SEISMIC VULNERABILITY ASSESSMENT OF A FAMILY OF HORIZONTALLY CURVED STEEL BRIDGES USING RESPONSE SURFACE METAMODELS

SEISMIC VULNERABILITY ASSESSMENT OF A FAMILY OF HORIZONTALLY CURVED STEEL BRIDGES USING RESPONSE SURFACE METAMODELS

ABSTRACT

Civil infrastructure systems must be designed and constructed to resist the effects of natural and manmade hazards to ensure public safety and to support the socio-economic goals and needs of society.  In recent decades, earthquake hazards have been viewed as extremely important among the natural hazards impacting civil infrastructure systems across certain regions in the

United States.  The occurrence of three major earthquakes during that period (San Fernando in 1971, Loma Prieta in 1989, and Northridge in 1994) demonstrated the possible seismic vulnerabilities that existing bridges may contain.  These major seismic events also have provided the impetus for significant improvements in engineering practices for bridge seismic design, analysis, and vulnerability assessment.

Bridge seismic risk assessment tools have been proposed and utilized by many engineers and researchers since the inception of earthquake engineering in the 1970’s.  These tools have predominately used fragility curves, which are conditional probability statements that give the probability of a bridge reaching or exceeding a particular damage level for an earthquake of a given intensity level, for examining straight bridge structures.  Fragility curves for the bridge components and system are essential inputs into the final damage estimation algorithm for a given earthquake event.

Since these tools were developed for evaluating the seismic vulnerability of straight bridges, they cannot be applied to curved bridges.  There has been a steady growth in the use of horizontally curved steel bridges since approximately 1970, which coincides with the initiation period of the earthquake engineering field.  Effects of various curved bridge parameters, including radius of curvature, on the fragility of bridges across geographic regions must be investigated for their seismic assessment.

In this study the characteristics of structures in a target inventory were used to estimate fragilities for a family of horizontally curved steel bridges.  Consideration was restricted to the

 

class of bridge structures consisting of horizontally curved steel I-girder bridges.  Statistically significant predictors for seismic vulnerability assessment were identified using Design of Experiments (DOE) and other statistical tools, and appropriate seismic response surface metamodels (RSMs) were developed to rapidly predict seismic response for a family of horizontally curved steel bridges.  Fragility curves for horizontally curved steel I-girder bridges were estimated using the metamodels with Monte Carlo simulation.  The use of metamodels reduced the required computations and made it practical to carry out probabilistic response calculations in an efficient manner.  Various sources of structural uncertainty were considered and tracked throughout the study, including radius of curvature, number of spans, cross-frame spacing, girder spacing, span length.  This approach allowed for the direct implementation of findings into existing seismic risk assessment packages (e.g., FEMA Hazards U.S. Multi-Hazard loss assessment package, etc.).  Findings from the study show that this approach provides reliable fragility curves for a family of horizontally curved steel I-girder bridges in the target region.

TABLE OF CONTENTS

LIST OF FIGURES……………………………………………………………………………………………… viii

LIST OF TABLES………………………………………………………………………………………………… xii

ACKNOWLEDGEMENTS……………………………………………………………………………………. xiv

 

 

Chapter 1  INTRODUCTION…………………………………………………………………………………………….1

1.1 Background………………………………………………………………………………………………………………..1

1.2 Problem Statement………………………………………………………………………………………………………2 1.3 Objective, Scope and Organization………………………………………………………………………………..3

 

Chapter 2  LITERATURE SEARCH ………………………………………………………………………………….5

2.1 Historical Review………………………………………………………………………………………………………..5

2.1.1 Horizontally Curved Steel Bridges ………………………………………………………………… 6

2.2 Fragility Curves ………………………………………………………………………………………………………….8

2.2.1 Expert Based Fragility Curves………………………………………………………………………. 9 2.2.2 Empirical Fragility Curves…………………………………………………………………………. 10 2.2.3 Analytical Fragility Curves ………………………………………………………………………… 13

2.2.4 Analytical Fragility Curve Development Using Metamodels ……………………………… 17

2.3 Conclusion ……………………………………………………………………………………………………………….18

 

Chapter 3  RESPONSE SURFACE METAMODEL METHODOLOGY FOR GENERATION OF

BRIDGE FRAGILITY CURVE……………………………………………………………………………………….19

3.1 Metamodels………………………………………………………………………………………………………………19

3.2 Experimental Designs………………………………………………………………………………………………..21

3.2.1 Full Factorial Design………………………………………………………………………………… 22 3.2.2 Central Composite Design …………………………………………………………………………. 23

3.3 Response Surface Metamodels ……………………………………………………………………………………25

3.4 Response Surface Metamodels for Seismic Fragility Assessment ……………………………………31

3.5 Conclusion ……………………………………………………………………………………………………………….34

Chapter 4  3-D ANALYTICAL MODELING APPROACH OF HORIZONTALLY CURVED

STEEL BRIDGE…………………………………………………………………………………………………………….35

4.1 Modeling Approach…………………………………………………………………………………………………..36

4.1.1 Superstructure…………………………………………………………………………………………. 38

4.1.2 Substructure……………………………………………………………………………………………. 39 4.2 Model Validation………………………………………………………………………………………………………42

4.2.1 Examined Bridge Description …………………………………………………………………….. 43

4.2.2 3-D Analytical Model……………………………………………………………………………….. 48 4.2.3 Validation Procedure………………………………………………………………………………… 51

4.2.3.1 Field Testing………………………………………………………………………………… 51 4.2.3.2 Static 1 ……………………………………………………………………………………….. 53 4.2.3.3 Static 2 ……………………………………………………………………………………….. 56 4.2.3.4 Static 3 ……………………………………………………………………………………….. 58 4.2.3.5 Static 4 ……………………………………………………………………………………….. 60 4.2.3.6 Discussion …………………………………………………………………………………… 62

4.3 Seismic Response Methodology………………………………………………………………………………….63

4.3.1 Mode shapes…………………………………………………………………………………………… 65 4.3.2 Seismic Response…………………………………………………………………………………….. 67

4.4 Conclusions………………………………………………………………………………………………………………72

Chapter 5  HORIZONTALLY CURVED STEEL BRIDGE INVENTORY AND GROUND

MOTION DEVELOPMENT……………………………………………………………………………………………74

5.1 Horizontally Curved Steel Bridge Inventory Analysis ……………………………………………………75

5.2 Potential Key Parameters for Horizontally Curved Steel Bridge………………………………………77

5.2.1 Macro-Level Parameters……………………………………………………………………………. 78

5.2.1.1 Number of Spans …………………………………………………………………………… 78 5.2.1.2 Maximum Span Length …………………………………………………………………… 80 5.2.1.3 Deck Width ………………………………………………………………………………….. 81 5.2.1.4 Column Height……………………………………………………………………………… 82 5.2.1.5 Radius of Curvature……………………………………………………………………….. 84 5.2.1.6 Girder Spacing……………………………………………………………………………… 85 5.2.1.7 Cross-Frame Spacing …………………………………………………………………….. 86

5.2.2 Micro-Level Parameters…………………………………………………………………………….. 87

5.3 Synthetic Ground Motions………………………………………………………………………………………….88 5.4 Conclusions………………………………………………………………………………………………………………92

 

Chapter 6  SCREENING OF HORIZONTALLY CURVED STEEL BRIDGE PARAMETERS 93

6.1 Screening Experiments for Inputs………………………………………………………………………………..95

6.2 Screen Experiments for Outputs: Seismic Response………………………………………………………98

6.3 Parameter Screening ………………………………………………………………………………………………….99 6.4 Conclusions…………………………………………………………………………………………………………….108

Chapter 7  SEISMIC FRAGILITY CURVES FOR HORIZONTALLY CURVED STEEL

BRIDGES ……………………………………………………………………………………………………………………109

7.1 RSMs Construction………………………………………………………………………………………………….110 7.2 Seismic Performance Levels……………………………………………………………………………………..126

7.3 Seismic Fragility Curve Generation……………………………………………………………………………129

7.3.1 Seismic Fragility Curves of Bridge Component…………………………………………….. 131 7.3.2 Holistic Seismic Fragility Curves ………………………………………………………………. 138 7.3.3 Fragility Curve Case Studies…………………………………………………………………….. 141

7.4 Conclusions…………………………………………………………………………………………………………….149

 

Chapter 8  CONCLUSIONS, IMPACT AND FUTURE RESEARCH…………………………………150

8.1 Summary and Conclusions ……………………………………………………………………………………….150

8.2 Impact ……………………………………………………………………………………………………………………154 8.3 Areas for Future Research ………………………………………………………………………………………..155

Bibliography ………………………………………………………………………………………………………………..156 Appendix A  PLACKETT-BURMAN DESIGN……………………………………………………………….166

Appendix B  CENTRAL COMPOSITE DESIGN …………………………………………………………….171

Chapter 1

 

INTRODUCTION

1.1 Background

Transportation networks are spatially distributed systems whereby components are exposed to natural and man-made hazards.  Transportation networks significantly affect worldwide social and economic stability due to the dependence on the reliable supply of goods and services (Dueñas-Osorio, 2005).  Highways, railroads, airports and harbors represent critical elements of the social infrastructure needed to balance supply and demand activities on national and international scales.

If an earthquake strikes near urban regions, it is essential that the transportation systems remain operational.  Past earthquakes have demonstrated that loss of critical highway components (e.g., bridges, roadways, etc.) can severely impact the economy of the regions and recovery activities (Murachi et al., 2003).

Bridges are one of the most vulnerable highway components during an earthquake (Shinozuka et al., 2000; Choi et al., 2004; Nielson, 2005).  It is necessary that the seismic vulnerability of bridges for various damage states be evaluated while carrying out a transportation system seismic risk analysis.  The generation of vulnerability information in the form of fragility curves is a common approach when assessing bridge seismic vulnerability (Shinozuka et al., 2000; Choi et al., 2004; Nielson, 2005; Padgett, 2007).  A fragility curve provides a conditional probability that gives the likelihood that a structure will meet or exceed a certain level of damage for a given ground motion intensity.  Information provided from a fragility curve can be used for prioritizing bridge retrofit, pre-earthquake planning and post-earthquake response and evaluation.

These curves usually account for a multitude of uncertainty sources related to estimating seismic hazards, including bridge characteristics, type, configuration and others.

Presently, the bridge type mainly considered for fragility curve development is a straight structure.  However, in many instances bridges at major highway interchanges and in urban environments have a horizontally curved (e.g., curved in plan) superstructure.  Horizontally curved steel bridges make up a significant portion of the approximately 597,500 bridges in United States road network (FHWA, 2008).  In fact, nationwide, over one third of all steel bridges constructed are curved (Davidson et al., 2002).  Therefore, the effect of radius of curvature on the fragility of this bridge type should be investigated.

In addition, most research to date on estimating bridge fragility has focused on statistical extrapolation of results for an individual bridge.  To adequately assess seismic vulnerability of a family of bridges (e.g., curved bridge) across various geographic regions, it is necessary that fragilities be generated and estimated based on direct individual dynamic analysis or statistical interpolation.  In particular, when a large number of dynamic analyses are required to compute seismic response of a population of bridges, it is vital to employ approximation methods to efficiently and adequately predict seismic response.  Therefore, statistical methodologies that can assist with expanding the population of bridges that are studied without greatly increasing computational time, such as via the use of response surface metamodels (RSMs), are desired.

1.2 Problem Statement

Horizontally curved, steel, I-girder bridges continue to be built with increasing frequency in all seismic zones in the United States.  Even though such bridges are more vulnerable than straight bridges during an earthquake, currently there is no seismic vulnerability criterion incorporating fragility curves in the United States for these types of bridges.

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1.3 Objective, Scope and Organization

Seismic fragility curves that solely consider straight bridges have been developed using time consuming nonlinear time-history analyses.  To efficiently produce fragility curves for a population of horizontally curved steel I-girder bridges, the use of response surface metamodels (RSMs), one of a number of rigorously generated approximate analysis methods based on statistical methodologies, is proposed.  Therefore, the ultimate objective of this research was to generate fragility curves for a family of horizontally curved steel I-girder bridges in a specific geographic region (i.e., Pennsylvania, Maryland, New York) using RSMs.  Effects of various curved bridge parameters, including radius of curvature, on the fragility curves developed for the studied bridge family were also investigated.  Secondary objectives for the research included: (1) application of 3-D nonlinear analytical models to horizontally curved steel bridge dynamics, (2) development of the spherical bearing model, (3) key parameters on seismic response for horizontally curved steel bridges.

 

To accomplish these objectives, the research was organized as follows:

 

• Literature Search that reviewed dynamic studies on curved steel bridges, recent studies on bridge seismic fragility curves, and development of seismic fragility curves using a metamodeling techniques.

 

• RSM Development that reviewed RSMs and experimental designs, determined appropriate experimental design to generate seismic bridge fragility analyses, and developed the RSM methodology for bridge fragilities.

 

• 3-D Modeling that developed 3-D nonlinear analytical models for horizontally curved steel I-girder bridges, validated 3-D nonlinear analytical model based on experimental data, and investigated seismic response of horizontally curved steel I-girder bridges.

 

• Synthetic Ground Motion Development that determined a target region for the horizontally curved steel I-girder bridge inventory, performed inventory statistical analyses for horizontally curved steel I-girder bridges across the target region, and developed synthetic acceleration time histories.

 

• Parameter Screening that established screening experiments, performed nonlinear time history analysis using the 3-D analytical models, and identified key horizontally curved steel I-girder bridge parameters influencing seismic response using statistical screening

 

• Seismic Fragility Curve Development that constructed RSMs for the target region, identified the appropriate seismic capacities and performance levels and produced seismic fragility curves using RSMs in conjunction with Monte Carlo simulation.

SEISMIC VULNERABILITY ASSESSMENT OF A FAMILY OF HORIZONTALLY CURVED STEEL BRIDGES USING RESPONSE SURFACE METAMODELS

 

 

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