The Pennsylvania State University

The Graduate School

College of Engineering

RISK ASSESSMENT OF HIGHWAY BRIDGES UNDER

MULTI-HAZARD EFFECT OF FLOOD-INDUCED SCOUR

AND EARTHQUAKE

A Dissertation in

Civil Engineering

by

Taner Yilmaz

© 2015 Taner Yilmaz

Submitted in Partial Fulfillment

of the Requirements

for the Degree of

Doctor of Philosophy

May 2015

ii

The dissertation of Taner Yilmaz was reviewed and approved* by the following:

Swagata Banerjee Basu

Assistant Professor of Civil Engineering

Dissertation Advisor

Chair of Committee

Gordon P. Warn

Associate Professor of Civil Engineering

Prasenjit Basu

Assistant Professor of Civil Engineering

M. Jeya Chandra

Professor of Industrial and Manufacturing Engineering

Peggy A. Johnson

Professor of Civil Engineering

Department Head

*Signatures are on file in the Graduate School.

iii

ABSTRACT

Natural disasters may have significant impact on the functionality of highway transportation

systems resulting in unacceptable socio-economic losses. Flood and earthquake hazards can be

considered as two most significant natural threats to safety of bridges. The overarching need for safety

and serviceability of critical transportation infrastructure system requires highway bridges to be

analyzed and designed not only for discrete hazard events, but also for possible multiple-hazard (or

multi-hazard) conditions. For a highway network spanning over a seismically-active flood-prone

region, the occurrence of earthquakes in the presence of flood-induced scour is a possible multi-hazard

scenario for bridges in the network. The varied dynamic characteristics of a bridge due to the

occurrence of scour may affect the response of the bridge under earthquake loading, and eventually

may increase the risk of bridge failure.

Despite the rising concern of research communities on this topic, the issues related to the

multi-hazard effect of flood-induced scour and earthquake on highway bridges have not been

satisfactorily answered. In addition, no guideline is currently available in design codes to ensure

seismic safety of bridges with potentially scoured foundations. This dissertation aims to improve a

comprehensive knowledge-base on risk and reliability analyses of highway bridges subjected to this

multi-hazard by developing a multi-hazard risk assessment framework for bridges and quantifying

variability in multi-hazard fragility and risk of bridges through a thorough uncertainty analysis.

Outcome of this research provides research communities and government agencies a better

understanding of the multi-hazard effect of flood-induced scour and earthquake on the risk and

reliability of highway bridges. It also serves as a foundation for future researches on developing

strategic plans for repair or retrofit prioritization for highway bridges under similar multi-hazard

conditions.

iv

TABLE OF CONTENTS

Page

List of Figures vii

List of Tables x

Acknowledgements xii

Chapter 1 Introduction 1

1.1 Motivation 1

1.2 Objectives 4

1.3 Methodology 4

1.4 Organization of the Dissertation 5

Chapter 2 Review of Existing Literature on Risk and Reliability of Bridges and Multiple

Hazard Effects 7

2.1 Risk Assessment of Highway Bridges 7

2.2 Uncertainties in Risk Assessment of Bridges 9

2.3 Multi-Hazard Approach for Analyzing Civil Infrastructure Systems 10

2.3.1 Flood-Induced Scour at Bridge Foundations 11

2.3.2 Multi-hazard Effect of Earthquake and Flood-Induced Scour 14

2.4 Load and Resistance Factor Design in Seismic Design of Bridges 17

Chapter 3 Performance of Two Real-Life California Bridges under Regional Seismic and

Flood Hazards 19

3.1 Study Bridges 19

3.2 Regional Seismic and Flood Hazards 21

3.2.1 Regional Seismic Hazard 21

3.2.2 Regional Flood Hazard 23

v

3.2.3 Flood-induced Scour at Bridge Foundations 24

3.3 Finite Element Analyses of Bridges 25

3.3.1 Bridge Modeling 25

3.3.2 Modal Analysis of Bridges 29

3.4 Fragility Curves and Surfaces 31

3.4.1 Time History Analyses of Bridges 31

3.4.2 Component-Level Damage States 32

3.4.3 Component-Level Fragility Curves 35

3.4.4 System-Level Fragility Curves 38

3.4.5 Fragility Surfaces 39

3.5 Risk Evaluation 41

3.6 Closure 44

Chapter 4 Uncertainty Analysis of Risk of Highway Bridges Integrating Seismic and Flood

Hazards 45

4.1 Uncertain Input Parameters 45

4.2 Sensitivity of Uncertain Parameters 47

4.2.1 Regional Flood and Seismic Hazards 47

4.2.2 Sensitivity of Bridge Response to Uncertain Parameters 48

4.2.3 Tornado Diagram Analysis 49

4.2.4 Advanced First Order Second Moment Reliability Analysis 51

4.2.5 Sensitivity of Scour Depths to Uncertain Input Parameters 53

4.3 Uncertainty Analysis 55

4.3.1 Generation of Random Samples 55

4.3.2 Bridge Fragility Curves 56

4.3.3 Confidence Intervals of Fragility Curves 61

4.3.4 Risk Curves of the Bridge 65

vi

4.4 Closure 67

Chapter 5 Multi-Hazard Vulnerability Assessment of Generic Bridges in the West Coast of

the U.S. 69

5.1 Review of Bridge Inventory in Hazard-Critical Regions 69

5.2 Characteristic Bridges 73

5.3 Hazard Matrix 76

5.4 Fragility Analysis 78

5.4.1 Modal Behavior of Generic Bridges 79

5.4.2 Fragility Curves 80

5.5 Closure 86

Chapter 6 Conclusions 88

6.1 Summary 88

6.2 Key Conclusions 90

6.3 Significance of the Study 91

6.4 Recommendations for Future Work 91

References 93

Appendix A Ground Motion Records Used in Time History Analyses 100

Appendix B Peak Annual Streamflow Data at the Flow Measurement Stations 116

Appendix C Details of Analytical Modeling of Bridge Components in Finite Element Analyses 119

Appendix D Latin Hypercube Sampling Design 128

Appendix E Results of Fragility Parameters in Uncertainty Analyses 129

Appendix F Results of System-Level Fragility Parameters of Bridge-1 with 90% Confidence 134

vii

LIST OF FIGURES

Page

Figure 1-1: (a) Flood-induced scour at Schoharie Creek Thruway Bridge in NY (USGS 1997); (b)

Deck collapse at I-10E Freeway Bridge in West Los Angeles (FEMA 1994) 2

Figure 1-2: Earthquake and flood hazard potential in the U.S.: (a) seismic hazard map of the U.S

(USGS 2008a); (b) declared flooding events from 1965 to 2003 (USGS 2006) 3

Figure 1-3: General flowchart 5

Figure 3-1: (a) Schematic view of Bridge-1, (b) cross-sections of bridge pier and pile shaft, and

(c) general elevation view of a typical bent 20

Figure 3-2: (a) Schematic view of Bridge-2, (b) general elevation view of a pier and (c) pier

cross-section 21

Figure 3-3: Seismic hazard curves at bridge sites 22

Figure 3-4: Mean flood hazard curves at Bridge-1 and Bridge-2 sites 24

Figure 3-5: Abutment modeling of (a) Bridge-1 (b) Bridge-2 29

Figure 3-6: Fundamental mode shapes of Bridge-1 30

Figure 3-7: Fundamental mode shapes of Bridge-2 30

Figure 3-8: Sample pier top horizontal displacement histories for (a) Bridge-1, (b) Bridge-2 32

Figure 3-9: Component-level fragility curves of Bridge-1; (a) pier flexural damage, (b) abutment

passive deformation, (c) bearing longitudinal deformation, and (d) shear key and

bearing transverse deformations 37

Figure 3-10: Component-level fragility curves of Bridge-2; (a) pier flexural damage at minor,

moderate and major damage states, (b) pier flexural damage at collapse state, (c)

abutment active deformation, (d) abutment passive deformation and bearing

longitudinal deformation 38

Figure 3-11: System-level fragility curves of (a) Bridge-1 and (b) Bridge-2 39

Figure 3-12: Fragility surfaces of Bridge-1 and Bridge-2 42

Figure 3-13: Seismic risk curves (a) Bridge-1 (b) Bridge-2 44

Figure 4-1: Flood hazard curve with 90% confidence at the bridge site 47

Figure 4-2: Tornado diagrams for pier curvature ductility obtained in the absence of flood-

induced scour under ground motions (a) GM1, (b) GM2, (c) GM3, and (d) GM4 50

viii

Figure 4-3: Tornado diagrams under ground motion GM1 obtained in the presence of scour due to

a 20-yr flood event for EDP (a) Δlong,p, (b) Δtrans, (c) Δb,long, and (d) Δb,trans 51

Figure 4-4: Relative variance contributions of uncertain parameters on (a) μφ, (b) Δlong,p, (c) Δtrans,

(d) Δb,long, and (e) Δb,trans for no flood condition 53

Figure 4-5: Relative variance contributions of uncertain parameters on (a) μφ, (b) Δlong,p, (c) Δtrans,

(d) Δb,long, and (e) Δb,trans for 20-year flood condition 53

Figure 4-6: Tornado diagrams for the scour depth at (a) Bent-2, (b) Bent-3, and (c) Bent-4 of the

bridge under 10-year flood 55

Figure 4-7: Seismic fragility curves for pier flexural damage under (a) no flood, (b) 1-year flood,

(c) 2-year flood, (d) 10-year flood, and (e) 20-year flood conditions 57

Figure 4-8: Seismic fragility curves at minor damage state under the 20-year flood hazard for (a)

pier flexural damage (b) abutment passive deformation in longitudinal direction, (c)

abutment transverse deformation, (d) bearing longitudinal deformation, (e) bearing

transverse deformation, and (f) shear key deformation 59

Figure 4-9: System-level seismic fragility curves of the bridge under (a) no flood, (b) 1-year

flood, (c) 2-year flood, (d) 10-year flood, and (e) 20-year flood conditions 60

Figure 4-10: Lognormal probability papers for median values from system-level fragility curves

at (a) minor damage, (b) moderate damage, (c) major damage, and (d) collapse state

under 2-year flood condition 63

Figure 4-11: Schematic illustration of fragility curves with different confidence levels 64

Figure 4-12: 90% confidence intervals of system-level fragility curves of the bridge under (a) no

flood, (b) 1-year flood, (c) 2-year flood, and (d) 10-year flood conditions 64

Figure 4-13: Multi-hazard risk of the bridge: (a) No flood condition, (b) 1-year flood condition,

(c) 2-year flood condition, (d) 10-year flood condition, (e) 20-year flood condition,

and (f) dispersion of risk 66

Figure 5-1: Number of bridges with respect to the number of spans in (a) California, (b)

Washington 72

Figure 5-2: Maximum span lengths of bridges for the inventory of (a) California, (b) Washington 73

Figure 5-3: Deck width of bridges for the inventory of (a) California, (b) Washington 73

Figure 5-4: Schematic drawings of Type A1 and Type A2 bridges; (a) elevation view, (b)

substructure alternatives, (c) box-girder details 75

Figure 5-5: Locations of the selected sites 77

Figure 5-6: (a) Mean flood hazard curves, (b) mean seismic hazard curves 78

Figure 5-7: (a) Fundamental mode shapes and modal periods of generic bridges at no flood

condition 79

ix

Figure 5-8: Component-level fragility curves of Bridge Type A1 at Site-1 for (a) pier damage, (b)

abutment damage in long. dir. (c) abutment damage in trans. dir. (d) bearing

deformation in long. dir. 82

Figure 5-9: Component-level fragility curves of Bridge Type A2 at Site-1 for (a) pier damage, (b)

shaft (enlarged cross-section) damage, (c) abutment damage in long. dir. (d)

abutment damage in trans. dir. (e) bearing deformation in long. dir. 83

Figure 5-10: System-level fragility curves of (a) Bridge Type A1, and (b) Bridge Type A2 at Site-

1 84

Figure C-1: (a) Representative element discretization at a typical bridge bent, (b) typical fiber

section assigned to pier elements 120

Figure C-2: Comparison of analytical and experimental load-displacement curves of test columns

from (a) Lehman and Moehle (2000), (b) Wehbe et al. (1999) 120

Figure C-3: Abutment backwall-backfill interaction for (a) seat-type abutment, (b) diaphragm

abutment 121

Figure C-4: Abutment response in transverse direction 122

Figure C-5: Hysteresis model for exterior shear key, after Megally et al. 2001 (Bozorgzadeh et al.

2007) 123

Figure C-6: Backbone curve assigned to the shear key elements in the generic bridges 124

Figure C-7: PTFE/elastomeric bearings backbone curve in horizontal direction 125

Figure C-8: Comparison of analytical and experimental load-deformation response of a test

bearing 125

Figure C-9: Backbone curve for modeling the pounding of adjacent bridge decks 126

x

LIST OF TABLES

Page

Table 3-1: Estimated maximum scour depths at foundations of Bridge-1 and Bridge-2 25

Table 3-2: Modal periods of Bridge-1 and Bridge-2 31

Table 3-3: Damage threshold limits for Bridge-1 35

Table 3-4: Damage threshold limits for Bridge-2 35

Table 4-1: Uncertain Modeling Parameters 46

Table 4-2: Ground motion records used in the sensitivity analyses 49

Table 5-1: Bridge classes in California 70

Table 5-2: Bridge classes in Washington 71

Table 5-3: Selected sites investigated for the integrated flood and earthquake hazards 77

Table 5-4: Estimated mean scour depths (in m) 78

Table 5-5: Modal periods of Type A1 and Type A2 bridges 80

Table 5-6: Damage threshold limits for the generic bridge 81

Table 5-7: Median values for component and system level fragility curves of Bridge Type A1 85

Table 5-8: Median values for component and system level fragility curves of Bridge Type A2 86

Table A-1: Ground motion records used for Bridge-1 Analyses 100

Table A-2: Ground motion records used for Bridge-2 Analyses 103

Table A-3: Ground motion records used for the generic bridges at Site-1 107

Table A-4: Ground motion records used for the generic bridges at Site-2 109

Table A-5: Ground motion records used for the generic bridges at Site-3 111

Table A-6: Ground motion records used for the generic bridges at Site-4 113

Table B-1: Peak Annual Streamflow Measured at the USGS Data Station Site Number 11370500 116

Table B-2: Peak Annual Streamflow Measured at the USGS Data Station Site Number 11051500 117

Table B-3: Peak Annual Streamflow Measured at the USGS Data Station Site Number 11303000 117

xi

Table B-4: Peak Annual Streamflow Measured at the USGS Data Station Site Number 11051500 118

Table B-5: Peak Annual Streamflow Measured at the USGS Data Station Site Number 11147500 118

Table C-1: Accepted values of the pounding model parameters 127

Table D-1: Latin Hypercube Sampling Design for Uncertainty Analysis 128

Table E-1: Median values of seismic fragility curves at minor and moderate damage state for pier

flexural damage 129

Table E-2: Median values of seismic fragility curves at major damage and collapse state for pier

flexural damage 130

Table E-3: Median values of seismic fragility curves for abutment passive deformation 130

Table E-4: Median values of seismic fragility curves for abutment transverse deformation 131

Table E-5: Median values of seismic fragility curves for bearing longitudinal deformation 131

Table E-6: Median values of seismic fragility curves for bearing transverse deformation 132

Table E-7: Median values of seismic fragility curves for shear key deformation 132

Table E-8: Median values of system-level seismic fragility curves at minor and moderate damage

states 133

Table E-9: Median values of system-level seismic fragility curves at major damage and collapse

states 133

Table F-1: Median values of system-level fragility curves of Bridge-1 corresponding to 5%, 50%,

95, and that computed when all input parameters are deterministic 134

xii

ACKNOWLEDGEMENTS

Whenever I had challenging times in the course of my Ph.D. studies, I motivated myself by

dreaming the moment I would write the acknowledgments. And with the joy of arriving at that

moment, I realize that it would not have been possible to reach this point without the support of many

wonderful people who have had an impact on my Ph.D. journey.

I would like to express my deepest gratitude to my advisor, Dr. Swagata Banerjee Basu, for

her constant support, generous guidance, and unlimited patience. It has been a great pleasure for me to

work with her, not only due to her wide knowledge and experience I have benefited from, but also for

her being a great mentor. I would also like to thank my thesis committee members, Dr. Peggy A.

Johnson, Dr. Gordon P. Warn, Dr. Prasenjit Basu, and Dr. Jeya M. Chandra for serving in my thesis

committee, giving their valuable time and precious comments and suggestions on my research.

The financial support of the National Science Foundation through the award number 1131359

and the Thomas D. Larson Pennsylvania Transportation Institute is gratefully acknowledged. I would

also like to acknowledge the George E. Brown, Jr. Network for Earthquake Engineering Simulation

for using the NEEShub platform during the completion of the analytical study.

I am so happy to have known a very nice group of graduate students at Penn State: Bach,

Sandhya, Alben, Purna, Jaskanwal to name a few. I have collected valuable memories, and gained a

long list of good friends. Mehmet, Ilker, Ali, Baris, Elif, Duygu, Kivanc, Nergiz, Safakcan, Tugce are

only a part of that list. Thank you so much for your friendship and good times. I would also like to

thank my friends in Turkey: Murat, Elif, and Seda for their continuous support and encouragement.

Finally; I am extremely thankful to my family, my mother Betul Nese, my father Talat, my

sister Ufuk, my brothers Dursun Murat and Cengiz, my lovely nieces Melis and Begum, and my little

nephew Uzay, for their unconditional support and love. I feel so fortunate to have such a beautiful

family.

xiii

I dedicate this work to my mother

1

CHAPTER 1

INTRODUCTION

1.1 Motivation

Highway transportation system is one of the key modes of ground transportation of a nation.

Past incidences indicate that the damage of highway bridges during natural disasters such as

earthquakes, windstorms and floods may have significant impact on the functionality of highway

transportation systems resulting in unacceptable socio-economic losses due to post-event repair of

damaged bridges and system downtime. For an instance, only repair of damaged bridges after the 1989

Loma Prieta and 1994 Northridge earthquakes cost $280 million and $190 million, respectively (Basoz

and Kiremidjian 1996). The overarching need for safety and serviceability of critical transportation

infrastructure system under extreme natural hazards requires highway bridges to be analyzed and

designed not only for discrete hazard events, but also for possible multiple-hazard (or multi-hazard)

conditions. This dissertation aims to respond to the need for risk and reliability analyses of highway

bridges subjected to the multi-hazard effect of earthquake and flood-induced scour.

Having caused a substantial number of bridge failures in the U.S. (Wardhana and Hadipriono

2003), flood and earthquake hazards can be considered as two most significant natural threats to safety

of bridges. Examples of impacts of flood and earthquake events on bridges are presented in Figure 1-1.

While Figure 1-1(a) shows the scour induced at the foundation of Schoharie Creek Thruway Bridge in

NY due to the flood event in 1987, Figure 1-1(b) shows the collapse of the deck of the I-10E freeway

bridge in west Los Angeles during the 1994 Northridge Earthquake. As can be observed from Figure

1-1(a), scour can lead to an extensive effect on structural stability of a bridge by removing bed

materials from around bridge piers (Arneson et al. 2012) and thus, by changing the fixity conditions of

vertical support systems at foundation level. Accordingly, lateral load-carrying capacity of bridges

2

may get reduced and bridges become more flexible under lateral loading. The varied dynamic

characteristics of a bridge due to the occurrence of scour may affect the response of the bridge under

lateral loading, such as the one during earthquakes; this may eventually increase the risk of bridge

failure. To ensure bridge stability against scour, the American Association of State Highway and

Transportation Officials (AASHTO) mandated foundation stability check against flood-induced scour

for a design level flood event (AASHTO 2012). However, no guideline is currently available in design

codes to ensure seismic safety of bridges with potentially scoured foundations.

(a) (b)

Figure 1-1: (a) Flood-induced scour at Schoharie Creek Thruway Bridge in NY (USGS 1997); (b)

Deck collapse at I-10E Freeway Bridge in West Los Angeles (FEMA 1994)

Flood and earthquake are identified as “National Threats” by the United State Geological

Survey (USGS). The seismic hazard map of the U.S. (USGS 2008a) for an exceedance probability of

10% in 50 years of various levels of seismic intensity (in terms of peak ground acceleration) is shown

in Figure 1-2(a). On this map, a greater seismic hazard at a location is expressed with a darker color.

Figure 1-2(b) shows the number of flooding disaster declarations in the U.S. between the years 1965

and 2003, which indicates the relative flood hazard potential within the U.S. On this map, green,

yellow, orange and red areas represent one, two, three, and four or more declarations, respectively.

These two hazard maps show several regions of US that have both seismic and flood hazards in

moderate to high intensity scale. Therefore for a highway network spanning over a seismically-active

flood-prone region, the occurrence of earthquakes in the presence of flood-induced scour is a possible

multi-hazard scenario for bridges in the network. For an example, the highway transportation network

3

in California represents such a network. Hence, the aforementioned multi-hazard scenario has

potential to influence seismic design and retrofit of bridges in such regions as long as network safety

and functionality are of concern.

(a) (b)

Figure 1-2: Earthquake and flood hazard potential in the U.S.: (a) seismic hazard map of the U.S

(USGS 2008a); (b) declared flooding events from 1965 to 2003 (USGS 2006)

Floods and earthquakes are low-probability, high-consequence events. Probabilistically, the

occurrence of two independent hazard events with large return periods within a certain time interval or

the service life of bridges is reasonably small. Nevertheless, the conditional multi-hazard is a possible

scenario for the bridges located in critical hazard locations. For example, an earthquake with a

magnitude of 4.5 struck the state of Washington on January 30th of 2009 just three weeks after a major

flood event hit the same region (Banerjee and Prasad 2013). Hence, such sequential occurrences of

discrete events within relatively small time intervals should not be disregarded due to their multi-

hazard significance. In recent years, the significance of risk and reliability assessment of bridges in

multi-hazard environments has been recognized by the bridge engineering community; yet, research is

needed to generate a comprehensive knowledge-base on the consideration of multi-hazard approaches

in order to achieve cost-efficient and safer bridge designs in the future. This is the motivation of the

current dissertation.

4

1.2 Objectives

The key objective of this dissertation is to assess the reliability of bridges located in

seismically-active flood-prone regions of the U.S. by quantifying their risks under the multi-hazard

effect of earthquake and flood-induced scour. Despite the rising concern of research communities on

this topic, the issues related to the multi-hazard effect of integrated flood-induced scour and

earthquake on highway bridges have not been satisfactorily answered. The present research aims to

improve the knowledge-base on this by achieving the following primary objectives:

1. Generate fragility curves and surfaces to estimate failure probabilities of bridges for

different earthquake and flood intensities. These surfaces can also be used in future

performance evaluation of highway transportation systems under regional multi-hazard.

2. Develop a risk assessment framework for bridges under this multi-hazard effect.

Generated fragility and risk curves within this framework serve as base tools for

enhancing reliability and minimizing post-event losses of highway bridges for the same

multi-hazard event in the future.

3. Quantify variability in multi-hazard fragility and risk of bridges through a thorough

uncertainty analysis.

1.3 Methodology

The general framework followed throughout this research is represented with the flowchart

shown in Figure 1-3. Within the scope of this dissertation, the integrated effect of flood and

earthquake hazards is considered through a conditional multi-hazard approach assuming bridges are

exposed to flood-induced scour at the time of seismic event. The research is mainly composed of three

phases. In the first phase, the entire methodology is applied to real-life bridges to access multi-hazard

performance of bridges. In the second phase, the same framework is utilized to perform uncertainty

analysis. The last phase presents analyses of generic bridges considering four combinations of seismic

and flood hazards based on their hazard levels. These are – (1) High flood and moderate seismic

5

hazards, (2) moderate seismic and moderate flood hazards, (3) moderate flood and high seismic

hazards, (4) high flood and high seismic hazards.

Figure 1-3: General flowchart

1.4 Organization of the Dissertation

This dissertation is comprised of six chapters with the following contents:

Chapter 2 presents a literature review and background on risk and reliability of bridges and

multi-hazard analysis including earthquake and flood-induced scour. This chapter also provides a brief

background on load and resistance factor design of bridges under seismic events.

Chapter 3 presents a detailed study on modeling and performance evaluation of two real-life

California bridges under multi-hazard condition of flood and earthquakes. In this chapter, the general

framework of risk assessment of bridges under this multi-hazard scenario is discussed.

Nonlinear Time

History Analyses

Regional Flood

Hazard

Investigated

Bridges

Varied frequency

flood events

Fragility Curves

and Surfaces

Risk

Curves

Regional Seismic

Hazard

Damage States

Foundation

without scour

Scoured

foundation

3D Finite Element Models of Bridges

Uncertainty Analysis

6

Chapter 4 presents uncertainty analysis to quantify variations in bridge fragility curves and

risk curves under the multi-hazard scenario discussed herein. The methodology includes a sensitivity

study involving Tornado diagram and Advanced First Order Second Moment reliability analyses to

screen significant uncertain parameters to which bridge response is mostly sensitive.

Chapter 5 presents the multi-hazard vulnerability assessment of generic bridges with

characteristics design features in the west coast of the U.S. Bridge fragility curves are developed

considering four hazard-critical sites in the West Coast of the U.S.

Chapter 6 presents the key conclusions and significance of the study. It also highlights areas

for potential future research on the topic discussed here.

7

CHAPTER 2

REVIEW OF EXISTING LITERATURE ON RISK AND RELIABILITY OF

BRIDGES AND MULTIPLE HAZARD EFFECTS

This chapter presents a brief synthesis of past studies relevant to risk and uncertainty analysis

and multi-hazard performance evaluation of highway bridges under earthquake and flood-induced

scour. Although the focus of this dissertation is on highway bridges, past studies on multi-hazard

performance evaluation for other types of structures and hazards are also discussed to provide an

overall idea on recent advances in the emerging field of multi-hazards engineering. This chapter

concludes with a brief discussion on the load and resistance factor design of bridges adopted in

seismic design codes.

2.1 Risk Assessment of Highway Bridges

A significant advancement has been made over past two decades to develop risk assessment

methodologies for highway bridges and infrastructure systems under extreme events. These risk

assessment methodologies aimed at enhancing reliability of systems, minimizing losses during

hazardous situations, identifying cost-effective mitigation strategies and improving post-disaster

restoration policies (Pitilakis et al. 2006). Examples of such risk assessment methodologies for bridges

and highway network systems are Basoz and Kiremidjian (1996), Werner et al. (2000), Mackie and

Stojadinovic (2005), to name a few. Literature also suggests that a quantitative measure of risk can be

treated as one of the performance indicators of structures (or systems) for risk-informed condition

assessment, decision making and expenditure allocation (Ayyub and Popescu 2003, Ellingwood 2005,

Deco and Frangopol 2011).

Risk is associated with consequences that would result due to the occurrence of regional

scenario events in future. Though risk assessment methodologies can be discussed for any type of

8

hazard and structures, this section primarily focuses on seismic risk of bridges as it relates to the topic

of the dissertation. Seismic risk assessment methodologies generally follow probabilistic approaches

and are composed of three components: hazard model, vulnerability model, and loss model. Seismic

hazard of a certain region can be represented with seismic hazard curves that provide annual

exceedance probabilities of seismic events with varied intensity levels. Vulnerability model of bridges

can be represented with fragility curves that describe the likelihood of a bridge or a class of bridges

being damaged at a specific damage level under a given ground motion intensity. A comprehensive

state-of-the-art review on seismic fragility assessment of highway bridges is presented in Billah and

Allam (2014), which includes review of available fragility assessment methodologies, their basic

features, limitations and applications. Finally, the loss model incorporates post-event consequences –

direct losses such as post-event bridge restoration and indirect losses such as socio-economic losses

arising from various sources including traffic delay, network downtime and loss of opportunity.

A number of past research attempted to evaluate seismic risk of highway networks at different

regions of the U.S. (Chang et al. 2000, Shiraki et al. 2007, Zhou et al. 2010, Padgett et al. 2010).

Although the general framework of seismic risk methodologies are well defined in literature and well

adopted in practice, research is very limited on risk assessment of bridges under multi-hazard

scenarios particularly when seismic and flood hazards are involved. This may be due to the fact that

past studies on this multi-hazard did not consider real-life (or existing) bridges; hence, no region-

specific hazard information at bridge sites was available to apply in the risk assessment framework for

calculating multi-hazard risk of bridges. This dissertation attempts to fill this existing knowledge gap

by integrating multi-hazard analysis to the risk assessment framework for highway bridges. Research

outcomes will facilitate risk-based decision-making for highway bridges under the multi-hazard

scenario investigated herein.

9

2.2 Uncertainties in Risk Assessment of Bridges

In the framework of probabilistic risk assessment, uncertainties in various forms (e.g., model,

parametric, and statistical) exist in different modules of the framework. Therefore, the quantification

of uncertainty becomes equally imperative along with the risk assessment of highway bridges and the

systems under extreme events. An accurate picture of risk can be achieved by propagation of all

sources of uncertainty, from hazard occurrence to the response of structural systems, through the risk

analysis (Ellingwood 2007).

Taking the Los Angeles area highway transportation system as a testbed, Banerjee et al.

(2009) showed that quantitative measure of system seismic risk may vary significantly due to the

uncertainty associated with bridge seismic vulnerability model expressed in the form of fragility

curves. Hence, it was recognized that bridge vulnerability model is one of the major sources to

introduce uncertainty in system risk estimation. A number of studies have been performed thus far to

identify critical sources from which uncertainties propagate to seismic fragility curves of bridges

(Padgett et al. 2007, Pang et al. 2014, Nielson and DesRoches 2006, Tubaldi et al. 2010, Padgett et al.

2013, Karim and Yamazaki 2001, Kunnath et al. 2006). While some studies paid individual attention

to uncertainties from modeling parameters, modeling assumptions and ground motions to assess their

impacts on seismic fragility curves of bridges, combined effects of two or more of these uncertainties,

including that from the bridge geometry and underlying soil, on bridge seismic characteristics have

also been studied. Research identified notable influences of uncertainties from bridge geometry

(Padgett et al. 2007, Pang et al. 2014), modeling parameters (Nielson and DesRoches 2006, Tubaldi et

al. 2010, Padgett et al. 2013), strong motion characteristics (Karim and Yamazaki 2001), data suites of

synthetic ground motions (Padgett et al. 2007), and ground motion scaling procedures (Kunnath et al.

2006) on seismic fragilities of bridges. In additions, uncertainties associated with underlying soil is

observed to play crucial roles while modeling soil-structure interaction at bridge foundations and

evaluating the effect of liquefiable soil layers on bridge fragility estimates (Kunnath et al. 2006,

Padgett et al. 2013). Hence, observations made from these previous studies suggest that a rigorous

10

analysis involving uncertainties associated with structural, geotechnical and hazard modeling

parameters is warranted for a reliable estimation of risk of highway bridges under regional hazards.

2.3 Multi-Hazard Approach for Analyzing Civil Infrastructure Systems

The need for a broad approach that considers collective impacts of various natural or man-

made hazards on the performance of civil infrastructure systems and system components has

increasingly taken attention of the professional community (Grigoriu and Kafali 2007). Multi-hazard

approaches aid in reduction of overall construction costs while maintaining the same or higher level of

safety of infrastructure components and systems. They also have critical role in modern bridge

management philosophies (Alampalli et al. 2011). The term multi-hazard can correspond to the

multiple consideration of random natural or man-made hazards for the optimal system performance.

On the other hand, triggering of one hazard due to the occurrence of another hazard (e.g. earthquake

and earthquake-triggered liquefaction) or occurrence of two independent hazard events within a

relatively small time interval (earthquake and flood events) can be considered as multi-hazard

conditions.

Risk assessment of infrastructure in a multi-hazard environment and analyzing infrastructure

vulnerabilities to multiple hazards are of prime importance at present for the emerging field in

engineering (MCEER 2007). For bridge structures, Ettouney et al. (2005) emphasized the recent

developments and innovations in computing, analytical and sensing technologies for considering the

complexity of structural systems under the multi-hazard conditions, and proposed a quantitative

approach for multi-hazard considerations. For a multi-hazard scenario involving earthquake and flood-

induced scour, research is performed over last few years to comprehend bridge performance under this

multi-hazard (Ghosn et al. 2003, Wang et al. 2012, Banerjee and Prasad 2013, Prasad and Banerjee

2013, Alipour et al. 2013, Wang et al. 2014a,b). Specific findings from these studies are discussed in

following subsections. Yet, none of the previous research (except for Banerjee and Prasad 2013) has

extended its scope to estimate risk of bridges under the above-stated multi-hazard condition. This may

11

be due to the fact that past studies related to this topic did not consider real-life (or existing) bridges;

hence, no region-specific hazard information at bridge sites was available to apply in the risk

assessment framework for calculating multi-hazard risk of bridges.

Though ample literature is not available on bridge performance evaluation for the stated multi-

hazard condition, a number of studies are performed on multi-hazard risk analyses of various other

types of structures under different hazard combinations. For example, Kafali and Grigoriu (2008)

assessed the performance of offshore platforms subjected to seismic and hurricane hazards. In their

work, seismic activity matrix, hurricane matrix and system fragility are combined to evaluate system

failure probabilities at slight, moderate, and extensive damage levels. This study concluded that at

different reliability levels of structures, different hazard actions can be dominant. As another example,

the consistency of risk of buildings under multi-hazard of wind and earthquake was investigated by

Crosti et al. (2011). In that study, they concluded that a design satisfying code requirements subjected

to multi-hazards does not necessarily achieve the level of safety indicated for single hazard.

Within a multi-hazard framework, fragility surfaces can be developed to show continuous

vulnerability functions integrating different hazards and intensity levels. Lee and Rosowsky (2006)

performed a fragility analysis for light-frame wood buildings under combined snow and earthquake

loads, and developed fragility surfaces under the combined effect of these two load effects. In the

same study, failure probabilities were obtained using a multi-hazard convolution scheme for

calculation of appropriate percentage of design snow load to be used in seismic fragility analysis. In

this dissertation, fragility surfaces of bridges for earthquake and flood hazards are developed in which

intensities of both hazards are varied over wide ranges. The following subsections outline past studies

on scour resulted from flood events and the multi-hazard analysis of bridges involving earthquake and

flood-induced scour.

2.3.1 Flood-Induced Scour at Bridge Foundations

The effect of scour on bridges is considered here through estimated maximum depth of scour

holes form around bridge piers during a flood event. It is assumed that bridge abutments are well-

12

protected against scour. There are three types of scour affecting bridge piers – contraction,

degradation, and local scour. Contraction scour is a result of faster flow velocities where river width

gets narrower due to a natural contraction of the stream channel or by a bridge. Degradation scour is

caused by the long-term erosion of river bed at both upstream and downstream of a bridge. Local

scour at piers develops due to the formation of vortices at pier bases. Within the scope of this

dissertation, full concentration is given to the local pier scour induced by flood events, and contraction

and degradation types of scour are ignored. For this reason, hereafter the term ‘scour’ refers to local

pier scour only.

In the present research, scour depths (ys) at bridge foundations are estimated using the

following equation suggested by the HEC-18 (Arneson et al. 2012):

43.0

1

65.0

1

32110.2 Fry

aKKKyys

(2-1)

where y1 is the flow depth directly upstream to the bridge pier, a is the pier width; K1, K2 and K3 are

correction factors for pier nose shape, angle of attack of flow and bed condition, respectively. Fr1 is

the Froude number as defined by 1/ ygV , where V and g respectively represent mean velocity of the

upstream flow and gravitational acceleration. Taking close approximations of river cross-sections at

the bridge sites, Manning’s equation is used to determine y1 and V simultaneously for reasonable

values of stream slope and roughness coefficients. Further detail on the calculation of scour depth can

be found in HEC-18 (Arneson et al. 2012).

Equation 2-1 can be applied for both live-bed and clear water scour conditions. Live-bed scour

condition arises when there is transport of bed material from the upstream reach into the crossing,

whereas for clear-water scour, there is no movement of the bed material. Live-bed scour condition has

a cyclic nature; scour hole develops during the rising stage of a flood and refills on their own during

the falling stage (Arneson et al. 2012). Live-bed scour is considered in the present research.

13

The scour prediction equation (Equation 2-1) recommended by Federal Highway

Administration (FHWA) in the HEC-18 document was found to overpredict the pier scour in most

cases when compared with the actual field data (Johnson 1995). Besides, this is a deterministic

equation which aims to supply conservative designs. However, scour prediction equation contains

uncertainties, such as model, parameter and data uncertainties. Johnson and Dock (1998) developed a

probabilistic framework of this equation for probabilistic estimates of scour depths. A comprehensive

study on uncertainty evaluation associated with the scour prediction and reliability-based confidence

bands for bridge scour estimates are presented in NHRP Report 716 (Lagasse et al. 2013).

Scour depth prediction at a bridge location is highly dependent on the velocity of the flow, and

hence the intensity of flood event. The flow discharge for a certain frequency flood event can be

quantified by flood hazard curves at a location of interest. Flood hazard curve at bridge sites can be

developed through flood-frequency analysis (Interagency Advisory Committee on Water Data 1982)

by processing annual peak discharge data that are recorded at the nearest stream gage stations to the

bridge sites (obtainable from USGS National Water Information System (USGS 2015)). It is realized

that due to the complexity of river basins, flow discharges at bridge sites may not always be the same

as these are recorded at the nearest stream gage stations. For a site where stream gage data is not

readily available, USGS has developed the National Streamflow Statistics (NSS) software compiling

regional regression equations for estimating streamflow statistics at ungaged sites (Ries et al. 2007).

These regional regression equations were derived such that streamflow statistics can be transferred

from gaged to ungaged sites through the use of watershed and climatic characteristics as explanatory

or predictor variables. More information on this is available at Lagasse et al. (2013).

Flood-induced scour at pier foundations change fixity conditions of vertical support systems

of bridges. Based on a study on pile foundation of an existing bridge, Bennett al. (2009) found that

lateral capacity of pile groups reduced with the occurrence of scour. From the study performed by

14

Hung and Yau (2014), it is found that scour at bridge piers can lead to significant degradation of

strength capacity and lateral stiffness of bridge piers under flood-induced loads. Dynamic tests to

monitor bridge response also showed that bridge dynamic response differs for scour-affected

foundation conditions (Foti and Sabia 2011). Based on these observations, it can be presumed that

scour may increase the risk of bridges under lateral loading such as the one due to earthquakes. On the

contrary, the increased flexibility of bridges may help in reducing seismic inertial forces. Nonetheless,

the seismic design philosophy used for a bridge may play a role to attain its overall seismic safety in

case of scour resulted from flood events. Hence, to ensure seismic safety of bridges under possible

flood conditions, it is important to check bridge seismic performance in the presence and absence of

scour resulting from various frequency flood events.

2.3.2 Multi-Hazard Effect of Earthquake and Flood-Induced Scour

In spite of the growing recognition of the multi-hazard performance evaluation of bridges,

only a few past studies have discussed the combined effect of earthquake and flood-induced scour on

bridge performance (Ghosn et al. 2003, Wang et al. 2012, Alipour et al. 2013, Prasad and Banerjee

2013, Banerjee and Prasad 2013, Wang et al. 2014a,b). In these studies, example bridges with various

structural attributes were analyzed for various combinations of scour depths and seismic events, and

bridge failure probabilities for each of these combinations were determined. It is generally observed

that bridge seismic fragility characteristics change with scour depth depending on the type of bridge

foundation. Bigger (large diameter) foundations tend to minimize the impact of scour on bridge

dynamic response (Banerjee and Prasad 2013). Other than analyzing bridges as structural systems,

bridge components such as piers are also analyzed to evaluate their failure probabilities for a combined

load effect of scour, truck and earthquake (Liang and Lee 2013a,b).

Beyond the multi-hazard performance evaluation of bridges, some of the past studies also

focused on the reliability analysis and the calculation of scour load factors (Ghosn et al. 2003, Alipour

et al. 2013, Wang et al. 2014b). In these studies, scour load factor was calculated while fixing the load

factor pertinent to design earthquake hazard. Note that, the scour load factor was identified as the ratio

15

of scour depth to be applied to the bridge to the scour depth corresponding to the design flood level

(which is the flood event with a return period of 100 years). As an early effort, Ghosn et al. (2003)

employed Ferry-Borges model to combine scour and earthquake effects for the calculation of bridge

reliability indices. In this study, a simple 2-D model was used for the structure and a basic force-based

limit state (column overtipping) was considered for reliability calculations. A series of assumptions

were made in regard to the time and intensity of scour and earthquake events to utilize load

combination models in reliability calculations. Some examples of such assumptions are – the intensity

of any extreme event was taken constant at its peak value for the time duration of the event, scour

depths were taken as independent from a year to another. A scour load factor of 0.25 combined with

an earthquake load factor of 1.0 was recommended to account for the combination of scour and

earthquake.

A reliability-based approach was also used by Alipour et al. (2013) for calibration of scour

load factors. However, the no-flood case was not considered in the calculation of the joint failure

probability of the bridge under combined scour and earthquake hazard. In this study, scour load-

modification factors of 1.42 and 1.12 were suggested for moderate and major damage states,

respectively. Nevertheless, these values can be considered to be unrealistic, since the use of suggested

factors for scour depth results in scour depths exceeding the design scour depth.

In both of the above studies (Ghosn et al. 2003 and Alipour et al. 2013), reliability indices

were computed by comparing the joint failure probability under the multi-hazard with an acceptable

target reliability index. Ghosn et al. (2003) derived the target reliability index from the past safe bridge

designs for seismic loading. On the other hand, Alipour et al. (2013) used a relatively high target

reliability index (e.g. 3.5) which was comparable to the one used in traffic loading combinations in

bridge designs. Hence, the final result of calibrated load factors significantly depends on target

reliability index.

Following a different methodology compared to two aforementioned previous studies on load

factor calibration, Wang et al. (2014b) presented a risk-based approach for derivation of scour load

16

factors. In this approach, scour is included in the seismic risk analysis such that the percentage of

maximum scour depth for which the seismic risk of the scoured bridge being equal to the joint risk of

the bridge under the combined earthquake and scour hazards is sought. An approach called “multi-

hazard convolution” was used for calculation of joint mean annual failure probability (MAFP). The

joint MAFP was obtained by convolving the fragility surface of the bridge with the two hazard curves

(earthquake and scour), similar to the method followed by Lee and Rosowsky (2006). The calculations

are based on the failure criteria of the ultimate limit state of bridge columns, which is governed by

ductility limit states. A scour load factor of 0.59 was suggested for a combined earthquake hazard with

a load factor of 1.0. In this study, derived load factors were concluded to be insensitive to the

discharge of the river and the (box-girder) bridge length, while being sensitive to the selection of the

scour modeling factor.

All these previous studies provided valuable information and insight to the multihazard

problem of bridges involving earthquake and flood; however, region specific hazard information is

lost in these studies. In addition, most of these studies considered scour to be a source of hazard

(Ghosn et al. 2003, Wang et al. 2012, Alipour et al. 2013, Liang and Lee 2013a,b, Wang et al.

2014a,b). Note that bridge scour is a consequence of flood hazard, and hence it does not necessarily

represent any load effect to a bridge. Therefore, region-specific analyses are required to accurately

predict the impact of regional flood events on bridge seismic behavior. This is indeed important as the

characteristics of a specified frequency flood event (such as a 100-year flood) may change from one

region to the other depending on various factors such as topology and annual rainfall. The same is

equally true for seismic hazard. Besides, bridges should be selected from different regions having

moderate to high seismic and flood hazards. Hence, this dissertation attempts to improve the current

knowledge-base by introducing a more accurate methodology and comprehensive analysis for

understanding the behavior of both real-life and generic bridges under this multi-hazard scenario.

17

2.4 Load and Resistance Factor Design in Seismic Design of Bridges

In bridge design practice, working stress and load factor designs have been replaced with load

and resistance factor (LRFD) design procedures in the last couple of years. Federal Highway

Administration (FHWA) and state Departments of Transportation (DOTs) are targeting to use LRFD

standards for all bridges designed after 2007 (AASHTO 2012). In California, LRFD specifications

with California amendments have been implemented to all new bridge designs since 2006 (Caltrans

2011).

With the advancement in knowledgebase on performance-based principles in seismic design

of bridges, general force-based seismic design procedures in the LRFD bridge design specifications

are complemented with displacement-based procedures that can lead to more efficient designs

satisfying performance objectives. American Association of State Highway and Transportation

Officials (AASHTO) recommends displacement capacity of the bridges which are designed in

accordance with LRFD specifications be checked using a displacement-based procedure (AASHTO

2012). Such procedures are already incorporated in the seismic design requirements of California

Department of Transportation (Caltrans) and South Carolina Department of Transportation (SCDOT)

(Caltrans 2013, SCDOT 2008). AASHTO published a guide a specification for LRFD seismic bridge

design (AASHTO 2011) which was developed based on the previously completed efforts (e.g.

NCHRP 12-49 guidelines, Caltrans Seismic Design Criteria and SCDOT specifications).

Performance goals defined for a performance-based design is composed of three elements:

importance of the structure, design hazard intensity, and the damage and functionality criteria.

Caltrans (2013) identified minimum seismic design requirements for ordinary bridges which are

expected to remain standing but may suffer significant damage requiring closure under the design

earthquake level. In this design methodology, minimum ductility capacity is sought for seismic-critical

members while all remaining members (i.e. bent cap beams, joints and superstructure) are designed to

remain elastic during a seismic event with a capacity protection philosophy. AASHTO (2011, 2012)

considers nearly the identical performance objectives as described by Caltrans (2013). The design

18

earthquake hazard level under which these performance objectives are required has a return period of

1000 years (7% probability of exceedance in 75 years).

Extreme events such as earthquakes, blast, collision, and ice loads are separately considered in

the load combinations of AASHTO (2012), as the joint probability of these events are stated to be

extremely low. For the extreme event load combination, a load factor of 1.0 is specified for earthquake

effects; while flood-induced scour is not affiliated with water loads in the same combination. In

addition, AASHTO requires that local pier scour and contraction scour depths should not be combined

with earthquake loads unless specific site conditions dictate otherwise, or alternatively one half of the

total scour may be considered in combination with earthquakes. However, any comprehensive

approach in regard to the multi-hazard interaction of flood-induced scour and earthquakes is not well

addressed. Thus, this shows the need for a sound and convenient approach for this multi-hazard to be

included in bridge design specifications in order to achieve effective and reliable bridge designs in the

future.

Unlike other regular loads (e.g. gravity, hydrostatic loads), scour is intrinsically not a load

effect; but it changes the conditions of the substructure and alter the consequences of other load effects

on a structure significantly (AASHTO 2012). Therefore, the use of analytical load combination

models (e.g. Turkstra’s rule, Ferry-Borges model, Wen’s load coincident method, or Monte Carlo

simulations) may not be applicable for combining scour and earthquake effects. Meanwhile,

converting scour effects with equivalent force effects for this purpose would be very indirect and

approximate. The objective here should be to achieve an approach which conform to the bridge design

practice, and adopt the modern seismic performance-based design principles. This motivates to derive

a method in which the multi-hazard effect can be applied to supplement seismic design procedures.

19

CHAPTER 3

PERFORMANCE OF TWO REAL-LIFE CALIFORNIA BRIDGES UNDER

REGIONAL SEISMIC AND FLOOD HAZARDS

With the objective of analyzing real-life bridges under the regional multi-hazard scenario, the

study chooses two bridges in California that are constructed at different times and located at different

regions. The multi-hazard performance of these two bridges is assessed by considering a flood event

followed by a seismic event. To capture wide ranges of these two hazards, various frequency flood

events and various levels of seismic hazard are considered based on regional hazard information

acquired for the bridge sites. The multi-hazard performance of these bridges is expressed in the form

of fragility curves and surfaces. While the fragility curves represent bridge vulnerability for specific

combinations of flood and seismic hazards, the same is expressed in fragility surfaces for all possible

combinations of these two natural hazards. The vulnerability information expressed in fragility curves

and surfaces are utilized to generate risk curves of these bridges. These risk curves provide annual

exceedance probabilities of various levels of bridge restoration cost for the specified multi-hazard

condition.

3.1 Study Bridges

The first bridge, henceforth referred to as Bridge-1, is located in Shasta County. This bridge is

on State Highway 44 and crosses the Sacramento River, the largest river in California. Built in 2010,

the bridge replaces an old bridge at this site. Schematic drawings and general geometric details of the

bridge are presented in Figure 3-1. The bridge has 4 spans with a total length of 231.2 m and is

founded on a soil medium comprised of primarily gravels with sand matrix. The entire structure

contains two individual bridges that provide simultaneous service to both directions of traffic. Bridge

superstructures are composed of prestressed concrete box-girders and connected with a monolithic

20

concrete closure pour at the middle. The bridge has seat-type abutments. Each column bent on either

side of the bridge superstructure is composed of two circular, 1.83 m-diameter circular reinforced

concrete piers monolithically connected with box girders at the top. All piers have equal cross-

sectional and material properties. At foundations, piers are extended below ground level; these

extended parts are referred to as pile shafts. Pile shafts have the same cross-sectional and material

properties as of the piers until a certain depth below which steel casings are used around pile shafts.

Diameter of pile shafts with steel casing is 2.44 m. According to the information from borehole data at

the bridge site, the extended pile shafts are surrounded by gravelly or gravelly-sandy soil deposits over

a firm rock layer at the bottom. Pile shafts are socketed into this rock layer at greater depths.

Figure 3-1: (a) Schematic view of Bridge-1, (b) cross-sections of bridge pier and pile shaft, and (c)

general elevation view of a typical bent

The second bridge, henceforth referred to as Bridge-2, is located in San Joaquin County. Built

in 1972, this bridge is on Interstate 5 and crosses San Joaquin River. Figure 3-2 provides schematic

Bent 2 Bent 3

50.68 50.68 231.2

64.92

Bent 4

Abut. 1 Abut. 5

64.92 #36 (D=36 mm)

25 bundles

D = 1.830

Clear cover = 75 mm

#25 (D=25 mm) hoops

CIDH Piles / Pier columns

25 mm steel casing

D = 2.440

Pile shaft with steel casing

total of 50

Center Line

3.44~4.35 3.44~4.35 3.44~4.35 3.44~4.35 3.43 4.875 4.875 4.88

2.6

0

1.401.40

0.15 0.15

1.40

0.2

65

0.2

5 1.00

0.2

65

0.15 0.15

1.40

2.6

0

Closure Pour

0.300.30

16.86~20.50 22.58

D = 1.83

2.44

H = H = H = H =

LEFT BRIDGE RIGHT BRIDGE139.000

131.120 130.870 128.870

Steel casing cutoff elev.

1.451

9.75

13.0010.51

Pile socket elev.

B2 B3 B4

142.050 142.100 142.710

B2 B3 B4

River bed

6.212 6.387 5.999

B2 B3 B4

6.397 6.598 6.238

B2 B3 B4

6.589 6.789 6.238

B2 B3 B4

6.335 6.536 6.176

B2 B3 B4

*All units are in meter unless otherwise stated

(a) (b)

(c)

21

drawings and general geometric details of the bridge. The bridge has 6 spans with a total length of

235.3 m. It has a reinforced concrete box-girder that is monolithically connected to wall-type piers.

Each pier is founded on a group of precast prestressed concrete piles with a reinforced concrete pile

cap. Details of these pile foundations are given in Figure 3-2. The soil medium underlying the bridge

foundation mainly consists of silty sands. The bridge has integral abutments on both sides and an in-

span hinge between Bent 3 and Bent 4. At the hinge, the bridge girder is separated by a 25.4 mm (1

inch) gap such that one side of the girder sits on elastomeric bearings placed on the other side of the

girder.

Figure 3-2: (a) Schematic view of Bridge-2, (b) general elevation view of a pier and (c) pier cross-

section

3.2 Regional Seismic and Flood Hazards

3.2.1 Regional Seismic Hazard

Identification of region specific seismic and flood hazard levels and selection of their critical

combinations are important because structural safety depends on maximum demands from multiple

4.5

7

2.337 2.337 2.337 2.337 2.337 2.337

10.262

S trans

1.067 1.067

0.203

2.2

96

0.3

05

0.1

78

16.154

0.1

4

0.1

62

0.9

14

R 0

.457

m

Hpile

H pier

Bent 3Bent 2Abut 1

H pier

Hpile

H river bed

S trans

3.658

8.814 14.935

14.041 14.660

Bent 6Bent 5Bent 4

8.534 12.116 6.172

9.803 15.757

Abut 7

15.889

H river bed

2.561 3.048 5.639

22.016 23.815

3.810

1.118 1.118 1.27 1.448 1.271.930 3.861

S long

Number of piles

(row X column) 1 X 9 3 X 10 3 X 10 3 X 9 3 X 8 3 X 9 1 X 5

1.219 1.219 1.219 1.219 1.219

Transverse spacing of piles

Longitudinal spacing of piles

#8 @ 0.30 m

#8 @ 0.30 m#4 @ 0.46 m

Additional #8 @ 0.60 m for Pier 2 & Pier 3

Additional #8 @ 0.30 m for Pier 6

At the top of columns:

D=0.381

c)

*All units are in meter unless otherwise stated

39.90 44.20 36.88 44.20 18.57

In-span hinge

44.20 235.3

7.32

Abut. 1

Pier 2 Pier 3 Pier 4

Pier 5

Pier 6

Abut. 7

(a)

(b) (c)

22

hazards. To pursue this study, regional seismic hazard is considered through – (i) seismic hazard

curves that provide information on regional seismicity and (ii) historic ground motion dataset that can

be used for time history analyses of bridges. Seismic hazard curves provide annual exceedance

probabilities of seismic events having various intensity levels. These curves are utilized for risk

evaluation of bridges as discussed later in this chapter. Generation of site specific seismic hazard

curves is beyond the scope of the present study. Hence, seismic hazard curves developed by the United

States Geological Survey (USGS) (USGS 2008b) are considered here. Figure 3-3 shows the seismic

hazard curves at locations of Bridge-1 and Bridge-2 for site-specific soil conditions. Peak ground

acceleration (PGA) is used here as the measure of seismic intensity, which is chosen due to easy

interpretation between seismic intensity and hazard level.

Figure 3-3: Seismic hazard curves at bridge sites

A large set of ground motions with varying hazard levels is desirable for seismic vulnerability

analysis of bridges. Selected ground motions should reflect seismic characteristic of the region of

interest and be compatible with local soil condition. For this purpose, corrected and filtered historic

ground motion time histories recorded in close proximity to the bridge sites are obtained from the Next

Generation Attenuation (NGA) database of the Pacific Earthquake Engineering Research Center

(PEER) (PEER 2015). Two separate sets of ground motions are developed for the two bridges. These

0.001 0.01 0.1 1 10PGA (g)

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

An

nu

al P

rob

abil

ity o

f E

xce

edan

ce

Bridge-1

Bridge-2

23

ground motion datasets constitute earthquakes recorded within 170 km radius from respective bridge

sites. Horizontal orthogonal components of these earthquakes are considered for time history analysis.

Note that relatively low seismic activity, compared to other parts of California, has been historically

recorded at both bridge sites. However, the possibility of occurring future strong earthquakes in these

locations cannot be ignored. Therefore, some of the ground motion records are scaled with a factor of

two such that performance of these bridges under strong ground motions can be observed. Thus, a

dataset containing 104 earthquake records is generated for Bridge-1 among which number of records

having PGA values 0.1-0.2g, 0.2-0.3g, 0.3-0.4g and > 0.4g are 62, 19, 15 and 8, respectively. For

Bridge-2, 160 ground motion records are utilized to form the dataset in which 64, 63, 24 and 9

recordings respectively fall into the abovementioned PGA ranges. Ground motions with PGA less than

0.1g are ignored from both datasets. Ground motion records used in time history analyses of Bridge-1

and Bridge-2 are listed in Appendix A.

3.2.2 Regional Flood Hazard

Flood hazard curves are generated to express regional flood hazards at bridge sites. These

curves provide peak flow discharges corresponding to flood events having various annual exceedance

probabilities. Flood hazard curve at bridge sites are developed through flood-frequency analysis as

explained in Chapter 2.3.1 by processing annual peak discharge data that are recorded at the nearest

stream gage stations to the bridge sites. The peak annual streamflow data considered for developing

flood hazard curves at Bridge-1 and Bridge-2 sites are presented in Appendix B. It is realized that due

to the complexity of river basins, flow discharges at bridge sites may not always be the same as these

are recorded at the nearest stream gage stations. However, having a stream gage installed exactly at a

bridge site is less probable in reality. For the present study, comprehensive river basin information for

Sacramento and San Joaquin rivers is obtained from flood insurance studies performed by the Federal

Emergency Management Agency (FEMA) at the bridge locations (FEMA 2009a, b). Obtained

information is utilized to corroborate the flood hazard curves developed for Bridge-1 and Bridge-2

sites.

24

Figure 3-4 shows mean (i.e., at 50% confidence level) flood hazard curves developed at

Bridge-1 and Bridge-2 locations. Flow data from the nearest stream gauge stations are also plotted in

the figure. FEMA flood insurance study of Shasta County (FEMA 2009a) mentioned that the Shasta

Dam located at the upstream of Bridge-1 (where data are recorded) controls up to 1% annual chance

flood (i.e. 100-years flood) with a maximum discharge of 2237 m3/s at the bridge site. Therefore, the

flood hazard curve of Bridge-1 has a maximum flow discharge of 2237 m3/s as shown in Figure 3-4.

FEMA flood insurance study for San Joaquin County (2009b) did not mention any such limitation of

flow discharge at the Bridge-2 site. Therefore, results obtained from flood-frequency analysis are

directly used for the mean flood hazard curve at the Bridge-2 site.

99.8 99 95 80 60 40 20 5 1Probability of Exceedance (%)

10

100

1000

10000

An

nu

al P

eak

Dis

char

ge

(m3/s

) Bridge-1

Recorded Data

Bridge-2

Recorded Data

Figure 3-4: Mean flood hazard curves at Bridge-1 and Bridge-2 sites

3.2.3 Flood-induced Scour at Bridge Foundations

In the present study, flood events with annual exceedance probabilities of 90%, 50%, 10%,

5%, 2%, and 1% (corresponding to 1.1-year, 2-year, 10-year, 20-year, 50-year and 100-year floods)

are studied for the multi-hazard risk evaluation of Bridge-1 and Bridge-2. As can be observed from

Figure 3-4, flood events with return periods more than 20 years have the same peak discharge as of the

20-year flood event at the site of Bridge-1. Therefore, the multi-hazard analyses with 50-year and 100-

year flood events are redundant for this bridge.

25

Scour depths at the bridge sites are estimated by using Equation 2-1, and the resulting values

at all bents are listed in Table 3-1. This table shows that scour depths for Bridge-2 do not reach the

pile cap at any pier location. It is important to note here that the values presented in Table 3-1 are

reasonable estimates of scour. In case when an exact magnitude of scour is needed, a comprehensive

calculation of scour through detailed hydraulic analysis is warranted. Such a detailed hydraulic

analysis is beyond the scope of the present study.

Table 3-1: Estimated maximum scour depths at foundations of Bridge-1 and Bridge-2

Bridge-1

Flood return period 1.1-year 2-year 10-year

≥ 20-

yeara

Q (m3/s) 318.5 804.6 1963.3 2237

Scour

Depth

ys (m)

Bent 2 1.85 2.47 3.16 3.28

Bent 3 1.83 2.46 3.16 3.27

Bent 4 1.28 2.33 3.08 3.20

Bridge-2

Flood return period 1.1-year 2-year 10-year 20-year 50-year 100-year

Q (m3/s) 90.2 322.0 1121.4 1589.9 2349.6 3044.1

Scour

Depth

ys (m)

Pier 2b 0.00 0.00 1.92 2.13 2.37 2.53

Pier 3 1.32 1.74 2.21 2.38 2.58 2.73

Pier 4 1.37 1.78 2.24 2.40 2.61 2.75 aflood events with return period equal to or more than 20 years have the same peak discharge bthe pier is not under water for no flood, 1.1-year flood and 2-year flood conditions

3.3 Finite Element Analyses of Bridges

3.3.1 Bridge Modeling

The generation of fragility curves for the bridges requires a large number of numerical

simulations of the bridges subjected to various combined seismic and flood hazard levels. The

simulations of the bridges are performed with the finite element (FE) analysis platform OpenSees

(McKenna and Fenves 2012). The three dimensional FE models of the bridges include some realistic

assumptions and idealizations as described below. The details of analytical modeling of bridge

components in FE analyses are presented in Appendix C.

Superstructure:

For performance-based seismic analysis of bridges, the use of single-beam stick model is a

reasonable assumption for modeling bridge girders as these components are generally expected to

26

remain elastic during seismic excitations. Likewise, the present study uses linear elastic beam

elements to represent bridge girders. These elements are assumed to run along center lines of

respective girders such that equivalent stiffness and mass properties calculated about centroid of

girders can be lumped on them. As per Caltrans (2013) recommendations, an effective flexural rigidity

equal to the average of 0.5-0.75 times the gross stiffness is used for reinforced concrete box girder

sections of Bridge-2. For the prestressed concrete box girder sections of Bridge-1, no stiffness

reduction is applied. The closure pour connecting two girders in Bridge-1 is modeled with a series of

linear elastic beam elements.

Bridge piers:

Displacement-based fiber elements in OpenSees are used to model circular reinforced concrete

extended shafts of Bridge-1 and reinforced concrete wall-type piers of Bridge-2. As recommended by

Caltrans (2013), the material model for concrete proposed by Mander et al. (1988) is considered for

the stress-strain relations of both unconfined and confined concrete sections. In OpenSees, Concrete07

and Steel02 materials are assigned to define material models of concrete and reinforcing steel,

respectively. The wall-type piers in Bridge-2 was not confined enough (as can be seen from Figure 3-

2), which made the confined concrete properties in these piers nearly equal to the unconfined concrete

properties.

To validate the modeling of bridge piers in OpenSees, the same modeling approach is used for

a number of reinforced concrete columns that were experimentally tested in past. The lateral load-

displacement responses of these columns obtained from OpenSees are observed to be well in

accordance with that acquired from past experiments (as detailed in Appendix C.1). Hence, the

element formulation employed for piers is sufficient for use in nonlinear modeling of the bridges.

Foundations:

At foundations, interaction between foundations and surrounding soil is represented through a

series of soil springs placed at various depths along the length of foundation elements. These soil

springs are basically zero-length elements that characterize the nonlinear soil resistances developed

27

due to the movement of bridge foundations in three translational directions. For both bridges,

nonlinear soil resistances in two horizontal directions are modeled with conventional p-y springs. For

Bridge-2, shaft resistance (along pile length) is modeled with t-z springs. For the modeling of soil

springs, pySimple1 and tzSimple1 materials from OpenSees library are utilized. At various depths, p-y

relations are calculated following the recommendations of the American Petroleum Institute (2003),

whereas Mosher’s (1984) relation is utilized to calculate t-z relations. Full fixity conditions are

considered at pile bottoms for both bridges. Pile shafts with steel casing of Bridge-1 and prestressed

concrete piles of Bridge-2 are modeled with linear elastic beam-column elements as they are expected

to stay elastic during seismic excitations.

Abutments:

Modeling of bridge abutments differs from Bridge-1 to Bridge-2. The key components for the

modeling of seat-type abutments of Bridge-1 are bearings, shear keys, and abutment response in the

longitudinal and transverse directions, while the same for integral abutments of Bridge-2 are abutment

piles and abutment response in the longitudinal and transverse directions. Figure 3-5 shows schematic

abutment models of Bridge-1 and Bridge-2. The current subsection mostly discusses abutment

response in the longitudinal and transverse directions, leaving the bearing and shear keys of Bridge-1

for the following two subsections.

In the longitudinal direction of Bridge-1, the assembly of backwall-backfill interaction and the

gap between bridge girder and abutment backwall is modeled in OpenSees with elastic-perfectly

plastic gap elements. During seismic excitations, passive resistance arises from the backwall-backfill

interaction when bridge girder pushes on backwall after the gap is completely closed. This resistance

is represented with an elastic-perfectly plastic backbone curve as suggested by Caltrans (2013), and

recommended passive resistance capacity is increased by 50% in order to account for dynamic loading

conditions. The same modeling technique, except for a gap in element definition, is used for the

backwall-backfill interaction at abutment in the longitudinal direction of Bridge-2. For this bridge,

abutment piles take an active role with the movement of integrated bridge girder-abutment system

28

(due to integral abutments) during seismic excitations. These abutment piles are modeled in the similar

way as of foundation piles. In the transverse direction, abutments of both bridges are modeled as

recommended by Aviram et al. (2008).

Bearings in Bridge-1:

PTFE/elastomeric bearings are used at both abutments of Bridge-1. These bearings are

generally designed for thermal expansion as they can accommodate horizontal translations (due to low

friction provided at the interface of PTFE disks and stainless steel surface) and rotations (by the

elastomeric bearing pad at the bottom of PTFE disks) (Konstantinidis et al. 2008). To capture the

complex nature of this bearing, two linear and two nonlinear elements are introduced. Linear elements

are employed to account for vertical deformation and rotation of the bridge girder about global

transverse axis of the bridge. In two horizontal directions, nonlinear elements with elastic-perfectly

plastic hysteretic backbone curves are assigned to model lateral seismic responses. These backbone

curves are characterized with initial stiffness and yield force that are equal to, respectively, the shear

stiffness of elastomeric bearing pad and the friction force developing at the PTFE-stainless steel

interface. Bearing properties in each horizontal direction of the bridge are considered to be the same.

Typical design values of shear modulus of elastomer and friction coefficient at the PTFE-stainless

steel interface are taken as G=107.5 psi and μ=0.06, respectively (Caltrans 2000, 1994). Such

modeling of PTFE/elastomeric bearings is validated by comparing numerical load-deformation

response of a PTFE/elastomeric bearing with that obtained from an experimental study performed by

Konstantinidis et al. (2008). This comparison confirmed the use of abovementioned backbone curves

for a realistic modeling of PTFE/elastomeric bearing in large structures (like Bridge-1) with several

nonlinear components.

Shear keys in Bridge-1

Exterior shear keys are provided only in the transverse direction of Bridge-1 abutments.

According to the geometric and material properties of these shear keys, they are expected to fail in a

combined shear-flexure mode instead of a pure shear mode. This failure mode follows the

29

observations made from an experimental study on similar exterior shear keys (Bozorgzadeh et al.

2007). In OpenSees, these elements are characterized with nonlinear force-deformation relation on the

basis of hysteretic model proposed by Megally et al. (2002).

In-span hinge in Bridge-2

Modeling of the in-span hinge in Bridge-2 includes longitudinal response of elastomeric

bearings and pounding of adjacent bridge decks. Linear elastic-perfectly plastic elements are used to

model longitudinal response of elastomeric bearings. Initial stiffness of this element is represented by

the shear stiffness of elastomer and its force capacity is taken to be equal to the frictional resistance

developed between the concrete surface and elastomer. The interface friction coefficient is taken as

0.40 (Caltrans 2013). Pounding between adjacent bridge decks is modeled with zero-length elements

having bilinear hysteretic backbone curves and a gap representing the physical gap between adjacent

bridge decks at the hinge location. The properties of this backbone curve are obtained from

Muthukumar (2003). This backbone curve approximates the total energy lost due to pounding of two

adjacent bridge decks during seismic excitations.

Figure 3-5: Abutment modeling of (a) Bridge-1 (b) Bridge-2

3.3.2 Modal Analysis of Bridges

Modal analyses of bridges in the presence and absence of flood-induced scour are performed

prior to nonlinear time-history analyses. Figure 3-6 and 3-7 depict the first four fundamental modes

(and related modal periods) of Bridge-1 and Bridge-2, respectively at their original states (i.e. without

scour). Table 3-2 lists the fundamental modal periods of these bridges at all flood levels. As can be

1. Bearing element in transverse direction

2. Shear key element

3. Abutment spring in transverse direction

4. Abutment back wall

element with a gap property

5. Bearing element in

longitudinal direction 6. Full restraint except free

movement in transverse

direction

1 2

3

4

5 i j

6

Bridge

girder

Abutment rigid link Girder rigid link

TOP VIEW

1. Abutment spring in

transverse direction 2. Abutment back wall

element in longitudinal

direction 3. Abutment pile (soil

springs not shown)

3D VIEW

Bridge girder 1

3

2

(a) (b)

30

seen from this table, modal periods of Bridge-1 in the longitudinal and transverse directions increase

with the increase in scour depth up to that resulted from a 10-year flood event. For Bridge-2, the

change in fundamental modal period is small compared to that for Bridge-1, and no change is

observed beyond 20-year flood event.

Figure 3-6: Fundamental mode shapes of Bridge-1

Figure 3-7: Fundamental mode shapes of Bridge-2

Longitudinal: T1=0.66 sec. Transverse: T2=0.54 sec.

Vertical: T3=0.54 sec. Torsional: T

4=0.46 sec.

Longitudinal-1: T1=0.72 sec. Longitudinal-2: T2=0.67 sec.

Transverse: T3=0.44 sec. Vertical: T

4=0.42 sec.

31

Table 3-2: Modal periods of Bridge-1 and Bridge-2

Bridge-1

No

Flood

1.1-yr

flood

2-yr

flood

10-yr

flood

≥ 20-yr

flood

Maximum pier scour - 1.85 m 2.47 m 3.16 m 3.28 m

Longitudinal mode (sec) 0.66 0.72 0.74 0.77 0.77

Transverse mode (sec) 0.54 0.58 0.60 0.62 0.62

Vertical mode (sec) 0.54 0.54 0.54 0.55 0.55

Torsional mode (sec) 0.46 0.48 0.48 0.49 0.49

Bridge-2

No

Flood

1.1-yr

flood

2-yr

flood

10-yr

flood

20-yr

flood

50-yr

flood

100-yr

flood

Maximum pier scour - 1.37 m 1.78 m 2.24 m 2.40 m 2.61 m 2.75 m

1st longitudinal mode (sec) 0.72 0.72 0.72 0.72 0.73 0.73 0.73

2nd longitudinal mode (sec) 0.67 0.67 0.67 0.68 0.68 0.68 0.68

Transverse mode (sec) 0.44 0.45 0.46 0.46 0.47 0.47 0.47

Vertical mode (sec) 0.42 0.42 0.42 0.42 0.42 0.42 0.42

3.4 Fragility Curves and Surfaces

3.4.1 Time History Analyses of Bridges

Nonlinear time history analyses of Bridge-1 and Bridge-2 are performed under the ground

motions selected for respective bridge site. Responses of potentially critical bridge components (such

as piers, abutments, bearings and shear keys) are recorded for each of the analysis. To exemplify,

response time histories of Bridge-1 and Bride-2 at pier tops are shown in Figure 3-8. For Bridge-1,

transverse displacement at the top of a pier (left bridge, left column) in Bent 3 under the ground

motion NGA0008 (1941 Northern California Earthquake, scaled with 2.0) is plotted in Figure 3-8(a).

Figure 3-8(b) shows longitudinal displacement at the top of Pier 2 of Bridge-2 under the ground

motion NGA0790 (1989 Loma Prieta Earthquake, scaled with 2.0). Only a portion of response time

histories are displayed in this figure for a close observation on bridge seismic responses at different

flood conditions. As it shows, a slight change in pier top displacement is observed for Bridge-1 with

increasing flood hazard level, while no such change is found for Bridge-2. Note that the responses

plotted here are for two specific earthquakes and at two specific locations of the bridges. For both

bridges, pier top displacement is not the only factor controlling seismic damage of these bridges. The

fragility analysis presented later in the paper provides a comprehensive overview of bridge responses

32

at different bridge components and for all the ground motions considered for analyzing the two

bridges.

5 6 7 8 9 10 11 12 13 14 15Time (sec)

-60

-40

-20

0

20

40

60

Pie

r T

op D

ispla

cem

ent

(mm

)

No flood

1.1-yr flood

2-yr flood

10-yr flood

20-yr flood

10 11 12 13 14 15 16 17 18 19 20

Time (sec)

-40

-20

0

20

40

60

80

Pie

r T

op D

ispla

cem

ent

(mm

)

No flood

1.1-yr flood

2-yr flood

10-yr flood

20-yr flood

50-yr flood

100-yr flood

(a) (b)

Figure 3-8: Sample pier top horizontal displacement histories for (a) Bridge-1, (b) Bridge-2

3.4.2 Component-Level Damage States

Obtained results from time history analyses are processed to generate fragility curves of

Bridge-1 and Bridge-2 at component and system levels. Component-level fragility curves characterize

performance of various bridge components (such as piers) at different damage states, whereas the

same at the system level indicate the overall performance of the bridge. Bridge damage states at

component levels are decided by comparing structural response of those components with pre-defined

threshold limits (as obtained from literature and detailed later) that signify intermediate and ultimate

limit states (such as minor damage, moderate damage, major damage and collapse; HAZUS (2013)) of

those components. While developing system-level fragility curves of bridges, it is desirable that

damage states of different bridge components be allied to global performance of bridges (such as fully

operational, operational, life safety, and collapse; FHWA (2006)) such that component- and system-

level damage states complement each other.

In this study, component-level fragility curves are generated for bridge components which

have relatively high damage potential and may lead to moderate to major damage of bridges (if not

collapse) under the multi-hazard condition. Such components are identified as piers, abutments, shear

33

keys and abutment bearings for Bridge-1 and piers, abutments and bearings at in-span hinges for

Bridge-2. For the components having direct effect on vertical stability and load carrying capacity of a

bridge, a full range of damage states are addressed including major damage and complete collapse that

may result in closure of the bridge from traffic. On the other hand, the components which do not

directly affect the vertical stability of the bridge, their lower damage states (such as minor and

moderate damage) are only considered. Threshold limits of various component damage states are

obtained from previous studies and summarized in Tables 3-3 and 3-4 for Bridge-1 and Bridge-2,

respectively.

Bridge piers may have two major seismic failure modes, flexural and shear. For both bridges,

no shear failure is observed for any of the selected ground motions. Hence, damage of bridge piers

under the multi-hazard scenario is evaluated based on flexural response of piers. Curvature ductility μφ

is used as the engineering demand parameter (EDP) for the assessment of flexural damage of bridge

piers, since it is independent of any length parameter, and the capacity of a pier can be quantified

solely according to its sectional properties under a certain axial load. Threshold limits of curvature

ductility are taken from Ramanathan (2012). This literature defined these threshold limits on the basis

of a comprehensive review of lateral load tests of reinforced concrete bridge piers and by categorizing

test results according to pre-1971 brittle piers, 1971-1990 strength degrading piers and post-1990

ductile piers. Accordingly, the threshold limits of curvature ductility of piers of Bridge-1 and Bridge-2

are obtained for minor, moderate, major damage and collapse states and presented in Table 3-3 and 3-

4.

Seismic damage at bridge abutments can be initiated from three different abutment

deformations: longitudinal deformation in the passive direction (Δlong,p) and in the active direction

(Δlong,a) and deformation in the transverse direction (Δtrans). For Bridge-1, abutment damage in the

longitudinal direction is identified only due to its passive deformation (Δlong,p) as deformation in the

active direction is ignored in the model definition due to the nature of this abutment. Threshold limit

of Δlong,p at minor damage state is taken as the yield displacement of the backwall-backfill interaction

34

curve. At moderate damage, threshold limit of Δlong,p is taken to be the maximum displacement which

is 5% of the backwall height for granular backfills (Shamsabadi et al. 2007). Similar to Δlong,p,

threshold limit of Δtrans at minor damage state is taken as the yield displacement of the backbone curve

in the transverse direction. However, abutment deformations in the transverse direction are found to be

within elastic range (i.e., lower than the minor damage threshold limit) for both bridges under all

ground motions. In addition to Δlong,p, abutment damage of Bridge-2 is identified in terms of Δlong,a. In

this case, threshold limits for minor and moderate damage states are directly taken from Ramanathan

(2012).

Seismic damage of shear keys in Bridge-1 is assessed with respect to transverse deformation

of shear key elements (Δsk). Threshold limits of Δsk at minor, moderate and major damage states are

determined from the element load-deformation curve. Performance levels such as the onset of

yielding of shear key reinforcement and yielding of all rebars crossing the crack zone are identified in

order to define these damage states.

Seismic damage of PTFE-elastomeric bearings in Bridge-1 is assessed based on horizontal

deformation of bearing elements (Δb). Beyond yielding, threshold limit of Δb at minor damage state is

set to 40 mm considering that damage in this component does not necessarily begin to occur right after

the bridge deck starts to slide. On the other extreme, collapse state of this bearing is defined with the

deformation for which bridge deck falls off from the bearing. In between minor damage and collapse,

two intermediate damage states (moderate and major) are assumed to be evenly distributed. Threshold

limits of Δb for moderate and major damage are decided based on the experimental results obtained by

Konstantinidis et al. (2008) on PTFE-elastomeric bearings under seismic loading, in which gradual

deformation of PTFE bearing pads was observed until excessive shedding. These threshold values are

listed in Table 3-3. For bearing deformation in the transverse direction, only minor and moderate

damage threshold limits are specified with the same values adopted for bearing deformation in the

longitudinal direction.

35

Seismic damage of elastomeric bearings at the in-span hinge of Bridge-2 is evaluated based on

their horizontal longitudinal deformation (Δb,long). Threshold limits at moderate damage and collapse

state correspond to the longitudinal deformation when sliding starts at concrete-elastomer interface

and bridge deck falls off from the bearings, respectively. Threshold limit at major damage is taken as

the average of that for moderate damage and collapse state.

Table 3-3: Damage threshold limits for Bridge-1

Component EDP Minor Moderate Major Collapse

Piers Curvature

ductility 0.40.1 0.80.4 0.120.8 0.12

Abutment

Long. def. in

passive direction

(mm)

9632 , plong plong,96 - -

Trans. def. 26087 , plong plong,260 - -

Shear key Trans. def. (mm) 20117 sk 422201 sk sk422 -

PTFE-

elastomeric

bearing

Long. def. (mm) 21340 , longb 387213 , longb 560387 , longb longb,560

Trans. def.(mm) 21340 , transb transb,213 - -

Table 3-4: Damage threshold limits for Bridge-2

Component EDP Minor Moderate Major Collapse

Piers Curvature ductility 0.20.1 5.30.2 0.55.3 0.5

Abutment

Long. def. in

passive direction

(mm)

17057 , plong plong,170 - -

Long. def. in active

direction (mm) 10238 , along along,102 - -

Elastomeric

bearing Long. def. (mm) 8830 , longb 28288 , longb 335282 , longb longb,335

3.4.3 Component-Level Fragility Curves

A seismic fragility curve can be defined with a two-parameter log-normal distribution

(Shinozuka et al. 2000):

ln

( ; , )j k

j k k

k

x cF x c

(3-1)

36

where the fragility function F() represents the failure probability of a bridge component at damage

state k (such as minor, moderate, major and collapse state) under a ground motion j with PGA xj.

Fragility parameters, 𝑐𝑘 and ζ𝑘, refer to median and log-normal standard deviation at damage state k,

respectively. In the current study, fragility parameters are estimated by using the method of maximum

likelihood, in which the likelihood function L is expressed as

1

1

; , 1 ; ,j j

N r r

j k k j k k

j

L F x c F x c

(3-2)

in which rj expresses the damage condition of the bridge component at damage state k under PGA xj. It

takes value equal to 1 or 0 depending on whether or not component damage state k is exceeded for xj.

The log-standard deviation indicates the scatterness (or, dispersion) of data. A single dispersion value

of ζk = 0.6 is adopted from HAZUS (2013) for all damage states in order to prevent the intersection of

any two fragility curves. Hence, the change in median value provides the measure for the variation in

bridge fragility characteristics due to varied loading condition.

Figure 3-9 shows seismic fragility curves of key nonlinear components of Bridge-1 at various

flood-hazard levels. Median values of all fragility curves are given in these figures. As the same log-

standard deviation value is used for all fragility curves, these curves can be compared in terms of their

median values. Lower median value signifies higher seismic vulnerability. As the figure indicates,

bridge piers are the only component that can lead to major damage and complete collapse of the bridge

under the multi-hazard scenario. However, the seismic vulnerability of this component is found to be

least sensitive to the flood hazard, except for that at the minor damage state. This is because,

displacement and rotation at the top and at the foundation level of piers increase simultaneously in the

presence of scour at foundations. Due to such simultaneous increase, the resultant displacement and

rotation of bridge piers between two ends do not change enough to cause notable variation in pier

flexural damage and its seismic vulnerability with increasing scour depth. Among other bridge

components, the change in seismic vulnerability with scour depth is observed only for bridge bearings

(in the longitudinal direction) at the minor damage state. This is due to increased longitudinal

37

displacement at the superstructure level. Overall, the result presented in Figure 3-9 indicates that

regional flood hazard does not impose any significant threat to seismic vulnerability of bridge

components, particularly at higher damage levels. This is a reasonable outcome for a newly

constructed bridge with ductile piers and large diameter pile shafts socketed into rock layers.

0.0 0.2 0.4 0.6 0.8 1.0 1.2PGA (g)

0.0

0.2

0.4

0.6

0.8

1.0

Pro

bab

ilit

y o

f E

xce

edin

g a

Dam

age

Sta

te Minor Damage

Moderate Damagecmod. = 0.688

Major Damage &Collapse Statecmaj.= ccol. = 0.815

No fl.

1.1-yr

2-yr

10-yr

20-yr

cmin.

0.409

0.364

0.364

0.364

0.364

0.0 0.2 0.4 0.6 0.8 1.0 1.2

PGA (g)

0.0

0.2

0.4

0.6

0.8

1.0

Pro

bab

ilit

y o

f E

xce

edin

g a

Dam

age

Sta

te

No flood

1.1-yr flood

2-yr flood

10-yr flood

20-yr flood

0.0 0.2 0.4 0.6 0.8 1.0 1.2PGA (g)

0.0

0.2

0.4

0.6

0.8

1.0

Pro

bab

ilit

y o

f E

xce

edin

g a

Dam

age

Sta

te

Minor Damage

cmin. = 0.741

Moderate Damage

cmod. = 0.894

(a) (b)

0.0 0.2 0.4 0.6 0.8 1.0 1.2PGA (g)

0.0

0.2

0.4

0.6

0.8

1.0

Pro

bab

ilit

y o

f E

xce

edin

g a

Dam

age

Sta

te

No flood

1.1-yr flood

2-yr flood

10-yr flood

20-yr flood

Minor Damage

Moderate Damage

cmod. = 1.935

cmin.

0.451

0.423

0.395

0.384

0.384

0.0 0.2 0.4 0.6 0.8 1.0 1.2

PGA (g)

0.0

0.2

0.4

0.6

0.8

1.0

Pro

bab

ilit

y o

f E

xce

edin

g a

Dam

age

Sta

te

No flood

1.1-yr flood

2-yr flood

10-yr flood

20-yr flood

Minor damage due toshear key deformation

cmin. = 0.815

Minor damage due tobearing transverse deformation

cmin. = 1.035

(c) (d)

Figure 3-9: Component-level fragility curves of Bridge-1; (a) pier flexural damage, (b) abutment

passive deformation, (c) bearing longitudinal deformation, and (d) shear key and bearing transverse

deformations

Seismic fragility curves developed for critical components of Bridge-2 are shown in Figure 3-

10. This figure suggests that piers are the only component of Bridge-2 that may lead to major damage

and collapse of the bridge under seismic excitations in the presence and absence of scour. Significant

changes in seismic fragility of this component are observed at major damage and collapse states with

the increase in flood hazard level. This is because the exposed height of bridge piers increases with

scour depth (“H river bed” decreases; Figure 3-2) making bridge piers more vulnerable under seismic

38

ground motions. For all other cases including minor and moderate damage of bridge piers, slight to no

change in seismic vulnerability is observed with increasing flood hazard level.

MinorDamage

ModerateDamage

MajorDamage

0.0 0.2 0.4 0.6 0.8 1.0 1.2PGA (g)

0.0

0.2

0.4

0.6

0.8

1.0

Pro

bab

ilit

y o

f E

xce

edin

g a

Dam

age

Sta

te

No fl.

1.1-yr

2-yr

10-yr

20-yr

50-yr

100-yr

cmin. cmod. cmaj.

0.230 0.407 0.684

0.224 0.407 0.659

0.224 0.407 0.659

0.222 0.359 0.599

0.222 0.359 0.566

0.222 0.359 0.566

0.222 0.354 0.525

0.0 0.2 0.4 0.6 0.8 1.0 1.2

PGA (g)

0.0

0.2

0.4

0.6

0.8

1.0

Pro

bab

ilit

y o

f E

xce

edin

g a

Dam

age

Sta

te

No flood

1.1-yr flood

2-yr flood

10-yr flood

20-yr flood

50-yr flood

100-yr flood

ccol.

0.842

0.748

0.720

0.689

0.689

0.634

0.634

(a) (b)

cmin. cmod.

0.204 1.081

0.204 1.081

0.202 1.081

0.197 1.081

0.192 0.980

0.192 0.980

0.192 0.980

No fl.

1.1-yr

2-yr

10-yr

20-yr

50-yr

100-yr

Minor Damage

Moderate Damage

0.0 0.2 0.4 0.6 0.8 1.0 1.2PGA (g)

0.0

0.2

0.4

0.6

0.8

1.0

Pro

bab

ilit

y o

f E

xce

edin

g a

Dam

age

Sta

te

No flood

1.1-yr flood

2-yr flood

10-yr flood

20-yr flood

50-yr flood

100-yr flood

Minor damage due tobearing deformation

cmin. = 1.087

Minor damage due toabutment passive deformation

cmin. = 1.245

0.0 0.2 0.4 0.6 0.8 1.0 1.2PGA (g)

0.0

0.2

0.4

0.6

0.8

1.0

Pro

bab

ilit

y o

f E

xce

edin

g a

Dam

age

Sta

te

(c) (d)

Figure 3-10: Component-level fragility curves of Bridge-2; (a) pier flexural damage at minor,

moderate and major damage states, (b) pier flexural damage at collapse state, (c) abutment active

deformation, (d) abutment passive deformation and bearing longitudinal deformation

3.4.4 System-Level Fragility Curves

As previously mentioned in Chapter 3.4.2, damage state criteria of critical bridge components

are described such that global damage states for the bridges can be defined in a consistent manner.

Hence, system-level damage state of a bridge under a particular ground motion and flood scenario is

determined by taking the worst damage among all critical bridge components. Progressive collapse is

not taken into account for the cases when collapse state is obtained at a bridge component. Fragility

parameters of the system-level fragility curves are estimated by using the method of maximum

likelihood, similar to the procedure described in Chapter 3.4.3.

39

System-level fragility curves of Bridge-1 and Bridge-2 are presented in Figure 3-11. For both

of the bridges, moderate damage, major damage and collapse states are controlled by the damage in

bridge piers. Therefore, no change in bridge seismic fragility with increasing flood hazard level is

observed for Bridge-1 at these damage states, whereas the change is significantly large at major

damage and collapse states for Bridge-2. At various flood hazard levels, minor damage state of

Bridge-1 is jointly governed by bearing response in the longitudinal direction and response of bridge

piers. For Bridge-2, abutment active deformation primarily governs this damage state. Accordingly,

variations in fragility curves are observed with increasing flood hazard level.

0.0 0.2 0.4 0.6 0.8 1.0 1.2PGA (g)

0.0

0.2

0.4

0.6

0.8

1.0

Pro

bab

ilit

y o

f E

xce

edin

g a

Dam

age

Sta

te

Minor Damage

Moderate Damage

cmod. = 0.688

Major Damage &Collapse State

cmaj. = ccol. = 0.815

No fl.

1.1-yr

2-yr

10-yr

20-yr

cmin.

0.409

0.364

0.354

0.345

0.345

MinorDamage

ModerateDamage

Major Damage

CollapseState

0.0 0.2 0.4 0.6 0.8 1.0 1.2PGA (g)

0.0

0.2

0.4

0.6

0.8

1.0

Pro

bab

ilit

y o

f E

xce

edin

g a

Dam

age

Sta

te

No fl.

1.1-yr fl.

2-yr fl.

10-yr fl.

20-yr fl.

50-yr fl.

100-yr fl.

(a) (b)

Figure 3-11: System-level fragility curves of (a) Bridge-1 and (b) Bridge-2

3.4.5 Fragility Surfaces

Fragility surfaces provide a comprehensive visualization of the combined effect of earthquake

and flood hazards on bridge failure probabilities at various damage levels. In these, hazard intensities

are generally plotted along two horizontal axes, and the surface denotes the exceedance probability of

a bridge damage state. A number of studies have been performed in the past to develop fragility

surfaces considering two intensity measures from the same natural hazard (like earthquake), though a

very little effort is made to generate fragility surfaces demonstrating the combined effect of more than

one natural hazards (e.g. Wang et al. 2014a, Lee and Rosowsky 2006). To develop fragility surface,

the present study considers peak annual flow discharge as the flood hazard intensity measure and PGA

as the earthquake hazard intensity measure. These intensity measures are considered to be two

40

statistically independent random variables and their joint cumulative probability distribution provides

the failure probability of the bridge under the multi-hazard scenario. A bivariate lognormal distribution

is used to define the joint probability density. Hence, the fragility surface is defined here as follows:

2 1

1 2 1, 2, 1, 2, 1 2 1, 2, 1, 2, 1 2

0 0

( , ; , , , ) , ; , , ,

x x

k k k k k k k kF x x c c f x x c c dx dx (3-3)

Here x1 and x2 represent samples from random variables representing PGA and annual peak

flow discharge, respectively; c1,k and c2,k are corresponding median values at damage state k and 1,k

2,k are log-standard deviations. The probability density function f (..) of the bivariate lognormal

distribution can be defined in the following equations.

1 2 1, 2, 1, 2,

1 2 1, 2,

1, ; , , , exp

2 2k k k k

k k

qf x x c c

x x

(3-4)

2 2

1 1, 2 2,

1, 2,

ln lnk k

k k

x c x cq

(3-5)

Similar to fragility curves, distribution parameters for fragility surfaces can be calculated

through the maximum likelihood method. Log-standard deviation for seismic hazard ζ1,k is taken to be

equal to 0.6 in order to keep consistency between fragility curves and surfaces. The likelihood

function is give as

1

1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2,

1

, ; , , , 1 , ; , , ,j j

N r r

j j k k k k j j k k k k

j

L F x x c c F x x c c

(3-6)

where j is a multi-hazard case involving earthquake and flood hazards, rj =1 or 0 depending on

whether or not a damage state k is exceeded for a ground motion with PGA = x1,j and flood event with

annual peak flow discharge = x2,j. N represents the total number of multi-hazard cases. Figure 3-12

shows the fragility surfaces of Bridge-1 and Bridge-2 developed based on system-level bridge damage

data, and corresponding fragility parameters are listed in the attached table. As the figure shows,

fragility surface for Bridge-1 is developed only at minor damage state (Figure 3-12(a)). For other three

41

damage states of the bridge, median values of fragility curves showed no variation with increasing

flood hazard level (Figure 3-11). Hence, fragility surfaces of the bridge at these three damage states

would be linear extensions of respective fragility curves along the axis presenting flood hazard

intensity. For Bridge-2, however, fragility surfaces are developed for all four damage states.

At minor damage of both bridges and moderate damage of Bridge-2, median values of peak

flow discharge are calculated to be very small which indicate insignificant impact of flood hazard on

the multi-hazard performance of these bridges at these damage states. The same is also evident from

fragility curves of these bridges developed at the same damage states which show slight changes in

bridge fragility characteristics with increasing flood hazard level (Figure 3-11). Fragility surfaces at

major damage and collapse state of Bridge-2 demonstrates the significance of flood hazard on bridge

multi-hazard performance, which is also recognized from fragility curves of the bridge at these higher

damage states.

3.5 Risk Evaluation

A risk-based framework is utilized to predict the negative consequences from future

occurrences of the aforementioned multi-hazard event in California. For the two California bridges,

expected risk due to regional hazards is expressed in the form of risk curves. On a risk curve, annual

exceedance probabilities of various levels of performance degradation can be identified. In general,

post-event consequences of bridge damage are represented with socio-economic losses arising from

various sources such as post-event bridge restoration, traffic delay, network downtime and loss of

opportunity. Among these, the post-event bridge restoration cost is considered in the present risk

assessment framework as it is the direct consequence from bridge damage under regional multi-

hazard. Bridge owners are concerned for this loss utmost. Seismic hazard at bridge sites is required to

be known for risk evaluation of the bridges. Seismic hazard curves identify the annual exceedance

probabilities of a range of seismic events at the bridge site.

42

Damage

State c1,k c2,k ζ2,k

Bridge-1 Minor

damage 0.410 0.0247 1.18

Bridge-2

Minor

damage 0.194 0.014 0.70

Moderate damage

0.424 0.143 4.83

Major

damage 0.722 4.987 6.40

Collapse state

0.865 10.309 3.90

(a) Bridge-1, minor damage

(b) Bridge-2, minor damage (c) Bridge-2, moderate damage

(d) Bridge-2, major damage (e) Bridge-2, collapse state

Figure 3-12: Fragility surfaces of Bridge-1 and Bridge-2

00.2

0.40.6

0.81

1.2

50

500

1000

1500

2000

0

0.2

0.4

0.6

0.8

PGA(g)Discharge (m3/s)

Pro

babili

ty o

f E

xceedance

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

00.2

0.40.6

0.81

1.2

50500

10001500

20002500

3000

0

0.2

0.4

0.6

0.8

PGA(g)Discharge (m3/s)

Pro

babili

ty o

f E

xceedance

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

00.2

0.40.6

0.81

1.2

50500

10001500

20002500

3000

0

0.2

0.4

0.6

0.8

PGA(g)Discharge (m3/s)

Pro

babili

ty o

f E

xceedance

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

00.2

0.40.6

0.81

1.2

50500

10001500

20002500

3000

0

0.2

0.4

0.6

PGA(g)Discharge (m3/s)

Pro

babili

ty o

f E

xceedance

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

00.2

0.40.6

0.81

1.2

50500

10001500

20002500

3000

0

0.1

0.2

0.3

0.4

0.5

0.6

PGA(g)Discharge (m3/s)

Pro

babili

ty o

f E

xceedance

0

0.1

0.2

0.3

0.4

0.5

0.6

43

Following a multi-hazard scenario m, bridge restoration cost CRm can be estimated as (Zhou et

al. 2010):

4

1

| ,Rm m m m n k

k

C p DS k a d C r

(3-7)

where pm(DS = k|am,dm) is the probability that the bridge can sustain the damage state k under a ground

motion with PGA = am that occurs in the presence of scour resulted from a flood event with annual

peak flow discharge = dm. For no flood condition, pm(DS = k|am,dm) is calculated for seismic hazard

only. Cn stands for bridge replacement cost (in dollars) and rk is the damage ratio corresponding to the

damage state k. Damage ratio refers to the proportion of repair cost of a bridge suffered from the

damage state k to the total replacement cost. Values of rk as recommended in HAZUS (2013) are

considered in this study. Bridge replacement costs are calculated by multiplying bridge deck areas

with the average unit replacement costs. According to Caltrans 2012 construction statistics (Caltrans

2012), average bridge replacement cost per unit area of prestressed concrete box-girder and reinforced

concrete box-girder bridges are taken as $1805.6/m2 and $1833.3/m2, respectively.

Figure 3-13 shows risk curves of Bridge-1 and Bridge-2 under regional multi-hazard

scenarios. These curves represent annual exceedance probabilities of different levels of bridge

restoration costs (i.e., risks) due to various intensities of earthquake and flood hazards. To generate

these curves, information presented in regional seismic hazard curves is utilized. For a combination of

earthquake and flood hazards, values of pm(DS = k|am,dm) for two bridges are obtained from their

respective fragility curves (Figure 3-11). For Bridge-1, no change is observed in bridge risk curve with

increasing flood hazard level. This observation is obvious as the seismic fragility characteristics of the

bridge are mostly insensitive to flood hazard. For varying flood hazard level, the slight variation

observed in the fragility curves of the bridge at minor damage state was not enough to produce any

notable variation in the bridge risk curve. For Bridge-2, however, seismic risk increases with

increasing flood hazard level. For an example, there is 0.03% annual chance that expected bridge

restoration cost will exceed $2,000,000 due to regional seismic hazard only, whereas the same is

44

$2,740,000 (37% increase) due to regional seismic hazard in the presence of scour resulted from a

100-year flood event. Such an increase in the risk of Bridge-2 is an obvious outcome of enhanced

bridge seismic vulnerability, particularly at higher damage levels, in the presence of flood induced

scour.

0 2,000,000 4,000,000 6,000,000 8,000,000Bridge Restoration Cost ($)

10-5

10-4

10-3

10-2

10-1

100

Annual

Pro

bab

ilit

y o

f E

xce

eden

ce

No flood

1.1-yr flood

2-yr flood

10-yr flood

20-yr flood

0 1,000,000 2,000,000 3,000,000 4,000,000 5,000,000

Bridge Restoration Cost ($)

10-5

10-4

10-3

10-2

10-1

100

An

nu

al P

rob

abil

ity

of

Exce

eden

ce

No flood

1.1-yr flood

2-yr flood

10-yr flood

20-yr flood

50-yr flood

100-yr flood

(a) (b)

Figure 3-13: Seismic risk curves (a) Bridge-1 (b) Bridge-2

3.6 Closure

This chapter finds that component- and system-level fragilities of Bridge-1 (on Sacramento

River) developed for the multi-hazard scenario is insensitive to regional flood hazard, whereas

fragility curves of Bridge-2 piers (on San Joaquin River) gradually weaken with increasing flood

hazard level. The same observation is also made from fragility surfaces and risk curves of these

bridges. This observation attributes to the fact that large-diameter pile shafts used as foundation

element for Bridge-1 and the seismic design philosophy (ductile design) adopted for this bridge

considerably aided in minimizing the impact of regional flood events on the seismic vulnerability of

the bridge. For Bridge-2, on contrary, increased exposed height of bridge piers with increasing scour

depth makes the bridge more seismically vulnerable as flood hazard level increases. For this bridge,

scour depth never reaches to the pile cap, even under the scenario of 100-year flood event. Hence, the

impact on flood-induced scour on this bridge is primarily reflected on bridge piers.

45

CHAPTER 4

UNCERTAINTY ANALYSIS OF RISK OF HIGHWAY BRIDGES INTEGRATING

SEISMIC AND FLOOD HAZARDS

This chapter presents a rigorous uncertainty analysis employing sensitivity study, random

sampling technique and Monte Carlo simulations in order to obtain the variability in risk of bridges

under the multi-hazard condition of flood and earthquake hazards. For this purpose; the real-life bridge

analyzed in Chapter 3, Bridge-1, is taken into consideration. The analysis herein concentrates on the

uncertainties in input parameters related to the bridge, underlying soil and flood hazard. For seismic

hazard, uncertainties are embedded within recorded earthquakes and the USGS-provided regional

seismic hazard curve. Tornado diagram and Advanced First Order Second Moment (AFOSM) reliability

analyses are performed as part of the sensitivity study in order to screen the most significant uncertain

parameters to which bridge seismic response is greatly sensitive. Following this, random combinations

of identified key uncertain parameters are generated using Latin Hypercube Sampling (LHS) technique.

For each of these random combinations, bridge fragility curves are developed for various levels of

seismic and flood hazards. These fragility curves are observed to vary due to inherent uncertainty of

input parameters and statistical uncertainty in estimating fragility parameters. Finally, Monte Carlo

simulations are performed to evaluate 90% confidence intervals of bridge fragility curves and risk curves

of the bridge under the stated multi-hazard condition.

4.1 Uncertain Input Parameters

Quantification of uncertainties associated with different model parameters and their influences

on bridge performance are important for reliable performance evaluation of bridges under the combined

action of earthquake and flood-induced scour. The present study considers possible variations in key

input parameters (listed in Table 4-1) to estimate the variability of the seismic response of the studied

46

bridge. Uncertainties in material properties of the structure are considered through the compressive

strength of concrete (fce) and yield strength of reinforcing steel (fye). Mass of the bridge is also considered

to be an uncertain parameter due to possible variations in slab thickness, material densities and due to

re-pavement procedures during regular maintenance. For the PTFE-elastomeric bearing, uncertainties

may get introduced through the shear modulus of elastomer (Gel) and friction coefficient at the PTFE-

stainless steel interface (µptfe). According to Caltrans (2013) recommendations, initial abutment stiffness

(Kabut) may vary between upper and lower bounds depending on whether the embankment fill material

meets Caltrans standards. Hence, Kabut is taken here as a random variable. Uncertain properties of

surrounding soil layers at bridge foundations are considered in terms of uncertainties in unit weight of

soil (γsoil) and peak friction angle (ϕp,soil). For these eight uncertain structural and geotechnical

parameters, appropriate probability distributions and associated distribution parameters are assumed

based on relevant past studies as detailed in Table 4-1.

Table 4-1: Uncertain Modeling Parameters Parameter, Xi Units Distribution Distribution Parameters Reference

fce Concrete compressive

strength

MPa Normal Choi (2002)a

Substructure

elements

μ= 32.5 δ= 0.125

Bridge girders μ= 40.3 δ= 0.125

fye Yield strength of

reinforcing bars

MPa Lognormal λ= 6.16 ζ= 0.08 Ellingwood and

Hwang (1985)b

fmass Mass (factor of unit

density of concrete)

- Uniform lower=0.90 upper=1.10 Nielson (2005)

Gel Shear modulus of

elastomeric pad

psi Uniform lower=95 upper=120 Caltrans (2000)

µptfe Friction coefficient of

PTFE-stainless steel

surface

- Uniform lower=0.04 upper=0.08 Caltrans (1994)

Kabut Initial abutment

stiffness

kN/m

m/m

Uniform lower=14.35 upper=28.7

0

Caltrans (2013)

γsoil Unit weight of soil kN/m3 Normal (*) δ=0.10 Zhang (2006)

ϕp,soil Friction angle of soil degree Normal (*) δ=0.12 Zhang (2006) a = mean value and = coefficient of variation b = lognormal mean and = log-standard deviation

* mean values determined from the borehole data vary for each soil layer

47

4.2 Sensitivity of Uncertain Parameters

A sensitivity study is performed to quantify relative influences of uncertain parameters on the

multi-hazard response of the bridge. This study will provide a basis to identify major uncertain

parameters to which bridge response is greatly sensitive. So that uncertainty analyses can be performed

with a reduced number of input parameters, yielding to a saving in computational effort. To pursue this

sensitivity study; regional flood and seismic hazards, under which the response of the bridge is obtained,

are discussed first.

4.2.1 Regional Flood and Seismic Hazards

The multi-hazard performance of the studied bridge is defined in terms of seismic fragility

characteristics of the bridge in the absence and presence of scour induced by varied frequency flood

events in the region. Flood hazard curve, which identifies annual exceedance probabilities of peak flow

discharges corresponding to various flood hazard levels, for 50% statistical confidence was previously

developed to express the mean flood hazard at the site of Bridge-1, as presented in Figure 3-4. Flood

hazard curve at the bridge site for 5% and 95% statistical confidence levels are also developed and

shown in Figure 4-1. A detailed discussion on generation of such flood hazard curves at various

confidence levels can be found in Banerjee and Prasad (2013).

99.8 99 95 80 60 40 20 5 1Probability of Exceedance (%)

10

100

1000

10000

Annual

Pea

k D

isch

arge

(m3/s

)

5% Confidence level

50% Confidence level

95% Confidence level

Recorded data

Figure 4-1: Flood hazard curve with 90% confidence at the bridge site

As can be observed from the figure, flood hazard curves are subjected to a maximum discharge

of 2237 m3/s. Hence, the characteristics of any flood event with return period between 20 and 100 years

48

(i.e. with annual exceedance probability of 5% to 1%) are the same as that of a 20-year flood event. For

multi-hazard risk analysis of the bridge, the present study considers discrete flood events with annual

exceedance probabilities of 90%, 50%, 10% and 5% (corresponds to 1-yr, 2-yr, 10-yr and 20-yr floods).

Peak flow discharges corresponding to each of these flood events can be obtained from Figure 4-1 and

resulting scour depths at bridge foundations can be estimated from the equation suggested by HEC-18

(Equation 2-1). The scour depths estimated for flood discharges with 50% confidence were presented in

Table 3-1. Later part of this chapter discusses the possible variation in estimated scour depths due to

uncertain parameters, including the variation in flood discharges at a certain flood hazard level.

For seismic vulnerability assessment of bridges, a large set of ground motion records is desirable

in order to account for uncertainties associated with the seismic hazard. In the multi-hazard framework

of the present study, ground motions recoded at the neighborhood of the bridge are used such that

regional seismic characteristics and local soil condition can be considered through these motions. The

same ground motion dataset employed in Chapter 3 is used for uncertainty analyses in the present

chapter. As these ground motion records are region-specific, they convey regional hazard information

in the multi-hazard risk assessment framework of the bridge.

4.2.2 Sensitivity of Bridge Response to Uncertain Parameters

The hierarchical effects of uncertain input parameters (listed in Table 4-1) on the seismic

response of the bridge in the absence and presence of flood-induced scour are investigated through

sensitivity analysis. To pursue this study, statistical independence of input uncertain parameters is

assumed. Two sensitivity analysis methods, Tornado diagram and Advanced First Order Second

Moment (FOSM) reliability analyses, are used in parallel to identify key uncertain parameters that can

significantly impact bridge performance. In both methods, nonlinear time-history analyses of the bridge

are performed for ground motion records NGA0828 and NGA0829 (listed in Table 4-2), each under no

flood (hence, no scour) and 20-year flood conditions. Horizontal components of these motions are

interchanged to avoid directional biasness. While GM1 and GM2 are unscaled versions of NGA0828,

49

NGA0829 is scaled with a factor of two to obtain GM3 and GM4. Altogether eight time-history analyses

of the bridge are performed for the sensitivity analysis under scour and no-scour conditions.

Table 4-2: Ground motion records used in the sensitivity analyses

No. PEER NGA id Horizontal

Component 1

Horizontal

Component 2 PGA (g)

GM1 NGA0828 000 090 0.62

GM2 NGA0828 090 000 0.62

GM3 NGA0829 270 360 0.85

GM4 NGA0829 360 270 0.85

The sensitivity study is conducted for five different engineering demand parameters (EDPs)

which identify the seismic performance of different critical components of the bridge. These EDPs are

pier curvature ductility (μφ), abutment passive deformation in the longitudinal direction (Δlong,p) and in

the transverse direction (Δtrans), bearing deformation in the longitudinal direction (Δb,long) and in the

transverse direction (Δb,trans). μφ, Δlong,p, Δtrans and Δb,long determines bridge damage at piers (due to

flexure), abutments (in both translation directions) and bearings (in the longitudinal direction). Δb,trans is

used to determine damage in bearings and shear keys in the transverse direction.

4.2.3 Tornado Diagram Analysis

Tornado diagram is a useful graphical tool showing the sensitivity of a response value with

respect to the variation of input parameters. At first, EDPs are obtained from all eight nonlinear time-

history analyses when uncertain input parameters (listed in Table 4-1) are kept at their respective mean

values. These EDP values are regarded to be deterministic and shown in tornado diagrams with vertical

lines. Following this, EDPs are estimated when uncertain input parameters are varied one at a time

between their lower and upper bounds. These lower and upper bounds of input parameters are

respectively taken at their 2th and 98th percentile values (i.e. ±2 standard deviations). While one input

uncertain parameter is varied, other parameters are kept at their respective mean values. Thus, two values

of each EDP are obtained from each time-history analysis with the two extreme bounds (upper and

lower) of each uncertain parameter. The absolute difference of an EDP between the two bounds is

referred to as the swing of tornado diagram that corresponds to an input uncertain parameter for which

50

the variation in that EDP is observed. This procedure is repeated sequentially for all uncertain

parameters, and resulting swings in each EDP are calculated. Longer the swing, higher the influence of

the corresponding input parameter on the output. Finally, the uncertain parameters are ranked with

respect to the swings of each EDP such that the diagram takes a tornado shape. Such a tornado diagram

shows relative influence of the random input parameters on the calculated output.

Figure 4-2 shows the tornado diagram for pier curvature ductility μφ in the absence of scour for

all four ground motions. Similar results for μφ are obtained for 20-year flood condition. For other four

EDPs, Figure 4-3 shows tornado diagrams when the time-history analysis is performed under GM1 in

the presence of scour resulted from a 20-year flood event. Tornado diagrams for all other analysis cases

(with various combinations of ground motions and flood conditions) with similar outcomes are not

shown here to prevent repetition. All the diagrams indicate that fye, fmass, fce, Kabut and p,soil are five most

critical uncertain parameters (with different hierarchy) to which bridge response is greatly sensitive.

Variations in µptfe and Gel have insignificant (or no) impacts on the seismic response of the bridge in the

absence and presence of flood-induced scour.

14 16 18 20 22

fye

fmass

Kabut

fce

soil

p,soil

Gel

ptfe

GM 1

14 16 18 20 22 24

fye

fmass

Kabut

fce

soil

p,soil

Gel

ptfe

GM 2

12 14 16 18 20

fye

fmass

Kabut

fce

soil

p,soil

Gel

ptfe

GM 3

16 18 20 22 24

fye

fmass

Kabut

fce

soil

p,soil

Gel

ptfe

GM 4

(a) (b) (c) (d)

Figure 4-2: Tornado diagrams for pier curvature ductility obtained in the absence of flood-induced

scour under ground motions (a) GM1, (b) GM2, (c) GM3, and (d) GM4

51

100 104 108 112 116 120

long,p (mm)

fye

fmass

Kabut

fce

soil

p,soil

Gel

ptfe

40 50 60 70 80 90

trans (mm)

fye

fmass

Kabut

fce

soil

p,soil

Gel

ptfe

156 160 164 168 172 176

b,long (mm)

fye

fmass

Kabut

fce

soil

p,soil

Gel

ptfe

50 60 70 80 90

b,trans (mm)

fye

fmass

Kabut

fce

soil

p,soil

Gel

ptfe

(a) (b) (c) (d)

Figure 4-3: Tornado diagrams under ground motion GM1 obtained in the presence of scour due to a

20-yr flood event for EDP (a) Δlong,p, (b) Δtrans, (c) Δb,long, and (d) Δb,trans

4.2.4 Advanced First Order Second Moment Reliability Analysis

Advanced First Order Second Moment (AFOSM) reliability method (also known as Hasofer-

Lind method (Haldar and Mahadevan 2000)) is used to observe the individual and combined influences

of input random variables on bridge response. This analysis is performed in parallel to the Tornado

diagram analysis to have unbiased identification of key uncertain parameters. The AFOSM method

considers basic random variables to follow normal distributions. Therefore, non-normal probability

distributions of fye, fmass, Gel, ptfe, and Kabut are converted to two-parameter equivalent normal

distributions in order to apply AFOSM method to study parameter sensitivity (Haldar and Mahadevan

2000, Rackwitz and Fiessler 1978). In this method, a response measure Y can be expressed as a function

of random input variables Xm (where i =1 to 8):

),...,,( 821 XXXgY (4-1)

The Taylor series expansion of Y about the mean value can be written as:

...!2

1

!1

1),...,,(

28

1

8

1

8

1821

jii

Xj

j

Xi

ii

XiXXX

XX

gXX

X

gXgY

ji

i

(4-2)

where μXi is the mean value of random parameter Xi. AFOSM method considers only the first order terms

of Y, and thus, truncation of Equation 4-2 at the linear terms yields:

52

ii

XiXXXX

gXgY

i

8

1!1

1),...,,(

821 (4-3)

Variance of Y, Y can be calculated by taking the second moment of Y. Neglecting the higher

order terms, Y can be expressed as:

ji ij

jiYX

XXXg

X

XXXgXX

821

8

1

8218

1

2 ,...,,,...,,,cov

(4-4)

Since input parameters are statistically independent, the diagonal terms (i.e., cov[Xi, Xi]) of the

covariance matrix are the variance of Xi and the off-diagonal terms (i.e., cov[Xi, Xj]; i ≠ j) are equal to

zero. Therefore, the variance of Y can be calculated as:

28

1

82122 ,...,,

i i

XYX

XXXgi

(4-5)

In the current study, the response value Y is considered to be EDPs resulting from each ground

motion analysis. Therefore, the partial derivative terms in Equation 4-5 are calculated numerically using

the finite difference equation as follows:

i

NiiNii

i x

xxxxgxxxxg

X

XXXg

2

,,...,,,,...,,,...,, 2121821

(4-6)

A ratio of relative variance

2

8212 ,...,,

i

XX

XXXgi

of parameter Xi to the total variance

2

Y

of Y is obtained for each uncertain input parameter. Such a ratio represents relative variance contribution

of an input variable on Y. Figures 4-4 and 4-5 show the relative variance contributions of eight input

parameters on EDPs under no flood and 20-year flood conditions, respectively. As can be observed from

these figures, seismic response of the bridge is sensitive to fye, fmass, fce, and Kabut; the same parameters

showed most significant effects on EDPs in tornado diagram analysis. Similar to the tornado diagram

analysis, AFOSM reliability analysis identifies insignificant or no impacts of uncertainties associated

with Gel, µptfe, and γsoil on bridge response.

53

0 0.2 0.4 0.6 0.8 1Relative variance

Kabut

soil

p,soil

Gel

ptfe

fmass

fce

fye

0 0.2 0.4 0.6 0.8 1

Relative variance 0 0.2 0.4 0.6 0.8 1

Relative variance

GM 1

GM 2

GM 3

GM 4

0 0.2 0.4 0.6 0.8 1

Relative variance 0 0.2 0.4 0.6 0.8 1

Relative variance (a) (b) (c) (d) (e)

Figure 4-4: Relative variance contributions of uncertain parameters on (a) μφ, (b) Δlong,p, (c) Δtrans, (d)

Δb,long, and (e) Δb,trans for no flood condition

0 0.2 0.4 0.6 0.8 1Relative variance

Kabut

soil

p,soil

Gel

ptfe

fmass

fce

fye

0 0.2 0.4 0.6 0.8 1

Relative variance 0 0.2 0.4 0.6 0.8 1

Relative variance

GM 1

GM 2

GM 3

GM 4

0 0.2 0.4 0.6 0.8 1

Relative variance 0 0.2 0.4 0.6 0.8 1

Relative variance (a) (b) (c) (d) (e)

Figure 4-5: Relative variance contributions of uncertain parameters on (a) μφ, (b) Δlong,p, (c) Δtrans, (d)

Δb,long, and (e) Δb,trans for 20-year flood condition

4.2.5 Sensitivity of Scour Depths to Uncertain Input Parameters

Flood discharge for a certain hazard level may vary due to uncertainties involved in developing

flood hazard curves. To quantify this variation, 90% confidence band of the flood hazard curve at the

bridge site is developed as presented in Figure 4-1. Besides flood discharge, input parameters in the

scour calculation equation (Equation 2-1) may be uncertain. It is, therefore, obvious that expected scour

depths calculated for various flood hazard levels (in Table 3-1) will vary. Hence, it is worth to investigate

the sensitivity of scour depth to different uncertain input parameters in order to understand the possible

impact of scour depth uncertainty on the multi-hazard response of the bridge. Tornado diagram analysis,

as detailed in Section 4.2.3, is performed for this sensitivity study. In this case, swings of the tornado

diagram are evaluated in terms of the variation in scour depth due to the variability in scour calculation

parameters. Uncertainties in flow discharge (Q), Manning’s coefficient of the river (n) and scour

54

calculation coefficients K2 and K3 are taken as uncertain parameters. Pier width (thereby the coefficient

K1) and slope of the river are considered to be deterministic. Depth (y1) and mean velocity of the flow

(V) at upstream of bridge piers are concurrently calculated using the Manning’s equation for a given

flow discharge, Q. The lower and upper bounds for each uncertain input parameter are taken at their 5th

and 95th percentile values, respectively (to be consistent with the flood hazard curve). For an example,

Q takes values of 1637 m3/s, 1963 m3/s, and 2237 m3/s, respectively, for 5%, 50%, and 95% confidence

levels when a 10-year flood event is considered (Figure 4-1). Similar variations of Q for other flood

hazard levels are obtained from Figure 4-1. Following Johnson and Dock (1998), K2 and K3 are assumed

to follow normal distributions with a coefficient of variation of 5%. Manning’s coefficient is considered

to follow lognormal distribution with a coefficient of variation equal to 28% (Ghosn et al. 2003).

Figure 4-6 shows Tornado diagrams for scour depths estimated at all pier bents of the bridge for

a flood event with 10-year return period (i.e. 10-year flood). Vertical lines in these diagrams are the

scour depths calculated using mean values (i.e. with 50% statistical confidence) of input parameters. For

each of the swings, scour depths are observed to vary within 10% with respect to the mean scour depth

(vertical line). The same analysis is performed for other flood events, and similar results are observed.

As can be seen from Figure 4-6, scour depth is most sensitive to uncertainties in K2 and K3, and

less sensitive to Q. It was shown in Chapter 3 that the risk of the studied bridge under the same regional

multi-hazard condition has insignificant change, particularly at higher risk levels, due to the variation of

flood-induced scour depth ranging from 0 (for no flood case) to 3.28m (maximum scour from 20-yr

flood event). Hence, the uncertainty analysis discussed in this following part of the chapter does not

consider scour to be an uncertain parameter. At each flood case, the most expected scour depth (listed

in Table 3-1) is used for the analysis. Analysis results will show varied ranges of multi-hazard risk of

the bridge at different flood hazard levels due to key uncertain parameters related to the structural and

geotechnical attributes of the bridge.

55

2.75 3.00 3.25 3.50

Scour depth (m)

K2

K3

n

Q

2.75 3.00 3.25 3.50

Scour depth (m)

K2

K3

n

Q

2.75 3.00 3.25 3.50

Scour depth (m)

K2

K3

n

Q

(a) (b) (c)

Figure 4-6: Tornado diagrams for the scour depth at (a) Bent-2, (b) Bent-3, and (c) Bent-4 of the

bridge under 10-year flood

4.3 Uncertainty Analysis

4.3.1 Generation of Random Samples

Observations from the sensitivity analysis guided the screening of key uncertain parameters to

be included in the quantification of uncertainty associated with the multi-hazard risk of the bridge. Such

selection of key uncertain parameters helped in employing computational effort more efficiently. Based

on the results of tornado diagram and AFOSM reliability analyses, fye, fce, fmass, Kabut, and p,soil are taken

to be the most critical input parameters for the seismic response of the bridge in the presence and absence

of scour. Other parameters pertaining to bridge modeling and site soil condition are considered to be

deterministic.

Probability distributions for these five key uncertain input parameters are considered as shown

in Table 4-1. For each parameter, 20 random samples are generated based on which 20 random

combinations of these input parameters are developed through Latin hypercube sampling (LHS)

technique (McKay 1992). This random sampling technique does not allow repetition of any sample

value in the combination. Hence, 20 random combinations are unique in terms of the values of uncertain

parameters. LHS design considered in uncertainty analysis is presented in Appendix D. For each of these

randomly combined input parameter sets, finite element analyses (FEAs) of the bridge are performed

for the selected ground motion dataset under each flood condition (i.e., no, 1-yr, 2-yr, 10-yr, and 20-yr

floods). FEA results are used to develop bridge fragility curves on the basis of which risk curves of the

bridge are generated for the same regional multi-hazard condition.

56

4.3.2 Bridge Fragility Curves

In Chapter 3, bridge fragility curves were generated when uncertain modeling parameters (Table

4-1) are taken at their mean (the most expected) values. In the current uncertainty study; damage states

of the critical bridge components (i.e. piers, abutments, shear keys, and bearings) are determined as

described in Chapter 3.4.2, considering the damage threshold limits presented in Table 3-3. Fragility

curves of the bridge in component and system-level are computed with the same procedure as presented

in Chapters 3.4.3 and 3.4.4.

For 20 random combinations of input variables, fragility curves are developed at all damage

states of critical bridge components under each multi-hazard loading case; a few of them are shown here

to demonstrate the result. Seismic fragility curves developed for pier flexural damage of the bridge are

presented in Figure 4-7. For various combinations of seismic and flood hazards, variability in fragility

curves at all damage states is observed which is an obvious outcome of uncertainties in input parameters

of the bridge and soil. Higher variation is observed at the minor (i.e. lowest) damage state of bridge

piers. Similar variations in fragility curves are observed for other critical components of the bridge

(Figure 4-8). To show the global performance of the bridge, system-level fragility curves are developed

and presented in Figure 4-9. Median values (ζk = 0.6 for all damage states) of all component- and system-

level fragility curves are given in Appendix E.

57

0.0 0.2 0.4 0.6 0.8 1.0 1.2PGA (g)

0.0

0.2

0.4

0.6

0.8

1.0

Pro

babil

ity o

f E

xce

edin

g a

Dam

age

Sta

te

Minor damage

Moderate damage

0.0 0.2 0.4 0.6 0.8 1.0 1.2

PGA (g)

0.0

0.2

0.4

0.6

0.8

1.0

Pro

babil

ity o

f E

xce

edin

g a

Dam

age

Sta

te

Major damage

Collapse state

(a)

0.0 0.2 0.4 0.6 0.8 1.0 1.2PGA (g)

0.0

0.2

0.4

0.6

0.8

1.0

Pro

babil

ity o

f E

xce

edin

g a

Dam

age

Sta

te

Minor damage

Moderate damage

0.0 0.2 0.4 0.6 0.8 1.0 1.2

PGA (g)

0.0

0.2

0.4

0.6

0.8

1.0

Pro

babil

ity o

f E

xce

edin

g a

Dam

age

Sta

te

Major damage

Collapse state

(b)

0.0 0.2 0.4 0.6 0.8 1.0 1.2PGA (g)

0.0

0.2

0.4

0.6

0.8

1.0

Pro

babil

ity o

f E

xce

edin

g a

Dam

age

Sta

te

Minor damage

Moderate damage

0.0 0.2 0.4 0.6 0.8 1.0 1.2

PGA (g)

0.0

0.2

0.4

0.6

0.8

1.0

Pro

babil

ity o

f E

xce

edin

g a

Dam

age

Sta

te

Major damage

Collapse state

(c)

Figure 4-7: Seismic fragility curves for pier flexural damage under (a) no flood, (b) 1-year flood, (c)

2-year flood, (d) 10-year flood, and (e) 20-year flood conditions

58

0.0 0.2 0.4 0.6 0.8 1.0 1.2PGA (g)

0.0

0.2

0.4

0.6

0.8

1.0P

robabil

ity o

f E

xce

edin

g a

Dam

age

Sta

te

Minor damage

Moderate damage

0.0 0.2 0.4 0.6 0.8 1.0 1.2

PGA (g)

0.0

0.2

0.4

0.6

0.8

1.0

Pro

babil

ity o

f E

xce

edin

g a

Dam

age

Sta

te

Major damage

Collapse state

(d)

0.0 0.2 0.4 0.6 0.8 1.0 1.2PGA (g)

0.0

0.2

0.4

0.6

0.8

1.0

Pro

babil

ity o

f E

xce

edin

g a

Dam

age

Sta

te

Minor damage

Moderate damage

0.0 0.2 0.4 0.6 0.8 1.0 1.2

PGA (g)

0.0

0.2

0.4

0.6

0.8

1.0

Pro

babil

ity o

f E

xce

edin

g a

Dam

age

Sta

te

Major damage

Collapse state

(e)

Figure 4-7 Cont’d: Seismic fragility curves for pier flexural damage under (a) no flood, (b) 1-year

flood, (c) 2-year flood, (d) 10-year flood, and (e) 20-year flood conditions

59

0.0 0.2 0.4 0.6 0.8 1.0 1.2PGA (g)

0.0

0.2

0.4

0.6

0.8

1.0

Pro

babil

ity o

f E

xce

edin

g a

Dam

age

Sta

te

0.0 0.2 0.4 0.6 0.8 1.0 1.2

PGA (g)

0.0

0.2

0.4

0.6

0.8

1.0

Pro

babil

ity o

f E

xce

edin

g a

Dam

age

Sta

te

(a) (b)

0.0 0.2 0.4 0.6 0.8 1.0 1.2PGA (g)

0.0

0.2

0.4

0.6

0.8

1.0

Pro

babil

ity o

f E

xce

edin

g a

Dam

age

Sta

te

0.0 0.2 0.4 0.6 0.8 1.0 1.2

PGA (g)

0.0

0.2

0.4

0.6

0.8

1.0

Pro

babil

ity o

f E

xce

edin

g a

Dam

age

Sta

te

(c) (d)

0.0 0.2 0.4 0.6 0.8 1.0 1.2PGA (g)

0.0

0.2

0.4

0.6

0.8

1.0

Pro

babil

ity o

f E

xce

edin

g a

Dam

age

Sta

te

0.0 0.2 0.4 0.6 0.8 1.0 1.2

PGA (g)

0.0

0.2

0.4

0.6

0.8

1.0

Pro

babil

ity o

f E

xce

edin

g a

Dam

age

Sta

te

(e) (f)

Figure 4-8: Seismic fragility curves at minor damage state under the 20-year flood hazard for (a) pier

flexural damage (b) abutment passive deformation in longitudinal direction, (c) abutment transverse

deformation, (d) bearing longitudinal deformation, (e) bearing transverse deformation, and (f) shear

key deformation.

60

0.0 0.2 0.4 0.6 0.8 1.0 1.2PGA (g)

0.0

0.2

0.4

0.6

0.8

1.0

Pro

babil

ity o

f E

xce

edin

g a

Dam

age

Sta

te

Minor damage

Moderate damage

0.0 0.2 0.4 0.6 0.8 1.0 1.2

PGA (g)

0.0

0.2

0.4

0.6

0.8

1.0

Pro

babil

ity o

f E

xce

edin

g a

Dam

age

Sta

te

Major damage

Collapse state

(a)

0.0 0.2 0.4 0.6 0.8 1.0 1.2PGA (g)

0.0

0.2

0.4

0.6

0.8

1.0

Pro

babil

ity o

f E

xce

edin

g a

Dam

age

Sta

te

Minor damage

Moderate damage

0.0 0.2 0.4 0.6 0.8 1.0 1.2

PGA (g)

0.0

0.2

0.4

0.6

0.8

1.0

Pro

babil

ity o

f E

xce

edin

g a

Dam

age

Sta

te

Major damage

Collapse state

(b)

0.0 0.2 0.4 0.6 0.8 1.0 1.2PGA (g)

0.0

0.2

0.4

0.6

0.8

1.0

Pro

babil

ity o

f E

xce

edin

g a

Dam

age

Sta

te

Minor damage

Moderate damage

0.0 0.2 0.4 0.6 0.8 1.0 1.2

PGA (g)

0.0

0.2

0.4

0.6

0.8

1.0

Pro

babil

ity o

f E

xce

edin

g a

Dam

age

Sta

te

Major damage

Collapse state

(c)

Figure 4-9: System-level seismic fragility curves of the bridge under (a) no flood, (b) 1-year flood, (c)

2-year flood, (d) 10-year flood, and (e) 20-year flood conditions.

61

0.0 0.2 0.4 0.6 0.8 1.0 1.2PGA (g)

0.0

0.2

0.4

0.6

0.8

1.0P

robabil

ity o

f E

xce

edin

g a

Dam

age

Sta

te

Minor damage

Moderate damage

0.0 0.2 0.4 0.6 0.8 1.0 1.2

PGA (g)

0.0

0.2

0.4

0.6

0.8

1.0

Pro

babil

ity o

f E

xce

edin

g a

Dam

age

Sta

te

Major damage

Collapse state

(d)

0.0 0.2 0.4 0.6 0.8 1.0 1.2PGA (g)

0.0

0.2

0.4

0.6

0.8

1.0

Pro

babil

ity o

f E

xce

edin

g a

Dam

age

Sta

te

Minor damage

Moderate damage

0.0 0.2 0.4 0.6 0.8 1.0 1.2

PGA (g)

0.0

0.2

0.4

0.6

0.8

1.0

Pro

babil

ity o

f E

xce

edin

g a

Dam

age

Sta

te

Major damage

Collapse state

(e)

Figure 4-9 Cont’d: System-level seismic fragility curves of the bridge under (a) no flood, (b) 1-year

flood, (c) 2-year flood, (d) 10-year flood, and (e) 20-year flood conditions.

4.3.3 Confidence Intervals of Fragility Curves

Notable variations in bridge fragility curves are observed due to inherent uncertainties in input

parameters (Figures 4-7 to 4-9). However, the observed variations do not provide a good platform to

estimate confidence intervals of fragility curves through which uncertainty in bridge fragility

characteristics can be quantified. This is because, 20 random combinations of uncertain input parameters

did not produce enough unique fragility curves at a certain damage state and flood hazard level. For an

example, only 7 unique median fragility parameters c (hence, 7 unique fragility curves) are obtained at

minor damage state of the bridge for no flood condition (Figure 4-9(a)). This number drastically reduces

for higher damage levels. At moderate damage state of the bridge, mostly all fragility curves developed

for various random sets of input parameters overlap, and thus only one to two unique values of median

62

fragility parameter c are obtained at this damage state for any flood hazard level (Figure 4-9). While less

variation in c may be an indicator of less variability in fragility curves due to parameter uncertainty,

statistical uncertainty associated with the estimation of fragility parameters cannot be ignored. This led

to the use of Monte Carlo simulation technique to generate samples of median fragility parameters to

capture the statistical uncertainty in fragility curves (Banerjee et al. 2009, Banerjee and Shinozuka

2008).

Uncertainty in bridge fragility curves are measured in terms of 90% confidence intervals (i.e.

between 5% and 95% exceedance probabilities) of median fragility parameter, c. This is done through

a three-step procedure as described in Banerjee and Shinozuka (2008). In Step-I, 512 values of ground

motion intensity parameter (*

ix ) and corresponding failure probability (*

ib ) of the bridge are randomly

generated through Monte Carlo simulation assuming that these parameters are uniformly distributed in

the range of 0-1.0g and 0-1, respectively. For each ],[ **

ii bx , damage condition *

ikr (i = 1, 2, 3,.., 512) at

damage state k is obtained as:

otherwise

bcx

ifr i

k

ki

ik

0

/ln1 *

*

* (4-7)

where ck represents median value of fragility curves at damage state k and its values are obtained from

Figure 4-9. In Step-II, 512 combinations of ],[ **

iki rx are used in the maximum likelihood method

(Equation 3-2) to obtain one set of realization of fragility parameters*

kc and *

k . In Step-III, Step-I and

Step-II are repeated for 500 times to generate 500 sets of realization of*

kc and *

k . Hence, 500

realizations are obtained for each ck in Figure 4-9.

Realizations of *

kc are plotted on a lognormal probability paper assuming that *

kc will follow

lognormal distribution. This hypothesis is tested by drawing linear fits in the probability paper. Figure

4-10 shows the lognormal probability plots for median values simulated at all damage states of the

63

bridge under 2-year flood condition. It should be noted that each probability paper contains *

kc

simulated for all unique values of ck at damage state k. Similar plots are obtained for various other flood

conditions (including no flood condition). From each probability plot, ck values corresponding to 5%,

50%, and 95% statistical confidence (i.e., with 95%, 50%, and 5% exceedance probabilities,

respectively) are obtained and referred to as c0.05, c0.50, and c0.95, respectively. These values are used to

construct fragility curves with 5%, 50%, and 95% confidence levels as schematically presented in Figure

4-11. Fragility curve at 95% confidence level indicates that for 95% cases median fragility parameter

(c) will be higher than c0.95. Hence, in 95% of cases probability of bridge damage at a damage state k for

a PGA will be less than that coming from the fragility curve with 95% confidence level.

1.00.80.60.40.2cminor (g)

-4

-3

-2

-1

0

1

2

3

4

Sta

ndar

d N

orm

al V

aria

te, Z

0.05

0.2

0.40.6

0.8

0.95

CD

F

1.2

1.00.80.60.40.2

cmoderate (g)

-4

-3

-2

-1

0

1

2

3

4S

tan

dar

d N

orm

al V

aria

te, Z

0.05

0.2

0.40.6

0.8

0.95

CD

F

1.2

(a) (b)

10.80.60.40.2cmajor (g)

-4

-3

-2

-1

0

1

2

3

4

Sta

ndar

d N

orm

al V

aria

te, Z

0.05

0.2

0.40.6

0.8

0.95

CD

F

1.2

10.80.60.40.2

ccollapse (g)

-4

-3

-2

-1

0

1

2

3

4

Sta

ndar

d N

orm

al V

aria

te, Z

0.05

0.2

0.40.6

0.8

0.95

CD

F

1.2

(c) (d)

Figure 4-10: Lognormal probability papers for median values from system-level fragility curves at (a)

minor damage, (b) moderate damage, (c) major damage, and (d) collapse state under 2-year flood

condition

64

PGA (g)0.0

0.5

1.0

Pro

bab

ilit

y o

f E

xce

edin

g a

Dam

age

Sta

te

95% confidence

50% confidence

5% confidence

c0.95 c0.50 c0.05

Figure 4-11: Schematic illustration of fragility curves with different confidence levels

0.0

0.2

0.4

0.6

0.8

1.0

Pro

bab

ilit

y o

f E

xce

edin

g a

Dam

age

Sta

te

0.0 0.2 0.4 0.6 0.8 1.0 1.2PGA (g)

95 % confidence

50 % confidence

5 % confidence

MinorDamage

Moderatedamage

Collapsestate

Majordamage

0.0

0.2

0.4

0.6

0.8

1.0

Pro

bab

ilit

y o

f E

xce

edin

g a

Dam

age

Sta

te

0.0 0.2 0.4 0.6 0.8 1.0 1.2PGA (g)

95 % confidence

50 % confidence

5 % confidence

MinorDamage

Moderatedamage

Collapsestate

Majordamage

(a) (b)

0.0

0.2

0.4

0.6

0.8

1.0

Pro

bab

ilit

y o

f E

xce

edin

g a

Dam

age

Sta

te

0.0 0.2 0.4 0.6 0.8 1.0 1.2PGA (g)

95 % confidence

50 % confidence

5 % confidence

MinorDamage

Moderatedamage

Collapsestate

Majordamage

0.0

0.2

0.4

0.6

0.8

1.0

Pro

bab

ilit

y o

f E

xce

edin

g a

Dam

age

Sta

te

0.0 0.2 0.4 0.6 0.8 1.0 1.2PGA (g)

95 % confidence

50 % confidence

5 % confidence

MinorDamage

Moderatedamage

Collapsestate

Majordamage

(c) (d)

Figure 4-12: 90% confidence intervals of system-level fragility curves of the bridge under (a) no

flood, (b) 1-year flood, (c) 2-year flood, and (d) 10-year flood conditions

Figure 4-12 shows fragility curves with 5%, 50%, and 95% confidence levels at all four damage

states of the bridge for no-flood, 1-year flood, 2-year flood and 10-year flood conditions. Fragility curves

for 20-year flood case are almost the same as of those for 10-year flood case; hence, these are not shown

65

in the figure. Failure probabilities of the bridge for various combinations of seismic and flood hazards

are obtained from these fragility curves and used to evaluate the multi-hazard risk of the bridge.

Appendix F presents all the resulting median values of the system-level fragility curves with 5%, 50%,

and 95% confidence.

4.3.4 Risk Curves of the Bridge

Risk curves of Bridge-1 are generated from fragility curves with 5%, 50%, and 95% confidence

levels and presented in Figure 4-13(a) to Figure 4-13(e). In generation of risk curves, risk evaluation

methodology introduced in Chapter 3.5 is followed. The mean seismic hazard curve produced by USGS

(2008b) at the bridge site (Figure 3-3) is considered for risk curve calculations. USGS provides mean

hazard curves derived based on logic tree analysis performed considering uncertainties associated with

different phases of seismic hazard assessment procedure (e.g. earthquake models, moment-area

relationships, statistical uncertainties) (Petersen et al. 2014).

Along horizontal axes of risk curve plots in Figure 4-13, expected loss due to future natural

hazards is represented in terms of restoration cost (mRC ) and the ratio of restoration to replacement cost

(mR nC C ). These figures also show deterministic risk curves developed using fragility parameter cdet,

computed when all input parameters (listed in Table 4-1) are taken at their mean values (i.e. input

parameters are deterministic). As can be observed from these figures, the use of cdet provides nearly the

same estimate of risk that is calculated using fragility curves with 50% confidence level. For an example,

annual chances of mR nC C being equal to or more than 0.25 are 0.0104% and 0.0102% obtained

respectively from deterministic risk curve and that developed at 50% confidence level shown in Figure

4-13(a). Hence, deterministic risk curves can be regarded as mean risk curves of the bridge.

66

0.0 0.1 0.2 0.3 0.4 0.5CRm/Cn

10-6

10-5

10-4

10-3

10-2

10-1

100

Annual

Pro

bab

ilit

y o

f E

xce

eden

ce

0.0 2.0 4.0 6.0 8.0

CRm (million $)

5 % confidence

50 % confidence

95 % confidence

Using cdet

0.0 0.1 0.2 0.3 0.4 0.5CRm/Cn

10-6

10-5

10-4

10-3

10-2

10-1

100

Annual

Pro

bab

ilit

y o

f E

xce

eden

ce

0.0 2.0 4.0 6.0 8.0

CRm (million $)

5 % confidence

50 % confidence

95 % confidence

Using cdet

(a) (b)

0.0 0.1 0.2 0.3 0.4 0.5CRm/Cn

10-6

10-5

10-4

10-3

10-2

10-1

100

Annual

Pro

bab

ilit

y o

f E

xce

eden

ce

0.0 2.0 4.0 6.0 8.0

CRm (million $)

5 % confidence

50 % confidence

95 % confidence

Using cdet

0.0 0.1 0.2 0.3 0.4 0.5CRm/Cn

10-6

10-5

10-4

10-3

10-2

10-1

100

Annual

Pro

bab

ilit

y o

f E

xce

eden

ce

0.0 2.0 4.0 6.0 8.0

CRm (million $)

5 % confidence

50 % confidence

95 % confidence

Using cdet

(c) (d)

0.0 0.1 0.2 0.3 0.4 0.5CRm/Cn

10-6

10-5

10-4

10-3

10-2

10-1

100

Annual

Pro

bab

ilit

y o

f E

xce

eden

ce

0.0 2.0 4.0 6.0 8.0

CRm (million $)

5 % confidence

50 % confidence

95 % confidence

Using cdet

0.1 0.2 0.3 0.4 0.5CRm/Cn

0.05

0.10

0.15

0.20

CO

V

2.0 4.0 6.0 8.0

CRm (million $)

No flood

1-year flood

2-year flood

10-year flood

20-year flood

(e) (f)

Figure 4-13: Multi-hazard risk of the bridge: (a) No flood condition, (b) 1-year flood condition, (c) 2-

year flood condition, (d) 10-year flood condition, (e) 20-year flood condition, and (f) dispersion of risk

67

At the mean risk level, multi-hazard risk of the bridge is least sensitive to the change in flood

hazard level. It is realized, however, that the dispersion of risk due to uncertain fragility curves may vary

from one flood hazard level to another. Hence, coefficient of variation (COV) of risk at various levels

of bridge repair to replacement costs (mR nC C ) are calculated for five flood cases and presented in

Figure 4-13 (f). For such calculation of COV, the distribution of risk for any specific value of mR nC C

is assumed to follow normal distribution. As can be observed from Figure 4-13 (f), COV of risk increases

with increasing flood hazard level. For an example, 11.9% COV of risk is obtained at mR nC C = 0.25

for no flood scenario. This value increases to 12.7-12.9% when a multi-hazard scenario with varied

flood hazard level (from 1-year to 20-year flood) is considered. Such an increase in the dispersion of

risk due to the presence of flood hazard is persistent throughout risk curves even if COV values decrease

with increasing level of risk.

4.4 Closure

Research presented in this chapter demonstrates the significance of risk and uncertainty analyses

for the multi-hazard performance assessment of highway bridges. Observations from tornado diagram

and AFOSM reliability analyses performed as part of the sensitivity study indicate that the compressive

strength of concrete, yield strength of reinforcing steel, mass of the bridge, abutment stiffness and peak

friction angle of subsurface soil are the five most significant parameters that influence the performance

of the bridge. Uncertainties involved in the values of soil unit weight, shear modulus of elastomer and

friction coefficient at the PTFE-stainless steel interface are ignored in the uncertainty analysis due to

their insignificant or no impacts on bridge response. Confidence intervals (90%) of fragility curves

obtained through random sampling of uncertain parameters and Monte Carlo simulations show notable

variations in bridge fragility characteristics at various levels of the multi-hazard condition considered

herein. Scatter in the estimated multi-hazard risk of the study bridge is observed when these uncertain

bridge fragility curves are considered. These observations suggest that the variation in risk due to

68

uncertain parameter and varied flood hazard level cannot be ignored to assure bridge safety under the

stated multi-hazard condition.

69

CHAPTER 5

MULTI-HAZARD VULNERABILITY ASSESSMENT OF GENERIC BRIDGES IN

THE WEST COAST OF THE U.S.

This chapter presents an evaluation of multi-hazard performance of characteristic bridges that

are located in seismically-active flood-prone regions. The hazard maps presented in Figure 1-2 reveals

that West Coast of the U.S can be regarded as a critical region with moderate to high potential of

exposure to earthquake and flood hazard events compared to other parts of the U.S. Several hazard-

critical sites with varied patterns of hazard intensities are identified in the West Coast of the U.S. for

investigation. Bridge inventory studies performed for California and Washington states facilitate in

generating representative river-crossing bridges with characteristic design features. Results obtained in

this chapter can be used to update design guidelines of highway bridges for the multi-hazard effect of

earthquake and flood.

5.1 Review of Bridge Inventory in Hazard-Critical Regions

National Bridge Inventory (NBI) (NBI 2013) is reviewed in detail to identify the general

characteristics of river-crossing highway bridges in California and Washington. The inventory data is

filtered with respect to the following NBI information that are relevant to the focus of this research:

Item 42B: Bridges over waterways only are taken into consideration.

Item 42A: Bridges on which highway or highway-pedestrian service exists are only taken

into consideration.

Item 41: Bridges which are either open without any traffic restriction or new structure not

yet open to traffic are taken into consideration.

Item 43B: Type of designs designated as tunnels or culverts are ignored.

Item 43A: Type of materials such as woods, masonry, aluminum, and other are ignored.

70

Item 45: Single-span bridges are ignored.

According to the inventory data, there are a total of 24955 bridges in California, 64% of them

(15947 bridges) being over waterways. 11947 of these 15947 bridges conform to the abovementioned

bridge selection criteria. 67% percent (i.e., 7680 bridges) of these bridges are multi-span bridges, which

are the focus of the current research. Ramanathan (2012) has performed a general inventory study for

California bridges, and generated bridge classes to investigate their seismic fragilities. Three bridge

design eras were considered in that literature: “Pre-1971”, “1971-1990”, and “Post-1990”. 1975 and

1990 can be regarded as important milestones for improvements in seismic design principles of bridge

construction. The statistics of bridges constructed after 1990 is important for revealing modern trends

of seismic bridge design. The bridge classification introduced by Ramanathan (2012) is applied on the

filtered bridge inventory of California, and the resulting distribution is presented in Table 5-1.

Table 5-1. Bridge classes in California

Support Material Type of

Design

NBI Info After 1990 TOTAL

Item

43A Item 43B Number in % Number in %

Continuous Concrete Box-girder 2,6 05,06,21 352 24.3 892 11.8

Continuous Concrete Girder 2,6 02,03,04,22 148 10.2 1239 16.4

Continuous Concrete Slab 2,6 01 621 42.8 3575 47.5

Continuous Steel Girder 4 02,03,04,22 21 1.4 218 2.9

Continuous Steel Box-girder 4 05,06,21 0 0.0 5 0.1

Simply-

supported Concrete Box-girder 1,5 05,06 76 5.2 113 1.5

Simply-

supported Concrete Girder 1,5 02,03,04,22 64 4.4 642 8.5

Simply-

supported Concrete Slab 1,5 01 93 6.4 345 4.6

Simply-

supported Steel Girder 3 02,03,04,22 74 5.1 503 6.7

Simply-

supported Steel Box-girder 3 05,06,21 2 0.1 2 0.0

Total = 1451 Total = 7534

A similar inventory review is applied on Washington bridge data. According to this review,

there are 7902 bridges in Washington state, 70% of them (i.e., 5542 bridges) are over waterways. 4508

71

of these 5542 bridges conform to the abovementioned criteria. Multi-span bridges constitute 39%

percent (1765 bridges) of the selected dataset. For the filtered bridge inventory for Washington, the

number of bridges falling into the designated bridge classes are presented in Table 5-2.

Table 5-2. Bridge classes in Washington

Support Material Type of

Design

NBI Info After 1990 TOTAL

Item

43A Item 43B Number in % Number

in

%

Continuous Concrete

Box-

girder 2,6 05,06,21 21 7.1 132 7.8

Continuous Concrete Girder 2,6 02,03,04,22 102 34.5 394 23.2

Continuous Concrete Slab 2,6 01 35 11.8 444 26.1

Continuous Steel Girder 4 02,03,04,22 26 8.8 68 4.0

Continuous Steel

Box-

girder 4 05,06,21 1 0.3 1 0.1

Continuous Concrete Frame 2,6 07 17 5.7 78 4.6

Simply-

supported Concrete

Box-

girder 1,5 05,06 2 0.7 14 0.8

Simply-

supported Concrete Girder 1,5 02,03,04,22 65 22.0 348 20.5

Simply-

supported Concrete Slab 1,5 01 18 6.1 166 9.8

Simply-

supported Steel Girder 3 02,03,04,22 9 3.0 53 3.1

Simply-

supported Steel

Box-

girder 3 05,06,21 0 0.0 0 0.0

Simply-

supported Concrete Frame 1,5 07 0 0.0 3 0.2

Total = 296 Total = 1701

The review of California bridge inventory (Table 5-1) shows that continuous concrete box-

girder, continuous concrete girder and continuous concrete slab type of bridges are three most common

types of river-crossing bridges in California. In comparison, the bridge design practice in Washington

shows a slight difference as can be examined from Table 5-2. In Washington, continuous box-girder

bridges are not as common as it is in California; instead, simply-supported concrete girder bridges are

used mostly along with continuous concrete girder and continuous slab type of bridges. Note that in the

bridge classification scheme used here, prestressed concrete and concrete bridges are considered

together within the same material group (i.e., concrete).

72

With respect to the number of spans, Figure 5-1 presents histograms of the most common types

of bridges as observed in Table 5-1 and Table 5-2. Other than the abovementioned bridge classification

scheme, bridges with prestressed concrete and concrete materials are considered separately in this figure.

The following abbreviations are used for bridge types: C-C-BG for continuous concrete box-girder, C-

PC-BG for continuous prestressed concrete box-girder, C-PC-G for continuous prestressed concrete

girder, SS-PC-G for simply-supported prestressed concrete girder, and C-C-S for continuous concrete

slab. Figure 5-1 shows that 3-span bridges are the most common type in the bridge inventories for all

types of bridges.

0

200

400

600

800

1000

1200

1400

Num

ber

2 3 4 5 6 7Number of Spans

C-C-BG

C-PC-BG

C-PC-G

SS-PC-G

C-C-S

> 6

0

50

100

150

200

250

Num

ber

2 3 4 5 6 7Number of Spans

C-C-BG

C-PC-BG

C-PC-G

SS-PC-G

C-C-S

> 6

(a) (b)

Figure 5-1: Number of bridges with respect to the number of spans in (a) California, (b) Washington

The maximum span lengths of the most common bridge types are shown in Figure 5-2. As can

be observed from Figure 5-2, slab type of superstructures are generally used in bridges with relatively

short span lengths compared to other types of superstructures. In recent years, bridge engineering

practice is moving away from this type of bridges due to the available practical and economic

alternatives such as prestressed (including post-tensioned) girders. With prestressed girders, it is

becoming possible to have fewer number of spans for the same overall length of bridges. The average

of maximum span lengths for C-C-BG, C-PC-BG, C-PG-G, SS-PC-G, C-C-S bridges are found to be

29m, 44m, 28m, 23m, and 8m, respectively for California bridges, and 34m, 62m, 34m, 26m, and 10m,

respectively for Washington bridges.

73

0

40

80

120

160

200

Max

. S

pan

Len

gth

(m

)

2 3 4 5 6Number of Spans

C-C-BG

C-PC-BG

C-PC-G

SS-PC-G

C-C-S

0

50

100

150

200

250

Max

. S

pan

Len

gth

(m

)

2 3 4 5 6Number of Spans

C-C-BG

C-PC-BG

C-PC-G

SS-PC-G

C-C-S

(a) (b)

Figure 5-2: Maximum span lengths of bridges for the inventory of (a) California, (b) Washington

Figure 5-3 show the variation of deck widths for the most common type of bridges in California

and Washington. The average of deck widths for C-C-BG, C-PC-BG, C-PG-G, SS-PC-G, C-C-S bridges

are found to be 16.4m, 16.8m, 16.6m, 15.5m, and 13.2m, respectively for California bridges, and 11.3m,

15.7m, 13.4m, 10.6m, and 11.5m, respectively for Washington bridges.

0

20

40

60

80

100

Dec

k w

idth

(m

)

2 3 4 5 6Number of Spans

C-C-BG

C-PC-BG

C-PC-G

SS-PC-G

C-C-S

0

20

40

60

80

Dec

k w

idth

(m

)

2 3 4 5 6Number of Spans

C-C-BG

C-PC-BG

C-PC-G

SS-PC-G

C-C-S

(a) (b)

Figure 5-3: Deck width of bridges for the inventory of (a) California, (b) Washington

5.2 Characteristic Bridges

Performance of characteristic bridges subjected to the multi-hazard condition of earthquake and

flood is evaluated through generic bridges. For this purpose, a continuous concrete box-girder bridge

reflecting the state-of-the-art practice of bridge design and construction is selected here. The design

bridge is accepted to be straight and regular. Bridges having skewness, curve or any other irregularity

74

can similarly be analyzed by using the procedures presented in this research. Schematic drawings of the

generic bridges is presented in Figure 5-4.

As previously mentioned, three-span bridges are found to be the most common type of bridges.

Therefore, the generic bridges are developed with three spans having a maximum span length of 45m at

the middle which reflects the compatible range for this bridge type. Lengths of side spans are deduced

from the review of the inventory such that maximum span length is approximately 1.3 times the side

span length. The bridge is assumed to have a deck width of 17m which can accommodate three driving

lanes. The dimensions of the box-girder is determined according to the findings of Ramanathan (2012),

and recommendations of Caltrans (2008). The bridge has seat-type abutments that accommodates steel-

reinforced elastomeric bearings with typical dimensions of 508mm×356mm×64mm. A 5cm-long

expansion gap is taken between the bridge girder and abutment backwall.

In order to cover the influence of foundations on multi-hazard performance, two foundation

alternatives are investigated:

(1) - Extended pier-shaft with constant diameter (Type I shaft of Caltrans (2013))

(2) - Extended pier-shaft with enlarged diameter (Type II shaft of Caltrans (2013))

Pile group with a pile cap is not considered as an alternative foundation type. This is because

Type I and Type II shafts are increasingly being constructed in California primarily due to the ease of

construction in wet conditions (especially when there is space and time restrictions for bridge

replacement projects) and their high capacity in resisting lateral forces such as the one from earthquake.

Both Type I and Type II shafts are designed as ductile members as described in Caltrans (2013).

Within the performance-based seismic design philosophy, these members are intentionally designed to

deform inelastically for several cycles without significant degradation of strength or stiffness during

design seismic events. For Type II shafts, capacity-protection principle is satisfied by using the

necessary reinforcements in the enlarged section. Expected compressive strength of concrete used in

substructure and superstructure elements are taken as 32.5 MPa and 40.3 MPa (design strengths of 25

MP and 31 MPa), respectively. Expected yield strength of reinforcement (Grade 60 reinforcement) is

75

taken as 475 MPa. Longitudinal reinforcement ratios in pier-shafts with diameter D = 1.52m, and the

enlarged section with diameter D = 2.13m are accepted as 2% and 1%, respectively. Pier-shafts are

assumed to be well confined with transverse reinforcements that satisfy the minimum criteria for the

plastic hinge regions of bridge piers.

Figure 5-4: Schematic drawings of Type A1 and Type A2 bridges; (a) elevation view, (b) substructure

alternatives, (c) box-girder details

Hp = 7.0 m

Lb = 9.0 m

W = 17.0 m

Hs = 14.0 m

(a)

Dp = 1.52 m

Type A1

(Caltrans Type I Shaft) Type A2

(Caltrans Type II Shaft)

Rock or Firm Soil

Medium Sand Medium Sand Scour

Rock or Firm Soil

Lm = 45 m La = 35 m

Hp = 7 m

La = 35 m

Hs = 14 m

Abut. 1 Bent 2 Bent 3 Abut. 4

Hp = 7.0 m

Hs = 14.0 m

Dp = 1.52 m

Dp = 2.13 m

W = 17.0 m

Lb = 9.0 m

(b)

ttop = 206 mm Lbox = 2819 mm

Hgirder = 2000 mm

tbot.

= 206 mm

twall

= 305 mm

(c)

76

For both Type A1 and Type A2 bridges, the focused failure modes are the pier-shaft flexural

damage, bearing damage (including abutment seat width failure), abutment damage, and shear key

damage. At all study sites, a uniform soil profile of medium sand is assumed down until a depth at

which pile shafts are accepted to be fixed to a firm soil or rock socket. Typical peak friction angle of

35˚ and wet unit weight of soil of 1.9 t/m3 are taken for medium sand.

The finite element models of the generic bridges are produced with the same methodology as

described for Bridge-1 in Chapter 3.3.1. As an exception, the abutment bearings in the design bridge are

modeled the same way as applied to in-span hinge bearings of Bridge-2 in Chapter 3. The shear keys at

the abutments of the design bridge are accepted to have a yield capacity of 0.5 times the superstructure

abutment reaction as recommended in Caltrans (2013). The backbone curve of the shear key elements

is taken as described in Megally et al. (2002), and post-yield stiffness value is assumed to be 2.5% of

the initial stiffness as recommended in Aviram et al. (2008).

5.3 Hazard Matrix

Vulnerability of generic bridges is attained by analyzing them under the regional multi-hazard

condition forming at a multiple locations scattered within the region of interest. For this purpose, 4 sites

with different levels of earthquake and flood hazard potentials are selected as listed in Table 5-3. Figure

5-5 marks the locations of these sites on map. The selected sites are located at the USGS streamflow

measurement stations, regardless of the existence of any actual river-crossing highway bridge at these

locations. The assumption is made in order to satisfactorily combine various levels of seismic and flood

hazard intensities within the West Coast of the U.S.

For each selected site (as given in Table 5-3), a separate set of ground motion records with

varying hazard levels is constituted for seismic fragility analysis of the generic bridges. The generation

of these ground motion data sets is similar to that applied in Chapter 3.2.1. The ground motion records

used in time history analyses of the generic bridges are listed in Appendix A.

77

Table 5-3: Selected sites investigated for the integrated flood and earthquake hazards

Site River

USGS

Streamflow

Station ID

100-year Flood

Discharge

(m3/s)

1000-year

Earthquake

PGA (g)

Site-1 Sacramento 11370500 3949 0.24

Site-2 Stanislaus 11303000 1181 0.28

Site-3 Santa Ana 11051500 491 1.01

Site-4 Salinas 11147500 1272 0.42

Figure 5-5: Locations of the selected sites (courtesy of google.com)

Figure 5-6 shows the mean flood and seismic hazard curves at the study sites. Flood hazard

curve at a study site is developed through flood-frequency analysis utilizing the streamflow data of

USGS at the exact same location which allows for a more accurate representation of flood hazard. In

the flood hazard curves, any regulation effect is neglected for the objective of having proportional peak

discharge values with the increasing levels of flood events. The peak annual streamflow data considered

for developing flood hazard curves at all sites are given in Appendix B. The mean seismic hazard curves

are obtained from USGS (2008b) for the local soil condition accepted for the study sites. The 100-year

flood peak discharge and 1000-year earthquake PGA values presented for each study site in Table 5-3

show a comparison of the intensity of hazard levels of each site relative to each other.

Site 1

Site 2

Site 3

Site 4

78

99.8 99 95 80 60 40 20 5 1Probability of Exceedance (%)

0.01

0.1

1

10

100

1000

10000

Annual

Pea

k D

isch

arg

e (m

3/s

)

Site-1

Site-2

Site-4

Site-3

0.001 0.01 0.1 1 10PGA (g)

10-5

10-4

10-3

10-2

10-1

100

An

nu

al P

rob

abil

ity

of

Exce

edan

ce

Site-1

Site-2

Site-4Site-3

(a) (b)

Figure 5-6: (a) Mean flood hazard curves, (b) mean seismic hazard curves

The mean scour depth at the foundation of the design bridge is estimated for flood events with

annual exceedance probabilities of 50%, 10%, 2%, and 1% (corresponding to 2-year, 10-year, 20-year,

50-year and 100-year floods) and presented in Table 5-4. In finding the estimated scour depths, Equation

2-1 is employed with a consideration of mean scour modeling factor of 0.93 as recommended by Johnson

and Dock (1998). As a general case, river bed slope and Manning’s coefficient are assumed to be 0.0015

and 0.025, respectively. Note that the river bed elevations and flow at both piers are assumed to be the

same; thereby, the estimated scour depths at both locations are equal.

Table 5-4: Estimated mean scour depths (in m)

Flood Return Period Site-1 Site-2 Site-3 Site-4

2-year 2.88 1.71 0.92 1.72

10-year 3.59 2.41 1.60 2.55

20-year 3.82 2.66 1.88 2.79

50-year 4.10 2.96 2.26 3.06

100-year 4.29 3.18 2.56 3.24

5.4 Fragility Analysis

The framework introduced in Chapter 3 is reapplied for the multi-hazard assessment of

characteristic bridges in the present investigation. Seismic performance of the generic bridges is

evaluated in the absence and presence of scour induced by a 100-year flood event. The multi-hazard

conditions attributed to the intermediate flood events (2-year, 10-year, 20-year, 50-year floods) are not

analyzed in the first place for effective use of computational power. Instead, multi-hazard behavior of

79

the bridges is first assessed from a comparison between bridge performance at no scour (i.e., no flood)

and scoured (from 100-year flood) case at each study site.

5.4.1 Modal Behavior of Generic Bridges

Figure 5-7 shows the first four fundamental modes of generic bridges at their original state (i.e.

without scour). Table 5-5 lists the fundamental modal periods of these bridges under no flood and for

100-year flood conditions. Even if there is some difference in modal periods for bridge types A1 and

A2, mode shapes of these two bridges are nearly identical for both scour and no scour conditions.

Figure 5-7: Fundamental mode shapes and modal periods of generic bridges at no flood condition

Longitudinal:

T1=0.774 sec. for Bridge A1

T1=0.657 sec. for Bridge A2

Transverse:

T2=0.539 sec. for Bridge A1

T2=0.484 sec. for Bridge A2

Torsional:

T3=0.344 sec. for Bridge A1

T3=0.337 sec. for Bridge A2

Vertical:

T4=0.327 sec. for Bridge A1

T4=0.325 sec. for Bridge A2

80

Table 5-5: Modal periods of Type A1 and Type A2 bridges

Study

Site

Flood

condition

Max.

pier

scour

Bridge A1 Bridge A2

Long. Trans. Vert. Tors. Long. Trans. Vert. Tors.

No flood - 0.774 0.539 0.327 0.344 0.657 0.484 0.325 0.337

Site-1

100-year

flood 4.29 m 1.054 0.639 0.334 0.356 0.873 0.582 0.331 0.351

Site-2

100-year

flood 3.18 m 0.983 0.617 0.332 0.354 0.821 0.561 0.329 0.348

Site-3

100-year

flood 2.56 m 0.942 0.604 0.331 0.352 0.790 0.548 0.329 0.346

Site-4

100-year

flood 3.24 m 0.987 0.619 0.332 0.354 0.824 0.562 0.329 0.348

As can be examined from Table 5-5, bridge type A2 is more rigid compared to bridge type A1

due to the enlarged shaft cross-section at the substructure of this bridge. Both bridge types become

flexible in the longitudinal and transverse directions with the occurrence of scour, and accordingly

modal periods increases with the occurrence of scour. However, torsional and vertical modal periods

are hardly affected from the occurrence of scour at bridge foundations.

5.4.2 Fragility Curves

Nonlinear time history analyses of bridges A1 and A2 are performed for each study site under

the attributed ground motion datasets. The resulting bridge responses are processed to assess the damage

levels at each critical bridge member, and accordingly component- and system-level fragility curves are

developed. Table 5-6 shows the damage threshold limits accepted for the critical bridge components,

which are determined in accordance with the discussion presented in Chapter 3. It is important to note

here that the bearing damage at minor and moderate damage states is considered here in conjunction

with the unseating failure that leads to the collapse state of bridges as a result of excessive longitudinal

displacement of bridge decks.

81

Table 5-6: Damage threshold limits for the generic bridge Bridge

Component EDP Minor Moderate Major Collapse

Piers Curvature

ductility 0.40.1 0.80.4 0.120.8 0.12

Abutment

Long. def. in

passive direction

(mm)

10435 , plong plong,104 - -

Trans. def. 15050 , plong plong,150 - -

Shear key Trans. def. (mm) 15015 sk sk150 - -

Abutment

bearings

Long. def. (mm) 8640 , longb 31086 , longb 533310 , longb longb,533

Trans. def.(mm) 8640 , transb transb,86 - -

Figure 5-8 and 5-9 show component-level fragility curves of bridge types A1 and A2,

respectively for bridge Site-1. The median values of all component-level and system-level fragility

curves (with an identical dispersion value of 0.6) at all study sites are presented in Table 5-7 and 5-8.

In fragility analyses, no damage is obtained at shear keys and bearings due to the transverse deformation.

Study bridges are observed to have low vulnerability characteristics at higher damage states, as no

collapse state damage case is encountered under the applied ground motion data sets.

As examined from Figure 5-8 and 5-9, abutment bearings are the most vulnerable bridge

components at low damage states. The bridge components at superstructure level are detrimentally

affected by the occurrence of scour at bridge foundations. On the other hand, scour has a beneficial

impact on pier vulnerabilities. Pier fragility curves move to the right from no flood case to 100-year

flood case which signifies that the seismic fragility of bridge piers reduces with scour. This is because

the added flexibility at the foundation level due to scour protects piers from getting under enhanced

curvature deformation, and thus facilitate in reducing pier flexural damage. This type of behavior is

observed for both bridge substructure types, as the enlarged foundation in bridge type A2 is not making

a visible difference compared to the prismatic pier-shaft foundation. Nevertheless, the fragility results

of the enlarged cross-section used in bridge type A2 reveals (Figure 5-9(b)) that the seismic performance

of these components are almost not affected from the occurrence of flood.

82

0.0 0.2 0.4 0.6 0.8 1.0 1.2PGA (g)

0.0

0.2

0.4

0.6

0.8

1.0

Pro

bab

ilit

y o

f E

xce

edin

g a

Dam

age

Sta

te

No flood

100-yr flood

cmin. cmod.

0.448 1.125

0.706 >3.0

Minor Damage

ModerateDamage

0.0 0.2 0.4 0.6 0.8 1.0 1.2

PGA (g)

0.0

0.2

0.4

0.6

0.8

1.0

Pro

bab

ilit

y o

f E

xce

edin

g a

Dam

age

Sta

te

No flood

100-yr flood

cmin. cmod.

0.520 1.083

0.407 0.966

Minor Damage

Moderate Damage

(a) (b)

0.0 0.2 0.4 0.6 0.8 1.0 1.2PGA (g)

0.0

0.2

0.4

0.6

0.8

1.0

Pro

bab

ilit

y o

f E

xce

edin

g a

Dam

age

Sta

te

No flood

100-yr flood

cmin. cmod.

0.786 2.414

0.583 1.899

Minor Damage

ModerateDamage

0.0 0.2 0.4 0.6 0.8 1.0 1.2

PGA (g)

0.0

0.2

0.4

0.6

0.8

1.0

Pro

bab

ilit

y o

f E

xce

edin

g a

Dam

age

Sta

te

No flood

100-yr flood

cmin. cmod.

0.179 0.520

0.131 0.397

MinorDamage

ModerateDamage

(c) (d)

Figure 5-8: Component-level fragility curves of Bridge Type A1 at Site-1 for (a) pier damage, (b)

abutment damage in long. dir. (c) abutment damage in trans. dir. (d) bearing deformation in long. dir.

83

0.0 0.2 0.4 0.6 0.8 1.0 1.2PGA (g)

0.0

0.2

0.4

0.6

0.8

1.0

Pro

babil

ity o

f E

xce

edin

g a

Dam

age

Sta

teNo fl.

100-yr fl.

cmin. cmod.

0.379 1.049

0.580 1.927

MinorDamage Moderate

Damage

0.0 0.2 0.4 0.6 0.8 1.0 1.2

PGA (g)

0.0

0.2

0.4

0.6

0.8

1.0

Pro

babil

ity o

f E

xce

edin

g a

Dam

age

Sta

te

No flood

100-yr flood

cmin.

0.985

1.045

Minor Damage

(a) (b)

0.0 0.2 0.4 0.6 0.8 1.0 1.2PGA (g)

0.0

0.2

0.4

0.6

0.8

1.0

Pro

babil

ity o

f E

xce

edin

g a

Dam

age

Sta

te

No flood

100-yr flood

cmin. cmod.

0.588 1.544

0.474 1.119

Minor Damage

Moderate Damage

0.0 0.2 0.4 0.6 0.8 1.0 1.2

PGA (g)

0.0

0.2

0.4

0.6

0.8

1.0

Pro

babil

ity o

f E

xce

edin

g a

Dam

age

Sta

te

No flood

100-yr flood

cmin. cmod.

0.952 >3.0

0.679 2.414

Minor Damage

Moderate Damage

(c) (d)

0.0 0.2 0.4 0.6 0.8 1.0 1.2PGA (g)

0.0

0.2

0.4

0.6

0.8

1.0

Pro

babil

ity o

f E

xce

edin

g a

Dam

age

Sta

te

No flood

100-yr flood

cmin. cmod.

0.220 0.577

0.141 0.474

MinorDamage

Moderate Damage

(e)

Figure 5-9: Component-level fragility curves of Bridge Type A2 at Site-1 for (a) pier damage, (b)

shaft (enlarged cross-section) damage, (c) abutment damage in long. dir. (d) abutment damage in trans.

dir. (e) bearing deformation in long. dir.

84

The system-level fragility curves of bridge design types A1 and A2 at Site-1 are presented in

Figure 5-10. It can be inferred from this figure that bridge fragility curves are governed by the bearings

at low damage states (i.e. minor and moderate damage states), while piers govern the higher damage

states. This outcome is in well accordance with the observations made in Chapter 3 for real-life bridges.

Fragility curve results reveal that the use of Caltrans type II shafts allows for a slightly higher pier

fragilities (for the portion above the enlarged cross-section), but a reduced overall bridge fragilities.

0.0 0.2 0.4 0.6 0.8 1.0 1.2PGA (g)

0.0

0.2

0.4

0.6

0.8

1.0

Pro

babil

ity o

f E

xce

edin

g a

Dam

age

Sta

te

No flood

100-yr flood

cmin. cmod.

0.179 0.520

0.131 0.396

MinorDamage

ModerateDamage

0.0 0.2 0.4 0.6 0.8 1.0 1.2

PGA (g)

0.0

0.2

0.4

0.6

0.8

1.0

Pro

babil

ity o

f E

xce

edin

g a

Dam

age

Sta

te

No flood

100-yr flood

cmin. cmod.

0.211 0.577

0.141 0.474

MinorDamage

ModerateDamage

(a) (b)

Figure 5-10: System-level fragility curves of (a) Bridge Type A1, and (b) Bridge Type A2 at Site-1

For other bridge sites, fragility analyses of both bridge types are performed for the regional

multi-hazard conditions. Results are presented in Table 5-7 and 5-8, respectively for A1 and A2 type

bridges. As can be observed, a mixed trend in fragilities is observed when results from different sites

are compared (for the same bridge and same flood case). Even though Site-3 has the highest seismic

hazards among all sites, fragility curves of bridges obtained for this site are not necessarily the weakest

when no flood situation is considered. This is because seismic hazard alone cannot fully describe the

seismic response of a bridge under earthquake excitations. On flood hazard case, however, maximum

changes in bridge fragility characteristics from no- to 100-year flood are observed (in majority of cases)

for Site-1 which has the strongest flood hazard curve among all sites. Similarly, the minimum change is

observed for Site-3 in most of the cases. This is fairly obvious as flood hazard curves provide peak flood

discharge (for specific hazard level) which is a direct input for scour calculation. Scour increases with

the increase in peak flood discharge. Although bridge dynamic response may not change (improves or

85

degrades) in a linear fashion with increasing scour depth, it is expected that the trend is not abrupt. That

means, if a positive change is observed in bridge dynamic response due to a change in scour depth from

0 to 1m, the change is not negative (could be zero though) when the depth increases to 2m and beyond.

Overall, bridge multi-hazard behavior under earthquake and flood greatly vary from one site to another

as hazard characteristics are very much region specific.

Table 5-7: Median values for component and system level fragility curves of Bridge Type A1

Bridge

Components

Minor Damage Moderate Damage Major Damage

No Flood 100-year

Flood No Flood

100-year

Flood No Flood

100-year

Flood

Pier Damage

Site-1 0.448 0.706 1.125 >3.0

Site-2 0.426 0.597 1.077 1.855 1.855 2.241

Site-3 0.514 0.659 1.413 1.628 1.782 1.951

Site-4 0.393 0.620 1.104 1.699 1.699 2.447

Abutment Damage in Long.

Dir.

Site-1 0.520 0.407 1.083 0.966

Site-2 0.516 0.419 1.035 0.983

Site-3 0.652 0.615 1.503 1.503

Site-4 0.516 0.436 1.138 1.112

Abutment Damage in Trans.

Dir.

Site-1 0.786 0.583 2.414 1.899

Site-2 0.796 0.640 1.923 1.681

Site-3 0.963 0.732 2.206 1.701

Site-4 0.756 0.618 1.885 1.585

Bearing Deformation in

Long. Dir.

Site-1 0.179 0.131 0.520 0.397

Site-2 0.192 0.141 0.507 0.413 >3.0 2.241

Site-3 0.308 0.297 0.622 0.615 >3.0 1.951

Site-4 0.203 0.164 0.492 0.424 >3.0 2.097

System-Level

Site-1 0.179 0.131 0.520 0.396

Site-2 0.192 0.141 0.507 0.413 1.855 2.241

Site-3 0.290 0.280 0.612 0.605 1.782 1.951

Site-4 0.203 0.164 0.492 0.424 1.699 2.097

86

Table 5-8: Median values for component and system level fragility curves of Bridge Type A2

Bridge

Components

Minor Damage Moderate Damage Major Damage

No Flood 100-year

Flood No Flood

100-year

Flood No Flood

100-year

Flood

Pier Damage

Site-1 0.379 0.580 1.049 1.927

Site-2 0.373 0.512 1.047 1.687 1.855 2.241

Site-3 0.475 0.607 1.349 1.628 1.782 1.951

Site-4 0.339 0.495 1.013 1.427 1.589 2.097

Shaft Damage

Site-1 0.985 1.045

Site-2 0.983 0.945

Site-3 1.293 1.349

Site-4 0.959 1.005

Abutment Damage in Long. Dir.

Site-1 0.588 0.474 1.544 1.119

Site-2 0.596 0.492 1.545 1.035

Site-3 0.687 0.648 1.628 1.503

Site-4 0.591 0.479 1.419 1.138

Abutment Damage in Trans. Dir.

Site-1 0.952 0.679 >3.0 2.414

Site-2 0.921 0.746

Site-3 1.224 0.939 2.684 2.206

Site-4 0.927 0.714 2.097 1.885

Bearing Deformation in Long.

Dir.

Site-1 0.220 0.141 0.577 0.474

Site-2 0.234 0.173 0.586 0.478 >3.0 2.241

Site-3 0.324 0.304 0.687 0.636

Site-4 0.231 0.183 0.582 0.465 >3.0 2.447

System-Level

Site-1 0.211 0.141 0.577 0.474

Site-2 0.226 0.173 0.586 0.478 1.855 2.241

Site-3 0.309 0.294 0.663 0.636 1.782 1.951

Site-4 0.227 0.183 0.582 0.465 1.589 2.097

5.5 Closure

This study showed that scour at bridge foundations has a more dominant impact on bridge

fragilities at low damage states, as bridge fragilities get enhanced with the occurrence of scours. The

increased displacements at bridge deck level directly influences the related bridge components, such as

bearings (including seat width failure), and abutments. However, it is realized that scour has a beneficial

87

influence on bridge piers due to the increased displacements at both foundation and deck level, and at

high damage states scour has an insignificant effect. This may be resembled to a base-isolation case.

Thus, damage which is expected to occur at bridge piers are transferred to other bridge components,

particularly deck level bridge components for the investigated bridge designs herein.

88

CHAPTER 6

CONCLUSIONS

6.1 Summary

Flood-induced scour causes loss of lateral support at bridge foundations. The increased

flexibility of a bridge due to scoured foundations may lead to an increase in the risk of failure under

lateral loading from earthquakes. This dissertation aims to assess the reliability of bridges located in

seismically-active flood-prone regions of the U.S. by quantifying their risks under the multi-hazard

effect of earthquake and flood-induced scour.

The applied methodology is introduced with the analysis of two real-life and two

characteristics river-crossing highway bridges for regional multi-hazard scenarios involving

earthquakes and floods. The real-life bridges, referred to as Bridge-1 and Bridge-2, are located at

different regions in California and constructed at different times. For these two bridge sites, flood

hazard curves are developed through flood frequency analysis and corroborated using the information

presented by FEMA flood insurance studies for the same regions. For a number of flood cases with

varied intensity levels, scour depths are calculated at bridge piers. To observe the combined effect of

various frequency flood and seismic events on performance of these bridges, fragility curves are

generated at component and system levels. It is found that component- and system-level fragilities of

Bridge-1 developed for the multi-hazard scenario is insensitive to regional flood hazard, whereas

fragility curves of Bridge-2 piers gradually weaken with increasing flood hazard level. The same

observation is also made from fragility surfaces and risk curves of these bridges developed for the

same regional multi-hazard conditions.

In order to demonstrate the significance of uncertainty analysis for the multi-hazard

performance assessment of highway bridges, variations in bridge fragility and risk curves are

89

evaluated for Bridge-1, that is already analyzed with mean input parameters. Observations from

tornado diagram and AFOSM reliability analyses performed as part of the sensitivity study indicate

that the compressive strength of concrete, yield strength of reinforcing steel, mass of the bridge,

abutment stiffness and peak friction angle of subsurface soil are the five most significant parameters

that influence the performance of the bridge. Uncertainties involved in the values of soil unit weight,

shear modulus of elastomer and friction coefficient at the PTFE-stainless steel interface are ignored in

the uncertainty analysis due to their insignificant or no impacts on bridge response. Confidence

intervals (90%) of bridge fragility curves obtained through random sampling of critical uncertain

parameters and Monte Carlo simulations show notable variations in bridge fragility characteristics at

various levels of the multi-hazard condition. Scatter in the estimated multi-hazard risk of the study

bridge is observed when uncertainty in bridge fragility characteristics is considered.

Multi-hazard performance of two characteristic bridges located in seismically-active flood-

prone regions is evaluated to comprehend the knowledge-base on this topic. These bridges with

characteristic design features are generated based on the review of bridge inventories in California and

Washington states. Hence, these characteristic bridges statistically represent the most popular type of

bridges constructed in this region. These bridges are assumed to be located at four hazard-critical sites

(with various combinations of seismic and flood hazards) in the West Coast of the U.S. For regional

multi-hazard conditions at these sites, bridge fragility curves are generated. These fragility curves

reveal that the seismic vulnerability of bridge components at superstructure level is amplified due to

the presence of flood-induced scour at bridge foundations, whereas seismic vulnerability of bridge

piers improves with scour. This is because scour helps bridge piers to perform better under earthquake

loading due to concurrent displacement increase at both foundation and deck levels, which is identical

to a base-isolation effect. The increased displacement at deck level of bridges with scour, however,

results in higher damage of bridge components at superstructure level under seismic excitations.

90

6.2 Key Conclusions

The key conclusions as inferred from this dissertation are listed below:

1. Multi-hazard performance of bridges under earthquake and flood-induced scour may

differ for different bridge types, especially for different types of foundations. Bridges

for which scour does not alter foundation flexibility but the exposed height of bridge

piers increases, seismic fragility of those bridges at higher damage states increases

with increasing levels of flood hazard due to magnified pier vulnerabilities. On the

opposite side, when scour has the direct impact on foundation systems, bridge piers

are protected against damage. This case is identical to a base-isolation effect and it

results in reduced pier fragilities under seismic hazard. However, the increased

superstructure level displacements make bridges more seismically vulnerable at low

damage states under the multi-hazard condition. Thus, multi-hazard of earthquakes

and flood-induced scour should not be ignored for satisfying the performance

objectives in regards to bridge serviceability that is directly connected with low

damage states.

2. In reference to the abovementioned discussions, seismic design philosophy adopted

for bridge designs aids in minimizing the impact of regional flood events on the

seismic vulnerability of bridges. It is significant to take this multi-hazard into account

for satisfying both serviceability and ultimate state performance objectives.

3. Risk of bridges under the multi-hazard condition estimated using fragility curves with

50% confidence level can be closely approximated by that calculated using mean

values of all modeling parameters. However, the variation in risk due to parameter

uncertainty and varied flood hazard level cannot be ignored to assure bridge safety

under the stated multi-hazard condition. The reason is that the dispersion of risk

increases due to the presence of flood hazard at the bridge site while the risk itself

decreases with increasing level of multi-hazard.

91

6.3 Significance of the Study

The findings of this dissertation substantially enhance the knowledge-base on risk and

reliability of bridges under the multi-hazard effect of earthquake and flood-induced scour. For the first

time, real-life bridges are analyzed for the evaluation of fragility and risks under this regional multi-

hazard condition. Besides, quantification of uncertainty in the evaluation of multi-hazard risk of

bridges is discussed in a comprehensive manner. Such efforts not only generate new knowledge but

also bring research communities a realistic perspective on this topic. The investigation on multi-hazard

performance of characteristics bridges located at a variety of hazard-critical locations illustrates the

significance of seismic design of bridges that may be exposed to the same multi-hazard condition.

Results from this research help government agencies (e.g. State DOT’s or other federal agencies) to be

aware of this critical multi-hazard and its post-event consequences on bridges. This can lead to an

improved bridge design practice with possible updates of bridge design codes incorporating the effects

of this multi-hazard. Finally, this research can serve as a foundation for future researches and actions

on the development of strategic plans for repair or retrofit prioritization under similar multi-hazard

conditions.

6.4 Recommendations for Future Work

Though this research significantly contributed to develop new knowledge on the multi-hazard

performance of highway bridges under flood and earthquake, there are opportunities to expand the

research further. Potential future work as listed below can be recommended to reinforce the knowledge

gained in this dissertation and to enhance its findings:

The investigation on generic bridges presented in Chapter 5 can be extended to

different other common types of bridges, number of spans, and maximum span

lengths in order to achieve a more general conclusion that is applicable to a wider

range of bridge design alternatives.

92

Uncertainty analysis applied for the real-life bridges as presented in Chapter 4 can be

repeated for generic bridges in order to achieve a generalized outcome on uncertainty

quantification in multi-hazard assessment of bridges.

Reliability calculations can be performed on characteristic bridges under the multi-

hazard of flood-induced scour and earthquake. This could lead to a recommendation

of a design approach to address the combination of flood and earthquake hazard

events that can be incorporated in bridge design codes. The developed methodology

can be applied for different performance objectives, such as failure and serviceability

limit states.

The framework can be used to calculate multi-hazard resilience of bridges that takes

into account the post-event recovery in addition to damage and post-event losses.

93

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100

APPENDIX A

GROUND MOTION RECORDS USED IN TIME HISTORY ANALYSES

Tables A-1 and A-2 show the ground motion (GM) records used in time history analyses of

Bridge-1 and Bridge-2 (investigated in Chapter 3), respectively. Tables A-3 to A-6 present the GM

records employed for the time history analyses of the generic bridges (investigated in Chapter 5) at Site-

1, Site-2, Site-3, and Site-4, respectively. In these tables, ndata, dt, and PGA denote the number of data

points, time increment, and unscaled peak ground acceleration value of a GM record. For all of the GM

records listed in Tables A-3 to A-6, the horizontal components of the records are applied on bridge

models interchangeably.

Table A-1: Ground motion records used for Bridge-1 Analyses

NGA no Earthquake Name Station Information ndata dt PGA

(g) Scale

Comp

onenta

NGA0005

Northwest Calif-01

1938-09-12 06:10 (5.5)

USGS 1023 Ferndale

City Hall 8000 0.005 0.11 1.0 int.

NGA0005

Northwest Calif-01

1938-09-12 06:10 (5.5)

USGS 1023 Ferndale

City Hall 8000 0.005 0.11 2.0 int.

NGA0008

Northern Calif-01

1941-10-03 16:14 (6.4)

USGS 1023 Ferndale

City Hall 7997 0.005 0.11 1.0 int.

NGA0008

Northern Calif-01

1941-10-03 16:14 (6.4)

USGS 1023 Ferndale

City Hall 7997 0.005 0.11 2.0 int.

NGA0011

Northwest Calif-03

1951-10-08 04:11 (5.8)

USGS 1023 Ferndale

City Hall 8000 0.005 0.11 1.0 int.

NGA0011

Northwest Calif-03

1951-10-08 04:11 (5.8)

USGS 1023 Ferndale

City Hall 8000 0.005 0.11 2.0 int.

NGA0016

Northern Calif-02

1952-09-22 11:41 (5.2)

USGS 1023 Ferndale

City Hall 8000 0.005 0.07 2.0 int.

NGA0020

Northern Calif-03

1954-12-21 19:56 (6.5)

USGS 1023 Ferndale

City Hall 7997 0.005 0.19 1.0 int.

NGA0020

Northern Calif-03

1954-12-21 19:56 (6.5)

USGS 1023 Ferndale

City Hall 7997 0.005 0.19 2.0 long.

NGA0025

Northern Calif-04

1960-06-06 01:17 (5.7)

USGS 1023 Ferndale

City Hall 8000 0.005 0.07 2.0 int.

NGA0034

Northern Calif-05

1967-12-10 12:06 (5.6)

USGS 1023 Ferndale

City Hall 8000 0.005 0.19 1.0 int.

NGA0101

Northern Calif-07

1975-06-07 08:46 (5.2)

CDMG 89005 Cape

Mendocino 2921 0.005 0.16 1.0 int.

101

Table A-1: Ground motion records used for Bridge-1 Analyses (Cont’d)

NGA no Earthquake Name Station Information ndata dt PGA Scale Comp

onenta

NGA0101

Northern Calif-07 1975-

06-07 08:46 (5.2)

CDMG 89005 Cape

Mendocino 2921 0.005 0.16 2.0 int.

NGA0102

Northern Calif-07 1975-

06-07 08:46 (5.2)

USGS 1023 Ferndale

City Hall 8000 0.005 0.11 1.0 int.

NGA0102

Northern Calif-07 1975-

06-07 08:46 (5.2)

USGS 1023 Ferndale

City Hall 8000 0.005 0.11 2.0 trans.

NGA0103

Northern Calif-07 1975-

06-07 08:46 (5.2)

CDMG 1398 Petrolia,

General Store 3537 0.005 0.14 1.0 int.

NGA0103

Northern Calif-07 1975-

06-07 08:46 (5.2)

CDMG 1398 Petrolia,

General Store 3537 0.005 0.14 2.0 int.

NGA0105

Northern Calif-07 1975-

06-07 08:46 (5.2)

CDMG 1278 Shelter

Cove, Sta B 3180 0.005 0.08 2.0 int.

NGA0106

Oroville-01 1975-08-01

20:20 (5.89)

CDWR 1051 Oroville

Seismograph Station 2440 0.005 0.08 2.0 int.

NGA0109

Oroville-04 1975-08-02

20:59 (4.37)

CIT 1544 Medical

Center 2500 0.005 0.06 2.0 int.

NGA0111

Oroville-04 1975-08-02

20:59 (4.37)

CDMG 1546 Up &

Down Cafe (OR1) 2200 0.005 0.06 2.0 int.

NGA0112

Oroville-03 1975-08-08

07:00 (4.7)

CIT 1542 Broadbeck

Residence 2728 0.005 0.15 1.0 int.

NGA0112

Oroville-03 1975-08-08

07:00 (4.7)

CIT 1542 Broadbeck

Residence 2728 0.005 0.15 2.0 int.

NGA0113

Oroville-03 1975-08-08

07:00 (4.7) CIT 1543 DWR Garage 2665 0.005 0.20 1.0 int.

NGA0113

Oroville-03 1975-08-08

07:00 (4.7) CIT 1543 DWR Garage 2665 0.005 0.20 2.0 int.

NGA0114

Oroville-03 1975-08-08

07:00 (4.7)

CDMG 1550 Duffy

Residence (OR5) 2400 0.005 0.08 2.0 int.

NGA0115

Oroville-03 1975-08-08

07:00 (4.7)

CDMG 1493 Johnson

Ranch 2623 0.005 0.13 1.0 int.

NGA0115

Oroville-03 1975-08-08

07:00 (4.7)

CDMG 1493 Johnson

Ranch 2623 0.005 0.13 2.0 int.

NGA0116

Oroville-03 1975-08-08

07:00 (4.7)

CDMG 1496 Nelson

Ranch (OR7) 2599 0.005 0.10 2.0 int.

NGA0117

Oroville-03 1975-08-08

07:00 (4.7)

CIT 1545 Oroville

Airport 2711 0.005 0.06 2.0 int.

NGA0118

Oroville-03 1975-08-08

07:00 (4.7)

CDMG 1549 Pacific

Heights Rd (OR4) 2500 0.005 0.07 2.0 int.

NGA0119

Oroville-03 1975-08-08

07:00 (4.7)

CDMG 1551 Summit

Ave (OR6) 2600 0.005 0.10 2.0 int.

NGA0120

Oroville-03 1975-08-08

07:00 (4.7)

CDMG 1546 Up &

Down Cafe (OR1) 2399 0.005 0.12 1.0 int.

NGA0120

Oroville-03 1975-08-08

07:00 (4.7)

CDMG 1546 Up &

Down Cafe (OR1) 2399 0.005 0.12 2.0 int.

NGA0280

Trinidad 1980-11-08

10:27 (7.2)

CDMG 89324 Rio Dell

Overpass - FF 3934 0.005 0.10 2.0 int.

102

Table A-1: Ground motion records used for Bridge-1 Analyses (Cont’d)

NGA no Earthquake Name Station Information ndata dt PGA Scale Comp

onenta

NGA0281

Trinidad 1980-11-08

10:27 (7.2)

CDMG 89324 Rio Dell

Overpass, E Ground 4397 0.005 0.15 1.0 int.

NGA0281

Trinidad 1980-11-08

10:27 (7.2)

CDMG 89324 Rio Dell

Overpass, E Ground 4397 0.005 0.15 2.0 int.

NGA0282

Trinidad 1980-11-08

10:27 (7.2)

CDMG 89324 Rio Dell

Overpass, W Ground 4397 0.005 0.15 1.0 int.

NGA0282

Trinidad 1980-11-08

10:27 (7.2)

CDMG 89324 Rio Dell

Overpass, W Ground 4397 0.005 0.15 2.0 int.

NGA0421

Trinidad offshore 1983-

08-24 13:36 (5.7)

CDMG 89324 Rio Dell

Overpass, E Ground 4289 0.005 0.16 1.0 int.

NGA0421

Trinidad offshore 1983-

08-24 13:36 (5.7)

CDMG 89324 Rio Dell

Overpass, E Ground 4289 0.005 0.16 2.0 int.

NGA0422

Trinidad offshore 1983-

08-24 13:36 (5.7)

CDMG 89324 Rio Dell

Overpass, W Ground 4289 0.005 0.13 1.0 int.

NGA0422

Trinidad offshore 1983-

08-24 13:36 (5.7)

CDMG 89324 Rio Dell

Overpass, W Ground 4289 0.005 0.13 2.0 int.

NGA0825

Cape Mendocino 1992-

04-25 18:06 (7.01)

CDMG 89005 Cape

Mendocino 1500 0.02 1.35 2.0 int.

NGA0826

Cape Mendocino 1992-

04-25 18:06 (7.01)

CDMG 89509 Eureka -

Myrtle & West 2200 0.02 0.17 1.0 int.

NGA0826

Cape Mendocino 1992-

04-25 18:06 (7.01)

CDMG 89509 Eureka -

Myrtle & West 2200 0.02 0.17 2.0 int.

NGA0827

Cape Mendocino 1992-

04-25 18:06 (7.01)

CDMG 89486 Fortuna -

Fortuna Blvd 2200 0.02 0.12 1.0 int.

NGA0827

Cape Mendocino 1992-

04-25 18:06 (7.01)

CDMG 89486 Fortuna -

Fortuna Blvd 2200 0.02 0.12 2.0 int.

NGA0828

Cape Mendocino 1992-

04-25 18:06 (7.01) CDMG 89156 Petrolia 1800 0.02 0.62 1.0 int.

NGA0828

Cape Mendocino 1992-

04-25 18:06 (7.01) CDMG 89156 Petrolia 1800 0.02 0.62 2.0 int.

NGA0829

Cape Mendocino 1992-

04-25 18:06 (7.01)

CDMG 89324 Rio Dell

Overpass - FF 1800 0.02 0.42 1.0 trans.

NGA0829

Cape Mendocino 1992-

04-25 18:06 (7.01)

CDMG 89324 Rio Dell

Overpass - FF 1800 0.02 0.42 2.0 int.

NGA0830

Cape Mendocino 1992-

04-25 18:06 (7.01)

CDMG 89530 Shelter

Cove Airport 1800 0.02 0.20 1.0 int.

NGA0830

Cape Mendocino 1992-

04-25 18:06 (7.01)

CDMG 89530 Shelter

Cove Airport 1800 0.02 0.20 2.0 int. a The horizontal components of a GM record are applied on the orthogonal directions of a bridge model as

follows:

int.: Two analyses are performed by interchanging the components of the record.

long.: The first component of the GM record (as listed in NGA database) is applied on the longitudinal direction

of a bridge model, and the second component is applied on the transverse direction.

trans.: The first component of the GM record is applied on the transverse direction of a bridge model, and the

second component is applied on the longitudinal direction.

103

Table A-2: Ground motion records used for Bridge-2 Analyses

NGA no Earthquake Name Station Information ndata dt PGA Scale Comp

onenta

NGA0026

Hollister-01 1961-04-

09 07:23 (5.6)

USGS 1028 Hollister

City Hall 8000 0.005 0.121 1.0 int.

NGA0026

Hollister-01 1961-04-

09 07:23 (5.6)

USGS 1028 Hollister

City Hall 8000 0.005 0.121 2.0 trans.

NGA0099

Hollister-03 1974-11-

28 23:01 (5.14)

USGS 1028 Hollister

City Hall 6606 0.005 0.14 1.0 int.

NGA0099

Hollister-03 1974-11-

28 23:01 (5.14)

USGS 1028 Hollister

City Hall 6606 0.005 0.14 2.0 trans.

NGA0147

Coyote Lake 1979-08-

06 17:05 (5.74)

CDMG 47380 Gilroy

Array #2 5372 0.005 0.29 1.0 int.

NGA0147

Coyote Lake 1979-08-

06 17:05 (5.74)

CDMG 47380 Gilroy

Array #2 5372 0.005 0.29 2.0 trans.

NGA0148

Coyote Lake 1979-08-

06 17:05 (5.74)

CDMG 47381 Gilroy

Array #3 5361 0.005 0.26 1.0 int.

NGA0149

Coyote Lake 1979-08-

06 17:05 (5.74)

CDMG 57382 Gilroy

Array #4 5437 0.005 0.27 1.0 int.

NGA0212

Livermore-01 1980-01-

24 19:00 (5.8)

CDWR 1265 Del Valle

Dam (Toe) 6201 0.005 0.17 1.0 int.

NGA0212

Livermore-01 1980-01-

24 19:00 (5.8)

CDWR 1265 Del Valle

Dam (Toe) 6201 0.005 0.17 2.0 int.

NGA0214

Livermore-01 1980-01-

24 19:00 (5.8)

CDMG 57187 San

Ramon - Eastman Kodak 4196 0.005 0.11 1.0 int.

NGA0214

Livermore-01 1980-01-

24 19:00 (5.8)

CDMG 57187 San

Ramon - Eastman Kodak 4196 0.005 0.11 2.0 int.

NGA0221

Livermore-02 1980-01-

27 02:33 (5.42)

CDMG 57T01

Livermore - Fagundas

Ranch 4000 0.005 0.24 1.0 int.

NGA0223

Livermore-02 1980-01-

27 02:33 (5.42)

CDMG 57187 San

Ramon - Eastman Kodak 4337 0.005 0.19 1.0 int.

NGA0322

Coalinga-01 1983-05-

02 23:42 (6.36)

CDMG 46314 Cantua

Creek School 4000 0.01 0.28 1.0 int.

NGA0449

Morgan Hill 1984-04-

24 21:15 (6.19) CDMG 47125 Capitola 7200 0.005 0.12 1.0 int.

NGA0449

Morgan Hill 1984-04-

24 21:15 (6.19) CDMG 47125 Capitola 7200 0.005 0.12 2.0 long.

NGA0456

Morgan Hill 1984-04-

24 21:15 (6.19)

CDMG 47380 Gilroy

Array #2 5996 0.005 0.19 1.0 int.

NGA0456

Morgan Hill 1984-04-

24 21:15 (6.19)

CDMG 47380 Gilroy

Array #2 5996 0.005 0.19 2.0 int.

NGA0457

Morgan Hill 1984-04-

24 21:15 (6.19)

CDMG 47381 Gilroy

Array #3 7996 0.005 0.19 1.0 int.

NGA0457

Morgan Hill 1984-04-

24 21:15 (6.19)

CDMG 47381 Gilroy

Array #3 7996 0.005 0.19 2.0 int.

NGA0458

Morgan Hill 1984-04-

24 21:15 (6.19)

CDMG 57382 Gilroy

Array #4 7996 0.005 0.28 1.0 int.

NGA0458

Morgan Hill 1984-04-

24 21:15 (6.19)

CDMG 57382 Gilroy

Array #4 7996 0.005 0.28 2.0 int.

104

Table A-2: Ground motion records used for Bridge-2 Analyses (Cont’d)

NGA no Earthquake Name Station Information ndata dt PGA Scale Compo

nenta

NGA0460

Morgan Hill 1984-04-

24 21:15 (6.19)

CDMG 57425 Gilroy

Array #7 5996 0.005 0.14 1.0 int.

NGA0460

Morgan Hill 1984-04-

24 21:15 (6.19)

CDMG 57425 Gilroy

Array #7 5996 0.005 0.14 2.0 int.

NGA0461

Morgan Hill 1984-04-

24 21:15 (6.19)

CDMG 57191 Halls

Valley 7996 0.005 0.21 1.0 long.

NGA0465

Morgan Hill 1984-04-

24 21:15 (6.19)

USGS 1656 Hollister

Diff Array #4 7997 0.005 0.10 1.0 int.

NGA0465

Morgan Hill 1984-04-

24 21:15 (6.19)

USGS 1656 Hollister

Diff Array #4 7997 0.005 0.10 2.0 int.

NGA0498

Hollister-04 1986-01-

26 19:20 (5.45)

USGS 1656 Hollister

Diff Array #1 8000 0.005 0.11 1.0 int.

NGA0498

Hollister-04 1986-01-

26 19:20 (5.45)

USGS 1656 Hollister

Diff Array #1 8000 0.005 0.11 2.0 int.

NGA0499

Hollister-04 1986-01-

26 19:20 (5.45)

USGS 1656 Hollister

Diff Array #3 8000 0.005 0.10 1.0 int.

NGA0499

Hollister-04 1986-01-

26 19:20 (5.45)

USGS 1656 Hollister

Diff Array #3 8000 0.005 0.10 2.0 int.

NGA0502

Mt. Lewis 1986-03-31

11:55 (5.6)

CDMG 57191 Halls

Valley 7999 0.005 0.16 1.0 int.

NGA0502

Mt. Lewis 1986-03-31

11:55 (5.6)

CDMG 57191 Halls

Valley 7999 0.005 0.16 2.0 long.

NGA0732

Loma Prieta 1989-10-

18 00:05 (6.93)

USGS 1002 APEEL 2 -

Redwood City 7165 0.005 0.25 1.0 int.

NGA0732

Loma Prieta 1989-10-

18 00:05 (6.93)

USGS 1002 APEEL 2 -

Redwood City 7165 0.005 0.25 2.0 trans.

NGA0733

Loma Prieta 1989-10-

18 00:05 (6.93)

CDMG 58393 APEEL

2E Hayward Muir Sch 7990 0.005 0.17 1.0 int.

NGA0733

Loma Prieta 1989-10-

18 00:05 (6.93)

CDMG 58393 APEEL

2E Hayward Muir Sch 7990 0.005 0.17 2.0 int.

NGA0737

Loma Prieta 1989-10-

18 00:05 (6.93)

CDMG 57066 Agnews

State Hospital 8000 0.005 0.15 1.0 int.

NGA0737

Loma Prieta 1989-10-

18 00:05 (6.93)

CDMG 57066 Agnews

State Hospital 8000 0.005 0.15 2.0 int.

NGA0738

Loma Prieta 1989-10-

18 00:05 (6.93)

USN 99999 Alameda

Naval Air Stn Hanger 5916 0.005 0.24 1.0 int.

NGA0743

Loma Prieta 1989-10-

18 00:05 (6.93)

USGS 1479 Bear Valley

#10, Webb Residence 7969 0.005 0.10 1.0 int.

NGA0743

Loma Prieta 1989-10-

18 00:05 (6.93)

USGS 1479 Bear Valley

#10, Webb Residence 7969 0.005 0.10 2.0 int.

NGA0744

Loma Prieta 1989-10-

18 00:05 (6.93)

USGS 1481 Bear Valley

#12, Williams Ranch 7816 0.005 0.16 1.0 int.

NGA0744

Loma Prieta 1989-10-

18 00:05 (6.93)

USGS 1481 Bear Valley

#12, Williams Ranch 7816 0.005 0.16 2.0 int.

NGA0752

Loma Prieta 1989-10-

18 00:05 (6.93) CDMG 47125 Capitola 7991 0.005 0.48 1.0 long.

105

Table A-2: Ground motion records used for Bridge-2 Analyses (Cont’d)

NGA no Earthquake Name Station Information ndata dt PGA Scale Comp

onenta

NGA0754

Loma Prieta 1989-10-

18 00:05 (6.93)

CDMG 57504 Coyote

Lake Dam (Downst) 7990 0.005 0.17 1.0 int.

NGA0754

Loma Prieta 1989-10-

18 00:05 (6.93)

CDMG 57504 Coyote

Lake Dam (Downst) 7990 0.005 0.17 2.0 trans.

NGA0757

Loma Prieta 1989-10-

18 00:05 (6.93)

CDMG 58664

Dumbarton Bridge West

End FF 3250 0.02 0.13 1.0 int.

NGA0757

Loma Prieta 1989-10-

18 00:05 (6.93)

CDMG 58664

Dumbarton Bridge West

End FF 3250 0.02 0.13 2.0 long.

NGA0758

Loma Prieta 1989-10-

18 00:05 (6.93)

USGS 1662 Emeryville -

6363 Christie 7841 0.005 0.25 1.0 int.

NGA0758

Loma Prieta 1989-10-

18 00:05 (6.93)

USGS 1662 Emeryville -

6363 Christie 7841 0.005 0.25 2.0 trans.

NGA0759

Loma Prieta 1989-10-

18 00:05 (6.93)

CDMG 58375 Foster

City - APEEL 1 11999 0.005 0.29 1.0 int.

NGA0760

Loma Prieta 1989-10-

18 00:05 (6.93)

USGS 1515 Foster City -

Menhaden Court 6005 0.005 0.10 1.0 int.

NGA0760

Loma Prieta 1989-10-

18 00:05 (6.93)

USGS 1515 Foster City -

Menhaden Court 6005 0.005 0.10 2.0 int.

NGA0761

Loma Prieta 1989-10-

18 00:05 (6.93)

USGS 1686 Fremont -

Emerson Court 7949 0.005 0.17 1.0 int.

NGA0761

Loma Prieta 1989-10-

18 00:05 (6.93)

USGS 1686 Fremont -

Emerson Court 7949 0.005 0.17 2.0 int.

NGA0764

Loma Prieta 1989-10-

18 00:05 (6.93)

CDMG 57476 Gilroy -

Historic Bldg. 7991 0.005 0.26 1.0 int.

NGA0766

Loma Prieta 1989-10-

18 00:05 (6.93)

CDMG 47380 Gilroy

Array #2 7990 0.005 0.35 1.0 int.

NGA0767

Loma Prieta 1989-10-

18 00:05 (6.93)

CDMG 47381 Gilroy

Array #3 7989 0.005 0.46 1.0 long.

NGA0768

Loma Prieta 1989-10-

18 00:05 (6.93)

CDMG 57382 Gilroy

Array #4 7990 0.005 0.30 1.0 long.

NGA0770

Loma Prieta 1989-10-

18 00:05 (6.93)

CDMG 57425 Gilroy

Array #7 7990 0.005 0.31 1.0 trans.

NGA0772

Loma Prieta 1989-10-

18 00:05 (6.93)

CDMG 57191 Halls

Valley 7990 0.005 0.12 1.0 int.

NGA0772

Loma Prieta 1989-10-

18 00:05 (6.93)

CDMG 57191 Halls

Valley 7990 0.005 0.12 2.0 int.

NGA0777

Loma Prieta 1989-10-

18 00:05 (6.93)

USGS 1028 Hollister

City Hall 7818 0.005 0.23 1.0 int.

NGA0778

Loma Prieta 1989-10-

18 00:05 (6.93)

USGS 1656 Hollister

Diff. Array 7928 0.005 0.26 1.0 int.

NGA0780

Loma Prieta 1989-10-

18 00:05 (6.93)

USGS 1590 Larkspur

Ferry Terminal (FF) 7803 0.005 0.12 1.0 int.

NGA0780

Loma Prieta 1989-10-

18 00:05 (6.93)

USGS 1590 Larkspur

Ferry Terminal (FF) 7803 0.005 0.12 2.0 int.

NGA0783

Loma Prieta 1989-10-

18 00:05 (6.93)

CDMG 58472 Oakland -

Outer Harbor Wharf 2000 0.02 0.28 1.0 int.

106

Table A-2: Ground motion records used for Bridge-2 Analyses (Cont’d)

NGA no Earthquake Name Station Information ndata dt PGA Scale Comp

onenta

NGA0784

Loma Prieta 1989-10-

18 00:05 (6.93)

CDMG 58224 Oakland -

Title & Trust 7990 0.005 0.20 1.0 int.

NGA0785

Loma Prieta 1989-10-

18 00:05 (6.93)

CDMG 68003 Olema -

Point Reyes Station 2000 0.02 0.13 1.0 int.

NGA0785

Loma Prieta 1989-10-

18 00:05 (6.93)

CDMG 68003 Olema -

Point Reyes Station 2000 0.02 0.13 2.0 int.

NGA0786

Loma Prieta 1989-10-

18 00:05 (6.93)

CDMG 58264 Palo Alto

- 1900 Embarc. 8000 0.005 0.21 1.0 int.

NGA0790

Loma Prieta 1989-10-

18 00:05 (6.93)

CDMG 58505 Richmond

City Hall 7989 0.005 0.13 1.0 int.

NGA0790

Loma Prieta 1989-10-

18 00:05 (6.93)

CDMG 58505 Richmond

City Hall 7989 0.005 0.13 2.0 int.

NGA0799

Loma Prieta 1989-10-

18 00:05 (6.93)

CDMG 58223 SF Intern.

Airport 7990 0.005 0.28 1.0 int.

NGA0800

Loma Prieta 1989-10-

18 00:05 (6.93)

CDMG 47179 Salinas -

John & Work 7990 0.005 0.10 1.0 int.

NGA0800

Loma Prieta 1989-10-

18 00:05 (6.93)

CDMG 47179 Salinas -

John & Work 7990 0.005 0.10 2.0 int.

NGA0806

Loma Prieta 1989-10-

18 00:05 (6.93)

USGS 1695 Sunnyvale -

Colton Ave. 7850 0.005 0.21 1.0 int.

NGA0806

Loma Prieta 1989-10-

18 00:05 (6.93)

USGS 1695 Sunnyvale -

Colton Ave. 7850 0.005 0.21 2.0 trans.

NGA0808

Loma Prieta 1989-10-

18 00:05 (6.93)

CDMG 58117 Treasure

Island 7991 0.005 0.13 1.0 int.

NGA0808

Loma Prieta 1989-10-

18 00:05 (6.93)

CDMG 58117 Treasure

Island 7991 0.005 0.13 2.0 trans.

NGA1622

Stone Canyon 1972-09-

04

USGS 1210 Bear Valley

#1, Fire Station 1063 0.02 0.13 1.0 int.

NGA1622

Stone Canyon 1972-09-

04

USGS 1210 Bear Valley

#1, Fire Station 1063 0.02 0.13 2.0 int.

NGA1866 Yountville 2000-09-03

USGS 1761 Sonoma

Fire Station #1 12200 0.005 0.15 1.0 int.

NGA1866 Yountville 2000-09-03

USGS 1761 Sonoma

Fire Station #1 12200 0.005 0.15 2.0 int.

NGA2020 Gilroy 2002-05-14

CDMG 47381 Gilroy

Array #3 5200 0.01 0.16 1.0 int.

NGA2020 Gilroy 2002-05-14

CDMG 47381 Gilroy

Array #3 5200 0.01 0.16 2.0 int. a The horizontal components of a GM record are applied on the orthogonal directions of a bridge model as

follows:

int.: Two analyses are performed by interchanging the components of the record.

long.: The first component of the GM record (as listed in NGA database) is applied on the longitudinal direction

of a bridge model, and the second component is applied on the transverse direction.

trans.: The first component of the GM record is applied on the transverse direction of a bridge model, and the

second component is applied on the longitudinal direction.

107

Table A-3: Ground motion records used for the generic bridges at Site-1

NGA no Earthquake Name Station Information ndata dt PGA Scaleb

NGA0147

Coyote Lake 1979-08-06

17:05 (5.74)

CDMG 47380 Gilroy Array

#2 5372 0.005 0.29 1.0 2.0

NGA0458

Morgan Hill 1984-04-24

21:15 (6.19)

CDMG 57382 Gilroy Array

#4 7996 0.005 0.28 1.0 2.0

NGA0459

Morgan Hill 1984-04-24

21:15 (6.19)

CDMG 57383 Gilroy Array

#6 5996 0.005 0.28 1.0 2.0

NGA0733

Loma Prieta 1989-10-18

00:05 (6.93)

CDMG 58393 APEEL 2E

Hayward Muir Sch 7990 0.005 0.17 1.0 2.0

NGA0735

Loma Prieta 1989-10-18

00:05 (6.93)

CDMG 58378 APEEL 7 -

Pulgas 7990 0.005 0.12 1.0 -

NGA0737

Loma Prieta 1989-10-18

00:05 (6.93)

CDMG 57066 Agnews State

Hospital 8000 0.005 0.15 - 2.0

NGA0738

Loma Prieta 1989-10-18

00:05 (6.93)

USN 99999 Alameda Naval

Air Stn Hanger 5916 0.005 0.24 1.0 2.0

NGA0739

Loma Prieta 1989-10-18

00:05 (6.93)

USGS 1652 Anderson Dam

(Downstream) 7921 0.005 0.24 1.0 2.0

NGA0748

Loma Prieta 1989-10-18

00:05 (6.93)

CDMG 58262 Belmont -

Envirotech 7989 0.005 0.12 1.0 -

NGA0752

Loma Prieta 1989-10-18

00:05 (6.93) CDMG 47125 Capitola 7991 0.005 0.48 1.0 2.0

NGA0754

Loma Prieta 1989-10-18

00:05 (6.93)

CDMG 57504 Coyote Lake

Dam (Downst) 7990 0.005 0.17 - 2.0

NGA0755

Loma Prieta 1989-10-18

00:05 (6.93)

CDMG 57217 Coyote Lake

Dam (SW Abut) 7991 0.005 0.29 1.0 2.0

NGA0757

Loma Prieta 1989-10-18

00:05 (6.93)

CDMG 58664 Dumbarton

Bridge West End FF 3250 0.02 0.13 1.0 -

NGA0758

Loma Prieta 1989-10-18

00:05 (6.93)

USGS 1662 Emeryville -

6363 Christie 7841 0.005 0.25 1.0 2.0

NGA0761

Loma Prieta 1989-10-18

00:05 (6.93)

USGS 1686 Fremont -

Emerson Court 7949 0.005 0.17 1.0 2.0

NGA0762

Loma Prieta 1989-10-18

00:05 (6.93)

CDMG 57064 Fremont -

Mission San Jose 7990 0.005 0.13 1.0 -

NGA0763

Loma Prieta 1989-10-18

00:05 (6.93)

CDMG 47006 Gilroy -

Gavilan Coll. 7991 0.005 0.33 1.0 2.0

NGA0764

Loma Prieta 1989-10-18

00:05 (6.93)

CDMG 57476 Gilroy -

Historic Bldg. 7991 0.005 0.26 1.0 2.0

NGA0766

Loma Prieta 1989-10-18

00:05 (6.93)

CDMG 47380 Gilroy Array

#2 7990 0.005 0.35 1.0 2.0

NGA0767

Loma Prieta 1989-10-18

00:05 (6.93)

CDMG 47381 Gilroy Array

#3 7989 0.005 0.46 1.0 2.0

NGA0768

Loma Prieta 1989-10-18

00:05 (6.93)

CDMG 57382 Gilroy Array

#4 7990 0.005 0.30 1.0 2.0

NGA0769

Loma Prieta 1989-10-18

00:05 (6.93)

CDMG 57383 Gilroy Array

#6 7991 0.005 0.16 - 2.0

NGA0770

Loma Prieta 1989-10-18

00:05 (6.93)

CDMG 57425 Gilroy Array

#7 7990 0.005 0.31 1.0 2.0

108

Table A-3: Ground motion records used for the generic bridges at Site-1 (Cont’d)

NGA no Earthquake Name Station Information ndata dt PGA Scaleb

NGA0771

Loma Prieta 1989-10-18

00:05 (6.93)

USGS 1678 Golden Gate

Bridge 7615 0.005 0.16 1.0 2.0

NGA0773

Loma Prieta 1989-10-18

00:05 (6.93)

CDMG 58498 Hayward -

BART Sta 7990 0.005 0.16 1.0 2.0

NGA0783

Loma Prieta 1989-10-18

00:05 (6.93)

CDMG 58472 Oakland -

Outer Harbor Wharf 2000 0.02 0.28 1.0 2.0

NGA0784

Loma Prieta 1989-10-18

00:05 (6.93)

CDMG 58224 Oakland - Title

& Trust 7990 0.005 0.20 1.0 2.0

NGA0785

Loma Prieta 1989-10-18

00:05 (6.93)

CDMG 68003 Olema - Point

Reyes Station 2000 0.02 0.13 1.0 -

NGA0786

Loma Prieta 1989-10-18

00:05 (6.93)

CDMG 58264 Palo Alto -

1900 Embarc. 8000 0.005 0.21 1.0 2.0

NGA0787

Loma Prieta 1989-10-18

00:05 (6.93)

USGS 1601 Palo Alto -

SLAC Lab 7915 0.005 0.23 1.0 2.0

NGA0790

Loma Prieta 1989-10-18

00:05 (6.93)

CDMG 58505 Richmond

City Hall 7989 0.005 0.13 1.0 -

NGA0794

Loma Prieta 1989-10-18

00:05 (6.93)

CDMG 58130 SF - Diamond

Heights 7989 0.005 0.10 1.0 -

NGA0796

Loma Prieta 1989-10-18

00:05 (6.93) CDMG 58222 SF - Presidio 7990 0.005 0.14 1.0 -

NGA0799

Loma Prieta 1989-10-18

00:05 (6.93)

CDMG 58223 SF Intern.

Airport 7990 0.005 0.28 1.0 2.0

NGA0801

Loma Prieta 1989-10-18

00:05 (6.93)

CDMG 57563 San Jose -

Santa Teresa Hills 2501 0.02 0.28 1.0 2.0

NGA0803

Loma Prieta 1989-10-18

00:05 (6.93)

CDMG 58235 Saratoga - W

Valley Coll. 7990 0.005 0.31 1.0 2.0

NGA0806

Loma Prieta 1989-10-18

00:05 (6.93)

USGS 1695 Sunnyvale -

Colton Ave. 7850 0.005 0.21 1.0 2.0

NGA0809

Loma Prieta 1989-10-18

00:05 (6.93) UCSC 15 UCSC 5001 0.005 0.34 1.0 2.0

NGA0810

Loma Prieta 1989-10-18

00:05 (6.93)

CDMG 58135 UCSC Lick

Observatory 7990 0.005 0.46 1.0 2.0

NGA0811

Loma Prieta 1989-10-18

00:05 (6.93) UCSC 14 WAHO 5001 0.005 0.52 1.0 2.0

NGA0826

Cape Mendocino 1992-04-

25 18:06 (7.01)

CDMG 89509 Eureka -

Myrtle & West 2200 0.02 0.17 1.0 2.0

NGA0827

Cape Mendocino 1992-04-

25 18:06 (7.01)

CDMG 89486 Fortuna -

Fortuna Blvd 2200 0.02 0.12 1.0 -

NGA0830

Cape Mendocino 1992-04-

25 18:06 (7.01)

CDMG 89530 Shelter Cove

Airport 1800 0.02 0.20 1.0 2.0 b Time history analyses are performed for the GM records with the scale factor indicated in the table.

109

Table A-4: Ground motion records used for the generic bridges at Site-2

NGA no Earthquake Name Station Information ndata dt PGA Scaleb

NGA0147

Coyote Lake 1979-08-06

17:05 (5.74)

CDMG 47380 Gilroy Array

#2 5372 0.005 0.29 1.0 2.0

NGA0154

Coyote Lake 1979-08-06

17:05 (5.74)

CDMG 47126 San Juan

Bautista, 24 Polk St 5692 0.005 0.10 1.0 -

NGA0454

Morgan Hill 1984-04-24

21:15 (6.19)

CDMG 47006 Gilroy -

Gavilan Coll. 5996 0.005 0.10 1.0 -

NGA0456

Morgan Hill 1984-04-24

21:15 (6.19)

CDMG 47380 Gilroy Array

#2 5996 0.005 0.19 1.0 2.0

NGA0457

Morgan Hill 1984-04-24

21:15 (6.19)

CDMG 47381 Gilroy Array

#3 7996 0.005 0.19 1.0 2.0

NGA0458

Morgan Hill 1984-04-24

21:15 (6.19)

CDMG 57382 Gilroy Array

#4 7996 0.005 0.28 1.0 2.0

NGA0459

Morgan Hill 1984-04-24

21:15 (6.19)

CDMG 57383 Gilroy Array

#6 5996 0.005 0.28 1.0 2.0

NGA0460

Morgan Hill 1984-04-24

21:15 (6.19)

CDMG 57425 Gilroy Array

#7 5996 0.005 0.14 1.0 -

NGA0465

Morgan Hill 1984-04-24

21:15 (6.19)

USGS 1656 Hollister Diff

Array #4 7997 0.005 0.10 1.0 -

NGA0733

Loma Prieta 1989-10-18

00:05 (6.93)

CDMG 58393 APEEL 2E

Hayward Muir Sch 7990 0.005 0.17 1.0 2.0

NGA0737

Loma Prieta 1989-10-18

00:05 (6.93)

CDMG 57066 Agnews State

Hospital 8000 0.005 0.15 1.0 2.0

NGA0739

Loma Prieta 1989-10-18

00:05 (6.93)

USGS 1652 Anderson Dam

(Downstream) 7921 0.005 0.24 1.0 2.0

NGA0744

Loma Prieta 1989-10-18

00:05 (6.93)

USGS 1481 Bear Valley #12,

Williams Ranch 7816 0.005 0.16 2.0 -

NGA0752

Loma Prieta 1989-10-18

00:05 (6.93) CDMG 47125 Capitola 7991 0.005 0.48 1.0 2.0

NGA0754

Loma Prieta 1989-10-18

00:05 (6.93)

CDMG 57504 Coyote Lake

Dam (Downst) 7990 0.005 0.17 1.0 2.0

NGA0755

Loma Prieta 1989-10-18

00:05 (6.93)

CDMG 57217 Coyote Lake

Dam (SW Abut) 7991 0.005 0.29 1.0 2.0

NGA0757

Loma Prieta 1989-10-18

00:05 (6.93)

CDMG 58664 Dumbarton

Bridge West End FF 3250 0.02 0.13 1.0 -

NGA0758

Loma Prieta 1989-10-18

00:05 (6.93)

USGS 1662 Emeryville -

6363 Christie 7841 0.005 0.25 1.0 2.0

NGA0761

Loma Prieta 1989-10-18

00:05 (6.93)

USGS 1686 Fremont -

Emerson Court 7949 0.005 0.17 1.0 2.0

NGA0762

Loma Prieta 1989-10-18

00:05 (6.93)

CDMG 57064 Fremont -

Mission San Jose 7990 0.005 0.13 1.0 -

NGA0763

Loma Prieta 1989-10-18

00:05 (6.93)

CDMG 47006 Gilroy -

Gavilan Coll. 7991 0.005 0.33 1.0 2.0

NGA0764

Loma Prieta 1989-10-18

00:05 (6.93)

CDMG 57476 Gilroy -

Historic Bldg. 7991 0.005 0.26 1.0 2.0

110

Table A-4: Ground motion records used for the generic bridges at Site-2 (Cont’d)

NGA no Earthquake Name Station Information ndata dt PGA Scaleb

NGA0766

Loma Prieta 1989-10-18

00:05 (6.93)

CDMG 47380 Gilroy Array

#2 7990 0.005 0.35 1.0 2.0

NGA0767

Loma Prieta 1989-10-18

00:05 (6.93)

CDMG 47381 Gilroy Array

#3 7989 0.005 0.46 1.0 2.0

NGA0768

Loma Prieta 1989-10-18

00:05 (6.93)

CDMG 57382 Gilroy Array

#4 7990 0.005 0.30 1.0 2.0

NGA0769

Loma Prieta 1989-10-18

00:05 (6.93)

CDMG 57383 Gilroy Array

#6 7991 0.005 0.16 1.0 2.0

NGA0770

Loma Prieta 1989-10-18

00:05 (6.93)

CDMG 57425 Gilroy Array

#7 7990 0.005 0.31 1.0 2.0

NGA0772

Loma Prieta 1989-10-18

00:05 (6.93) CDMG 57191 Halls Valley 7990 0.005 0.12 1.0 -

NGA0773

Loma Prieta 1989-10-18

00:05 (6.93)

CDMG 58498 Hayward -

BART Sta 7990 0.005 0.16 1.0 2.0

NGA0776

Loma Prieta 1989-10-18

00:05 (6.93)

CDMG 47524 Hollister -

South & Pine 11991 0.005 0.28 1.0 2.0

NGA0777

Loma Prieta 1989-10-18

00:05 (6.93)

USGS 1028 Hollister City

Hall 7818 0.005 0.23 1.0 2.0

NGA0778

Loma Prieta 1989-10-18

00:05 (6.93)

USGS 1656 Hollister Diff.

Array 7928 0.005 0.26 1.0 2.0

NGA0784

Loma Prieta 1989-10-18

00:05 (6.93)

CDMG 58224 Oakland - Title

& Trust 7990 0.005 0.20 1.0 2.0

NGA0786

Loma Prieta 1989-10-18

00:05 (6.93)

CDMG 58264 Palo Alto -

1900 Embarc. 8000 0.005 0.21 1.0 2.0

NGA0787

Loma Prieta 1989-10-18

00:05 (6.93)

USGS 1601 Palo Alto -

SLAC Lab 7915 0.005 0.23 1.0 2.0

NGA0801

Loma Prieta 1989-10-18

00:05 (6.93)

CDMG 57563 San Jose -

Santa Teresa Hills 2501 0.02 0.28 1.0 2.0

NGA0803

Loma Prieta 1989-10-18

00:05 (6.93)

CDMG 58235 Saratoga - W

Valley Coll. 7990 0.005 0.31 1.0 2.0

NGA0806

Loma Prieta 1989-10-18

00:05 (6.93)

USGS 1695 Sunnyvale -

Colton Ave. 7850 0.005 0.21 1.0 2.0

NGA0809

Loma Prieta 1989-10-18

00:05 (6.93) UCSC 15 UCSC 5001 0.005 0.34 1.0 2.0

NGA0810

Loma Prieta 1989-10-18

00:05 (6.93)

CDMG 58135 UCSC Lick

Observatory 7990 0.005 0.46 1.0 2.0

NGA0811

Loma Prieta 1989-10-18

00:05 (6.93) UCSC 14 WAHO 5001 0.005 0.52 1.0 2.0 b Time history analyses are performed for the GM records with the scale factor indicated in the table.

111

Table A-5: Ground motion records used for the generic bridges at Site-3

NGA no Earthquake Name Station Information ndata dt PGA Scaleb

NGA0071

San Fernando 1971-02-09

14:00 (6.61) USGS 128 Lake Hughes #12 3660 0.01 0.33 1.0 2.0

NGA0511

N. Palm Springs 1986-07-

08 09:20 (6.06)

USGS 5224 Anza - Red

Mountain 2201 0.005 0.12 1.0 -

NGA0516

N. Palm Springs 1986-07-

08 09:20 (6.06)

USGS 5157 Cranston Forest

Station 2221 0.005 0.16 1.0 -

NGA0519

N. Palm Springs 1986-07-

08 09:20 (6.06)

CDMG 12331 Hemet Fire

Station 6000 0.005 0.13 1.0 -

NGA0521

N. Palm Springs 1986-07-

08 09:20 (6.06)

USGS 5043 Hurkey Creek

Park 2237 0.005 0.21 1.0 2.0

NGA0530

N. Palm Springs 1986-07-

08 09:20 (6.06)

CDMG 12025 Palm Springs

Airport 6000 0.005 0.17 1.0 -

NGA0534

N. Palm Springs 1986-07-

08 09:20 (6.06)

CDMG 12204 San Jacinto -

Soboba 5200 0.005 0.23 1.0 2.0

NGA0537

N. Palm Springs 1986-07-

08 09:20 (6.06)

CDMG 12206 Silent Valley

- Poppet Flat 4800 0.005 0.12 1.0 -

NGA0538

N. Palm Springs 1986-07-

08 09:20 (6.06) USGS 5038 Sunnymead 4108 0.005 0.13 1.0 -

NGA0539

N. Palm Springs 1986-07-

08 09:20 (6.06)

CDMG 13172 Temecula -

6th & Mercedes 8000 0.005 0.11 1.0 -

NGA0542

N. Palm Springs 1986-07-

08 09:20 (6.06)

CDMG 13201 Winchester

Page Bros R 8000 0.005 0.11 1.0 -

NGA0590

Whittier Narrows-01 1987-

10-01 14:42 (5.99)

CDMG 24402 Altadena -

Eaton Canyon 7999 0.005 0.22 1.0 -

NGA0595

Whittier Narrows-01 1987-

10-01 14:42 (5.99)

USC 90094 Bell Gardens -

Jaboneria 1715 0.02 0.25 1.0 2.0

NGA0600

Whittier Narrows-01 1987-

10-01 14:42 (5.99)

USGS 951 Brea Dam

(Downstream) 5988 0.005 0.23 1.0 2.0

NGA0606

Whittier Narrows-01 1987-

10-01 14:42 (5.99)

ACOE 108 Carbon Canyon

Dam 5996 0.005 0.21 1.0 -

NGA0611

Whittier Narrows-01 1987-

10-01 14:42 (5.99)

USC 90078 Compton -

Castlegate St 1559 0.02 0.33 1.0 -

NGA0614

Whittier Narrows-01 1987-

10-01 14:42 (5.99)

USC 90079 Downey -

Birchdale 1431 0.02 0.30 1.0 2.0

NGA0626

Whittier Narrows-01 1987-

10-01 14:42 (5.99)

CDMG 14403 LA - 116th St

School 7999 0.005 0.34 1.0 -

NGA0652

Whittier Narrows-01 1987-

10-01 14:42 (5.99)

USC 90084 Lakewood - Del

Amo Blvd 1488 0.02 0.23 1.0 -

NGA0683

Whittier Narrows-01 1987-

10-01 14:42 (5.99)

USC 90095 Pasadena - Old

House Rd 1501 0.02 0.26 1.0 2.0

NGA0692

Whittier Narrows-01 1987-

10-01 14:42 (5.99)

USC 90077 Santa Fe

Springs - E.Joslin 1891 0.02 0.43 1.0 -

NGA0700

Whittier Narrows-01 1987-

10-01 14:42 (5.99)

CDMG 24436 Tarzana -

Cedar Hill 7998 0.005 0.60 1.0 2.0

112

Table A-5: Ground motion records used for the generic bridges at Site-3 (Cont’d)

NGA no Earthquake Name Station Information ndata dt PGA Scaleb

NGA0848

Landers 1992-06-28

11:58 (7.28) SCE 23 Coolwater 11186 0.0025 0.37 1.0 -

NGA0850

Landers 1992-06-28

11:58 (7.28)

CDMG 12149 Desert Hot

Springs 2500 0.02 0.14 1.0 -

NGA0864

Landers 1992-06-28

11:58 (7.28) CDMG 22170 Joshua Tree 2200 0.02 0.25 1.0 2.0

NGA0880

Landers 1992-06-28

11:58 (7.28)

USGS 100 Mission Creek

Fault 14000 0.005 0.13 1.0 -

NGA0881

Landers 1992-06-28

11:58 (7.28) USGS 5071 Morongo Valley 14000 0.005 0.16 1.0 -

NGA0882

Landers 1992-06-28

11:58 (7.28)

USGS 5070 North Palm

Springs 14000 0.005 0.13 1.0 -

NGA0900

Landers 1992-06-28

11:58 (7.28)

CDMG 22074 Yermo Fire

Station 2200 0.02 0.22 1.0 -

NGA0952

Northridge-01 1994-01-

17 12:31 (6.69)

USC 90014 Beverly Hills -

12520 Mulhol 2398 0.01 0.51 1.0 2.0

NGA0953

Northridge-01 1994-01-

17 12:31 (6.69)

USC 90013 Beverly Hills -

14145 Mulhol 2999 0.01 0.46 1.0 2.0

NGA0960

Northridge-01 1994-01-

17 12:31 (6.69)

USC 90057 Canyon Country

- W Lost Cany 1999 0.01 0.44 1.0 2.0

NGA0963

Northridge-01 1994-01-

17 12:31 (6.69)

CDMG 24278 Castaic - Old

Ridge Route 2000 0.02 0.49 1.0 2.0

NGA0972

Northridge-01 1994-01-

17 12:31 (6.69)

CDMG 13122 Featherly

Park - Maint 2000 0.02 0.10 1.0 -

NGA0987

Northridge-01 1994-01-

17 12:31 (6.69)

USC 90054 LA - Centinela

St 2999 0.01 0.37 1.0 2.0

NGA0995

Northridge-01 1994-01-

17 12:31 (6.69)

CDMG 24303 LA -

Hollywood Stor FF 2000 0.02 0.34 1.0 2.0

NGA0998

Northridge-01 1994-01-

17 12:31 (6.69)

USC 90021 LA - N

Westmoreland 2999 0.01 0.37 1.0 -

NGA0999

Northridge-01 1994-01-

17 12:31 (6.69)

CDMG 24400 LA - Obregon

Park 2000 0.02 0.47 1.0 -

NGA1003

Northridge-01 1994-01-

17 12:31 (6.69) USC 90091 LA - Saturn St 3159 0.01 0.45 1.0 -

NGA1006

Northridge-01 1994-01-

17 12:31 (6.69)

CDMG 24688 LA - UCLA

Grounds 3000 0.02 0.39 1.0 2.0

NGA1007

Northridge-01 1994-01-

17 12:31 (6.69)

CDMG 24605 LA - Univ.

Hospital 4000 0.01 0.35 1.0 -

NGA1010

Northridge-01 1994-01-

17 12:31 (6.69)

USGS 5082 LA -

Wadsworth VA Hospital

South 11033 0.005 0.34 1.0 -

NGA1012

Northridge-01 1994-01-

17 12:31 (6.69) UCSB 99999 LA 00 6002 0.01 0.32 1.0 2.0

NGA1049

Northridge-01 1994-01-

17 12:31 (6.69)

USC 90049 Pacific Palisades

- Sunset 2499 0.01 0.33 1.0 -

113

Table A-5: Ground motion records used for the generic bridges at Site-3 (Cont’d)

NGA no Earthquake Name Station Information ndata dt PGA Scaleb

NGA1055

Northridge-01 1994-01-17

12:31 (6.69)

USC 90095 Pasadena - N

Sierra Madre 1991 0.01 0.23 1.0 -

NGA1070

Northridge-01 1994-01-17

12:31 (6.69)

USC 90019 San Gabriel - E

Grand Ave 3499 0.01 0.21 1.0

NGA1077

Northridge-01 1994-01-17

12:31 (6.69)

CDMG 24538 Santa Monica

City Hall 2000 0.02 0.59 1.0 -

NGA1081

Northridge-01 1994-01-17

12:31 (6.69) UCSB 78 Stone Canyon 4000 0.01 0.34 1.0 2.0

NGA1641

Sierra Madre 1991-06-28

(5.61)

CDMG 24402 Altadena -

Eaton Canyon 2000 0.02 0.33 1.0 -

NGA1642

Sierra Madre 1991-06-28

(5.61)

CDMG 23210 Cogswell

Dam - Right Abutment 2000 0.02 0.28 1.0 2.0

NGA1646

Sierra Madre 1991-06-28

(5.61)

USGS 5296 Pasadena -

USGS/NSMP Office 4687 0.005 0.23 1.0 -

NGA1770

Hector Mine 1999-10-16

(7.13)

CDMG 22791 Big Bear

Lake - Fire Station 5000 0.01 0.17 1.0 -

NGA1787

Hector Mine 1999-10-16

(7.13) SCSN 99999 Hector 4531 0.01 0.31 1.0 2.0

NGA1829

Hector Mine 1999-10-16

(7.13)

USGS 5328 San Bernardino

- Mont. Mem Pk 12381 0.005 0.11 1.0 - b Time history analyses are performed for the GM records with the scale factor indicated in the table.

Table A-6: Ground motion records used for the generic bridges at Site-4

NGA no Earthquake Name Station Information ndata dt PGA Scaleb

NGA0030

Parkfield 1966-06-28 04:26

(6.19)

CDMG 1014 Cholame -

Shandon Array #5 4392 0.01 0.38 1.0 2.0

NGA0031

Parkfield 1966-06-28 04:26

(6.19)

CDMG 1015 Cholame -

Shandon Array #8 2612 0.01 0.26 1.0 -

NGA0033

Parkfield 1966-06-28 04:26

(6.19)

CDMG 1438 Temblor pre-

1969 3033 0.01 0.29 1.0 -

NGA0057

San Fernando 1971-02-09

14:00 (6.61)

CDMG 24278 Castaic - Old

Ridge Route 3000 0.01 0.30 1.0 2.0

NGA0071

San Fernando 1971-02-09

14:00 (6.61) USGS 128 Lake Hughes #12 3660 0.01 0.33 1.0 -

NGA0147

Coyote Lake 1979-08-06

17:05 (5.74)

CDMG 47380 Gilroy Array

#2 5372 0.005 0.29 1.0 2.0

NGA0322

Coalinga-01 1983-05-02

23:42 (6.36)

CDMG 46314 Cantua Creek

School 4000 0.01 0.28 1.0 2.0

NGA0326

Coalinga-01 1983-05-02

23:42 (6.36)

CDMG 36228 Parkfield -

Cholame 2WA 4000 0.01 0.11 1.0 -

NGA0330

Coalinga-01 1983-05-02

23:42 (6.36)

CDMG 36411 Parkfield -

Cholame 4W 4000 0.01 0.14 1.0 -

NGA0331

Coalinga-01 1983-05-02

23:42 (6.36)

CDMG 36227 Parkfield -

Cholame 5W 4000 0.01 0.14 1.0 -

NGA0332

Coalinga-01 1983-05-02

23:42 (6.36)

CDMG 36451 Parkfield -

Cholame 6W 3200 0.01 0.11 1.0 -

114

Table A-6: Ground motion records used for the generic bridges at Site-4 (Cont’d)

NGA no Earthquake Name Station Information ndata dt PGA Scaleb

NGA0334

Coalinga-01 1983-05-02

23:42 (6.36)

CDMG 36407 Parkfield -

Fault Zone 1 4000 0.01 0.14 1.0 -

NGA0337

Coalinga-01 1983-05-02

23:42 (6.36)

CDMG 36138 Parkfield -

Fault Zone 12 4000 0.01 0.11 1.0 -

NGA0338

Coalinga-01 1983-05-02

23:42 (6.36)

CDMG 36456 Parkfield -

Fault Zone 14 4000 0.01 0.27 1.0 -

NGA0339

Coalinga-01 1983-05-02

23:42 (6.36)

CDMG 36445 Parkfield -

Fault Zone 15 4000 0.01 0.17 1.0 2.0

NGA0340

Coalinga-01 1983-05-02

23:42 (6.36)

CDMG 36457 Parkfield -

Fault Zone 16 4000 0.01 0.17 1.0 2.0

NGA0341

Coalinga-01 1983-05-02

23:42 (6.36)

CDMG 36413 Parkfield -

Fault Zone 2 4000 0.01 0.12 1.0 -

NGA0342

Coalinga-01 1983-05-02

23:42 (6.36)

CDMG 36408 Parkfield -

Fault Zone 3 4000 0.01 0.15 1.0 2.0

NGA0345

Coalinga-01 1983-05-02

23:42 (6.36)

CDMG 36431 Parkfield -

Fault Zone 7 4000 0.01 0.12 1.0 -

NGA0346

Coalinga-01 1983-05-02

23:42 (6.36)

CDMG 36449 Parkfield -

Fault Zone 8 4000 0.01 0.12 1.0 -

NGA0352

Coalinga-01 1983-05-02

23:42 (6.36)

CDMG 36420 Parkfield -

Gold Hill 3W 4000 0.01 0.13 1.0 -

NGA0359

Coalinga-01 1983-05-02

23:42 (6.36)

CDMG 36455 Parkfield -

Vineyard Cany 1E 4000 0.01 0.18 1.0 2.0

NGA0363

Coalinga-01 1983-05-02

23:42 (6.36)

CDMG 36176 Parkfield -

Vineyard Cany 3W 4000 0.01 0.12 1.0 -

NGA0458

Morgan Hill 1984-04-24

21:15 (6.19)

CDMG 57382 Gilroy Array

#4 7996 0.005 0.28 1.0 2.0

NGA0459

Morgan Hill 1984-04-24

21:15 (6.19)

CDMG 57383 Gilroy Array

#6 5996 0.005 0.28 1.0 -

NGA0700

Whittier Narrows-01 1987-

10-01 14:42 (5.99)

CDMG 24436 Tarzana -

Cedar Hill 7998 0.005 0.60 1.0 2.0

NGA0739

Loma Prieta 1989-10-18

00:05 (6.93)

USGS 1652 Anderson Dam

(Downstream) 7921 0.005 0.24 1.0 2.0

NGA0752

Loma Prieta 1989-10-18

00:05 (6.93) CDMG 47125 Capitola 7991 0.005 0.48 1.0 2.0

NGA0755

Loma Prieta 1989-10-18

00:05 (6.93)

CDMG 57217 Coyote Lake

Dam (SW Abut) 7991 0.005 0.29 1.0 2.0

NGA0763

Loma Prieta 1989-10-18

00:05 (6.93)

CDMG 47006 Gilroy -

Gavilan Coll. 7991 0.005 0.33 1.0 2.0

NGA0764

Loma Prieta 1989-10-18

00:05 (6.93)

CDMG 57476 Gilroy -

Historic Bldg. 7991 0.005 0.26 1.0 2.0

NGA0766

Loma Prieta 1989-10-18

00:05 (6.93)

CDMG 47380 Gilroy Array

#2 7990 0.005 0.35 1.0 2.0

NGA0767

Loma Prieta 1989-10-18

00:05 (6.93)

CDMG 47381 Gilroy Array

#3 7989 0.005 0.46 1.0 2.0

NGA0768

Loma Prieta 1989-10-18

00:05 (6.93)

CDMG 57382 Gilroy Array

#4 7990 0.005 0.30 1.0 2.0

115

Table A-6: Ground motion records used for the generic bridges at Site-4 (Cont’d)

NGA no Earthquake Name Station Information ndata dt PGA Scaleb

NGA0770

Loma Prieta 1989-10-18

00:05 (6.93)

CDMG 57425 Gilroy Array

#7 7990 0.005 0.31 1.0 2.0

NGA0776

Loma Prieta 1989-10-18

00:05 (6.93)

CDMG 47524 Hollister -

South & Pine 11991 0.005 0.28 1.0 2.0

NGA0777

Loma Prieta 1989-10-18

00:05 (6.93)

USGS 1028 Hollister City

Hall 7818 0.005 0.23 1.0 2.0

NGA0778

Loma Prieta 1989-10-18

00:05 (6.93)

USGS 1656 Hollister Diff.

Array 7928 0.005 0.26 1.0 2.0

NGA0801

Loma Prieta 1989-10-18

00:05 (6.93)

CDMG 57563 San Jose -

Santa Teresa Hills 2501 0.02 0.28 1.0 2.0

NGA0803

Loma Prieta 1989-10-18

00:05 (6.93)

CDMG 58235 Saratoga - W

Valley Coll. 7990 0.005 0.31 1.0 -

NGA0809

Loma Prieta 1989-10-18

00:05 (6.93) UCSC 15 UCSC 5001 0.005 0.34 1.0 -

NGA0810

Loma Prieta 1989-10-18

00:05 (6.93)

CDMG 58135 UCSC Lick

Observatory 7990 0.005 0.46 1.0 -

NGA0811

Loma Prieta 1989-10-18

00:05 (6.93) UCSC 14 WAHO 5001 0.005 0.52 1.0 2.0

NGA0953

Northridge-01 1994-01-17

12:31 (6.69)

USC 90013 Beverly Hills -

14145 Mulhol 2999 0.01 0.46 1.0 -

NGA0960

Northridge-01 1994-01-17

12:31 (6.69)

USC 90057 Canyon Country

- W Lost Cany 1999 0.01 0.44 1.0 -

NGA0960

Northridge-01 1994-01-17

12:31 (6.69)

USC 90057 Canyon Country

- W Lost Cany 1999 0.01 0.44 2.0 -

NGA0963

Northridge-01 1994-01-17

12:31 (6.69)

CDMG 24278 Castaic - Old

Ridge Route 2000 0.02 0.49 1.0 2.0

NGA1049

Northridge-01 1994-01-17

12:31 (6.69)

USC 90049 Pacific Palisades

- Sunset 2499 0.01 0.33 1.0 2.0

NGA1081

Northridge-01 1994-01-17

12:31 (6.69) UCSB 78 Stone Canyon 4000 0.01 0.34 1.0 - b Time history analyses are performed for the GM records with the scale factor indicated in the table.

116

APPENDIX B

PEAK ANNUAL STREAMFLOW DATA AT THE FLOW MEASUREMENT

STATIONS

Tables B-1 to B-5 show the peak annual streamflow measured at the USGS data stations that

are utilized for the generation of flood hazard curves. The data presented in Table B-1 and Table B-2

are employed for the generation of flood hazard curves at the sites of Bridge-1 and Bridge-2 (discussed

in Chapter 3), respectively. The data presented in Tables B-3 to B-5 are employed for the generation of

flood hazard curves at Site-2, Site-3, and Site 4 (discussed in Chapter 5), respectively. Table B-1 is also

considered for the generation of flood hazard curves at Site-1 (discussed in Chapter 5).

Table B-1: Peak Annual Streamflow Measured at the USGS Data Station Site Number 11370500

Year Peak Flow

(m3/s) Year

Peak Flow

(m3/s) Year

Peak Flow

(m3/s) Year

Peak Flow

(m3/s)

1944 216.6 1962 325.6 1980 1452.7 1998 1599.9

1945 263.1 1963 1282.8 1981 436.1 1999 875.0

1946 832.5 1964 373.8 1982 1750.0 2000 1557.4

1947 216.6 1965 1529.1 1983 1846.3 2001 447.4

1948 620.1 1966 489.9 1984 1098.7 2002 436.1

1949 365.3 1967 1591.4 1985 447.4 2003 880.7

1950 342.6 1968 1509.3 1986 2177.6 2004 1560.3

1951 1192.1 1969 1585.7 1987 444.6 2005 1152.5

1952 999.6 1970 2234.2 1988 444.6 2006 1458.3

1953 2070.0 1971 1064.7 1989 444.6 2007 455.9

1954 1447.0 1972 444.6 1990 339.8 2008 413.4

1955 328.5 1973 1166.7 1991 291.7 2009 385.1

1956 1523.4 1974 2305.0 1992 702.3 2010 464.4

1957 1489.5 1975 1064.7 1993 1571.6 2011 1523.4

1958 2231.4 1976 402.1 1994 438.9 2012 470.1

1959 923.1 1977 334.1 1995 2137.9 2013 461.6

1960 334.1 1978 1127.0 1996 1588.6

1961 410.6 1979 424.8 1997 2242.7

117

Table B-2: Peak Annual Streamflow Measured at the USGS Data Station Site Number 11051500

Year Peak Flow

(m3/s) Year

Peak Flow

(m3/s) Year

Peak Flow

(m3/s) Year

Peak Flow

(m3/s)

1930 143.0 1951 2237.0 1972 111.3 1993 291.7

1931 62.6 1952 974.1 1973 371.0 1994 125.7

1932 515.4 1953 286.0 1974 277.8 1995 739.1

1933 242.7 1954 282.9 1975 257.1 1996 509.7

1934 120.6 1955 154.3 1976 162.0 1997 2140.8

1935 673.9 1956 1441.3 1977 36.5 1998 996.8

1936 812.7 1957 265.3 1978 747.6 1999 455.9

1937 736.2 1958 1172.3 1979 393.6 2000 475.7

1938 1449.8 1959 160.6 1980 959.9 2001 171.3

1939 160.3 1960 93.7 1981 165.1 2002 180.4

1940 1056.2 1961 45.6 1982 843.8 2003 100.2

1941 974.1 1962 356.8 1983 1277.1 2004 129.1

1942 770.2 1963 371.0 1984 934.5 2005 436.1

1943 1101.5 1964 113.8 1985 167.6 2006 985.4

1944 211.8 1965 645.6 1986 1044.9 2007 119.2

1945 574.8 1966 275.5 1987 181.5 2008 134.5

1946 467.2 1967 739.1 1988 77.6 2009 75.6

1947 125.4 1968 120.3 1989 74.5 2010 184.1

1948 331.3 1969 1489.5 1990 58.0 2011 875.0

1949 151.2 1970 733.4 1991 116.9 2012 165.4

1950 416.3 1971 189.7 1992 157.7 2013 119.2

Table B-3: Peak Annual Streamflow Measured at the USGS Data Station Site Number 11303000

Year Peak Flow

(m3/s) Year

Peak Flow

(m3/s) Year

Peak Flow

(m3/s) Year

Peak Flow

(m3/s)

1941 249.5 1960 16.2 1979 118.4 1998 146.4

1942 281.5 1961 7.3 1980 137.6 1999 121.8

1943 557.8 1962 105.9 1981 47.0 2000 110.7

1944 101.9 1963 230.2 1982 85.5 2001 47.6

1945 241.5 1964 39.6 1983 148.9 2002 42.5

1946 169.6 1965 928.8 1984 161.4 2003 40.5

1947 78.2 1966 64.6 1985 51.3 2004 38.2

1948 183.8 1967 223.4 1986 191.4 2005 43.6

1949 154.0 1968 43.3 1987 62.6 2006 177.5

1950 176.1 1969 758.9 1988 36.0 2007 51.5

1951 1373.4 1970 436.1 1989 37.4 2008 41.6

1952 308.7 1971 98.5 1990 31.7 2009 35.1

1953 303.0 1972 59.2 1991 29.4 2010 37.9

1954 130.3 1973 118.4 1992 37.4 2011 82.1

1955 80.1 1974 147.5 1993 70.8 2012 77.9

1956 1769.8 1975 221.4 1994 37.7 2013 85.2

1957 136.2 1976 41.9 1995 73.6

1958 413.4 1977 3.0 1996 111.3

1959 44.5 1978 137.1 1997 207.3

118

Table B-4: Peak Annual Streamflow Measured at the USGS Data Station Site Number 11051500

Year Peak Flow (m3/s)

1999 4.2

2000 7.0

2001 1.4

2002 0.5

2003 17.3

2004 83.8

2005 18.1

2006 9.5

2007 12.1

2008 1.8

2009 89.5

2010 141.6

2011 4.4

2012 2.9

Table B-5: Peak Annual Streamflow Measured at the USGS Data Station Site Number 11147500

Year Peak Flow

(m3/s) Year

Peak Flow

(m3/s) Year

Peak Flow

(m3/s) Year

Peak Flow

(m3/s)

1940 125.2 1957 9.6 1981 109.9 1998 348.3

1941 279.5 1958 368.1 1982 297.3 1999 59.2

1942 189.7 1959 27.7 1983 464.4 2000 188.6

1943 402.1 1960 86.6 1984 72.2 2001 305.8

1944 186.6 1962 267.9 1985 89.5 2002 8.0

1945 177.3 1963 71.6 1986 270.1 2003 78.7

1946 70.8 1964 6.7 1987 36.2 2004 100.2

1947 30.6 1965 96.8 1988 27.4 2005 492.7

1948 83.0 1970 120.9 1989 48.1 2006 224.0

1949 131.7 1971 56.6 1990 3.3 2007 3.2

1950 120.6 1972 4.1 1991 108.2 2008 64.3

1951 46.7 1973 413.4 1992 274.1 2009 1.8

1952 243.0 1974 226.5 1993 421.9 2010 116.1

1953 77.9 1975 119.5 1994 64.8 2011 286.0

1954 41.3 1978 410.6 1995 804.2 2012 36.2

1955 29.4 1979 94.9 1996 198.5 2013 51.5

1956 339.8 1980 523.9 1997 276.4 2014 1.7

119

APPENDIX C

DETAILS OF ANALYTICAL MODELING OF BRIDGE COMPONENTS IN FINITE

ELEMENT ANALYSES

This appendix presents the details of analytical modeling of bridge components in finite element

analyses of the investigated bridges. The discussion related to superstructure elements is not included in

this appendix, since these elements, which are expected to stay in elastic range, are modeled with

ordinary linear elastic beam elements.

C.1 Reinforced Concrete Piers

C.1.1. Displacement-Based Fiber Elements

Displacement-based fiber elements are mainly used for modeling nonlinearity in flexural

response of piers. Fiber sections assigned on pier elements are aggregated with linear elastic sectional

properties which represent the shear and torsional responses. Figure C-1 shows the representative

element discretization of a bent (over the generic bridge Type A1) and a typical fiber section with the

assigned stress-strain relations of unconfined concrete, confined concrete, and reinforcing steel.

C.1.2. Validation of Pier Elements

For the objective of validation of pier elements, experimental load-displacement response of

two test columns are compared with their analytical response as displayed in Figure C-2. The

experimental data of cantilever column tests under quasi-static cyclic lateral loading are obtained from

PEER Structural Performance Database (2013). The column tests referred in Lehman and Moehle (2000)

and Wehbe et al. (1999) are modeled in OpenSees using the displacement-based fiber elements with the

same material and geometric properties, and boundary conditions. These analytical models are subjected

to the same loading protocol as used in the experiments.

120

Figure C-1: (a) Representative element discretization at a typical bridge bent, (b) typical fiber section

assigned to pier elements

-150 -100 -50 0 50 100 150

Displacement (mm)

-400

-200

0

200

400

Shea

r F

orc

e (k

N)

Analytical

Experimental

-200 -150 -100 -50 0 50 100 150 200

Displacement (mm)

-400

-200

0

200

400

Shea

r F

orc

e (k

N)

Analytical

Experimental

(a) (b)

Figure C-2: Comparison of analytical and experimental load-displacement curves of test columns

from (a) Lehman and Moehle (2000), (b) Wehbe et al. (1999)

C.2 Abutment Backwall-Backfill Interaction in Longitudinal Direction

In the finite element models of the investigated bridges, abutment backwall-backfill interaction

is represented with the elastic-perfectly plastic backbone curve suggested by Caltrans (2013). Figure C-

3 shows the backbone curves used for seat-type and diaphragm type of abutments. For the seat-type

Note: This is a schematic drawing. Number of nodes and

elements vary depending on the bridge model. Soil springs are

not shown.

Fixity node

Rigid link

Bridge girder

Displacement-based

fiber elements

Rock or Firm Soil

Soil

(a)

Unconfined concrete

Confined concrete

Reinforcing steel

(b)

Steel02 material in OpenSEES

Mander et al. (1988) material

model for unconfined and

confined concrete are

represented with Concrete07

material in OpenSees

121

abutments, the passive resistance of backfill gets active when the gap (Δgap) between the abutment

backwall and the bridge deck is closed. For the diaphragm type of abutments, the same resistance

immediately becomes active with the deflection in the direction of backfill with the absence of gap

between the backwall and the bridge deck.

Deflection

Force

Klong

Pbw

gap Deflection

Force

Klong

Pdia

(a) (b)

Figure C-3: Abutment backwall-backfill interaction for (a) seat-type abutment, (b) diaphragm

abutment

In Caltrans (2013), the passive pressure force resisting the movement at the abutment (Pbw or

Pdia) is calculated according to Equation C-1. In this research, this resistance capacity is increased by

50% to account for the dynamic loading conditions during an earthquake excitation.

7.1

239 diabwediabw

horhkPaAPorP (m, kN) (C-1)

where Ae is the effective abutment wall area, hbw and hdia are the effective height of abutment for seat-

type and diaphragm type of abutments, respectively. The details on these parameters can be found in

Caltrans (2013). The abutment stiffness of the backbone curves given in Figure C-3 is calculated as:

m

horhwKK diabw

ilong7.1

(C-2)

where w is the projected width of the backwall or diaphragm for seat and diaphragm abutments,

respectively. Ki (introduced as Kabut in Table 4-1) is the initial stiffness which is recommended as 28.7

kN/mm/m for embankment fill material meeting the requirements of Caltrans Standard Specifications.

For embankment fill material not meeting the requirements, Ki is recommended as 14.35 kN/mm/m.

122

C.3 Abutment Response in Transverse Direction

Abutment response of the bridges in transverse direction is modeled using the methodology

recommended by Aviram et al. (2008). In this methodology, zero-length elements are defined in

transverse direction at each end of the rigid link representing the abutment. These elements are assigned

with an elastic-perfectly plastic backbone curves representing the backfill, wing wall and pile system

response. The backbone curve used for the response of the whole abutment in transverse direction

(Figure C-4) is obtained through modification of the backbone curve of abutment backwall-backfill

interaction suggested by Caltrans (2013) (as given in Figure C-3b) utilizing wall effectiveness factor of

CL=2/3 and participation coefficient (Cw=4/3).

Deflection

Force

Ktrans

Ftrans

Figure C-4: Abutment response in transverse direction

Effective wall length is calculated as:

wCw Leff (C-3)

where w is the wing wall length, which can be taken as 1/2-1/3 of the backwall length as recommended

by Aviram et al. (2008). Force capacity (Ftrans) and stiffness (Ktrans) of the backbone curve of the

abutment in transverse direction are computed as:

7.1

5.1239 wweffwwwtrans

hkPawhCF (C-4)

m

hwKCK ww

effiwtrans7.1

(C-5)

123

where hww is the wing wall height. As can be noticed in Equation C-4 that, the force capacity is again

increased by 50% to account for dynamic loading conditions. The backbone curve obtained through

Equation C-4 and C-5 is distributed equally to each zero-length element.

C.4 Shear Keys

Nonlinear response of shear key elements is described with the hysteresis model proposed by

Megally et al. (2012) as demonstrated in Figure C-5. Equations used for calculation of the parameters

(e.g. Vc, Vs, VII, VIII, ΔII, ΔIII, etc.) identifying this backbone curve can be found in Bozorgzadeh et al.

(2007). These parameters and accordingly the backbone curve changes for geometrical and material

properties of the shear key and abutment stem wall. As an example, the backbone curve assigned to the

shear key elements in the generic bridges in Chapter 5 is presented in Figure C-6. It is generally observed

from the element response that the deformation in transverse direction does not reach to the displacement

level of ΔIII. Thus, in OpenSees models, shear key elements are modeled with bilinear hysteretic

elements.

Figure C-5: Hysteresis model for exterior shear key, after Megally et al. 2001 (Bozorgzadeh et al.

2007)

124

DeflectionF

orc

eI=15mm II=150mm III=299mm

VII=6044 kN

VIII=7404 kN

VIV=5893 kN

Figure C-6: Backbone curve assigned to the shear key elements in the generic bridges

C.5 PTFE/Elastomeric Bearings

C.5.1. Modeling of Nonlinear Response in Horizontal Direction

For modeling the response of a PTFE/elastomeric bearing in horizontal direction, linear elastic-

perfectly plastic backbone curve as presented in Figure C-7 is assigned to the nonlinear elements in two

orthogonal horizontal directions. The initial stiffness (Kshear) and yield force (Fyield) of the backbone

curve can be computed as:

rt

shearh

AGK

(C-6)

bearingyield NF (C-7)

where G is the shear modulus of elastomer, A is the cross-sectional area of elastomer, hrt is the net

elastomer thickness, µ is the friction coefficient at the PTFE-stainless steel interface, and Nbearing is the

axial force acting on the bearing, which can be approximately taken as the axial force under gravity

loading.

125

DeflectionF

orc

esliding

Fyield

Kshear

Figure C-7: PTFE/elastomeric bearings backbone curve in horizontal direction

C.5.2. Validation of Nonlinear Element in Horizontal Direction

Figure C-8 demonstrates the comparison of the experimental response of a PTFE/elastomeric

bearing tested by Konstantinidis et al. (2008) with its numerical load-deformation response when the

modeling explained in Section C.5.1 is employed.

-300 -200 -100 0 100 200 300

Horizontal Displacement (mm)

-200

-100

0

100

200

Hori

zon

tal

Fo

rce

(kN

)

Analytical

Experimental

Vertical Load=1784 kN

Bearing: T-48mm

Figure C-8: Comparison of analytical and experimental load-deformation response of a test bearing

C.5.3. Linear Response of the Bearing in Vertical Direction and Rotational and Vertical Response

The linear stiffness assigned to the element employed for modeling the bearing response in

vertical direction can be calculated as:

rt

cv

h

AEK

(C-8)

126

where Ec is the effective compressive modulus of the elastomer. The linear stiffness assigned to the

element employed for modeling the rotational response about the global transverse axis of the bridge

can be calculated as:

rt

bc

h

IEK

5.0 (C-9)

where Ib is the moment of inertia of the plan of the bearing.

C.6 Elastomeric Bearings

Modeling of elastomeric bearings is identical to that employed for PTFE/elastomeric bearings,

except the coefficient of friction value adopted. For elastomeric bearings, yield force in horizontal

direction is taken as the frictional resistance developed between the concrete surface and elastomer.

C.7 Pounding of Adjacent Bridge Decks at the In-Span Hinge of Bridge-2

The impact model proposed by Muthukumar (2003) is employed for modeling the pounding of

adjacent bridge decks at the in-span hinge of Bridge-2. The backbone curve assigned to the pounding

elements is shown in Figure C-9.

F

gap=25.4mm

Fm=15893 kN

Kt1

Fy=3878 kN

Kt2

y

=2.54mm

m

=25.4mm

Figure C-9: Backbone curve for modeling the pounding of adjacent bridge decks

In this model, the total expected energy loss during an impact event was defined as:

1

1 21

n

ekE

nmh

(C-10)

127

where kh is the impact stiffness parameter, n is the Hertz coefficient, e is the coefficient of restitution,

and δm is the maximum penetration of the two decks. The impact model parameters are obtained with

the following three equations:

my a (C-11)

21

m

effta

EKK

(C-12)

221 m

effta

EKK

(C-13)

where δy is the yield deformation and Keff is the effective stiffness, which is defined as:

mheff kK (C-14)

The accepted values of the parameters employed in Equations C-10 to C-14 are adopted from

Nielson (2005) and presented in Table C-1.

Table C-1: Accepted values of the pounding model parameters

Impact stiffness parameter kh (kN-mm-3/2) 869

Hertz coefficient n 1.5

Coefficient of restitution e 0.8

Maximum penetration of the two decks δm (mm) 25.4

Yield deformation δy (mm) 2.54

a 0.1

128

APPENDIX D

LATIN HYPERCUBE SAMPLING DESIGN

Table D-1: Latin Hypercube Sampling Design for Uncertainty Analysis

Sa

mp

le fce (MPa) fye

(MPa)

Kabut

(kN/

mm/

m)

fmass

φp, soil (˚)

(column) (girder) Lyr.

1a

Lyr.

2

Lyr.

3

Lyr.

4

Lyr.

5

Lyr.

6

Lyr.

7

Lyr.

8

1 32.09 39.80 483.31 20.35 0.93 47.9 48.4 51.0 48.5 48.6 47.1 49.0 51.7

2 36.45 45.20 434.08 18.23 1.02 44.0 44.4 46.8 44.5 44.6 43.3 45.0 47.5

3 24.44 30.30 489.30 24.11 1.05 43.1 43.5 45.8 43.6 43.7 42.3 44.0 46.4

4 33.97 42.13 539.65 23.42 1.10 48.8 49.3 52.0 49.4 49.5 48.0 49.9 52.7

5 31.15 38.63 478.91 15.50 1.13 38.4 38.7 40.8 38.8 38.9 37.7 39.2 41.4

6 28.05 34.79 512.20 21.35 1.02 45.0 45.4 47.9 45.5 45.6 44.3 46.0 48.5

7 28.58 35.44 496.79 19.98 0.77 46.5 46.9 49.5 47.0 47.1 45.7 47.5 50.1

8 31.63 39.23 467.47 26.16 0.96 40.1 40.5 42.7 40.6 40.7 39.4 41.0 43.3

9 39.74 49.27 469.68 27.17 0.95 43.8 44.2 46.6 44.3 44.4 43.1 44.7 47.2

10 37.22 46.16 456.62 28.23 1.18 35.6 35.9 37.8 36.0 36.1 35.0 36.3 38.4

11 27.20 33.72 499.67 16.66 0.98 36.9 37.3 39.3 37.4 37.5 36.3 37.7 39.8

12 38.77 48.07 440.27 22.31 1.06 41.6 42.0 44.3 42.1 42.2 40.9 42.5 44.9

13 33.06 40.99 446.27 5.64 1.00 45.8 46.2 48.7 46.3 46.4 45.0 46.7 49.4

14 30.85 38.25 452.77 13.30 1.08 52.0 52.5 55.3 52.6 52.7 51.1 53.1 56.1

15 32.59 40.41 408.34 21.89 0.96 39.0 39.4 41.6 39.5 39.6 38.4 39.9 42.1

16 29.41 36.46 523.65 33.68 0.91 42.2 42.6 44.9 42.7 42.8 41.5 43.1 45.5

17 29.76 36.91 475.50 16.81 0.88 40.9 41.3 43.6 41.4 41.5 40.3 41.8 44.2

18 35.86 44.47 461.14 25.06 1.03 30.0 30.3 32.0 30.4 30.5 29.5 30.7 32.4

19 34.38 42.63 520.67 19.23 1.01 39.4 39.8 42.0 39.9 40.0 38.8 40.3 42.5

20 35.17 43.61 413.56 29.24 0.98 34.4 34.7 36.6 34.8 34.9 33.8 35.1 37.1 athe standard deviation computed from LHS design is applied on each friction angle at a soil layer

129

APPENDIX E

RESULTS OF FRAGILITY PARAMETERS IN UNCERTAINTY ANALYSES

Table E-1: Median values of seismic fragility curves at minor and moderate damage state for pier

flexural damage

Minor Damage Moderate Damage

Sam

ple

No

Flood

1-yr

Flood

2-yr

Flood

10-yr

Flood

20-yr

Flood

No

Flood

1-yr

Flood

2-yr

Flood

10-yr

Flood

20-yr

Flood

1 0.438 0.397 0.385 0.373 0.373 0.688 0.688 0.688 0.688 0.688

2 0.423 0.364 0.364 0.364 0.364 0.688 0.688 0.688 0.688 0.688

3 0.409 0.374 0.374 0.395 0.395 0.688 0.688 0.688 0.688 0.688

4 0.423 0.364 0.374 0.374 0.374 0.688 0.688 0.688 0.688 0.688

5 0.409 0.385 0.395 0.384 0.384 0.688 0.688 0.688 0.688 0.688

6 0.423 0.364 0.374 0.385 0.385 0.688 0.688 0.688 0.688 0.688

7 0.538 0.470 0.423 0.423 0.423 0.815 0.741 0.688 0.688 0.688

8 0.423 0.397 0.374 0.364 0.364 0.688 0.688 0.688 0.688 0.688

9 0.423 0.409 0.397 0.397 0.397 0.688 0.688 0.688 0.688 0.688

10 0.364 0.354 0.354 0.363 0.363 0.688 0.688 0.688 0.688 0.688

11 0.423 0.385 0.385 0.409 0.409 0.688 0.688 0.688 0.688 0.688

12 0.409 0.364 0.364 0.364 0.364 0.688 0.688 0.688 0.688 0.688

13 0.407 0.421 0.409 0.409 0.409 0.688 0.688 0.688 0.688 0.688

14 0.396 0.397 0.409 0.395 0.395 0.688 0.688 0.688 0.688 0.688

15 0.409 0.385 0.364 0.364 0.364 0.688 0.688 0.688 0.688 0.688

16 0.488 0.409 0.397 0.397 0.397 0.815 0.688 0.688 0.688 0.688

17 0.470 0.409 0.409 0.409 0.409 0.688 0.688 0.688 0.688 0.688

18 0.364 0.364 0.364 0.354 0.354 0.688 0.688 0.688 0.688 0.688

19 0.438 0.384 0.364 0.385 0.385 0.688 0.688 0.688 0.688 0.688

20 0.397 0.364 0.364 0.364 0.364 0.688 0.688 0.688 0.688 0.688

130

Table E-2: Median values of seismic fragility curves at major damage and collapse state for pier

flexural damage

Major Damage Collapse State

Sam

ple

No

Flood

1-yr

Flood

2-yr

Flood

10-yr

Flood

20-yr

Flood

No

Flood

1-yr

Flood

2-yr

Flood

10-yr

Flood

20-yr

Flood

1 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815

2 0.741 0.688 0.688 0.815 0.815 0.815 0.815 0.815 0.815 0.815

3 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815

4 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815

5 0.815 0.741 0.741 0.741 0.741 0.815 0.815 0.741 0.815 0.815

6 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815

7 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.894 0.894

8 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815

9 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815

10 0.815 0.688 0.741 0.741 0.741 0.815 0.815 0.815 0.815 0.815

11 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815

12 0.815 0.688 0.688 0.815 0.815 0.815 0.815 0.815 0.815 0.815

13 0.741 0.741 0.741 0.741 0.741 0.815 0.741 0.741 0.741 0.741

14 0.815 0.741 0.741 0.741 0.741 0.815 0.741 0.741 0.815 0.815

15 0.815 0.688 0.688 0.815 0.815 0.815 0.815 0.815 0.815 0.815

16 0.815 0.815 0.815 0.815 0.815 0.894 0.815 0.815 1.005 1.005

17 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815

18 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815

19 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815

20 0.815 0.745 0.745 0.815 0.815 0.815 0.815 0.815 0.815 0.815

Table E-3: Median values of seismic fragility curves for abutment passive deformation

Minor Damage Moderate Damage

Sam

ple

No

Flood

1-yr

Flood

2-yr

Flood

10-yr

Flood

20-yr

Flood

No

Flood

1-yr

Flood

2-yr

Flood

10-yr

Flood

20-yr

Flood

1 0.741 0.741 0.741 0.741 0.741 0.894 0.894 0.894 0.894 0.894

2 0.741 0.741 0.741 0.741 0.741 0.894 0.894 0.894 0.894 0.894

3 0.741 0.741 0.741 0.741 0.741 1.149 0.894 0.894 0.894 0.894

4 0.741 0.741 0.741 0.741 0.741 0.894 0.894 0.894 0.894 0.894

5 0.741 0.741 0.741 0.741 0.741 0.894 0.894 0.894 0.894 0.894

6 0.741 0.741 0.741 0.741 0.741 0.894 0.894 0.894 0.894 0.894

7 0.741 0.741 0.741 0.741 0.741 1.416 1.035 1.035 1.035 1.035

8 0.741 0.741 0.741 0.741 0.741 0.894 0.894 0.894 0.894 0.894

9 0.741 0.741 0.741 0.741 0.741 1.035 0.894 0.894 0.894 0.894

10 0.741 0.741 0.741 0.741 0.741 0.894 1.005 1.005 1.005 1.005

11 0.741 0.741 0.741 0.741 0.741 0.894 0.894 0.894 0.894 0.894

12 0.741 0.741 0.741 0.741 0.741 0.894 0.997 0.894 0.894 0.894

13 0.741 0.741 0.741 0.741 0.741 0.894 0.894 1.005 0.894 0.894

14 0.741 0.834 0.741 0.741 0.741 0.894 1.035 0.894 0.894 0.894

15 0.741 0.741 0.741 0.741 0.741 0.894 0.894 0.894 0.894 0.894

16 0.741 0.741 0.741 0.741 0.741 1.035 0.894 0.894 0.894 0.894

17 0.741 0.741 0.741 0.741 0.741 0.894 0.894 0.894 0.894 0.894

18 0.741 0.741 0.741 0.741 0.741 0.894 0.894 0.894 0.894 0.894

19 0.741 0.741 0.741 0.741 0.741 0.894 0.894 0.894 0.894 0.894

20 0.741 0.834 0.741 0.741 0.741 0.894 1.035 0.894 0.894 0.894

131

Table E-4: Median values of seismic fragility curves for abutment transverse deformation

Minor Damage

Sample No Flood 1-yr Flood 2-yr Flood 10-yr Flood 20-yr Flood

1 > 5.0 > 5.0 > 5.0 > 5.0 > 5.0

2 > 5.0 > 5.0 > 5.0 > 5.0 > 5.0

3 > 5.0 > 5.0 > 5.0 > 5.0 > 5.0

4 > 5.0 > 5.0 > 5.0 > 5.0 > 5.0

5 1.935 1.935 1.935 1.935 1.935

6 > 5.0 > 5.0 > 5.0 > 5.0 > 5.0

7 > 5.0 > 5.0 > 5.0 > 5.0 > 5.0

8 > 5.0 > 5.0 > 5.0 > 5.0 > 5.0

9 > 5.0 > 5.0 > 5.0 > 5.0 > 5.0

10 > 5.0 > 5.0 > 5.0 > 5.0 > 5.0

11 > 5.0 > 5.0 > 5.0 > 5.0 > 5.0

12 > 5.0 > 5.0 > 5.0 > 5.0 > 5.0

13 0.741 0.741 0.741 0.741 0.741

14 1.459 1.193 1.005 1.005 1.005

15 > 5.0 > 5.0 > 5.0 > 5.0 > 5.0

16 > 5.0 > 5.0 > 5.0 > 5.0 > 5.0

17 > 5.0 > 5.0 > 5.0 > 5.0 > 5.0

18 > 5.0 > 5.0 > 5.0 > 5.0 > 5.0

19 > 5.0 > 5.0 > 5.0 > 5.0 > 5.0

20 > 5.0 > 5.0 > 5.0 > 5.0 > 5.0

Table E-5: Median values of seismic fragility curves for bearing longitudinal deformation

Minor Damage Moderate Damage

Sam

ple

No

Flood

1-yr

Flood

2-yr

Flood

10-yr

Flood

20-yr

Flood

No

Flood

1-yr

Flood

2-yr

Flood

10-yr

Flood

20-yr

Flood

1 0.451 0.436 0.423 0.423 0.423 1.935 1.935 1.935 1.935 1.935

2 0.451 0.423 0.423 0.384 0.384 1.935 1.935 1.935 1.935 1.935

3 0.423 0.384 0.384 0.348 0.348 1.935 1.935 1.935 1.935 1.935

4 0.436 0.384 0.384 0.384 0.384 1.935 1.935 1.935 1.935 1.935

5 0.423 0.384 0.384 0.348 0.348 1.449 1.449 1.449 1.176 1.176

6 0.436 0.384 0.384 0.384 0.384 1.935 1.935 1.935 1.935 1.935

7 0.476 0.451 0.451 0.451 0.451 1.935 1.935 1.935 1.935 1.935

8 0.436 0.423 0.423 0.384 0.384 1.935 1.935 1.935 1.935 1.935

9 0.451 0.451 0.436 0.423 0.423 1.935 1.935 1.935 1.935 1.935

10 0.395 0.384 0.348 0.348 0.348 1.935 1.449 1.449 1.176 1.176

11 0.436 0.384 0.384 0.384 0.384 1.935 1.935 1.935 1.416 1.416

12 0.451 0.423 0.395 0.384 0.384 1.935 3.045 1.935 1.935 1.935

13 0.467 0.423 0.395 0.384 0.384 1.449 1.957 1.449 1.449 1.449

14 0.436 0.384 0.384 0.384 0.370 1.449 1.935 1.449 1.449 1.449

15 0.436 0.423 0.423 0.384 0.384 1.935 1.935 1.935 1.935 1.935

16 0.436 0.423 0.423 0.409 0.395 1.935 1.935 1.935 1.935 1.935

17 0.451 0.451 0.423 0.423 0.423 1.935 1.935 1.935 1.935 1.935

18 0.384 0.384 0.384 0.370 0.370 1.935 1.935 1.935 1.935 1.935

19 0.451 0.423 0.409 0.384 0.384 1.935 1.935 1.935 1.935 1.935

20 0.436 0.409 0.384 0.384 0.384 1.935 1.935 1.935 1.935 1.935

132

Table E-6: Median values of seismic fragility curves for bearing transverse deformation

Minor Damage Moderate Damage

Sam

ple

No

Flood

1-yr

Flood

2-yr

Flood

10-yr

Flood

20-yr

Flood

No

Flood

1-yr

Flood

2-yr

Flood

10-yr

Flood

20-yr

Flood

1 1.193 1.035 1.035 1.035 1.035 > 5.0 > 5.0 > 5.0 > 5.0 > 5.0

2 1.035 1.035 1.035 0.894 0.894 > 5.0 > 5.0 > 5.0 > 5.0 > 5.0

3 1.035 0.894 0.894 0.894 0.894 > 5.0 > 5.0 > 5.0 > 5.0 > 5.0

4 1.035 1.035 1.035 0.894 0.894 > 5.0 > 5.0 > 5.0 > 5.0 > 5.0

5 1.005 1.005 0.894 0.894 0.894 > 5.0 > 5.0 > 5.0 > 5.0 > 5.0

6 1.035 1.035 1.035 0.894 0.894 > 5.0 > 5.0 > 5.0 > 5.0 > 5.0

7 1.459 1.459 1.459 1.459 1.459 > 5.0 > 5.0 > 5.0 > 5.0 > 5.0

8 1.035 1.035 1.035 1.035 1.035 > 5.0 > 5.0 > 5.0 > 5.0 > 5.0

9 1.035 1.035 1.035 1.035 1.035 > 5.0 > 5.0 > 5.0 > 5.0 > 5.0

10 0.894 0.894 0.894 0.800 0.800 > 5.0 3.045 1.935 1.935 1.935

11 1.459 1.193 1.035 1.035 1.035 > 5.0 > 5.0 > 5.0 > 5.0 > 5.0

12 1.035 0.894 0.894 0.894 0.894 > 5.0 > 5.0 > 5.0 > 5.0 > 5.0

13 1.935 1.935 1.935 1.935 1.935 > 5.0 > 5.0 > 5.0 > 5.0 > 5.0

14 1.193 1.005 1.005 1.005 1.005 > 5.0 > 5.0 > 5.0 > 5.0 > 5.0

15 1.035 1.035 1.035 0.894 0.894 > 5.0 > 5.0 > 5.0 > 5.0 > 5.0

16 1.193 1.035 1.035 1.035 1.035 > 5.0 > 5.0 > 5.0 > 5.0 > 5.0

17 1.459 1.459 1.035 1.035 1.035 > 5.0 > 5.0 > 5.0 > 5.0 > 5.0

18 1.035 0.894 0.894 0.894 0.894 > 5.0 > 5.0 > 5.0 > 5.0 > 5.0

19 1.459 1.035 1.035 1.035 1.035 > 5.0 > 5.0 > 5.0 > 5.0 > 5.0

20 0.815 1.035 0.894 0.894 0.894 > 5.0 > 5.0 > 5.0 > 5.0 > 5.0

Table E-7: Median values of seismic fragility curves for shear key deformation

Minor Damage Moderate Damage

Sam

ple

No

Flood

1-yr

Flood

2-yr

Flood

10-yr

Flood

20-yr

Flood

No

Flood

1-yr

Flood

2-yr

Flood

10-yr

Flood

20-yr

Flood

1 0.815 0.815 0.815 0.815 0.815 > 5.0 > 5.0 > 5.0 > 5.0 > 5.0

2 0.815 0.815 0.688 0.688 0.688 > 5.0 > 5.0 3.045 3.045 3.045

3 0.815 0.815 0.815 0.741 0.741 > 5.0 > 5.0 > 5.0 > 5.0 > 5.0

4 0.815 0.815 0.815 0.815 0.815 > 5.0 > 5.0 > 5.0 > 5.0 > 5.0

5 0.894 0.894 0.800 0.800 0.800 > 5.0 > 5.0 > 5.0 > 5.0 > 5.0

6 0.815 0.815 0.815 0.815 0.815 > 5.0 > 5.0 > 5.0 > 5.0 > 5.0

7 0.932 0.932 0.932 0.932 0.932 > 5.0 > 5.0 > 5.0 > 5.0 > 5.0

8 0.815 0.815 0.745 0.745 0.745 > 5.0 > 5.0 > 5.0 > 5.0 > 5.0

9 0.815 0.745 0.745 0.688 0.688 > 5.0 > 5.0 > 5.0 2.715 2.715

10 0.688 0.688 0.688 0.688 0.688 1.935 1.935 1.935 1.935 1.935

11 0.894 0.894 0.894 0.894 0.894 > 5.0 > 5.0 > 5.0 > 5.0 > 5.0

12 0.688 0.688 0.688 0.688 0.688 > 5.0 3.045 3.045 3.045 3.045

13 1.935 1.935 1.935 1.935 1.935 > 5.0 > 5.0 > 5.0 > 5.0 > 5.0

14 0.894 0.894 0.894 0.800 0.800 > 5.0 > 5.0 > 5.0 > 5.0 > 5.0

15 0.688 0.688 0.688 0.688 0.688 > 5.0 3.045 3.045 3.045 3.045

16 0.815 0.815 0.815 0.815 0.815 > 5.0 > 5.0 > 5.0 > 5.0 > 5.0

17 0.815 0.932 0.932 0.815 0.815 > 5.0 > 5.0 > 5.0 > 5.0 > 5.0

18 0.688 0.688 0.688 0.688 0.688 > 5.0 > 5.0 > 5.0 > 5.0 > 5.0

19 0.815 0.815 0.815 0.815 0.815 > 5.0 > 5.0 > 5.0 > 5.0 > 5.0

20 0.688 0.688 0.688 0.688 0.688 2.715 2.715 1.935 1.935 1.935

133

Table E-8: Median values of system-level seismic fragility curves at minor and moderate damage

states

Minor Damage Moderate Damage

Sam

ple

No

Flood

1-yr

Flood

2-yr

Flood

10-yr

Flood

20-yr

Flood

No

Flood

1-yr

Flood

2-yr

Flood

10-yr

Flood

20-yr

Flood

1 0.409 0.397 0.385 0.364 0.364 0.688 0.688 0.688 0.688 0.688

2 0.409 0.364 0.364 0.345 0.345 0.688 0.688 0.688 0.688 0.688

3 0.397 0.354 0.354 0.339 0.339 0.688 0.688 0.688 0.688 0.688

4 0.397 0.345 0.354 0.354 0.354 0.688 0.688 0.688 0.688 0.688

5 0.397 0.363 0.373 0.339 0.339 0.688 0.688 0.688 0.688 0.688

6 0.397 0.345 0.354 0.354 0.354 0.688 0.688 0.688 0.688 0.688

7 0.441 0.409 0.409 0.409 0.409 0.815 0.741 0.688 0.688 0.688

8 0.397 0.397 0.374 0.345 0.345 0.688 0.688 0.688 0.688 0.688

9 0.409 0.409 0.397 0.397 0.397 0.688 0.688 0.688 0.688 0.688

10 0.354 0.345 0.324 0.324 0.324 0.688 0.688 0.688 0.688 0.688

11 0.397 0.354 0.354 0.373 0.373 0.688 0.688 0.688 0.688 0.688

12 0.409 0.364 0.354 0.345 0.345 0.688 0.688 0.688 0.688 0.688

13 0.396 0.409 0.384 0.373 0.373 0.688 0.688 0.688 0.688 0.688

14 0.385 0.363 0.373 0.373 0.359 0.688 0.688 0.688 0.688 0.688

15 0.397 0.385 0.364 0.345 0.345 0.688 0.688 0.688 0.688 0.688

16 0.409 0.397 0.397 0.385 0.374 0.815 0.688 0.688 0.688 0.688

17 0.409 0.409 0.397 0.397 0.397 0.688 0.688 0.688 0.688 0.688

18 0.345 0.345 0.345 0.334 0.334 0.688 0.688 0.688 0.688 0.688

19 0.421 0.374 0.364 0.354 0.354 0.688 0.688 0.688 0.688 0.688

20 0.397 0.354 0.345 0.345 0.345 0.688 0.688 0.688 0.688 0.688

Table E-9: Median values of system-level seismic fragility curves at major damage and collapse states

Major Damage Collapse State

Sam

ple

No

Flood

1-yr

Flood

2-yr

Flood

10-yr

Flood

20-yr

Flood

No

Flood

1-yr

Flood

2-yr

Flood

10-yr

Flood

20-yr

Flood

1 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815

2 0.741 0.688 0.688 0.815 0.815 0.815 0.815 0.815 0.815 0.815

3 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815

4 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815

5 0.815 0.741 0.741 0.741 0.741 0.815 0.815 0.741 0.815 0.815

6 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815

7 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.894 0.894

8 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815

9 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815

10 0.815 0.688 0.741 0.741 0.741 0.815 0.815 0.815 0.815 0.815

11 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815

12 0.815 0.688 0.688 0.815 0.815 0.815 0.815 0.815 0.815 0.815

13 0.741 0.741 0.741 0.741 0.741 0.815 0.741 0.741 0.741 0.741

14 0.815 0.741 0.741 0.741 0.741 0.815 0.741 0.741 0.815 0.815

15 0.815 0.688 0.688 0.815 0.815 0.815 0.815 0.815 0.815 0.815

16 0.815 0.815 0.815 0.815 0.815 0.894 0.815 0.815 1.005 1.005

17 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815

18 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815

19 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815 0.815

20 0.815 0.745 0.745 0.815 0.815 0.815 0.815 0.815 0.815 0.815

134

APPENDIX F

RESULTS OF SYSTEM-LEVEL FRAGILITY PARAMETERS OF BRIDGE-1 WITH

90% CONFIDENCE

Table F-1: Median values of system-level fragility curves of Bridge-1 corresponding to 5%, 50%, 95,

and that computed when all input parameters are deterministic

Case Minor Damage Moderate Damage

c0.05 c0.5 c0.95 cdet c0.05 c0.5 c0.95 cdet

No Flood 0.454 0.392 0.339 0.409 0.882 0.750 0.638 0.688

1-Yr Flood 0.419 0.373 0.333 0.364 0.786 0.714 0.648 0.688

2-Yr Flood 0.423 0.370 0.325 0.354 0.741 0.688 0.639 0.688

10-Yr Flood 0.417 0.362 0.314 0.345 0.741 0.688 0.639 0.688

20-Yr Flood 0.412 0.360 0.315 0.345 0.741 0.688 0.639 0.688

Case Major Damage Collapse State

c0.05 c0.5 c0.95 cdet c0.05 c0.5 c0.95 cdet

No Flood 0.891 0.808 0.733 0.815 0.899 0.820 0.748 0.815

1-Yr Flood 0.891 0.774 0.673 0.815 0.892 0.809 0.733 0.815

2-Yr Flood 0.889 0.777 0.679 0.815 0.891 0.805 0.726 0.815

10-Yr Flood 0.889 0.800 0.721 0.815 0.932 0.825 0.730 0.815

20-Yr Flood 0.889 0.800 0.721 0.815 0.932 0.825 0.730 0.815

VITA

TANER YILMAZ

Education

Ph.D. Civil Engineering, May 2015

Major in Structural Engineering

The Pennsylvania State University, University Park, PA

M.Sc. Civil Engineering, December 2008

Major in Structural Engineering

Middle East Technical University, Ankara, Turkey

B.Sc. Civil Engineering, June 2005

Middle East Technical University, Ankara, Turkey

Research Experience

2011-present Graduate Research Assistant, Department of Civil and Environmental Engineering,

The Pennsylvania State University

2009-2011 Teaching Assistant, Department of Civil Engineering, Middle East Technical University

Professional Experience

2007-2009 Structural Engineer, Pro-Sem Engineering Architecture Consulting, Ankara, Turkey

2005-2007 Structural Engineer, En-Su Engineering and Consulting, Ankara, Turkey

Awards and Honors

Research Scholar, National Science Foundation, 2011-2015

Fellowship, College of Engineering Recruitment Fund, The Pennsylvania State University, 2012

The best M.Sc. thesis award by Turkish Road Association, 2009

Publications

1. Yilmaz, T., Banerjee, S., Johnson, P. A. (2015). “Risk and uncertainty analyses of highway bridges

integrating seismic and flood hazards.” Structural Safety (submitted for review).

2. Yilmaz, T., Banerjee, S., Johnson, P. A. (2014) “Performance of two real-life California bridges

under regional natural hazards.” Journal of Bridge Engineering, ASCE (under review).

3. Yilmaz, T., and Banerjee, S. (2013). “Seismic risk of highway bridges in flood-prone regions.”

Proceedings of the 11th International Conference on Structural Safety and Reliability, New York.

4. Yilmaz, T., and Caner A. (2012). “Target damage level assessment for seismic performance

evaluation of two-column reinforced concrete bridge bents.” Journal of Bridge Structures, IOS Press,

8(3-4), 135-146.

5. Caner, A., Yanmaz, A. M., Yakut, A., Avsar, O., Yilmaz, T. (2008). “Service life assessment of

existing highway bridges with no planned regular inspections.” Journal of Performance of Constructed

Facilities, ASCE, March/April, 108-114.