PREDICTION OF INDIRECT LOSSES, DIRECT LOSSES, AND SEISMIC RESILIENCE OF AGING HIGHWAY BRIDGES

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PREDICTION OF INDIRECT LOSSES, DIRECT LOSSES, AND SEISMIC RESILIENCE OF AGING HIGHWAY BRIDGES

ABSTRACT

Natural disasters over the past decades, especially earthquakes, have caused varying levels of devastation to transportation systems around our nation.  Bridges are typically the most vulnerable components of the transportation network during severe seismic excitations. Bridges are also prone to other natural phenomena that can lead to significant damage to its structural health over its intended or reduced life span. Some of these natural phenomena cause the bridge to “age”, affecting the overall bridge performance resulting in partial to complete bridge failure. One way a bridge responds to either phenomenon is characterized by its resilience.

Within the scope of this study, one of the primary focuses was to assess a bridge sector for a pre-defined seismic event to estimate the financial costs. The full extent of the damage to this bridge does not only surround the costs associated with the bridge rehabilitation, but it also includes the costs associated with the delays faced by bridge users and the impacted highway network. These costs are just one of the factors that influence the seismic resilience of a given bridge system. The seismic resilience of a bridge relates to how well the bridge performs during seismic activity and the length of time it takes to reach some percentage of its original functionality. This resilience can be predicted with mathematical derivations that incorporate the results of a vulnerability analysis of the bridge for a given ground excitation, an assessment of the costs incurred from the earthquake damage, and an in depth look into how the bridge recovers.

Throughout this thesis, the seismic resilience of the targeted bridge sector will be further investigated for each of the three factors. However, the first intended outcome of this research is to shed light on a comprehensive recovery model for variable bridge damage and to create a MATLAB function that can compute direct and indirect losses given specified data inputs. In addition, a secondary outcome is to apply these findings to a bridge network that experienced aging over its life cycle due to the corrosion of structural steel components.

 

TABLE OF CONTENTS

LIST OF FIGURES…………………………………………………………………………………………… vi

LIST OF TABLES……………………………………………………………………………………………. vii

ACKNOWLEDGEMENTS………………………………………………………………………………. viii

CHAPTER 1: INTRODUCTION AND THESIS ORGANIZATION…………………….. 1

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

1.2 Introduction…………………………………………………………………………………………. 4

1.3 Motivation…………………………………………………………………………………………… 5

1.4 Objectives and Scope……………………………………………………………………………. 6

1.5 Thesis Organization………………………………………………………………………………. 9

CHAPTER 2: LITERATURE REVIEW……………………………………………………………. 11

2.1 Quantifying Bridge Structural Vulnerability…………………………………………… 11

2.1.1 Bridge Damage…………………………………………………………………………….. 11

2.1.2 Empirical Fragility Curves…………………………………………………………….. 13

2.1.3 Analytical Fragility Curves……………………………………………………………. 15

2.2 Assessing Bridge Losses Post-Seismic Event…………………………………………. 16

2.2.1 Direct Losses……………………………………………………………………………….. 16

2.2.2 Indirect Losses……………………………………………………………………………… 17

2.2.3 Simplified Traffic Flow Analysis…………………………………………………….. 20

2.3 Predicting the Recovery of a Bridge Sector……………………………………………. 24

2.4 Calculating the Resilience of a Bridge Sector…………………………………………. 29

CHAPTER 3: SEISMIC RESILIENCE CASE STUDY EXPLORATION………….. 33

3.1 Explanation of Previous Case Study……………………………………………………… 33

3.2 Approximated Bridge Functionality………………………………………………………. 34

3.3 Assumed Recovery Function………………………………………………………………… 35

CHAPTER 4: LOSS MODEL & RESILIENCE MATLAB PROGRAM…………….. 37

4.1 Direct Losses……………………………………………………………………………………… 37

4.1.1 Five Damage Levels and Four Recovery Velocities………………………….. 39

4.1.2 Twenty Outcomes and Twenty-four Restoration Strategies………………… 41

4.1.3 Explanation of Five Variable Parameters………………………………………… 43

4.2 Indirect Losses……………………………………………………………………………………. 46

4.3 Bridge Losses and Resilience Program Methodology……………………………… 48

4.4 MATLAB Program Creation………………………………………………………………… 53

4.5 Metrics for Program Refinement and Validation…………………………………….. 55

4.6 MATLAB Bridge Losses and Resilience Program Results………………………. 62

4.7 Conclusions and Sources of Error/Limitations of Program………………………. 65

CHAPTER 5: RECOVERY MODEL………………………………………………………………… 67

5.1 Existing Bridge Recovery Models…………………………………………………………. 67

5.2 Sigmoidal Recovery Model………………………………………………………………….. 70

CHAPTER 6: RESILIENCE OF BRIDGES SUBJECTED TO CORROSION……. 75

6.1 Chloride Induced Corrosion…………………………………………………………………. 75

6.2 Chloride-Induced Corrosion…………………………………………………………………. 78

CHAPTER 7: CONCLUSIONS AND FUTURE APPLICATIONS…………………….. 85

7.1 Conclusions and Sources of Error…………………………………………………………. 85

7.2 Future Application of Current Study……………………………………………………… 86

Appendix A………………………………………………………………………………………………………. 87

INITIAL BRIDGE LOSSES AND RESILIENCE PROGRAM………………… 87

Appendix B………………………………………………………………………………………………………. 93

REVISED BRIDGE LOSSES AND RESILIENCE PROGRAM………………. 93

Appendix C…………………………………………………………………………………………………….. 100

RECOVERY PROFILE AND RESILIENCE PROGRAM…………………….. 100

Appendix D…………………………………………………………………………………………………….. 105

BRIDGE LOSSES PROGRAM FOR AGING BRIDGES………………………. 105

REFERENCES……………………………………………………………………………………………….. 115

CHAPTER 1: INTRODUCTION AND THESIS ORGANIZATION

1.1 Background

Structural earthquake damage devastates many buildings and structures around the world, affecting and claiming the lives of numerous individuals. These natural disasters leave behind a path of destruction and months of repair/rehabilitation. Freeways and bridges are often severely damaged during earthquakes and the repair time can be very extensive. Depending on the importance of the freeway (how much traffic it carries daily), traffic disruption can come with severe consequences for high population areas such as Los Angeles or New York City. Earthquake damage is a short-term threat to bridges that can occur at any given time during a bridge’s life cycle. One key seismic event that fueled the structural engineering community to pay more attention to the recovery of bridges and resilience was the 1994 Northridge Earthquake.  The National

Transportation Recovery Strategy was implemented by the US Department of Transportation to place emphasis on the transportation network recovery process and create a greater level of resilience nationwide through effective transportation recovery, planning, and implementation (USDOT 2009).

Corrosion is another natural disaster that can affect the structural integrity of a bridge network. When structural steel is left without adequate protection it will corrode due to the influence of its surrounding environment causing the bridge to age or weather.

One particular case of aging is due to chloride-induced corrosion of bridge components (RC columns and steel bridge bearings) that are exposed to marine environments or regions where deicing salts are used for snow and ice removal (Ghosh and Padgett 2010). Unlike earthquake damage, the corrosion of structural bridge elements is a long-term threat that can cause detrimental effects to a bridge’s performance. Structural engineering investigations of the West Virginia Silver Bridge collapse of 1967 and the Connecticut Mianus River Bridge collapse of 1983 concluded that the corrosion of the respective structural steel elements led to both catastrophic bridge failures (FHWA 2012).

Bridge resilience is the ability of social units (e.g., organizations and communities) to mitigate hazards, contain the effects of disasters when they occur, and carry out recovery activities in ways that minimize social disruption and mitigate the effects of future disasters (Venkittaraman and Banerjee 2013). Resilience can be measured as the ratio of the integration of the bridge’s recovery path over a specified time interval. This resilience can be quantified using a probabilistic approach to integrate the vulnerability of the bridge, a model of the losses incurred due to the damage induced by the natural phenomenon, and a post-event recovery model.

The use of fragility curve analyses allow for an engineer to estimate the seismic vulnerability of a bridge. A fragility curve is a probability function that dictates the probability of a bridge exceeding a predefined damage level during a specified seismic intensity based on outlined conditions (Venkittaraman and Banerjee 2013). Using the developed fragility probabilities, the bridge damage losses can be calculated.

The losses for a specified bridge failure can have significant variation, but it relies heavily on the level of damage the bridge incurs. A bridge failure with low or moderate damage will not have as high losses as one with severe damage or total collapse. The damage level of the bridge is dependent on its seismic vulnerability, which is synonymous to the fragility curves. However, the losses will also be dictated by the recovery of the bridge. A bridge that recovers faster will have lower losses in comparison to a bridge that has a much slower recovery.

The recovery model also dictates just how long losses will be accrued until the bridge reaches some level of system recovery. Bridge recovery can be short term, long term, or unreachable depending on the level of damage. It is clear that each of these three factors influence one another as well as controlling the overall bridge seismic resilience. This thesis provides a detailed investigation into the determination of bridge losses and resilience and the factors that influence them. Bridge losses were also investigated for damage due to seismic events and chloride induced corrosion of structural steel bridge components.

 

 

 

 

 

 

 

 

 

 

1.2 Introduction

This thesis utilizes the previous work performed by Deco et al. (2013) to establish a MATLAB program for calculating bridge losses and resilience. This program is based on the conclusions and theoretical approach presented in the referenced case study. Deco et al. (2013) describes an approach for calculating the direct losses, two forms of indirect losses, and resilience for a bridge that is subjected to seismic damage. The MATLAB program follows the formulas and parameters used, but does not include any probability analysis for parameters that are not fixed. As well, the use of a Monte Carlo simulation based on Latin hypercube sampling is not performed. Random variables are taken as their max or mean values from the case study when applicable. As well, the program uses assumed fragility curve data for assigning the damage state probabilities.

The results of the created MATLAB program are compared to the results from Deco et al. (2013) to ensure that the program has a reasonable level of validity due to the assumption of some variables. The fragility curve probability data are calibrated and refined to achieve this goal.

The work in this thesis expands upon the previous work in Deco et al. (2013) by refining the code to apply to a multi-hazard bridge failure. The created program is altered to account for both seismic damage and the damage due to chloride-induced corrosion accumulation of different time spans.

1.3 Motivation

The motivation for this study stems from two areas of uncertainty. The first area relates to the indirect costs caused by traffic disruption as a result of minimal to extensive bridge damage. Direct costs, which refer to the rehabilitation/reconstruction of the bridge, removal of debris, and the construction of a temporary bypass, are easy to calculate using the summation of all three multiplied by a factor associated with the damage state of the bridge. However, indirect costs are influenced by many time varying parameters related to the bridge and any related links or detours that arise to provide temporary transit to bridge users. Previous studies have stated that indirect costs can be five to twenty times as much as that of the direct costs (Dennemann 2009). This makes the indirect costs a huge factor in assessing seismic damage. As a result, this study creates a numerical program within MATLAB for assessing indirect costs as well as direct costs and bridge resilience.

The second area of uncertainty relates to bridge recovery. Many recovery models have been proposed for mapping the path a bridge takes to reach full or partial functionality (Cimellaro et al. 2010). Some of the current recovery model patterns in existence include linear, exponential, and trigonometric. The biggest issue is that there is no mathematical recovery function that controls over the others in approximating the actual recovery of a bridge. As a result, this study aims to present a recovery model that provides a higher level of certainty versus the others.

 

 

1.4 Objectives and Scope

The scope of this thesis focuses on the analysis of two bridges from different bridge networks. This study is primarily done to develop and validate a MATLAB program for predicting direct losses, indirect losses, and resilience due to bridge damage from an earthquake event. Upon completion, developed MATLAB program will be used in the second part of this research to evaluate bridge losses of an aging bridge. The first analysis pertains to an existing California highway located between the cities of Corona and Murrieta. For this analysis, there are three objectives related to the overall goal of determining the seismic resilience of this bridge sector on I-15. The objectives of this first study include:

 

  1. Decomposition of a previous bridge resilience case study – A previous study was performed by Deco et al. (2013) to determine the seismic resilience of the I15 bridge sector. This case study is further analyzed to understand the logic and process followed, in order to complete the second objective of this study.

 

  1. Seismic Resilience MATLAB Program Development – From the case study, the structural vulnerability and recovery function of the bridge sector are integrated with the bridge losses to determine the resilience of the bridge, which is

shown in Figure 1-1. A MATLAB program was developed that aims to complement the conclusions observed in the case study. This program has the ability to accept: (1) user input from various sources (AASHTO historical records, Google Maps, and FHWA databases), (2) calculated bridge functionality determined from fragility curve analyses, (3) assumed recovery function(s), in order to output the losses and seismic resilience of the specified bridge segment.

 

  • Recovery Model Function Analysis – Different recovery models (linear, exponential, trigonometric, and negative exponential) were created to predict multiple recovery shapes of the bridge failure. The goal was to find a function that has the capability to produce a representative suite of potential recovery curves for a given seismic event and bridge sector.

 

Figure 1-1 show the three components that influence the calculation of the resilience for a particular bridge sector.

 

 

Figure 1-1: Bridge Resilience Progression (Seismic Analysis)

 

 

The second analysis relates to a highway bridge located in Memphis, TN. This subsequent analysis will use the conclusions drawn from the first study in order to calculate the bridge losses of a bridge sector that is exposed to chloride-induced corrosion. The objectives of the second study are to:

 

  1. Apply an existing MATLAB program to an aging bridge – The MATLAB

program created in the first study is altered in order to analyze a bridge over its life cycle of 100 years.

 

  1. Life Cycle Bridge Losses Study – The structural steel components of this particular bridge suffered from chloride-induced corrosion and the bridge is evaluated for a time span of 100 years. Pre-determined fragility curves of the bridge at time intervals of 25 years of corrosion accumulation were incorporated into the MATLAB program. The goal of this new MATLAB program was to observe how the bridge’s indirect and direct losses change over its life cycle of 100 years.

 

 

 

 

 

1.5 Thesis Organization

This thesis is arranged into seven chapters. The first chapter contains the front matter such as the background, research motivation, objectives, and the scope of the thesis. The remaining content of the thesis is organized into the following six chapters:

Chapter 2 is a literature review of the information available before the research was conducted. Within this chapter are references to specific authors and/or journals that provided fundamental theory, mathematical equations, and prior research findings and conclusions to help fuel the applications used in this thesis.

Chapter 3 investigates a previous case study done to find the resilience of a bridge sector located on I-15. This chapter focuses on identifying what data are needed or approximated in order to calculate bridge losses and resilience.

Chapter 4 documents the creation of a MATLAB program to calculate the direct losses, indirect losses, and resilience of the bridge referenced in the case study. Also included is a validation process for comparing data trends between the developed program and the case study it is based upon.

Chapter 5 presents a brief look at the past recovery models used for predicting the length of time and approximate path for a specified damaged bridge to follow during restoration. Also included are some of the main areas of concern for these recovery models and a look at a new function with the potential of being more comprehensive for bridge recovery prediction.

 

Chapter 6 focuses on the repurposing of the developed MATLAB program to make it applicable for use with an aging bridge subjected to chloride-induced corrosion and a seismic extreme event. The bridge losses of this bridge exposed to this form of aging is evaluated over its life cycle to observe its response.

Chapter 7 presents the key conclusions obtained from the research and suggestions for future applications of the data documented within this thesis. In addition, this chapter contains advice for further testing, and addresses areas of concern regarding the research findings.

PREDICTION OF INDIRECT LOSSES, DIRECT LOSSES, AND SEISMIC RESILIENCE OF AGING HIGHWAY BRIDGES

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