004) PGA
Water
Treatment
Plant
Intensity
Measure
Demand Parameter/
Damage Index
Comments
Descriptive – damage
state defined by duration
of well/ pump
malfunction
o HAZUS damage states used.
Jacobson
PGA
and Grigoriu
(2008)
Service
o Fragility curve given for wells and reservoirs – derived from
analysis of Portland, Oregon, water system (Ballantyne, 2000).
NIBS (2004) PGA (via
MMI)
Descriptive - damage
state defined by duration
of plant inoperation
o Fragility parameters given for wells and sub-components
o One damage state (failure) considered.
o HAZUS damage state
o Fragility parameters
subcomponents.
given
for
anchored
and
unanchored
o PGA converted from MMI
Pumping
Station
SRM-LIFE
(2006 –
2009)
PGA
As NIBS (2004)
o As NIBS (2004)
Ballantyne
et al. (2009)
PGA,
PGDf
Functionality and
restoration cost
(proportion of
replacement cost)
o Fragility curves not given.
Descriptive – damage
state defined by duration
of inoperation
o Five damage states defined.
NIBS (2004) PGA
o Three damage states considered: Light, Moderate Severe.
o Fragility parameters
subcomponents.
57
given
for
anchored
and
unanchored
Efficient Intensity Measures for Multiple Systems and Infrastructures
SRM-LIFE
(2006 –
2009)
PGA
Jacobson
PGA
and Grigoriu
(2008)
As NIBS (2004)
o As NIBS (2004)
Service
o Fragility curves given for substation, pump building, control
equipment, control building and main pump.
o Derived from analysis of Portland, Oregon, water system
(Ballantyne, 2000).
o One damage state (failure) considered.
Storage
Tanks
NIBS (2004) PGA,
PGDf
Descriptive - damage
state defined by extent
of cracking and buckling
o HAZUS Damage States
o Fragility parameters given for on-ground concrete, steel and wood
tanks (unanchored and anchored), above ground steel tanks and
buried concrete tanks (PGDf used for buried tank)
O’Rourke
and So
(2000)
PGA
Descriptive – type and
extent of structural
damage
o Four damage states defined: None (ds1), slight/minor (ds2),
extensive (ds3) and complete (ds4)
ALA
(2001a, b)
PGA,
PGDf
Descriptive definition of
damage state for each
component. Damage
factor defined as ratio of
restoration cost to
replacement cost
o Four damage states (ds2 – ds5) defined. Different descriptions of
damage for:
o - Roof damage
o - Anchor bolts damage
o - Overflow pipe damage
o - Elephant foot buckle
o - Inlet pipe leak
o - Wall uplift
o - Hoop Overstress
58
Recommendations for Intensity Measures to be Used in Lifeline Analysis
Pipelines
Katayama
et al. (1975)
PGA
Repair Rate /km
o Empirical Analysis
Isoyama
and
Katayama
(1982)
PGA
Repair Rate /km
o Empirical Analysis
Barenberg
(1988)
PGV;
PGS,
PGDf
Repair Rate /km
o Average damage for cast iron and steel welded pipes with
diameter ≥ 152 mm
Porter et al.
(1991)
PGDf
Repair Rate /km
o Dependent on pipe material
Wang et al.
(1991)
MSK
# Breaks /km
o Dependent on soil conditions
Honegger
and Eguchi
(1992)
PGDf
Repair Rate /km
o Dependent on pipe material
O’Rourke
and Ayala
(1993)
PGV
Repair Rate /km
o Dependent to pipe material
Eidinger et
al. (1995);
Eidinger
(1998)
PGV
Repair Rate /km
o Dependent on pipe material
Huebach
(1995)
PGDf
Repair Rate /km
o Dependent on pipe material and joint type.
59
Efficient Intensity Measures for Multiple Systems and Infrastructures
Ballantyne
and
Heubach
PGDf
Damage Rate
o 5 Vulnerability classes.
Isoyama et
al. (1998)
PGV
Repair Rate /km
o Dependent on pipe material and diameter
O’Rourke et
al. (1998)
PGA
Repair Rate /km
o Based on data from Northridge (1994) earthquake
Toprak
(1998)
PGA
Repair Rate /km
o Buried pipes
O’Rourke
and Jeon
(1999)
Vscaled
Repair Rate /km
o Vscaled is a function of PGV
Eidinger
and Avila
(1999)
PGV
Repair Rate /km
o Dependent on pipe material, diameter, joint-type and soil
Isoyama et
al. (2000)
PGA;
PGV
Repair Rate /km
o Cast-iron pipes
ALA 2001
PGV;
PGDf
Repair Rate /1,000’
o Separate fragility curves for wave (PGV) and deformation damage
(PGDf).
(1996)
o Dependent on pipe diameter
o PGDf assumed to be 88 % liquefaction, 12 % local uplift.
o Functions modified according to material and joint type
Eidinger
(2001)
60
PGV;
PGDf
Repair Rate /km
o Dependent on pipe material and joint type.
o Basis for ALA (2001) functions.
Recommendations for Intensity Measures to be Used in Lifeline Analysis
Hung
(2001)
PGA
Repair Rate /km
PinedaPorras and
Ordaz
(2003)
PGV
Repair Rate /km
o Empirical Relation.
o Data derived from Mexico City (1985) earthquake.
NIBS (2004) PGV;
PGDf
Repair Rate /km
o PGV relation from O’Rourke and Ayala (1993), PGDf relation from
Honegger and Eguchi (1992).
o Relation modified for ductile pipes.
O’Rourke
and Deyoe
(2004)
PGV;
strain
Repair Rate /km
o Separate relations defined for wave propagation and combined
wave propagation and PGDf.
Terzi et al.
(2006)
PGDf
Repair Rate /km
o Comparison of analytical (by FEM) and empirical approaches.
Yeh et al.
(2006)
PGA;
Strain
Repair Rate /km
o Empirical data from Chi-Chi (1999) earthquake.
PinedaPorras and
Ordaz
(2007)
PGV 2
PGA
Repair Rate /km
o Empirical relation derived from Mexico City (1985) earthquake
data set.
Pitilakis et
al. (2007)
PGDf;
PGV
Horizontal and Vertical
displacements
o Analytical deformation fragility analyses (via FEM) of buried
pipeline due to liquefaction (Lefkas earthquake) and fault
deformations
o Data from Lefkas 2003 earthquake.
Repair Rate /km
o Adaptation of O’Roarke and Ayala (2004) formulation for transient
strains
61
Efficient Intensity Measures for Multiple Systems and Infrastructures
Jacobson
[Mw, R];
and Grigoriu PGDf
(2008)
Relative joint
displacement; maximum
pipe strain
o Monte Carlo method to analyse fragility of pipes using response
surface.
o Separate surfaces considered for transient strains ([Mw, R]) and
permanent displacements (PGDf).
o Fragility surfaces for transient strains given for different soil
classes. One damage state (failure)
Sakai et al.
(2010)
PGV
derivative
Water supply pipe
damage ratio (%)
Canal
ALA
(2001a,b)
PGV;
PGD
Repair Rate /km
Tunnel
ALA
(2001a,b)
PGA
Descriptive – damage
state
Pitilakis et
al. (2007)
PGA
Waste Water
Treatment
Plant
NIBS (2004) PGA
SRM-LIFE
(2003)
Other
Components:
- Tunnels
- Pipelines
- Pumping
62
o Empirical data from Chuetsu (2004) earthquake.
o PGV spatial gradient used.
o Fragility curves for each damage state.
o Function of liner and material type.
o As for transportation networks.
Descriptive - Damage
State
o As NIBS (2004) for potable water.
PGA
As NIBS (2004)
o As NIBS (2004)
-
As Potable Water
o As for Potable Water
o Separate fragility function for lift stations
Recommendations for Intensity Measures to be Used in Lifeline Analysis
d) Electrical Systems
Elements at
Risk
Reference
Substations Ang et al.
and
(1996)
Components
Intensity Demand Parameter/
Measure Damage Index
PGA
Comments
Lateral capacity of
component.
o Computed fragilities compared with data from Loma Prieta.
o Substation fragility tested for component configuration sensitivity.
Pires et al.
(1996)
PGA
As Ang et al. (1996)
o As Ang et al. (1996)
Hwang and
Huo (1998);
Hwang and
Chou
(1998)
PGA; Sa
Maximum tensile stress
of porcelain pothead.
Overturning moment of
transformer.
o Synthetic ground motions fixed to PGA.
Vanzi
(1996)
PGA
o Fragility curves presented for components (Hwang and Huo,
1998) and for substations.
o Fault tree analysis of components (Hwang and Chou, 1998)
Fragility determined my
mechanical model of
component – tested on
Shaketable
o Separate
fragility
macrocomponent.
curves
for
microcomponents
o Station failure a probabilistic function of component failure.
Anagos and
Ostrom
(2000)
PGA
Failure of porcelain
columns and porcelain
head. Contact
misalignment
o Based on empirical data from California earthquakes.
Eidinger,
and Ostrom
(2004)
PGA
Loss of offsite power
o Basis for HAZUS (NIBS, 2004) fragility parameters
o Observed and analytical methods
o Parameters for multiple sub-components
63
and
Efficient Intensity Measures for Multiple Systems and Infrastructures
NIBS (2004)
Rasulo et
al. (2004)
PGA;
PGDf
PGA
Damage state defined
by Boolean definition of
% of components failing:
disconnect switches,
circuit breakers,
transformers and
building damage.
Ground failure damage
as for potable water
systems.
o 5 damage states: ds1 (< 5 % of component failure), ds2 (< 40 %),
ds3 (< 70 %), ds4 (< 100 %), ds5 (100 %).
Minimum cuts necessary
to interrupt electrical flow
o Fragility curves given for 11 individual components and the whole
substation.
o Separate curves for low medium and high voltage, and for
anchored and unanchored components.
o Based on damage
earthquakes.
Song et al.
(2005)
PGA; Sa;
arms
Vanzi et al.
(2005); Nuti
et al. (2007)
PGA; Sa
Shinozuka
et al.
(2007a)
PGA
64
Component fragilities
defined by response
ratio. Substation fragility
defined by probabilistic
model of component
failures
observed
during
the
Molise
(2002)
o Investigation of response of SDOF components within a
connected system.
o Fragility curves defined for system.
o Fragility curves given by Vanzi et al. (2005).
o Loss model derived from fragility curves.
Component failure
o Curves based on empirical data – defined for transformers, circuit
breakers and disconnect switches
Recommendations for Intensity Measures to be Used in Lifeline Analysis
Distribution
Circuits
Paolacci
and
Giannini
(2008)
Sa
Displacement at top of
element, deformation at
bottom of element,
relative displacement
with respect to base.
o Fragility curves for disconnect switches on ShakeTable.
Vanzi
(1996)
PGA
As for ―Substations and
Components‖
o As for ―Substations and Components‖
NIBS (2004)
PGA
Damage state defined
by % of circuits failed
o Five damage states: ds1 (0 %), ds2 (4 %), ds3 (12 %), ds4 (50 %),
ds5 (80 %).
o Standard and seismic designed components
65
Efficient Intensity Measures for Multiple Systems and Infrastructures
e) Gas and Oil Facilities
Elements
at Risk
Reference
Intensity Demand Parameter/
Measure Damage Index
Production
(Offshore
platforms
and wells)
NIBS (2004)
PGA;
PGDf
Damage State
Comments
o Five HAZUS damage states considered.
o Distinction between small (< 100,000 barrels/day)
medium/large (>100,000 barrels/day) refineries.
and
o Curves given for each damage state for unanchored and anchored
components.
o Curves also given for pumping plants with and without anchored
components.
o PGDf fragility as for water systems.
Storage
Tanks
O’Rourke
and So
(2000)
PGA
Damage State
ALA (2001a,
b)
PGA,
PGDf
Descriptive definition of
damage state for each
component.
o As for water systems
NIBS (2004)
PGA;
PGDf
Damage State
o Five HAZUS damage states considered.
o Empirical fragility curves derived from Californian earthquakes.
o Fragility curves given for four HAZUS damage states (excluding
ds1), for tanks with height to diameter ratio less than and greater
than 0.7, and for tanks less than and greater than 50 % full.
o Fragility curves given for tank farms with anchored and
unanchored components.
o PGDf fragility as for water systems.
66
Recommendations for Intensity Measures to be Used in Lifeline Analysis
Iervolino et
al. (2004)
PGA
Iervolino
(2003);
Fabbrocino et
al. (2005)
PGA
Virella et al.
(2006)
PGA
Berahman
and
Behnamfar
(2007)
PGA
Failure
o Dynamic analysis of unanchored sliding tanks.
o Fragility curves given for content depth over radius and for friction
coefficient at base of the tank.
Release from tank
o Fragility curves given for anchored storage tank (assumed to be
typical or Irpinia, Italy, and is code compliant) originally derived by
Iervolino (2003).
o Failure probability curves given for ―extensive loss‖ or ―moderate
leak‖ for near-full tanks and >50 % full tanks.
Buckling
o Finite element analysis of response of steel tank.
o No fragility curves given.
Damage State
o Empirical fragility curves for on-grade unanchored steel storage
tanks (more than 50 % full) using Bayesian analysis.
o Four damage states considered (HAZUS ds2, ds3, ds4 and ds5).
o Median and upper and lower bounds given.
o Separate curves for inclusion of Northridge data.
Razzaghi and
Eshghi
(2008)
PGA
Roof stress
o Fragility curves for cylindrical steel oil tanks derived using
numerical time history analysis.
o Two damage states considered (DS2 – plastic deformation, DS3 –
elephant foot buckling).
o Curves given for different height to diameter ratios and contents
volume.
67
Efficient Intensity Measures for Multiple Systems and Infrastructures
Pipelines
and
Distribution
Katayama et
al. (1975)
PGA
Repair Rate /km
o As for Water Systems
Isoyama and
Katayama
(1982)
PGA
Repair Rate /km
o Empirical fragility function for cast iron pipelines.
Eguchi
(1983)
IMM,
PGDf
Repair Rate /km
o Empirical fragility relations.
Baranberg
(1988)
PGV;
strain
Repair Rate /km
o As for Water Systems
Eguchi
(1991)
IMM
Repair Rate /km
o Empirical fragility curve.
Honegger
and Eguchi
(1992)
PGDf
Repair Rate /km
o As for Water Systems
O’Rourke
and Ayala
(1993)
PGV
Repair Rate /km
o As for Water Systems
Eidinger
(1995);
Eidinger et al.
(1998)
PGV
Repair Rate /km
o As for Water Systems
Ballantyne
and Heubach
(1996)
PGDf
Damage Rate
o As for Water Systems
Eidinger and
Avila (1999)
PGV
Repair Rate /km
o As for Water Systems
68
o 5 different pipe constructions compared.
Recommendations for Intensity Measures to be Used in Lifeline Analysis
O’Rourke et
al (1998)
PGA
Repair Rate /km
o As for Water Systems
Toprak
(1998)
PGA
Repair Rate /km
o As for Water Systems
O’Rourke
and Jeon
(1999)
Vscaled
Repair Rate /km
o As for Water Systems
Isoyama et
al. (2000)
PGA;
PGV
Repair Rate /km
o As for Water Systems
ALA (2001a,
b)
PGV
Repair Rate /km
o As for water systems
Chen et al.
(2002)
PGV;
PGA; SI
Damage Ratio
o Empirical fragility functions derived from 1999 Chi Chi earthquake
data.
o Dependent on pipe diameter
o Separate functions for PGA, PGV and SI, and for pipelines with
diameter < 60 mm, 60 – 150 mm and > 150 mm.
PinedaPorras and
Ordaz (2003)
PGV
Repair Rate /km
o As for Water Systems
NIBS (2004)
PGV;
PGDf
Repair Rate /km
o Fragility functions given for both PGV and PGDf.
PGA;
PGV; Ia;
SI
Repair Rate /km
Hwang et al.
(2004)
o Distinction between brittle (older gas welded steel pipes) and
ductile (pipes with submerged arc welded joints).
o Empirical fragility functions based on 1999 Chi Chi earthquake
data.
o Functions given for all four IMs (PGA, PGV, Ia, SI) and for three
model forms (linear, logarithmic and power).
69
Efficient Intensity Measures for Multiple Systems and Infrastructures
O’Rourke
and Deyoe
(2004)
PGV;
strain
Repair Rate /km
o As for water systems.
Ueno et al.
(2004)
PGDf
Bend Angle (°)
o FEM analysis of pipe system based on common design for Tehran
area.
o Six pipe designs compared, distinguished by thickness and
diameter.
o Fragility curves developed using residential construction type as a
proxy.
o 8 residential types considered.
Wijewickreme PGDf
et al. (2005)
Failure Probability
PinedaPossas and
Ordaz (2007)
PGV 2
PGA
Repair Rate /km
o Empirical relation derived from Mexico City (1985) earthquake
data set.
LESSLOSS
(2007)
PGDf
Failure criterion –
number or cracks
o Fragility curve determined using analytical method (FEM).
Pumping
NIBS (2004)
Plants/
Compressor
Stations
PGA
Damage State
o Four damage states considered: slight/minor, moderate, extensive
and complete.
70
o Finite element analysis of retrofit pipelines.
o Fragility curve given in terms of longitudinal spread.
o Comparison with other relations.
o Separate fragility curves given for plants
components and unanchored components.
with
anchored
Recommendations for Intensity Measures to be Used in Lifeline Analysis
f) Harbour Systems
Elements
at Risk
Reference
Intensity Demand Parameter/
Measure Damage Index
Comments
Waterfront
Structures
Werner et
al. (1997)
PGA
Total costs (Costs +
Losses)
o
Empirical curve for Wharf 300 (Kobe) under contingency level
acceleration
NIBS (2004)
PGDf
Descriptive – damage
state,
o
Five damage states - defined by extent of ground settlement and
pile failure
Ichii (2003;
2004)
PGA
Normalised seaward
displacement and repair
cost.
o
Gravity-type Caisson quay walls.
o
Four damage states.
o
Curves defined for equivalent NSPT, aspect width and sand
deposit thickness.
o
Monge and
Argyroudis
(2003)
PGD
Descriptive – damage
state
o
Four damage states (based on HAZUS description)
Pitilakis et
al. (2007)
PGDf
Descriptive damage
state.
o
Validation of Ichii (2003) and NIBS (2004) models using linear
analysis of harbour model – based on Lefkas earthquake and
port.
o
Ichii (2003) slightly overestimates damage – NIBS (2004)
preferred.
71
Efficient Intensity Measures for Multiple Systems and Infrastructures
Na et al.
(2008)
PGA
For gravity wall:
normalised seaward
displacement (%), tilting
(°).
o
Four damage states.
o
Methodology described, but no fragility curves given.
o
Uncertainty analysis
o
Four damage states: serviceable, repairable, near-collapse,
collapse.
o
Example fragility curves given for standard and retrofitted
components.
Residual horizontal
displacements
o
Four damage states (as above).
o
Fragility curves for pile supported wharves.
For Apron: differential
settlement (%), tilting (°)
Na and
Shinozoka
(2009)
PGA
Na et al.
(2009)
PGA
Kakderi and
Pitilakis
(2010)
PGA
(rock)
Normalised residual
horizontal seaward
displacement
o
Gravity-type (monolithic) quay walls.
o
Fragility curves based on wall height and soil condition.
PGA;
PGDf
Descriptive – damage
state
o
RISK-UE Appendix.
o
Four damage states.
o
Separate curves for anchored and unanchored components.
Descriptive – damage
state defined by damage
to structural members
and differential
displacement.
o
As NIBS (2004).
o
Separate curves for anchored and unanchored components.
o
Separate curves for PGA and PGDf.
As for NIBS (2004) Rail
systems.
o
As for NIBS (2004) rail systems
Cargo
Monge and
handling
Argyroudis
and storage (2003)
components
NIBS (2004)
Fuel
Facilities
NIBS (2004)
72
PGA;
PGDf
PGA
Uncertain for waterfront
structure components.
Recommendations for Intensity Measures to be Used in Lifeline Analysis
g) Miscellaneous (Non-structural, Hospitals, Communications, Airports)
Elements
at Risk
Reference
Intensity Demand Parameter/
Measure Damage Index
Comments
Hospitals
Monti and
Nuti (1996)
PGA
Failure of
subcomponents and
system
o Analysis of failure of components and system for Castel di Sangro
Hospital in the Abruzzi region of Italy.
Nuti and
Vanzi
(1998)
IMM
Average distance to
nearest hospital per
casualty
o Probabilistic vulnerability analysis of hospital system in Abruzzi
region.
Nuti et al.
(2004)
IMM
Average distance to
nearest hospital per
casualty
o Analysis and validation of
earthquakes, Italy.
Kuwata and
Takada
(2007)
PGA
Component/System
Failure
o Empirical fragility curves based on RC buildings in Kobe
earthquake.
o Comparison of different retrofit strategies
model based on 2002 Molise
o Pre-1981 and Post-1981 codes compared.
o Two damage states (moderate and severe).
o Fragility curves also given for water and electricity components, with
system vulnerability assessed via event-tree logic
Retamales
et al. (2008)
PGA
(PFA)
Drift ratio and failure of
equipment
o Shaketable test on simulated operating room.
o Descriptive damage for room as a whole system.
o Fragility curves given for some non-structural components (e.g. wall
monitor)
73
Efficient Intensity Measures for Multiple Systems and Infrastructures
Cimellaro et
al. (2009)
Sa, Sd
Inter-story drift
o Fragility analysis of both structural and non-structural components
based on model hospital facility (California) built to 1970 UBC.
o HAZUS input and damage states used and curves given in terms of
return period (not IM).
o Curves given for different limit states and retrofit strategies
Communication
RayChaudhiri
and
Shinozuka
(2010)
PGA;
Alexoudi
and Monge
(2003)
PGA
NIBS (2004)
PGA
Peak inter-story drift
(structure), component
failure (components)
o Extensive fragility analysis for hospital system based on 1970 UBC.
o Numerical analysis for structural system, fault tree logic for water
and electrical system, and other components.
o Fragility curves also given for different retrofit strategies.
Damage State
o RISK-UE model for loss to telecommunication facilities.
o Adoption of HAZUS (NIBS, 2004) approach.
Damage State
o Fragility curves only given for communications facilities.
o Four damage states considered (none/slight, moderate, extensive,
complete).
o Separate curves given for facilities with anchored components and
those with unanchored components.
Nonstructural
LopezGarcia and
Soong
(2003a,b)
PGA
[PFA]
Relative displacement of
component
o Fragility curves derived for sliding block masses representative of
unanchored (2003a) and anchored (2003b) components.
o Three limit states considered (relative displacement, z = 25mm,
50mm and 75mm).
o Different curves given for different friction coefficients and vertical
motion coefficients.
74
Recommendations for Intensity Measures to be Used in Lifeline Analysis
Eidinger
(2009)
PGA;
PFA;
PGV;
PGDf
Repair Rate /km
(pipelines);
Drift ratio (glass);
o Adaptation of HAZUS damage states (ds1 = none, ds2 = minor
injury, ds3 = major injury, ds4 = possible fatality, ds5 = instant
fatality)
Various descriptive
damage states for each
element.
o Elements Considered: Sprinklers, windows, suspended ceilings,
elevators, raised floors, HVAC, office equipment, mechanical
equipment, generators.
o Most curves use PGA, except pipeline facilities (PGV,PGDf)
o Basis for FEMA Cost-Benefit Analysis.
Porter et al.
(2010)
PFA
Unit [component] failure
rate
o 52 empirical fragility functions defined for
mechanical, electrical and plumbing equipment
components
of
o PFA estimated by multiplying PGA by a factor accounting for the
distribution of components at different levels in the building
Airport
Roark et al.
(2000)
PGA
Damage State
o Theoretical fragility curve given for Mid-America airport, with and
without retrofit design.
o Five damage states considered.
Argyroudis
and Monge
(2003)
PGDf;
PGA, Sa
Damage State
NIBS (2004)
PGA;
PGDf; Sa
Damage State
o RISK-UE approach to vulnerability assessment of airport facilities.
o Adoption of HAZUS methodology (NIBS, 2004).
o Fragility curves given for runways (PGDf) using three damage
states (slight/moderate, extensive and complete).
o All other components of airport system as for railway networks (fuel
facilities, maintenance facilities) or buildings (control tower,
terminal).
75
Efficient Intensity Measures for Multiple Systems and Infrastructures
7
Conclusive Remarks
There is a wide range of intensity descriptors used to assess vulnerability (and losses)
through the development of adequate fragility curves. Table 6.1 and Appendix A represent a
comprehensive working list of the different descriptors used in different lifeline systems and
infrastructures. The decisions as to which IMs should be used may, of course, be subject to
further scrutiny and re-evaluation as new fragility functions are developed within the SYNERG project. Preliminary recommendations for appropriates IMs for each system are shown in
Table 7.1.
As has been emphasized throughout this report, the context of application has an influence
over the practicality of adopting specific IMs in a seismic risk analysis over urban or regional
scales. Nowhere is this more clearly illustrated than in bridge fragility. A review of the
literature indicates a near consensus on that for engineered structures and elements that
spectral quantities may be preferred over peak values (Mackie and Stojadinovich, 2005;
Luco and Cornell, 2007). Yet the majority of fragility curves for bridges, both components
and full systems, persist in the use of PGA (Nielson, 2003). This may illustrate the disparity
in studying fragility for detailed models of individual structures, and applying the models to
portfolios of bridges. For a spatially distributed database of structures there are further
uncertainties. These may include disparity in construction material, quality and code
standard, in addition to site effects such as topography and basin resonance. These
uncertainties may be compounded for long span bridges where spatial effects such as
differential ground shaking and soil types need to be considered. Where such uncertainties
influence the risk analysis the adoption of structure-independent IMs is necessary, even if
this requires a less efficient or sufficient IM (Mackie and Stojadinovich, 2005; Padgett et al.,
2008).
From the review presented in this report, it is clear that both PGA and PGV will continue to
play an important role in fragility analysis for many lifeline systems. The spectral quantities
Sa and Sd are also important for the application of many analytical methods to determine
fragility for many types of structures, and must also be included here. Despite the increased
efficiency and sufficiency of inelastic IMs, their application to fragility analysis has not yet
become widespread. As new ground motion models are developed for this particular family
of IMs it is possible that SYNER-G may provide an important test of the application of these
IMs to full vulnerability analyses. From a practical perspective there are many ground motion
attenuation models for a range of IMs available for use in Europe, with further models
anticipated as an output of the concurrent SHARE project.
The importance of PGDf in lifeline risk analysis should also be clear from this review. Ground
deformation and failure is a crucial area of uncertainty that presents a challenge from the
perspective of fragility inputs. For the case of damage due to direct fault rupture IMs of the
form considered here may not be of use. For slope failure and liquefaction, however, it is
necessary to consider an intermediate step of probabilistic analysis to determine the
likelihood and extent displacement for a given quantity of strong shaking. Whilst this may be
undertaken via direct numerical simulation, it is likely that an IM proxy may also be needed.
There does not appear to be as strong a consensus as to which IM may be appropriate for
this purpose. Potential candidates include CAV, Ia, Neq and SI. Attenuation models for some
76
Conclusive Remarks
of these IMs are not nearly so abundant, and further investigation into their efficiency in
predicting ground displacements may be necessary
Table 7.1 Recommended IMs for Different Systems
Common IM’s
Sa, Sd, PGA, IEMS
Sa, Sd, PGA, PGV,
IEMS
Steel
Sa, Sd
Timber/Wood
Sa, Sd, PGA, PGV
Transportation Bridges
PGA, PGV, Sa, SI,
PGDf
Tunnels
PGA, PGDf
Roads
PGDf, PGV
Railway Tracks
PGDf
System Facilities
PGA, PGDf
Water
Source (wells)
PGA
[Potable and Treatment Plant
PGA
Waste]
Pumping Station
PGA
Storage Tanks
PGA, [PGDf if
below ground]
Pipelines
PGV, PGDf, PGA,
ε,
Canal
PGV, PGDf
Tunnel
PGA
Waste Water Treatment PGA
Harbour
Waterfront Structures
PGA, PGDf
Cargo Handling/Storage PGA, PGDf
Fuel Facilities
PGA
Electrical
Substations
and PGA, Sa, PGDf
Components
Distribution Circuits
PGA
Gas and Oil
Production
PGA, PGDf
Storage
PGA, [PGDf if
below ground]
Pipelines
PGV, PGDf, ε,
PGA, SI
Pumping/Compression
PGA
Recommended IM
Sa [Sd]
Sa [Sd]
Miscellaneous
PFA [Sa or Sd to define
structural response]
PGA, PFA
PGA, PFA
PGA, PGDf [runways], Sa
[irregular buildings – e.g.
control towers]
System
Building
Sub-System
Masonry
Reinforced Concrete
Non-structural
PGA, PFA
Hospitals
Communication
Airport
PGA, PFA, Sa, IMM
PGA
PGA, PGDf, Sa
Sa [Sd]
Sa [Sd]
PGA, Sa, PGVf
PGA, PGDf
PGDf
PGDf
PGA, PGDf
PGA
PGA
PGA
PGA
PGV, PGDf
PGV, PGDf
PGA
PGA
PGA, PGDf
PGA, PGDf
PGA
PGA
PGA
PGA, PGDf
PGA
PGV, PGDf
PGA
77
Efficient Intensity Measures for Multiple Systems and Infrastructures
The information contained within this report is intended to provide an insight into the current
state-of-the-art IMs for use in seismic vulnerability analysis. For some applications it has
been possible to identify ―best practice‖ IMs. Elsewhere the adoption of certain IMs may be
undertaken using judgment. It is hoped that the material presented here will help reconcile
the current state of the art in seismic hazard analysis in Europe, with the inputs needed to
extend this into an accurate and robust lifeline vulnerability analysis. It may be anticipated
that this particular topic is revisited towards the conclusion of the SYNER-G project and its
outcomes can, themselves, form a guide for best practice in lifeline vulnerability studies
globally.
78
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Efficient Intensity Measures for Multiple Systems and Infrastructures
Appendix A
A
Strong Motion Intensity Measures for
Application to Fragility Analysis of Buildings
and Lifelines
A fundamental input for the purposes of designing structures with earthquake resistance is a
quantitative representation of the seismic input. Depending on the structure under
consideration, the seismic input can take many forms. The simplest definitions of ground
motion intensity when input for structural design are single parameters that may be extracted
directly from an accelerogram. These include peak ground acceleration (PGA), peak ground
velocity (PGV) and peak ground displacement (PGD). For more complex analysis of the
response of a structure to seismic loads, the ground motion may be defined in terms of
spectral parameters and/or measure of the duration and energy of the strong motion. Also
common, however, is the use of time histories, either observed or simulated, for numerical
analysis. In this Appendix the most widely used IMs are defined. Where examples are
necessary the El Centro NS ground motion record of the 1940 Imperial Valley earthquake is
used.
A.1
PEAK GROUND ACCELERATION
For strong motion given by an acceleration time history ut  , the peak ground acceleration
(PGA) is defined as:
PGA  max ut 
As a simple measure of the strength of the seismic action, PGA is the most widely used
parameter in seismic hazard analysis and earthquake design. It simply represents the
maximum absolute acceleration produced at the site, typically measured in units of g, gals,
m s-2 or cm s-2. An example of this is given in Fig. A.1 for the El Centro strong motion record
from the 1940 Imperial Valley earthquake. A question emerges as to whether the PGA
should be taken from the uncorrected strong motion record, or the filtered record. Some
debate on this issue is given in Douglas (2003). Whilst it is possible that no consensus has
emerged, for consistency with spectral ordinates it may be more appropriate to derive PGA
from the corrected record, although differences are likely to be small depending on the high
cut-off frequency.
96
A.1
Appendix A: Strong Motion Intensity Measures
Fig A.1 Peak Ground Acceleration (PGA) indicated on the El Centro NS acceleration
record
The correlation between PGA and earthquake damage has been the subject of some
investigation. Since it corresponds to high frequency motion, the correlation between PGA
and damage is clearly dependent on the structure under consideration. It is useful for
analyses of structures with periods less than 0.3 s, but displays very little correlation with
damage to longer period structures (Douglas, 2003). Evidence of damage due to high PGA
may often be found in the near-field regions of moderate earthquakes (Brun et al., 2004).
Low rise masonry structures and non-structural elements (e.g. chimneys, balustrades) may
respond unfavourably to high PGA even over short durations of acceleration. Similarly,
electrical components and machinery may also be subject to damage from high PGA.
A.2
PEAK GROUND VELOCITY AND DISPLACEMENT
Peak ground velocity and peak ground displacement correspond to the maximum absolute
values of the velocity and displacement time histories, respectively:
PGV  max u t 
A.2a
PGD  max ut 
A.2b
These are usually measured in terms of m s-1 and cm s-1 and m and cm, respectively. PGV
and PGD provide controls on the longer period ordinates of motion.
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Efficient Intensity Measures for Multiple Systems and Infrastructures
Fig. A.2 Peak Ground Velocity (PGV) indicated on the El Centro NS (1940) velocity
record
PGV is recognised to display a stronger correlation with earthquake damage, in both direct
investigation and via macroseismic intensity as a proxy, than PGA. This may be due to its
control over ground motions in the 0.3 to 2.0 s range, which correspond to the typical periods
of many civil structures. Furthermore, PGV is also shown to correlate with damage in
pipelines and road systems. This has lead to its widespread adoption in analyses of seismic
risk to lifelines.
The control that PGD has on defining the long period part of the spectrum is more relevant
for very long period structures. However, signal processing procedures and baseline drift
mean that PGD is harder to constrain accurately. This has limited the application of PGD as
a useful parameter in damage estimation (Kramer, 1996).
A.3
PEAK GROUND MOTION RATIOS
The ratio of PGV to PGA (measured in seconds) is related to the dominant frequency
content of the motion. Dimensional analysis would suggest that it can be interpreted as the
period of an equivalent harmonic wave, thus indicating the significant periods of motion
(Kramer, 1996). The correlation between PGV/PGA and structural damage indicates
systems subjected to low PGV/PGA can sustain more significant peak inelastic deformation,
stiffness deterioration and hysteretic energy dissipation than those subjected to high
PGV/PGA (Zhu et al., 1988). The result is greater damage in structures that are subjected to
higher PGV/PGA. In addition to the impact on structural damage, the PGV/PGA ratio is
suggested as a means of constraining the corner period between constant velocity and
acceleration in the elastic response spectrum (Bommer et al., 2010).
A second, and not so widely used, parameter is the PGD/PGV ratio. There are few studies
indicating the effect of this parameter on structural response. Dimensional analysis indicates
that PGD/PGV also corresponds to the period of an equivalent harmonic wave. It could be
deduced therefore that this wave corresponds to the longer period part of the spectrum.
98
Appendix A: Strong Motion Intensity Measures
Investigation by Tehranizadeh and Meshkat-Dini (2007) suggests that whilst strong
directivity effects manifest in high PGV/PGA, they also produce low PGD/PGV. This would
indicate that these ratios are good for identifying near-fault pulses in strong motion records.
Their impact in structural response is less clear, although analysis by Mackie and
Stojadinovich (2005) shows them both to be inefficient IMs for describing structural damage
to bridge components.
A.4
ENERGY DEPENDENT PARAMETERS
A.4.1 Root Mean Square Acceleration
For an acceleration history denoted by a(t) the root mean square acceleration is determined
via:
a rms 
1
te  t0
 ut  dt
te
2
to
A.3
Where t0 and te indicate the beginning and end of the duration under consideration. The
duration may be the full length of the entire record or an alternative definition, usually one of
those given in section A.5. arms is effectively a measure of the average rate of energy
imparted by the motion. It may also be considered the sum of the input energy at all
frequencies of the record (Danciu and Tselentis, 2007).
Also defined, but rarely used, are root mean square velocity (vrms) and displacement (drms).
These are derived in the manner shown in Eq. (A.3), albeit with u t  and u t  used in place
of acceleration, and measured in units of cm/s and cm respectively.
A.4.2 Arias Intensity
In the original formulation by Arias (1970), Arias Intensity describes the cumulative energy
per unit weight absorbed by an infinite set of single degree of freedom oscillators with
frequencies uniformly distributed in the range (0, ∞) (Travasarou et al., 2003). The general
case is given by Kayen and Mitchell (1997):
I XX 
arccos  
g 1
2

 u t  dt
2
xx
A.4
0
Where Ixx is the Arias Intensity experienced by the SDOF oscillators aligned in the x-direction
with ξ damping, under ground motion in the x-direction. Arias Intensity is usually only
considered for the case of zero damping (ξ = 0), in which case Eq. (A.4) reduces to the more
common form:
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Efficient Intensity Measures for Multiple Systems and Infrastructures
I XX 


u t  dt
2g 
2
xx
0
A.5
One particularly useful property of Arias Intensity is that the arithmetic mean of the values for
two orthogonal components of motion (IXX + IYY) is orientation independent. As such, no
rotational scaling is required to find as may be the case for spectral motions. Furthermore,
several ground motion attenuation models have been developed for Arias Intensity that are
beginning to find widespread use. These are derived from global data sets of strong motion
records (Kayen and Mitchell, 1997; Travasarou et al., 2003), in addition to more regionspecific models such as those for Greece (Danciu and Tselentis, 2007) and New Zealand
(Stafford et al., 2009).
As with arms, the same integral procedure for Arias Intensity can be applied to the velocity
and displacement traces of the motion. These produce Velocity Intensity (IV) and
Displacement Intensity (ID), measured in cm and cm-s respectively. Unlike Arias Intensity,
however, rather than multiplying the integral by the constant  2 g , the velocity and
displacement integrals are multiplied by 1 PGV and 1 PGD , respectively, to produce:
 u t  dt
I VXX 
1
PGV
I DXX 
1 te
u x t 2 dt
PGD 0
te
0
2
x
These two parameters are very rarely used and generally demonstrate poor correlation with
structural damage.
A.5
STRONG MOTION DURATION
The definition of the duration of strong motion is a complex issue that has resulted in the
development of many different metrics to measure the strength of sustained ground motion.
A detailed appraisal of many of the measure of ground motion duration can be found
Bommer and Martinez-Perreira (1999, 2000), but the more common measures shall be
discussed here.
―Bracketed‖ duration (tbr) is a common means of defining the duration of strong motion. It
simply refers to the length of time between the first and last exceedence of a given threshold
value. An example of this for a high threshold (0.05g) is shown in Fig. A.3 for the El Centro
NS record. As noted by Bommer and Martinez-Pereira (1999), this definition ignores the
characteristics of the strong shaking phase and can be unstable if the threshold is low.
100
A.6
A.7
Appendix A: Strong Motion Intensity Measures
Fig. A.3 Squared acceleration trace of the El Centro NS acceleration record
An alternative approach is the ―uniform‖ duration (tuni). This is the total duration for which the
acceleration exceeds the threshold value. This requires summation of all the duration across
all the oscillations as shown in Fig. A.4 for a shorter section of the El Centro NS record.
Fig. A.4 Uniform duration indicated on a truncated portion of Fig. A.3
Uniform duration is represented as the sum of all the windows for which acceleration
exceeds the threshold level. This metric is less sensitive to the selection of the threshold
level than bracketed duration, but has the disadvantage of not representing a continuous
time window (Bommer and Martinez-Pereira, 1999).
A third, and more commonly used, type of strong motion duration is ―significant duration‖
(tsig). This duration is defined using the cumulative Arias Integral, to produce a ―Husid‖ plot,
as shown in Fig. A.5 (this has been normalised to illustrate Arias Integral as a fraction of the
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Efficient Intensity Measures for Multiple Systems and Infrastructures
Arias intensity of the full record). The significant duration is calculated as the time-window
between the IAlower and IAhigher fraction levels. The most commonly used time window is the
0.05 – 0.95 Ia window, shown in Fig. A.6. Other commonly used windows may include 0 –
0.95 Ia or 0.05 – 0.75 Ia.
Fig. A.5 Husid plot for the El Centro acceleration record – red line indicates 0.05Ia –
0.95Ia region
Fig. A.6 Significant duration (red) of the El Centro NS acceleration record
Bommer and Martinez-Pereira (1999) introduce a modification to the definition of significant
duration, which results in ―effective‖ duration (teff). The parameter is calculated from:
teff = tf – t0
Where t0 is the time when the Husid plot exceeds a specified level of Arias Intensity (0.1 m/s
used in the original paper) and tf the end of the strong shaking phase. This is defined as the
time at which the remaining energy of the record is equal to an absolute amount ΔI af, a value
taken as 0.135 m/s originally
102
A.8
Appendix A: Strong Motion Intensity Measures
A.6
CUMULATIVE ABSOLUTE VELOCITY
The cumulative absolute velocity (CAV) has a similar interpretation to arms. It is simply
derived by integration over the absolute ground acceleration for the entire record:
CAV   ut  dt
t
A.9
0
As CAV is derived from integration over the whole record it is sensitive to the cutoff time of
the record, and also to high frequency content. To overcome this, some applications
integrate over only acceleration exceeding a given threshold. The most common of these is
the 5 cm s-2 threshold (Kramer and Mitchell, 2006), which is formulated as:
n
ti
i 1
ti 1`
CAV   
where
 ut  dt
A.10
  0 if a < 5 cm s-2, 1 otherwise.
The method of integrating the acceleration trace to determine CAV can also be applied to
the velocity trace. This direct analogy results in the quantity cumulative absolute
displacement (CAD), defined thus:
CAD   u t  dt
t
A.11
0
CAD is usually given in metres or, more commonly, centimetres. It could reasonably be
expected that CAD may show better correlation with long-period motions, and therefore
better effectiveness for long period structures. Finally, when applying the same integral to
the absolute displacement trace we define a further parameter which is Cumulative Absolute
Impulse (CAI), measured in cm-s:
CAI   u t  dt
t
A.12
0
A.7
COMPOUND METRICS
The parameters introduced to this point are derived directly from the acceleration, velocity
and displacement histories. Two additional metrics are considered in studies of optimal IMs
103
Efficient Intensity Measures for Multiple Systems and Infrastructures
are the characteristic intensity (IC) (Park et al., 1984; Park and Ang, 1985) and the Fajfar
(1990) index (If). The characteristic intensity is calculated by:


.5
0.5
I C cm1.5 s 2.5  a1rms
Tsig
A.13
This parameter is believed to describe the destructiveness of a given ground motion. It
originates from correlations with structural damage as defined by the structural damage
index (Danciu and Tselentis, 2007).
Fajfar’s (1990) index is derived from a similar principle, but is intended as a measure of the
destructiveness of ground motions to medium-period structures. It is a measure of the
destructiveness of ground motion in the constant velocity part of the spectrum, and as such it
is PGV that modifies the significant duration:


0.25
I f cm  s 0.75  PGV  Tsig
A.8
A.14
EFFECTIVE NUMBER OF CYCLES OF MOTION
The nature of earthquake damage to structures and structural elements is affected by the
strength of motion and also by the duration. A review of studies detailing the influence of
strong motion duration on such structures is given by Hancock and Bommer (2006). Of
particular relevance to geotechnical engineering applications is the number of cycles of
loading. Cyclic loads applied to saturated soils can result in dramatic loss of soil strength
producing soil liquefaction.
Many studies of geotechnical performance of soils consider cycles of uniform amplitude (or
uniform cycles). Observed strong motion, however, displays many non-uniform
characteristics. To relate observed cycles of motion to the characteristics required for
numerical modelling of geotechnical and structural response it is necessary to define the
―Number of Effective [or equivalent] cycles‖ (Neff). Calculation of this parameter requires
counting of the number of cycles in the motion record. The number of effective cycles is
determined via the formula of Malhotra (2002):
N eff
1 2tn  u
   i
2 i 1  u max



2
A.15
Where ui is the amplitude of the ith half cycle, umax the amplitude of the largest half-cycle and
tn the total number of cycles. Several methods for counting the number of cycles are
discussed in Hancock and Bommer (2005). These include peak counting, level crossing,
range counting (i.e. the rainflow algorithm) and spectral proxies.
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Appendix A: Strong Motion Intensity Measures
A.9
RESPONSE SPECTRA
This describes the input of motion as a function of the response of an elastic single degree
of freedom (SDOF) oscillator with ξ % damping and natural period T (seconds). This is
widely used in earthquake engineering as it clearly indicates the strength of ground motion
that may adversely affect structures at given frequencies. The response spectrum is
commonly calculated using the Nigam and Jennings (1969) algorithm. Using the properties
of the equation of motion, the response spectra for acceleration (Sa), velocity (Sv) and
displacement (Sd) are related thus (Chopra, 1995):
 2
S v T   
T

 S d T 

A.16
 2 
S a T   
 S d T 
T 
2
A.17
Fig. A.7 Response Spectra for the El Centro NS strong motion record, a) Pseudospectral acceleration, b) Pseudo-spectral velocity and c) Spectral Displacement
105
Efficient Intensity Measures for Multiple Systems and Infrastructures
Sa and Sv are derived via the period dependent formulation, they are commonly referred to
as pseudo-spectral velocity and acceleration. Fig. A.7 illustrates the acceleration, velocity
and displacement response spectra for the El Centro NS record, for different levels of
damping (fraction of critical damping).
Spectral acceleration is widely used as an input for analysis of structures under seismic
excitation, and has been for decades. Typically this is done via the use of Newmark’s (1973)
idealisation of the elastic response spectrum, as is commonly found in seismic design codes
across the world. In recent years, however, strong ground motion models have increasingly
adopted spectral ordinates. This allows for the estimation of the response spectrum from
deterministic scenario events or from a probabilistic uniform hazard spectrum.
A.10 SPECTRUM INTENSITY
This term describes a group of ground motion parameters adapted from the Housner
Spectrum Intensity (SI), calculated by:
SI   
1
C1

t2
t1
S v  , T dT
A.18
Where T is the period of the velocity response spectrum SV for damping factor ξ, and C1, t1
and t2 are constants. In Housner’s (1952) original formulation t1 and t2 took the values of 0.1
s and 2.5 s respectively, whilst C1 was 1. In more common usage the integral in A.18 is
normalised with period, changing C1 to 2.4. A similar formulation was made by Von Thun et
al. (1988), who utilise spectral acceleration at a fixed ξ = 0.05 rather than velocity,
consequently adjusting t1 and t2 to 0.1 and 0.5 respectively.
SI is effectively a measure of the intensity of ground shaking. Given the spectral limits,
however, the correlation with damage is strongest in buildings with a fundamental period in
the 0.1 to 2.5 s range (Martinez-Rueda, 1998). The measure has often been used as a tool
for scaling time histories for use in structural analyses (Hidalgo and Clough, 1974; Nau and
Hall, 1984; Matsumura, 1992). This has resulted in some modifications to the parameters in
order to limit the spectral range to those periods most relevant to the fundamental period of
the structure (Martinez-Rueda, 1998; Ueong, 2009). The correlation between SI (and its
variants) and damage is often stronger than that of PGA or PGV, although this is dependent
on the structure(s) considered.
A.11 EFFECTIVE PEAK ACCELERATION AND VELOCITY
These parameters were introduced by the Applied Technology Council (1978), and originally
helped constrain the elastic design spectrum. They are defined as:
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Appendix A: Strong Motion Intensity Measures
EPA 
1 1 n

  S a Ti 
2.5  n i 1

A.19
1 1 n

  S v Ti 
2.5  n i 1

A.20
EPV 
Where Sa and Sv are the 5 % damped acceleration and velocity, respectively, at period T,
where T = 1 s (and n = 1) for EPV (Kramer, 1996). Modifications to these formulae have
been proposed by Kurama and Farrow (2003), who suggest reducing the period range for
EPV to 0.8 ≤ T (s) ≤ 1.2 and normalising by 2.5, and by Yang et al. (2009), who suggest
restricting the spectral range for both EPA and EPV to ± 0.2 s of the predominant period of
ground motion then normalising by 2.5. These modifications are intended to be applied to
near-field records to account for the influence of near field pulses.
A.12 ELASTIC INPUT ENERGY
The elastic input energy is derived from the motion of a damped SDOF oscillator acted upon
by a force  mxg :
mxg  x   cx  k  0
A.21
where x is the relative displacement of mass with respect to the ground, xg the displacement
of the ground, c the damping coefficient and k the restoring force. Integrating Eq. (A.21) with
respect to x gives:
mxt2 2   cxdx   fdx   xt dx g
A.22
where xt = x + xg is the absolute displacement. The RHS of Eq. (A.22) is the absolute energy,
which can also be expressed as:


Ea   x  xg x g dt
A.23
The maximum elastic input energy is therefore defined as the maximum Ea over oscillators in
the range 0 ≤ T ≤ t:
107
Efficient Intensity Measures for Multiple Systems and Infrastructures
t
Ei T   max   ut t   ut u t dt 
 0

A.24
where ut t  is the response acceleration of the SDOF system with fundamental period T, and
ut  and u t  are the ground acceleration and velocity respectively. The absolute input
energy can be converted into an equivalent velocity Vei via:
Vei T  
2 Ei T 
m
A.25
Attenuation models for elastic input energy, or equivalent velocity, have been derived for
Greece (Dancu and Tselentis, 2007) and also using a global set of strong motion records
(Decanini and Molllaioli, 1998).
A.13 INELASTIC AND STRUCTURE-SPECIFIC MEASURES OF INTENSITY
The recognition that the response of a structure under ground motion displays strongly nonlinear characteristics reveals the shortcomings of using elastic response parameters as a
measure of intensity. Nonlinearity includes both the inelastic response of structures with a
given damping ratio (ξ1) and ductility (d1), and the effect of higher modes of elastic and
inelastic motion.
Where ground motion is characterised by a response spectrum, building response analyses
can be selective in the spectral ordinates used to determine fragility curves. For a structure
of known elastic fundamental period T1, acceleration input for models of building response
may often take the form of Sa at period T1, or occasionally Sa at a standard ordinate close to
T1 (e.g. Sa (1 s) for structures with medium period response, or Sa (0.2 s) for acceleration
sensitive elements). This parameter Sa(Tl) represents elastic response for the fundamental
mode. In many applications structural response analysis the elastic spectral displacement
(Sd) is preferred. This is derived directly from spectral acceleration using Eq. (A.17).
Consequently Sd is a direct proxy for elastic Sa at a given period T. Following the
nomenclature of Luco and Cornell (2007), elastic Sa for the fundamental mode of the
structure is given as:
~ S T 
IM 1E  PF11 S d T1 , 1  
a
1
A.26
where PF1 is the model structure’s first mode participation factor, and ξ1 is the damping ratio
(not necessarily equal to 5 %). To take into consideration inelastic displacement, equation
108
Appendix A: Strong Motion Intensity Measures
Eq. (A.26) can be multiplied by the ratio of the spectral displacement of an elastic-perfectlyplastic oscillator Sd(T1, ξ1, dy) to the elastic oscillator:
IM 1I  PF1 S T1 , 1 , d y  
1
I
d
S dI T1 , 1 , d y 
S d T1 , 1 
IM 1E
A.27
where dy is the yield displacement, which can be determined from a pushover analysis of the
structure.
For taller structures higher modes can influence the response of the structure. Using the
sum-of-squares rule for modal combination, the IM can be adapted to take into consideration
the first two modes of the structure:
IM 1E &2 E 
PF  S
2
1
d
T1 , 1 2  PF22 S d T2 ,  2 2
PF12 
IM 1E
PF11
A.28
PF22  S d T2 ,  2 
PF12  S d T1 , 1 
A.29
 1  R22E / 1E
where
R2 E / 1 E 
which can be similarly adapted to take into consideration inelastic response in the first mode
by incorporating Eq. (A.27):
IM 1I &2 E 
S dI T1 , 1 , d y 
S d T1 , 1 
IM 1E &2 E  1  R22E / 1E
PF12 
IM 1I
PF11
A.30
Eq. (A.29) can also be adapted for the use of an ―equivalent‖ elastic SDOF oscillator, which
is derived in the same manner as for inelastic response:
IM 1eq  PF11 S deq, T1 , 1 , d y  
S deq T1 , 1 , d y 
S d T1 , 1 
IM 1E
A.31
Other IMs are defined in the main body of this report where relevant.
109