D 2 - Home | VCE Pipelines and Distribution .....25 6.3.3 Storage .....26 6.4 ELECTRICAL SYSTEMS...

D 2.12

DELIVERABLE

PROJECT INFORMATION

Project Title: Systemic Seismic Vulnerability and Risk Analysis for

Buildings, Lifeline Networks and Infrastructures Safety Gain

Acronym: SYNER-G

Project N°: 244061

Call N°: FP7-ENV-2009-1

Project start: 01 November 2009

Duration: 36 months

DELIVERABLE INFORMATION

Deliverable Title: D2.12 – Efficient Intensity Measures for Components

Within a Number of Infrastructures

Date of issue: 30 April 2011

Work Package: WP2 Development of a Methodology to Evaluate Systemic Vulnerability

Deliverable/Task Leader: University of Pavia

Reviewer: Norwegian Geotechnical Institute

REVISION: Final

Project Coordinator: Institution:

e-mail: fax:

telephone:

Prof. Kyriazis Pitilakis Aristotle University of Thessaloniki [email protected] + 30 2310 995619 + 30 2310 995693

mailto:[email protected]

i

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

iii

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

v

Deliverable Contributors

University of Pavia Graeme Weatherill

Helen Crowley

Rui Pinho

Table of Contents

vii

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

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

4 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

Efficient Intensity Measures for Multiple Systems and Infrastructures

viii

4.15 MEHANNY (2009) .................................................................................................... 18

4.16 YANG ET AL. (2009) ................................................................................................ 18

5 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

6 Recommendations for Intensity Measures to be Used in Lifeline Analysis................ 22

6.1 BUILDINGS .............................................................................................................. 22

6.2 TRANSPORTATION NETWORKS AND BRIDGES .................................................. 23

6.2.1 Roadways and Railway Tracks ..................................................................... 23

6.2.2 Tunnels ........................................................................................................ 23

6.2.3 Bridges ......................................................................................................... 24

6.3 WATER AND WASTE SYSTEMS ............................................................................ 25

6.3.1 Extraction and Treatment ............................................................................. 25

6.3.2 Pipelines and Distribution ............................................................................. 25

6.3.3 Storage ........................................................................................................ 26

6.4 ELECTRICAL SYSTEMS ......................................................................................... 26

6.4.1 Distribution ................................................................................................... 26

6.4.2 Generation ................................................................................................... 26

6.5 GAS AND OIL SYSTEMS ........................................................................................ 27

6.5.1 Pipelines....................................................................................................... 27

6.5.2 Components ................................................................................................. 27

6.5.3 Storage Tanks .............................................................................................. 28

6.6 HARBOUR SYSTEMS ............................................................................................. 28

6.6.1 Waterfront Structures ................................................................................... 28

6.6.2 Cargo Handling and Storage Components ................................................... 29

6.6.3 Fuel Facilities ............................................................................................... 29

6.7 OTHER FACILITIES (HOSPITALS, COMMUNICATION, AIRPORT AND NON-STRUCTURAL ELEMENTS ..................................................................................... 29

6.7.1 Non-Structural Elements .............................................................................. 29

6.7.2 Hospitals ...................................................................................................... 30

6.7.3 Communications ........................................................................................... 30

6.7.4 Airports ......................................................................................................... 30

7 Conclusive Remarks ....................................................................................................... 76

References .............................................................................................................................. 79

Table of Contents

ix

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

List of Figures

xi

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

List of Tables

xiii

List of Tables

Table 6.1 Fragility Studies for Lifeline Systems and Components ...................................... 32

Table 7.1 Recommended IMs for Different Systems .......................................................... 77

Introduction

1

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)


2

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.

Introduction

3

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.

Seismic Fragility Analysis

5

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:

IMIMIMdsDPDPP i

log|

(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.

Defining Optimum Intensity Measures

7

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:

IMDM

IMdIMDMdGDMLSGLS,

|||| (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).

IMEDPDM

IMdIMEDPdGEDPDMdGDMDVGDV,,

||| (3.2)

The remaining terms and the conditional probabilities are the same as those in Eq. (3.1).


8

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.


9

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:

bIMaEDP (3.3)

which transforms into IMbaEDP logloglog 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.


10

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:

dfn

PDEEDPn

i

i

1

2ˆloglog

where

n

i

iEDPn

PDE1

1ˆ

(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:

22

eT (3.5)

The epistemic uncertainty may be given by expert judgment or via simulation


11

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:

0|

T

IMEDP

(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:

EDPdIMdEDPP

loglog1|

(3.7)

Substituting Eq. (3.3) into Eq. (3.7) gives:


12

b

b

adIM

IMdEDPP

logloglog

|

(3.8)

The proficiency (ζ) is therefore defined by:

b

(3.9)

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.

Summary of Studies to Define Optimum Intensity Measures

13

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:

aSaa RTSS 1

* where 1TSTSR afaSa

(4.1)

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 ≤ Tf/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


14

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 structure-independent 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.


15

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 moment-resisting 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:

i

t

ta

aic

a dTS

STS

e

s

%5,

%5,ln%5,ln

1

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 first-period dominated structures, and IM1Iand2E performs better for higher-mode structures. They


16

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 SI 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 first-order approximation. It should be recognized, however, that IMM is not dependent on a single


17

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:

IMbbIMM 1010 log (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


18

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 non-linear 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 Tf 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:

1

1

1 TRSTSIM aaSR

(4.4a)

131

1 TRSTSIM aaCR

(4.4b)

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.

Suitable Intensity Measures for Different Infrastructure Systems

19

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


20

phenomena. This includes liquefaction (both lateral spreading and ground settlement), co-seismic 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 PGDf 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.

Suitable Intensity Measures for Different Infrastructure Systems

21

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):

S

trC

PGV (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.


22

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 Sa, 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.

Recommendations for Intensity Measures to be Used in Lifeline Analysis

23

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


24

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, soil-structure 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


25

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.


26

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 first-order delineation of the generation facilities whose response may be adequately


27

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.


28

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.


29

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),


30

which forms the basis of the FEMA Cost-Benefit calculations. With the exception of non-structural 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


31

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.


32

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

o 5 Damage states.

NIBS (2004) Sd; equivalent PGA for components

Displacement Ductility 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

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.


33

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 o As RISK-UE approach.

o Application to Catania.

Pitilakis et al. (2004)

Sd; PGA As RISK-UE approach o As RISK-UE approach.

o Application to Thessaloniki.

Pasquale et al. (2005)

IMCS MSK Defined Damage Intensity

o Vulnerability curves derived from damage probability matrices.

D’Ayala

(2005) Sa (Mean Response); Sd

EMS Damage Scale; Displacement Ductility

o Two approaches compared: force-based (Sa) and displacement- based (Sd).

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.


34

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 EMS Building Damage o Macroseismic based loss model for Grenoble.

o Damage probability matrices used.

Barbat et al. (2008)

Sd 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


35

Erberik (2008)

PGA Base Shear o Three damage states – insignificant, moderate and severe/collapse.

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 (in-plane 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 in-plane walls.

Ruiz-Garcia and Negrete (2009)

Sd Drift ratio o Two damage states defined by extent of cracking.

o Low rise URM typical of Latin America

Rota (2008); Rota et al. (2010)

PGA Top Displacement o Four damage states considered.

o Stochastic analysis of uncertainty on building parameters.

Reinforced Concrete


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 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).

Song et al. (2000)

Sa Inter-story drift angle, roof displacement angle

o FEM of two RC frame structures built to 1980’s California

design code.


36

Dymiotis et al. (2000)

PGA; Sa Yield rotation; critical inter-story drift.

o Regular 10-story RC frame considered.

o Two limit states: ultimate and serviceability, as defined by Eurocode 8.

Dumova-Joanoska (2000)

IMM Park and Ang damage index

o Non-linear analysis of RC frame structures using synthetic earthquakes scaled to IMM.

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 Top displacement o Displacement-based analysis for 15-story RC structural wall.

o Fragility estimates given for case with uncertainties and case without.

Sasani et al. (2002)

Significant PGA

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.


37

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.

o Fragility curves derived from empirical data for six damage states. Correlation of DIHRC to other damage scales also given.

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 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


38

Erberik and Elnashai (2004)

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.

Schotanus et al. (2004)

Sa Response surface o Application of response surface method to 3D RC structure.

o Separate curves given for different directions of loading.

Dimova and Negro (2005)

PGA Maximum inter-story drift and DIHRC; Park and Ang Index

o Experimental fragility curves for 1-story RC structure.

o Four damage grades defined.

Rossetto and Elnashai (2005)

Sd DIHRC o Fragility curves for 3-story RC in-filled frame structure – designed to 1982 Italian Code.

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.


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 with steel reinforcement grade allowed to vary.


39

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 et al. (2006)

Sa Inter-story drift o Fragility curves for two-story gravity designed RC structures, close to CEUS standard.


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) Roof drift ratio (for pre-collapse); maximum inter-story drift ratio

o Fragility curve for 4-story RC structure designed to IBC 2003.

o Nonlinear dynamic analysis for pre-collapse response, IDA for collapse response.

Heuste and Bai (2007)

Sa; Sd; PGA Maximum inter-story drift o Fragility curves for 5-story RC flat slab office building, typical of CEUS. Three limit states considered.

o Comparison of retrofit schemes and summary of comparable analyses.


40

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 Mid-Rise 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 RC-masonry from Italian earthquake damage data.

o Comparison of empirical curves with analytical curves derived by DBELA and SP-BELA.


Erberik (2008)

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.


41

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 et al. (2008)

Sa 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.


42

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 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, aS ,

vS ,SI, PGA, PGV

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.


43

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. (2008a)

Sa 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.


44

Kazantzi et al. (2008b)

Sa (2% 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 %).

Ellingwood and Kinali (2009)

Sa Maximum inter-story drift angle

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).

Timber/ Wood

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 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.


45

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)


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.

Kim et al. (2006)


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 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.

Li and Ellingwood (2007)

Sa 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).

Pang et al. (2007)


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.


46

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.


Onishi and Hayashi (2008)

sSv 31 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)

Sa Peak drift ratio o Loss model (including fragility analysis) for two structures (1-story and 2-story) with different floor plans.

o Curve for the collapse limit state shown, derived using time history analysis from California earthquake records.


47

b) Transportation Systems

Elements

at Risk

Reference Intensity

Measure

Demand Parameter/

Damage Index

Comments

Bridges Basoz and Kiremidjian (1997, 1998); Basöz et al. (1999)

PGA 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

o Five damage states considered (none, minor, moderate, major, collapse).

Tanaka et al. (2000)

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).


48

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.


49

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 Stojadinovich (2003)

23 IMs tested; Sa

21 Different EDPs tested; Longitudinal Drift Ratio


o Large scale comparison of IM-EDP combinations for the optimal model.

Sharma and Mandar (2003)

Sa Maximum Displacement o Fragility analysis for timber-pile bridge bent.

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.


50

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

Inelastic Displacement Ductility Ratio; Park and Ang damage index

o Fragility curves derived from nonlinear time history analysis for pre-stressed concrete bridge.

o Five damage states considered (none, slight, moderate, extensive and complete).

NIBS (2004) Sa (1.0s); PGDf

- o Fragility curves derived by Basoz and Mander (1999).

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.


134 IMs tested. 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 Ratio-CAD, 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.


51


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.


Sa 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 Shinozuka (2007)

PGA 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.


52

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 Depends on component (column ductility, component deformation)

o Nonlinear time history analysis for 8 configurations of bridges typical of CEUS.

o Four damage states considered (As Nielson and DesRoches, 2007a) and fragility curves given for components and system (with uncertainty) for each damage state.

Sharma et al. (2007)

Sa Drift Ratio o Capacity spectrum method applied to determine fragility for timber bridges.

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.


53

Banarjee and Shinozuka (2008)

PGA Rotational ductility demand

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.

Kashighandi et al. (2008)

PGDf Curvature ductility 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)

PGA 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.

o Four damage classes (slight, moderate, extensive and complete), with parameters given for each component and each class.

Zhang et al. (2008a,b)

PGA; PGDf

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 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


54

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; PGV/PGA

Deformation demand; 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 considered (none, minor, moderate, extensive, complete).

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.


55

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 - o Analytical fragility analysis for shallow tunnels in alluvial deposits.

o Fragility curves given for different soil classes.

Pitilakis et al. (2007) LESSLOSS

PGA Ratio of developing moment to moment resistance of tunnel lining.

o Tunnel response modelled via FEM.

o Four damage states considered (None, Minor, Moderate, Extensive).

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.


56

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


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.


57

c) Water Systems

Elements at

Risk

Reference Intensity

Measure

Demand Parameter/

Damage Index

Comments

Water Source (Wells)

NIBS (2004) PGA Descriptive – damage state defined by duration of well/ pump malfunction

o HAZUS damage states used.

o Fragility parameters given for wells and sub-components

Jacobson and Grigoriu (2008)

PGA Service o Fragility curve given for wells and reservoirs – derived from analysis of Portland, Oregon, water system (Ballantyne, 2000).

o One damage state (failure) considered.

Water Treatment Plant

NIBS (2004) PGA (via MMI)

Descriptive - damage state defined by duration of plant inoperation

o HAZUS damage state

o Fragility parameters given for anchored and unanchored subcomponents.

o PGA converted from MMI

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 Three damage states considered: Light, Moderate Severe.

Pumping Station

NIBS (2004) PGA Descriptive – damage state defined by duration of inoperation

o Five damage states defined.

o Fragility parameters given for anchored and unanchored subcomponents.


58

SRM-LIFE (2006 – 2009)



PGA 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


59

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.


60

Ballantyne and Heubach (1996)

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

o Dependent on pipe diameter

Eidinger and Avila (1999)

PGV Repair Rate /km o Dependent on pipe material, diameter, joint-type and soil


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).

o PGDf assumed to be 88 % liquefaction, 12 % local uplift.

o Functions modified according to material and joint type

Eidinger (2001)

PGV; PGDf

Repair Rate /km o Dependent on pipe material and joint type.

o Basis for ALA (2001) functions.


61

Hung (2001)

PGA Repair Rate /km

Pineda-Porras 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.

o Data from Lefkas 2003 earthquake.

Yeh et al. (2006)

PGA; Strain

Repair Rate /km o Empirical data from Chi-Chi (1999) earthquake.


PGA

PGV 2

Repair Rate /km o Empirical relation derived from Mexico City (1985) earthquake data set.


PGDf; PGV

Horizontal and Vertical displacements Repair Rate /km

o Analytical deformation fragility analyses (via FEM) of buried pipeline due to liquefaction (Lefkas earthquake) and fault deformations

o Adaptation of O’Roarke and Ayala (2004) formulation for transient strains


62


[Mw, R]; PGDf

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 (%)

o Empirical data from Chuetsu (2004) earthquake.

o PGV spatial gradient used.

Canal ALA (2001a,b)

PGV; PGD

Repair Rate /km

Tunnel ALA (2001a,b)

PGA Descriptive – damage state

o Fragility curves for each damage state.

o Function of liner and material type.


PGA o As for transportation networks.

Waste Water Treatment Plant

NIBS (2004) PGA Descriptive - Damage State

o As NIBS (2004) for potable water.

o Separate fragility function for lift stations

SRM-LIFE (2003)


Other Components: - Tunnels - Pipelines - Pumping

- - As Potable Water o As for Potable Water


63

d) Electrical Systems

Elements at

Risk

Reference Intensity

Measure

Demand Parameter/

Damage Index

Comments

Substations and Components

Ang et al. (1996)

PGA 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.

o Fragility curves presented for components (Hwang and Huo, 1998) and for substations.

o Fault tree analysis of components (Hwang and Chou, 1998)

Vanzi (1996)

PGA Fragility determined my mechanical model of component – tested on Shaketable

o Separate fragility curves for microcomponents and macrocomponent.

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


64


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 %).

o Separate curves for low medium and high voltage, and for anchored and unanchored components.

Rasulo et al. (2004)

PGA Minimum cuts necessary to interrupt electrical flow

o Fragility curves given for 11 individual components and the whole substation.

o Based on damage observed during the Molise (2002) earthquakes.

Song et al. (2005)

PGA; Sa; arms

Component fragilities defined by response ratio. Substation fragility defined by probabilistic model of component failures

o Investigation of response of SDOF components within a connected system.

o Fragility curves defined for system.

Vanzi et al. (2005); Nuti et al. (2007)

PGA; Sa o Fragility curves given by Vanzi et al. (2005).

o Loss model derived from fragility curves.

Shinozuka et al. (2007a)

PGA Component failure o Curves based on empirical data – defined for transformers, circuit breakers and disconnect switches


65

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.

Distribution Circuits

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


66

e) Gas and Oil Facilities

Elements

at Risk

Reference Intensity

Measure

Demand Parameter/

Damage Index

Comments

Production (Offshore platforms and wells)


Damage State o Five HAZUS damage states considered.

o Distinction between small (< 100,000 barrels/day) and medium/large (>100,000 barrels/day) refineries.

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 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.

ALA (2001a, b)

PGA, PGDf

Descriptive definition of damage state for each component.

o As for water systems


Damage State o Five HAZUS damage states considered.

o Fragility curves given for tank farms with anchored and unanchored components.

o PGDf fragility as for water systems.


67

Iervolino et al. (2004)

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.

Iervolino (2003); Fabbrocino et al. (2005)

PGA 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.

Virella et al. (2006)

PGA Buckling o Finite element analysis of response of steel tank.

o No fragility curves given.

Berahman and Behnamfar (2007)

PGA 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.


68

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.

o 5 different pipe constructions compared.

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)


Ballantyne and Heubach (1996)

PGDf Damage Rate o As for Water Systems

Eidinger and Avila (1999)



69

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

o Dependent on pipe diameter


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 Separate functions for PGA, PGV and SI, and for pipelines with diameter < 60 mm, 60 – 150 mm and > 150 mm.



NIBS (2004) PGV; PGDf

Repair Rate /km o Fragility functions given for both PGV and PGDf.

o Distinction between brittle (older gas welded steel pipes) and ductile (pipes with submerged arc welded joints).

Hwang et al. (2004)

PGA; PGV; Ia; SI

Repair Rate /km 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).


70

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 et al. (2005)

PGDf Failure Probability o Finite element analysis of retrofit pipelines.

o Fragility curve given in terms of longitudinal spread.

Pineda-Possas and Ordaz (2007)

PGA

PGV 2

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).

o Comparison with other relations.

Pumping Plants/ Compressor Stations

NIBS (2004) PGA Damage State o Four damage states considered: slight/minor, moderate, extensive and complete.

o Separate fragility curves given for plants with anchored components and unanchored components.


71

f) Harbour Systems

Elements

at Risk

Reference Intensity

Measure

Demand Parameter/

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)


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.


72

Na et al. (2008)

PGA For gravity wall: normalised seaward displacement (%), tilting (°). For Apron: differential settlement (%), tilting (°)


o Methodology described, but no fragility curves given.

o Uncertainty analysis

Na and Shinozoka (2009)

PGA Uncertain for waterfront structure components.

o Four damage states: serviceable, repairable, near-collapse, collapse.

o Example fragility curves given for standard and retrofitted components.

Na et al. (2009)

PGA Residual horizontal displacements

o Four damage states (as above).

o Fragility curves for pile supported wharves.

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.

Cargo handling and storage components

Monge and Argyroudis (2003)

PGA; PGDf

Descriptive – damage state

o RISK-UE Appendix.


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.

Fuel Facilities

NIBS (2004) PGA As for NIBS (2004) Rail systems.

o As for NIBS (2004) rail systems


73

g) Miscellaneous (Non-structural, Hospitals, Communications, Airports)

Elements

at Risk

Reference Intensity

Measure

Demand Parameter/

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.

o Comparison of different retrofit strategies

Nuti et al. (2004)

IMM Average distance to nearest hospital per casualty

o Analysis and validation of model based on 2002 Molise earthquakes, Italy.

Kuwata and Takada (2007)

PGA Component/System Failure

o Empirical fragility curves based on RC buildings in Kobe earthquake.

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)


74

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

Ray-Chaudhiri and Shinozuka (2010)

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.

Communi- cation

Alexoudi and Monge (2003)

PGA Damage State o RISK-UE model for loss to telecommunication facilities.

o Adoption of HAZUS (NIBS, 2004) approach.

NIBS (2004) PGA 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.

Non-structural

Lopez-Garcia 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.


75

Eidinger (2009)

PGA; PFA; PGV; PGDf

Repair Rate /km (pipelines); Drift ratio (glass); Various descriptive damage states for each element.

o Adaptation of HAZUS damage states (ds1 = none, ds2 = minor injury, ds3 = major injury, ds4 = possible fatality, ds5 = instant fatality)

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 components of mechanical, electrical and plumbing equipment

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.


Argyroudis and Monge (2003)

PGDf; PGA, Sa

Damage State o RISK-UE approach to vulnerability assessment of airport facilities.

o Adoption of HAZUS methodology (NIBS, 2004).

NIBS (2004) PGA; PGDf; Sa

Damage State 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).


76

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 SYNER-G 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

Conclusive Remarks

77

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

System Sub-System Common IM’s Recommended IM

Building Masonry Sa, Sd, PGA, IEMS Sa [Sd] Reinforced Concrete Sa, Sd, PGA, PGV,

IEMS Sa [Sd]

Steel Sa, Sd Sa [Sd] Timber/Wood Sa, Sd, PGA, PGV Sa [Sd]

Transportation Bridges PGA, PGV, Sa, SI, PGDf

PGA, Sa, PGVf

Tunnels PGA, PGDf PGA, PGDf Roads PGDf, PGV PGDf Railway Tracks PGDf PGDf System Facilities PGA, PGDf PGA, PGDf

Water [Potable and Waste]

Source (wells) PGA PGA Treatment Plant PGA PGA Pumping Station PGA PGA Storage Tanks PGA, [PGDf if

below ground] PGA

Pipelines PGV, PGDf, PGA, ε,

PGV, PGDf

Canal PGV, PGDf PGV, PGDf Tunnel PGA PGA Waste Water Treatment PGA PGA

Harbour Waterfront Structures PGA, PGDf PGA, PGDf Cargo Handling/Storage PGA, PGDf PGA, PGDf Fuel Facilities PGA PGA

Electrical Substations and Components

PGA, Sa, PGDf PGA

Distribution Circuits PGA PGA Gas and Oil Production PGA, PGDf PGA, PGDf

Storage PGA, [PGDf if below ground]

PGA

Pipelines PGV, PGDf, ε, PGA, SI

PGV, PGDf

Pumping/Compression PGA

PGA

Miscellaneous Non-structural PGA, PFA PFA [Sa or Sd to define structural response]

Hospitals PGA, PFA, Sa, IMM PGA, PFA Communication PGA PGA, PFA Airport PGA, PGDf, Sa PGA, PGDf [runways], Sa

[irregular buildings – e.g. control towers]


78

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.

References

79

References

Akkar, S., Sucuoglu, H., and Yakut, H., 2006. Displacement-Based Fragility Functions for Low- and Mid-Rise Ordinary Concrete Buildings. Earthquake Spectra 214: 901 – 927.

Alexoudi, M., 2005. Contribution to seismic assessment of lifelines in urban areas. Development of holistic methodology for seismic risk, PhD Thesis, Department of Civil Engineer, AUTh, Greece in Greek.

Alexoudi, M.N, Manou, D.K, Hatzigogos, Th.N., 2007. The influence of probabilistic loading and site-effects in the earthquake risk assessment of water system. The case of Düzce. Proceeding of 10th International Conference on Applications of Statistics and Probability

in Civil Engineering, Tokyo, Japan, July 31- 3 August, Paper Number: 176. American Lifelines Alliance, 2001a. Seismic Fragility Formulations for Water Systems. Part 1

– Guideline. ASCE-FEMA, 104 pp. American Lifelines Alliance, 2001b. Seismic Fragility Formulations for Water Systems. Part 2

– Commentary. ASCE-FEMA, 239 pp Applied Technology Council (ATC), 1978. ATC 3-06 tentative provisions for the development

of seismic regulations for buildings. Palo Alto, California. Applied Technology Council (ATC), 1985. ATC-13-Earthquake Damage Evaluation Data for

California, Redwood City, California. Applied Technology Council (ATC),1991. 2ATC25 – Seismic vulnerability and impact of

disruption of lifelines in the conterminous United States. Redwood City, CA, Applied

Technology Council.

Anagos, T., and Ostrom, D. K., 2000. Electrical Substation Equipment Damage Database for Updating Fragility Estimates. Proceedings of the 12th World Conference on Earthquake

Engineering, Auckland, New Zealand. Paper No. 2262. Anastasopoulos, I., Gerolymos, N., Drosos, V., Georgarakos, T., Kourkoulis, R., and

Gazetas, G., 2008. Behaviour of deep immersed tunnel under combined normal fault rupture, deformation and subsequent seismic shaking. Bulletin of Earthquake

Engineering 6: 213 – 239. Ang, A. H.-S., Pires, J. A., and Villaverde, R., 1996. A model for the seismic reliability

assessment of electric power transmission systems. Reliability Engineering and System

Safety 51: 7 – 22.

Argyroudis, S., Pitilakis, K., Boussoulas, N., Nakou, F., 2007. Vulnerability Assessment of Shallow Metro Tunnels in Greece, In Proceedings of the 4th International Conference on

Geotechnical Earthquake Engineering, June 25-28, Thessaloniki, Greece, paper ID: 1693.

Argyroudis, S. and Monge, O., 2003. RISK-UE WP06 – Appendix 3: Airport Transportation System. RISK-UE report. 1 – 20.

Arias, A., 1970. A measure of earthquake intensity. In Seismic Design for Nuclear Power

Plants. R. J. Hansen Editor. MIT Press. Cambridge, Massachusetts. 438 – 483. Ayoub, A., Mijo, C., and Chenouda, M., 2004. Seismic Fragility Analysis of Degrading


80

Structural Systems. Proceedings of the 13th World Conference on Earthquake

Engineering. Vancouver, Canada. 2004. Bai, J. –W., Hueste, M. B. D., and Gardoni, P., 2009. Probabilistic Assessment of Structural

Damage due to Earthquakes for Buildings in Mid-America. Journal of Structural

Engineering 135(10): 1155 – 1163. Ballantyne, D, and Heubach, W., 1996. Use of GIS to evaluate earthquake hazard effects

and mitigation on pipeline systems- Case studies. Proceedings from the Sixth Japan-

U.S Workshop on Earthquake Resistant Design of Lifeline Facilities and

Countermeasures Against Soil Liquefaction, Technical Report NCEER -96-0012. Ballantyne D., Perimon T., Martins P., 2009. Water Treatment Plant Seismic Risk

Assessment for the Joint Water Commission, Hillsboro, Oregon. Proceedings of TCLEE

2009, Lifeline Earthquake Engineering in a Multihazard Environment, ASCE, June 28- July 1, Oakland, California

Baker, J. W., and Cornell, C.A., 2005. A vector-valued ground motion intensity measure consisting of spectral acceleration and epsilon. Earthquake Engineering & Structural

Dynamics 34: 1193 – 1217. Balideh, S., Goshtasbi, K., Aghababaei, H., Khaji, N., and Merzai, H., 2009. Seismic

Analysis of Underground Spaces to Propagation of Seismic Waves Case Study: Masjed Soleiman Dam Cavern. Journal of Applied Sciences 99: 1615 – 1627.

Banarjee, S., and Shinozuka, M., 2007. Nonlinear Static Procedure for Seismic Vulnerability Assessment of Bridges. Computer-Aided Civil and Infrastructure Engineering 22: 293 – 305.

Banarjee, S., and Shinozuka, M., 2008. Mechanistic quantification of RC bridge damage states under earthquake through fragility analysis. Probabilistic Engineering Mechanics 23: 12 – 22.

Barbat, A.H., Pujades, L.G., and Lantada, N., 2006. Performance of Buildings under Earthquakes in Barcelona, Spain. Computer-Aided Civil and Infrastructure Engineering 21: 573 – 593.

Barbat, A. H., Pujades, L. G., and Lantada, N., 2008. Seismic damage evaluation in urban areas using the capacity spectrum method: Application to Barcelona. Soil Dynamics and

Earthquake Engineering 28: 851 – 865. Barenberg, M.E., 1988. Correlation of Pipeline Damage with Ground Motions. Journal of

Geotechnical Engineering ASCE 114(6): 706-711. Basöz, N. I., and Kiremidjian, A.S., 1997. Evaluation of Bridge Damage Data from the Loma

Prieta and Northridge, California Earthquakes. PhD Thesis. The John A. Blume Earthquake Engineering Centre. Department of Civil & Environmental Engineering. Stanford University.

Basöz, N. I., Kiremidjian, A.S., 1998. Evaluation of Bridge Damage Data from the Loma Prieta and Northridge, California Earthquake. MCEER Technical Report. MCEER-98-0004, State University of New York, Buffalo.

Basöz, N. I., Kiremidjian, A.S., 1999. Statistical Analysis of Bridge Damage Data from the 1994 Northridge, CA, Earthquake. Earthquake Spectra 151: 25 – 54.

Bekr, O. A.Y., and Erberik, M. A., 2008. Vulnerability of Turkish Low-Rise and Mid-Rise Reinforced Concrete Frame Structures. Journal of Earthquake Engineering 121: 2 - 11.

Berahman, F., Behnamfar, F., 2007. Seismic fragility curves for unanchored on-grade steel storage tanks: Bayesian approach. Journal of Earthquake Engineering 11:166-192.

Bermudez, C. A., Barbat, A. H., Pujadas, L. G., and González-Driego, J. R., 2008. Seismic Vulnerability and Fragility of Steel Buildngs. Proceedings of the 14th World Conference

on Earthquake Engineering. Beijing, China.

References

81

Bommer, J. J., and Martinez-Pereira, A., 1999. The Effective Duration of Earthquake Strong Motion. Journal of Earthquake Engineering 32: 127 – 172.

Bommer, J. J., and Martinez-Pereira, A., 2000. Strong Motion Parameters: Definition, Usefulness and Predictability. Proceedings of the 12th World Conference on Earthquake

Engineering, Auckland, New Zealand. Paper No. 206. Bommer, J. J., Stafford, P. J., and Akkar, S., 2010. Empirical ground motion prediction

equations and their application to Eurocode 8. Bulletin of Earthquake Engineering 8: 5 – 26.

Borzi, B., Pinho, R., and Crowley, H., 2008a. Simplified pushover-based vulnerability analysis for large-scale assessment of RC buildings. Engineering Structures 30: 804 – 820.

Borzi, B., Crowley, H., and Pinho, R., 2008b. Simplified Pushover Based Loss Assessment SP-BELA Method for Masonry Buildings. International Journal of Architectural Heritage

2: 353 – 376. Bozorgnia, Y., Hachem, M. M., and Campbell, K. W., 2010. Ground Motion Prediction

Equation ``Attenuation Relationship'' for Inelastic Response Spectra. Earthquake Spectra 26: 1 – 23.

Bradley, B., A., Cubrinovski, M., Dhakal, R. P., and MacRae, G. A., 2008. Intensity measures for the seismic performance of pile foundations. Soil Dynamics and

Earthquake Engineering 29: 1046 – 1058. Bray, J. D., and Travasarou, T., 2007. Simplified Procedure for Estimating Earthquake-

Induced Deviatoric Slope Displacements. Journal of Geotechnical and

Geoenvironmental Engineering 133(4): 381 – 392. Brun, M., Reynouard, J. M., Jezequel, L., and Ile, N., 2004. Damaging potential of low-

magnitude near-field earthquake on low-rise shear walls. Soil Dynamics and Earthquake

Engineering 24: 587 – 603. Buratti, N., Ferracuti, B., and Savoia, M., 2010. Response Surface with random factors for

seismic fragility of reinforced concrete buildings. Structural Safety 32: 42 – 51. Cabañas, L., Benito, B., and Herráiz, M., 1997. An approach to the measurement of potential

structural damage of earthquake motions. Earthquake Engineering & Structural

Dynamics 26: 79 – 92. Campbell, K. W., and Bozorgnia, Y., 2008. NGA Ground Motion Model for the Geometric

Mean Horizontal Component of PGA, PGV, PGD and 5% Damped Linear Elastic Response Spectra for Periods Ranging from 0.01 to 10 s. Earthquake Spectra 24: 139 – 171.

Carro, M., De Amicis, M., Luzi, L., and Marzorati, S., 2003. The application of predictive modeling techniques to landslides induced by earthquakes: the case study of the 26 September 1997 Umbria–Marche earthquake Italy. Engineering Geology 69: 139 – 159.

Celik, O. C., and Ellingwood, B. R., 2010. Seismic fragilities for non-ductile reinforced concrete frames: Role of aleotoric and epistemic uncertainties. Structural Safety 32: 1 – 12.

Chen, W. W., Shih, B., Chen, Y.-C., Hung, J. –H., and Hwang, H. H., 2002. Seismic response of natural gas and water pipelines in the Ji-Ji earthquake. Soil Dynamics and

Earthquake Engineering 22: 1209 – 1214. Choe, D.-E., Gardoni, P., Rosowski, D., and Haukaas, T., 2009. Seismic fragility estimates

of reinforced concrete bridges subject to erosion. Reliability Engineering & System

Safety 31: 275 – 283. Choi, E., DesRoches, R., Nielson, B., 2004. Seismic fragility of typical bridges in moderate

seismic zones. Engineering Structures 26: 187 – 199.


82

Chopra, A. K., 1995. Dynamics of Structures: Theory and Application to Earthquake Engineering. Prentice Hall, New Jersey.

Cimellaro, G. P., Fumo, C., Reihorn, A. F., and Bruneau, M., 2009. Quantification of Disaster Resilience of Health Care Facilities. MCEER Technical Report. MCEER-09-0009. September 14 2009.

Codermatz, R., Nicolich, R., and Slejko, D., 2003. Seismic risk assessments and GIS technology : applications to infrastructures in the Friuli-Venezia Giulia region NE Italy. Earthquake Engineering and Structural Dynamics 32: 1677 – 1690.

Colombi, M., Borzi, B., Crowley, H., Onida, M., Meroni, F., and Pinho, R., 2008. Deriving vulnerability curves using Italian earthquake damage data. Bulletin of Earthquake

Engineering 63: 485-504 Cordova, P.P., Deierlein, G.G., Mehanny, S.S.F., and Cornell, C. A., 2000. Development of a

two-parameter seismic intensity measure and probabilistic assessment procedure. In Proceedings of the Second U.S.-Japan Workshop on Performance-Based Earthquake

Engineering Methodology for Reinforced-Concrete Building Structures., 11 – 13 September, 2000, Sapporo, Hokkaido, Japan.

Cornell, C.A., and Krawinkler, H., 2000. Progress and Challenges in Seismic Performance Assessment. PEER Center News. 32: 1 - 4

Cornell, C.A., Jalayer, F., Hamburger, R.O., and Foutch, D.A., 2002. Probabilistic basis for 2000 SAC/FEMA steel moment frame guidelines, Journal of Structural Engineering 1284: 526-533.

Curadelli, R. O., and Riera, J. D., 2004. Reliability based assessment of the effectiveness of metallic dampers in buildings under seismic excitations. Engineering Structures 26: 1931 – 1938.

Danciu, L., and Tselentis, G.-A., 2007. Engineering Ground Motion Parameters Attenuation Relationships for Greece. Bulletin of the Seismological Society of America 97(1B): 162 – 183.

D’Ayala, D. F., 2005. Force and Displacement Based Vulnerability Assessment for Traditional Buildings. Bulletin of Earthquake Engineering 3: 235 – 265.

Decanini, L. D., and Mollaioli, F., 1998. Formulation of Elastic Earthquake Input Energy Spectra. Earthquake Engineering & Structural Dynamics 27: 1503 – 1522.

De Stefano, M. Nudo, R., and Viti, S., 2004. Evaluation on the second order effects of the seismic performance of RC framed structures: a fragility analysis. 13th World Conference

on Earthquake Engineering. Vancouver, Canada. 2004. Dimova, S. L., and Elenas, A., 2002. Seismic intensity parameters for fragility analysis of

structures with energy dissipating devices. Structural Safety 24: 1 – 28. Dimova, S. L., and Negro, P., 2005. Seismic assessment of and industrial framed structure

designed according to Eurocodes. Part 2: Capacity and Vulnerability. Engineering

Structures 27: 724 – 735. Dimova, S. L., and Negro, P., 2006. Assessment of the Seismic Fragility of Structures with

Consideration of the Quality of Construction. Earthquake Spectra 224: 909 – 936. Ding, J. –H., Jin, X. –L., Guo, Y. –Z., and Li, G. –G., 2006. Numerical simulation for large-

scale seismic response analysis of immersed tunnel. Engineering Structures 28: 1367 – 1377.

DiPasquale, E., Çakmak, A. S., 1989. On the relation between local and global damage indices. NCEER Technical Report. NCEER-90-0022. State University of New York, Buffalo.

References

83

Douglas, J., 2003. Earthquake ground estimation using strong-motion records: a review of equations for the estimation of peak ground motion and response spectral ordinates. Earth Science Reviews 61: 43 – 104.

Dumova-Jovanoska, E., 2000. Fragility curves for reinforced concrete structures in Skopje Macedonia region. Soil Dynamics and Earthquake Engineering 19: 455 – 466.

Dymiotis, C., Kappos, A. J., Chryssanthopoulos, M. K., 2000. Seismic Reliability Assessment of Multi-Story RC Frames. Proceedings of the 12th World Conference on Earthquake

Engineering, Auckland, New Zealand. 2000. Eguchi R.T., 1983. Seismic Component Vulnerability Models for Lifeline risk Analysis. J.

Wiggins Co, Technical Report No. 82-1396-22 Eguchi, R.T., 1991. Early Post – Earthquake Damage Detection for Underground Lifelines,

Final report to the National Science Foundation, Dames and Moore P.C, Los Angeles, California.

Eidinger J.M, Maison B, Lee D, and Lau B., 1995. East Bay Municipality Utility District Water Distribution Damage in 1989 Loma Prieta Earthquake. Proceedings of the Fourth U.S

Conference on Lifeline Earthquake Engineering, ASCE, TCLEE, Monograph 6, ASCE, pp. 240-247.

Eidinger, J. 1998. Lifelines, Water Distribution System in the Loma Prieta, California, Earthquake of October 17, 1989, Performance of the Build Environment –Lifelines, US

Geological Survey Professional Paper 1552-A, pp. A63-A80, A. Schiff Ed. Eidinger, J. and Avila E., 1999. Guidelines for the seismic upgrade of Water Transmission

Facilities, ASCE, TCLEE, Monograph No. 15. Eidinger, J., 2001. Seismic Fragility Formulations for Water Systems. G & E Engineering

Systems Inc. Technical Report. 47.01.01. Eidinger, J., and Ostrom, D., 2004. National Institute of Building Sciences: Earthquake Loss

Estimation Methods Technical Manual – Electric Power Utilities. G & E Engineering

Systems Inc. Technical Report. R23-04. Eidinger, J., 2009. Fragility of Non-structural Components for FEMA Cost-Benefit Analysis.

G & E Engineering Systems Inc. Technical Report. May 27 2009. Elenas, A., 2000. Correlation between seismic acceleration parameters and overall structural

damage indices of buildings. Soil Dynamics & Earthquake Engineering 20: 93 – 100. Ellingwood, B. R., Rosowsky, D.V., Li, Y. and Kim, J.H., 2004. Fragility Assessment of Light-

Frame Wood Construction Subjected to Wind and Earthquake Hazards. Journal of

Structural Engineering 130(12): 1921 – 1930. Ellingwood, B. R., Celik, O. C., and Kinali, K., 2007. Fragility assessment of building

structural systems in Mid-America. Earthquake Engineering and Structural Dynamics 36: 1935 – 1952.

Ellingwood, B. R., and Kinali, K., 2009. Quantifying and communicating uncertainty in seismic risk assessment. Structural Safety 31: 179 – 187.

Erberik, M. A., and Elnashai, A. S., 2004. Vulnerability analysis of flat slab structures. 13th

World Conference on Earthquake Engineering, Vancouver, Canada, 2004 Erberik, M. A., 2008 Fragility-based assessment of typical mid-rise and low-rise RC buildings

in Turkey. Engineering Structures 305: 1360-1374 Erberik, M.A., 2008. Generation of fragility curves for Turkish masonry buildings considering

in-plane failure modes. Earthquake Engineering & Structural Dynamics 37: 387 – 405. Fabbrocino, G., Iervolino, I., Orlando, F., and Salzano, E., 2005. Quantitative risk analysis of

oil storage facilities in seismic areas. Journal of Hazardous Materials A123: 61 – 69.


84

Faccioli, E., Frassine, L., Finazzi, D., Pessina, V., Lagomarsino, S., Giovinazzi, S., Resemini, S., Curti, E., Podestà, S., and Scuderi, S., 2004. RISK-UE: WP11 – Synthesis of the Application to Catania City. 1 – 59.

Fajfar, P., Vidic, T., and Fishinger, M., 1990. A measure of earthquake motion capacity to damage medium-period structures. Soil Dynamics and Earthquake Engineering 9: 236 – 242.

Filatrault, A. and Folz, B., 2002. Performance-Based Seismic Design of Wood Framed Buildings. Journal of Structural Engineering 121(1). 39 – 47.

Franchin, P., Lupoi, A., Pinto, P.E. and Shotanus, M. I. J., 2003. Seismic Fragility of Reinforced Concrete Structures Using a Response Surface Approach. Journal of

Earthquake Engineering 71: 45 – 77. Gardoni, P., Kiureghian, A. R., and Mosalam, K. M., 2002. Probabilistic Models and Fragility

Estimates for Bridge Components and Systems. Pacific Earthquake Engineering

Research Centre Technical Report. PEER 2002/13. 1 – 173. Gencturk, B., Elnashai, A. S., and Soong, J., 2008. Fragility relationships for Populations of

Woodframe Structures based on Inelastic Response. Journal of Earthquake Engineering 121: 119 – 128.

Giovenale, P., Cornell, C.A., and Esteva, L., 2004. Comparing the adequacy of alternative ground motion intensity measures for the estimation of structural responses. Earthquake

Engineering & Structural Dynamics 33: 951 – 979. Goulet, C. A., Haselton, C. B., Mitrani-Reiser, J., Beck, J. L., Deierlein, G. G., Porter, K. A.,

and Stewart, J. P., 2007. Evaluation of the seismic performance of a code-conforming reinforced-concrete frame building—from seismic hazard to collapse safety and economic losses. Earthquake Engineering & Structural Dynamics 36: 1973 – 1997.

Gueguen, P., Michel, C., and LeCorre, L., 2007. A Simplified approach for vulnerability assessment in moderate-to-low seismicity regions: application to Grenoble France. Bulletin of Earthquake Engineering 5: 467 – 490.

Güneyisi, E. M., Altay, G., 2008. Seismic fragility assessment of the effectiveness of viscous dampers in R/C buildings under scenario earthquakes. Structural Safety 30: 461 – 480.

Hancock, J., and Bommer, J. J., 2005. The effective number of cycles of earthquake ground motion. Earthquake Engineering & Structural Dynamics 34: 637 – 644.

Hancock, J., and Bommer, J. J., 2006. A State-of-Knowledge Review of the Influence of Strong Motion Duration on Structural Damage. Earthquake Spectra 223: 827 – 845.

Hamada, M., 1991. Estimation of earthquake damage to lifeline systems in Japan. Proceedings of the 3rd Japan-US workshop on earthquake resistant design of lifeline

facilities and countermeasures for soil liquefaction, San Francisco, CA. Hashash, Y.M.A., Hook, J.J., Schmidt, B., and Yao, J. I-C., 2001. Seismic design and

analysis of underground structures. Tunnelling and Underground Space Technology. 16: 247 – 293.

Heubach, W., 1995. Seismic Damage Estimation for Buried Pipeline Systems. Proceedings

of the Fourth US Conference on Lifeline Earthquake Engineering, TCLEE, Monograph, 6: 312-319.

Heuste, M. B. D., and Bai, J.-W., 2007. Seismic retrofit of a reinforced concrete flat-slab structure: Part II – seismic fragility analysis. Engineering Structures 29: 1178 – 1188.

Hidalgo, P., and Clough, R. W., 1974. Earthquake simulator study of a reinforced concrete frame. Report UCB/EERC-74/13. EERC, University of California, Berkeley, CA.

Honegger, D.G. and Eguchi, R.T., 1992. Determination of the Relative Vulnerabilities to Seismic Damage for San Diego Country Water Authority SDCWA Water Transmission Pipelines.

References

85

Horie, K., Hayashi, H., Okimura, T., Tanaka, S., Maki, N., and Torii, N., 2004. Development of Seismic Risk Assessment Method Reflecting Building Damage Levels: Fragility Functions for Complete Collapse of Wooden Buildings. Proceedings of the 13th World

Conference on Earthquake Engineering, Vancouver, Canada. Housner, G. W., 1952. Intensity of Ground Motion During Strong Earthquake. California

Institute of Technology. Pasadena, California. Hung J. -H., 2001 The analysis of water pipeline Damages of Wufeng Shiang in the 921 Ji-Ji

Earthquake, Master’s Thesis, National Taipei University of Technology, Taipei, Taiwan (in Chinese)

Hwang, H. and Lin, H., 1997. GIS-based evaluation of seismic performance of water delivery systems, Technical Report, CERI, the University of Memphis, Memphis, TN, 110pp.

Hwang, H., and Chou, T., 1998. Evaluation of seismic performance of an electric substation using event tree/fault tree technique. Probabilistic Engineering Mechanics 132: 117 – 124.

Hwang, H., and Huo, J.-R., 1998. Seismic fragility analysis of electric substation equipment and structures. Probabilistic Engineering Mechanics 132: 107 – 116.

Hwang, H., Jernigan, J.B., Lin, Y.-W., 2000. Evaluation of Seismic Damage to Memphis Bridges and Highway Systems. Journal of Bridge Engineering 5: 322-330.

Hwang, H., Liu, J.B., Chiu, Y.-H., 2001. Seismic Fragility Analysis of Highway Bridges. Mid-

America Earthquake Center Technical Report. MAEC RR-4, Center for Earthquake Research Information, The University of Memphis, Memphis, TN.

Hwang, H., Cjiu, Y.-H., Chen, W.-Y., and Shih, B.-J., 2004. Analysis of Damage to Steel Gas Pipelines Caused by Ground Shaking Effects during the Chi-Chi, Taiwan, Earthquake. Earthquake Spectra 204: 1095 – 1110.

Ichii, K., 2003. Application of Performance-Based Seismic Design Concept for Caisson-Type Quay Walls, PhD Dissertation, Kyoto University.

Ichii, K., 2004. Fragility Curves for Gravity-Type Quay Walls Based on Effective Stress Analyses, Proceedings of the 13th World Conference on Earthquake Engineering,

Vancouver, BC Canada. Iervolino, I., 2003. Quantitative Seismic Risk Analysis in Process Industry. PhD Thesis.

Department of Structural Analysis and Design. University of Naples Frederico II. Iervolino I., Fabbrocino G., Manfredi G., 2004. Fragility of standard industrial structures by a

response surface based method. Journal of Earthquake Engineering 86: 927-945. Isoyama, R. & Katayama, 1982. Reliability Evaluation of Water Supply Systems during

Earthquakes Report of the Institute of Industrial Science, University at Tokyo, February, 30(1)

Isoyama, R., Ishida, E., Yune, K., Shirozu T., 1998. Seismic Damage Estimation Procedure for Water Supply Pipelines. Proceedings of Water & Earthquake ’98 Tokyo, IWSA

International Workshop, Anti-Seismic Measures on Water Supply, International Water Services Association and Japan Water Works Association, Tokyo Japan.

Isoyama, R., Ishida, E., Yune, K. & Shirozu, T., 2000. Seismic damage estimation procedure for water supply pipelines, Proceedings of the Twelfth World Conference on Earthquake

Engineering, Paper No. 1762. Jacobson, A., and Grigoriu, M., 2008. Fragility Analysis of Water Supply Systems. MCEER

Technical Report. MCEER-08-0009. March 10 2008. Jeong, S. –H., and Elnashai, A., 2007. Fragility relationships for torsionally-imbalanced

buildings using three-dimensional damage characterisation. Engineering Structures 29: 2172 – 2182.


86

Ji, J., Elnashai, A., and Kuchma, D. A., 2009. Seismic Fragility Relationships of Reinforced-Concrete High Rise Buildings. The Structural Design of Tall and Special Buildings 18: 259 – 277.

Jibson, R. W., 2007. Regression models for estimating coseismic landslide displacement. Engineering Geology 91: 209 – 218.

Kakderi, K. and Pitilakis K., 2010. Seismic analysis and fragility curves of gravity waterfront structures, Fifth International Conference on Recent Advances in Geotechnical

Earthquake Engineering and Soil Dynamics and Symposium in Honour of Professor I. M.

Idriss, May 24-29, San Diego, CA, Paper No. 6.04a. Kappos A.J, Stylianidis K.C, Pitilakis K., 1998. Development of seismic risk scenarios based

on a hybrid method of vulnerability assessment. Natural Hazards 172:177–192 Kappos, A., Panagopoulos, G., Panagiotopoulos, Ch., Penelis, G., 2006. A Hybrid Method

for the Vulnerability Assessment of R/C and URM Buildings. Bulletin of Earthquake

Engineering 4: 391–413. Karakostas, C., Makarios, T., Lekidis, V., and Kappos, A., 2006. Evaluation of Vulnerability

Curves for Bridges: A Case Study. Proceedings of the 1st European Conference on

Earthquake Engineering, Geneva, Switzerland. Paper No. 1435. Karim, K.R., Yamazaki, F., 2001. Effect of earthquake ground motions on fragility curves of

highway piers based on numerical simulation. Earthquake Engineering and Structural

Dynamics 30: 1839 – 1856. Karim, K.R., Yamazaki, F., 2003. A Simplified Method of Constructing Fragility Curves for

Highway Bridges. Earthquake Engineering and Structural Dynamics 32(10): 1603-1626. Kashighandi, P., Brandenberg, S. J., Zhang, J., Huo, Y. and Zhao, M., 2008. Fragility of

Older-vintage Continuous California Bridges to Liquefaction and Lateral Spreading. Proceedings of the 14th World Conference on Earthquake Engineering, Beijing, China.

Katayama, T., Kubo, K., Sato, N. 1975 Earthquake Damage to Water and Gas Distribution Systems. Proceedings of the U.S National Conference on Earthquake Engineering, Oakland, California, EERI, pp. 396-405.

Kayan, R. E., and Mitchell, R. A., 1997. Assessment of Liquefaction Potential During Earthquakes by Arias Intensity. Journal of Geotechnical and Geoenvironmental

Engineering. 123(12) : 1162 – 1174. Kazantzi, A. K., Righiniotis, T. D., and Chryssanthopoulos, M. K., 2008a. The effect of joint

ductility on the seismic fragility of a regular moment resisting steel frame designed to EC8 provisions. Journal of Constructional Steel Research 64: 987 – 996.

Kazantzi, A. K., Righiniotis, T. D., and Chryssanthopoulos, M. K., 2008b. Fragility and Hazard Analysis of a Welded Steel Moment Resisting Frame. Journal of Earthquake

Engineering 12: 596 – 615. Kim, S. –H., and Feng, M. Q., 2003 Fragility analysis of bridges under ground motion with

spatial variation. International Journal of Non-Linear Mechanics 38: 705 – 721. Kim, S. –H., and Shinozuka, M., 2004. Development of fragility curves of bridges retrofitted

by column jacketing. Probabilistic Engineering Mechanics 19: 105 – 112. Kim, J.H., and Rosowsky, D.V., 2005. Fragility Analysis for Performance-Based Seismic

Design of Engineered Wood Shearwalls. Journal of Structural Engineering 131(11): 1764 – 1773.

Kim, J.H., Kent, S.M., and Rosowsky, D.V., 2006. The Effect of Biological Deterioration on the Seismic Performance of Woodframe Shearwalls. Computer-Aided Civil and

Infrastructure Engineering 21: 205 – 215.

References

87

Kinali, K., and Ellingwood, B. R. 2007. Seismic fragility assessment of steel frames for consequence based engineering: A case study for Memphis, TN. Engineering Structures 29: 1115 – 1127.

Kirçil, M.S., and Polat, Z., 2006. Fragility analysis of mid-rise R/C frame buildings. Engineering Structures 28: 1335 - 1345

Kostov, M., Vaseva, E., Kaneva, A., Koleva, N., Varbanov, G., Stefanov, D., Darvarova, E., Solakov, D., Simeonova, S., and Christoskov, L., 2004. RISK-UE WP13: Application to Sofia 1 – 64.

Kramer, S. L., 1996. Geotechnical Earthquake Engineering. Prentice Hall, New Jersey. Kramer, S. L., and Mitchell, R. A., 2006. Ground Motion Intensity Measures for Liquefaction

Hazard Evaluation. Earthquake Spectra 222: 413 - 438 Krawinkler, H., 2002. A general approach to seismic performance assessment, in

Proceedings of International Conference on Advances and New Challenges in

Earthquake Engineering, Research, ICANCEER 2002, Hong Kong, August 19-20. Kurama, Y. C., and Farrow, K. T., 2003. Ground motion scaling methods for different site

conditions and structure characteristics. Earthquake Engineering & Structural Dynamics 32(14): 2425 – 2450.

Kuwata, Y., and Takada, S., 2007. Seismic Risk Assessment of Lifeline Considering Hospital Functions. Asian Journal of Civil Engineering Building and Housing 83: 315 – 328.

Kwon, O. –S., and Elnashai, A., 2006. The effect of material and ground motion uncertainty on the seismic vulnerability curves of RC Structure. Engineering Structures 28: 289 – 303.

Lagomarsino, S., 2006. On the vulnerability assessment of monumental buildings. Bulletin of

Earthquake Engineering 4: 445 – 463. Lagomarsino, S., Giovinazzi, S., 2006. Macroseismic and mechanical models for the

vulnerability and damage assessment of current buildings. Bulletin of Earthquake

Engineering 4: 415 – 443. Lagaros, N. D., and Fragiadakis, M., 2007. Fragility Assessment of Steel Frames using

Neural Networks. Earthquake Spectra 234: 735 – 752. Lagaros, N. D., 2008. Probabilistic Fragility Analysis: A tool for assessing design rules of RC

buildings. Earthquake Engineering and Engineering Vibration 7: 45 – 56. Lang, K., 2002. Seismic vulnerability of existing buildings. Institute of Structural Engineering.

Swiss Federal Institute of Technology. February, 2002. Lee, K.H., and Rosowsky, D.V., 2006. Fragility analysis of woodframe buildings considering

combined snow and earthquake loading. Structural Safety 28: 289 – 303. LESSLOSS, 2006 Deliverable 89 – Technical report on the assessment of vulnerability

functions for pipelines, shallow tunnels and waterfront structures. LESSLOSS, 2007a. Deliverable 93 – Vulnerability assessment for landslides. LESSLOSS, 2007b. Deliverable 117 – Damage scenarios for selected urban areas for water

and gas systems, sewage mains, tunnels and waterfront structures: Thessaloniki, Istanbul European side, Düzce.

Li, Y., and Ellingwood, B. R., 2007. Reliability of woodframe residential construction subjected to earthquakes. Structural Safety 29: 294 – 307.

Li, Q., and Ellingwood, B. R., 2008. Damage inspection and vulnerability analysis of existing buildings with steel moment-resisting frames. Engineering Structures 30: 338 – 351.

Lopez Garcia, D., and Soong, T. T., 2003a. Sliding fragility of block-type non-structural components Part 1: Unrestrained Components. Earthquake Engineering and Structural

Dynamics 32: 111 – 129.


88

Lopez Garcia, D., and Soong, T. T., 2003b. Sliding fragility of block-type non-structural components Part 2: Restrained Components. Earthquake Engineering and Structural

Dynamics 32: 131 – 149. Luco, N, and Cornell, C. A., 2007. Structure-Specific Scalar Intensity Measures for Near-

Source and Ordinary Earthquake Ground Motions. Earthquake Spectra 232: 357 – 392. Lupoi, A., Franchin, P., Pinto, P. E., and Monti, G., 2005. Seismic design of bridges

accounting for spatial variability of ground motion. Earthquake Engineering and

Structural Dynamics 34: 327 – 348. Mackie K., and Stojadinovic B., 2003. Seismic Demands for Performance-Based Design of

Bridges. PEER Report 2003/16. Pacific Earthquake Engineering Research Center, University of California, Berkeley, CA.

Mackie K., and Stojadinovic B., 2005. Fragility Basis for California Highway Overpass Bridge Seismic Decision Making. PEER Report 2005/12. Pacific Earthquake Engineering

Research Center, University of California, Berkeley, CA. Mackie, K., and Stojadinovich, B., 2006. Fragility Analysis of PEER Center Testbed Bridges.

1st European Conference on Earthquake Engineering & Seismology, Geneva, Switzerland. Paper No. 1219.

Malhotra, P. K., 2002. Cyclic Demand Spectrum. Earthquake Engineering & Structural

Dynamics 31: 1441 – 1457. Martinez-Rueda, J. E., 1998. Scaling procedure for Natural Accelerograms Based on a

System of Spectral Intensity Scales. Earthquake Spectra 141: 135 – 152. Maruyama, Y., Yamazaki, F., Mizujo, K., Yogai, H., and Tsuchiya, Y., 2008. Development of

Fragility Curves for Highway Embankment Based on Damage Data from Recent Earthquakes in Japan. Proceedings of the 14th World Conference on Earthquake

Engineering, Beijing, China. Masi, A., 2003 Seismic vulnerability assessment of gravity load designed R/C frames.

Bulletin of Earthquake Engineering 13: 371-395 Mataki Sh., Deguchi T., Honda K., Suzuki T., 1996. Investigation of aseismic design

methods for highly- reliable telecommunication conduit facilities in liquefied ground. Proceedings from the Sixth Japan- U.S Workshop on Earthquake Resistant Design of

Lifeline Facilities and Countermeasures Against Soil Liquefaction, Technical Report NCEER -96-0012.

Matasovic N, Kavazanjian Ed, and Anderson R., 1998. Performance of Solid Waste Landfills in Earthquakes. Earthquake Spectra 14(2): 319-334

Matsumura, K., 1992. On the intensity measure of strong motions related to structural failures. Proceedings of the 10th World Conference on Earthquake Engineering. 375 – 380.

Mehanny, S. S. F., 2009. A broad-range power-law form scalar-based seismic intensity measure. Engineering Structures 31: 1354 – 1368

Milutinovic, Z.V., and Trendafiloski, W. S., 2003. RISK-UE WP4: Vulnerability of current buildings. 1 - 110

Monge, O., and Argyroudis, S., 2003. RISK-UE WP6 – Appendix 4: Port Transportation System. Risk-UE Report. 1 – 25.

Monti, G., and Nuti, C., 1996. A procedure for assessing the functional reliability of hospital systems. Structural Safety 184: 277 – 292.

Moschonas I., Kappos A., Panetsos P., Papadopoulos V., Makarios T., Thanopoulos P., 2009. Seismic Fragility Curves for Greek Bridges: Methodology and Case Studies, Bulletin of Earthquake Engineering 72: 439-468.

References

89

Na, U.J., S.R. Chaudhuri and M. Shinozuka, 2008. Probabilistic assessment for seismic performance of port structures. Soil Dynamics and Earthquake Engineering 28: 147–158.

Na, U. J., and Shinozuka, M., 2009 Simulation-based seismic loss estimation of seaport transportation system. Reliability Engineering and System Safety 94: 722 - 731

Na, U.J., S. R. Chaudhuri and M.Shinozuka, 2009. Performance Evaluation of Pile Supported Wharf under Seismic Loading. Proceedings of the 2009 Technical Council on

Lifeline Earthquake Engineering Conference: Lifeline Earthquake Engineering in a

Multihazard Environment, Oakland, California, ASCE, edited by A. Tang and S. Werner, pp. 1032-1041.

Nateghi, F., and Shahsavar, V.L., 2004. Development of Fragility and Reliability Curves for Seismic Evaluation of a Major Prestressed Concrete Bridge. Proceedings of the 13th

World Conference on Earthquake Engineering, Vancouver, Canada. Paper No. 1351. National Institute of Building Sciences (NIBS), 2004. HAZUS-MH: Users’s Manual and

Technical Manuals. Report prepared for the Federal Emergency Management Agency, Washington, D.C.

Nau, J. M., and Hall, W. J., 1984. Scaling methods for earthquake response spectra. Journal

of Structural Engineering 1107: 1533 - 1548 Newmark, N., 1967. Problems in wave propagation in soil and rocks. Proceedings of

International Symposium on Wave Propagation and Dynamic Properties of Earth

Materials, University of New Mexico Press. 7 – 26. Newmark, N., 1973. A Study of Vertical and Horizontal Earthquake Spectra. N.M. Newmark

Consulting Engineering Services, Directorate of Licensing, U.S. Atomic Energy Commission, Washington D.C..

Nielson B., 2003. Bridge Seismic Fragility-Functionality Relationships: A Requirement for Loss Estimation in Mid-America. Mid America Earthquake Center, University of Illinois, Online report:

http://mae.cee.illinois.edu/documents/slc_online_magazine_2003_may_nielson.pdf Nielson, B., and DesRoches, R., 2007a Seismic fragility methodology for highway bridges

using a component level approach. Earthquake Engineering and Structural Dynamics. 36: 823 – 839.

Nielson, B., and DesRoches, R., 2007b Analytical Seismic Fragility Curves for Typical Bridges in the Central and Eastern United States. Earthquake Spectra 233: 615 – 633.

Nigam, N. C., and Jennings, P. C., 1969. Calculation of Response Spectra from Strong-Motion Earthquake Records. Bulletin of the Seismological Society of America 592: 909 – 922.

Nuti, C., and Vanzi, I., 1998. Assessment of Post-Earthquake Availablility of Hospital System and Upgrading Strategies. Earthquake Engineering and Structural Dynamics 27: 1403 – 1423.

Nuti, C., Vanzi, I., and Santini, S., 1998. Seismic risk of Italian hospitals. Proceedings of the

11th European Conference on Earthquake Engineering, Paris, France, 6 – 11 September, 1998.

Nuti, C., Santini, S., and Vanzi, I., 2004. Damage, Vulnerability and Retrofitting Strategies for the Molise Hospital System Following the 2002 Molise, Italy, Earthquake. Earthquake

Spectra 20(S1): S285 – S299. Nuti, C., Rasulo, A., and Vanzi, I., 2007. Seismic safety evaluation of electric power supply

at urban level. Earthquake Engineering and Structural Dynamics 36: 245 – 263. Onishi, Y., and Hayashi, Y., 2008. Fragility Curves for Wooden Houses Considering Aged

Deterioration of the Earthquake Resistance. Proceedings of the 14th World Conference

on Earthquake Engineering, Beijing, China.

http://mae.cee.illinois.edu/documents/slc_online_magazine_2003_may_nielson.pdf


90

O’Rourke, T.D., Gowdy, T.E., Stewart, H.E., Pease, J.W., 1991. Lifeline and geotechnical aspects of the 1989 Loma Prieta earthquake. Proceedings of the 2nd International

Conference in Geotechnical Earthquake Engineering and Soil Dynamics, St-Louis, MO. O'Rourke, M.J. and Ayala, G., 1993. Pipeline damage due to wave propagation. Journal of

Geotechnical Engineering. ASCE 119(9): 1490-1498. O' Rourke, T.D., Toprak, S, & Sano, Y., 1998. Factors affecting water supply damage

caused by the Northridge earthquake. Proceedings of the Sixth US National Conference

on Earthquake Engineering. Seattle, WA O’Rourke, T.D. & Jeon, S.-S., 1999. Factors affecting the earthquake damage of water

distribution systems, Proceedings of the Fifth US Conference on Lifeline Earthquake

Engineering, Seattle, WA O’Rourke, T. D. & So, P,. 2000. Seismic Fragility Curves for On-Grad Steel Tanks.

Earthquake Spectra 164: 801 – 815. O’Rourke, M. and Deyoe, E., 2004. Seismic Damage to Segmented Buried Pipe. Earthquake

Spectra 204: 1167–1183. Padgett, J. A., and DesRoches, R., 2008. Methodology for the development of analytical

fragility curves for retrofitted buildings. Earthquake Engineering and Structural Dynamics 37: 1157 – 1174.

Padgett, J. E., Nielson, B. G., and DesRoches, R., 2008. Selection of optimal intensity measures in probabilistic seismic demand models of highway bridge portfolios. Earthquake Engineering and Structural Dynamics 37: 711 – 725.

Pakbaz, M. C., and Yareevand, A., 2005. 2-D Analysis of circular tunnel against earthquake loading. Tunnelling and Underground Space Technology 20: 411 – 417.

Pang, W.C., Rosowsky, D.V., Pei, S., and van de Lindt, J.W., 2007. Evolutionary Parameter Hysteretic Model for Wood Shear Walls. Journal of Structural Engineering 133(8): 1118 – 1129.

Pang, W., Rosowsky, D.V., Ellingwood, B.R. and Wang, Y., 2009. Seismic Fragility Analysis and Retrofit of Conventional Residential Wood-Frame Structures in the Central United States. Journal of Structural Engineering 135(3): 262 – 271.

Paolacci, F., and Giannini, R., 2009. Seismic Reliability Assessment of a High-Voltage Disconnect Switch Using an Effective Fragility Analysis. Journal of Earthquake

Engineering 13: 217 – 235. Park, Y.J., and Ang, AH. -S., 1985. Mechanistic seismic damage model for reinforced

concrete. Journal of Structural Engineering 111: 722 – 739. Park, D., Sagong, M., Kwak, D. –Y., Jeong, C.-G., 2009a. Simulation of tunnel response

under spatially varying ground motion. Soil Dynamics and Earthquake Engineering 29: 1417 – 1424.

Park, J., Towashiraporn, P., Craig, J.I., Goodno, B.J., 2009b. Seismic fragility analysis of low-rise unreinforced masonry structures. Engineering Structures 31: 125 – 137.

Pasquale, G. D., Orsini, G., Romeo, R. W., 2005. New Developments in Seismic Risk Assessment in Italy. Bulletin of Earthquake Engineering 3: 101 – 128.

Pei, S., and van de Lindt, J.W., 2009. Methodology for earthquake-induced loss estimation: An application to woodframe buildings. Structural Safety 31. 31 – 42.

Penelis, G.G., Kappos, A.J., and Stylianidis, K.C., 2002. RISK-UE WP4 – Unreinforced masonry buildings 1st level analysis

Penelis, G.G., Kappos, A.J., Stylianidis, K.C., and Panagiotopoulos, Ch., 2002 RISK-UE WP4 – Unreinforced masonry buildings 2nd level analysis

References

91

Pfyl-Lang, K., Zwicky, P., Kind, F., and Zbinden., A., 2006. Seismic vulnerability functions for Switzerland. Proceedings of the First European Conference on Earthquake

Engineering and Seismology, Geneva, Switzerland. Pires, J. A., Ang, A. H. –S., and Villaverde, R., 1996. Seismic reliability of electrical power

transmission systems. Nuclear Engineering and Design 160: 427 – 439. Pineda-Porras, O., Ordaz, M., 2003. Seismic vulnerability function for high diameter buried

pipelines: Mexico City’s primary water system case. ASCE International Conference on

Pipeline Engineering & Construction 2: 1145-1154. Pineda-Porras, O., and Ordaz, M., 2007. A New Seismic Intensity Parameter to Estimate

Damage in Buried Pipelines due to Wave Propagation. Journal of Earthquake

Engineering 115: 773 – 786. Pitilakis, K., Kappos, A., Hatzigogos, Th., Anastasiadis, A., Anastasiadis, D., Alexoudi, M.,

Argyroudis, S., Penelis, G., Panagiotopoulos, Ch., Panagopoulos, G., Kakderi, K., Papadopoulos, I., and Dikas, N., 2004. Risk-UE WP14: Synthesis of the Application to Thessaloniki City. 1 – 72.

Pitilakis, K., Alexoudi, M., Kakderi, K., Manou, D., Batum, E., Raptakis, D., 2005. Vulnerability analysis of water systems in strong earthquakes. The case of Lefkas Greece and Düzce Turkey. In Proceedings of the International Symposium on the

Geodynamics of Eastern Mediterranean: Active Tectonics of the Aegean, June 15-18, Istanbul, Turkey.

Pitilakis, K., Alexoudi, M., Kakderi, K., Argyroudis, S., Paolucci, R., and Ansel, A., 2007. Techical Report of the Assessment of Vulnerability Functions for Pipelines, Shallow Tunnels and Waterfront Structures. LESSLOSS Deliverable D89, 1 – 116.

Polese, M., Verderame, G. M., Mariniello, C., Iervolino, I., and Manfredi, G., 2008. Vulnerability analysis for gravity load designed RC buildings in Naples – Italy. Journal of

Earthquake Engineering, 12(S2): 234-245 Porter, K.A, Scawthorn, C, Honegger, D.G, O’Rourke, T.D, and Blackburn, F., 1991.

Performance of Water Supply Pipelines in Liquefied Soil. Proceedings 4th US – Japan

Workshop on Earthquake Disaster Prevention for Lifeline Systems, NIST Special Publication 840.

Porter, K.A., Johnson, G., Sheppard, R., and Bachman, R., 2010. Fragility of Mechanical, Electrical and Plumbing Equipment. Earthquake Spectra. 262: 451 – 472.

Ramamoorthy, S. K., Gardoni, P., and Bracci, J. M., 2006. Probabilistic Demand Models and Fragility Curves for Reinforced Concrete Frames. Journal of Structural Engineering 132(10): 1563 – 1572.

Ramamoorthy, S. K., Gardoni, P., and Bracci, J. M., 2008. Seismic Fragility and Confidence Bounds for Gravity-Designed Reinforced Concrete Frames of Varying Height. Journal of

Structural Engineering 1344: 639 – 650. Rashidov, T., Kuzmina, Mirjalilov A., Rashidov, I., 2000. Vulnerability of lifeline systems in

Tashkent, Uzbekistan. In the Proceedings of the 6th Conference on Seismic Zonation, Palm Springs, CA, Balkema.

Rasulo, A., Goretti, A, and Nuti, C., 2004. Performance of Lifelines during the 2002 Molise, Italy, Earthquake. Earthquake Spectra. 20(S1): S301 – S314.

Ray-Chaudhiri, S., and Shinozuka, M., 2010. Enhancement of seismic sustainability of critical facilities through system analysis. Probabilistic Engineering Mechanics 25: 235 – 244.

Razzaghi, M. S., and Eshghi, S., 2008. Development of Analytical Fragility Curves for Cylindrical Steel Oil Tanks. Proceedings of the 14th World Conference on Earthquake

Engineering, Beijing, China.


92

Retamales, R., Mosqueda, G., Filiatrault, A., and Reihorn, A., 2008. New Experimental Capabilities and Loading Protocols for Seismic Qualification and Fragility Assessment of Non-Structural Systems. MCEER Technical Report. MCEER-08-0026. November 24, 2008.

Riddell, R., 2007. On ground motion intensity indices. Earthquake Spectra 231: 147 – 173. Roark, M. S., Truman, K. Z. and Gould, P. L., 2000. Seismic Vulnerability of Airport

Facilities. Proceedings of the 12th World Conference on Earthquake Engineering, Auckland, New Zealand. Paper No. 0003.

Rosowsky, D. V., 2002. Reliability-based Seismic Design of Wood Shear Walls. Journal of

Structural Engineering 128(11): 1439 – 1453. Rossetto, T., and Elnashai, A. 2003. Derivation of vulnerability functions for European-type

RC structures based on observational data. Engineering Structures 25: 1241 – 1263. Rossetto, T., and Elnashai, A., 2005. A new analytical procedure for the derivation of

displacement-based vulnerability curves from populations of RC structures. Engineering

Structures 27: 397 – 409. Rota, M., Penna, A., and Strobbia, C. L., 2008. Processing Italian damage data to derive

typological fragility curves. Soil Dynamics and Earthquake Engineering 28: 933 – 947. Rota, M., Penna, A., and Magene, G., 2010. A method for deriving analytical fragility curves

for masonry buildings based on stochastic nonlinear analysis. Engineering Structures. In Press.

Ruiz-Garcia, J., Negrete, M., 2009. A Simplified Drift-Based Assessment Procedure for Regular Confined Masonry Buildings in Seismic Regions. Journal of Earthquake

Engineering 13: 520 – 539. Ruiz-Garcia, J., Negrete, M., 2009. Drift-based fragility assessment of confined masonry

walls in seismic zones. Engineering Structures 31: 170 – 181. Sakai, H., Pulido, N., and Hasegawa, K., 2010. A new seismic damage estimation approach

for lifelines: Application to the 2004 Niigata-ken Chuetsu earthquake, Japan. Earthquake

Engineering & Structural Dynamics. Submitted. Sarabandi, P., Pachakis, D., King, S. and Kiremidjian. A., 2004. Empirical fragility functions

from recent earthquakes. 13th World Conference on Earthquake Engineering, Vancouver, Canada.

Sasani, M., and Kiureghian, A. D., 2001. Seismic Fragility of RC Structural Walls: Displacement Approach. Journal of Structural Engineering 127(2): 219 – 228.

Sasani, M., Kiureghian, A. D., and Bertero, V. V., 2002. Seismic fragility of short period reinforced concrete structural walls under near-source ground motions. Structural Safety 24: 123 – 138.

Scawthorn Ch. 1996. Reliability – based Design of Water Supply Systems. Proceedings from

the Sixth Japan- U.S Workshop on Earthquake Resistant Design of Lifeline Facilities and

Countermeasures Against Soil Liquefaction, Technical Report NCEER -96-0012. Schotanus, M. I. J., Franchin, P., Lupoi, and A., Pinto., 2004. Seismic fragility analysis of 3D

structures. Structural Safety 26: 421 – 441. Shama, A. A., and Mander, J. B.,2003. The seismic performance of braced timber pile bents.

Earthquake Engineering and Structural Dynamics 32: 463 – 482. Shama, A. A., Mander, J. B., Friedland, I. M., and Allicock, D. R., 2007. Seismic vulnerability

of Timber Bridges and Timber Substructres. MCEER Technical Report. MCEER-07-0008. June 7 2007.

Shinozuka, M., Feng, M. Q., Kim, H.-K., and Kim, S.-H., 2000 Nonlinear Static Procedure for Fragility Curve Development. Journal of Engineering Mechanics, 126(12): 1287 – 1295.

References

93

Shinozuka, M., M.Q. Feng, H.-K. Kim, T. Uzawa, T. Ueda, 2003b. Statistical Analysis of Fragility Curves, MCEER Technical Report MCEER-03-0002, State University of New York, Buffalo.

Shinozuka, M., Dong, X., Chen, T. C., and Jin, X., 2007a. Seismic performance of electric transmission network under component failures. Earthquake Engineering and Structural

Dynamics. 36: 227 – 244. Shinozuka, M., Banerjee, S., and Kim, S. -H., 2007b. Statistical and Mechanistic Fragility

Analysis of Concrete Bridges. MCEER Technical Report. MCEER-07-0015. September 10, 2007

Shinozuka, M., Banerjee, S, and Kim, S.-H., 2007c. Fragility Considerations in Highway Bridge Design. MCEER Technical Report. MCEER-07-0023. December 14 2007.

Shome, N., Cornell, C.A., Bazzurro, P. and Carballo, J. E., 1998. Earthquakes, Records and Nonlinear Responses. Earthquake Spectra 143: 469 – 500.

Song, J., and Ellingwood, B. R., 1999. Seismic reliability of special moment steel frames with welded connections: II. Journal of Structural Engineering 1254: 372 – 384.

Song, J., Kishi, N. G., and Ellingwood, B. R., 2000. Probabilistic Modelling of Special Moment Frames Under Earthquake. Proceedings of the 12th World Conference on

Earthquake Engineering, Auckland, New Zealand. 2000. Song, J., Kiureghian, A. F., and Sackman, J. L., 2005. Seismic Response and Reliability of

Electrical Substation Equipment and Systems. Pacific Earthquake Engineering Research

Centre. PEER Research Report. 2005/16. SRMLIFE, 2003-2007. Development of a global methodology for the vulnerability

assessment and risk management of lifelines, infrastructures and critical facilities. Application to the metropolitan area of Thessaloniki, Research Project, General

Secretariat for Research and Technology, Greece, in Greek. Stafford, P. J., Berrill, J. B., and Pettinga, J. R., 2009. New predictive equations for Arias

intensity from crustal earthquakes in New Zealand. Journal of Seismology 13: 31 – 52. Tanaka, S., Kameda, H., Nojima, N., and Ohnishi, S., 2000. Evaluation of Seismic Fragility

for Highway Transportation Systems. Proceedings of the 12th World Conference on

Earthquake Engineering. Auckland, New Zealand. Paper No. 0546. Tehranizadeh, M., and Meshkat-Dini, A., 2007. Non-linear Response of High-Rise Buildings

to Pulse Type Strong Ground Motions. Proceedings of the 2007 Conference of the

Australian Earthquake Engineering Society. Wollongong, Australia. Paper No. 38. Terzi, V., Alexoudi, M., Pitilakis, K., Hatzigogos, Th., 2006. Vulnerability assessment for

pipelines under permanent ground deformations. Comparison between analytical and empirical approaches. 3rd European Conference on Computation Solid and Structural

Mechanics, Lisbon, 5-8 June. Toprak, S. 1998 Earthquake Effects on Buried Lifeline Systems. PhD Dissertation, Cornell

University Todorovska, M. I., Trifunac, M. D., and Lee, V. W., 2007. Shaking hazard compatible

methodology for probabilistic assessment of permanent ground displacement across earthquake faults. Soil Dynamics and Earthquake Engineering 27: 586 – 597.

Tothong, P. and Cornell, C.A., 2006. Probabilistic Seismic Demand Analysis using Advanced Ground Motion Intensity Measures, Attenuation Relationships, and Near-Fault Effects. Pacific Earthquake Engineering Research Center. PEER Report 2006/11.

Tothong, P., and Luco, N., 2007. Probabilistic seismic demand analysis using advanced ground motion intensity measures. Earthquake Engineering & Structural Dynamics 36: 1837 – 1860


94

Tothong, P., and Cornell, C.A., 2008. Structural performance assessment under near-source pulse-like ground motions using advanced ground motion intensity measures. Earthquake Engineering & Structural Dynamics 37: 1013 – 1037.

Travasarou, T., 2003. Optimal ground motion intensity measures for probabilistic assessment of seismic slope displacements. PhD Dissertation. University of California, Berkeley, CA.

Travasarou, T., Bray, J. D., and Abrahamson, N. A., 2003. Empirical attenuation relationship for Arias Intensity. Earthquake Engineering & Structural Dynamics 32:1133 – 1155.

Tselentis, G. –A., and Danciu, L., 2008. Empirical Relationships between Modified Mercalli Intensity and Engineering Ground Motion Parameters in Greece. Bulletin of the

Seismological Society of America 984: 1863 - 1875 Ueno, J., Takada, S., Ogawa, Y., Matsumoto, M., Fujita, S., Hassani, N., and Ardakani, F.

S., 2004. Research and Development on Fragility of Components for the Gas Distribution Systems in Greater Tehran, Iran. Proceedings of the 13th World Conference

on Earthquake Engineering, Vancouver, Canada. Paper No. 193. Ueong, Y. S., 2009. A study on the feasibility of SI for identification of earthquake damages

in Taiwan. Soil Dynamics and Earthquake Engineering 29: 185 – 193. Vacareanu, R., Radoi, R., Negulescu, C., and Aldea, A., 2004. Seismic vulnerability of RC

buildings in Bucharest, Romania. Proceedings of the 13th World Conference on

Earthquake Engineering. Vancouver, Canada Vanzi, I., 1996. Seismic reliability of electric power networks: methodology and application.

Structural Safety 184: 311 – 327. Vanzi, I., Bettinali, F., Sigismondo, S., 2005. Fragility curves of electrical substation

equipment via the Cornell method. Proceedings of the 9th International Conference on

Structural Safety and Reliability, Rome. Vamvatsikos, D., and Cornell, C.A., 2002. Applied incremental dynamic analysis.

Earthquake Spectra 202: 523 – 553. Vamvatsikos, D., and Cornell, C.A., 2005. Developing efficient scalar and vector intensity

measures for IDA capacity estimation by incorporating elastic spectral shape information. Earthquake Engineering & Structural Dynamics 34: 1573 – 1600.

Virella, J.C., Godoy, L.A., Suarez, L.E., 2006. Dynamic buckling of anchored steel tanks subjected to horizontal earthquake excitation. Journal of Constructional Steel Research 62: 521-531.

Von Thun, J., Roehm, L., Scott, G., and Wilson, J., 1988. Earthquake ground motion for design and analysis of dams. Earthquake Engineering & Soil Dynamics II – Recent

Advances in Ground Motion Evaluation. Geotechnical Special Publication. 20: 463 – 481. Wang LRL, Wang JCC, Ishibashi I., 1991 GIS applications in seismic loss estimation model

for Portland, Oregon water and sewer systems. US Geological Survey, Open File Report. Wang, H., Wang, G., Wang, F., Sassa, K., and Chen, Y., 2008. Probabilistic modelling of

seismically triggered landslides using Monte Carlo simulations. Landslides 5: 387 – 395. Wells, D. L., and Coppersmith, K. J., 1994. New empirical relationships among magnitude,

rupture length, rupture width, rupture area and surface displacement. Bulletin of the

Seismological Society of America 84: 974 – 1002. Wen Y.K., Ellingwood B.R., Veneziano D. and Bracci J., 2003. Uncertainty Modeling in

Earthquake Engineering, Mid-America Earthquake Center. Project FD-2 Report, Illinois. Werner, S. D., Dickenson, S. E., and Taylor, C. E., 1997. Seismic Risk Reduction at Ports:

Case Studies and Acceptable Risk Evaluation. Journal of Waterway, Port, Coastal, and

Ocean Engineering. 123: 337 – 346.

References

95

Wijewickreme, D., Honegger, D., Mitchell, A. and Fitzell, T., 2005. Seismic Vulnerability Assessment and Retrofit of a Major Natural Gas Pipeline System: A Case History. Earthquake Spectra 212: 539 – 567.

Yang, D., Pan, J., and Li, G.. 2009. Non-structure-specific intensity measure parameters and characteristic period of near-fault ground motions. Earthquake Engineering & Structural

Dynamics 38: 1257 – 1280. Yamaguchi, N., and Yamazaki, F., 2000. Fragility Curves for Buildings in Japan Based on

Damage Surveys after the 1995 Kobe Earthquake. Proceedings of the 12th World

Conference on Earthquake Engineering. Auckland, New Zealand. 2000 Yamazaki F., Motomura H., Hamada T., 2000. Damage Assessment of Expressway

Νetworks in Japan based on Seismic Monitoring. Proceedings of 12th World Conference

on Earthquake Engineering, Auckland, New Zealand. CD-ROM, Paper No. 0551. Yeh, C.-H., Shih, B.-J., Chang, C.-H., Chen, W., Liu, G.-Y.and Hung., H.-Y., 2006. Seismic

Damage Assessment of Potable Water Pipelines, Proceedings of the 4th International

Conference on Earthquake Engineering, Paper No. 247, Oct. 12-13, Taipei, Taiwan. Youngs, R. R., Arabasz, W. J., Anderson, R. E., Ramelli, A. R., Ake, J. P. Slemmons, D.B.,

McCalpin, J. P., Doser, D.I., Fridrich, C.J., Swan III, F.H., Rogers, A.M., Yount, J.C., Anderson, L.W., Smith, K.D., Bruhn, R.L., Knuepfer, P.L.K., Smith, R.B., dePolo, C.M., O'Leary, D.W., Coppersmith, K.J., Pezzopane, S.K., Schwartz, D.P., Whitney, J.W., Olig, S.S., and Toro, G.R., 2003. A Methodology for Probabilistic Fault Displacement Hazard Analysis PFHDA. Earthquake Spectra 19: 191 – 219.

Zhang, J., and Huo, Y., 2008. Optimum Isolation Design for Highway Bridges using Fragility Function Method. Proceedings of the 14th World Conference on Earthquake

Engineering, Beijing, China. Zhang, J., Huo, Y., Brandenberg, S. J., and Kashighandi, P., 2008a. Fragility Functions of

Different Bridge Types Subject to Seismic Shaking and Lateral Spreading. Proceedings

of the 14th World Conference on Earthquake Engineering, Beijing, China. Zhang, J., Huo, Y., Brandenberg, S. J., and Kashighandi, P., 2008b. Effects of structural

characterisations on fragility functions of bridges subject to seismic shaking and lateral spreading. Earthquake Engineering & Engineering Vibration 74: 369 – 382.

Zhang, J., and Huo, Y., 2009. Evaluating effectiveness and optimum design of isolation devices for highway bridges using the fragility function method. Engineering Structures 31: 1648 – 1660.

Zhong, J., Gardoni, P., Rosowsky, D., and Haukaas, T., 2008. Probabilistic Seismic Demand Models and Fragility Estimates for Reinforced Concrete Bridges with Two-Column Bents. Journal of Engineering Mechanics 1346: 495 – 504.

Zhong, J., Gardoni, P., and Rosowsky, D., 2009. Bayesian Updating of Seismic Demand Models and Fragility Estimates for Concrete Bridges with Two-Column Bents. Journal of

Earthquake Engineering 135: 716 – 735. Zhu, T. J., Tso, W. K., and Heidebrecht, A. C., 1988. Effect of Peak Ground a/v Ratio on

Structural Damage. Journal of Structural Engineering 114(5): 1019 – 103


96

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 tu , the peak ground acceleration (PGA) is defined as:

tuPGA max A.1

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.

Appendix A: Strong Motion Intensity Measures

97

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:

tuPGV max A.2a

tuPGD max 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.


98

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.


99

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:

e

o

t

te

rms dttutt

a2

0

1

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 tu and tu 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):

dttu

gI xxXX

0

2

21

arccos

A.4

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:


100

dttu

gI xxXX

0

2

2

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 region-specific 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 g2 , the velocity and

displacement integrals are multiplied by PGV1 and PGD1 , respectively, to produce:

e

XX

t

xV dttuPGV

I0

21

A.6

e

XX

t

xD dttuPGD

I0

21

A.7

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.


101

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


102

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 A.8

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 ΔIaf, a value taken as 0.135 m/s originally


103

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:

t

dttuCAV0

A.9

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

i

t

t

i

i

dttuCAV1 `1

A.10

where 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:

t

dttuCAD0

A.11

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:

t

dttuCAI0 A.12

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


104

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:

5.05.15.25.1

sigrmsC TascmI

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:

25.075.0

sigf TPGVscmI A.14

A.8 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):

tn

i

i

effu

uN

2

1

2

max2

1

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.


105

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):

TST

TS dv

2

A.16

TST

TS da

22

A.17

Fig. A.7 Response Spectra for the El Centro NS strong motion record, a) Pseudo-

spectral acceleration, b) Pseudo-spectral velocity and c) Spectral Displacement


106

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:

2

1

,1

1

t

tv dTTS

CSI

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:


107

n

i

ia TSn

EPA1

1

5.2

1

A.19

n

i

iv TSn

EPV1

1

5.2

1

A.20

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 gxm :

0 kxcxxm g

A.21

where x is the relative displacement of mass with respect to the ground, gx the displacement

of the ground, c the damping coefficient and k the restoring force. Integrating Eq. (A.21) with respect to x gives:

gtt dxxfdxdxxcxm 22

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:

dtxxxE gga

A.23

The maximum elastic input energy is therefore defined as the maximum Ea over oscillators in the range 0 ≤ T ≤ t:


108

t

ti dttututuTE0

max A.24

where tut is the response acceleration of the SDOF system with fundamental period T, and

tu and tu are the ground acceleration and velocity respectively. The absolute input energy can be converted into an equivalent velocity Vei via:

m

TETV

i

ei

2

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 non-linear 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:

111

1

11~, TSTSPFIM adE

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


109

Eq. (A.26) can be multiplied by the ratio of the spectral displacement of an elastic-perfectly-plastic oscillator Sd(T1, ξ1, dy) to the elastic oscillator:

E

d

y

I

d

y

I

dI IMTS

dTSdTSPFIM 1

11

11

11

1

11,

,,,,

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:

EEE

ddEE

IMPF

PFR

TSPFTSPFIM

11

1

2

12

1/2

2

22

2

2

2

11

2

12&1

1

,,

A.28

where

11

2

1

22

2

2

1/2,

,

TSPF

TSPFR

d

d

EE

A.29

which can be similarly adapted to take into consideration inelastic response in the first mode by incorporating Eq. (A.27):

IEEEE

d

y

I

d

EI IMPF

PFRIM

TS

dTSIM 11

1

2

12

1/22&1

11

11

2&1 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:

E

d

y

eq

d

y

eq

deq IMTS

dTSdTSPFIM 1

11

11

11,

1

11,

,,,,

A.31

Other IMs are defined in the main body of this report where relevant.

D 2 - Home | VCE Pipelines and Distribution .....25 6.3.3 Storage .....26 6.4 ELECTRICAL SYSTEMS...

Documents

Transcript of D 2 - Home | VCE Pipelines and Distribution .....25 6.3.3 Storage .....26 6.4 ELECTRICAL SYSTEMS...