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2018 Resilience of Transportation Networks Subject to Bridge Damage and Road Closures Richard Twumasi-Boakye

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COLLEGE OF ENGINEERING

RESILIENCE OF TRANSPORTATION NETWORKS SUBJECT TO BRIDGE DAMAGE

AND ROAD CLOSURES

RICHARD TWUMASI-BOAKYE

A Dissertation submitted to the Department of Civil and Environmental Engineering in partial fulfillment of the requirements for the degree of Doctor of Philosophy

2018

Richard Twumasi-Boakye defended this dissertation on July 19, 2018. The members of the supervisory committee were:

John O. Sobanjo Professor Directing Dissertation

Eric Chicken University Representative

Ren Moses Committee Member

Eren E. Ozguven Committee Member

The Graduate School has verified and approved the above-named committee members, and certifies that the dissertation has been approved in accordance with university requirements.

To my family

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ACKNOWLEDGMENTS

I take this opportunity to acknowledge all those who have guided, assisted and supported me during my period of research leading to the completion of this dissertation. First, I would like to express my sincerest gratitude to Dr. John Sobanjo for his immense support, mentoring and guidance throughout my studies at the Florida State University.

I would also like to thank Dr. Ren Moses, Dr. Eren Ozguven, and Dr. Eric Chicken who served as my doctoral committee members for their invaluable inputs and support.

Words are insufficient to express my appreciation to the Olawale family for their love and inspiration throughout my graduate studies. Special thanks to Pastor Mark Amoateng, M.D., and Ms. Althea Devenish for their counsel and prayers. Further thanks to all my colleagues, and friends, Sylvester Inkoom, James Akrasi, Jaqueline Masaki, and Filiberto Asare-Akuffo, for their friendship, love, and encouragement.

My heartfelt appreciation goes to my family (Mr. Alex Twumasi-Boakye, Mrs. Elizabeth Twumasi-Boakye, Ms. Barbara Twumasi-Boakye, Ms. Angelina Twumasi-Boakye, Dr. Alberta Twumasi-Boakye, and Mr. Alex Twumasi-Boakye Jr.) for their love and prayers throughout my studies: May God immeasurably bless you.

Finally, my greatest gratitude goes to the Almighty God for His grace, mercies, provision, and guidance. “By You I have been sustained from my birth; You are He who took me from my mother's womb; My praise is continually of You.” Psalm 71:6. Thank you Lord!

TABLE OF CONTENTS

List of Tables ...... ix List of Figures ...... xi Abstract ...... xiv

1. BACKGROUND ...... 1 1.1 Introduction ...... 1 1.2 Motivation and Problem Definition ...... 5 1.3 Research Objectives ...... 5 1.4 Outline of the Thesis ...... 6

2. LITERATURE REVIEW ...... 9 2.1 Introduction ...... 9 2.2 Overview of Performance Measures for Civil Infrastructures ...... 11 2.3 Defining Resilience ...... 13 2.4 Main Categories of Transportation Network Resilience Studies ...... 14 2.4.1 Qualitative Concepts...... 14 2.4.2 Quantitative Concepts...... 18 2.5 Key Issues in the Transportation Network Resilience Dialogue...... 23 2.5.1 The Need for Network-level Transportation Network Resilience Studies ...... 23 2.5.2 Quantifying the Recovery Phase of Resilience ...... 25 2.6 Towards the Development of a Resilience Index...... 26 2.7 Further Discussions ...... 31 2.8 Chapter Summary ...... 37

3. METHODOLOGY ...... 38 3.1 Introduction ...... 38 3.2 Total Additional User Cost ...... 38 3.2.1 Measure of Vehicle Miles Traveled (VMT) ...... 39 3.2.1 Vehicle Operating Cost ...... 39 3.2.3 Measure of Vehicle Hours Traveled (VHT) ...... 40

3.2.4 Delay Cost ...... 41 3.3 Schematic Framework for At-Risk Bridge Selection and Accessibility Measure ...... 42 3.3.1 Computing Bridge Exposure Probabilities to Categorical Hurricane Events ...... 42 3.3.2 Allocating Damage States to Bridges Using both Historical and NBI Data Fields ..... 44 3.4 Development of Resilience Index ...... 45 3.4.1 Equilibrium-based Traffic Assignment ...... 45 3.4.2 Measure of Vehicle Distance Traveled (VDT) ...... 47 3.4.3 Measure of Vehicle Hours Traveled (VHT) ...... 47 3.4.4 High Impact Zone Location Metric ...... 47 3.4.5 Measuring Network Functionality ...... 49 3.4.6 Computing Resilience Index ...... 50 3.5 Numerical Illustration ...... 55 3.5.1 Resilience Estimation and Index Computation ...... 58 3.5.2 Hypothetical Network Application ...... 64 3.5.3 Sensitivity Analysis ...... 69 3.6 Chapter Summary ...... 74

4. EVALUATING TRANSPORTATION USER COST ...... 75 4.1 Evaluating User Cost for Simulated Regional Networks ...... 75 4.2 Study Area ...... 80 4.3 Transportation Network Configuration ...... 80 4.4 Traffic Flow Estimation ...... 80 4.5 Data Sources ...... 81 4.6 Scenario-Based Modeling ...... 82 4.7 Results and Discussion ...... 84 4.6 Chapter Summary ...... 91

5 . ACCESSIBILITY-BASED RESILIENCE MEASURE ...... 92 5.1 Senior Community Resilience using Accessibility as Measure to Healthcare ...... 92 5.2 Methodology ...... 92 5.2.2 Discussion for Damage State Analysis ...... 95 5.2.3 Identifying Bridges at Risk to Hurricane-induced Damage ...... 95

5.2.4 Computing Resilience...... 96 5.3 Case Study for Accessibility Analysis ...... 97 5.3.1 Data Set...... 98 5.4 Results and Discussion ...... 99 5.5 Chapter Summary ...... 103

6 . REGIONAL NETWORK RESILIENCE ...... 104 6.1 Regional Network Resilience for Tampa Bay Area ...... 104 6.2 Summary of Methodology ...... 105 6.3 Application Example ...... 108 6.3.1 Network Configuration ...... 109 6.3.2 Network Scenario Modeling ...... 109 6.4 Results and Discussion ...... 111 6.5 Chapter Summary ...... 117

7. POST-HAZARD RECOVERY EVALUATION ...... 118 7.1 Evaluating the Recovery Phase of Resilience based on Post-Hurricane Bridge Damages 118 7.2 Recovery Phase of Resilience ...... 119 7.3 Data Identification and Merging Procedures ...... 121 7.4 Results and Discussion ...... 124 7.5 Chapter Summary ...... 132

8. SUMMARY ...... 134 8.1 Concluding Remarks ...... 134 8.2 Limitations and Recommendation for Future Studies...... 137

APPENDICES ...... 139

A. BRIDGE AND ROADWAY EXPOSURE PROBABILITIES ...... 139 B. MATLAB CODES FOR NUMERICAL ILLUSTRATION ...... 149 C. POST-HAZARD BRIDGE AND ROAD CLOSURE TIMES ...... 184

References ...... 213

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Biographical Sketch ...... 231

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LIST OF TABLES

2. 1 Brief description of essential terminologies ...... 12

2. 2 Some key components of resilience definitions found in literature ...... 15

2. 3 Summary table for selected literature which focus on resilience measures for transportation network ...... 22

2. 4 Some practical resilience index formulations in literature (2011 – 2016) ...... 32

2. 5 Literature summary on the resilience of transportation networks (focus on research efforts from 2008 to 2016) ...... 36

3. 1 Simulation results for individual bridge closure scenarios ...... 65

3. 2 Resilience index results for individual bridge closure scenarios ...... 66

3. 3 Selected bridges for multi closure scenario ...... 67

3. 4 Simulation results and resilience index computation for multiple bridge closures ...... 67

4. 1 Travel time and distance differences between original and detour paths ...... 86

4. 2 Additional VHT, VMT and user cost computations for bridge closure scenarios...... 89

5. 1 Qualitative damage state descriptions defined by amending HAZUS for typical hurricane- induced bridge damage ...... 93

5. 2 NBI fields considered for bridge damage state assessment ...... 94

6. 1 Bridge closure durations after hurricane events (sample data) ...... 106

6. 2 Illustrative results for I-275 bridge closure ...... 113

6. 3 Performance index and resilience index for bridge closure scenarios ...... 116

7. 1 Summary table ...... 124

7. 2 Descriptive statistics for all inspected infrastructures ...... 124

7. 3 Anova results ...... 129

7. 4 Damaged bridges ...... 129

7. 5 Fitted distributions for recovery times ...... 132

C. 1 Post-hazard restoration times for interstate bridges ...... 184

C. 2 Post-hazard restoration times for non-interstate bridges ...... 191

C. 3 Post-hazard restoration times for interstate roadways ...... 205

C. 4 Post-hazard restoration times for non-interstate roadways ...... 205

LIST OF FIGURES

1. 1 Reported natural disasters worldwide between 1900 and 2010 ...... 3

1. 2 Damage to girders and piers due to impact from tugboat and barge (Padgett et. al, 2008) ..... 3

1. 3 Storm surge-induced loading (Padgett et. al, 2008) ...... 4

2. 1 Hazards with most damages in terms of cost...... 10

2. 2 Resilience triangle indicating functionality loss (concept from Bruneau et. al, 2003) ...... 13

2. 3 Principles of Resilience (developed from Foster, 1997) ...... 16

2. 4 The dependency diagram as the basis for fuzzy inference (developed from Serulle et al., 2011)...... 29

2. 5 Proposed steps involved in developing a composite resilience index ...... 31

3. 1 Framework for identifying damaged bridges critical to aging-dense areas ...... 43

3. 2 NBI fields selected for computing bridge damage states...... 44

3. 3 Transportation network resilience diagrams based on bridge damages ...... 51

3. 4 Diagram for MSA traffic assignment algorithm ...... 57

3. 5 Transportation network for numerical illustration ...... 64

3. 6 Multiple bridge closures recovery sequence ...... 68

3. 7 Network resilience curve for multiple bridge closures ...... 69

3. 8 Network resilience index curves for individual bridge closures, varied predicted recovery times, and scheduled recovery durations from 1 to 100 days...... 70

3. 9 Network resilience indexes for individual bridge closures for varied predicted recovery times assuming a scheduled recovery duration (Ti) of 10 days...... 73

4. 1 Network configuration for Tampa Bay regional planning model ...... 82

4. 2 Road network showing five bridges connecting Pinellas to Hillsborough and Manatee Counties ...... 83

4. 3 Traffic counts and CUBE Voyager volume outputs at bridge locations ...... 84

4. 4 a.) LNTT at 30 minutes Isochrone Increments. b.) LNTT (I-275 removal) at 30 minutes Isochrone Increments ...... 85

4. 5 Highway network indicating bridge closures and alternative routes ...... 87

4. 6 Comparison of VHT, VMT and daily total additional user cost results for current method and proposed network based approach ...... 90

5. 1 SSH from SLOSH model and selected local bridges based on SSH threshold for the Tampa Bay area ...... 96

5. 2 Resilience based on bridge damage states used in this study ...... 97

5. 3 Maps showing Pinellas County with the locations of hospitals and expected damaged bridges near to aging-dense zones...... 98

5. 4 Results indicating differences in FFTT and CTT prior to and after bridge closures, as well as FFTT and CTT based functionality measures...... 101

5. 5 Minimum FFTT and CTT to hospitals for each aging-dense location for base network for a and b, and bridge closure-network for c and d ...... 102

6. 1 Total number of major hurricane strikes (1900 – 2010) by Florida county developed using ArcGIS software (data from NOAA)...... 108

6. 2 Map showing the regional transportation network for the case study area ...... 110

6. 3 Maps showing the shortest path for TBRPM scenarios after I-275 closure and high impact areas (developed using Cube Voyager and ArcGIS software) ...... 112

6. 4 Resilience diagrams illustrating I-275 bridge closure scenarios (not to scale) ...... 114

7. 1 Transportation network resilience diagram showing bridge recovery sequence ...... 121

7. 2 Schematic diagram for estimating bridge recovery time ...... 123

7. 3 Fitted probability distribution functions for hurricane categories 1 (a.), 3(b.) and 4 (c.) .... 125

7. 4 Empirical cumulative distribution function curves for bridge inspection response times ... 128

A. 1 Bridge exposure probability for Hurricane Category 1 ...... 139

A. 2 Bridge exposure probability for Hurricane Category 2 ...... 140

A. 3 Bridge exposure probability for Hurricane Category 3 ...... 141

A. 4 Bridge exposure probability for Hurricane Category 4 ...... 142

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A. 5 Bridge exposure probability for Hurricane Category 5 ...... 143

A. 6 Roadway exposure probability for Hurricane Category 1 ...... 144

A. 7 Roadway exposure probability for Hurricane Category 2 ...... 145

A. 8 Roadway exposure probability for Hurricane Category 3 ...... 146

A. 9 Roadway exposure probability for Hurricane Category 4 ...... 147

A. 10 Roadway exposure probability for Hurricane Category 5 ...... 148

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ABSTRACT

Resilience simply means to rebound when exposed to a disruptive event. Damage to bridges in transportation networks usually result in long detours and increased travel time hence have massive cost implications. Transportation networks composed of major bridge infrastructures frequently depend on the bridges to carry high traffic volumes. Transportation network resilience explains the ability of transportation networks to contain and recover from disruptions. Transportation network resilience entails the transportation network’s capability to continue functioning in spite of hazard-induced breakdown to network segments and how quickly those sections can be restored for the network to return to pre-disaster performance levels. Most resilience-related research in this area have primarily focused on physical bridge resilience without necessarily considering the resilience impact of bridge damage on the overall or regional network. This thesis is focused on filling this research gap by considering the resilience of transportation networks subject to bridge damage and road closures. This research further proposes the use of regional travel demand models and Geographic Information Systems (GIS) visualization techniques for network level impact visualization and accessibility analyses. The socio-technical approach associated with transportation system resilience is broad and multidisciplinary, focusing on the network’s ability to sustain functionality and recover speedily when faced with disruptions or shocks. Academic works in this area are generally viewed in terms of having qualitative or quantitative frameworks. There is also significantly less literature evaluating response and recovery phases of resilience. Developed resilience indexes have sparsely touched on many salient aspects of resilience; hence they are only applicable to very specific scenarios. Further investigative efforts are therefore necessary for post-disaster phases of resilience, evaluating the applicability of resilience indexes on multiple hazard events for transportation networks, and developing resilience indexes based on regional road network models while considering all network links and not just alternative routes. Temporary, long-term, and partial closures to bridges can result in enormous cost implications. However, bridge closures are inevitable not only due to the likelihood of hazard- induced damages, but routine maintenance, repair, and rehabilitation (MR&R) activities may also warrant closures. It is a current practice that vehicles are rerouted to the shortest alternative route (detour approach) during bridge closures. In an initial study, a scenario-based network

xiv approach for evaluating the impact of bridge closures on transportation user cost is proposed. Both the detour-based and network-based approaches were applied to the Tampa Bay regional network model while considering five bridge closure scenarios. User costs were computed in terms of delay and vehicle operating costs. Findings indicated that for closures to I-275, Gandy, Highway 580 and W.C.C Causeway bridges, there were increases of about 42%, 18%, 61%, and 45% respectively, in total user costs for the network-based approach when compared with the current detour-only approach, indicating a significant network impact captured by the network- based approach. The proposed methodology captures the effects of bridge closures on all road segments within the regional network jurisdiction, provides a more rigid framework for analysis by ensuring user costs are computed efficiently while avoiding overestimation, takes into account the fact that road users may have advance knowledge of roadway conditions prior to trips hence significantly influencing route choices, and provides sufficient information for agencies to implement preemptive measures to cater for network-level disruptions due to bridge closures. Also, regional network resilience was assessed, first through a schematic framework developed for selecting at-risk bridges during hurricane events by: (i) computing exposure probabilities for hurricane events at bridge locations; (ii) developing bridge damage state functions and damage state rating assignments using historical data from the National Bridge Inventory (NBI) database; (iii) identification of bridges at risk to hurricane-induced damage; and (iv) computing aging accessibility to hospitals from which resilience was measured. Results indicated an increase from about 1200 minutes to 2100 minutes and from about 900 to 1100 minutes, for the congested travel time (CTT) and free flow travel time (FFTT), respectively, representing about 75% and 15% for CTT and FFTT, respectively. Furthermore, an additional total travel distance of 52.85 miles was observed for CTT and FFTT. The mean travel times after bridge closures increased from 8.43 to 15.1 minutes and from 6.6 to 7.76 minutes for CTT and FFTT, respectively. The resulting resilience index scaled from 0 to 1 was computed with 1 representing a network which can recover immediately after a disruption (or a network without any performance loss) and zero for one that may never recover to its pre-disaster form. Restoration to moderately damaged bridge led to functionality improvement from 0.87 to 0.94 considering FFTT, and from 0.57 to 0.83 considering the CTT. Reinstating extensively-damaged bridges resulted in functionality increase from 0.94 to 0.96, and 0.83 to 0.85, respectively, for

FFTT and CTT. The resilience index for this study was computed as 0.94 and 0.81 for FFTT and CTT respectively, implying a significant loss in senior mobility hence the need for mitigation measures A framework for assessing the regional network resilience was developed by leveraging scenario-based traffic modeling and Geographic Information System (GIS) techniques. High impact zones location identification metrics were developed and implemented in preliminarily identifying areas affected by bridge closures. Resilience index measures were developed by utilizing practical functionality metrics based on vehicle distance and hours traveled. These are illustrated for the Tampa Bay area. Findings for ten bridge closure scenarios and recovery schemas indicate substantial regional network functionality losses during closures. I-275 bridge closure yielded the highest functional loss to the regional network: the aggregated resilience index below 0.5 reflects severe network performance deficit and mobility limitations. Closure to the WCC Causeway bridge results in a network level resilience index value of 0.87, while the indexes for the other scenarios range between 0.76 and 0.97. These results reflect the high dependency of the network on the I-275 bridge. Damage to this bridge is foreseen to have a massive impact on the network in terms of travel cost. Lower resilience index values imply either significant functionality losses or lengthy closure durations or both. To demonstrate the proposed methodology, a hypothetical network illustration indicated that: (i) Single bridge closure scenarios recorded significant performance losses for bridges which directly connected to the destination zone; (ii) Resilience indexes echoed the need to compare predicted recovery times to scheduled restoration times since index measures are either compensated or penalized the speed of predicted recovery with respect to scheduled recovery durations; (iii) Sensitivity analyses reinforced the previous assertion by accounting for both performance loss and restoration or recovery times; (iv) Multiple closures had a significant impact on network performance hence rapidity is vital in improving network resilience. Like any study, there are some limitations identified in this research. While it was clearly identified that variation in response and recovery times may have a significant impact on explaining and formulating resilience measures, there is insufficient data on the road closure and bridge closure durations after hazard events. Such databases will help researchers in evaluating resilience more accurately. Furthermore, even though case studies in this thesis took into account large networks, the utilized models were based on static traffic assignment which suffices for

xvi long-term transportation planning. However, it is recommended that use of dynamic traffic assignment models should be explored since they are known to reflect more accurate travel times. This is especially important for equity-based case study applications with respect to post- disaster accessibility. The use of user equilibrium assignment which accounts for each road user minimizing his or her travel time was used for this study, it is recommended that the system optimal solution which minimizes the overall network travel time should be considered since it may be of specific interest to agencies. Solution-based resilience studies are encouraged, especially efforts which incorporate the influx of connected and autonomous vehicles and other shared mobility solutions. This study also recognized the need for collaborative efforts between management authorities and researchers to facilitate the development and implementation of necessary policies and systems for the enhancement of transportation systems’ resilience.

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CHAPTER 1

BACKGROUND

1.1 Introduction

Lifeline systems have been of growing concern, especially considering their vulnerability to hazard-induced damages. Findings from previous studies mention transportation infrastructure as one of the most vital lifeline systems (Hopkins et al., 1993). Extreme natural events such as hurricanes, tornadoes, earthquakes, and wildfires, as well as intentional hazards are threats to critical infrastructure systems including transportation networks. The locations of bridges, an integral part of the transportation network configuration, indicate that they are critical to mobility. Bridges which serve as cross-terrain and cross-waterbody structures play a significant role in minimizing travel costs. Structural and functional losses to such bridges often lead to mobility limitations and increased user costs (Twumasi-Boakye and Sobanjo, 2017). For this reason, it is imperative that they are made more robust. Effective measures are also needed to facilitate rapid post-disaster recovery. Therefore, it is necessary to establish an efficient approach to pre-event evaluation of transportation infrastructure. The traditionally acknowledged concept for evaluating the ability of infrastructure to resist the effects of hazards, and recover quickly is termed, resilience. Resilience evaluates a system’s ability to resist and absorb the impacts of disruptions (Bruneau et al., 2003) by building on the strengths or weaknesses measured by other indicators such as reliability, robustness, risk and vulnerability (Faturechi and Miller-Hooks, 2014a). In this literature review, the definition of resilience is applied to regional transportation networks by explaining regional network resilience as the ability of regional transportation networks to minimize functional losses due to major components breakdown and recover rapidly to pre-disruption conditions. Many studies over the last decade have addressed resilience assessment methods for infrastructure systems. Previous efforts to quantify the resilience of transportation networks include studies by Murray- Tuite (2006) and Zhang et al. (2009). Murray-Tuite (2006) proposed adaptability, safety, mobility and recovery as four dimensions of resilience, and highlighted indicators such as multimodality, incident occurrence, evacuation time, inter-zonal travel time, and level of service. Bocchini and Frangopol (2010) used Total Travel Time (TTT) and Total Travel Distance (TTD)

1 for resilience evaluation by considering multiple bridge configurations in the proposed resilience assessment concept. Bocchini and Frangopol (2013) in a study on bridge network restoration after earthquake events developed a multicriteria intervention optimization approach which was exemplified on a large network. A thorough review of the respective literature shows that while most studies excel in the identification and development of relevant resilience metrics, few studies focus on the development of single measure indicators (index) for resilience. Pertinent studies which report on resilience index formulation include efforts by Attoh-Okine et al. (2009) and Serulle et al. (2011). Other researches have taken the form of qualitative concepts (Vugrin et al., 2011; Tamvakis and Xenidis, 2012; Hughes and Healy, 2014) as well as quantitative frameworks (Cox et al., 2011; Omer et al., 2011; Reggiani, 2013; Adjetey-Bahun et al., 2016; Gillen and Hasheminia, 2016; Karamlou et al., 2016; Donovan and Work, 2017). Application of resilience metrics to realistic networks, especially regional transportation models, is lacking in the literature. Developed metrics applied to test networks are mostly based on assumptions specific to those sample networks. Additionally, high impact zone location metrics important for identifying jurisdictions that need immediate attention during hazard events are yet to be developed. Globally, there is a growing awareness of the susceptibility of transportation networks to damages resulting from both natural and man-made hazards. These damages result in massive financial costs (see Figure 1.1) in terms of repairs as well as economic productivity due to subsequent road closures. Even though most natural hazards are rare events, the cost implications of these events are significant hence should be considered when evaluating the performance of transportation networks. Florida has recorded more major hurricanes (37) than any other United States’ state between 1851 and 2010 (Center, 2007). An extensive study by Sobanjo and Thompson (2013) evaluated the risks Florida bridges are exposed to, attributable to both natural and anthropogenic hazards. Hazards such as, hurricanes, tornadoes, flooding and scour, and wildfires, were investigated. Hurricanes were identified as a main cause of bridge damage among natural hazards, with coastal bridges being of primary concern.

Figure 1. 1 Reported natural disasters worldwide between 1900 and 2010 Source: http://www.emdat.be/disaster_trends/index.html (International Disaster Database EM- DAT)

Reports on hurricane Katrina revealed that the mixture of winds, rains and storm surges resulted in severe damages to coastal bridges. Substantial amounts of these damages were reported as the displacement of bridge decks (Figures 1.2 and 1.3) and the collapse of facilities for movable bridges (Padgett et al., 2008). Vulnerability of coastal bridges to hurricanes (Padgett et al., 2012) and their corresponding consequences (Stearns and Padgett, 2011) in the form of agency costs have further been evaluated (Maxey, 2006).

Figure 1. 2 Damage to girders and piers due to impact from tugboat and barge (Padgett et. al, 2008)

Figure 1. 3 Storm surge-induced loading (Padgett et. al, 2008)

Unexpected closures to major bridges have been reported to cause widespread traffic disruptions. Thus, it is necessary to study the impacts of such closures on large transportation networks. On September 16, 2004, storm surges and waves resulting from hurricane Ivan had massive consequences on I-10 bridges over Escambia Bay causing the displacement of several bridge spans as well as complete pier removal (Hitchcock et al., 2008). A period of 66 days after the hurricane event was needed to reconstruct and reopen the Escambia Bay Bridge to traffic (Hitchcock et al., 2008). The loss of this bridge resulted in an approximately 209 km (130 miles) traffic detour (Talbot, 2005) implying increased transportation user costs. The importance of bridges as lifelines cannot be overstated. A section of I-85 Bridge in Atlanta collapsed after a massive fire (12.19 meters wall of fire) on March 20, 2017. Three sections of I-85 northbound and southbound required replacement and it took over six weeks to reopen the South bound of the bridge to traffic (Burns and Brett, 2017). The estimated daily vehicular traffic on this Atlanta roadway section was 220,000 vehicles per day. Due to this high traffic volume, the bridge closure resulted in traffic on I-285 bypass increasing by 50% the following day due to traffic gridlock, with traffic conditions in the Atlanta area substantially affected (Noll, 2017). A methodological framework for pre-disaster resilience evaluation of realistic regional networks based on hypothetical post-event damage state conditions is essential to mitigate the effects of unexpected closures.

1.2 Motivation and Problem Definition

The National Infrastructure Advisory Council (NIAC) on “Transportation Sector Resilience”, indicated that deficits in the comprehension of network-level consequences resulting from major disruptive events is one of the main grey areas in the transportation network resilience discussion (Baylis et al., 2015). This thesis seeks to contribute to the ongoing debate on transportation network resilience by presenting efforts to quantify resilience at the network or regional level. There is a major impact of bridge damages in the form of long detours and increased travel time on transportation network bridges make trips significantly shorter. This implies that when these bridges are out of order, these networks are greatly impacted by major personal and commercial cost implications. Attention has not been given to the effects of bridge damage on transportation network models, and more so considering regional transportation network impacts. While most efforts are focused on making bridges more resilient, a resilient transportation network (overall) presents a stronger solution to reducing the ripple effects of bridge damage on network performance. Furthermore, it is important to improve the resilience of such transportation strategies. The need for investing in resilient infrastructure is deemed important for Transportation Network Resilience (TNR). Losses due to shocks can be categorized primarily as component and operational losses. Component losses are due to damage to physical transportation network infrastructure while operational losses are the resulting delays in travel, or mobility limitations. Both losses have direct and indirect effects on the socio-economic stability of cities and may lead to loss of lives and security.

1.3 Research Objectives

The central question which serves as a focal point for this research is: “How can transportation network resilience be assessed based on bridge damages when considering regional transportation network models?” Essentially, this research considers both unexpected damages to individual bridges of significant importance, and the network level damage to bridges and the roadway. To answer this question succinctly, it is imperative to address certain

5 germane questions that would provide adequate and insightful information on resilience and the requisite metrics to be used for its measure. Queries in this research are synchronous to the primary objectives of resiliency which are: reduced negative consequences when failure occurs, and reduced time to recover. These important queries can be generally grouped into the following questions: (i) what are the consequences of road closures resulting from bridge damage?; (ii) what are the main characteristics and indicators of road transportation network resilience?; and (iii) how can a single resilience index measure be developed? In order to achieve this, transportation network resilience (TNR) is subdivided into three main components, namely; transportation cost, transportation network performance, and recovery. Transportation costs reflect user costs which represent personal transportation costs by individual road users, and commercial cost are industry or commercial based trip costs (usually higher than personal costs). Recovery or rapid response captures the speed with which agencies respond to the specific perturbation, conduct feasibility studies, initiate a line of action and the time taken to complete restoration works. Lead time refers to the timeframe within which the replacement, reconstruction or repairs are completed in the event of damages (in this case bridge damages). The speed with which agencies can restore the network to full functionality is an integral aspect of resilience evaluation. In view of these, this research is subdivided into the following objectives: 1. To develop a framework for evaluating TNR at the regional level. 2. To identify and develop performance metrics for efficiently explaining the resilience of regional networks. 3. To develop an approach for computing the resilience index measures for transportation networks. 4. To enhance the comprehension of regional TNR by extending practical measures to real life applications and case studies.

1.4 Outline of the Thesis

To achieve the main objective of developing a framework for evaluating the resilience of transportation networks subject to bridge damage and road closures, this dissertation was subdivided into various tasks. In this chapter (Chapter 1), the background was presented to highlight the problem, state the research objectives explicitly, point out the envisaged

6 contributions of the study, and describe the organization of the thesis. The contents of the subsequent chapters are described in the following paragraphs. Chapter 2 is an in-depth literature review of the available methods for evaluating the resilience of transportation networks. This chapter covers the development of qualitative and quantitative concepts in evaluating transportation network resilience (TNR). The chapter also discusses the various performance metrics used in previous studies and echoes the need for metrics applicable to the regional level TNR evaluation. The chapter finally discusses trends in the development of resilience indexes, and recommendations are made for future research work based on gaps. Chapter 3 covers the approaches, methodologies, and data sources used in this thesis. The concept of resilience is broad, and methods for evaluating TNR are diverse. For this reason, this chapter takes into account performance measures applicable to regional level TNR, considers accessibility as a measure of TNR, the development of new metrics for significantly impacted zones during post hazards, development of a schematic framework for preliminarily selecting at- risk bridges during closures, and a computational methodology for estimating a recovery time sensitive TNR index measure. Chapter 4 explains the need for regional network studies by evaluating additional transportation user costs at the regional level. In this chapter, delay and vehicle operating costs are used to estimate user costs resulting from bridge closures at the regional level compared to the status quo which involves the use of detour lengths. Chapter 5 presents the use of accessibility as a measure of resilience. Accessibility presents a different dimension on resilience evaluation especially since it highlights direct impacts on lives and mobility. Here, its importance as a measure in the context of making a case for investment in resilience infrastructure is stressed. A schematic framework for selecting damaged bridges is presented and followed by the measure of aging accessibility to hospitals using least-cost measures from free flow and congested travel times. Chapter 6 describes the development of resilience index measures for using the case study of the Tampa Bay area. Resilience performance measures are used to compute indexes based on selected recovery times. Ten bridge closure scenarios are used to evaluate the resilience of the transportation network. Scenarios include individual, multiple and partial closures to bridges and their impact on network resilience.

Chapter 7 investigates the recovery phase of resilience by using agency data, reports, and internet queries. The essence of this chapter is to have an overview of response and total recovery times for damaged bridges after hurricane events. This information is identified as an integral aspect of resilience especially since resilience is a function of both performance and recovery times. Chapter 8 provides an explicit overview of this thesis and includes, concluding remarks, limitations, and recommendation for future work. This chapter provides a summary of the findings in this study and further highlights methods, solution-based concepts, and topics of future interests with respect to transportation network resilience.

CHAPTER 2

LITERATURE REVIEW

2.1 Introduction

Transportation networks are critical infrastructures and important lifeline systems which are requisite for the movement of people and goods. This capacity for movement between locations is essential for efficient economic activities as well as daily living. Mobility includes the shipment of raw materials, finished products and wastes, which are all central to guaranteeing a sustainable environment. In the event of natural hazards such as hurricanes, earthquakes, volcanoes, and wildfires, transportation networks are pivotal for rescue, recovery and reconstruction assignments. Resilience of transportation systems is defined by their ability to retain performance during and after disasters while undergoing minimal to no loss and their ability to quickly return to the normal state of operation after disasters (Pant, 2012). The Undersecretary for Policy (U.S. Department of Transportation) was quoted as saying, “Creating a transportation system that is more resilient will be perhaps the most significant challenge we have in the century going forward” (Baylis et al., 2015). Globally, the growing awareness of the hazard-induced vulnerabilities of transportation networks to damages has led to several studies in estimating hazards risks on transportation networks and bridges (Sobanjo and Thompson, 2013; Sobanjo et al., 2013), as well as associated agency costs (Sobanjo and Thompson, 2001). Although mostly rare events, natural hazards obviously have massive cost implications (Figure 2.1). Some of these financial costs result from repairs, rehabilitation, and loss of economic productivity due to road closures. It is also important to mention that even though natural hazards are highlighted in many studies, other threats such as internal failures of infrastructure, combinations of natural hazards and technological major risks, and malevolent acts (targeted attacks/terrorism) also have catastrophic consequences hence influence the resilience of transportation networks. This realization has resulted in a surge in research studies and literature in the field of civil infrastructure performance and resilience. Resilience-based research contributions in the forms of journal articles, dissertations, technical reports and conference proceedings over the past decade have introduced various definitions, conceptual frameworks and case-study applications.

Resilience essentially builds on the strong points and improves the shortcomings of other performance metrics such as reliability, robustness, risk, and vulnerability (Faturechi et al., 2014b). Most recognized review studies on transportation system resilience, scarcely focused specifically on resilience. Instead, more detailed discussions on them are aligned to related terminologies such as vulnerability and reliability. The vulnerability and resilience of road networks has been discussed by Mattsson and Jenelius (2015). However, in the mentioned review article, significant emphasis was placed on the vulnerability of the public transport, air transport and road networks. Resilience was not discussed thoroughly. A comprehensive overview on transportation infrastructure performance by Faturechi and Miller-Hooks’ (2014b) also centered on various network performance metrics, predominantly addressing vulnerability studies with minimal discussion on resilience and disaster management (see Khademi et al., 2015; Özdamar et al., 2014; Reggiani et al., 2015; Hosseini, 2016).

160 140 120 100 80 60

40 DAMAGE(BILLION USD) 20 0 Hurricane Drought and Northridge Drought and Hurricane Hurricane Midwest Drought and Hurricane Hurricane Katrina Heat (1988) Earthquake Heat (1980) Sandy Andrew Floods Heat (2012) Ike (2008) Rita (2005) (2005) (1994) (2012) (1992) (2008) HAZARD EVENTS

Figure 2. 1 Hazards with most damages in terms of cost. Data source: https://www.trustedchoice.com/insurance-articles/weather-nature/most-expensive- disasters/

The National Infrastructure Advisory Council (NIAC) on “Transportation Sector Resilience,” (Baylis et al., 2015) concluded with some important findings on the ongoing dialogue on transportation resilience which are summarized as follows: (i) deficits in the comprehension of network-level consequences resulting from major disruptive events; (ii)

10 advancing from the establishment of national resilience policies to the integration of the aforesaid into strategic plans which translate into risk management; and (iii) the necessity to invest in resilient infrastructure especially since there is no existing national consensus on this subject. With the aforesaid in sight, the primary objectives of this review chapter are delineated as: (i) a synthesis of available and pertinent literature on resilience as applied to civil infrastructure with preeminence given to transportation networks (mainly roadways); (ii) categorical organization of the various methodologies used for the evaluation of resilience measures based on qualitative (including progress in the conceptual understanding of the resilience cycle and new resilience metric identification studies) and quantitative (including new resilience computational logic and case study applications) conceptual frameworks; (iii) the advantages and limitations of current approaches in relation to practical applications which contribute to the grey areas in transportation system resilience; (iv) a discussion on network-level resilience studies; and (v) recommendations for future works. This chapter, thus, specifically reviews current trends in transportation networks resilience studies over the last decade. The concept of resilience and its use in various fields are initially described concisely, prior to streamlining the literature review to focus on transportation network applications. Details discussions are provided, including, finally, recommendations, and suggestions for future research.

2.2 Overview of Performance Measures for Civil Infrastructures

In the process of reviewing the state-of-the-art, it is observed that several performance metrics exist for evaluating hazard impacts. In order to ensure the specificity of this review as focused on resilience, performance metrics such as robustness, reliability, risk, vulnerability, survivability, sustainability, redundancy, adaptability and flexibility, are not discussed in-depth. However, since some of these concepts are adopted within the framework of resilience, they are briefly defined in Table 2.1.

Table 2. 1 Brief description of essential terminologies Terminology Definition as applied to Transportation Networks References This concept characterizes a threat on a system by considering the probability of event occurrence and the consequences. The measure of risk is the product Risk of these two. Component failures in transportation (Taylor et. al., 2006) systems are usually measured using risk analysis; however, systems of multiple components require alternative measures. This is a probabilistic measure of a systems (Scaparra and Reliability functionality or satisfactory performance after Church, 2008) disaster events. Vulnerability captures the weakness and susceptibility of a system to threats influencing operational performance. This concept is mostly (Berdica, 2002; Vulnerability described qualitatively since unlike risk, disaster Jenelius et al., 2006) event probabilities are not computed or accounted for. However, potential consequences on system performance are considered. This is mainly the capability of a system to fulfill its Survivability mission in a timely manner in the presence of attacks, (Ellison et al., 1999) failures, or accidents. This measures the system’s ability to resist and (Snelder et al., 2012; Robustness absorb disturbance while remaining intact at exposure Nagurney and Qiang, to shocks or threats. 2007) Flexibility refers to the ability of networks to adapt to (Morlok and Chang, changes resulting from disturbances. It also measures 2004; Flexibility how the system adjusts to shocks and is usually Faturechi and Miller- dependent on contingency planning efforts. Hooks, 2014b) Sustainability is a model that addresses simultaneously today’s needs and the impacts on (Bocchini et al., Sustainability future generations. It is characterized by a holistic 2013) view and brings together three dimensions: ecology, economy, and society.

2.3 Defining Resilience

The word “resilience” shows its roots from the Latin word “resilire”, meaning to “rebound” or to “recoil” (Collins Concise Dictionary, 1978; Laprie, 2008; Rose, 2009). Besides its use in daily dialogue, this terminology has found its place in academia as applied to various spheres of study. In recent times, resilience as a lexicon for measure has become prominent in the domain of transportation engineering. The key components of germane resilience definitions are outlined in Table 2.2. Bruneau et al. (2003) proposed both a conceptual framework and a quantitative measure in an attempt to define the seismic resilience of communities. The study named the infrastructural qualities used to define resilience in terms of four R’s, namely; Robustness (measure of resistance), Redundancy (alternate options or choices), Resourcefulness (prioritization during emergency support), and Rapidity (speed to recovery, safety and system stability). An essential component of the study by Bruneau et al. (2003) is the introduction of the resilience triangle concept, as shown in Figure 2.2. The main function of this triangle is to represent the hazard-induced loss of functionality. The triangle’s depth signifies the severity of system performance loss and the length of the triangle shows the time needed for recovery. The area within the resilience triangle relates directly to the resiliency, with smaller areas indicating greater resilience. The objective of building resiliency into a system is to reduce the size of this triangle, mainly through the espousal of various resilience strategies that target disruption mitigation, preparedness, response and recovery (Ta et al., 2009).

Figure 2. 2 Resilience triangle indicating functionality loss (concept from Bruneau et. al, 2003)

Bruneau et al. (2003) continued to mathematically define community earthquake loss of resilience, R, by the quality of infrastructure, over time to recovery (range t0 to t1) as shown below:

푡 푅 = ∫ 1[100 − 푄(푡)]푑푡 (2.1) 푡0 Where Q(t) = quality of infrastructure (percent)

In the subsequent sections of this chapter, the state-of-the-art on TNR are critically reviewed and presented in consistence with the scope of transportation network resilience.

2.4 Main Categories of Transportation Network Resilience Studies

Transportation network resilience studies are grouped as having either qualitative or quantitative approaches. For the purpose of this literature review, qualitative concepts were not limited to studies involving policy decisions and the identification of resilience indicators but were expanded to include TNR metric formulations and contributions to the comprehension of the resilience cycle without numerical illustrations. Quantitative concepts include studies that deal with mathematical formulations, resilience index computations, case study applications and numerical illustrations. A subsection is also included to highlight studies which include both qualitative and quantitative concepts.

2.4.1 Qualitative Concepts

The discussion on TNR has led to various qualitative measures to help comprehend the concept of resilience. This section includes progress in the conceptual understanding of the resilience cycle and new resilience metric identification studies. The Victoria Transport Policy Institute, VTPI (2010a) in a report on basic access and mobility, defined basic access as “the ability of people to access goods, service, and activities essential for any society.” Basic mobility was referred to as “physical travel that provides basic access.” Post-disaster accessibility was also indicated as a credible method for evaluating transportation networks.

Table 2. 2 Some key components of resilience definitions found in literature Author(s) Domain Identified Attributes of Resilient Systems (per Author definition) i.) Persistence. ii.) Ability to absorb perturbation. iii.) State variable (Holling, 1973) Ecology relationship maintenance. (Todini, 2000) Water Supply Systems Overcoming stress/failure (Bruneau et al., 2003; i.) Hazard mitigation ii.) Contain disasters. iii.) Efficient recovery iv. Community Tierney and Bruneau, 2007) Future event mitigation (Li et al., 2014) Community i.) Adapt, resist, or change during hazard. ii.) Sustained functionality level (Briguglio et al., 2006) Economy i.) Recovery from shocks. ii.) Adjust to shock effects. (Rose, 2007) Economy Sustained functionality (Campbell, 2008) Material i.) Absorb energy when deformed. ii.) Energy recovery (NIAC, 2009) Infrastructure i.) Hard magnitude reduction. ii.) Disruption duration reduction. i.) Sustained functionality. ii.) Hazard damage prediction and assessment (Wang et al., 2016) Supply Chain capacity i.) Performance ii.) Recovery speed iii.) Amount of external restoration (Murray-Tuite, 2006) effort

Transportation Networks Transportation Networks i.) Absorb hazard consequences ii.) Hazard impact reduction iii.) Maintain (Goodchild et al., 2009) mobility (Zhang et al., 2009) Ratio of post-disaster to pre-disaster performance (Heaslip et al., 2010) i.) Maintain level of service (LOS) ii.) Restoration to demonstrated LOS (Litman, 2008) Maintain hazard conditions without calamitous failure (Amdal and Swigart, 2010) Sustained functionality through multi-mobility choices.

i.) Quality that facilitates system recovery, reliability and sustainability ii.) (Wang, 2015) Accounts for long-term changes

This study revealed that the quality of a system can be evaluated or measured by its ability to provide quality transportation service under the worst conditions, instead of the best conditions. Foster (1993, 1997) pointed out influencing factors of resilience as shown in Figure 2.3. It is important to appreciate that while vulnerability studies help agencies to quantify the scope of damage, the adaptive capacity, which reflects self-annealing after a breakdown, helps in understanding the extent to which the current network performs during disruptions. However, a critical component of any resilience study is the speed to recovery of physical components which result in full functional restoration of the system. In a framework for infrastructure resilience, Vugrin et al. (2010) indicated that system performance metrics and measurement procedures are applicable for both natural and manmade disruptions affecting all critical infrastructure and key resources defined by the United States Department of Homeland Security. In the study, the sum of system impact and total recovery efforts were used to quantify the resilience with a lower value implicative of greater resilience. Three fundamental system capacities that determine system resilience: absorptive capacity, adaptive capacity, and restorative capacity, were determined. This framework is applicable for resilience assessment and enables evaluation, and may serve as a guide to improving system resilience.

Figure 2. 3 Principles of Resilience (developed from Foster, 1997)

In order to support infrastructure repair, replacement, and serviceability in the post disaster scenario, Croope and McNeil (2011) developed a Critical Infrastructure Resilience- Disaster Support System framework. This deals with procedures to decrease vulnerability of infrastructure systems and increase resistance of systems to disruptions. This system supports the integration of mitigation measures into the infrastructure management decision-making process, primarily to increase system resilience. The system is divided into the following subsystems: i) Spatial Decision Support System implemented using GIS and HAZUS; ii) Critical Infrastructure Management System which is based on benefit-cost analysis principles; iii) Resilience Management Information System founded on resilience concepts; and iv) Results Presentation System which includes a resilience evaluation subsystem. Omer et al. (2013) defined three resilience metrics and proposed a modeling concept for measuring the resiliency of regional road networks. The identified metrics in this study were travel time, environmental resiliency, and cost resilience. Travel time was used as a measure of the impact of disruptions to travel time between network nodes, while environmental resiliency captured the effects of delays on the environment. The researchers used several performance metrics and level of service metrics, while considering the impact of recovery and adaptation time. The authors defined four ways of integrating resilience into a system, including, a reduction in vulnerability, an increase in adaptive capacity, agile response, and effective recovery. The resilience measurement process for regional networks was termed the Networked Infrastructure Resilience Assessment (NIRA) (Omer et al., 2013). This process is comprised of four stages: system mapping; network risk analysis; network resiliency assessment; and resiliency strategy evaluation. In this study, only the network vulnerability aspect of resilience was evaluated, with a focus on resulting consequences. This approach is effective as an initial measure for revealing the degree of component failure or damage, however does not present a single indicator measure of resilience which is necessary for agency evaluation of transportation networks. A major contribution of this effort however is the consideration of resiliency strategy evaluation which is uncommon in published studies. Other qualitative studies on TNR have focused on disaster or crisis management. Efficient system recovery depends on both technical and institutional response readiness. A proposed holistic strategy plan indicated a summary of actions important for protecting critical infrastructure in order to ensure their resilience (Stergiopoulos et al., 2016). This holistic strategy

17 identified actions at the organizational, regulatory and executive/operating levels or sectors with emphasis on effective structures and public-private partnerships, relevant codes and simplified regulatory frameworks, and the evaluation, risk assessments, protection and resilience (including readiness tests) of all critical infrastructures. Some studies have considered urban network resilience (Lhomme et al., 2013), with another study focused on adopting emergency response systems and management in order to minimize loss of human lives through the use of intelligent transportation systems (ITS), vehicular ad hoc networks, as well as mobile and cloud computing technologies (Alazawi et al., 2011). An approach presented by Hernantes et al. (2013) addressed the role of stakeholders in crisis management by identifying resilience building as one of the specific problems connected to critical infrastructures. Hernantes et al. (2013) through the use of modeling and simulation concepts developed an approach which identified interrelationships among stakeholders during preparation and reaction to crisis. Although existing qualitative approaches have efficiently helped in communicating analytical considerations to make during TNR evaluation, contributions are yet to result in a practical framework applied to a realistic case study at the network level. There are several studies on the vulnerability of transportation networks, however fewer studies exist on adaptive capacities of networks under disruptive events. Most importantly, though identified as essential, there are minimal contributions from literature on evaluation of the recovery phase of resilience. The recovery phase is further discussed in a later section.

2.4.2 Quantitative Concepts

With a clear understanding of TNR having been achieved over the past two decades of research studies, various quantitative methods have been developed to estimate TNR. The proposed resilience triangle by Bruneau et al. (2003) has been a widely-accepted concept for evaluating TNR. The resilience triangle makes it possible to capture performance over a timescale from the onset of a disruption to the time disrupted components are completely restored. Modifications of this triangle have been made in many studies to reflect very specific hazard events, types of disruptions, and various recovery characteristics (Ta et al., 2009; Frangopol and Bocchini, 2011). The first step for evaluating TNR is by determining its vulnerability to a specific hazard. Gunderson et al., (2002) indicated that the resilience of a transportation system depends on vulnerability and adaptive capacity (Adaptive capacity was

18 defined as the ability of the system to allocate resources in response to a disruption, with higher adaptive capacity indicative of the system’s ability to withstand higher shocks, (Gunderson et al., 2002).), and continued to define vulnerability as the ease with which a disturbance or disruption may result in the system deviating from its normal behavior, representing the system’s sensitivity to disruption. Vulnerability studies estimate the extent of hazard-induced disruptions, while adaptive capacity evaluates the system’s ability to contain shocks by resource allocation. Pant (2012) similarly in a proposed resilience cycle mentioned the fact that transportation networks undergo self-annealing after a network breakdown. This allows the system to contain current demands. Pertinent studies include, Murray-Tuite (2006) building on previous work by Godschalk (2003) by quantifying four dimensions of resilience namely: adaptability, mobility, safety, and the ability to recover quickly. The focus of this work was to evaluate system optimum (SO) and user equilibrium (UE) traffic assignments. By using simulation, the researcher examined the influence of UE and SO traffic assignments on adaptability (a measure of different infrastructure uses), safety (quantity of incidents along roadway), mobility (essentially a time-dependent measure) and recovery (external support for system’s level of service). Results of this simulation in the test network indicated that the UE traffic assignment performed better than SO to some extent with respect to adaptability and safety. SO on the other hand, performed better in terms of mobility and recovery. Measures were however restricted to a sample network and cannot be generalized for transportation systems. (Note: In a User Equilibrium traffic assignment, “paths connecting any O-D pair are divided into two categories, i.e. those carrying flow, on which travel time equals the minimum O-D travel time; and those not carrying flow, on which travel time is greater than (or equal to) the minimum O-D travel time.” (Daskin and Sheffi, 1985). System Optimum traffic assignment minimizes total travel time spent in the network while satisfying flow conservation constraints (i.e., all O-D trip rates are assigned to the network). (Daskin and Sheffi, 1985).) Traffic assignment and demand modeling are well identified as effective approaches to reducing vulnerability (Omer et al., 2011). This is especially important for network-level studies. Recent studies on seismic resilience of transportation networks by Alipour and Shafei (2016) resulted in a framework for assessing the resilience of aging highway networks. Initial investigation of the effects of deterioration on aging bridge capacity was carried out afterwhich

19 fragility analysis was applied. Using Los Angeles and Orange counties as case study, a traffic assignment model which accounted for changes in capacity and demand was used (Alipour and Shafei 2016). Most road networks are represented in graph theory using edges/links and nodes, for most traffic assignment models. Nodes could be symbolic of junctions, towns or intersections, while the edges typically represent the roadway network. A transportation network was similarly represented using a graph with all edges (roadways) being bidirectional (Ip and Wang, 2009), and the nodes representing towns. Here, the weighted average and weighted sum approaches were used for computing city node resilience and network resilience respectively. When considering city node resilience, the number of reliable independent paths connecting all other town nodes within the network was considered. The network resilience was then determined by combining all nodes. This concept may prove effective in extending to a real-life network application. The combination of this approach with previously discussed traffic assignment models would ensure that even though certain edges of the network are disrupted, the functional edges would be assigned the current demand. This may serve as a good basis for evaluating adaptive capacity. Road network models are usually analyzed using Geographic Information System (GIS) tools, with travel distances and times forming core metrics for network analysis. Travel time was considered as the key performance measure with the ratio pre-disruption to post-disruption travel time signifying the base resiliency of a system (Omer et al., 2011). Adams et al. (2012) presented an analytical method which used available data on economic importance, vulnerability and operational resilience to identify high risk or low operational resilient segments along the I-90/94 corridor in the State of Wisconsin. This analysis of economic importance incorporated commodity flows, traffic volumes, and level of service along the corridor. Using GIS network analysis tool, alternative routes were determined and eventually operation resilience was evaluated by considering operational impacts on travel distance, travel times and service level. A combination of risk ratings and alternative route outputs were used to determine the overall rating for each corridor segment. Having previously mentioned adaptive capacity as an essential aspect of TNR, it is expedient to remark that this can be enhanced through the deployment of parallel systems such as ferries (Omer et al., 2011). The necessity for redundancy and multimodality of transportation

20 networks cannot be overstated as this is evident from various studies (Heaslip et al., 2010; Serulle et al., 2011; Rashidy and Hassan, 2014; SteadieSeifi et al., 2014). Multiple travel modes and sufficient alternative routes serve as methods of enhancing mobility during roadway disruptions. Nogal et al. (2015) developed a tool to quantify damages suffered by a traffic network. Statistical analysis was performed on the resilience of a traffic network under extreme climatological events, a dynamic restricted equilibrium model (see also Pastor et al., 2015) was adopted, and a travel cost function including the effect of weather to determine traffic network resilience was utilized. The parameters used for the cost functions due to hazard effects were considered random and followed generalized beta distributions while fragility curves of the target network were defined using Monte Carlo method and Latin Hypercube sampling. The authors (Nogal et al., 2015) argued that the local vulnerability of the network can be defined based on previous experiences and expert opinion, and as a result of uncertainties involved, the assigned parameter representing the local network vulnerability was assumed to be a random variable. Hence, the generalized beta distribution was chosen since it allows the definition of the random variable on the parameter interval. This method was applied on an illustrative network with synthetic hazards. Fragility curves were identified as a useful tool for evaluating the vulnerability of a traffic network, aiding in decision-making for hazard prevention and response. Table 2.3 shows a breakdown of six quantitative approaches for measuring resilience as found in literature - a summary of the research work, case study, metrics used for measuring resilience and most importantly the identified limitations. Existing literatures indicate efforts to develop conceptual frameworks and a logical premise for identifying resilience indicators. The subsequent step involved is the development of a composite transportation network resilience index which can serve as a single indicator measure for agencies. Additionally, quantifying the recovery phase of the resilience cycle has been sparsely investigated in literature. Such key issues relevant to establishing a practical resilience framework are discussed in the following section.

Table 2. 3 Summary table for selected literature which focus on resilience measures for transportation network

Publications (Murray-Tuite, 2006) (Zhang et al., 2009) (Leu at al., 2010) (Adams et al., 2012) (Omer et al., 2011) (Serulle et al., 2011) Freight Transportation Ground Transportation Type of Study TNR TNR Resilience (Highway TNR Transportation Network Corridor) Gulf Coast Test Network I-90/94 Interstate Intermodal Melbourne Manhattan, New Santo Domingo, Case Study (Simplified version of Corridor from Hudson Transportation Metropolitan Area York City Dominican Republic Reston, Virginia) to Beltoit Wisconsin System Data Set from Santo TransCAD for Logical Network Domingo Metropolitan Traffic Assignment- modeling intermodal Real Data from GPS with simplified unit used as well as Methodology simulation using network and GIS Network Analysis Navigation Maps demand and capacity inputs from engineering DYNASMART-P generating inputs. judgment and empirical transportation data data. Degree, Betweeness, Clustering Network availability, Mobility, Risk priority number, Indicators/Metrics Adaptability, Mobility, coefficient, Network accessibility, Accessibility, Change in vehicle Travel time Used Safety, Recovery Topological integrity, Traveler perception, Reliability, LOS miles traveled Distance gap, Spatial Transportation cost. distribution of risk. Recovery Stage yes no no no no no Inclusion Composite no no no no yes yes Resilience Index i.) Analysis does not i.) This work i.) Resilience index i.) Metrics such as: take system recovery develops a measure does not take into redundancy, diversity, i.) Network recovery i.) Analysis does not into account. of resilience however account system efficiency, autonomous is not analyzed take system recovery ii.) Resilience not an index for its recovery as a metric. components, strength ii.) No strategies to into account. measure primarily Limitations evaluation. ii.) This work does not and collaboration were enhance resilience ii.) Resilience focuses on travel ii.) Disaster intensity provide a solution- not used in this study. iii.) Measures are not measure cannot be time. Other measures not considered. based approach to ii.) Recovery analysis clearly quantified generalized. when included will iii.) No strategies to evaluate resilience no holistic. enhance this enhance resilience. improvement methods. framework.

2.5 Key Issues in the Transportation Network Resilience Dialogue

The concept of resilience is well understood, however, specific areas need further clarification to fuel policy decisions and national consensus on financial investment. Three of these areas with respect to TNR which have been echoed in previous studies are; the network or regional impact of hazards, quantifying the recovery phase of resilience and the development of a resilience index. Advances in those areas are discussed in the subsequent section of this chapter.

2.5.1 The Need for Network-level Transportation Network Resilience Studies

One of the main findings from NIAC’s report on transportation sector resilience was the lacking comprehension of network-level consequences resulting from major disruptive events. A clear trend in the discussions on qualitative and quantitative TNR evaluation approaches is the deficit in real-life applications of proposed concepts. TNR frameworks are applied to hypothetical networks, roadway corridors or case studies of small city networks. Practical regional network-level resilience studies are completely missing in literature to the best of the researcher’s knowledge. This has made it difficult to develop a widely-accepted framework for TNR measurement. Many vulnerability studies consider hazard consequences in terms of physical damages, agency costs and user costs. However, in the scope of TNR, the primary objective is to identify how physical damages impact traffic flow metrics, mobility and accessibility at the network level. Due to the complexity of regional networks, applications on generic and small network case studies are insufficient in explaining an effective way of computing resilience. The need for network-level applications based on validated models which are void of data falsification or errors is stressed. The impacts of natural hazards or important infrastructure failures often include the loss of accessibility not only locally but at the regional level. The understanding of the network-level (regional) impacts of hazards aids in informed agency mitigation and response efforts. The proof of regional impacts of hazards on the transportation network adds weight to the need for national investment in ensuring TNR. Most road closures and disruptions result in the use of alternative detour routes which are usually determined as the shortest distances between origin and destination points. Previous studies have however indicated the ripple effects of sectional roadway closures on other parts of

23 transportation networks (Dalziell and Nicholson, 2001; Erath et al., 2009; Tanasić et al., 2013). A study on simulated regional network models by Twumasi-Boakye and Sobanjo (2017) indicated that network travel times and user costs are mostly underestimated when considering localized impacts of bridge closures especially when simply considering alternative routes. Twumasi-Boakye and Sobanjo (2017) proved this on a practical regional network by using the Tampa Bay regional planning model. Metropolitan Planning Organizations (MPOs) typically provide travel data as inputs for such jurisdictional analyses. Such studies are important in understanding the regional impact of road closures. TNR frameworks applied to such models will prove vital in strengthening the debate on advancing from the establishment of national resilience policies to strategic planning integration. Assumptions made during traffic assignment are also vital when evaluating TNR. During disruptions, especially those resulting from natural hazards, travel behavior and demand changes are imminent, hence traffic models need to reflect these variable demands. Agency relief efforts to alleviate the effects of hazard events in terms of evacuation, and such alter roadway conditions, while travel behavior of the ordinary road users may also change significantly (see also Dalziell and Nicholson, 2001). A post-disaster vulnerability analysis for designing emergency transportation networks in Tehran, Iran was proposed by Khademi et al. (2015). This approach was used to evaluate post-earthquake response and recovery routes by identifying specific zones which are most susceptible to disruptions. The need for analysis which accounts for variable travel demand and behavior was highlighted, especially during the prioritization of evacuations and other post disaster emergency trips. There is still minimal literature on post hazard travel behavior which is relevant to determining network performance, a key component for determining metrics for computing resilience, especially at the network level. However, several efforts have been made in recent years to address the issue with post-disaster recovery and emergency response (Nakanishi et al., 2014; Chen and Ting-Yi, 2016; Dojutrek et al., 2016; Soltani-Sobh et al., 2016; Mojtahedi and Oo, 2017). Such studies and efforts from the operational research and transportation communities can be adopted and further developed to enhance this aspect of resilience.

2.5.2 Quantifying the Recovery Phase of Resilience

While many research efforts have focused on evaluating the resilience of transportation systems, the aspect of quantifying the recovery times of transportation infrastructure and transportation system functionality has not been thoroughly investigated. This area of study is very essential since the measure of resilience depends on how quickly it takes the system to be reinstated to normal functionality. The understanding of the time to recovery of systems will provide responsible agencies relevant information on the indicators that influence recovery, hence the necessary steps to adopt to improve rapidity. Murray-Tuite (2008) assessed four approaches to mitigating incident related congestion. These strategies included opening a high occupancy vehicle (HOV) lane to all traffic, using variable speed limit to smoothing traffic flow, diverting traffic by en-route rerouting, and diverting traffic via variable message signs. Microscopic simulation was used for this work. In the abovementioned study, resilience was described as strategy-based recovery performance in comparison with complete performance reduction by doing nothing. The ratio of specific recovery strategy to do-nothing scenario in this case provides a resilience measure. Results indicated that the most effective strategies for increasing the transportation system resilience were opening HOV lanes and using diverting traffic via variable message. Findings from this work may prove useful to transportation agencies in making better decisions on the time and locations for strategy implementation to reduce congestion caused by incidents. Even though this approach may prove effective for resilience studies on small networks, the ripple network-level effects of disruptions may not be easily evaluated in this manner. Furthermore, opening HOV lanes and using variable messages for diverting traffic, may also be an insufficient solution. The necessity to obtain a quantitative measure for the resilience of systems in order to determine how the system may be improved was emphasized by D’Lima and Medda (2015). This study was based on resilience definition by Pimm (1991) who described resilience as the speed with which a variable reverts to equilibrium after being displaced from it mainly because of disruptive events or shocks. This study particularly focused on systems which return to a state of equilibrium after disruptions, and quantify resilience with a measure of the rapidity of the systems’ recovery. The proposed quantitative approach involved the use of a mean-reverting stochastic model to evaluate shock-effects, after which they applied the model to the London Underground. A mean-reverting parameter adopted from Uhlenbeck and Ornstein (1930) was

25 determined to serve as a resilience measure in a specified stochastic mean-reverting model with the assumption that system perturbations are random and disruption caused in the subsequent time internal follows a Gaussian distribution with square root of the length of the interval representing the variance. The adopted mean-reverting model was chosen since it is the standard model in literature, and its choice was based on the premise that systems return to normal functioning after shock dissipation (reversion). The form of this stochastic model is seen below:

푆푦푠푡푒푚 푆푡푎푡푒 = 푅푎푛푑표푚 푠ℎ표푐푘 + 푅푒푐표푣푒푟푦 (2.2)

This approach excels in developing a methodology for determining how quickly systems can retain equilibrium after disruptive events, that is, recovery. Consideration is not given to how the system accommodates shocks prior to recovery efforts - a component vital for evaluating the system’s resilience. Efforts from this study can however be extended to practical case studies for evaluating speed to recovery. Considering the available literature reviewed, very few studies tackle the post-disaster phases (response and recovery) of transportation system resilience. Several literatures however, do exist on recovery optimization, restoration process, and system costs minimization and maximization (Matisziw et al., 2010; Aksu and Ozdamar, 2014; Özdamar et al., 2014; Kepaptsoglou et al., 2014). Though the above-mentioned studies were not undertaken within the framework of resilience, the concepts used can be incorporated in the post-disaster phase.

2.6 Towards the Development of a Resilience Index

Resilience measures have seen various refinements over the years, however the development of a TNR index has proved to be an arduous task due to the complex nature of transportation networks and the uncertainties in most identified metrics. However, the need for such an interpretable index cannot be overstated. A single indicator value of measure based on a well-defined scale will provide engineers, stakeholders and agencies an idea of the current state of transportation infrastructure and its response and effects on the community during unforeseen disruptions. Such measures are paramount to warranting mitigation actions, agency capacity building, and improvements in hazard preparedness for improved response times. Studies have indicated composite indices play a major role in policy-making since they simplify complex

26 measurements and focus attention on major issues (Singh et al., 2007; Atkinson et al., 1997). Some pertinent studies contributing to the developing of a resilience index are discussed in this section. A modification of the resilience index model developed by Hashimoto et al. (1982) led to two proposed methodologies for computing what was later termed lag-1 resilience by Li and Lence (2007). The quantitative frameworks proposed were the vector autoregressive moving average (VARMA), and the first-order reliability method (FORM). The resulting resilience index model modified from Hashimoto et al. (1982) is shown below:

푝(푡2)≥0 푅(푡1, 푡2) = [ ] (2.3) 푝(푡1)>0 where

R(푡1, 푡2) – resilience between times, 푡1 and , 푡2 p(푡1),p(푡2) – performance function at times, 푡1 and , 푡2

In terms of probability and systems failure:

퐹푆(푡1,푡2) 푅(푡1, 푡2) = [ ] (2.4) 퐹(푡1) where

F(푡1) – failure probability at time, 푡1

FS(푡1, 푡2) – system failure probability at time, 푡1 with recovery at time, , 푡2

Attoh-Okine et al. (2009) formulated a resilience index of urban infrastructure using belief functions. The authors recognized the abundance of qualitative explanations addressing resiliency and vulnerability in literature, stating however, that most of these were without objective resilience index computations (an observation still evident from this review study). Using a belief function framework, Attoh-Okine et al. (2009) developed a resilience index for urban infrastructure. The authors argued that this approach proves better suited for subjective, independent information and hierarchical data. The application of this index was extended to an exemplar urban highway infrastructure network and it was recommended that this method be used to develop sensitivity analysis to determine how infrastructure level changes can affect

27 resilience index. (Note: The theory of belief functions provides a non-Bayesian way of using mathematical probability to quantify subjective judgements by assessing probabilities for related questions and considering implications of these probabilities for the question of interest. (Shafer, 1976)). Attoh-Okine et al. (2009) further modified equations from Li and Lence (2007) using belief functions to obtain:

푃퐿(푡1) ⨁ 푃퐿(,푡2) 푅(푡1, 푡2) = [ ] (2.5) 푃퐿(푡1)

[1−퐵퐸퐿(푡̅̅1̅)] ⨁ [1−퐵퐸퐿(푡̅̅2̅)] 푅(푡1, 푡2) = [ ] (2.6) [1−퐵퐸퐿(푡̅̅1̅)] where BEL – belief function PL – plausibility

푃퐿(푡1) = [1 − 퐵퐸퐿(푡̅1)] (2.7)

푃퐿(푡2) = [1 − 퐵퐸퐿(푡̅2)] (2.8) from Dempster’s rule ⨁ is defined as: 1 푚(퐶) = 푚 (퐴) ⨁ 푚 (퐵) = ∑ 푚 (퐴)푚 (퐵) (2.9) 1 2 퐾 퐴∩퐵=퐶≠0 1 2 where

퐾 = 1 − ∑퐴∩퐵≠0 푚1(퐴)푚2(퐵) (2.10)

An approach for computing a Measure of Resilience (MOR) for intermodal transportation systems has also been established by Zhang et al. (2009). The authors indicated that intermodal networks consist of two components namely: the road network and intermodal terminals. With a combination of results from performance indicators linked to travel speed using a regression model, a performance index (PI) was developed. This measures the ratio of travel speed to free flow speed. The result is then weighted by truck miles travelled. The value of the PI developed ranged from 0 to 1 with higher values indicating better network performance in terms of mobility, and resilience was finally measured by the performance index before and after the disaster.

Heaslip et al. (2010) presented a formal definition of transportation resilience as “the ability for the system to maintain its demonstrated level of service or to restore itself to that level of service in a specified timeframe.” The conceptual foundation of this methodology employs concepts of resiliency cycle and transportation system performance hierarchy. This framework brings the resiliency cycle, resiliency cycle time, and performance hierarchy together into a Cartesian plane. A network performance index as a measure of resilience was achieved by defining the combined relationship between variables having effects on resilience by Fuzzy Inference System. Based on the work by Heaslip et al. (2010), Serulle et al. (2011) expanded and refined the concepts on measurement of transportation network resiliency at the pre-event level. The methodology contains four tiers as shown in Figure 2.4. In total, nine variables, which summarize the main infrastructure qualities and user behaviors inside a transportation system were selected to serve as metrics for resiliency. These variables are processed using Fuzzy rule based inference into an index called Transportation Network Resilience Index (TNRI) whose value ranges from 0 to 9 with value closer to 9 representing a more resilient system.

Figure 2. 4 The dependency diagram as the basis for fuzzy inference (developed from Serulle et al., 2011).

Research efforts by Rashidy and Hassan (2014) resulted in the formulation of a composite resilience index (CRI) for road transport networks. Redundancy, vulnerability and mobility, were used as metrics for evaluating road network resilience at the junction, link and origin-destination levels, respectively. Redundancy indicator in this work was based on the concept of information entropy, considering alternative routes (static). Spare capacity availability under different levels of service and network loading represented the dynamic component. The vulnerability indicator was developed by considering, link capacity, flow, length, free flow, and traffic congestion density. Fuzzy logic and exhaustive search optimization techniques were used to weight the different metrics. Fuzzy logic was also used for merging mobility characteristics into a single mobility indicator. Finally, the weighted average and principal component analysis approaches were used to develop the CRI which incorporated the interdependencies of the various metrics. This methodology was then applied to a hypothetical road network in Delft, Netherlands. The researchers recommended that this approach can assist administrators understand the dynamic characteristics of resilience in the event diverse disruptions while emphasizing network deficiencies and preparing efficiently in terms of future mitigation efforts. Figure 2.5 presents a proposed framework for finding resilience indexes for a network. Combining measures from computed indicators by using appropriate aggregation methods will result in a composite index. Aggregation methods applied in previous literature include; principal component analysis (PCA), equal weighting, unequal weighting, and analytical hierarchy processes (Briguglio et al., 2009; Saisana and Tarantola, 2002; McManus et al., 2008; Estoque and Murayama, 2014; Reisi et al., 2014). It is especially important to take note of these approaches since most of the above-mentioned indexes weighting approaches were not specifically applied to TNR. The methods for combining measures in Figure 2.5 can be classified as weighting methods (equal and unequal weighting), structured techniques (analytical hierarchical processes, fuzzy inference, or their combination), and other mathematical methods. Table 2.4 summarizes some practical resilience index formulations in literature which can be adopted in network-level case study applications. In order to address the importance or relevance for investment in transportation infrastructure resilience, a well-developed and accepted measure of resilience must be established. Building on the mentioned concepts is therefore expedient. Scaled performance measures (indexes) have been applied in various fields due to its merits in communicating to agencies and the general public.

Figure 2. 5 Proposed steps involved in developing a composite resilience index

2.7 Further Discussions

While genuine efforts have been made to its definition and need, the measurement and evaluation of TNR has proved to be an arduous task. Reliability and vulnerability methods have been used in several quarters to quantify network resilience, however, this is arguable since these methods only give us an idea of the network’s performance when under duress. Resilience essentially considers performance over the timeline from pre-disaster and post-disaster (including complete recovery). Hence it is essential for developed methodologies to capture various time periods from the onset of a disruption to the total recovery phase. Transportation networks should be able to meet present traffic demands (which may be variable). Practical variable demand traffic assignment models need to be used for realistic case studies for simulating categorical hazard events. Again, it was identified that case studies for resilience evaluation do not consider future year traffic demand models. Most metropolitan planning organizations (MPO) have designed regional planning models and future year models based on travel behavior and demographic data. Such models can be modified and applied for estimating TNR. The multimodal elements of some of these models allow for studies on alternative modes as well as other resilience improvement strategies.

Table 2. 4 Some practical resilience index formulations in literature (2011 – 2016) Author Resilience Index Computation Metric Definitions Adjetey-Bahun et al. (2016) 휏(푡) D(t) = passenger delay at time t Resilience index based on 퐷(푡) = τ(t) = passenger system time (normal condition) 휏푑(푡) travel (delay) time 푇 τd(t) = passenger system time (perturbation) ∫ (푃퐿(푡))푑푡 RPL = system resilience 푅 = 0 푃퐿 푇 PL = local system performance 푇 T = time to recovery ∑ (푃퐿(푖)) ∆푡 푅 ≅ 푖=1 푃퐿 푇 [ ] [ ] 푃퐿 ∈ 0,1 , 푅푃퐿 ∈ 0,1 Rashidy and Hassan (2014) Equal weighting (eq) CRIeq = composite resilience index (eq) NVI = network vulnerabiity indicator Resilience index based on ((1 − 푁푉퐼) + 푁푅퐼 + 푁푀퐼) NRI = network redundancy indicator weighted vulnerability, 퐶푅퐼푒푞 = NMI = network mobility indicator redundancy and mobility 푎 PC = jth principal component j measures Principal Component Analysis (pc) aij = weight of jth principal component

Xi = original variables (NVI, NRI, NMI) 휀2 푛 푖푗 λj = eigenvalue for data covariance matrix 푃퐶푗 = ∑푖=1 푎푖푗푋푖, 푎푖푗 = 휆푗 εij = factor loading 푚 CRIpc = composite resilience index (pc) 휆푗 퐶푅퐼푝푐 = ∑ 푚 푃퐶푗 ∑ 휆푗 푗=1 푗=1 푵 Arcidiacono et al. Network Functionality 풇풆 (풕) = Network functionality (2012) 푪푻(풕) = post-disaster capacity Resilience index based 푻 푻 푵 푪 (풕) 푪 (풕_풅풊풔) = pre-disaster capacity on loss in network 풇풆 (풕) = 푪푻(풕_풅풊풔) 푸푻푪 = category functionality functionality (defined 풉 푻푪풆 Transportation Category Functionality 풘 = weight coefficient for by capacity reduction) 풆,풉 transportation category h. 푻푪풆 푬 푪푭 ∑풆=푻푪 풘풆,풉 . 풇풆 ퟎ 풇 ≤ 푳 푸푻푪 = 풉 , 풘풊풕풉 풇푬 = { 풆 풆 풇풆 = element of transportation system 풉 푻푪풆 풆 푪푭 푪푭 ∑ 풇풆 풇풆 > 푳풆 푳 풆=푻푪풉 풘풆,풉 풆 = lower bound limit 푹 = resilience value of transportation Resilience Index 푻 system 푻+푻 푳푪 푸푻 = functionality

푻푳푪 = control period 푹푻(푻, 푻푳푪) = ∫ 푸푻(풕)/푻푳푪풅풕

푻

Table 2. 4 - continued Author Resilience Index Computation Metric Definitions

Omer et al. (2011) 푡푛(푝푟푒−푠ℎ표푐푘) tn = network travel time 푅푡푛푒푡푤표푟푘 = Resilience index based on 푡푛(푝표푠푡−푠ℎ표푐푘) tij = travel time from node i to node j travel time. Ratio of pre- 푡푖푗(푝푟푒−푠ℎ표푐푘) Rt_network = network travel time resiliency 푅푡_푛표푑푒 = shock to post-shock travel 푡푖푗(푝표푠푡−푠ℎ표푐푘) Rt_node = node-to-node travel time resiliency times provides a measure 푡 R = node-to-node resiliency over specified time ∫ 푅푡(푡)푑푡 of resilience. 푅 = 0 period ∆푡

Ip and Wang (2011) n = number of nodes Resilience index based on m = number of edges 푃푘(푖, 푗) = ∏ 푞l number of reliable paths. μi = population of city node 푙∈퐿푘(푖,푗) wi = weight of node Number of reliable passageways node pairs i-j ri = resilience of node q = normal operation reliability of edge 푁푃(푖, 푗) = ∑ 푃푘(푖, 푗) = ∑ ∏ 푞l Lk(i,j) = k-th passageway for node i-j ∀푘 푙푖푛푘(푖,푗) ∀푘 푙푖푛푘(푖,푗) 푙∈퐿푘(푖,푗) 푛 Pk(i,j) = reliability of passageway Lk(i,j)

푤푖 = 푢푖⁄∑ 푢푗 , 푖 = 1,2, … , 푛. R(G) = resilience of network represented by 푗=1 graph G. Self-exhausted node weight 푛

푣푖 = 푢푖⁄∑ 푢푗 − 푢푖 , 푖 = 1,2, … , 푛. 푗=1

Node resilience

푟푖 = ∑ 푣푗푁푃(푖, 푗) = ∑ 푣푗 ∑ ∏ 푞l , 푖 = 1,2, … , 푛.

푗=1,푗≠푖 푗=1,푗≠푖 ∀푘 푙푖푛푘(푖,푗) 푙∈퐿푘(푖,푗)

Transportation network resilience 푛 푛

푅(퐺) = ∑ 푤푖푟푖 = ∑ 푤푖 ∑ 푣푗 ∑ ∏ 푞l , 푖 = 1,2, … , 푛

푖=1 푖=1 푗=1,푗≠푖 ∀푘 푙푖푛푘(푖,푗) 푙∈퐿푘(푖,푗)

Multimodal transportation systems are known to offer more efficient, reliable and flexible freight transportation (SteadieSeifi et al., 2014). It is therefore recommended that future efforts consider the role of multimodality in contribution to the resilience of transportation systems. Such research efforts may focus on the interdependencies and uncertainties of multimodal transportation systems. Contextual solutions for multiple hazards are necessary for an effective TNR study. Research efforts are not focused on multiple hazards; however, it is of essence to develop frameworks for various hazard instances. The need for efforts building on the effects on interdependencies on TNR is essential since transportation systems are seen as systems of systems (one transportation system/mode may have an effect on the other). Previous literature in this area exist (Attoh-Okine et al., 2009; Arcidiacono et al., 2012; Kepaptsoglou et al., 2014) and have to be further studied. Hierarchical analysis considering risks posed by natural hazards, internal failures and intentional hazards need to be accounted for. The understanding of the risk (probability of occurrence and consequence) due to multiple hazards and subsequent recovery times will provide a strong measure of resilience. The main reason for this is that transportation networks which may prove to be resilient in the case of hurricanes may not have the same resilience levels in the event of other hazards. Dealing with multi-hazards is a challenge when evaluating resilience primarily because infrastructure systems are susceptible or vulnerable to multiple stressors (Chang, 2009), hence it is necessary to find solutions and support decisions which consider them in that context. The issue of multi-event disaster resilience is also discussed by Zobel and Khansa (2014). Even though the simplicity of small road network case studies is useful in demonstrating the applicability of methodological frameworks, it may not be an accurate interpretation of network performance since disruptions at sections of a network may have rippling effects at the regional level. The need for such studies is echoed since most natural hazards have a broader network impact. Developed quantitative methods will be appreciated and adequately tested when applied to more complex regional models. Table 2.5 summarizes transportation system resilience studies within the past eight years. These studies indicate that current studies have been focused on building quantitative frameworks for resilience measurement. Research efforts have mostly focused on natural hazards and its impacts on transportation networks and the community. However, other hazards such as intentional hazards (terrorism), internal failures and combinations of natural hazards and technological major risks need further

34 investigation. Some research efforts have identified the importance of such hazards to TNR (Berche et al., 2009; Lou and Lihui, 2011; Cox et al., 2011; Dorbritz, 2011; Berche et al., 2012). The area of intentional hazards is very relevant especially due to the fact that transit systems are major terrorist targets. Since 2010, there have been nine railway system attacks in Europe and Asia, and about nineteen attacks between 2000 and 2010. Review studies, mathematical frameworks and case study applications on the impacts of internal failures and intentional hazards for TNR would be important contributions to the discussion on TNR and the need for national investment. The need for investing in a resilient infrastructure is deemed important for TNR. Losses due to shocks can be categorized primarily as component and operational losses. Component losses are due to damage to physical transportation network infrastructure while operational losses are the resulting delays in travel, or mobility limitations. Both losses have direct and indirect effects on the socio-economic stability of cities and may lead to loss of lives and security. To begin with, damage to physical infrastructure can result in fatalities and these are evident in the various natural and intentional hazard events over the decades. Extended periods of resulting road closures have massive transportation user costs implications due to delays. Travel delays also lead to environmental pollution through vehicular exhaust discharge, and this has detrimental health impacts. Another effect of slow response and extended periods of limited mobility is the lack of accessibility to important health and domestic needs which can cause loss of lives especially with respect to the population suffering from chronic diseases, the more frail aging population, and unexpected emergency situations such as sudden shocks and accident/crash victims. Improved resilience of transportation networks through national investment is therefore of utmost necessity. Paramount gains of such investments according to the studies discussed include: reduced delays due to enhancement of multimodality in transportation systems; reduced component and subsequent operational losses due to investment in efficient the maintenance and strengthening of transportation infrastructure; and finally improvement in critical infrastructure accessibility when component loss is inevitable through developed stakeholder involvement and institutional readiness to ensure rapid response and recovery times hence reducing transportation user costs, loss of lives and environmental degradation.

Table 2. 5 Literature summary on the resilience of transportation networks (focus on research efforts from 2008 to 2016) Qualitative Quantitative Single Value Research Paper Year of Review Concept and/or Concepts and/or Resilience Index Demand Future Year Model Practical Resilience Publication Studies Survey Studies Case Studies Indicator Variability Evaluation Improvement Schemes Alipour and Shafei 2016 X X Adjetey-Bahun et al. 2016 X X X Marshall et al. 2016 X X Ibanez et al. 2016 X Wang 2015 X D’Lima and Medda 2015 X Zhang et al. 2015 X X X Mattsson and Jenelius 2015 X Nogal et al. 2015 X Pastor et al. 2015 X Hughes and Healy 2014 X X Imran et al. 2014 X Faturechi and Miller-Hooks 2014c X X Rashidy and Hassan 2014 X X X Adjetey-Bahun et al. 2014 X Atun 2013 X Omer et al. 2013 X Reggiani 2013 X Tamvakis and Xenidis 2012 X Freckleton et al. 2012 X Miller-Hooks et al. 2012 X X X Croope and McNeil 2011 X Dorbritz 2011 X Cox et al. 2011 X Ip and Wang 2011 X X Serulle et al. 2011 X X Frangopol and Bocchini 2011 X Omer et al. 2011 X X X Heaslip et al. 2010 X Amdal and Swigart 2010 X Leu et al. 2010 X Vugrin et al. 2010 X Goodchild et al. 2009 X X Zhang et al. 2009 X X X Ta et al. 2009 X X Attoh-Okine et al. 2009 X Ip and Wang 2009 X X Berche et al. 2009 X Caplice et al. 2008 X Ortiz et al. 2008 X Litman 2008 X Murray-Tuite 2008 X X

2.8 Chapter Summary

In this chapter, a comprehensive literature review specifically focused on transportation network resilience (TNR) is presented. The essence of resilience is to explain a system’s ability to maintain functionality in the event of disruptions. This involves the transportation system’s capability of safe mobility during perturbations. When shocks occur, these systems are expected to ‘absorb’ the shocks by possessing some redundancy which allows for normal functioning while disruptions fade. Complete work on resiliency should result in a measure for transportation networks as a function of network performance during various hazard events, vulnerability of transportation infrastructure to hazards, recovery cost and rapidity. This literature review discusses previous work in TNR and highlights areas of specific interest for future work. As part of this comprehensive study, three main problem areas in the study of TNR were identified, namely: (i) minimal network-level study applications of resilience; (ii) insufficient practical methods in quantifying the recovery phase of resilience; (iii) need for the development of a resilience index demonstrated on real-life regional network models. First of all, the need for investment in resilient infrastructure can only be appreciated through more practical network-level studies which will serve as a strong premise for a national consensus on investing in resilient infrastructure. In addition to identifying the grey areas that need further research, this review identified important studies in other fields which may serve as references in addressing the deficits in TNR studies. Also, pertinent aspects of recent TNR studies are summarized with practical resilience index formulations highlighted. Resilience measures when well interpreted will pave the way for specific lines of action and provide useful information with respect to decision making on disaster planning, response, recovery, mitigation and the development of more efficient statewide emergency management systems. It is therefore recommended that further investigative efforts be directed towards evaluating the applicability of resilience indexes on multiple hazard events for transportation networks. Furthermore, collaborative efforts between management authorities and researchers are encouraged to facilitate the development and implementation of essential policies and/or systems for the enhancement of transportation systems’ resilience.

CHAPTER 3

METHODOLOGY

3.1 Introduction

In this chapter, the various methods of computing resilience discussed in Chapter 2 were streamlined to determine the performance metrics which are well suited for evaluating network level resilience. Since the role of bridges to efficient mobility is significant in this research, the susceptibility of bridges to damages at the network level was also considered within the proposed frameworks. Furthermore, performance metrics were then used to estimate transportation network resilience. Finally, a numerical illustration on a hypothetical network is used for evaluating TNR for single and multiple bridge closure scenarios. This chapter is arranged to transition to the next couple of chapters which provide case study applications based on the formulations, assumptions and approaches discussed here. In this chapter, transportation user cost is first used as a metric to explain the regional impact of closures as this approach is hypothesized to me more effective than methods that consider detour routes. This metric will help in establishing the need for regional network resilience studies without presumption. Following this is the development of a regional resilience index from selected performance metrics and indicators including an accessibility based resilience measure, and finally a numerical illustration on network resilience is presented.

3.2 Total Additional User Cost

An important metric in estimating the regional or network level impact of bridge and road closures in transportation user costs. While the common practice in estimating additional user cost is based on detour lengths, here, it is proposed that at the regional network level, the expected ripple effects of closures leads to significant overall network loss which may be grossly underestimated when considering detour routes. A case study which enhances the clarity of the previous assertion is seen in Chapter 4 of this thesis. In order to compute the total additional user costs, delay costs (DC) and vehicle operating costs (DC) are estimated from vehicle hours traveled (VHT) and vehicle miles traveled (VMT) respectively. These metrics which are

obtained from model outputs are then assigned monetary value of travel time and distances. The difference in base (uninterrupted) transportation network model and case scenarios with bridge closures result in the additional user cost estimation. The metrics and formulations are described subsequently.

3.2.1 Measure of Vehicle Miles Traveled (VMT)

This measure gives an estimate of the miles traveled by vehicles within a specified region for a specified timeframe. This measure indicates whether bridge closures lead to increases in vehicle mileage. This measure has been used as a component in evaluating transportation alternatives by total cost analysis (DeCorla-Souza et al., 1997); with other work done (Litman, 2002) investigating equity impacts on reducing state’s VMT. This component is also a vital input in computing transportation user costs. For each closure scenario, VMT can be computed as:

VMT(s) = ∑i≠j VMTij(s) (3.1)

VMTij(s) = vijdij(s) (3.2) where,

VMTij = vehicle miles traveled between nodes i-j.

vij = volume of vehicles between nodes i-j.

dij = link distance between nodes i-j (miles).

3.2.1 Vehicle Operating Cost

This estimate is utilized in evaluating the cost of road closures, or in this case, bridge closures and is assumed to be the change in the vehicle operating cost. The change in vehicle operation is the difference between the travel cost with road closure and travel cost without road closure. This approach is adopted from Dalziell and Nicholson, (2001), however, the vehicle operating cost per trip is computed as the product of VMT and dollar value cost as seen below:

∑푖 ∑푗 푉푀푇퐶푖푗퐶푃푀 − ∑푖 ∑푗 푉푀푇푂푖푗퐶푃푀 (3.3)

where,

푉푀푇퐶푖푗 = vehicle miles traveled during bridge damage or closure

퐶푃푀 = cost per mile ($)

푉푀푇푂푖푗 = vehicle miles traveled (no closure or base scenario)

While the above equation computes total cost per trip for all vehicles, it is imperative to distinguish between personal transportation costs and industrial or commercial transportation cost. In view of this, the above formula is modified with subscripts “p” and “t” for personal and commercial (truck) transportation cost respectively as:

Additional Personal Transportation Cost (in terms of additional distance traveled) is expressed as:

∑푖 ∑푗 푉푀푇푝퐶푖푗퐶푃푀 − ∑푖 ∑푗 푉푀푇푝푂푖푗퐶푃푀 (3.4)

Additional Commercial Transportation Cost (in terms of additional distance traveled) is expressed as:

∑푖 ∑푗 푉푀푇푡퐶푖푗퐶푃푀 − ∑푖 ∑푗 푉푀푇푡푂푖푗퐶푃푀 (3.5)

3.2.3 Measure of Vehicle Hours Traveled (VHT)

It is essential to initially consider the main measure of travel cost in terms of vehicle hours traveled (VHT). Here, this measure is computed for each travel path as the product of traffic volume and travel time. This can be estimated using the equation below:

VHT(s) = ∑i≠j VHTij(s) (3.6)

VHTij(s) = vijtij(s) (3.7) where,

VHTij = vehicle hours traveled between nodes i-j.

vij = volume of vehicles between nodes i-j.

tij = link congested travel time between nodes i-j (hours).

3.2.4 Delay Cost

Change in delay costs are computed as the difference between the travel time cost with road closure and travel time cost without road closure; and quantified as the product of VHT and time value of travel cost, i.e.,

∑푖 ∑푗 푉퐻푇퐶푖푗퐶푃퐻 − ∑푖 ∑푗 푉퐻푇푂푖푗퐶푃퐻 (3.8) where,

푉퐻푇퐶푖푗 = vehicle hours traveled during bridge damage or closure

퐶푃퐻 = time value of travel; cost per hour ($)

푉퐻푇푂푖푗 = vehicle hours traveled (no closure or base scenario)

Additional Personal Transportation Cost (in terms of additional time traveled) can be expressed as:

∑푖 ∑푗 푉퐻푇푝퐶푖푗퐶푃퐻 − ∑푖 ∑푗 푉퐻푇푝푂푖푗퐶푃퐻 (3.9)

Additional Commercial Transportation Cost (in terms of additional time traveled) can be expressed as:

∑푖 ∑푗 푉퐻푇푡퐶푖푗퐶푃퐻 − ∑푖 ∑푗 푉퐻푇푡푂푖푗퐶푃퐻 (3.10)

Total Additional User Cost is therefore computed as follows:

TUC = (∑푖 ∑푗 푉푀푇푝퐶푖푗퐶푃푀 − ∑푖 ∑푗 푉푀푇푝푂푖푗퐶푃푀 ) + (∑푖 ∑푗 푉푀푇푡퐶푖푗퐶푃푀 −

∑푖 ∑푗 푉푀푇푡푂푖푗퐶푃푀 ) + (∑푖 ∑푗 푉퐻푇푝퐶푖푗퐶푃퐻 − ∑푖 ∑푗 푉퐻푇푝푂푖푗퐶푃퐻 ) + (∑푖 ∑푗 푉퐻푇푡퐶푖푗퐶푃퐻 −

∑푖 ∑푗 푉퐻푇푡푂푖푗퐶푃퐻 ) (3.11)

3.3 Schematic Framework for At-Risk Bridge Selection and Accessibility Measure

In order to select at-risk bridges during the aftermath of hurricane events, the following sequential steps are proposed: (i) computing exposure probabilities for categorical hurricane events at bridge locations; (ii) developing and applying damage state functions in allocating damage states to bridges using both historical and National Bridge Inventory (NBI) data fields; (iii) identifying bridges at risk to hurricane-induced damage; (iv) identifying the bridges affecting aging-dense areas; and (v) estimating the effects of bridge closures to aging mobility and resilience through accessibility to hospitals based on congested and free flow travel times obtained from traffic assignment modeling. The framework for bridge selection illustrated in Figure 3.1.

3.3.1 Computing Bridge Exposure Probabilities to Categorical Hurricane Events

To forecast the occurrence of hurricanes based on historical records, the number of storm arrivals at an exact coastal location in a single year is being modeled as Poisson distribution. Hurricanes Category 3 is used as an example since Florida’s coast is prone to such storms and the resulting debilitating effects on physical infrastructure and mobility. Using Hazards United States (HAZUS) software wind data (Vickery et al., 2006), the exposure probabilities can be estimated. Wind speeds assigned to each census tract are categorized using the well-known Saffir-Simpson Hurricane Wind Scale from the National Hurricane Center. Number of storms arriving at a location in one year is defined as:

휆푛exp (−휆) 푃 = (3.12) 푛 푛!

퐹푇(푡) = 푃(푇 ≤ 푡) = 1 − 푒푥푝[−휆푡] (3.13) Where

푃푛 - probability of 푛 number of storms occurring in a year, and λ - mean rate of storms per year

퐹푇(푡) – cumulative distribution function of an exponential random variable, T, and t is a random variable representing a given period

Figure 3. 1 Framework for identifying damaged bridges critical to aging-dense areas

3.3.2 Allocating Damage States to Bridges Using both Historical and NBI Data Fields

In assessing the performance of bridges, pertinent prior studies on the impact of different hurricanes on bridges in different states of the country were consulted, to evaluate operational and traffic characteristics. The levels of damage are then assessed through probability analysis in addition to the engineering expert decision making to predict the expected damages to bridges in the region. Different coded fields (Figure 3.2) from the National Bridge Inventory (NBI) database were also utilized for the analysis. The database fields such as deck ratings, superstructure ratings, substructure ratings, culvert and channel ratings, are evaluated along with other explanatory variables such as age, location of bridge, type of bridge (fixed or movable), waterway adequacy, and traffic characteristics. From the data, damages are categorized into slight, moderate, extensive or complete levels based on the categories previously developed (Sobanjo and Thompson, 2013).

Figure 3. 2 NBI fields selected for computing bridge damage states

Functionality Measure:

푇 푁 퐴푐푐푖 (푡) 훾푒 (푡) = 푇 (3.14) 퐴푐푐푖 (푡_푑푖푠) where: 푇 th 퐴푐푐푖 (푡) – minimum travel time for i O-D prior to hazard 푇 th 퐴푐푐푖 (푡_푑푖푠) – minimum travel time for i O-D after hazard 푁 – transportation network Resilience

1 푇̅ 푅 = 1 − ∫ (1 − 훾푁(푡))푑푡 (3.15) 푇̅ 0 푒

Where: 푇̅ – mean time to recovery in days

3.4 Development of Resilience Index

This section explains the framework and steps for developing a resilience index based on performance metrics and indicators applicable to regional or large networks. Traffic assignment methods, performance metric and index computations are explained explicitly.

3.4.1 Equilibrium-based Traffic Assignment

Transportation demand models are usually structured around four sequential steps commonly referred to as the Four-Step Modeling Process. The steps involved in this process are: Trip Generation, Trip Distribution, Mode Choice, and Trip Assignment. To compute the link travel costs for the transportation network, a user equilibrium assignment is adopted. The user equilibrium assignment is based on Wardrop’s first principle which stipulates that no user can lower transportation cost unilaterally by changing routes (Daskin and Sheffi, 1985). This further implies that with drivers having a perfect knowledge of network travel costs, they are prone to choosing the best routes leading to a deterministic user equilibrium formulated as a nonlinear mathematical optimization program (Daskin and Sheffi, 1985) as:

푥 푚푖푛푖푚푖푧푒 푆 = ∑ 푞 푡 (푥 )푑푥, (3.16) 푞 ∫0 푞 푞 푢푣 푆푢푏푗푒푐푡 푡표 ∑푘 푓푘 = 푞푢푣 ∶ ∀푢, 푣 (3.17) 푢푣 푢푣 푥푞 = ∑푢 ∑푣 ∑푘 훿푞,푘 푓푘 ∶ ∀푞 (3.18) 푢푣 푓푘 ≥ 0 ∶ ∀ 푘, 푢, 푣 (3.19)

푥푞 ≥ 0 ∶ 푞 ∈ 푄 (3.20) Where 푆 – objective function k – path

푥푞 – equilibrium flows in link q

푡푞 – travel time on link q 푢푣 푓푘 – flow on path k connecting origin-destination pair u-v

푞푢푣 – trip rate between u and v

Q – set of all links in the network

푢푣 훿푞,푘 – definitional constraint (1 if link q belongs to path k, 0 otherwise)

The link congestion performance function formulated by the Bureau of Public Roads (BPR) was used to determine the average travel time for each link (TRB Special Report 209, 1985). The equation is as follows: 푥 훽 푡 (푥 ) = 푓푡 (1 + 훼 ( 푞⁄ ) ) (3.21) 푞 푞 푞 푐푞 where

푓푡푞 - free flow travel time on link q per unit time

푥푞 – volume of vehicles attempting to use link q

푐푞 – capacity on link q

푡푞(푥푞) – average travel time for vehicle on link q 훼 – Alpha coefficient, which is assigned a value of 0.15 in the original BPR curve 훽 – Beta coefficient, the exponent of the power function which is assigned a value of 4 in the original BPR curve

3.4.2 Measure of Vehicle Distance Traveled (VDT)

The approach of using Vehicle Distance Traveled (VDT) and Vehicle Hours Traveled (VHT) for computing transportation network performance is adopted from Dalziell and Nicholson (2001) who used similar metrics in estimating the risk and impact of natural hazards on a road network. These metrics have also been applied in vulnerability (Tanasic et al., 2013), and optimal resilience studies (Bocchini and Frangopol, 2010). In this section, VDT indicates the total vehicle travel distance and was computed for each link pair in the transportation network as the product of link traffic volume and link distance. Increase in link VDT from the uninterrupted network highlights functional loss or increase in travel costs. Formulations for VDT (VMT) have been discussed in detail in Section 3.2 of this chapter.

3.4.3 Measure of Vehicle Hours Traveled (VHT)

Travel time is well known as an important measure of mobility (Murray-Tuite, 2006) and has been identified as a practical measure for determining resilience of transportation networks (Omer et al., 2013; Faturechi and Miller-Hooks, 2014c). VHT is computed for each travel path as the product of traffic volume and travel time. This metric is essential since it reflects delay in travel. Formulations for VHT have been discussed in Section 3.2 of this chapter.

3.4.4 High Impact Zone Location Metric

Hazard-induced damages usually have widespread effects. However, in order to determine the resulting impact on transportation networks, it is imperative to identify specific locations where traffic gridlocks mostly occur. Already discussed metrics such as; VDT and VHT are beneficial in quantifying performance and resilience, while, metrics such as link travel time and link speeds aid in the identification of high impact areas. The differences in pre-disaster to post-disaster link speeds are represented spatially using GIS mapping techniques. This serves as an effective method for locating areas of significant speed reduction, or high impact zones. Here, a measure for percentage reduction in link speed is computed as the mean percentage

difference between link speeds for the base (no closure) and bridge damage traffic assignment scenarios. Furthermore, in an attempt to determine which links were most affected by the shock event, link speed reductions greater than or equal to 1.61, 4.83, and 8.05 kilometers per hour (kph) (1, 3, and 5 miles per hour (mph)) were used for identifying significantly affected links. While fallen sign structures, debris and inoperable traffic signals, from hurricane events may cause reduced link speeds, these are mostly resolved more rapidly than damaged bridges (Xie et al., 2015). Bridge closures may cause long term closures resulting in sustained reduced speeds and gridlocks on segments of regional networks if not addressed promptly. For real time roadway conditions however, other events unrelated to hazards (even immediately after hazard events) may cause congestion and therefore result in reduced link speeds, nevertheless impacts may be more localized than regional. The traffic assignment model therefore optimally reassigns traffic on routes to account for closures. Reductions in link metrics are therefore solely due to the bridge closure scenarios. Secondly, since the model is a static assignment model, each model rerun provides the same results per scenario. Reductions in posted speed limits from 48.28 to 40.23 kph (30 to 25 mph) have been reported to cause about 1.61 kph (1 mph) reduction in actual vehicle speeds (Scott and Maddox, 2001). This speed reduction reduces vehicle collision by 5% (Scott and Maddox, 2001). Therefore, network link pairs showing marginal post-disaster speed reductions can serve as indicators for preliminarily identifying adversely impacted roadways due to major bridge closures on the regional network. The average link speed of 1.61 kph (1 mph) suggests the posted speed would be reduced by approximately 8.05 kph (5mph). The choice of 8.05 kph (5 mph) reduction in the average link speed was to serve as an upper limit emphasizing links which were most affected by closures. 4.8 kph (3 mph) was chosen as the mean of 1.61 and 8.05 kph (1 and 5 mph) to serve as an intermediary between the upper and lower limits. This metric is relevant to agencies in terms of hazard response since such events require effective operational measures to enhance mobility in affected areas. This measure was computed as:

푆푅푞−푆퐵푞 ∑푛 {( )×100} 푞=1 푆 휔 = 퐵푞 , ∀ 푞 ∈ 푄, 푄: |(푆 − 푆 )| ≥ 1.61, 4.83, or 8.05푘푝ℎ (1, 3 표푟 5푚푝ℎ) 푛 푅 퐵 (3.22)

where, 휔 – high impact zone metric

푆푅푞 – Speed on link q for link removal scenario

푆퐵푞 - Speed on link q for base scenario

3.4.5 Measuring Network Functionality

A unified network performance measure for a specified network topology was given by Nagurney and Qiang (2007), which is the N-Q network efficiency/performance measure as seen below:

푑 ∑ 푞 푞휖푄휃 휑 = 휑(ℵ, 푑) = 푞, (3.23) 푛푄 Where; 휑 is network performance measure ℵ - network topology d – equilibrium volume vector dq – equilibrium volume for link q.

θq – equilibrium disutility for link q (minimum equilibrium travel time or cost)

푛푄– number of origin-destination (O-D) pairs in the network

In this formulation, N-Q measure and a performance index computational approach used by Zhang et al. (2009) were modified and adopted in determining network performance during bridge closures. In this approach, the ratio of congested speeds to free flow speeds for O-D pairs were weighted by VDT and VHT to provide two performance indexes (indicators). The performance metrics formulated below are mobility performance metrics for the regional transportation networks.

퐶푆푃퐷푖,푗푉퐷푇푖,푗 ∑푖∈푂,푗∈퐷 퐹퐹푆푖,푗 푃퐼푉퐷푇 = (3.24) ∑푖∈푂,푗∈퐷 푉퐷푇푖,푗

퐶푆푃퐷푖,푗푉퐻푇푖,푗 ∑푖∈푂,푗∈퐷 퐹퐹푆푖,푗 푃퐼푉퐻푇 = (3.25) ∑푖∈푂,푗∈퐷 푉퐻푇푖,푗 Where

푃퐼푉퐷푇 – VDT weighted performance indicator

푃퐼푉퐻푇 – VHT weighted performance indicator

퐶푆푃퐷푖,푗 – congested speed for nodes i-j

퐹퐹푆푖,푗 – free flow speed for nodes i-j Performance Measure, 휑

푃퐼푎푓푡푒푟_푠ℎ표푐푘 휑푘 = (3.26) 푃퐼푏푒푓표푟푒_푠ℎ표푐푘

휑푘 – performance measure for indicator, k (VDT or VHT)

푃퐼푎푓푡푒푟_푠ℎ표푐푘 – VDT or VHT weighted performance indicator after hazard event

푃퐼푏푒푓표푟푒_푠ℎ표푐푘 - VDT or VHT weighted performance indicator prior to hazard event

3.4.6 Computing Resilience Index

The concept of resilience triangle proposed by Bruneau et al., (2003) has been broadly applied in the evaluation of infrastructure resilience over the last decade (Ta et al., 2009; Zobel, 2010; Adams et al., 2012). In this concept, the area within the resilience triangle reflects the loss in performance over time, meaning larger areas outside the triangle indicates greater resilience.

The community earthquake loss of resilience, 푅퐿, was mathematically expressed in (Eq. 16) as the functional performance of the infrastructure integrated over the recovery period (Bruneau et al., 2003).

푡1 푅퐿 = ∫ [100 − 푄(푡)]푑푡 (3.27) 푡0 Where 푄(푡) – quality of infrastructure (percent)

푡0 – time of disruption event

푡1 – time of system recovery Transportation network resilience depends on vulnerability and adaptive capacity (Gunderson et al., 2002). While vulnerability represents the system’s sensitivity to disruption, adaptive capacity evaluates the system’s ability to contain shocks. Heaslip et al. (2009) in a

proposed resilience cycle identified self-annealing as a stage following network breakdown (network reaching lowest performance level after disruption) where transportation networks accommodate present demand. Self-annealing essentially accounts for gradual increase network performance levels by road users adapting to new travel paths through alternative route choices until the system reaches a new equilibrium, resulting in possible improvement in network performance (Heaslip et al., 2009). This is typically prior to complete physical system recovery or functionality restoration. In this numerical illustration, the discussed concepts are applied; however, the sensitivity of resilience to recovery time is factored by accounting for expected recovery times based on multi-level hazard induced bridge damages (Figure 3.3). This is important since by definition resilience does not only explain the ability of infrastructure to absorb effects of a hazard but the ability of the system to recover quickly. The original resilience triangle proposed by Bruneau et al. (2003) depicts this clearly. In the context of transportation networks, high performance loss coupled with long recovery times does not only lead to increased transportation user costs, but also accessibility related with societal impacts, especially among aging or frail groups (Twumasi-Boakye et al., 2018). This approach ensures that resilience is not solely defined by functionality losses (a measure of importance), but weighted by the best and worst-case representations of time to recovery. The ratio of the mean area to mean recovery time results in an indexed measure. The compliment of the indexed measure yields a resilience index scaled from 0 to 1, with higher values reflecting more resilient networks.

Figure 3. 3 Transportation network resilience diagrams based on bridge damages

Figure 3. 3 - continued

In Figure 3.3a, A1, A2, and A3 represent transportation network’s resilience based on hurricane-induced bridge damage states. Detailed descriptions for four identified bridge damage states (slight, moderate, extensive, and complete) are reported by Sobanjo and Thompson (2013). Bridge closures are however expected when bridges are moderately, extensively and completely damaged, hence these damage states are considered in the resilience analysis, similar to Karamlou et al. (2016). Any single bridge can be moderately, extensively or completely damaged after a hazard event. For pre-event evaluation of resilience, three possible damage state outcomes were accounted for in the resilience computation. Recovery times are expected to vary per damage state. This instance is based on the assumption that the damaged bridge(s) will be opened at the same time. As a result, the transportation network performance measure remains unchanged until recovery. Though this is possible in all cases for single bridge damage scenarios,

damage to multiple bridges will require different recovery schema. Figure 3.3b suffices when considering three damaged bridges, each with unique damage states (moderate, extensive, and complete). In the event of three damaged bridges, the moderately, extensively, and completely damaged bridges are modeled to recover in the listed order, leading to total transportation network recovery. Although unlikely, this simplified approach follows in the rare case where multiple bridges with the same damage state happen to recover at the same time. A new transportation network performance is reached when bridges at a specific damage state are restored. The resilience loss is computed by summing A1, A2 and A3, since unlike the first case (Figure 3.3a.), performance varies. Figure 3.1c. depicts the more complex situation of multiple bridge damages. This case reflects the practical case where bridges of the same damage state may recover at different times. Recovery times in this case may largely depend on the more uncertain agency response practices. The duration of closure is also influenced by the size of the damaged bridge or the quantity of damaged elements at the same damage level. As a result, Figure 3.1c includes recovery options where some extensively damage bridges may recover before moderately damaged bridges, and completely damaged bridges before extensively damaged bridges. The step-wise recovery approximates to the original resilience triangle proposed by Bruneau et al. (2003), however in this diagram it is hypothesized that most moderately damaged bridges will be restored rapidly. Again, it is important to state that Figure 3.3 describes performance loss and recovery times at various bridge damage states. This performance refers to the transportation network’s performance and not bridge structural integrity. Therefore, there is a general assumption that all the mentioned bridge damage states will result in bridge closures, hence the same loss of ‘transportation network’ functionality when considering individual bridges as in the case of Figure 3.3a (irrespective of damage state). However, the times to recovery are expected to vary for different bridge damage states, and this influences network resilience significantly. The recovery sequence adopted included the assumptions that resources are readily available for bridge repair and rehabilitation activities, and for the application examples, bridges of lower damage states were assumed to recover first as identified in previous literature (Dong et al., 2013). The resilience formulation is seen below:

1 푇푚표푑(h) mod(h) 푇푚표푑(h+1) mod(h+1) 푅푘 = 1 − [∫ [1 − 휑 (푡)]푑푡 + ∫ [1 − 휑 (푡)]푑푡 + ⋯ + 푇 0 푘 푇푚표푑(h) 푘 푇 ( ) 푇 ( ) 푇 ∫ 푚표푑(n) [1 − 휑mod n (푡)]푑푡 + ∫ 푒푥푡(h)[1 − 휑푒푥푡 h (푡)]푑푡 + ∫ 푒푥푡(h+1)[1 − 푇푚표푑(n−h) 푘 0 푘 푇푒푥푡(h) ( ) 푇 ( ) 푇 ( ) 휑푒푥푡 h+1 (푡)]푑푡 + ⋯ + ∫ 푒푥푡(n) [1 − 휑푒푥푡 n (푡)]푑푡 + ∫ 푐표푚푝(h) [1 − 휑푐표푚푝 h (푡)] 푑푡 + 푘 푇푒푥푡(n−h) 푘 0 푘 푇 ( ) 푇 ( ) ∫ 푐표푚푝(h+1) [1 − 휑푐표푚푝 h+1 (푡)] 푑푡 + ⋯ + ∫ 푐표푚푝(n) [1 − 휑푐표푚푝 n (푡)]푑푡] (3.28) 푇푐표푚푝(h) 푘 푇푐표푚푝(n−h) 푘 where,

푇푚표푑 – time for restoring moderately damaged infrastructure in days

푇푒푥푡 – time for restoring extensively damaged infrastructure in days

푇푐표푚푝 – time for restoring completely damaged infrastructure in days 푇 – mean time for network recovery in days 푝(ℎ) 휑푘 (푡) – performance measure for indicator, k (for each damage state h (where p = moderate (mod), extensive (ext), and complete (comp) damage states. h = specific bridge(s) under recovery from p damage state) n – total number of damaged bridges for each damage state

Formulation for single bridge closure scenarios:

Here, performance measures, 휑푘(푡), are constant, therefore,

1 푇푇 푅 = 1 − [∫ [1 − 휑 (푡)]푑푡] (3.29) 푘 푇 0 푘 where, 1 푇푇 = (푇 + 푇 +푇 ) 3 푚표푑 푒푥푡 푐표푚푝

Formulation for 3 bridges (or group of bridges) with unique damage states (Figure 1b):

1 푇푚표푑 푝(ℎ) 푇푒푥푡 푝(ℎ) 푇푐표푚푝 푝(ℎ) 푅푘 = 1 − [∫ [1 − 휑 (푡)]푑푡 + ∫ [1 − 휑 (푡)]푑푡 + ∫ [1 − 휑 (푡)]푑푡] 푇 0 푘 푇푚표푑 푘 푇푒푥푡 푘 (3.30)

Formulation for single bridge closure events with partial recovery prior to full recovery:

1 푇푚표푑(휂) 푚표푑(휂) 푇푚표푑(휃) 푚표푑(휃) 푇푒푥푡(휂) 푅푘 = 1 − [∫ [1 − 휑 (푡)]푑푡 + ∫ [1 − 휑 (푡)]푑푡 + ∫ [1 − 3푇 0 푘 푇푚표푑(휂) 푘 0 푇 푇 휑푒푥푡(휂)(푡)]푑푡 + ∫ 푒푥푡(휃) [1 − 휑푒푥푡(휃)(푡)]푑푡 + ∫ 푐표푚푝(휂) [1 − 휑푐표푚푝(휂)(푡)]푑푡 + 푘 푇푒푥푡(휂) 푘 0 푘 푇 ∫ 푐표푚푝(휃) [1 − 휑푐표푚푝(휃)(푡)]푑푡] (3.31) 푇푐표푚푝(휂) 푘 where, 휂 – partial recovery 휃 – complete recovery

3.5 Numerical Illustration

Numerical illustrations were performed using a hypothetical network in which the formulation for computing TNR was modified. Here, the method of successive averages (MSA) traffic assignment algorithm was applied to a sample network which was then subject to a number of single and multiple bridge closure scenarios. Also, a recovery time sensitive adjustment was made to the resilience index computation to either penalize or compensate the network based on the predicted recovery times related to scheduled times for recovery. The following notation is used to describe the transportation network adopted in the proposed approach. The network is represented by a graph as similarly used in previous studies by Ip and Wang (2011), however, in this case, a directed graph is adopted. Resilience can be estimated by identifying all independent paths joining nodes for pre-disaster and post-disaster scenarios. Given a transportation (roadway) network 휏 = {ℵ⁄퐾}, where ℵ represents the set of nodes and directed links 푘 ∈ 퐾. The travel cost which denotes the disutility of using a link k is represented by 푡푘(푥푘), a function of flow 푥푘, and this is defined by the Bureau of Public Roads

(BPR) equation. The travel cost refers to the travel time on link k, and the flow 푥푘is a function of the flow on link k: 푥푘is positive and strictly increasing. The Stochastic User Equilibrium (SUE) problem presents an iterative solution with link flows at iteration i; 푥푖, resulting in link costs 푡푖 which are utilized tin stochastic loading to produce an auxiliary flow pattern 푦푖. In MSA, the reducing step length 휆푖 = 1/푖 + 1 is used to ensure convergence (Maher, 1998).

휏 = {ℵ⁄퐾} represents the transportation network where,

ℵ is the set of nodes representing zonal locations in the network

퐾 is the set of edges serving as roads connecting the nodes in the network

푛 ∈ ℵ is the number of nodes in set ℵ

푚 ∈ 퐾 is the number of edges in set 퐾

퐿푘(푖, 푗), 푘 − 푡ℎ independent path between node pair i and j for all i and j

푃푏푘(푖, 푗), performance of the independent path between node pair i and j for all i and j prior to disruption

푃푎푘(푖, 푗), performance of the independent path between node pair i and j for all i and j after disruption

푅푖푛푑푒푥, network resilience represented by graph 휏

MSA Procedure:

Step 0) Initialization: Define the number of iterations N. Initial solution 푥0 is obtained by all-or- nothing assignment of demand on shortest paths computed with arc costs 푡0 = 푡(0), 푖 = 0.

Step 1) Update Link Costs: 푖 = 푖 + 1, 푡푖 = (푥푖−1).

Step 2) All-or-Nothing Assignment: Load the demand on the shortest path computed with arc costs. This yields a flow pattern.

Step 3) Compute Step Size: 휆푖 = 1/푖 + 1.

푖 푖−1 푖 푖−1 Step 4) Update Link Flows: 푥 = 푥 + 휆푖(푦 − 푥 ).

Step 5) Stopping Criterion: if 푖 < 푁, return to Step 1, otherwise 푥∗ = 푥푖, 푡∗ = 푡(푥푖) and STOP.

Step 6) If all node pairs are done, output results and stop.

Step 7) Repeat procedure for road closure scenarios.

Figure 3.4 describes the MSA algorithm where traffic volumes are split for different paths at each iteration step. For each iteration step, volumes have an MSA probability (1/iteration) of being selected for the new path and as such the proper number of trips is assigned to the new path.

Figure 3. 4 Diagram for MSA traffic assignment algorithm

The link cost (BPR) function is expressed as:

푥 훽 푡 (푥 ) = 푡 (1 + 훼( 푘⁄ ) ) (3.32) 푘 푘 0푘 푐푘 where

푡0푘 - free flow travel time on link k per unit time

푥푘 – volume of vehicles attempting to use link k

푐푘 – capacity on link k

푡푘(푥푘) – average travel time for vehicle on link k α – alpha coefficient, which is assigned a value of 0.15 in the original BPR curve β – beta coefficient, the exponent of the power function which is assigned a value of 4 in the original BPR curve

3.5.1 Resilience Estimation and Index Computation

The transportation network resilience can be evaluated once the data for all origin- destination paths have been obtained. This is achieved by evaluating the performance loss for bridge closure events and their randomly assigned closure durations based on bridge damage states. Multiple routes are possible for assigning vehicles from origin to destination and for this reason performance loss is evaluated by considering the ratio of post-disaster vehicle time traveled (VTT) to the vtt for the uninterrupted network. The performance of the uninterrupted transportation network is given as:

푚 푃푏푘(ℵ/푘) = ∑푘=1 푣푡푡푘 (3.33)

푣푡푡푘 = 푡푘푥푘, ∀푘 ∈ 퐾 (3.34)

where, 푃푏푘(ℵ/푘) represents the performance measure based on all reliable links on the network connecting all node pairs i and j.

Transportation user costs are beneficial in explaining the travel cost in monetary terms (Twumasi-Boakye and Sobanjo, 2017). This helps to clearly identify the additional financial costs associated with system losses as already stated in this thesis. This step is therefore identified as an important initial step in appreciating the need for post-disaster rapidity. This can be computed as Delay Costs (DC) and Vehicle Operating Cost (VOC). Delay costs represent the monetary value of travel time and this is computed as:

퐷퐶 (ℵ/푘) = ∑푘∈퐾 푣푡푡푘푐퐶ℎ − ∑푘∈퐾 푣푡푡푘푛퐶ℎ (3.35) where,

푣푡푡푘푐 = vehicle time traveled during bridge damage (closure)

퐶ℎ = time value of travel in cost per hour ($)

푣푡푡푘푛 = vehicle time traveled (uninterrupted network)

VOC represents the monetary value of travel distance and this is computed as: vdtk = 푥푘dk (3.36)

where,

vdtk= vehicle distance traveled on link k.

푥푘 = volume of vehicles on link k.

dk = link distance for k.

푉푂퐶 (ℵ/푘) = ∑푘∈퐾 푣푑푡푘푐퐶푚 − ∑푘∈퐾 푣푑푡푘푛퐶푚 (3.37) where,

푣푑푡푘푐 = vehicle distance traveled during bridge damage (closure)

퐶푚 = cost per mile ($)

푣푑푡푘푛 = vehicle distance traveled (uninterrupted network)

Therefore, the daily additional user cost (DAUC) is computed as:

DAUC (ℵ/푘) = DC (ℵ/푘) + VOC (ℵ/푘) (3.38)

While transportation networks are referred to as being in equilibrium in certain situations, this is not very accurate since it does not exist practically. It is however observed that links or edges have different impacts on the efficiency of the transportation network. This indicates that each component has various levels of criticality and affect network travel times differently. Resilience largely entails the assumptions that a disruption is imminent and attempts to capture the networks’ ability to contain and recover from such perturbations. Transportation agencies are usually aware of critical components of transportation networks; however, the impacts of their disruptions are not succinctly comprehended, especially for large scale networks. Here, the steps for identifying critical edges and quantifying performance loss due to network critical link or edge closures are outlined. Considering an edge, 푘푒 = {i, j} that is inoperable, the resulting subgraph with link or edge removal can be represented by (ℵ/푘푒 ). The measure of the resulting subgraph (ℵ/푘푒) can be denoted by 푀(ℵ/푘푒).

푚−휀 푀(ℵ/푘푒) = ∑푘=1 푘 , ∀푘 ∈ 퐾 (3.39)

The performance of a disrupted network, 푀(ℵ/푘푒) considering the breakdown of an edge, k is written as:

푚−휀 푃푎푘(ℵ/푘푒) = ∑푘=1 푣푡푡푘 , ∀푘 ∈ 퐾 (3.40) where 푚 − 휀 represents the number of edges in the resulting network post-hazard.

The measure of performance loss of the transportation network is:

푚 푃푏푘(ℵ/푘) ∑푘=1 푣푡푡푘 푃퐿(ℵ/푘) = 1 − ℵ = 1 − 푚−휀 , ∀푘 ∈ 퐾 (3.41) 푃푎푘( ) ∑푘=1 푣푡푡푘 푘푒

It therefore follows that 푃푎푘(ℵ/푘푒) ≥ 푃푏푘(ℵ/푘) and 푃퐿(ℵ/푘) ∈ (0, 1]. For values of 푃푎푘(ℵ/푘푒) s.t. 푃푎푘(ℵ/푘푒) → 푃푏푘(ℵ/푘), 푃퐿(ℵ/푘) → 0. In the case 푃푎푘(ℵ/푘푒) ≫ 푃푏푘(ℵ/푘), 푃퐿(ℵ/푘) → 1.

Loss of resilience can then be computed based on Bruneau et al., (2003) as:

푡1 푅퐿 = ∫ [푃퐿(ℵ/푘)]푑푡 (3.42) 푡0

It then follows that the resilience of the transportation network as a positive measure is computed as:

푡1 푅푚 = 1 − ∫ [푃퐿(ℵ/푘)]푑푡 (3.43) 푡0

The essence of transportation network resilience is to comprehend the network level impacts of hazard events and how already built networks are able to mitigate functional loss by coping with network demands and recovering to pre-event functionality. The importance of resilience as a metric of infrastructure importance cannot be overstated in that, unlike other metrics, resilience captures how long it takes broken down components of networks to be restored. Rapidity is a major component of resilience especially when considering larger transportation networks. Even though large networks may have sufficient redundancy to contain demands during localized breakdown, the network level increment in travel costs usually have major implications on additional daily transportation user costs (Twumasi-Boakye and Sobanjo, 2017) which when not rectified quickly can lead to significant economic losses. For this reason, resilience index formulations are presented in an effort to explain transportation network resilience using a single indicator measure. In the specific cases in this study, bridge infrastructures are the main components considered for the network.

Assumptions

1. Bridges are known to occur in five possible post-hazard states namely: 0- no damage, 1- slightly damaged, 2- moderately damaged, 3- extensively damaged, 4- completely damaged. Details on post-disaster bridge damage states are reported in previous studies (Padgett et al, 2008; Sobanjo and Thompson, 2013).

2. It is generally expected that bridges of lower damaged states recover prior to bridges with higher damage states. Therefore, a bridge in a severe damage state may need more time to be restored to full operation when compare with a slightly damaged bridge (Dong and Frangopol, 2015).

3. It is assumed that resources are available for post-hazard bridge MR&R activities hence no excessive delays in construction are expected.

Case 1-Single Bridge Closures In the event of individual bridge closures during network disruptions, resilience can be evaluated based on performance loss, and recovery time for the bridge MR&R influenced primarily by the bridge damage state. Resilience index formulation can be demonstrated to have a resilience index measure for uninterrupted networks based on damages to certain important bridges in the network. In this case, the damage states and recovery durations are for the case chosen ‘damaged’ bridge is not known a priori hence would have to be predicted. While this study does not focus on predicting recovery times, possible methods include fragility analysis, and parametric and non-parametric modeling. As with most studies of that nature, there are data needs to be met for high accuracy bridge recovery time predictions. Furthermore, since any of the damage states may occur, an option must exist to cater for such a situation. The formulation is as follows:

Option 1.

1 푡푝푟푒푑 푅푖푛푑푒푥 = 1 − [∫ [푃퐿(ℵ/푘)]푑푡] (3.44) 푇푖 푡0

Where 푡푝푟푒푑 is the predicted recovery time for the damaged bridge of a specific condition state. 푇푖 represents the scheduled time it takes MR&R activities to be completed on similar

bridges of the same condition state. The use of scheduled construction time is quite important since this time is mostly dependent on agency response, funding availability and effectiveness: agency as a component of resilience has been evaluated in previous studies by Serulle et al., (2011). The use of the scheduled time is because the measure of resilience is dependent on the predicted recovery time in comparison to the scheduled time. The restoration of the Escambia Bay Bridge after Hurricane Ivan took 66 days of 24/7 continuous work. As a result, the bridge was reopened 27 days ahead of schedule (Maxey 2006; Hitchcock et al., 2008). Estimating resilience index in such a case must account for the early restoration against the scheduled time hence ensure that the computed index value is higher. The converse would suffice should restoration periods take longer than the scheduled duration.

Option 2.

To account for multiple damage states, the equation is modified as:

1 푡푚푝푟푒푑 푅푖푛푑푒푥 = 1 − [∫ [푃퐿(ℵ/푘)]푑푡] (3.45) 푇푖 푡0 where 푡푚푝푟푒푑 is the predicted mean time for recovery considering the plausibility of occurrence of all bridge post-hazard condition states and is computed by:

푡푚푝푟푒푑 = 푚푒푎푛(푡푖) (3.46) where i = slight, moderate, extensive and complete (predicted recovery times for all bridge damage states)

푇푖 represents the mean of the scheduled recovery times it takes MR&R activities to be completed on similar bridges of the same condition states.

Case 2- Multiple Bridge Closures Recovery of multiple bridges are often more complex than damage to one bridge during an event. For instance, if 20 bridges are damaged during a hurricane event, those, damages to those bridges may put them in multiple damage states, and depending on several factors, even a group bridges within the same damage state may be reinstated at separate times. In certain cases, bridges of higher damage states are reinstated before bridges of lower damage states. The

aforesaid is quite rare and therefore an assumption is made that bridges of lower damage states will recover prior to those of higher damage states, however, recovery time variations within damage states are still considered.

1 푡푠푙(h) sl(h) 푡푠푙(h+1) sl(h+1) 푡푠푙(n) 푅푖푛푑푒푥 = 1 − [∫ [ 푃퐿(ℵ/푘)푖 ]푑푡 + ∫ [ 푃퐿(ℵ/푘)푖 ]푑푡 + ⋯ + ∫ [ 푃퐿(ℵ/ 푇푖 0 푡푠푙(h) 푡푠푙(n−h)

sl(n) 푡푚표푑(h) mod(h) 푡푚표푑(h+1) mod(h+1) 푘) ]푑푡 + ∫ [ 푃퐿(ℵ/푘) ]푑푡 + ∫ [ 푃퐿(ℵ/푘) ]푑푡 + ⋯ + 푖 푡푠푙(n) 푖 푡푚표푑(h) 푖

푡푚표푑(n) mod(n) 푡푒푥푡(h) 푒푥푡(h) 푡푒푥푡(h+1) 푒푥푡(h+1) ∫ [ 푃퐿(ℵ/푘) ]푑푡 + ∫ [ 푃퐿(ℵ/푘) ]푑푡 + ∫ [푃퐿(ℵ/푘) ]푑푡 + 푡푚표푑(n−h) 푖 푡푚표푑(n) 푖 푡푒푥푡(h) 푖

푡푒푥푡(n) 푒푥푡(n) 푡푐표푚푝(h) 푐표푚푝(h) 푡푐표푚푝(h+1) ⋯ + ∫ [ 푃퐿(ℵ/푘) ]푑푡 + ∫ [ 푃퐿(ℵ/푘) ] 푑푡 + ∫ [ 푃퐿(ℵ/ 푡푒푥푡(n−h) 푖 푡푒푥푡(n) 푖 푡푐표푚푝(h)

푐표푚푝(h+1) 푡푐표푚푝(n) 푐표푚푝(n) 푘) ] 푑푡 + ⋯ + ∫ [ 푃퐿(ℵ/푘) ]푑푡] (3.47) 푖 푡푐표푚푝(n−h) 푖

It is imperative to state explicitly that when defining a network with a resilience index, the index would be specific to a categorical hazard the transportation network and infrastructure is exposed to. Therefore, it suffices to state that the resilience index of a transportation network exposed to a hurricane category 1 event is 0.85, rather than simply stating that the resilience index for the transportation network is 0.85, or that transportation network exposed to hurricanes is 0.85. If a multi-hazard study is performed on the transportation network and a resilience index is estimated for each specific hazard case, the mean of computed resilience indexes may be used to define the network. Where hazard events have similar probabilities of occurrence, a simple average of the resilience indexes can be used to represent the aggregates network resilience. The aggregated index is then expressed as:

1 퐴푅 = ∑푛 푅푖 (3.48) 푖푛푑푒푥 푛 푖=1 푖푛푑푒푥

In the case of multiple events with large variation in event probabilities, a different approach must be adopted. An example is the case of categorical hurricane events. Assuming resilience indexes for a transportation network are computed for each hurricane category, the aggregated resilience index can then be computed based on using the hurricane event probabilities as weights in order to ensure that the effects of high impact categories on the

resilience index are balanced by the rare occurrence of such events. By doing this, the aggregate resilience index for the network is less skewed towards high impact rare events. In such cases, the aggregated resilience index can be computed using the weighted average.

3.5.2 Hypothetical Network Application

The numerical illustration details a sample network with eight nodes, 13 edges, and 8 bridges located at certain locations on the network as seen in Figure 3.5. The MSA algorithm already discussed is applied to this network considering movement from node 1 (origin) to node 8 (destination). For the purposes of this example, the free flow travel time on each link is assigned a value of 5 minutes, edge capacities are 1500 each and O-D is 7000. Resilience initially computed for scenarios involving individual bridge closures. Secondly, five bridges are closed at once and are reinstated sequentially until the network is uninterrupted. The first case represents bridge specific hazards while the second case represents hazards with widespread effects, for example, hurricanes, wildfires, and floods.

Figure 3. 5 Transportation network for numerical illustration

The numerical Illustration first involved evaluating user cost (delay cost) for single bridge closure events. In an effort to explain the importance of recovery durations, the computed VTT after each closure event was used to estimate DC for different recovery durations. Since user costs are computed as daily costs, for each additional day, additional user costs increased. For illustration, only delay costs were considered. The monetary value of travel time was determined as $37.58/veh-hr (Twumasi-Boakye and Sobanjo, 2017). Results for each bridge closure showed significant performance losses as observed in Table 3.1. Bridges with direct

service to the destination node had major impact on travel time during closures. Closures to bridges on links 3-6 and 4-7 led to the most severe effects on travel resulting in 158.6 percent and 173 percent increase in vehicle time traveled respectively.

Table 3. 1 Simulation results for individual bridge closure scenarios Uninterrupted Network link 1-3 closure link 2-3 closure Travel Travel Travel i j Flow VTT i j Flow VTT i j Flow VTT time time time 1 2 2331.0 9.4 21850.5 1 2 3885.0 38.7 150539.7 1 2 2331.0 9.4 21850.5 1 3 2331.0 9.4 21850.5 1 4 3115.0 18.9 59024.7 1 3 2331.0 9.4 21850.5 1 4 2338.0 9.4 22039.5 2 3 1610.0 6.0 9652.6 1 4 2338.0 9.4 22039.5 2 3 0.0 5.0 0.0 2 5 2275.0 9.0 20403.2 2 5 2331.0 9.4 21850.5 2 5 2331.0 9.4 21850.5 3 4 0.0 5.0 0.0 3 4 0.0 5.0 0.0 3 4 0.0 5.0 0.0 3 6 1610.0 6.0 9652.6 3 6 2331.0 9.4 21850.5 3 6 2331.0 9.4 21850.5 4 7 3115.0 18.9 59024.7 4 7 2338.0 9.4 22039.5 4 7 2338.0 9.4 22039.5 5 8 2275.0 9.0 20403.2 5 8 2331.0 9.4 21850.5 5 8 2331.0 9.4 21850.5 5 6 0.0 5.0 0.0 5 6 0.0 5.0 0.0 5 6 0.0 5.0 0.0 6 7 0.0 5.0 0.0 6 7 0.0 5.0 0.0 6 7 0.0 5.0 0.0 6 8 1610.0 6.0 9652.6 6 8 2331.0 9.4 21850.5 6 8 2331.0 9.4 21850.5 7 8 3115.0 18.9 59024.7 7 8 2338.0 9.4 22039.5 7 8 2338.0 9.4 22039.5

175370.8 348016.9 175370.8 link 3-6 closure link 4-7 closure link 5-6 closure Travel Travel Travel i j Flow VTT i j Flow VTT i j Flow VTT time time time 1 2 3500.0 27.2 95310.2 1 2 3451.0 26.0 89768.9 1 2 2331.0 9.4 21850.5 1 3 1050.0 5.2 5439.1 1 3 3549.0 28.5 101156.6 1 3 2331.0 9.4 21850.5 1 4 2450.0 10.3 25327.6 1 4 0.0 5.0 0.0 1 4 2338.0 9.4 22039.5 2 3 0.0 5.0 0.0 2 3 0.0 5.0 0.0 2 3 0.0 5.0 0.0 2 5 3500.0 27.2 95310.2 2 5 3451.0 26.0 89768.9 2 5 2331.0 9.4 21850.5 3 4 1050.0 5.2 5439.1 3 4 0.0 5.0 0.0 3 4 0.0 5.0 0.0 4 7 3500.0 27.2 95310.2 3 6 3549.0 28.5 101156.6 3 6 2331.0 9.4 21850.5 5 8 2450.0 10.3 25327.6 5 8 2961.0 16.4 48525.1 4 7 2338.0 9.4 22039.5 5 6 1050.0 5.2 5439.1 5 6 490.0 5.0 2454.2 5 8 2331.0 9.4 21850.5 6 7 0.0 5.0 0.0 6 7 1477.0 5.7 8426.4 6 7 0.0 5.0 0.0 6 8 1050.0 5.2 5439.1 6 8 2562.0 11.4 29162.8 6 8 2331.0 9.4 21850.5 7 8 3500.0 27.2 95310.2 7 8 1477.0 5.7 8426.4 7 8 2338.0 9.4 22039.5 453652.2 478845.6 197221.3 link 6-7 closure link 6-8 closure link 5-8 closure Travel Travel Travel i j Flow VTT i j Flow VTT i j Flow VTT time time time 1 2 2331.0 9.4 21850.5 1 2 3115.0 18.9 59024.7 1 2 1876.0 6.8 12822.4 1 3 2331.0 9.4 21850.5 1 3 1610.0 6.0 9652.6 1 3 2436.0 10.2 24888.2 1 4 2338.0 9.4 22039.5 1 4 2275.0 9.0 20403.2 1 4 2688.0 12.7 34229.4 2 3 0.0 5.0 0.0 2 3 0.0 5.0 0.0 2 3 0.0 5.0 0.0 2 5 2331.0 9.4 21850.5 2 5 3115.0 18.9 59024.7 2 5 1876.0 6.8 12822.4 3 4 0.0 5.0 0.0 3 4 0.0 5.0 0.0 3 4 0.0 5.0 0.0 3 6 2331.0 9.4 21850.5 3 6 1610.0 6.0 9652.6 3 6 2436.0 10.2 24888.2 4 7 2338.0 9.4 22039.5 4 7 2275.0 9.0 20403.2 4 7 2688.0 12.7 34229.4 5 8 2331.0 9.4 21850.5 5 8 3115.0 18.9 59024.7 5 6 1876.0 6.8 12822.4 5 6 0.0 5.0 0.0 5 6 0.0 5.0 0.0 6 7 714.0 5.0 3597.5 6 8 2331.0 9.4 21850.5 6 7 1610.0 6.0 9652.6 6 8 3598.0 29.8 107321.0 7 8 2338.0 9.4 22039.5 7 8 3885.0 38.7 150539.7 7 8 3402.0 24.8 84519.9 197221.3 397378.0 301491.4

Additional delay costs were observed to increase significantly with extended recovery durations. Massive cost repercussions are expected from lack of rapidity. For example, in the case of link 4-7 closure, additional delay cost is observed to increase from approximately $2 million to $19 million, between 10 and 100 days after bridge closure: this represents over 9000 percent increase in cost over a period of 90 days. This is because there is a cumulative 100 percent increase in user cost for any additional day of delayed recovery. This means that in explaining resilience, the factor of time must be well factored in index formulations. Transportation network resilience measures should include a penalization or compensation factor for extended durations of post disaster restoration relative to scheduled times. Network performance losses associated with individual bridge closures can be observed in Table 3.2. Results are explicit that index values reduce with decreasing scheduled recovery times. The values for resilience indexes are scaled from 0 to 1 with 1 representing a transportation network in pre-disaster conditions that is, no performance loss is recorded. Essentially, index values lower than 0.7 are critical and indicate that performance loss is significant or VTT has drastically increased: this also shows slow recovery times after performance loss.

Table 3. 2 Resilience index results for individual bridge closure scenarios No Scenario 1 2 3 4 5 6 7 8 closure Closed bridge (edge) - 1-3 2-3 3-6 4-7 5-6 6-7 6-8 5-8 Total VTT 175370.8 348016.9 175370.8 453652.2 478845.6 197221.3 197221.3 397378.0 301491.4 Functionality 1.00 0.50 1.00 0.39 0.37 0.89 0.89 0.44 0.58 Performance loss PL(ℵ) 0.00 0.50 0.00 0.61 0.63 0.11 0.11 0.56 0.42 Rindex (tpred=15, Ti =20) 1.00 0.63 1.00 0.54 0.52 0.92 0.92 0.58 0.69

In the case of multiple bridge closures, five bridges were randomly selected, and each bridge was randomly assigned a damage state between 1 and 4, the other three bridges were assigned to have no damages. Details of bridge damage states can be found in reports by Sobanjo and Thompson (2013) and Padgett et al., (2008). Expected closure durations were assigned for each damage state. This was based on previous work on seismic resilience for bridges by Dong and Frangopol, (2015) who sourced data from literature surveys and through engineering judgment. Recovery durations for each damage state were randomly assigned to each state. Scheduled recovery times were also assigned to each damage state by the same approach. Figure 3.6 shows the damaged bridges and the recovery sequence after closures.

Table 3. 3 Selected bridges for multi closure scenario Bridge Damage Closure Duration Number State (days) 2 (link 2-3) 3 46 5 (link 5-6) 2 16 6 (link 6-7) 2 28 7 (link 6-8) 4 70 8 (link 5-8) 1 1 1- Slight 2-Moderate 3- Extensive 4-Complete

After each recovery event, the transportation network is rerun using the MSA algorithm to obtain an optimal solution after 10000 iterations. The model outputs provide link travel times and flows which are then used to compute VTT and subsequently, the functionalities of the network. Table 3.4 summarizes the simulation outputs for multiple bridge closure events. It is succinct that there are significant performance losses attributed to the closure of 5 bridges and these losses decrease as the bridges are restored. It is also noteworthy that in two instances, bridge restorations led to the same results in VTT. This implies that even though that bridge offered redundancy to the network, its presence did not have an impact on travel since the optimal solution still required the demand to use the previously chosen route as an optimal solution. This adds to the argument that while redundancy is needful for ease of mobility during link disruptions, excess redundancy may lead to some unused links or roadways, and this is not economically sound.

Table 3. 4 Simulation results and resilience index computation for multiple bridge closures Closed Bridges VTT Opened Bridge(s) sequence Damage state(s) Closure duration 6-8, 2-3, 6-7, 5-6, 5-8 5318135.8 - - - 6-8, 2-3, 6-7, 5-6 504931.7 3-6 1 1 6-8, 2-3, 6-7 504931.7 3-6, 5-6 1, 2 16 6-8, 2-3 397378.0 3-6, 5-6, 6-7 1, 2, 2 28 6-8 397378.0 3-6, 5-6, 6-7, 2-3 1, 2, 2, 3 46 Uninterrupted Network 175370.8 3-6, 5-6, 6-7, 2-3, 6-8 1, 2, 2, 3, 4 70 Days after Days after Closure Closed Bridges last bridge T last bridge Functionality PL(ℵ) PL(ℵ)*t PL(ℵ)*t ` duration i i recovery, t recovery, ti 6-8, 2-3, 6-7, 5-6, 5-8 1 1 1 1 0.03 0.97 0.97 0.97 6-8, 2-3, 6-7, 5-6 16 15 19 18 0.35 0.65 9.79 *11.75 6-8, 2-3, 6-7 28 12 19 - 0.35 0.65 7.83 *11.75 6-8, 2-3 46 18 75 56 0.44 0.56 10.06 31.29 6-8 70 24 120 45 0.44 0.56 13.41 25.14 Uninterrupted Network - - - 1.00 0.00 - -

Total = 42.05 Total = 69.14 Rindex = 1 - (42.05/120) = 0.65

Figure 3. 6 Multiple bridge closures recovery sequence

The resilience diagram for the network subjected to multiple bridge closure with sequential recovery is seen in Figure 3.7. In the figure, two line representing resilience diagrams for predicted recovery time and scheduled recovery times. It is necessary to restate that the values for both predicted and scheduled recovery times were randomly chosen using reference literature. In this particular case, the predicted recovery time yield less resilience loss when compared with scheduled recovery time. This means that in computing the resilience index, the transportation network must be compensated to reflect more resilience since per schedule the resilience would have been lesser. Hence by using equation (8.16), the Ti chosen for the

scheduled time is higher in this case ensuring that resilience loss is slight reduced and therefore a higher resilience index is estimated.

1.00

0.90

0.80

0.70

0.60

0.50

0.40 Functionality

0.30

0.20

0.10

0.00 δ-20 - t0 0t0 20 40 60 80 100 120 140 Recovery time (days) Closure duration, T Closure duration, Ti

Figure 3. 7 Network resilience curve for multiple bridge closures

3.5.3 Sensitivity Analysis

The main reason for the sensitivity analyses is to depict the changes in resilience indexes depending on varying predicted recovery times and scheduled recovery times. To compare how various inputs due to uncertainty may affect resilience index outputs, sensitivity analyses were performed. For all the different performance losses computed for individual bridge closures scenarios, different predicted recovery times were chosen for scheduled time ranging from 1 to 100 days. This analyses also makes it possible to observe the influence of extended recovery times relative to scheduled times on resilience. Here we also realize that the higher the performance loss, the longer it is expected for bridges to be reinstated hence early scheduled times, for example from 1 to 10 days would not be realistic in such events: it is therefore seen that resilience index values begin at points below zero for early scheduled times. The converse holds for bridges resulting in less performance losses. Figure 3.8 also indicates that for scenarios

with minimal performance losses, the resilience index curves converge to 1 (pre-disaster condition) more rapidly than scenarios with higher network losses. The sensitivity analysis therefore accounts for both performance loss and restoration or recovery times. The suggested approach when applied will enable agencies to evaluate optimal times for recovery to minimize both losses due to user costs and delayed recovery. In certain instances, post-disaster bridge replacements take up to a year for recovery: in such cases, the damaged bridges are mostly of less importance to the transportation network and its closure lead to very small performance losses. As such the resilience index is insignificantly affected. For example, a damaged bridge for a large network may result in a network performance loss of 0.001 with expected schedule duration of 20 days, compared with a predicted duration of 200 days. From the formulation in this computational example, the index computation will be 0.99. The underlying need for rapidity is that even in the example given; the delay of 180 days may result in cumulative additional transportation user costs which may eventually be at least substantial, if not excessive. Figure 3.9 shows resilience index patterns for each closure at scheduled recovery period of 10 days. Here, the previous assertion that scenarios with high performance losses indicate lower resilience indexes at early scheduled durations are reinforced.

1.00 0.90 0.80 0.70 0.60 0.50 0.40

Resilience Resilience Index 0.30 0.20 0.10 0.00 0 20 40 60 80 100 Recovery time, Ti (days) tpred =2 tpred = 5 tpred = 10 tpred = 15

PL(ℵ) = 0.11

Figure 3. 8 Network resilience index curves for individual bridge closures, varied predicted recovery times, and scheduled recovery durations from 1 to 100 days.

1.00 0.90 0.80 0.70 0.60 0.50 0.40

Resilience Resilience Index 0.30 0.20 0.10 0.00 0 10 20 30 40 50 60 70 80 90 100 Recovery time, Ti (days)

tpred =2 tpred = 5 tpred = 10 tpred = 15

PL(ℵ) = 0.42

1.00 0.90 0.80 0.70 0.60 0.50 0.40

Resilience Resilience Index 0.30 0.20 0.10 0.00 0 20 40 60 80 100 Recovery time, Ti (days) tpred =2 tpred = 5 tpred = 10 tpred = 15

PL(ℵ) = 0.5

Figure 3. 8 – continued

1 0.9 0.8 0.7 0.6 0.5 0.4

Resilience Resilience Index 0.3 0.2 0.1 0 0 10 20 30 40 50 60 70 80 90 100 Recovery time, Ti (days)

tpred =2 tpred = 5 tpred = 10 tpred = 15

PL(ℵ) = 0.56

1.00 0.90 0.80 0.70 0.60 0.50 0.40

Resilience Resilience Index 0.30 0.20 0.10 0.00 0 10 20 30 40 50 60 70 80 90 100 Recovery time, Ti (days)

tpred =2 tpred = 5 tpred = 10 tpred = 15

PL(ℵ) = 0.61

Figure 3. 8 – continued

1.00

0.90

0.80

0.70

0.60

0.50

0.40 Resilience Resilience Index 0.30

0.20

0.10

0.00 0 10 20 30 40 50 60 70 80 90 100 Recovery time, Ti (days) tpred =2 tpred = 5 tpred = 10 tpred = 15

PL(ℵ) = 0.63

Figure 3. 8 – continued

1 0.9 0.8 0.7 0.6 0.5 0.4

0.3 Resilience Resilience Index 0.2 0.1 0 tpred =2 tpred = 5 tpred = 10 tpred = 15

PL(ℵ) = 0.50 PL(ℵ) = 0.61 PL(ℵ) = 0.63 PL(ℵ) = 0.11 PL(ℵ) = 0.56 PL(ℵ) = 0.42

Figure 3. 9 Network resilience indexes for individual bridge closures for varied predicted recovery times assuming a scheduled recovery duration (Ti) of 10 days.

3.6 Chapter Summary

The need to comprehend the network or regional level impacts of hazards on transportation network systems has been clearly stated in various literature. In this chapter, performance metrics were identified to efficiently explain network level performance losses and further utilized in resilience computations as well as index formulations. In order to evaluate how these metrics can be applied in achieving the objectives of this thesis, they are applied in a number of case studies and numerical illustrations in the subsequent chapters.

CHAPTER 4

EVALUATING TRANSPORTATION USER COST

4.1 Evaluating User Cost for Simulated Regional Networks

Bridges serve as major connectors on the transportation network, providing links over waterways, areas of high altitudes and inaccessible terrains. When bridges are closed, costs are incurred due to long detours. However, bridge closures are inevitable not only due to the likelihood of hazard-induced damages, but routine maintenance, repair and rehabilitation (MR&R) activities may warrant closures as well. Furthermore, when bridges have substandard vertical clearances or load capacity, certain trucks must detour since they cannot pass on or under those bridges. This “inconvenience” is typically quantified as user costs. Over the past decade, user cost models have been incorporated into bridge management systems to evaluate safety, quantify deficiencies and determine mobility merits of functional improvement to bridges (Sobanjo and Thompson, 2011). User costs typically refer to the costs incurred by road users as a result of the state of the facility in terms of possible deficiencies relative to the desired level of service. User costs comprise of three key components, namely: travel time cost; vehicle operating cost (VOC); and accident risk cost. Vehicle operating costs include expenses directly incurred as a result of vehicle operation. Such costs include energy, fluids, repair, maintenance and vehicle depreciation (Sobanjo and Thompson, 2011). In previous research, VOCs were associated with truck detours considering the inclusion of detour distance and travel time costs linked to the added detour time (Thompson et al., 1999). Other studies have also described the development of adjustment factors for the various components in estimating the VOC (Barnes and Langworthy, 2004; Sinha and Labi, 2007). There have been several user cost studies over the last two decades, basically using two main approaches: with most estimating based on the increased detour around the bridges, while a few have considered the impact on the transportation network. Using the detour approach, benefits of functional improvement on bridges have also been assessed in terms of user cost saving (Golabi et al., 1992; Blundell, 1997). Other important contributions in this are indicated in literature (Kleywegt and Sinha, 1994; Johnston et al., 1994; Son and Sinha, 1997).

Literature (Sinha and Labi, 2007) indicates travel time as one of the major issues in the evaluation of alternative transportation systems. The researchers (Sinha and Labi, 2007) further discussed several factors influencing the value and amount of travel time. There has also been the development of methods for incorporating delay costs in computing bridge user costs resulting from limitations in bridge traffic capacity (Bai et al., 2013). The network-based approach includes a previous study using a traffic assignment model to determine the effects of road closures on traffic patterns including a user cost component and benefit-cost ratio for various mitigation options (Dalziell and Nicholson, 2001). An evaluation of the effects of I-35W bridge collapse on road users in the Minnesota Twin Cities metropolitan area included an analysis of travel delay, considering scenarios prior to and after the bridge collapse (Xie and Levinson, 2001); the analysis was based on a simplified and scaled-down travel demand model. As mentioned above, it is current practice that vehicles are rerouted to the shortest alternative route in terms of distance during bridge closures or when there is need for functional improvements. While this approach may temporarily contain the effects of closures, it does not take into account the regional or the network impact caused. In addition to this, detour routes may have limited lane capacity hence may only accommodate a portion of rerouted traffic volume. The National Bridge Inventory (NBI) manual defines detour or bypass length as being indicative of the actual length to the nearest kilometer, and it is representative of the total additional travel for a vehicle which would result from closing of the bridge. In this study, a scenario-based network approach for evaluating the impact of bridge closures on transportation user cost is proposed. This study builds on previous work (Erath et al., 2009) and more recent studies (Tanasic et al., 2013). In a vulnerability assessment of bridges exposed to scour (Tanasic et al., 2013), the researchers considered various scenarios and utilized traffic simulation software to evaluate the redistribution of traffic flows. However, the main objective and approach in this study focuses on the regional impact of bridge closures and evaluates the cost repercussions of scenario-based equilibrium modeling as compared with the status quo. Five bridge closure scenarios were considered in this analysis: the I-275, Gandy, Highway 580, W.C.C Causeway, and the Sunshine Skyway bridges. These five bridges connect Pinellas County to Hillsborough and Manatee counties. This work is aimed at providing agencies a more thorough and rigid approach to decision making during bridge closures with regards to

containing expected demand in such a way to minimize user cost as well as help reduce congestion. The premise for this scenario-based network (network-based) approach is the fact that MR&R activities do not only affect traffic flow on bridges, but surrounding roads may be significantly affected as well (Kleywegt and Sinha, 1994). Furthermore, the worst case conditions of bridge closures typically have substantially more significant impacts on regional networks and travel characteristics hence a nearest alternative route analysis is insufficient to quantify additional user cost. The scenario-based approach considered in this study involved the use of Cube Voyager (TBRPM, 2010) software for traffic assignment. The first step was to evaluate the current detour-based approach while taking into account the five bridge closure scenarios. For this case study, only total closures to bridges were considered, implying that vehicles originally using those bridges are either to be rerouted through an alternative detour route or by equilibrium assignment in the proposed approach. The alternative detour route for each closure was determined based on the shortest distance between origin and destination points close to the bridges. Selections of detour routes are usually based on the nearest and shortest alternative route with similar approaches noted in literature (Mallela and Sadavisam, 2011). In order to determine whether or not the shortest distance had the least travel cost, further analysis was done with travel time as well, to confirm the alternative routes for all scenarios. Secondly, the daily traffic volumes of vehicles originally located on all the bridges were obtained from the base model (the network condition without any bridge closures). These traffic volumes are representative of the number of vehicles that require rerouting. The first two steps provided results for the current method of estimating user costs. The final stage of scenario-modeling analysis involved computing the additional travel time and distance, total vehicle miles traveled (VMT) and vehicle hours traveled (VHT) for the entire regional network model based on uninterrupted network and all five scenarios since this reflects the actual scope of impact of the bridge closures. VMT is computed as the product of the number of vehicles and the length of roadway traveled, while VHT is similarly computed from the traffic volume and time of traveled over a roadway section over some time interval (Chen et al., 2001). The differences between the base model and the five scenarios using the aforesaid metrics served as the basis for quantifying, VOC, delay costs, and finally the total additional user costs

Delay costs were computed as monetary value of travel time (MVTT) for passenger vehicles and trucks. Passenger vehicles were categorized as business and personal vehicles, with their respective MVTT as $36.89/veh-hr and $38.27/veh-hr (Mallela and Sadavisam, 2011), with mean value of $37.58/veh-hr. In addition to this, vehicle depreciation costs for passenger vehicles were found as $1.225/hr (in 2010 dollars) (Mallela and Sadavisam, 2011). Hence the total MVTT for passenger cars was $38.805/veh-hr (2010 dollars). For trucks, MVTTs were $23.06 and $29.65 in 2009 dollars for single-unit and combination-unit trucks respectively, while, vehicle depreciation was $3.09/hr and $9.29/hr respectively (2010 dollars) (Mallela and Sadavisam, 2011). The computed total MVTT for trucks was $32.545/veh-hr. All prices were finally converted to 2015 dollars using inflation factors in FDOT Transportation Cost Reports (2015) to obtain $42.24/veh-hr and $37.1/veh-hr, reflecting MVTTs for passenger cars and trucks respectively. In addition to delay costs, VOCs were computed in 2015 prices for both passenger vehicles and trucks as 48.8 cents/vehicle-mile (AAA, 2015) and $1.67/vehicle-mile for Southeastern region (Torrey et al., 2016) respectively. Accident costs which are usually a component of user cost computations are not included in this study. The current approach or model used for raising, strengthening and replacement (Thompson et al., 1999) calculates the user cost as shown below:

Dr Detour cost per truck, DCr = CVc × Dr + CTc × (4.1) DSr where,

CVc = average vehicle operating cost per mile of detour

CTc = average travel time cost per hour of detour

Dr = detour distance for the roadway in miles

DSr = speed on the detour route, mph

In order to evaluate the current detour-based approach, it was expedient to compute the additional travel distance and times resulting from the new detour route. The additional travel time due to bridge closure can be computed as follows:

푀 푁 ∆푇푖 = ∑푖 ∑푗≠푖(푡푖푗 − 푡푖푗) (4.2) where,

∆푇푖 = change in travel time due to bridge closure 푀 푡푖푗 = travel time from origin i to destination j for bridge closure conditions 푁 푡푖푗 = travel time from origin i to destination j for normal network conditions

The additional travel distance due to bridge closure can be computed as:

푀 푁 ∆퐷푖 = ∑푖 ∑푗≠푖(푑푖푗 − 푑푖푗) (4.3) where,

∆퐷푖 = change in travel distance due to bridge closure 푀 푑푖푗 = travel distance from origin i to destination j for bridge closure conditions 푁 푑푖푗 = travel distance from origin i to destination j for normal network conditions

The formulations and equations for computing total additional user costs are seen in Chapter 3, equations 3.1 – 3.11. The evaluation of user cost based on the current detour approach which considers simply the nearest alternative routes is estimated as follows:

Vehicle Operation Cost

푉푂퐶푝 = ∆퐷 × 푉푝푖 × 퐶푃푀푝 (4.4)

푉푂퐶푡 = ∆퐷 × 푉푡푖 × 퐶푃푀푡 (4.5)

푉푂퐶푝 – vehicle operating cost (personal vehicles)

푉푂퐶푡 – vehicle operating cost (trucks) ∆퐷 – additional detour length (miles)

푉푝푖 – volume of rerouted personal vehicles on detour path i.

푉푡푖 – volume of rerouted trucks on detour path i.

퐷퐶푝 = ∆푇 × 푉푝푖 × 퐶푃퐻푝 (4.6)

퐷퐶푡 = ∆푇 × 푉푝푖 × 퐶푃퐻푝푡 (4.7)

퐷퐶푝 – delay cost (personal vehicles)

퐷퐶푡 – delay cost (trucks) ∆퐷 – additional detour travel time (hours) ∆퐷 – additional detour travel time (hours)

4.2 Study Area

The location for this study is the Tampa Bay area. The Tampa Bay is a vast natural harbor and estuary which is linked to the Gulf of Mexico on the west central coast of Florida. This region comprises of the Hillsboro Bay, McKay Bay, Old Tampa Bay, Middle Tampa Bay, and Lower Tampa Bay. Being home to approximately four million residents, Tampa Bay is a heavily- utilized commercial and recreational waterway. Having four ports, it is regarded as a very important shipping center and being known for recreational purposes, bridges moving across this Bay are of high importance both for individuals and freight as well. Commercial trucks moving across the bridges may also cause damage to the bridges over time warranting closures for maintenance, repair and rehabilitation activities. The particular bridges in this area to be studied were identified as; Sunshine Skyway Bridge, Highway 580 bridge, I-275 bridge, Gandy bridge, and W. Courtney Campbell Causeway. Closures to bridges in this area may require long detours and severe delays, hence increased user cost.

4.3 Transportation Network Configuration

The transportation network model used in this study (see Figure 4.1) is the Tampa Bay Regional Planning Model (TBRPM) and was developed under the Regional Transportation Analysis (RTA) for planning activities in the Tampa Bay Area. The study area corresponds with the jurisdiction of the Florida Department of Transportation (FDOT) District Seven, and includes Hillsborough, Pinellas, Pasco, Hernando, and Citrus Counties in Florida.

4.4 Traffic Flow Estimation

A typical transportation demand model is structured around four sequential steps or the Four-Step Modeling Process. The steps used for travel demand forecasting include: Trip

Generation, Trip Distribution, Mode Choice, and Trip Assignment. These steps are followed when estimating, distributing, and assigning trips to specific transportation facilities, such as highway or transit systems. For this Tampa Bay network configuration, the model was executed using CUBE Voyager, a family of modeling and GIS software tools which is distributed by Citilabs. Trip Generation determines the number of trips ends from origin to destination for each TAZ. Here, zonal travel demand is determined by trip purpose and the demographics of each TAZ are used as input to compute the total daily person and vehicle trips. In Trip Distribution, the gravity model which is based on appeal logic is used. This is the ratio of the level of activity in each destination zone, to the observed spatial separation between production and the attraction TAZs. In Mode Choice, based on trip purposes, there is the allocation of person trips by transportation modes. Person trips by purpose are also converted into highway vehicle trips and available transit service. A nested logit mode choice model uses coefficients that quantify the sensitivity or elasticity of each modal choice variable to service changes. Finally, under Highway Assignment, the daily volumes of vehicle trips are simulated for all trip purposes, for each highway link.

4.5 Data Sources

Data used in this study includes data sources for trip production and attraction used in the Tampa network model and GIS shapefiles. Trip production data used in Cube Voyager for running the Tampa model were obtained from local sources, State of Florida, Census Bureau, and the Bureau of Economic and Business Resources. This data included information on dwelling units, percent of auto ownership, workers, businesses, hotels and motel units. Trip attraction data were sourced from the Florida Agency for Workforce Innovation, Labor Market Statistics, U.S. Department of Commerce, Bureau of Economic Analysis, Department of Highway Safety and Motor Vehicles, Florida Department of Education, and local sources (TBRPM Report, 2010). Bridge locations and county jurisdictions were also obtained as shapefiles from the Florida Geographic Data Library.

Figure 4. 1 Network configuration for Tampa Bay regional planning model

4.6 Scenario-Based Modeling

In this study, five bridge closure scenarios were considered. These five bridges connect Pinellas to Hillsborough and Manatee counties as shown in Figure 4.2. These areas have high population and employment densities hence closures to any of the bridges may have a significant impact on network performance. As mentioned earlier, the five bridges considered in the TBRPM were; Highway 580, Sunshine Skyway, Gandy, Howard Frankland (I-275), and W.

Courtney Campbell Causeway bridge. The first step prior to scenario modeling was to compare traffic counts, which are average annual daily traffic (AADT) and peak season weekday average daily traffic (PSWADT) to daily output volumes from Cube Voyager at the bridge locations. The essence of this comparison was to determine the accuracy of the equilibrium traffic assignment used in Cube Voyager.

Figure 4. 2 Road network showing five bridges connecting Pinellas to Hillsborough and Manatee Counties

Results as seen in Figure 4.3 indicate that the model outputs, though slightly higher are very consistent with traffic counts. The next step was to determine the shortest distance and travel times for the loaded network with origins and destinations located close to the aforementioned bridges considering an uninterrupted network. This served as a base for comparison to the five independent bridge closure scenarios, and evaluating the shortest distances and travel times for the same origins and destinations previously used. The difference between the uninterrupted and bridge closure scenarios resulted in additional travel times and distances. A major advantage of the TBRPM is the organization and detailed categorization of outputs. For each loaded network, there is available data on distance, travel time, and daily volumes for single occupancy vehicles (SOV), high occupancy vehicles (HOV), and trucks. This

information was used to compute VHT and VMT. For bridge closure scenarios, the effects of closures were computed as the additional travel distance and travel time resulting from detours. This was compared to the regional network approach proposed in this study. With the regional network approach, the effects of closures exceed just the resulting detour, but take into account all the links in the regional model resulting from equilibrium assignment. It is also important to note that for this study, transit assignment was excluded from the traffic assignment procedure since those volumes were negligible when compared to the total volume of roadway traffic.

180000 160000 140000 120000 100000 80000 60000

40000 Average Daily Volume Daily Average 20000 0 Bayside Bridge Sunshine Gandy Bridge W Courtney I-275 Bridge Highway 580 Skyway Bridge Campbell Causeway

PSWADT Traffic Volume (CUBE) AADT

Figure 4. 3 Traffic counts and CUBE Voyager volume outputs at bridge locations

4.7 Results and Discussion

Firstly, in an attempt to demonstrate the network-wide effect of bridge closures, the uninterrupted network (Figure 4.4a) was compared with I-275 bridge removal scenario (Figure 4.4b) through the use of graduated isochrones from the designated origin node to the other 3028 destination zones. Each graduated color is representative of a 30-minute loaded network travel time (LNTT). Findings reveal (as seen in Figure 4.4b) that for the bridge closure scenario, more graduated isochrones are observed, especially within Pinellas County, on the Gandy Bridge which serves as the nearest alternative route, and on the Sunshine Skyway Bridge. These results further support the assertion that bridge closures have network level ramifications which should not be overlooked when quantifying user cost.

a.) b.)

Origin Node Origin Node

Closed bridge

LEGEND Origin Node 30-min Isochrones

Figure 4. 4 a.) LNTT at 30 minutes Isochrone Increments. b.) LNTT (I-275 removal) at 30 minutes Isochrone Increments

Figure 4.5 displays the five bridge closure scenarios considered in this study, as well as the shortest alternative routes for each closure scenario. It can be observed that each indicated shortest route represents the nearest alternative path between the origin and destination nodes. For each scenario, the alternative routes were close to the inaccessible bridges, except for the Sunshine Skyway Bridge, which showed a very long detour. Based on the transportation network configuration, this is not unexpected. Using the current (detour-only) approach, results in Table 4.1 reflect the recorded travel times and distances, as well as the volume of vehicles expected to detour from the bridge locations. It can be noted from the results that both travel time and distances increase for all scenarios when rerouting vehicles through an alternative path. Furthermore, and as seen in Table 4.1, closure to Sunshine Skyway bridge leads to the most impact; with travel distance and time increasing by 37.48 miles and 70.49 minutes respectively on the detour route. It is also interesting to observe that though the closure to I-275 Bridge yields a 2.67 miles increase in travel distance, travel time increases by 50.49 minutes; the reason for this is that the expected congestion on the alternative route due to the diverted traffic that originally used the closed bridge. Most commuters between Pinellas and Hillsborough Counties utilize I-275 Bridge, which

has a total daily traffic volume of approximately 156,000 vehicles. Table 4.1 also indicates the computed VMT and VHT for all scenarios. The base model represents an uninterrupted network, and is reflective of existing traffic conditions and not a network in free flow state. This characterizes the daily behavior of commuters within the model jurisdiction.

Table 4. 1 Travel time and distance differences between original and detour paths TIME - DISTANCE- TIME - DISTANCE Total Vehicles/Flow- Closure Scenario Detour Path Detour Path Original Path - Original Detour Path (minutes) (miles) (minutes) Path (miles) (originally on bridge) I-275 bridge closed 74.19 13.21 23.7 10.54 156,581 Gandy Bridge closed 37.99 14.3 14.2 7.98 37,447 Highway 580 Bridge closed 23.89 6.24 15.12 4.27 37,463 W C. C. Causeway Bridge 47.54 18.82 27.83 13.33 58,913 closed Sunshine Skyway Bridge 113.55 58.66 43.06 21.18 65,571 closed Time Distance Closure Scenario Difference Difference VHT VMT (minutes) (miles) I-275 bridge closed 50.49 2.67 131,763.19 418,072.15 Gandy Bridge closed 23.79 6.32 14,847.81 236,666.22 Highway 580 Bridge closed 8.77 1.97 5,475.78 73,801.26 W C. C. Causeway Bridge 19.71 5.49 19,352.84 323,431.09 closed Sunshine Skyway Bridge 70.49 37.48 77,034.91 2,457,598.46 closed

I-275 Bridge closure results in the highest impact in terms of VHT while closing Sunshine Skyway Bridge contributes significant increase VMT, which is, 2,457,598.46 vehicle- miles, resulting from the long alternative detour route. These results can be seen in Figures 4.6a and 4.6b as well. Table 4.2 summarizes the results for the proposed network based approach for evaluating user costs. It should be noted that VHT and VMT are used as inputs for computing delay cost and VOC respectively. It is important to realize that the network-based approach considers the impact of each scenario on the entire regional network model. Hence, the computations for VOC and delay costs are for the entire network, and based on an equilibrium assignment. Results specify that closure of I-275 Bridge contributes to the highest increase in both VOC and delay costs for the regional network. A clear reason for using this approach is seen in the case of Sunshine Skyway Bridge closure. Whereas the results from the current methods reflect very long detours hence significant increase both VMT and VHT, the equilibrium assignment used here indicates a minimal impact of its closure on the entire network.

Findings from the network based approach are quite consistent since it is not expected that the entire volume of vehicles using the bridge will be detoured through the identified best alternative route since each trip is made up of a specific origin and destination.

Figure 4. 5 Highway network indicating bridge closures and alternative routes

Table 4.2 further shows results for various vehicle categorizations. Here, vehicles are grouped into trucks and other vehicles. Results are therefore summarized as truck miles traveled (TMT), truck hours traveled (THT), other vehicle miles traveled (OVMT), and other vehicle hours traveled (OVHT). While trends are similar to that for total VHT and VMT, it is observed

from the network based approach that closures to I-275 and W.C.C. Causeway bridges yield a decrease in TMT. THT does not indicate a decrease due to significant increase in travel time when compared with travel distance. This decrease in TMT can be attributed to the fact that not all trucks on the aforementioned bridges can be rerouted by the model due to the functional classifications of the various roadway segments. Results are further represented in terms of delay cost and VOC, and finally total additional costs are computed as well. In terms of total additional user costs for trucks, it is observed that there is an increase for all bridge closure scenarios besides the closure of Sunshine Skyway Bridge which results in an additional 37.48 miles detour route distance. Here again, results reveal network level impact due to bridge closures. The categorization of results for all network links serves as an additional advantage of the traffic demand modeling used in the regional network model for this study. Figure 4.6c indicates a significant increase in total cost for network based approach for all scenarios except for the Sunshine Skyway bridge closure scenario which had a very long detour route. The network based approach yielded a daily cost of $1,314,218.36 while the current approach resulted in $4,698,526.84. I-275, Gandy, Highway 580 and W.C.C Causeway bridges increased in total cost for the network based approach when compared with the current approach by 42, 18, 61, and 45percent respectively. It can therefore be inferred from the discussed results that network based analysis: (i) captures the effects of bridge closures on all road segments within the regional jurisdiction; (ii) provides a more rigid framework for analysis based on equilibrium assignment therefore ensuring user costs are computed efficiently while avoiding overestimation; (iii) takes into account the fact that road users may have advance knowledge of roadway or traffic conditions prior to making their trips hence significantly influencing route choices; and (iv) provides sufficient information for agencies to implement preventive measures or make additional effective traffic operation decisions to cater for network-level disruptions due to bridge closures.

Table 4. 2 Additional VHT, VMT and user cost computations for bridge closure scenarios Current Approach Network-Based Approach Trucks Only Trucks Only Total Cost Total Cost Closure Scenario THT TMT THT ($) TMT ($) ($) THT TMT THT ($) TMT ($) ($) I-275 bridge closed 12,305.25 39,043.41 456,524.94 65,202.49 521,727.44 14,311.62 * 530,961.01 * 457,832.25 Gandy Bridge Closed 603.47 9,619.04 22,388.85 16,063.80 38,452.65 1,345.80 3,284.16 49,929.36 5,484.55 55,413.91 Highway 580 Bridge closed 359.42 4,844.23 13,334.62 8,089.86 21,424.49 893.39 2,032.19 33,144.68 3,393.76 36,538.44 W C. C. Causeway Bridge closed 1,492.38 24,941.07 55,367.13 41,651.59 97,018.72 2,405.61 * 89,247.97 * 70,934.76 Sunshine Skyway Bridge closed 7,530.68 240,246.80 279,388.29 401,212.16 680,600.45 3,175.10 31,987.83 117,796.14 53,419.68 171,215.82 Other Vehicles Other Vehicles Total Cost Total Cost Closure Scenario OVHT OVMT OVHT ($) OVMT ($) ($) OVHT OVMT OVHT ($) OVMT ($) ($) I-275 bridge closed 119,457.93 379,028.74 5,045,903.09 184,966.02 5,230,869.11 216,477.64 747,726.73 9,144,015.69 364,890.64 9,508,906.34 Gandy Bridge Closed 14,244.34 227,047.18 601,680.78 110,799.02 712,479.80 18,998.17 119,378.60 802,482.50 58,256.76 860,739.26 Highway 580 Bridge closed 5,116.35 68,957.03 216,114.82 33,651.03 249,765.85 14,568.68 90,827.76 615,380.97 44,323.95 659,704.92 W C. C. Causeway Bridge closed 17,860.47 298,490.02 754,426.19 145,663.13 900,089.32 39,125.20 170,915.94 1,652,648.50 83,406.98 1,736,055.48 Sunshine Skyway Bridge closed 69,504.23 2,217,351.66 2,935,858.78 1,082,067.61 4,017,926.39 26,357.23 60,805.70 1,113,329.37 29,673.18 1,143,002.55 All Vehicles All Vehicles Total Cost Total Cost Closure Scenario VHT VMT VHT ($) VMT ($) ($) VHT VMT VHT ($) VMT ($) ($) I-275 bridge closed 131,763.19 418,072.15 5,502,428.03 250,168.52 5,752,596.55 230,789.26 703,937.05 9,674,976.70 291,761.88 9,966,738.59 Gandy Bridge Closed 14,847.81 236,666.22 624,069.63 126,862.82 750,932.45 20,343.97 122,662.76 852,411.86 63,741.30 916,153.17 Highway 580 Bridge closed 5,475.78 73,801.26 229,449.45 41,740.89 271,190.34 15,462.07 92,859.95 648,525.65 47,717.70 696,243.36 W C. C. Causeway Bridge closed 19,352.84 323,431.09 809,793.32 187,314.72 997,108.04 41,530.81 159,949.95 1,741,896.47 65,093.77 1,806,990.24 Sunshine Skyway Bridge closed 77,034.91 2,457,598.46 3,215,247.07 1,483,279.76 4,698,526.84 29,532.33 92,793.50 1,231,125.50 83,092.86 1,314,218.36 Note: All costs are computed on a daily basis. * Reduction in TMT and VOC

a.)

250,000

200,000

150,000

VHT Current Approach 100,000 Network Based 50,000

0 I-275 bridge Gandy Bridge Highway 580 W C. C. Sunshine closed Closed Bridge closed Causeway Skyway Bridge Bridge closed closed Scenarios

b.)

3,000,000

2,500,000

2,000,000

1,500,000 VMT Current Approach 1,000,000 Network Based

500,000

0 I-275 bridge Gandy Bridge Highway 580 W C. C. Sunshine closed Closed Bridge closed Causeway Skyway Bridge Bridge closed closed Scenarios c.) 12,000,000

10,000,000

8,000,000

6,000,000 Current Approach 4,000,000 Network Based

2,000,000

Total Additional ($) Cost/day UserAdditional Total I-275 bridge Gandy Bridge Highway 580 W C. C. Sunshine closed Closed Bridge closed Causeway Skyway Bridge Bridge closed closed Scenarios Figure 4. 6 Comparison of VHT, VMT and daily total additional user cost results for current method and proposed network based approach

4.6 Chapter Summary

In this chapter, a scenario-based approach on regional network models for evaluating user cost resulting from bridge closures is adopted. While current methods consider rerouting through the nearest alternative route, this approach commonly used for bridge detours is not holistic. This current method assumes that all or certain percentages (depending on the reason for detour) of average daily traffic (ADT) on the closed (or restricted) bridge will be using the alternative route, however; this is not the case in the practical sense especially when considering complete bridge closures. There is currently real time information for most States highway systems, including information on work zones and closure; hence commuters are furnished with enough information to efficiently plan their trips. This implies that even though the origins and destinations may be the same, travel paths may completely vary for each person trip depending on the location of their origins. Therefore, incorporating regional planning models which utilize an equilibrium assignment is encouraged. This method eliminates the error of assuming that all the vehicles using closed bridges will be detoured on the alternative shortest path. Therefore, alternative routes or detours which are excessively long may only be used by fewer commuters hence preventing overestimation of user cost. In this study, five bridge closure scenarios were considered. These five bridges connect Pinellas County to Hillsborough and Manatee counties. Results in this study indicated that since the proposed network based approach considered origin-destinations for all trips, errors in overestimation due to long detours such as in the case of Sunshine Skyway bridge (37.48 miles additional distance on alternative route) closure can be avoided. Furthermore, the network based approach generally indicated higher VOC and delay costs than that of the current approach for the other four scenarios, reflecting the network level impact of bridge closures captured by the proposed method. This modeling approach also allows for modeling various closure scenarios and effective project planning. While this study did not specifically consider detours and additional costs due to inadequate horizontal and vertical clearances, poor alignment, and workzone, which are mostly considered in bridge user cost computations, this approach can be extended to those areas as well.

CHAPTER 5

ACCESSIBILITY-BASED RESILIENCE MEASURE

5.1 Senior Community Resilience using Accessibility as Measure to Healthcare

The primary focus of this chapter is to assess senior community resilience by considering the physical transportation infrastructure within the communities. This study investigates three issues regarding community resilience, with a focus on bridge infrastructure: (1) the identification of coastal bridges susceptible to hurricane damage; (2) the expected damage condition/states evaluation of the exposed bridges focusing on critical bridges significant to aging mobility; and (3) the development of performance measures for the assessment of the impact of the closures of selected bridges on senior mobility. Using historical condition data from the National Bridge Inventory (NBI), these effects are evaluated at the network level for the case study region. The above is further explained with a developed resilience index.

5.2 Methodology

In order to achieve the goals for this case study, the analysis followed these sequential steps: (i) computing exposure probabilities for categorical hurricane events at bridge locations; (ii) developing and applying damage state functions in allocating damage states to bridges using both historical and NBI data fields; (iii) identifying bridges at risk to hurricane-induced damage; (iv) identifying the bridges affecting aging-dense areas; and (v) estimating the effects of bridge closures to aging mobility and resilience through accessibility to hospitals based on congested and free flow travel times obtained from traffic assignment modeling. The framework for bridge selection illustrated in Figure 5.1. A total of 82 damaged bridges from Florida, Louisiana, Mississippi and Alabama were used in mapping out the damage state of bridges in the case study region of this research. There were 25% of the bridges categorized as movable bridges, with the remaining being fixed bridges of different types. Based on an extensive review of damage history, the movable bridges are expected to suffer different levels of impact ranging from damage of elements such as the

operator facility, failure of gates, signals and motors due to wind, and storm impacts to mechanical and electrical faults. On the other hand, fixed bridges are anticipated to fail through unseating of decks, scouring, failure of slope protection and abutments as well as pier and column failure due to barge collision.

Table 5. 1 Qualitative damage state descriptions defined by amending HAZUS for typical hurricane-induced bridge damage Damage state Hazard Type Description Debris (tree logs, boats etc.) insignificant scour, minor damage to channel, and damage to non-structural elements such as street lights, luminaires, Hurricane lamps, mounted lights, small signs, and railing. Poses no serious structural (Bridges) problem. Structure may need minor repairs. Slight Minor damages such as loss of sign panels, twisting of luminaires, etc. Poses no serious structural problem. Structure may need minor repairs Hurricane Minor damages such as loss of sign panels, twisting of luminaires, etc. (Sign Structures) Poses no serious structural problem. Structure may need minor repairs Washouts at embankments/approach slabs and damage to slope protection system. Overtopping due to flood (deck/slab or culvert) and significant scour. Moderate damages including undermining, to abutments, columns, Hurricane piles, caps, footings, channel, and bulkhead. Moderate damages to fenders, (Bridges) navigational lights, warning gates, traffic signals, operator facilities, Moderate electrical conduit, cables, PLCs, transformers, and equipment. Poses serious structural/functional problems. Structure is repairable. Loss of horizontal members, and minor cracks on foundation. Moderate Hurricane damage to horizontal, vertical members, or foundation. Poses serious (Sign Structures) structural/functional problems. Structure is repairable. Extensive damage to culvert, deck, superstructure, substructure, and Hurricane pertinent bridge elements. Structure is repairable. Poses serious (Bridges) structural/functional problems. May require full replacement of structural Extensive component(s). Extensive damage to panels, chords, trusses, and foundation. Poses serious Hurricane structural/functional problems. Structure is repairable. May require full (Sign Structures) replacement of structural component(s). Hurricane Severe damage to all or critical structural and non-structural components. (Bridges) Structure needs to be completely replaced. Complete Hurricane Severe damage to all or critical structural components. Structure needs to (Sign Structures) be completely replaced.

A number of NBI fields were selected to assess the individual bridge operational characteristics and ratings. Four key variables were found to be statistically-correlated to the damage states of bridges based on the movable bridge data. These fields with correlation coefficient of 30% and higher were the superstructure condition rating, substructure condition

rating, posting evaluation, and scour critical condition. For fixed bridges, the key fields which were observed to have high correlation with levels of damage were the deck condition rating, superstructure condition rating, substructure condition rating, inventory rating, deck geometry evaluation, and scour critical condition. To assign the level of damage of bridges some assumptions were made, and steps followed, summarized as follows: 1. Bridge damage states were categorized based on the type of bridge (either fixed or movable). 2. Bridges with unknown foundations are expected to suffer the worst damage (either complete or extensive). 3. Non-waterway bridges as well as bridges which are not scour critical are ranked based on the inventory and operational characteristics (deck, superstructure and substructure ratings). 4. Bridges without deck, superstructure and substructure such as culverts and channels are assigned damage states based on other significant NBI fields. 5. Bridges could be assigned two damage states based on certain special characteristics.

Table 5.2 represents the initial list of NBI fields used in the damage state assessment of bridges.

Table 5. 2 NBI fields considered for bridge damage state assessment NBI Field Operational Characteristics Owner State, County, Local Functional Class Interstate / Non-Interstate Age Old (>=50yrs) / New(<50yrs) Year Reconstructed Recent / Previous Waterway Adequacy Adequate / Inadequate High (>3) / Low (<=3)/ Unknown Scour Critical Bridges Foundation Type of Service Highway / Railroad, Interchange Kind of Material Wood /Timber, Steel, Concrete Type of Design Fixed / Movable Condition ratings (Deck, Superstructure, High (>4) / Low (<=4) Substructure) Channel and Channel Protection Rating High (>7) / Low (<=7) Culverts Rating High (>8)/ Low (<=8) Minimum Vertical Underclearance Adequate / Inadequate Sufficiency Rating High (>50%)/ Low (<=50%) Status Functionally Adequate / Inadequate

5.2.2 Discussion for Damage State Analysis

From the analysis, it is observed that a total number of 1162 bridges out of the 1393 fixed bridges are expected to be subjected to slight or moderate damage conditions. The two damage states which amount to 83% of the entire inventory were found to be in consonance with the evaluation made by previous studies (Padgett et al., 2008; Sheppard and Miller, 2003) where many bridges were estimated as slight or moderate damage levels. Further results indicated that the remaining bridges have equal likelihood of experiencing extensive or moderate damages with each damage state amounting to 8% of the entire bridge count. It is noteworthy to state that about 87 bridges were classified to experience either complete or extensive damage state because of their peculiar characteristics. A total of 313 culverts were identified from the inventory with about 88% of them suffering slight damage while the rest experience other damage states as follows: 11% subjected to moderate damage state; 14% being extensive, and 12% complete damage levels, respectively. For the 21 recorded movable bridges, about 19% of them were expected to be impacted slightly, 32% of the movable bridges suffering extensive to complete damage levels, with 26% being extensive and 23% with complete damage.

5.2.3 Identifying Bridges at Risk to Hurricane-induced Damage

Bridges at risk to hurricane-induced damages were identified by combining bridge damage states with exposure probabilities. Storm surge heights (SSH) based on data from a previous Florida study (Sheppard and Miller, 2003) and the Sea, Lake, and Overland Surge from Hurricanes (SLOSH) model (Jelesnianski et al., 1992) were also used to identify local bridges at risk to damage. The SLOSH model is a computerized model developed by the National Weather Service (NWS) to estimate storm surge heights and winds resulting from historical, hypothetical, or predicted hurricanes. Local bridges at locations where SSH were greater than or equal to 12 feet were identified as being at risk to damage. The threshold of 12 feet was chosen since storm surge heights above that level are known to cause inundations, while SLOSH model outputs indicated that SSH for the case study area were mostly in the selected range. Aging-dense zones were selected as census block groups with over 35% of the total population being 65 years old and

above. All identified bridges within a quarter-mile radius to these locations were then selected as those having a direct influence on mobility to and from the aging-dense zones. The results are shown in Figure 5.1.

Figure 5. 1 SSH from SLOSH model and selected local bridges based on SSH threshold for the Tampa Bay area

5.2.4 Computing Resilience

Accessibility is used as a mobility measure in estimating the effects of bridge damages on commute of aged population to hospitals. This measure is expressed as the least cost (travel time) between origins (aging-dense zones) and destinations (hospital facilities) prior to and after the hurricane events. The approach is executed through the use of Environmental Systems Research Institute (ESRI)’s ArcGIS software, applying the closest facility extension. A similar concept was noted as being adopted in literature for determining geographic access to cancer care (Onega et al., 2008). In our study, travel time data was based on the Tampa Bay Regional Planning Model (TBRPM) provided by the Florida Department of Transportation (FDOT)’s District 7 Metropolitan Planning Organization (MPO). The model was exported into ArcGIS and used to obtain origin-destination matrices for both free flow travel time (FFTT) and congested travel times (CTT) with the aid of the network analyst extension. Resilience was computed by

combining measures of functionality and recovery times for bridge closure events as illustrated in Figure 5.2.

Figure 5. 2 Resilience based on bridge damage states used in this study

Functionality Measure:

푇 푁 퐴푐푐푖 (푡) 훾푒 (푡) = 푇 (5.1) 퐴푐푐푖 (푡_푑푖푠) where:

푇 th 퐴푐푐푖 (푡) – minimum travel time for i O-D prior to hazard 푇 th 퐴푐푐푖 (푡_푑푖푠) – minimum travel time for i O-D after hazard 푁 – transportation network Resilience

1 푇̅ 푅 = 1 − ∫ (1 − 훾푁(푡))푑푡 (5.2) 푇̅ 0 푒 where: 푇̅ – mean time to recovery in days

5.3 Case Study for Accessibility Analysis

The general area for Tampa Bay, the case study, is an area prone to hurricane strikes and storm surges. The Tampa Bay is a vast natural harbor and estuary which is linked to the Gulf of Mexico on the west central coast of Florida. The specific county for this case study is Pinellas County.

5.3.1 Data Set

Information for hospital facilities, census block groups, and Florida coastal hazards demarcations were obtained from Florida Geographic Data Library (FGDL). The NBI bridges shapefile was obtained from ESRI, while roadway shapefile and Tampa Bay Regional Planning Model (TBRPM), were retrieved from the Florida Standard Urban Transportation Model Structure (FSUTMS). The hospital shapefile contained attributes for hospital facility locations and capacities (number of beds) for the case study area. The census block groups also contained various demographic details for each block group division within the jurisdiction. The coastal hazards dataset contained cartographic representation of the coastal counties in the State of Florida that are vulnerable to coastal erosion and inundation from sea level rise or storm surge. The database file and its associated layers are utilized by coastal managers to comprehensively assess hurricane induced storm surge hazards along the coast of Florida.

Figure 5. 3 Maps showing Pinellas County with the locations of hospitals and expected damaged bridges near to aging-dense zones.

5.4 Results and Discussion

The accessibility analysis for this study included the selection of 140 census block groups that were identified as aging-dense zones, with these zones serving as incident areas. It has been previously indicated in this case study that 66 bridges critical to the mobility of the abovementioned zones are at risk of closure during a Category 3 Hurricane. Also, 15 designated hospital locations were identified, serving as facilities of interests for accessibility analysis. The scenarios adopted in this study assumes that the identified-at-risk bridges are damaged during the storm, hence, remains closed after the hurricane event for repair activities which are envisaged to take lengthy periods. Furthermore, as normal activities resume, accessibility of seniors to primary healthcare, expected to be affected, is evaluated. The network analysis methodology used in this study is quite rigorous since resilience is measured based on the senior accessibility to healthcare under normal road network functionality, compared with senior healthcare accessibility during closures of the identified bridges. In the network analysis, the TBRPM is utilized to initially capture FFTT and CTT for the Pinellas County for the base model (without bridge closures). The network is then modified to capture the damaged bridges within the TBRPM environment and re-analyzed until a new equilibrium is reached hence adequately representing FFTT and CTT during bridge closures. The closest facility analysis tool in network analyst (an extension in ArcGIS) is then used to obtain the minimum times for each aging-dense area to access healthcare prior to and after the hurricane event. Figure 5.4 depicts the effects of bridge closures on the travel times between the aging population zones and the hospitals. There was an observed increase from about 1200 minutes to 2100 minutes and from about 900 to 1100 minutes, for the CTT and FFTT, respectively. This indicates travel time increases of about 75% and 15% for CTT and FFTT, respectively. Furthermore, an additional total travel distance of 52.85 miles was observed for CTT and FFTT. The mean travel times after bridge closures increased from 8.43 to 15.1 minutes and from 6.6 to 7.76 minutes for CTT and FFTT, respectively. Figure 5.4a represents changes in minimum travel time after bridge closures for each aging-dense zone. Figures 5.4b and 5.4c are derived from equation 5.1, and account for functionality computed as the ratios of minimum travel times for each trip, prior to and after bridge closures. It is observed that while many age-dense zones did not record changes in FFTT as observed in Figure 5.4b, Figure 5.4c indicates significant changes for CTT resulting from the effects of congestion on travel. This is because post-hazard

recovery involves an increase in roadway demand leading to significant impact of bridge closures on network travel time. Such conditions warrant the prioritization and rapidity of bridge restoration activities in order to ensure that the emergent health needs of the aging population are met. Results shown in Figure 5.5 indicate minimum travel times and routes to various hospitals based on FFTT and CTT for both the base model (Figures 5.5a and 5.5b) and interrupted network (Figures 5.5c and 5.5d). The color variations seen indicate the minimum travel times from the centroid locations to the nearest hospital. While FFTT accessibility maps (Figures 5.5a and 5.5c) show some similarities, bridge closures are observed to significantly affect accessibility of the aging population to hospitals. This difference is further evident when comparing CTT accessibility maps (Figures 5.5b and 5.5d). These results support findings in Figure 5.4. Additionally, three aging-dense zones were observed as being without access to hospitals after bridge closures. These are seen on the South boundary of Pinellas County and are highlighted green in Figures 5.5c and 5.5d. Resilience indexes for the bridges were based on the functionalities computed from FFTT and CTT using equation 3.14, as well as the expected bridge recovery times after bridge damages. The damage states for the 66 identified bridges were considered as moderate, extensive, and complete levels; slightly damaged bridges were not taken into account in this study as those bridges are normally not expected to undergo total closures. In computing resilience index, it is expected that in most cases, moderately-damaged bridges will be restored before those bridges with extensive and finally, the restoration of completely-damaged bridges. Computations included the re-evaluation of the traffic assignment model for network functionality improvement after bridge restoration for each damage state. The resulting resilience index scaled from 0 to 1 is computed based on equation 5.2, with 1 representing a perfectly functional network and zero otherwise. It is expected that six days after all bridges are closed, moderately damaged bridges will be restored, and this results in functionality improvement from 0.87 to 0.94 considering FFTT, and from 0.57 to 0.83 considering the CTT. Extensively-damage bridges are expected to open 30 days after the hurricane event, resulting in functionality increase from 0.94 to 0.96, and 0.83 to 0.85, respectively, considering FFTT and CTT. All bridges are expected to be restored 29 days after extensively damaged bridges are opened. The resilience index for this study was computed as 0.94 and 0.81 for FFTT and CTT respectively, implying significant loss in senior mobility hence the need for mitigation measures.

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a.)

Travel Time Travel Time (minutes) 12

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11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96

116 136 101 106 111 121 126 131 Aging-Dense Zones CTT difference after bridge closure FFTT difference after bridge closure b.) 1

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101 106 111 116 121 126 131 136 Aging-Dense Zones c.) 1.2 1 0.8 0.6 0.4 0.2

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136 101 106 111 116 121 126 131 Aging-Dense Zones Figure 5. 4 Results indicating differences in FFTT and CTT prior to and after bridge closures, as well as FFTT and CTT based functionality measures.

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a.) b.)

c.) d.) .)

Figure 5. 5 Minimum FFTT and CTT to hospitals for each aging-dense location for base network for a and b, and bridge closure-network for c and d

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5.5 Chapter Summary

This chapter has presented an accessibility-based approach to healthcare for evaluating senior community resilience with a focus on bridge damages. The research approach adopted included the identification of bridges which are at high risk to damage as a result of Category 3 Hurricane events by computing wind exposure probabilities at each bridge location, assigning damage states to bridges by using NBI attribute fields and historic data, and finally identifying local bridges subjected to high storm surge heights during hurricanes. The adopted approach was based on previous studies which identified bridge damages to areas of high-wind exposure probabilities. The essence of this study was to provide an approach for identifying at-risk bridges by utilizing available data sources on hurricane winds, storm surge heights, operational characteristics (from NBI) of previously damaged bridges due to hurricanes, and NBI characteristics of bridges presently located in coastal areas exposed to categorical hurricanes. Furthermore, the importance of the identified bridges to aging-dense zones was evaluated as well as the effects of bridge closures to aging population accessibility to hospitals. Results indicated that 66 bridges were of specific interest (using proximity analysis) to areas with a high percentage of aging population. Movable bridges were identified as being very vulnerable during hurricanes. Accessibility analysis was modeled based on closest facility analysis by using the identified 140 aging-dense zones and 15 hospitals as origins (incident locations) and destinations (facilities), respectively. Significant increases in minimum travel time to hospitals were observed for both free flow travel time (FFTT) and congested travel times (CTT). This was more evident for CTT due to congested roadway conditions, yielding a resilience index of 0.81 compared to 0.94 from FFTT. Aging population accessibility to hospitals is of utmost importance due to human frailties that come with age, and because some age dense zones were more affected than others in this study. The need for increased financial investment in maintaining and reinforcing both state and locally maintained bridges are requisite for efficient senior mobility. With the population of those 65 years and above on the increase, this need is timely. Increase in roadway travel times, reduced functionalities, and decreased resilience communicated through this study highlights that senior members are affected by bridge closures.

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CHAPTER 6

REGIONAL NETWORK RESILIENCE

6.1 Regional Network Resilience for Tampa Bay Area

Florida has recorded more major hurricanes (37) than any other United States’ state between 1851 and 2010 (Center, 2007). An extensive study by Sobanjo and Thompson (2013) evaluated the risks Florida bridges are exposed to, attributable to both natural and anthropogenic hazards. Hazards such as, hurricanes, tornadoes, flooding and scour, and wildfires, were investigated. Hurricanes were identified as a main cause of bridge damage among natural hazards, with coastal bridges being of primary concern. Reports on hurricane Katrina revealed that the mixture of winds, rains and storm surges resulted in severe damages to coastal bridges. Substantial amounts of these damages were reported as the displacement of bridge decks and the collapse of facilities for movable bridges (Padgett et al., 2008). Vulnerability of coastal bridges to hurricanes (Padgett et al., 2012) and their corresponding consequences (Stearns and Padgett, 2011) in the form of agency costs have further been evaluated (Maxey, 2006). Unexpected closures to major bridges have been reported to cause widespread traffic disruptions. Thus, it is necessary to study the impacts of such closures on large transportation networks. On September 16, 2004, storm surges and waves resulting from hurricane Ivan had massive consequences on I-10 bridges over Escambia Bay causing the displacement of several bridge spans as well as complete pier removal (Hitchcock et al., 2008). A period of 66 days after the hurricane event was needed to reconstruct and reopen the Escambia Bay Bridge to traffic (Hitchcock et al., 2008). The loss of this bridge resulted in an approximately 209 km (130 miles) traffic detour (Talbot, 2005) implying increased transportation user costs. The importance of bridges as lifelines cannot be overstated. A section of I-85 Bridge in Atlanta collapsed after a massive fire (12.19 meters wall of fire) on March 20, 2017. Three sections of I-85 northbound and southbound required replacement and it took over six weeks to reopen the South bound of the bridge to traffic (Burns and Brett, 2017). The estimated daily vehicular traffic on this Atlanta roadway section was 220,000 vehicles per day. Due to this high traffic volume, the bridge

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closure resulted in traffic on I-285 bypass increasing by 50% the following day due to traffic gridlock, with traffic conditions in the Atlanta area substantially affected (Noll, 2017). A methodological framework for pre-disaster resilience evaluation of realistic regional networks based on hypothetical post-event damage state conditions is essential to mitigate the effects of unexpected closures. The National Infrastructure Advisory Council (NIAC) on “Transportation Sector Resilience”, indicated that deficits in the comprehension of network-level consequences resulting from major disruptive events is one of the main grey areas in the transportation network resilience discussion (Baylis et al., 2015). This study seeks to contribute to the ongoing debate on transportation network resilience by presenting preliminary efforts to quantify resilience at the network or regional level. The primary focus of this chapter is to determine transportation network resilience for regional models based on bridge closures using the developed methodology in Chapter 3. Essentially, this work takes into account the network level damage to bridges and the resulting impacts on regional road network jurisdictions. While current methods focus on the best alternative route during bridge closures, it is important to comprehend that the resulting impacts of such disruptions are extensive and have widespread effects. In this study, even though bridge closure scenarios and durations of closures are considered, specific interest is in the resilience of the transportation network system. Assessing transportation networks through scenario-based modeling is the suggested approach. Such techniques can help researchers and agencies to answer questions regarding the consequences of road closures resulting from disruptive events. Furthermore, this research identifies and quantifies practical indicators for evaluating transportation network resilience. A metric for identifying high impact zones for regional networks during disruptions is also developed in this work. Finally, an aggregated network resilience index measure is developed as a single value indicator of the level of resilience in an existing transportation network.

6.2 Summary of Methodology

With the aim of developing an aggregated resilience index measure, the following methodological steps were undertaken: (i) establishing the transportation network and adopting the concept of an equilibrium-based traffic assignment; (ii) identifying practical transportation network performance metrics and indicators; (iii) identifying high impact zone location metrics;

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(iv) developing a computational approach for measuring functionality; (v) adopting the proposed resilience triangle method (Bruneau et al., 2003) for computing a single resilience index; (vi) computing aggregated resilience index from individual indexes. The highlighted steps were integrated to obtain an aggregated resilience index: traffic flow results from the equilibrium based traffic assignment were utilized for computing measures of performance. A high impact zone metric developed in this study was utilized to preliminarily identify network segments with high speed differences resulting from closures. The performance measures from traffic assignment outputs were then used for computing the network functionality: the aggregated resilience index was estimated as the mean resilience (function of network functionality and recovery time) index based on identified metrics. These steps are succinctly discussed in the following sub-sections. Closure durations for previously recorded bridge closure events were obtained (Table 6.1) and used to establish the abovementioned recovery times. The recovery times reported are samples from internet queries and a limitation in this study as agencies presently do not have databases for hazard-induced bridge closure durations. These values were used in assigning mean closure times (time to recovery) to the specified bridges in this study. The estimated mean recovery times for interstate and non-interstate bridges were estimated as 61.7 and 59.7 days respectively. In the case of moderate, extensive and complete damages, the recovery times were 3, 48.5 and 133 days respectively for interstate bridges, and 1, 30, and 173 days for non- interstate bridges.

Table 6. 1 Bridge closure durations after hurricane events (sample data) Total Partial Date Date Closure Hazard Event Closed Bridge Location Restoration Closed Opened Duration (days) (days) Hurricane Interstate 10 twin spans 29-Aug-05 5-Jan-06 Louisiana 46 83 Katrina over Lake Pontchartrain Hurricane Interstate 10 West 29-Aug-05 2-Oct-05 Mississippi 20 31 Katrina Pascagoula Bridges Interstate 10 (Mobile Hurricane Bayway) and U.S. 90 & 29-Aug-05 2-Sep-05 Alabama - 3 Katrina 98 (Battleship Causeway) Interstate 10 (Mobile Hurricane Bayway) and U.S. 90 & 30-Aug-05 26-Feb-06 Alabama - 180 Katrina 98 (Battleship Causeway) Interstate 10 Bridge over Hurricane Ivan 16-Sep-04 20-Nov-04 Florida 17 66 Escambia Bay Hurricane North US-74 Interstate 95 10-Oct-16 17-Oct-16 - 7 Matthew Carolina

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Table 6. 1 - continued Total Partial Date Date Closure Hazard Event Closed Bridge Location Restoration Closed Opened Duration (days) (days) Hurricane Ivan Bob Sikes Bridge 16-Sep-04 22-Sep-04 Florida - 6 Hurricane Ivan Navarre Beach Causeway 16-Sep-04 3-Nov-04 Florida - 48 U.S. 98 Pensacola Bay Hurricane Ivan 16-Sep-04 21-Sep-04 Florida - 5 Bridge Hurricane Ivan Garcon Point Bridge 16-Sep-04 22-Sep-04 Florida - 6 U.S. 98 Lillian Highway Hurricane Ivan 16-Sep-04 19-Feb-05 Florida 17 137 Bridge U.S. 90 Escambia River Hurricane Ivan 16-Sep-04 22-Sep-04 Florida 1 6 causeway Florida 292 Perdido Key Hurricane Ivan 16-Sep-04 Jan. 2005 Florida - 120 Bridge Florida 196 (Bayfront Hurricane Ivan 16-Sep-04 Dec. 2004 Florida - 100 Parkway) Florida 291 (Davis Hurricane Ivan 16-Sep-04 17-Sep-04 Florida - 1 Highway) U.S. 98 in Santa Rosa Hurricane Ivan 16-Sep-04 17-Sep-04 Florida - 1 County Hurricane Ivan Florida 87 16-Sep-04 17-Sep-04 Florida - 1 Hurricane Chef Menteur Pass 29-Aug-05 30-Nov-05 Louisiana - 100 Katrina Bridge U.S. 90 & U.S. 98 Truck Hurricane Cochrane-Africatown 29-Aug-05 31-Aug-05 Alabama - 2 Katrina Bridge Hurricane Bayou Liberty bridge, La. 29-Aug-05 Feb. 2006 Louisiana - 180 Katrina 433 Hurricane Bayou Barataria, La. 302 29-Aug-05 5-Sep-05 Louisiana - 7 Katrina Hurricane Rigolets, U.S. 90 29-Aug-05 28-Sep-05 Louisiana - 30 Katrina Hurricane East Pearl River, U.S. 90 29-Aug-05 28-Sep-05 Louisiana - 30 Katrina Hurricane Handerson Point US-90 29-Aug-05 24-Jan-07 Mississippi - 172 Katrina Hurricane Popps Ferry 29-Aug-05 23-Dec-05 Mississippi - 176 Katrina

With the aim of developing a single indicator value for resilience, the equal weighting approach was used. This method has been used for computing composite indexes (Estoque and Murayama, 2014) and organizational resilience (Briguglio et al., 2009). Ip and Wang (2009) represented nodes and links in a transportation network as towns and roadways respectively by representing the network as an undirected graph. In this research, the weighted average and weighted sum approaches for estimating city node resilience and network resilience were used. The choice of an undirected graph suffices for road transportation networks where bidirectional flows are typical. Furthermore, the links in the undirected network have different lengths and capacities hence are weighted. Directed networks only allow flows in one direction hence are

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more suited for studies on railway systems. When estimating city node resilience, Ip and Wang (2009) considered the number of reliable independent paths connecting all other town nodes within the network. The network resilience was then determined by combining all nodes. The equal weighting method is used in this study since it is straightforward and succinct. The formulation is as follows:

∑푛 푅 푊 = 푘=1 푘 (6.1) 푛 where,

푅푘 - resilience index measure for each computed indicator, k. n - total number of index indicators

6.3 Application Example

The area for this study is the known as the Tampa Bay Region; an area prone to hurricane strikes and storm surges as seen in Figure 6.1. Being home to approximately four (4) million residents, Tampa Bay is a heavily utilized commercial and recreational waterway. Bridges moving across this bay are of high importance for mobility, and bridge damages are projected to have a debilitating impact on the transportation network leading to potential accessibility issues (Twumasi-Boakye et al., 2018). Details of the transportation network configuration and regional model are subsequently discussed.

Figure 6. 1 Total number of major hurricane strikes (1900 – 2010) by Florida county developed using ArcGIS software (data from NOAA).

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6.3.1 Network Configuration

The network model adopted for this study was the Tampa Bay Regional Planning Model (TBRPM) version 7.2; a regional model developed under the Regional Transportation Analysis (RTA) for planning activities (Technical Report, TBRPM v7, 2010). The study area corresponds with the jurisdiction of the FDOT, District Seven and includes Hillsborough, Pinellas, Pasco, Hernando, Citrus, and Manatee Counties of Florida. There exists heavy trip interchange between southern Hillsborough and Pinellas Counties making the bridges connecting these areas of high importance. Figure 3 shows the network configuration. This network is composed of 31797 links and 3029 zones, with twenty-nine (29) of these zones representing external stations. Traffic assignment was executed using Cube-Voyager 6.1.1 simulation software by Citilabs (Cube Voyager Modeling Training, 2013). The population of the RTA study area was over 2.8 million in 2006, reflecting an annual growth rate of approximately 2% since 2000. The travel forecasting process used in the model is the already mentioned four step travel demand forecasting process. The model was obtained from the Florida Standard Urban Transportation Model Structure (FSUTMS). Bridge locations and county jurisdictions were also obtained as shapefiles from the Florida Geographic Data Library (FGDL).

6.3.2 Network Scenario Modeling

In initial studies, five (5) bridge closure scenarios were considered in order to determine and compare resilience indicators. The five bridges considered are labeled in Figure 6.2 and identified as: Sunshine Skyway bridge (SSB), Bayside bridge (BAY-B), I-275 bridge (I-275B), Gandy bridge (GB), and W. Courtney Campbell Causeway (WCB). Selection of these bridges was based on their critical location to mobility and commercial activity within the Tampa Bay area. Furthermore, these bridges are cross-waterbody structures hence are at higher risk to hazard-induced (hurricane) damages. Figure 4 indicates the high traffic volumes at these bridge locations. This implies that closure to any of them will have an observable effect on the transportation network. This is true because they serve as links between Pinellas and Hillsborough counties as well as Pinellas and Manatee counties. Initial analysis served as the basis for further studies involving Pinellas, Hillsborough and Manatee counties which included the closure to I-275 westbound (WB) bridge and closure to both I-275 and Gandy bridges.

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Ten scenarios and recovery sequences were considered in the final analysis, and results are summarized in Table 6.2. For each damage scenario, the damaged bridge was closed in the network model in Cube Voyager and the regional model was rerun until a new equilibrium was reached. This process was repeated for all closure scenarios to obtain new link travel times, VHT and VDT. Unlike small networks, computational costs involved in modeling regional networks are high and data post processing is involving. For high impact zone analysis, model outputs for damage scenarios were matched with uninterrupted network data, prior to computing speed reduction for each link. This data was then imported into ArcMap version 10.2; a GIS based application for visualization.

Figure 6. 2 Map showing the regional transportation network for the case study area

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6.4 Results and Discussion

The initial analyses were done primarily to determine practical performance indicators. While travel times were considered an obvious measure of travel, VHT and VDT were determined as efficient for the large network since both metrics captured traffic volumes on all links. In addition, the mean link speed reduction metric was applied in this step to help identify the high impact area zones where further analysis may be warranted. Enhanced visualization using GIS analysis tools was adopted to determine model variations from base (undisrupted) model, and identify links of speed reduction. The visualization approach adopted in this research is essential since it serves as an efficient way to preliminarily evaluate and communicate the effects of the bridge closures on the regional transportation network prior to other numerical computations. Figures 6.3a-c reflect the results of a network analysis involving movement between Pinellas and Hillsborough counties. Results are demonstrated as shortest path routing between an origin and destination zones from Pinellas to Hillsborough counties depicted by 10-minute isochrones. The total travel time for the selected route was also determined and compared. Outcomes as seen in Figures 6.3a and 6.3b indicate travel times of 46.1 and 64.6 minutes for Free Flow Travel Time (FFTT) and Congested Travel Time (CTT) for the base scenario respectively. Figure 6.3c indicates an enormous increase in the shortest alternative path travel time for I-275 bridge closure scenario which was estimated as 109.86 minutes (approximately an hour above free flow travel time for the base model and 45 minutes above CTT base scenario). Total regional travel time increased by approximately 440 minutes, VDT increased from 121.34 x 106 to 122.51 x 106 vehicle-kilometers (veh-km), while VHT increased from 289 x 104 to 312 x 104 vehicle-hours (veh-hr). Percentage reduction (or increase) in speeds for the selected links based on the speed differences were computed and weighted to determine the average percentage link speed reduction for the bridge closure scenarios (see equation (11)). Figures 6.3d-f provide visualizations for average percentage link speed reductions for I-275 bridge closure scenario. Results depict highway links with increase (or decrease) in speed differences equal to or greater than 1.61 kph (1 mph), 4.83 kph (3 mph), and 8.05 kph (5 mph) respectively. It is observed that a closure to I-275 Bridge leads to considerable reduction in congested speeds on the other four (4)

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bridge locations. Pinellas County and neighboring locations close to the bridges also reflect reduction in congested speed. Further analyses were performed to compute the aggregated resilience index. The subsequent steps specifically focused on the identified high impact regions, that is, Pinellas, Hillsborough and Manatee counties. Index values were then estimated using equations (3.28) to (3.35). A numerical illustration of this approach is seen in Table 6.2. In this illustration, the uninterrupted network was initially disrupted by complete closure to I-275 bridge resulting in reduced functionality. Secondly, the eastbound direction of the I-275 bridge was reopened and this represents the case of partial closure (only the I-275 WB remained closed). Finally the entire bridge was reopened as the transportation system returned to pre-event functionality. The computed resilience index was based on pertinent bridges connecting Pinellas and Hillsborough counties.

Figure 6. 3 Maps showing the shortest path for TBRPM scenarios after I-275 closure and high impact areas (developed using Cube Voyager and ArcGIS software)

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Figure 6.4 diagrammatically explains the computation of resilience indexes for the three scenarios described in this study. Figure 6.4a which depicts partial closure to I-275 for VHT based performance is typical for closures to WCC Causeway, Gandy, Sunshine Skyway and Bayside bridges, the main difference being recovery times. Figure 6.4c represents the resilience diagram for I-275 closure with partial restoration (recovery) prior to complete bridge restoration.

Table 6. 2 Illustrative results for I-275 bridge closure Uninterrupted Network Bridges Length (km) FFS (kph) CSPD (kph) TT (minutes) Total VHT Total VDT WCC Causeway 13.71 88.51 48.06 15.48 15196.05 808274.82 Bayside 4.99 75.63 52.32 5.72 7472.69 391002.05 Gandy 8.93 72.42 65.16 8.23 5137.87 334757.48 Highway 580 1.96 53.11 18.93 6.18 3873.93 73685.02 Sunshine Skyway EB 15.16 88.51 48.22 17.63 9575.85 494209.73 Sunshine Skyway WB 15.29 88.51 50.89 17.99 9892.45 504239.58 I-275 Eastbound 9.37 80.47 51.40 10.94 14254.78 732753.64 I-275 Westbound 9.25 80.47 51.66 10.74 14040.60 725315.09 Complete closure to I-275 bridge Bridges Length (km) FFS (kph) CSPD (kph) TT (minutes) Total VHT Total VDT WCC Causeway 13.71 88.51 19.46 40.71 61117.15 1235913.07 Bayside 4.99 75.63 30.03 9.97 17808.58 534830.70 Gandy 8.93 72.42 17.82 30.04 42856.57 765209.77 Highway 580 1.96 53.11 8.34 14.07 11480.72 95934.49 Sunshine Skyway EB 15.16 88.51 39.25 22.37 15677.87 154391.60 Sunshine Skyway WB 15.29 88.51 40.76 22.46 15656.51 639325.97 Partial closure to I-275 bridge (WB) Bridges Length (km) FFS (kph) CSPD (kph) TT (minutes) Total VHT Total VDT WCC Causeway 13.71 88.51 44.50 16.82 17507.60 857029.06 Bayside 4.99 75.63 48.41 6.18 8654.16 418870.90 Gandy 8.93 72.42 54.77 9.78 7947.57 435976.76 Highway 580 1.96 53.11 19.55 5.98 3733.23 73417.47 Sunshine Skyway EB 15.16 88.51 48.47 17.53 9549.24 495642.31 Sunshine Skyway WB 15.29 88.51 51.05 17.94 9839.49 503056.52 I-275 Eastbound 9.37 80.47 29.27 19.19 22984.76 673535.54 Aggregated resilience index (ARI)

Network Total VHT Total VDT PIVHT PIVDT ϕPIVHT ϕPIVDT Tmod Text Tcomp Uninterrupted 79444.22 4064237.40 0.61 0.62 1 1 - - - Complete I-275 Closure 164597.4 3909284.10 0.29 0.32 0.47 0.53 3 48.5 133 Partial I-275 Closure 80216.06 3457528.55 0.51 0.54 0.84 0.88 1 18.5 33 RVHT = 0.468 RVDT= 0.527 ARI = 0.498

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Figure 6. 4 Resilience diagrams illustrating I-275 bridge closure scenarios (not to scale)

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Computations for Figure 6.4 are below: For Figure 6.4a: A1 = 3*(1-0.843) = 0.471; A2 = 48.5*(1-0.843) = 7.615; A3 = 133*(1-0.843) = 20.881

RVHT = (1-1/3*(0.471+7.615+20.881)/61.7) = 0.8435 A1 = 3*(1-0.878) = 0.366; A2 = 48.5*(1-0.878) = 5.917; A3 = 133*(1-0.878) = 16.226

RVDT = (1-1/3*(0.366+5.917+16.226)/61.7) = 0.8784

Aggregate Resilience Index = average (RVHT, RVDT) = 0.861

For Figure 6.4b: A1 = 3*(1-0.466) = 1.602; A2 = 48.5*(1-0.466) = 25.899; A3 = 133*(1-0.466) = 71.022

RVHT = (1-1/3*(1.602+25.899+71.022)/61.7) = 0.468 A1 = 3*(1-0.525) = 1.425; A2 = 48.5*(1-0.525) = 23.038; A3 = 133*(1-0.525) = 63.175

RVDT = (1-1/3*(1.425+23.038+63.175)/61.7) = 0.527

Aggregate Resilience Index = average (RVHT, RVDT) = 0.498

For Figure 6.4c: A1 = (1*(1-0.466)) + (2*(1-0.843)) = 0.848; A2 = (18.5*(1-0.466)) + (30*(1-0.843)) = 14.589; A3 = (33*(1-0.466)) + (100*(1-0.843)) = 33.322;

RVHT = (1-(A1 +A2+A3)/(3*61.7)) = 0.737 A1 = (1*(1-0.525)) + (2*(1-0.878)) = 0.719; A2 = (18.5*(1-0.525)) + (30*(1-0.878)) = 12.448; A3 = (33*(1-0.525)) + (100*(1-0.878)) = 27.875;

RVDT = (1-(A1 +A2+A3)/(3*61.7 ))= 0.778

Aggregate Resilience Index = average (RVHT, RVDT) = 0.758

Table 6.3 shows results for index computations for each metric. Closure to I-275 bridge is observed to result in a noticeable increase in travel time as well as VHT. It is however detected that in most cases indicators relating to travel time demonstrate higher index values compared with those involving vehicle distance traveled. This observation is attributed to the fact that increases in travel times are very prominent during congested conditions when traveling a fixed distance. Meaning, during bridge closures occurrences, rerouting through an alternative path may only increase travel distance to the point of the physical length of that alternative network route

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which does not necessarily change significantly, hence, while travel time could double for a trip, travel distance does not behave in the same fashion. This is clearly observed with the I-275 bridge closure scenario where VHT-related performance is much lower than VDT-related performance. Both metrics are however important since delay and operating costs vary when evaluating user costs. The aggregated network resilience index seen in Table 6.3 is scaled from zero to one, with one indicative of no change from existing conditions, or an uninterrupted network, and zero, representing a network with severe performance deficits. Results show that complete closure to I-275 bridge results in a low resilience index of 0.498, representing significant reduction in network performance. Closure to the WCC Causeway bridge however, results in a network level resilience index value of 0.87, while the indexes for the other scenarios range between 0.76 and 0.97. These results reflect the high dependency of the network on I-275 bridge. Damage to this bridge is envisaged to have a massive impact on the network in terms of travel cost. Lower resilience index values imply increased loss in resilience which communicates either significant functionality losses or lengthy closure durations or both. Travel costs are therefore observed to increase when resilience indexes are lower and this suggests an increase in transportation user costs and limitations in mobility.

Table 6. 3 Performance index and resilience index for bridge closure scenarios Scenarios Bridge Closures Recovery Sequence PIVHT PIVDT RVHT RVDT ARI 1 I-275 Bridge Complete Total Recovery 0.466 0.525 0.468 0.527 0.498

2 I-275 Bridge Partial Total Recovery 0.843 0.878 0.844 0.878 0.861 3 I-275 Bridge Complete Partial - Total Recovery - - 0.737 0.778 0.758

4 Gandy Bridge Complete Total Recovery 0.898 0.894 0.883 0.879 0.881 5 Sunshine Skyway Bridge Total Recovery 0.983 0.989 0.981 0.987 0.984 Complete 6 WCC Bridge Complete Total Recovery 0.882 0.897 0.865 0.882 0.873

7 Bayside Bridge Total Recovery 0.976 0.974 0.973 0.970 0.971 Complete 8 I-275 and Gandy Bridge Total Recovery 0.365 0.403 0.367 0.405 0.386 Complete 9 I-275 and Gandy Bridge Gandy Bridge - Total - - 0.370 0.431 0.401 Complete recovery 10 I-275 and Gandy Bridge Gandy Bridge - Partial - - 0.670 0.702 0.686 Complete I-275 - Total Recovery

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6.5 Chapter Summary

In this chapter, a developed framework and computational approach for evaluating the resilience of regional transportation networks was applied in a case study effort. This method provides a preliminary identification of zones which have been most impacted in the transportation network during bridge closure events. A new metric which preliminarily identifies areas for immediate action (high impact zones) has been developed by locating regions with minimal to high mean link speed reductions. The relevance of the proposed metric is stressed for a regional analysis for large networks and serves as pointers to areas that require further resilience evaluation. The use of scenario-based modeling in Cube Voyager, and GIS visualization techniques will aid in communicating the specific locations to direct immediate attention after hazard occurrence to responsible agencies. The aggregated resilience index developed in this study utilized metrics mainly used in transportation user cost computations (VDT and VHT). These metrics were combined with congested speeds and free flow speeds to provide a performance metric used to measure resilience. This is a modification of the mobility performance index based on truck distance traveled developed by Zhang et al. (2009). This modified index explains regional mobility effects or changes based on both distance traveled and time traveled. The development of the index accounted for the use of recovery times based on expected damage states for bridges. The developed aggregated index is effective in capturing resilience based on varying recovery times. Findings from an application example on the Tampa Bay regional network reflected significant regional resilience losses during bridge closures. Closure to I-275 bridge is observed to have the most significant impact on the network as the resilience index was below 0.5 signifying severe network functionality losses, increase in delays, and mobility limitations. Partial (one direction) restoration of the bridge prior to complete recovery results in resilience index improving to 0.758. These findings are relevant in ensuring that measures are put in place to contain the effects of unforeseen closures to such important bridges, whether in the event of hurricanes or other potential hazards. Findings show possibilities of traffic gridlocks on several roadways in the Pinellas and Hillsborough counties in the event of closure to I-275 bridge.

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CHAPTER 7

POST-HAZARD RECOVERY EVALUATION

7.1 Evaluating the Recovery Phase of Resilience based on Post-Hurricane Bridge Damages

It is essential in efforts to evaluate the resilience of transportation networks, to investigate the duration(s) for reinstating the network to full functionality after hazard events. While literature and results from earlier chapters in this thesis point to the importance of rapidity in evaluating TNR, the question still remains on how important and critical road network infrastructures such as bridges are reinstated after hazard events. Information on actual recovery times will provide researchers with sufficient information to model the time it takes to restore damaged bridges after hazards. In the previous chapters, recovery times in resilience framework were either obtained through assumptions and inferences from historic hurricane events, and previous literature (recovery times mostly informed by expert judgment and fragility analysis of specific bridge types). In the context of investing into resilient infrastructure, accurate knowledge on rapidity in restoring roadway infrastructures such as bridges will aid in reiterating the need for such investments and a national consensus. The restorations of bridges are dependent on post-disaster bridge inspection and management practices by responsible agencies. Post disaster inspections are essential since bridges do not completely collapse during a hurricane event may have undergone some damages which warrant closures for minor and major repairs, and rehabilitation actions. Estimating the recovery phase of resilience is a challenge commonly reported by researchers. For this reason, this chapter contributes to this aspect of resilience by using empirical data for evaluating post- disaster bridge recovery as part of the resilience framework. Infrastructure recovery is primarily hinged on agency response which details post-disaster evaluation and inspection, letting and bidding process, and the duration of construction/rehabilitation activities. Previous studies have evaluated the impact of bridge closures on transportation user cost at the regional scale (Twumasi-Boakye and Sobanjo, 2017), while others have studied the importance of bridges to vulnerable age groups (Twumasi-Boakye et al., 2018). Some studies have considered the use of fragility analysis for evaluating the resilience of bridges subjected to earthquakes (Frangopol and

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Bocchini, 2011). Resilience and recovery curves have been developed to determine the durations taken for bridges of various damaged states to recover, however, the need further research in this area remains. Here, the recovery phase of resilience is evaluated by reviewing post-disaster agency response, bidding, and construction times, project reports, and internet queries. The State of Florida has had several hurricane events over the past two decades. These events led to the loss of important infrastructure in the state. Bridges have been of particular interest due to its importance to mobility therefore responsible agencies have been actively involved in post- disaster inspection, letting and bidding, and rehabilitation of bridges. In order to review and evaluate recovery phase of resilience for transportation networks subjected to hurricane-induced bridge damage, this study seeks to: (i) Review bridge inspection data for the State of Florida with a focus of post-hazard (hurricane) inspection; (ii) Identify time lags between hurricane events and agency inspection, bidding and construction; (iii) Finding distributions which are most appropriate for describing post-hurricane bridge recovery times; (iv) Using historical events of post-hurricane bridge damages from online queries and agency reports to determine recovery times; and (v) Recommendations for agency response based on results discussed. These steps will provide information on bridge and eventually network recovery times during hurricane events. Furthermore, the mean time lags prior to agency response can be determined through fitted models which can further be used to model the response aspect of post-disaster bridge recovery.

7.2 Recovery Phase of Resilience

Many studies have focused on estimating civil infrastructure resilience (Chang, 2009; Serulle et al., 2011; Cimellaro et al., 2013) however there are research gaps in the post-disaster recovery phase of resilience. This aspect of resilience is very essential because resilience is a function of both performance loss and rapidity (time to recovery). The comprehension of the post-disaster recovery of infrastructure such as bridges will furnish responsible agencies with the needed information on factors influencing recovery to enact improvement measures for prompt recovery. The recovery phase of resilience can be divided into three main phases. The first phase of recovery entails the immediate post-disaster response from agencies. In the case of bridge infrastructure, the first response which involves bridge inspection is important to the recovery

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process as post-hazard bridge conditions are required for repair and rehabilitation activities. Therefore, the time taken for agencies to carryout bridge inspections after hazard events is the first step to bridge infrastructure recovery. Besides the relevance of this stage to recovery, this step is also crucial for safety since some standing bridges may not possess the structural integrity for usage and must be identified in order to avoid loss of human lives due to unexpected collapse. The next step in the recovery process after identifying infrastructure conditions is the bidding and letting process. Bridges that require maintenance, repair, and rehabilitation works will have to be let by a bidding process where contractors are selected based on the bidding terms. The prioritization of damaged bridges selected for this process may depend on the importance of the bridge to efficient mobility in terms of average annual daily traffic (AADT) on the bridge or the resulting detour length due to bridge closure. Availability of resources may also play a role in prioritization as this may determine which bridges are worked on and when contracts are let. Finally, the construction process plays a key role in recovery. This aspect depends on the amount and availability of resources as well as other environmental conditions. Furthermore, the size and damage state of the bridge infrastructure may influence the time it takes to complete construction. It is however necessary to recognize that bridges of high importance can have high resource allocation hence may be completed rather quickly. In order to determine the actual time it takes for the entire post-disaster recovery phase, it is imperative to evaluate the time it takes to complete specific MR&R activities. While records exist on bidding processes and completion on MR&R activities, those records do not explicitly tie the project to hazard events making it difficult to evaluate this aspect of recovery. In this study, information gathered from previous events sourced from project reports and internet queries will be utilized in providing a description of construction times (recovery). Figure 7.1 identifies the recovery sequence for 7 closed bridges (set of bridges) during a hazard event. Each recovery step leads to improved functionality of the transportation network. Figure 7.1a represents gradual recovery which reflects high resilience loss while Figure 7.1b indicates that significant functional improvement occurs rapidly meaning a more resilient network.

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Figure 7. 1 Transportation network resilience diagram showing bridge recovery sequence

Where RSeqi – Recovery Sequence i Each recovery sequence step represents either the time a single bridge or group of bridges recover within a specified time period. Each recovery sequence leads to a network functional improvement.

7.3 Data Identification and Merging Procedures

The use of pertinent agency data was essential in carrying out this study Figure 7.2. Data sources include NBI bridge inspection data for natural disaster damage (flood or storm) under field “INSPTYPE, M” for Florida Department of Transportation (FDOT) bridge management system (BMS) tables, FDOT Maintenance Management System (MMS) cost data for bridges,

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statewide bid data for bridge maintenance, repair and rehabilitation activities, data from internet queries and reports, and bridge attribute data from National Bridge Inventory (NBI) database. Further details on the 2004 and 2005 hurricane seasons were obtained in reports by Franklin et al. (2006) and Beven et al. (2008). The bridge inspection data included 3665 inspections for the years 2004 and 2005. MMS bridge data included 2540 repairs between 2004 and 2008, and bid items for 527 projects between 2005 and 2008. Previous studies by Sobanjo and Thompson (2013) and internet queries further provided information on major bridge damages and recovery times from hurricanes Ivan and Katrina. For each identified bridge for natural disaster inspection, the fields for inspection date and notes were queried in order to identify the specific hurricane/storm event for which the inspection was done and the lag in time prior to inspection from the hurricane landfall. The inspection of the “Notes” field was particularly important as it also provided information on whether the inspected bridge or infrastructure had any recorded damages. This field also served as very useful in identifying instances where assigned bridges for the natural disaster inspection were routine inspections. The “Bridge_ID” field also aided in separating bridges from non- bridge infrastructures and further served as the unique field for merging with the other data sources mentioned. Upon merging this dataset with NBI data fields, it was possible to evaluate time to response by infrastructure functional classification and owner. However, as discussed earlier, to estimate recovery time, the three-main requisite are response time, bidding and letting time, and construction (MR&R) duration. The first dataset provides information on response times. After evaluating response times and identifying ridges with recorded damages for each hurricane event, the next steps are to query the MMS cost data and the statewide bid data using the unique fields “BRKEY” and “BridgeNo” respectively. The main goals for these queries are to identify how long after inspections were the project let (from the statewide bid data), and the duration between letting the project and completing the MR&R activity (MMS cost data). Even though this schematic procedure should suffice in determining the total time for recovery for each damaged bridge, some issues were identified. While the data sources are comprehensive and commendable, three main issues did not help in facilitating the synchronization of datasets and evaluating bidding and MR&R durations.

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The first observation was that many identified bridges with recorded damages were not identified in the bid and MMS datasets. This may be attributed to the fact that minor damages may be grouped under larger projects for future MR&R activities or due to bridge importance and urgency of repair activities, some damaged bridges may be assigned to trusted contractors for MR&R works hence would not be part of the usual bidding process. Secondly, unlike the data for natural disasters which had notes for each field pointing to the purpose of inspection, the MMS and bid data had “Instructions” and “ItemDescription” fields respectively, however, these fields did not provide information for the cause of damage for which bidding and repairs were to be done. Finally, in instances where few damaged bridges were identified in the MMS cost dataset, it was observed that multiple records existed for some of the bridges even upon a further query to ensure that the selected beginning dates for construction were after the bridge inspection date. This reinforces the need for an additional data field for explaining the cause of damage. In order to obtain complete recovery times, the above data was augmented with historical records of hazard-induced bridge closures and recovery based on internet queries and disaster reports.

Figure 7. 2 Schematic diagram for estimating bridge recovery time

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7.4 Results and Discussion

Results in Table 7.1 indicate that out of 3665 hazard related inspections, 1566 were observations on sign structures while 2099 were bridges. It was also estimated that 41.88% of the recorded bridges were state maintained while 58.12% were locally maintained. Also, 415 out of 3665 inspections had hurricane related damages with 164 and 251 of damages related to bridges and sign structures respectively. Table 7.2 and Figure 7.3 provide results on fitted distributions for inspection data with regards to response times. It was observed that based on lower Anderson- Darling and Cramer-von Mises values, the lognormal distribution was the best fit for all reported hurricane inspection times. The mean times between fitted distributions only varied marginally however, based on test statistics, the lognormal distribution was best suited.

Table 7. 1 Summary table Hurricane Category Landfall in Florida Number of Inspections Recorded Damages Frances 3 September 5, 2004 988 16 Jeanne 3 September 26, 2004 521 30 Wilma 3 October 24, 2005 860 273 Katrina 1 August 25, 2005 712 49 Charley 4 August 13, 2004 351 29

Table 7. 2 Descriptive statistics for all inspected infrastructures Cramer-von Mises Anderson-Darling Hurricane Frances Mean Time Median Time Statistic p-value Statistic p-value Normal 4.86 4.00 9.85 <0.005 57.17 <0.005 Exponential 4.86 3.37 18.11 <0.001 98.68 <0.001 Weibull 4.91 4.34 4.56 <0.010 30.10 <0.010 Lognormal 4.77 4.06 2.18 <0.010 15.10 <0.005 Cramer-von Mises Anderson-Darling Hurricane Charley Mean Time Median Time Statistic p-value Statistic p-value Normal 4.33 3.00 3.34 <0.005 18.71 <0.005 Exponential 4.33 3.00 3.23 <0.001 19.61 <0.001 Weibull 4.36 3.70 1.33 <0.010 8.11 <0.010 Lognormal 4.31 3.35 0.94 <0.005 6.01 <0.005 Cramer-von Mises Anderson-Darling Hurricane Katrina Mean Time Median Time Statistic p-value Statistic p-value Normal 1.81 1.00 48.12 <0.005 229.93 <0.005 Exponential 1.81 1.25 31.40 <0.001 156.70 <0.001 Weibull 1.78 1.18 32.30 <0.010 159.86 <0.010 Lognormal 1.42 1.26 25.21 <0.005 124.91 <0.005

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Table 7. 2 - continued Cramer-von Mises Anderson-Darling Hurricane Jeanne Mean Time Median Time Statistic p-value Statistic p-value Normal 4.35 3.00 10.84 <0.005 55.31 <0.005 Exponential 4.35 3.02 4.29 <0.001 25.30 <0.001 Weibull 4.39 3.32 4.30 <0.010 23.79 <0.010 Lognormal 4.20 3.00 2.43 <0.005 14.53 <0.005 Cramer-von Mises Anderson-Darling Hurricane Wilma Mean Time Median Time Statistic p-value Statistic p-value Normal 7.66 3.50 11.02 <0.005 65.76 <0.005 Exponential 7.66 5.31 11.43 <0.001 68.24 <0.001 Weibull 7.67 5.05 9.97 <0.010 58.94 <0.010 Lognormal 9.28 3.94 9.34 <0.005 56.16 <0.005 Cramer-von Mises Anderson-Darling Hurricane (Total) Mean Time Median Time Statistic p-value Statistic p-value Normal 4.80 3.00 57.07 <0.005 299.56 <0.005 Exponential 4.80 3.33 15.64 <0.001 100.17 <0.001 Weibull 4.81 3.41 16.78 <0.010 103.70 <0.010 Lognormal 4.76 2.97 10.97 <0.005 75.10 <0.005

a.)

Figure 7. 3 Fitted probability distribution functions for hurricane categories 1 (a.), 3(b.) and 4 (c.)

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b.)

c.)

Figure 7. 3 - continued

Results from cumulative distribution function curves for bridge inspection response times for hurricane events seen in Figure 7.4 indicate that it took less than 4 days, 3 days, 3 days, 1 day, 3 days, and 3 days for 50% of total inspected bridges due to hurricanes Frances, Charley, Jeanne, Katrina, Wilma, and all hurricanes to be inspected respectively. 90% of the inspected bridges were inspected within 8 days after hurricanes Frances and Charley, within 10 days after hurricane Jeanne, within 2 days after hurricane Katrina, 16 days after hurricane Wilma and 13 days when considering all hurricane events. For categories 1, 3 and 4 hurricanes, results

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indicated that 50% of bridges were inspected within 1, 3 and 3 days respectively while 90% of bridges were inspected within 2, 14 and 8 days respectively. Overall it was observed that approximately half of the total inspection takes place within the first 3 days after hurricane events while about 90 % of all inspections are completed within two weeks. These times combined with mean response times computed provide a good measure of the time it takes for post-hurricane bridge infrastructure inspection which forms a main component in computing recovery times. Out of 3665 inspection records, 2116 records were uniquely identified as bridges while the rest were non-structural elements, 2033 of these were assigned to specific hurricane events. With respect to the 2033 bridges, 526, 205, 280, 138 and 884 of them were attributed to hurricanes Wilma, Katrina, Charley, Jeanne, and Frances respectively. Further analyses included investigating the effects of hurricane categories and bridge functional class on response times. The mean days to inspection for hurricane categories 1, 3, and 4 events were 1.2, 3.6 and 2.9 days respectively. Least square means for hurricane category effects with days to inspection as dependent variable indicated that mean days to inspection for all reported hurricane categories were significantly different under the null hypothesis of equality of means. Results are seen in Table 7.3. Mean times to response for arterials, collectors and local roads were 3.43, 3.26, and 3.01 days respectively. The mean days were not significantly different except for the instance of comparing local roads to arterials. It is important to note that even though local roads and arterials are significantly different (statistically) under a 95% confidence interval, they are quite similar since the p-value is close to 0.05. A summary of Anova results have been reported in Table 7.3. It was further observed that while comparing interstate to non-interstate bridges, the response times for the two categories were significantly different. The mean times to inspection were 2.14 and 3.36 days for interstate and non-interstate bridges respectively. While results were statistically different, it is expected that generally, rural and urban bridges would be inspected within 4 days with mean time to inspection indicating 3.46 days for rural bridges and 3.13 days for urban bridges. Similar can be said of state and locally maintained bridges which were on the average inspected 3.65 and 3.0 days respectively after hurricane events. Generally, results were explicit that bridges located on interstates were responded to more rapidly than non-interstate bridges. This may be attributed to the importance of interstate bridges in terms of high average

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annual daily traffic (AADT) and high truck traffic volumes. Furthermore, damages and closures to interstate bridges may lead to very long detours which can cause increased transportation user costs (Twumasi-Boakye and Sobanjo, 2017) and traffic gridlocks at the regional level.

100 90 80 70 60 50 40 30

20 Cumulative Function Cumulative Distribution 10 0 0 10 20 30 40 50 60 70 80 90 Response Time (days)

Hurricane Frances Hurricane Charley Hurricane Jeanne Hurricane Katrina Hurricane Wilma All Hurricanes

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Cumulative Function Cumulative Distribution 10

0 0 10 20 30 40 50 60 70 80 90 Response Time (days)

Hurricane Category 1 Hurricane Category 3 Hurricane Category 4

Figure 7. 4 Empirical cumulative distribution function curves for bridge inspection response times

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Table 7. 3 Anova results i/j Hurricane Category 1 Hurricane Category 3 Hurricane Category 4 Hurricane Category 1 - <.0001 <.0001 Hurricane Category 3 <.0001 - 0.0034 Hurricane Category 4 <.0001 0.0034 - i/j Arterials Collectors Local Arterials - 0.6755 0.0412 Collectors 0.6755 - 0.4316 Local 0.0412 0.4316 - i/j Interstate Non-interstate Interstate - <.0001 Non-interstate <.0001 - i/j Rural Urban Rural - 0.0295 Urban 0.0295 - i/j State Maintained Locally Maintained State Maintained - <.0001 Locally Maintained <.0001 -

Table 7. 4 Damaged bridges Bridge Hurricane Structure Date of Inspection Structure Type County Function ID Event Kind Event Date Culvert (includes Other Principal 010043 Charley Concrete Charlotte 8/13/2004 8/14/2004 frame culverts) Arterial-Urban Prestressed Principal Arterial - 010093 Charley Slab Charlotte 8/13/2004 8/14/2004 Concrete Other Rural Prestressed Principal Arterial - 010095 Charley Slab Charlotte 8/13/2004 8/14/2004 Concrete Other Rural Culvert (includes Other Principal 010940 Charley Concrete Charlotte 8/13/2004 8/14/2004 frame culverts) Arterial-Urban Prestressed Multi-beam or Other Principal 010092 Charley Charlotte 8/13/2004 8/15/2004 Concrete Multi-Girder Arterial-Urban Other Principal 120001 Charley Steel Movable - Lift Lee 8/13/2004 8/15/2004 Arterial-Urban Culvert (includes Other Principal 120006 Charley Concrete Lee 8/13/2004 8/15/2004 frame culverts) Arterial-Urban Culvert (includes Other Principal 120007 Charley Concrete Lee 8/13/2004 8/15/2004 frame culverts) Arterial-Urban Movable - 120050 Charley Steel Lee Collector-Urban 8/13/2004 8/15/2004 Bascule Steel Multi-beam or Principal Arterial - 120084 Charley Lee 8/13/2004 8/15/2004 continuous Multi-Girder Interstate Urban Prestressed Indian 885804 Frances Channel Beam Local- Urban 9/5/2004 9/8/2004 Concrete River Prestressed Indian 885808 Frances Slab Local- Urban 9/5/2004 9/8/2004 Concrete River Minor Arterial 940005 Frances Concrete Slab St. Lucie 9/5/2004 9/8/2004 Rural

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Table 7. 4 - continued Bridge Hurricane Structure Structure Date of Inspection County Function ID Event Kind Type Event Date Culvert (includes Principal Arterial - 080037 Frances Concrete Hernando 9/5/2004 9/8/2004 frame culverts) Other Rural Culvert (includes Hillsboro Principal Arterial - 100092 Frances Concrete 9/5/2004 9/8/2004 frame culverts) ugh Other Rural Prestressed 155501 Frances Tee Beam Pinellas Local- Urban 9/5/2004 9/8/2004 Concrete Culvert (includes Minor Arterial 040035 Frances Concrete De Soto 9/5/2004 9/9/2004 frame culverts) Rural Culvert (includes Principal Arterial - 160065 Frances Concrete Polk 9/5/2004 9/9/2004 frame culverts) Other Rural Culvert (includes Principal Arterial - 160131 Frances Concrete Polk 9/5/2004 9/9/2004 frame culverts) Other Rural Culvert (includes Minor Arterial- 160229 Frances Concrete Polk 9/5/2004 9/9/2004 frame culverts) Urban Prestressed Multi-beam or Hillsboro Other Principal 100585 Jeanne concrete 9/26/2004 9/27/2004 Multi-Girder ugh Arterial-Urban continuous Prestressed Multi-beam or Okeecho Principal Arterial - 910065 Jeanne 9/26/2004 9/28/2004 Concrete Multi-Girder bee Other Rural Concrete Okeecho Principal Arterial - 910095 Jeanne Slab 9/26/2004 9/28/2004 continuous bee Other Rural Prestressed Multi-beam or Major Collector 140124 Jeanne Pasco 9/26/2004 9/28/2004 Concrete Multi-Girder Rural Prestressed Indian 885802 Jeanne Slab Local- Urban 9/26/2004 9/29/2004 Concrete River Prestressed Multi-beam or Other Principal 700082 Jeanne Brevard 9/26/2004 10/8/2004 Concrete Multi-Girder Arterial-Urban Prestressed Multi-beam or Other Principal 700148 Jeanne Brevard 9/26/2004 10/8/2004 Concrete Multi-Girder Arterial-Urban Prestressed Multi-beam or Other Principal 700080 Jeanne Brevard 9/26/2004 10/11/2004 Concrete Multi-Girder Arterial-Urban Prestressed Multi-beam or Other Principal 700146 Jeanne Brevard 9/26/2004 10/11/2004 Concrete Multi-Girder Arterial-Urban Steel Multi-beam or Other Principal 700181 Jeanne Brevard 9/26/2004 10/12/2004 continuous Multi-Girder Arterial-Urban 865774 Katrina Concrete Tee Beam Broward Local- Urban 8/25/2005 8/26/2005 865775 Katrina Concrete Tee Beam Broward Local- Urban 8/25/2005 8/26/2005 865778 Katrina Concrete Slab Broward Local- Urban 8/25/2005 8/26/2005 865782 Katrina Concrete Slab Broward Local- Urban 8/25/2005 8/26/2005 Multi-beam or 867207 Katrina Concrete Broward Local- Urban 8/25/2005 8/26/2005 Multi-Girder Multi-beam or 867208 Katrina Concrete Broward Local- Urban 8/25/2005 8/26/2005 Multi-Girder Culvert (includes Minor Arterial- 890004 Katrina Concrete Martin 8/25/2005 8/27/2005 frame culverts) Urban Culvert (includes Principal Arterial - 890087 Katrina Concrete Martin 8/25/2005 8/27/2005 frame culverts) Other Rural Prestressed Multi-beam or Palm Other Principal 930339 Katrina 8/25/2005 8/27/2005 Concrete Multi-Girder Beach Arterial-Urban Prestressed Palm Minor Arterial- 930194 Katrina Slab 8/25/2005 8/27/2005 Concrete Beach Urban Steel Multi-beam or Principal Arterial - 010069 Wilma Charlotte 10/24/2005 10/24/2005 continuous Multi-Girder Interstate Rural Steel Multi-beam or Principal Arterial - 010070 Wilma Charlotte 10/24/2005 10/24/2005 continuous Multi-Girder Interstate Rural Multi-beam or Principal Arterial - 010073 Wilma Steel Charlotte 10/24/2005 10/24/2005 Multi-Girder Interstate Rural

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Table 7. 4 - continued Bridge Hurricane Structure Structure Date of Inspection County Function ID Event Kind Type Event Date Concrete Principal Arterial - 010078 Wilma Slab Charlotte 10/24/2005 10/24/2005 continuous Interstate Rural Prestressed Multi-beam or Principal Arterial - 120082 Wilma Lee 10/24/2005 10/24/2005 Concrete Multi-Girder Interstate Rural Prestressed Multi-beam or Principal Arterial - 120091 Wilma Lee 10/24/2005 10/25/2005 Concrete Multi-Girder Interstate Rural Prestressed Multi-beam or 120092 Wilma Lee Collector-Urban 10/24/2005 10/25/2005 Concrete Multi-Girder Prestressed Multi-beam or Principal Arterial - 120122 Wilma Lee 10/24/2005 10/25/2005 Concrete Multi-Girder Interstate Rural Culvert (includes Principal Arterial - 120139 Wilma Concrete Lee 10/24/2005 10/25/2005 frame culverts) Interstate Rural Prestressed 864065 Wilma Channel Beam Broward Local- Urban 10/24/2005 10/25/2005 Concrete

Table 7.4 provides a sample output of bridges identified with damages from inspection data. While merging inspection data to statewide bid data, only two damaged bridges were identified to have been let within three months from the reported hurricanes. These bridges were both let 42 days after hurricane Wilma related inspections. While data sources provided information on damaged bridges as a result of natural hazards, statewide bidding information and project costs, the combination of the data sources were insufficient in providing information on closure durations. Hence, previous reports on hurricane events as well as internet queries were used in estimating bridge closure durations. The sourced data were then categorized as interstate and non-interstate bridges. Results as observed in Table 7.5 indicate that interstate bridges and non-interstate bridges followed the lognormal and Weibull distributions respectively. The mean time for completely damaged bridges on interstates to be reopened was computed as approximately 79 days while it takes non-interstate bridges a mean time of 187 days. This supports results on response times which indicated priority for interstate bridges during post-disaster inspections. With regards to MR&R activities, it also expected that most damaged bridges on interstate roadways should reopen within two to three months, and up to six months for non-interstate bridges. This may be attributed to the fact that higher AADT on interstate bridges may necessitate immediacy in recovery efforts, resource allocation and construction times. Previous reports on major bridge damages on interstates have resulted in those bridges being rapidly reinstated due to their importance to regional mobility. Examples of such instances are closures to I-10 Bridge over Escambia Bay and I-85 Bridge in Atlanta from Hurricane Ivan

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and fire respectively. On September 16, 2004, storm surges and waves due to Hurricane Ivan had enormous consequences on I-10 bridges over Escambia Bay resulting in the displacement of several bridge spans as well as complete pier removal (Hitchcock et al., 2008). Recovery time of 66 days after the Hurricane event was needed to reconstruct and reopen the Escambia Bay Bridge to traffic (Hitchcock et al., 2008). The loss of this bridge resulted in an approximately 209 km (130 miles) traffic detour (Talbot, 2005) implying increased transportation user costs. Secondly, a section of I-85 Bridge in Atlanta collapsed after a massive fire on March 20, 2017. Three sections of I-85 northbound and southbound required replacement and it took over six weeks to reopen the South bound of the bridge to traffic (Burns and Brett, 2017). The estimated daily vehicular traffic on this Atlanta roadway section is 220,000, and because of the closure, traffic on I-285 bypass increased by 50% the following day due to traffic gridlock, with traffic conditions in the Atlanta area substantially affected (Noll, 2017). Considering the scales of damage to both bridges, it would have taken longer for MR&R activities however, due to their criticality to urban mobility, the bridges were reinstated rapidly.

Table 7. 5 Fitted distributions for recovery times Distributions Cramer-von Mises Anderson-Darling Mean (days) (Interstate) Statistic p-value Statistic p-value Normal 76.17 0.095 0.103 0.560 0.086 Exponential 76.17 0.114 >0.250 0.626 >0.250 Weibull 76.86 0.062 >0.250 0.401 >0.250 Lognormal 78.57 0.051 0.458 0.321 0.423 Distributions (Non- Cramer-von Mises Anderson-Darling Mean (days) Interstate) Statistic p-value Statistic p-value Normal 186.92 0.064 >0.250 0.459 >0.250 Exponential 186.92 0.196 0.076 1.013 0.113 Weibull 186.07 0.042 >0.250 0.308 >0.250 Lognormal 219.24 0.191 0.007 1.141 <0.005

7.5 Chapter Summary

In this chapter, efforts were made using available data sources and explanatory data analysis to explain the recovery phase of resilience- an aspect of resilience which requires further studies. This was done for bridge infrastructures by first categorizing post-disaster recovery into three phases namely: inspection response time, bidding and letting time, and construction time. These main components primarily inform engineers on the time elapsed before reinstating

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hazard-induced damaged bridges: it also serves as a way to evaluate recovery methods and efforts. A case study of Florida bridges which entailed the use of multiple data sources indicated that initial post-hurricane response times for bridge inspection is mostly between 3 to 4 days. Results further show that response times follow a lognormal distribution. Furthermore, interstate bridges are on the average responded to a day earlier that non-interstate bridges and this can be attributed to their high traffic volumes and the importance. Results from queried online data sources and reports also revealed that damaged interstate and non-interstate bridges follow lognormal and Weibull distributions respectively and take approximately 77 and 187 days to be completely reinstated. The data sources used for the recovery times were however limited as agencies do not have extensive data for recovery times of damaged bridges after hazard events. It is therefore recommended that agencies put in place a thorough method for collecting data related to hazard events, especially, bridge recovery times.

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CHAPTER 8

SUMMARY

8.1 Concluding Remarks

The comprehension of network-level consequences resulting from disruptive events is one of the main grey areas in the evaluation of transportation network resilience at the regional level. Explaining hazard impacts on regional network infrastructures and identifying significantly affected areas are essential for communicating the need for building resilient infrastructure. The Undersecretary for Policy (U.S. Department of Transportation) was quoted as saying, “Creating a transportation system that is more resilient will be perhaps the most significant challenge we have in the century going forward.” The National Infrastructure Advisory Council (NIAC) on “Transportation Sector Resilience,” (Baylis et al., 2015) concluded with some salient findings on the ongoing dialogue on transportation sector resilience which include, deficits in the comprehension of network-level consequences resulting from major disruptive events, the need to advance from the establishment of national resilience policies to the integration of the aforesaid into strategic plans which translate into risk management, and the necessity to invest in resilient infrastructure especially since there is no existing national consensus on this subject. Results from a detailed literature review on transportation network resilience further reinforced the previous assertion by NIAC and also realized the need for further studies on the resilience of regional transportation networks subjected to hazard events, the development of resilience index measures for explaining the extent to which regional networks are resilient, the understanding of the recovery phase of resilience, and real-life applications of resilience frameworks. The points mentioned above are imperative to leverage the need for resilient infrastructure investment. This thesis presents a framework to close the gap in the comprehension of transportation network resilience with a primary focus on regional networks subjected to hazard-induced bridge damage and road closures. To achieve the goals for this research, scenario-based traffic modeling and Geographic Information System (GIS) techniques were adopted. First, it was expedient to explain the problem and make a case for regional level resilience studies to echo findings from

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the thoroughly reviewed literature. For this reason, additional transportation user costs were utilized as a metric for evaluating the regional network impact of individual closures to important bridges. User costs were based on vehicle operating costs and delay costs computed from additional vehicle miles traveled and vehicle hours traveled respectively. This aspect exposed flaws in the status quo adopted by agencies which entail the use of detour length for computing costs associated with bridge closures. Furthermore, results from the study highlighted that small network or hypothetical networks used in previous studies are insufficient to explain the scale of ripple effects at the regional level when very important road network components are rendered inoperable due to closures. Comparison of additional user costs for regional networks and simply alternative routes indicated that transportation user costs were much more for the overall simulated regional network. Having succinctly identified the gaps in the literature and further explained the necessity for the research in the user cost evaluation, salient performance metrics for evaluating regional networks were noted. While various mobility and reliability measures were identified in the literature, many of them were considered impractical for evaluating largescale networks. In this thesis, vehicle distance traveled, vehicle hours traveled, link free flow speed, and link congested speeds were identified as essential to network-level performance evaluation and as input parameters for measuring functional loss and resilience. A vital part of this work entailed the use of a developed high impact zone location identification metric for identifying areas of marginal speed reductions. This is necessary since most large networks have high redundancy making it difficult to identify impacted jurisdictions. This method will provide agencies with preliminary information on areas to channel initial efforts during the loss of importance network links. In order to further comprehend and evaluate transportation network resilience, accessibility was identified as paramount, not only in network evaluation but especially in the context of making a case for resilient infrastructure investment. Accessibility to important locations based on link free flow and congested travel times were used as measures of resilience. The identified measures were extended to applications on real networks. The Tampa Bay Regional Planning Model was used for resilience evaluation by considering single and multiple closures bridge closures as well as varied restoration times including the possibility of partial restoration. Results from this work reflected significant regional resilience losses during bridge closures. Closure to I-275 bridge is observed to have the most significant impact on the network

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as the resilience index was below 0.5 signifying severe network functionality losses, increase in delays, and mobility limitations. This substantial loss is however minimized when recovery efforts include partial (one direction) restoration of the bridge prior to complete recovery. The resilience index improves to 0.758. The importance of I-275 bridge to the network is further reinforced, even as partial (westbound direction) operation of the bridge indicated a resilience index (0.861) comparable to complete closures to Gandy (0.881) and W. Courtney Campbell (0.873) bridges. These findings are relevant in ensuring that measures are put in place to contain the effects of unforeseen closures to such important bridges, whether in the event of hurricanes or other potential hazards. Findings show possibilities of traffic gridlocks on several roadways in the Pinellas and Hillsborough counties in the event of closure to I-275 bridge. To evaluate the use of accessibility a resilience metric, an accessibility-based approach to healthcare for assessing senior community resilience with a focus on bridge damages. The research approach adopted included the formation of a schematic framework for network level selection of bridges at-risk to damage resulting from Category 3 Hurricane events. This was done by computing wind exposure probabilities at each bridge location, assigning damage states to bridges by using NBI attribute fields and historical data, and finally identifying local bridges subjected to high storm surge heights during hurricanes. Results indicated that 66 bridges were of specific interest (using proximity analysis) to areas with a high percentage of the aging population. Movable bridges were identified as being significantly vulnerable during hurricanes. Closest facility analysis for the identified 140 aging-dense zones and 15 hospitals as origins (incident locations) and destinations (facilities), respectively showed substantial increases in minimum travel time to hospitals for both free flow travel time (FFTT) and congested travel times (CTT). There was an observed increase from about 1200 minutes to 2100 minutes and from about 900 to 1100 minutes, for the CTT and FFTT, respectively. This indicates travel time increases of about 75% and 15% for CTT and FFTT, respectively. Also, an additional total travel distance of 52.85 miles was observed for CTT and FFTT. The mean travel times after bridge closures increased from 8.43 to 15.1 minutes and from 6.6 to 7.76 minutes for CTT and FFTT, respectively. The impact of bridge closures was more evident for CTT due to congested roadway conditions, yielding a resilience index of 0.81 compared to 0.94 from FFTT. Furthermore, a traffic assignment computational algorithm known as the method of successive averages was adopted for vehicle routing during network disruptions. The following

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conclusions were drawn from the outcome of this analysis: (i) Single bridge closure scenarios recorded significant performance losses for bridges which directly connected to the destination zone; (ii) Resilience indexes echoed the need to compare predicted recovery times to scheduled restoration times since index measures are either compensated or penalized the speed of predicted recovery with respect to scheduled time serving as the upper limit; (iii) Multiple closures had a significant impact on network performance hence rapidity is vital in improving network resilience. While most discussions have centered on mitigating losses, it is expedient that resources are made available for agencies to ensure restoration rapidity which plays a vital role in resilience. The suggested approach when applied will enable agencies to identify important network edges and evaluate optimal times for recovery to minimize both losses due to user costs and delayed recovery.

8.2 Limitations and Recommendation for Future Studies

While the transportation user cost case study did not explicitly consider detours and additional costs due to inadequate horizontal and vertical clearances, poor alignment, and work zone, which are mostly considered in bridge user cost computations, the proposed approach can be extended to those areas as well. Furthermore, an essential aspect of user cost is accident costs- an aspect not considered in this thesis. It is therefore encouraged that future efforts account for the implication of post-hazard closures on associated network-level accident costs in a transportation user cost evaluation framework. This is currently possible since in recent years state agencies have been working on enhancing accident data by making spatial accident data available. This data can be used in a GIS platform for further studies. It should also be noted that the scenario-based approach for regional networks in this thesis is based on static traffic assignment. Even though metropolitan planning organizations generally use this method of traffic assignment for decision making, an improvement can be achieved by using a dynamic traffic assignment. Also, the traffic assignment used for the regional networks and illustrations in this study was based on user equilibrium assignment which involves each road user minimizing their travel time. However, the system optimal solution will prove efficient since the solution involves minimizing the total travel time for the network- an issue of interest to agencies. Future work should focus on investigating the influence of alternative modes of travel as a measure of redundancy in improving network resiliency during

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bridge and road closures. Regional level studies are encouraged due to the ripple effects of closures on ignored sections on regional networks. Recent review publications on resilience still reiterate this need. The need for practical applications for evaluating resilience as well as large network applications are still lacking, and this research gap needs further progressive work. Results from a case study on recovery time data highlighted the need to facilitate the collection of post-hazard road and bridge closure duration data. Such data sources are needed for resilience evaluation to determine the required mitigation measures for improving transportation network resilience. In this thesis, it was particularly identified that comprehensive data sources on post-hazard road closure and bridge damage restoration durations were limited. As such, it is difficult to accurately estimate the recovery phase of resilience and furthermore determine whether agencies are improving in recovery rapidity. Agencies are therefore encouraged to keep records of bridge closure durations, especially after hazard events as this will help in research studies on the recovery phase of resilience and will allow the proper calculations during the implementation of the proposed approach. Finally, methods of improving the resilience of transportation networks are paramount for developing a solution-based resilience framework. While this research highlights some key areas to consider, a comprehensive study on mitigating and improvement methods should be undertaken. In the last decade, there has been a surge in studies revolving around smart cities and connected and autonomous vehicles. Even though detailed regional studies are known to be computationally expensive, it is encouraged that multi-agent travel modeling techniques are employed to model travel pattern more accurately, especially for post-hazard scenarios. These models can also be used to integrate connected vehicles, multi-modal options and evaluate advanced transit solutions. It has become essential for future resilience-based transportation research to investigate how the travel patterns associated with mobility variations will influence network resilience. Also, answers to questions regarding how these technologies can be leveraged to enhance transportation network resilience are needful. This involves considering the influx of connected and autonomous vehicle at various penetration rates and how vehicle connectedness and communication technologies will influence post-hazard mobility especially in the case of natural hazards with widespread effects such as hurricanes, floods, tornadoes, and earthquakes.

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APPENDIX A

BRIDGE AND ROADWAY EXPOSURE PROBABILITIES

Florida Census Blocks Probability of Hurricane Category 1 Occurrence in 1 year at bridge location 0.000 – 0.007 0.007 – 0.020 0.020 – 0.034 0.034 – 0.049 0.049 – 0.095

Figure A. 1 Bridge exposure probability for Hurricane Category 1

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Florida Census Blocks Probability of Hurricane Category 2 Occurrence in 1 year at bridge location 0.000 – 0.002 0.002 – 0.005 0.005 – 0.010 0.010 – 0.020 0.020 – 0.049

Figure A. 2 Bridge exposure probability for Hurricane Category 2

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Florida Census Blocks Probability of Hurricane Category 3 Occurrence in 1 year at bridge location 0.000 – 0.001 0.001 – 0.005 0.005 – 0.010 0.010 – 0.015 0.015 – 0.020

Figure A. 3 Bridge exposure probability for Hurricane Category 3

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Florida Census Blocks Probability of Hurricane Category 4 Occurrence in 1 year at bridge location 0.000 – 0.001 0.001 – 0.003 0.003 – 0.006 0.006 – 0.010 0.010 – 0.015

Figure A. 4 Bridge exposure probability for Hurricane Category 4

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Florida Census Blocks Probability of Hurricane Category 5 Occurrence in 1 year at bridge location 0.000 0.000 – 0.001 0.001 – 0.003

Figure A. 5 Bridge exposure probability for Hurricane Category 5

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Florida Census Blocks Probability of Hurricane Category 1 Occurrence in 1 year at road location 0.000 – 0.012 0.012 – 0.020 0.020 – 0.034 0.034 – 0.049 0.049 – 0.095

Figure A. 6 Roadway exposure probability for Hurricane Category 1

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Florida Census Blocks Probability of Hurricane Category 2 Occurrence in 1 year at road location 0.000 – 0.003 0.003 – 0.007 0.007 – 0.015 0.015 – 0.020 0.020 – 0.049

Figure A. 7 Roadway exposure probability for Hurricane Category 2

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Florida Census Blocks Probability of Hurricane Category 3 Occurrence in 1 year at road location 0.000 – 0.001 0.001 – 0.005 0.005 – 0.010 0.010 – 0.015 0.015 – 0.020

Figure A. 8 Roadway exposure probability for Hurricane Category 3

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Florida Census Blocks

Probability of Hurricane Category 4 Occurrence in 1 year at road location 0.000 – 0.001 0.001 – 0.004 0.004 – 0.006 0.006 – 0.010 0.010 – 0.015

Figure A. 9 Roadway exposure probability for Hurricane Category 4

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Florida Census Blocks Probability of Hurricane Category 5 Occurrence in 1 year at road location 0.000 0.000 – 0.001 0.001 – 0.003

Figure A. 10 Roadway exposure probability for Hurricane Category 5

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APPENDIX B

MATLAB CODES FOR NUMERICAL ILLUSTRATION

**Method of Successive Averages, MSA (Uninterrupted network/ no closure)

**BPR Function** function [ tf ] = BPR(to, a, b, c, x) tf = to*(1+ a*((x/c)^b)); end

close all; clear; clc;

a = [0.62, 0.56, 1.14, 0.15]; b = [5.14, 3.6, 4];

Links = [1 2; 1 3; 1 4; 2 3; 2 5; 3 4; 3 6; 4 7; 5 6; 5 8; 6 7; 6 8; 7 8]; neighbors = [1 3 2 3 4 0 0; 2 2 3 5 0 0 0; 3 2 4 6 0 0 0; 4 1 7 0 0 0 0; 5 2 6 8 0 0 0; 6 2 7 8 0 0 0; 7 1 8 0 0 0 0; 8 0 0 0 0 0 0];

iterations = [50, 500, 1000, 5000, 10000]; to = 5; C = 1500; for i = 1:4 alpha = a(i); beta = b(i);

for j = 1:5 V = zeros(8,8); N = iterations(j); TMat = Inf*ones(8,8); for k = 1:13 TMat(Links(k,1),Links(k,2)) = 5; end

for p = 1:N X = zeros(11,11);

%Initialization DistL = Inf*ones(8,1);

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Prev = Inf*ones(8,1); DistL(1) = 0; Nodes = [1,2,3,4,5,6,7,8]; while(size(Nodes,2) ~= 0) m = size(Nodes,2); mind = Inf;

for k = 1:m if (DistL(Nodes(k)) < mind) mind = DistL(Nodes(k)); u = Nodes(k); end end

Nodes = Nodes(Nodes~=u); nn = neighbors(u,2);

if (nn ~= 0) for k = 1:nn v = neighbors(u,2+k); alt = (DistL(u)+ TMat(u,v));

if(DistL(v)> alt) DistL(v)= alt;

Prev(v) = u;

end end end end dest = 8; orig = 1; while (Prev(dest) ~= orig) Nint = Prev(dest);

X(Nint,dest) = 7000; dest = Nint; end Nint = Prev(dest); X(Nint,dest) = 7000; dest = Nint; for k = 1:13

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if (p > 1) V(Links(k,1),Links(k,2)) = V(Links(k,1),Links(k,2)) + (X(Links(k,1),Links(k,2)) - V(Links(k,1),Links(k,2)))/p; else V(Links(k,1),Links(k,2)) = X(Links(k,1),Links(k,2)); end TMat(Links(k,1),Links(k,2)) = BPR(to,alpha,beta,C,V(Links(k,1),Links(k,2))); end temp = zeros(13,4);

for k = 1:13 temp(k,1) = Links(k,1); temp(k,2) = Links(k,2); temp(k,3) = V(Links(k,1),Links(k,2)); temp(k,4) = TMat(Links(k,1),Links(k,2)); end

end Results = zeros(13,4); for k = 1:13 Results(k,1) = Links(k,1); Results(k,2) = Links(k,2); Results(k,3) = V(Links(k,1),Links(k,2)); Results(k,4) = TMat(Links(k,1),Links(k,2)); end

end end

**Method of Successive Averages, MSA (Closure to link 1-3) close all; clear; clc;

a = [0.62, 0.56, 1.14, 0.15]; b = [5.14, 3.6, 6.86, 4];

Links = [1 2; 1 4; 2 3; 2 5; 3 4; 3 6; 4 7; 5 6; 5 8; 6 7; 6 8; 7 8]; neighbors = [1 2 2 4 0 0 0; 2 2 3 5 0 0 0; 3 2 4 6 0 0 0; 4 1 7 0 0 0 0; 5 2 6 8 0 0 0; 6 2 7 8 0 0 0; 7 1 8 0 0 0 0; 8 0 0 0 0 0 0];

iterations = [50, 500, 1000, 5000, 10000]; to = 5;

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C = 1500; for i = 1:4 alpha = a(i); beta = b(i);

for j = 1:5 V = zeros(8,8); N = iterations(j); TMat = Inf*ones(8,8); for k = 1:12 TMat(Links(k,1),Links(k,2)) = 10; end

for p = 1:N X = zeros(11,11);

%Initialization DistL = Inf*ones(8,1); Prev = Inf*ones(8,1); DistL(1) = 0; Nodes = [1,2,3,4,5,6,7,8];

while(size(Nodes,2) ~= 0) m = size(Nodes,2); mind = Inf;

for k = 1:m if (DistL(Nodes(k)) < mind) mind = DistL(Nodes(k)); u = Nodes(k); end end

Nodes = Nodes(Nodes~=u); nn = neighbors(u,2);

if (nn ~= 0) for k = 1:nn v = neighbors(u,2+k); alt = (DistL(u)+ TMat(u,v));

if(DistL(v)> alt) DistL(v)= alt;

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Prev(v) = u;

end end end end dest = 8; orig = 1; while (Prev(dest) ~= orig) Nint = Prev(dest);

X(Nint,dest) = 7000; dest = Nint;

end Nint = Prev(dest); X(Nint,dest) = 7000; dest = Nint;

for k = 1:12 if (p > 1) V(Links(k,1),Links(k,2)) = V(Links(k,1),Links(k,2)) + (X(Links(k,1),Links(k,2)) - V(Links(k,1),Links(k,2)))/p; else V(Links(k,1),Links(k,2)) = X(Links(k,1),Links(k,2)); end TMat(Links(k,1),Links(k,2)) = BPR(to,alpha,beta,C,V(Links(k,1),Links(k,2))); end temp = zeros(12,4);

for k = 1:12 temp(k,1) = Links(k,1); temp(k,2) = Links(k,2); temp(k,3) = V(Links(k,1),Links(k,2)); temp(k,4) = TMat(Links(k,1),Links(k,2)); end

end Results = zeros(12,4); for k = 1:12 Results(k,1) = Links(k,1); Results(k,2) = Links(k,2); Results(k,3) = V(Links(k,1),Links(k,2)); Results(k,4) = TMat(Links(k,1),Links(k,2)); end

end

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end

**Method of Successive Averages, MSA (Closure to link 2-3) close all; clear; clc;

a = [0.62, 0.56, 1.14, 0.15]; b = [5.14, 3.6, 6.86, 4];

Links = [1 3; 1 2; 1 4; 2 5; 3 4; 3 6; 4 7; 5 6; 5 8; 6 7; 6 8; 7 8]; neighbors = [1 3 2 3 4 0 0; 2 1 5 0 0 0 0; 3 2 4 6 0 0 0; 4 1 7 0 0 0 0; 5 2 6 8 0 0 0; 6 2 7 8 0 0 0; 7 1 8 0 0 0 0; 8 0 0 0 0 0 0];

iterations = [50, 500, 1000, 5000, 10000]; to = 5; C = 1500; for i = 1:4 alpha = a(i); beta = b(i);

for j = 1:5 V = zeros(8,8); N = iterations(j); TMat = Inf*ones(8,8); for k = 1:12 TMat(Links(k,1),Links(k,2)) = 5; end

for p = 1:N X = zeros(11,11);

%Initialization DistL = Inf*ones(8,1); Prev = Inf*ones(8,1); DistL(1) = 0; Nodes = [1,2,3,4,5,6,7,8];

while(size(Nodes,2) ~= 0) m = size(Nodes,2); mind = Inf;

for k = 1:m if (DistL(Nodes(k)) < mind)

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mind = DistL(Nodes(k)); u = Nodes(k); end end

Nodes = Nodes(Nodes~=u); nn = neighbors(u,2);

if (nn ~= 0) for k = 1:nn v = neighbors(u,2+k); alt = (DistL(u)+ TMat(u,v));

if(DistL(v)> alt) DistL(v)= alt;

Prev(v) = u;

end end end end dest = 8; orig = 1; while (Prev(dest) ~= orig) Nint = Prev(dest);

X(Nint,dest) = 7000; dest = Nint;

end Nint = Prev(dest); X(Nint,dest) = 7000; dest = Nint;

155

for k = 1:12 temp(k,1) = Links(k,1); temp(k,2) = Links(k,2); temp(k,3) = V(Links(k,1),Links(k,2)); temp(k,4) = TMat(Links(k,1),Links(k,2)); end

end Results = zeros(12,4); for k = 1:12 Results(k,1) = Links(k,1); Results(k,2) = Links(k,2); Results(k,3) = V(Links(k,1),Links(k,2)); Results(k,4) = TMat(Links(k,1),Links(k,2)); end

end end

**Method of Successive Averages, MSA (Closure to link 3-6) close all; clear; clc;

a = [0.62, 0.56, 1.14, 0.15]; b = [5.14, 3.6, 6.86, 4];

Links = [1 2; 1 3; 1 4; 2 3; 2 5; 3 4; 4 7; 5 6; 5 8; 6 7; 6 8; 7 8]; neighbors = [1 3 2 3 4 0 0; 2 2 3 5 0 0 0; 3 1 4 0 0 0 0; 4 1 7 0 0 0 0; 5 2 6 8 0 0 0; 6 2 7 8 0 0 0; 7 1 8 0 0 0 0; 8 0 0 0 0 0 0];

iterations = [50, 500, 1000, 5000, 10000]; to = 5; C = 1500; for i = 1:4 alpha = a(i); beta = b(i);

for j = 1:5 V = zeros(8,8); N = iterations(j);

156

TMat = Inf*ones(8,8); for k = 1:12 TMat(Links(k,1),Links(k,2)) = 5; end

for p = 1:N X = zeros(11,11);

%Initialization DistL = Inf*ones(8,1); Prev = Inf*ones(8,1); DistL(1) = 0; Nodes = [1,2,3,4,5,6,7,8];

while(size(Nodes,2) ~= 0) m = size(Nodes,2); mind = Inf;

for k = 1:m if (DistL(Nodes(k)) < mind) mind = DistL(Nodes(k)); u = Nodes(k); end end

Nodes = Nodes(Nodes~=u); nn = neighbors(u,2);

if (nn ~= 0) for k = 1:nn v = neighbors(u,2+k); alt = (DistL(u)+ TMat(u,v));

if(DistL(v)> alt) DistL(v)= alt;

Prev(v) = u;

end end end end dest = 8; orig = 1; while (Prev(dest) ~= orig) Nint = Prev(dest);

157

X(Nint,dest) = 7000; dest = Nint;

end Nint = Prev(dest); X(Nint,dest) = 7000; dest = Nint;

for k = 1:12 temp(k,1) = Links(k,1); temp(k,2) = Links(k,2); temp(k,3) = V(Links(k,1),Links(k,2)); temp(k,4) = TMat(Links(k,1),Links(k,2)); end

end Results = zeros(12,4); for k = 1:12 Results(k,1) = Links(k,1); Results(k,2) = Links(k,2); Results(k,3) = V(Links(k,1),Links(k,2)); Results(k,4) = TMat(Links(k,1),Links(k,2)); end

end end

158

**Method of Successive Averages, MSA (Closure to link 4-7) close all; clear; clc;

a = [0.62, 0.56, 1.14, 0.15]; b = [5.14, 3.6, 6.86, 4];

Links = [1 2; 1 3; 1 4; 2 3; 2 5; 3 4; 3 6; 5 6; 5 8; 6 7; 6 8; 7 8]; neighbors = [1 3 2 3 4 0 0; 2 2 3 5 0 0 0; 3 2 4 6 0 0 0; 4 0 0 0 0 0 0; 5 2 6 8 0 0 0; 6 2 7 8 0 0 0; 7 1 8 0 0 0 0; 8 0 0 0 0 0 0];

iterations = [50, 500, 1000, 5000, 10000]; to = 5; C = 1500; for i = 1:4 alpha = a(i); beta = b(i);

for j = 1:5 V = zeros(8,8); N = iterations(j); TMat = Inf*ones(8,8); for k = 1:12 TMat(Links(k,1),Links(k,2)) = 10; end

for p = 1:N X = zeros(11,11);

%Initialization DistL = Inf*ones(8,1); Prev = Inf*ones(8,1); DistL(1) = 0; Nodes = [1,2,3,4,5,6,7,8];

while(size(Nodes,2) ~= 0) m = size(Nodes,2); mind = Inf;

for k = 1:m if (DistL(Nodes(k)) < mind) mind = DistL(Nodes(k)); u = Nodes(k);

159

end end

Nodes = Nodes(Nodes~=u); nn = neighbors(u,2);

if (nn ~= 0) for k = 1:nn v = neighbors(u,2+k); alt = (DistL(u)+ TMat(u,v));

if(DistL(v)> alt) DistL(v)= alt;

Prev(v) = u;

end end end end dest = 8; orig = 1; while (Prev(dest) ~= orig) Nint = Prev(dest);

X(Nint,dest) = 7000; dest = Nint;

end Nint = Prev(dest); X(Nint,dest) = 7000; dest = Nint;

for k = 1:12 temp(k,1) = Links(k,1);

160

temp(k,2) = Links(k,2); temp(k,3) = V(Links(k,1),Links(k,2)); temp(k,4) = TMat(Links(k,1),Links(k,2)); end

end Results = zeros(12,4); for k = 1:12 Results(k,1) = Links(k,1); Results(k,2) = Links(k,2); Results(k,3) = V(Links(k,1),Links(k,2)); Results(k,4) = TMat(Links(k,1),Links(k,2)); end

end end

**Method of Successive Averages, MSA (Closure to link 5-6) close all; clear; clc;

a = [0.62, 0.56, 1.14, 0.15]; b = [5.14, 3.6, 6.86, 4];

Links = [1 2; 1 3; 1 4; 2 3; 2 5; 3 4; 3 6; 4 7; 5 8; 6 7; 6 8; 7 8]; neighbors = [1 3 2 3 4 0 0; 2 2 3 5 0 0 0; 3 2 4 6 0 0 0; 4 1 7 0 0 0 0; 5 1 8 0 0 0 0; 6 2 7 8 0 0 0; 7 1 8 0 0 0 0; 8 0 0 0 0 0 0];

iterations = [50, 500, 1000, 5000, 10000]; to = 5; C = 1500; for i = 1:4 alpha = a(i); beta = b(i);

for j = 1:5 V = zeros(8,8); N = iterations(j); TMat = Inf*ones(8,8); for k = 1:12 TMat(Links(k,1),Links(k,2)) = 10;

161

end

for p = 1:N X = zeros(11,11);

%Initialization DistL = Inf*ones(8,1); Prev = Inf*ones(8,1); DistL(1) = 0; Nodes = [1,2,3,4,5,6,7,8];

while(size(Nodes,2) ~= 0) m = size(Nodes,2); mind = Inf;

for k = 1:m if (DistL(Nodes(k)) < mind) mind = DistL(Nodes(k)); u = Nodes(k); end end

Nodes = Nodes(Nodes~=u); nn = neighbors(u,2);

if (nn ~= 0) for k = 1:nn v = neighbors(u,2+k); alt = (DistL(u)+ TMat(u,v));

if(DistL(v)> alt) DistL(v)= alt;

Prev(v) = u;

end end end end dest = 8; orig = 1; while (Prev(dest) ~= orig) Nint = Prev(dest);

X(Nint,dest) = 7000; dest = Nint;

162

end Nint = Prev(dest); X(Nint,dest) = 7000; dest = Nint;

for k = 1:12 temp(k,1) = Links(k,1); temp(k,2) = Links(k,2); temp(k,3) = V(Links(k,1),Links(k,2)); temp(k,4) = TMat(Links(k,1),Links(k,2)); end

end Results = zeros(12,4); for k = 1:12 Results(k,1) = Links(k,1); Results(k,2) = Links(k,2); Results(k,3) = V(Links(k,1),Links(k,2)); Results(k,4) = TMat(Links(k,1),Links(k,2)); end

end end

**Method of Successive Averages, MSA (Closure to link 6-7) close all; clear; clc;

a = [0.62, 0.56, 1.14, 0.15]; b = [5.14, 3.6, 6.86, 4];

163

Links = [1 2; 1 3; 1 4; 2 3; 2 5; 3 4; 3 6; 4 7; 5 6; 5 8; 6 8; 7 8]; neighbors = [1 3 2 3 4 0 0; 2 2 3 5 0 0 0; 3 2 4 6 0 0 0; 4 1 7 0 0 0 0; 5 2 6 8 0 0 0; 6 1 8 0 0 0 0; 7 1 8 0 0 0 0; 8 0 0 0 0 0 0];

iterations = [50, 500, 1000, 5000, 10000]; to = 5; C = 1500; for i = 1:4 alpha = a(i); beta = b(i);

for j = 1:5 V = zeros(8,8); N = iterations(j); TMat = Inf*ones(8,8); for k = 1:12 TMat(Links(k,1),Links(k,2)) = 10; end

for p = 1:N X = zeros(11,11);

%Initialization DistL = Inf*ones(8,1); Prev = Inf*ones(8,1); DistL(1) = 0; Nodes = [1,2,3,4,5,6,7,8];

while(size(Nodes,2) ~= 0) m = size(Nodes,2); mind = Inf;

for k = 1:m if (DistL(Nodes(k)) < mind) mind = DistL(Nodes(k)); u = Nodes(k); end end

Nodes = Nodes(Nodes~=u); nn = neighbors(u,2);

if (nn ~= 0)

164

for k = 1:nn v = neighbors(u,2+k); alt = (DistL(u)+ TMat(u,v));

if(DistL(v)> alt) DistL(v)= alt;

Prev(v) = u;

end end end end dest = 8; orig = 1; while (Prev(dest) ~= orig) Nint = Prev(dest);

X(Nint,dest) = 7000; dest = Nint;

end Nint = Prev(dest); X(Nint,dest) = 7000; dest = Nint;

for k = 1:12 temp(k,1) = Links(k,1); temp(k,2) = Links(k,2); temp(k,3) = V(Links(k,1),Links(k,2)); temp(k,4) = TMat(Links(k,1),Links(k,2)); end

end Results = zeros(12,4); for k = 1:12

165

Results(k,1) = Links(k,1); Results(k,2) = Links(k,2); Results(k,3) = V(Links(k,1),Links(k,2)); Results(k,4) = TMat(Links(k,1),Links(k,2)); end

end end

**Method of Successive Averages, MSA (Closure to link 6-8) close all; clear; clc;

a = [0.62, 0.56, 1.14, 0.15]; b = [5.14, 3.6, 6.86, 4];

Links = [1 2; 1 4; 2 3; 2 5; 3 4; 3 6; 4 7; 5 6; 5 8; 6 7; 7 8]; neighbors = [1 2 2 4 0 0 0; 2 2 3 5 0 0 0; 3 2 4 6 0 0 0; 4 1 7 0 0 0 0; 5 2 6 8 0 0 0; 6 1 7 0 0 0 0; 7 1 8 0 0 0 0; 8 0 0 0 0 0 0];

iterations = [50, 500, 1000, 5000, 10000]; to = 5; C = 1500; for i = 1:4 alpha = a(i); beta = b(i);

for j = 1:5 V = zeros(8,8); N = iterations(j); TMat = Inf*ones(8,8); for k = 1:12 TMat(Links(k,1),Links(k,2)) = 10; end

for p = 1:N X = zeros(11,11);

%Initialization

166

DistL = Inf*ones(8,1); Prev = Inf*ones(8,1); DistL(1) = 0; Nodes = [1,2,3,4,5,6,7,8]; while(size(Nodes,2) ~= 0) m = size(Nodes,2); mind = Inf;

for k = 1:m if (DistL(Nodes(k)) < mind) mind = DistL(Nodes(k)); u = Nodes(k); end end

Nodes = Nodes(Nodes~=u); nn = neighbors(u,2);

if (nn ~= 0) for k = 1:nn v = neighbors(u,2+k); alt = (DistL(u)+ TMat(u,v));

if(DistL(v)> alt) DistL(v)= alt;

Prev(v) = u;

end end end end dest = 8; orig = 1; while (Prev(dest) ~= orig) Nint = Prev(dest);

X(Nint,dest) = 7000; dest = Nint; end Nint = Prev(dest); X(Nint,dest) = 7000; dest = Nint;

167

for k = 1:12 temp(k,1) = Links(k,1); temp(k,2) = Links(k,2); temp(k,3) = V(Links(k,1),Links(k,2)); temp(k,4) = TMat(Links(k,1),Links(k,2)); end

end Results = zeros(12,4); for k = 1:12 Results(k,1) = Links(k,1); Results(k,2) = Links(k,2); Results(k,3) = V(Links(k,1),Links(k,2)); Results(k,4) = TMat(Links(k,1),Links(k,2)); end

end end

**Method of Successive Averages, MSA (Closure to link 5-8) close all; clear; clc;

a = [0.62, 0.56, 1.14, 0.15]; b = [5.14, 3.6, 6.86, 4];

Links = [1 2; 1 3; 1 4; 2 3; 2 5; 3 4; 3 6; 4 7; 5 6; 6 7; 6 8; 7 8]; neighbors = [1 3 2 3 4 0 0; 2 2 3 5 0 0 0; 3 2 4 6 0 0 0; 4 1 7 0 0 0 0; 5 1 6 0 0 0 0; 6 2 7 8 0 0 0; 7 1 8 0 0 0 0; 8 0 0 0 0 0 0];

iterations = [50, 500, 1000, 5000, 10000];

168

to = 5; C = 1500; for i = 1:4 alpha = a(i); beta = b(i);

for j = 1:5 V = zeros(8,8); N = iterations(j); TMat = Inf*ones(8,8); for k = 1:12 TMat(Links(k,1),Links(k,2)) = 10; end

for p = 1:N X = zeros(11,11);

%Initialization DistL = Inf*ones(8,1); Prev = Inf*ones(8,1); DistL(1) = 0; Nodes = [1,2,3,4,5,6,7,8];

while(size(Nodes,2) ~= 0) m = size(Nodes,2); mind = Inf;

for k = 1:m if (DistL(Nodes(k)) < mind) mind = DistL(Nodes(k)); u = Nodes(k); end end

Nodes = Nodes(Nodes~=u); nn = neighbors(u,2);

if (nn ~= 0) for k = 1:nn v = neighbors(u,2+k); alt = (DistL(u)+ TMat(u,v));

if(DistL(v)> alt) DistL(v)= alt;

169

Prev(v) = u;

end end end end dest = 8; orig = 1; while (Prev(dest) ~= orig) Nint = Prev(dest);

X(Nint,dest) = 7000; dest = Nint;

end Nint = Prev(dest); X(Nint,dest) = 7000; dest = Nint;

for k = 1:12 temp(k,1) = Links(k,1); temp(k,2) = Links(k,2); temp(k,3) = V(Links(k,1),Links(k,2)); temp(k,4) = TMat(Links(k,1),Links(k,2)); end

end Results = zeros(12,4); for k = 1:12 Results(k,1) = Links(k,1); Results(k,2) = Links(k,2); Results(k,3) = V(Links(k,1),Links(k,2)); Results(k,4) = TMat(Links(k,1),Links(k,2)); end

170

end end

Multiple Bridge Closures

** Method of Successive Averages, MSA (Closure to links 6-8, 2-3, 6-7, 5-6, 5-8) close all; clear; clc;

a = [0.62, 0.56, 1.14, 0.15]; b = [5.14, 3.6, 6.86, 4];

Links = [1 2; 1 3; 1 4; 2 5; 3 4; 3 6; 4 7; 7 8]; neighbors = [1 3 2 3 4 0 0; 2 1 5 0 0 0 0; 3 2 4 6 0 0 0; 4 1 7 0 0 0 0; 5 0 0 0 0 0 0; 6 0 0 0 0 0 0; 7 1 8 0 0 0 0; 8 0 0 0 0 0 0];

iterations = [50, 500, 1000, 5000, 10000]; to = 5; C = 1500; for i = 1:4 alpha = a(i); beta = b(i);

for j = 1:5 V = zeros(8,8); N = iterations(j); TMat = Inf*ones(8,8); for k = 1:8 TMat(Links(k,1),Links(k,2)) = 10; end

for p = 1:N X = zeros(11,11);

%Initialization DistL = Inf*ones(8,1); Prev = Inf*ones(8,1); DistL(1) = 0; Nodes = [1,2,3,4,5,6,7,8];

while(size(Nodes,2) ~= 0)

171

m = size(Nodes,2); mind = Inf;

for k = 1:m if (DistL(Nodes(k)) < mind) mind = DistL(Nodes(k)); u = Nodes(k); end end

Nodes = Nodes(Nodes~=u); nn = neighbors(u,2);

if (nn ~= 0) for k = 1:nn v = neighbors(u,2+k); alt = (DistL(u)+ TMat(u,v));

if(DistL(v)> alt) DistL(v)= alt;

Prev(v) = u;

end end end end dest = 8; orig = 1; while (Prev(dest) ~= orig) Nint = Prev(dest);

X(Nint,dest) = 7000; dest = Nint;

end Nint = Prev(dest); X(Nint,dest) = 7000; dest = Nint;

for k = 1:8 if (p > 1) V(Links(k,1),Links(k,2)) = V(Links(k,1),Links(k,2)) + (X(Links(k,1),Links(k,2)) - V(Links(k,1),Links(k,2)))/p; else V(Links(k,1),Links(k,2)) = X(Links(k,1),Links(k,2));

172

end TMat(Links(k,1),Links(k,2)) = BPR(to,alpha,beta,C,V(Links(k,1),Links(k,2))); end temp = zeros(8,4);

for k = 1:8 temp(k,1) = Links(k,1); temp(k,2) = Links(k,2); temp(k,3) = V(Links(k,1),Links(k,2)); temp(k,4) = TMat(Links(k,1),Links(k,2)); end

end Results = zeros(8,4); for k = 1:8 Results(k,1) = Links(k,1); Results(k,2) = Links(k,2); Results(k,3) = V(Links(k,1),Links(k,2)); Results(k,4) = TMat(Links(k,1),Links(k,2)); end

end end

Restoration of link 5-8

** Method of Successive Averages, MSA (Closure to links 6-8, 2-3, 6-7, 5-6) close all; clear; clc;

a = [0.62, 0.56, 1.14, 0.15]; b = [5.14, 3.6, 6.86, 4];

Links = [1 2; 1 3; 1 4; 2 5; 3 4; 3 6; 4 7; 5 8; 7 8]; neighbors = [1 3 2 3 4 0 0; 2 1 5 0 0 0 0; 3 2 4 6 0 0 0; 4 1 7 0 0 0 0; 5 1 8 0 0 0 0; 6 0 0 0 0 0 0; 7 1 8 0 0 0 0; 8 0 0 0 0 0 0];

iterations = [50, 500, 1000, 5000, 10000]; to = 5; C = 1500; for i = 1:4

173

alpha = a(i); beta = b(i); for j = 1:5 V = zeros(8,8); N = iterations(j); TMat = Inf*ones(8,8); for k = 1:9 TMat(Links(k,1),Links(k,2)) = 10; end

for p = 1:N X = zeros(11,11);

%Initialization DistL = Inf*ones(8,1); Prev = Inf*ones(8,1); DistL(1) = 0; Nodes = [1,2,3,4,5,6,7,8];

while(size(Nodes,2) ~= 0) m = size(Nodes,2); mind = Inf;

for k = 1:m if (DistL(Nodes(k)) < mind) mind = DistL(Nodes(k)); u = Nodes(k); end end

Nodes = Nodes(Nodes~=u); nn = neighbors(u,2);

if (nn ~= 0) for k = 1:nn v = neighbors(u,2+k); alt = (DistL(u)+ TMat(u,v));

if(DistL(v)> alt) DistL(v)= alt;

Prev(v) = u;

end

174

end end end dest = 8; orig = 1; while (Prev(dest) ~= orig) Nint = Prev(dest);

X(Nint,dest) = 7000; dest = Nint;

end Nint = Prev(dest); X(Nint,dest) = 7000; dest = Nint;

for k = 1:9 if (p > 1) V(Links(k,1),Links(k,2)) = V(Links(k,1),Links(k,2)) + (X(Links(k,1),Links(k,2)) - V(Links(k,1),Links(k,2)))/p; else V(Links(k,1),Links(k,2)) = X(Links(k,1),Links(k,2)); end TMat(Links(k,1),Links(k,2)) = BPR(to,alpha,beta,C,V(Links(k,1),Links(k,2))); end temp = zeros(9,4);

for k = 1:9 temp(k,1) = Links(k,1); temp(k,2) = Links(k,2); temp(k,3) = V(Links(k,1),Links(k,2)); temp(k,4) = TMat(Links(k,1),Links(k,2)); end

end Results = zeros(9,4); for k = 1:9 Results(k,1) = Links(k,1); Results(k,2) = Links(k,2); Results(k,3) = V(Links(k,1),Links(k,2)); Results(k,4) = TMat(Links(k,1),Links(k,2)); end

end end

175

Restoration of link 5-8; 5-6

** Method of Successive Averages, MSA (Closure to links 6-8, 2-3, 6-7) close all; clear; clc;

a = [0.62, 0.56, 1.14, 0.15]; b = [5.14, 3.6, 6.86, 4];

Links = [1 2; 1 3; 1 4; 2 5; 3 4; 3 6; 4 7; 5 6; 5 8; 7 8]; neighbors = [1 3 2 3 4 0 0; 2 1 5 0 0 0 0; 3 2 4 6 0 0 0; 4 1 7 0 0 0 0; 5 2 6 8 0 0 0; 6 0 0 0 0 0 0; 7 1 8 0 0 0 0; 8 0 0 0 0 0 0];

iterations = [50, 500, 1000, 5000, 10000]; to = 5; C = 1500; for i = 1:4 alpha = a(i); beta = b(i);

for j = 1:5 V = zeros(8,8); N = iterations(j); TMat = Inf*ones(8,8); for k = 1:10 TMat(Links(k,1),Links(k,2)) = 10; end

for p = 1:N X = zeros(11,11);

%Initialization DistL = Inf*ones(8,1); Prev = Inf*ones(8,1); DistL(1) = 0; Nodes = [1,2,3,4,5,6,7,8];

while(size(Nodes,2) ~= 0) m = size(Nodes,2); mind = Inf;

for k = 1:m if (DistL(Nodes(k)) < mind) mind = DistL(Nodes(k));

176

u = Nodes(k); end end

Nodes = Nodes(Nodes~=u); nn = neighbors(u,2);

if (nn ~= 0) for k = 1:nn v = neighbors(u,2+k); alt = (DistL(u)+ TMat(u,v));

if(DistL(v)> alt) DistL(v)= alt;

Prev(v) = u;

end end end end dest = 8; orig = 1; while (Prev(dest) ~= orig) Nint = Prev(dest);

X(Nint,dest) = 7000; dest = Nint;

end Nint = Prev(dest); X(Nint,dest) = 7000; dest = Nint;

for k = 1:10 if (p > 1) V(Links(k,1),Links(k,2)) = V(Links(k,1),Links(k,2)) + (X(Links(k,1),Links(k,2)) - V(Links(k,1),Links(k,2)))/p; else V(Links(k,1),Links(k,2)) = X(Links(k,1),Links(k,2)); end TMat(Links(k,1),Links(k,2)) = BPR(to,alpha,beta,C,V(Links(k,1),Links(k,2))); end temp = zeros(10,4);

for k = 1:10

177

temp(k,1) = Links(k,1); temp(k,2) = Links(k,2); temp(k,3) = V(Links(k,1),Links(k,2)); temp(k,4) = TMat(Links(k,1),Links(k,2)); end

end Results = zeros(10,4); for k = 1:10 Results(k,1) = Links(k,1); Results(k,2) = Links(k,2); Results(k,3) = V(Links(k,1),Links(k,2)); Results(k,4) = TMat(Links(k,1),Links(k,2)); end

end end

Restoration of link 5-8; 5-6; 6-7

** Method of Successive Averages, MSA (Closure to links 6-8, 2-3) close all; clear; clc;

a = [0.62, 0.56, 1.14, 0.15]; b = [5.14, 3.6, 6.86, 4];

Links = [1 2; 1 3; 1 4; 2 5; 3 4; 3 6; 4 7; 5 6; 5 8; 6 7; 7 8]; neighbors = [1 3 2 3 4 0 0; 2 1 5 0 0 0 0; 3 2 4 6 0 0 0; 4 1 7 0 0 0 0; 5 2 6 8 0 0 0; 6 1 7 0 0 0 0; 7 1 8 0 0 0 0; 8 0 0 0 0 0 0];

iterations = [50, 500, 1000, 5000, 10000]; to = 5; C = 1500; for i = 1:4 alpha = a(i); beta = b(i);

for j = 1:5 V = zeros(8,8); N = iterations(j);

178

TMat = Inf*ones(8,8); for k = 1:11 TMat(Links(k,1),Links(k,2)) = 10; end

for p = 1:N X = zeros(11,11);

%Initialization DistL = Inf*ones(8,1); Prev = Inf*ones(8,1); DistL(1) = 0; Nodes = [1,2,3,4,5,6,7,8];

while(size(Nodes,2) ~= 0) m = size(Nodes,2); mind = Inf;

for k = 1:m if (DistL(Nodes(k)) < mind) mind = DistL(Nodes(k)); u = Nodes(k); end end

Nodes = Nodes(Nodes~=u); nn = neighbors(u,2);

if (nn ~= 0) for k = 1:nn v = neighbors(u,2+k); alt = (DistL(u)+ TMat(u,v));

if(DistL(v)> alt) DistL(v)= alt;

Prev(v) = u;

end end end end dest = 8; orig = 1; while (Prev(dest) ~= orig) Nint = Prev(dest);

179

X(Nint,dest) = 7000; dest = Nint;

end Nint = Prev(dest); X(Nint,dest) = 7000; dest = Nint;

for k = 1:11 if (p > 1) V(Links(k,1),Links(k,2)) = V(Links(k,1),Links(k,2)) + (X(Links(k,1),Links(k,2)) - V(Links(k,1),Links(k,2)))/p; else V(Links(k,1),Links(k,2)) = X(Links(k,1),Links(k,2)); end TMat(Links(k,1),Links(k,2)) = BPR(to,alpha,beta,C,V(Links(k,1),Links(k,2))); end temp = zeros(11,4);

for k = 1:11 temp(k,1) = Links(k,1); temp(k,2) = Links(k,2); temp(k,3) = V(Links(k,1),Links(k,2)); temp(k,4) = TMat(Links(k,1),Links(k,2)); end

end Results = zeros(11,4); for k = 1:11 Results(k,1) = Links(k,1); Results(k,2) = Links(k,2); Results(k,3) = V(Links(k,1),Links(k,2)); Results(k,4) = TMat(Links(k,1),Links(k,2)); end

end end

Restoration of link 5-8; 5-6; 6-7; 2-3

** Method of Successive Averages, MSA (Closure to links 6-8) close all; clear; clc;

180

a = [0.62, 0.56, 1.14, 0.15]; b = [5.14, 3.6, 6.86, 4];

Links = [1 2; 1 3; 1 4; 2 3; 2 5; 3 4; 3 6; 4 7; 5 6; 5 8; 6 7; 7 8]; neighbors = [1 3 2 3 4 0 0; 2 2 3 5 0 0 0; 3 2 4 6 0 0 0; 4 1 7 0 0 0 0; 5 2 6 8 0 0 0; 6 1 7 0 0 0 0; 7 1 8 0 0 0 0; 8 0 0 0 0 0 0];

iterations = [50, 500, 1000, 5000, 10000]; to = 5; C = 1500; for i = 1:4 alpha = a(i); beta = b(i);

for j = 1:5 V = zeros(8,8); N = iterations(j); TMat = Inf*ones(8,8); for k = 1:12 TMat(Links(k,1),Links(k,2)) = 10; end

for p = 1:N X = zeros(11,11);

%Initialization DistL = Inf*ones(8,1); Prev = Inf*ones(8,1); DistL(1) = 0; Nodes = [1,2,3,4,5,6,7,8];

while(size(Nodes,2) ~= 0) m = size(Nodes,2); mind = Inf;

for k = 1:m if (DistL(Nodes(k)) < mind) mind = DistL(Nodes(k)); u = Nodes(k); end end

181

Nodes = Nodes(Nodes~=u); nn = neighbors(u,2);

if (nn ~= 0) for k = 1:nn v = neighbors(u,2+k); alt = (DistL(u)+ TMat(u,v));

if(DistL(v)> alt) DistL(v)= alt;

Prev(v) = u;

end end end end dest = 8; orig = 1; while (Prev(dest) ~= orig) Nint = Prev(dest);

X(Nint,dest) = 7000; dest = Nint;

end Nint = Prev(dest); X(Nint,dest) = 7000; dest = Nint;

for k = 1:12 temp(k,1) = Links(k,1); temp(k,2) = Links(k,2); temp(k,3) = V(Links(k,1),Links(k,2)); temp(k,4) = TMat(Links(k,1),Links(k,2));

182

end

end Results = zeros(12,4); for k = 1:12 Results(k,1) = Links(k,1); Results(k,2) = Links(k,2); Results(k,3) = V(Links(k,1),Links(k,2)); Results(k,4) = TMat(Links(k,1),Links(k,2)); end

end end

183

APPENDIX C

POST-HAZARD BRIDGE AND ROAD CLOSURE TIMES

Table C. 1 Post-hazard restoration times for interstate bridges

Partial Complete Closure Date Date Hazard Event Closed Bridge Location Restorati Restoration Duration Comments Data Source Closed Opened on (days) (days) (days)

Interstate 10 twin Hurricane http://www.aaroads.com/gui spans over Lake 29-Aug-05 5-Jan-06 Louisiana 46 83 83 - Katrina de.php?page=hkatrinala Pontchartrain The lengthy span of Interstate 10 between Gautier and Moss Point Interstate 10 West suffered severe damage during the Hurricane http://www.aaroads.com/gui Pascagoula 29-Aug-05 2-Oct-05 Mississippi 20 31 31 height of Katrina. The strong Katrina de.php?page=hkatrinala Bridges winds pushed a barge into the bridge causing several of the decking components to shift. http://www.clarionledger.co m/story/news/2015/08/18/re Hurricane Interstate 110 29-Aug-05 - Mississippi 7 - - - building-highways- Katrina Biloxi Back Bay bridges/31953661/ Retrieved June 5, 2017 The Bankhead Tunnel was closed during the height of the storm but Interstate 10 reopened following Katrina's (Mobile Bayway) Hurricane departure. The Wallace Tunnel http://www.aaroads.com/gui and U.S. 90 & 98 29-Aug-05 2-Sep-05 Alabama - 3 3 Katrina suffered minor flooding and de.php?page=hkatrinala (Battleship remained open to at least one lane Causeway) of traffic per direction in the wake of the departing storm. Interstate 10 https://smartech.gatech.edu/ (Mobile Bayway) Hurricane 26-Feb- bitstream/handle/1853/9431/ and U.S. 90 & 98 30-Aug-05 Alabama - 180 180 - Katrina 06 Katrina.pdf?sequence=1&is (Battleship Allowed=y Causeway) Exit 30 eastbound Five concrete bridge spans Hurricane 29-Aug- http://www.aaroads.com/gui on-ramp to 29-Aug-05 Alabama - 365 365 associated with ramp were Katrina 06 de.php?page=hkatrinala Interstate 10 destroyed. It took 17 days to restore two- Interstate 10 https://www.parsons.com/pr 20-Nov- way traffic to the westbound Hurricane Ivan Bridge over 16-Sep-04 Florida 17 66 66 ojects/pages/i-10-escambia- 04 bridge, and 66 days for complete Escambia Bay bay.aspx reconstruction

184

Table C. 1 - continued

Partial Complete Closure Date Date Hazard Event Closed Bridge Location Restorati Restoration Duration Comments Data Source Closed Opened on (days) (days) (days)

http://www.wral.com/a- week-after-matthew- Hurricane US-74 Interstate 17-Oct- North 10-Oct-16 - 7 7 Flooding interstate-95-back-open- Matthew 95 16 Carolina through-nc/16125177/ Retrieved June 9, 2017 http://www.wjcl.com/article/ blue-moon-cafe-owner- Hurricane Interstate 95 7-Oct-16 9-Oct-16 Florida - 2 2 - offers-troops-a-reminder-of- Matthew bridge home-cooking/10042438 Retrieved June 19, 2017 The new eastbound I-10 Tex http://www.scpr.org/news/2 Wash Bridge near Desert Center 015/09/24/54619/i-10- I-10 Tex Wash 24-Sep- Storm 19-Jul-15 California - 67 67 has reopened two months after a bridge-reopens-following- Bridge 15 July 19 storm washed away the storm-washing-out-pr/ original bridge. Retrieved June 9, 2017 http://www.ajc.com/news/lo Suspected arson caused PVC cal/northbound-lanes- 12-May- tubing stored under bridge to reopen- Fire Interstate 85N 30-Mar-17 Georgia - 43 43 17 catch fire, critically weakening atlanta/8FJkU2X75t8tMILw structure and causing collapse kkOuUM/ Retrieved June 1, 2017 This bridge was damaged due to fire form a tanker truck accident https://ntl.bts.gov/lib/47000/ Interstate 75 / 20-Jun- on 06/04/08. Southbound traffic 47800/47813/FDOT- Fire 4-Jun-08 Florida 1 16 16 130103 08 on I-75 was directed to BDK83-977-11-rpt.pdf Northbound bridge during the Retrieved June 7, 2017 repair https://ntl.bts.gov/lib/47000/ Fuel tanker truck lost control 47800/47813/FDOT- Fire Interstate 95 Florida - 1 1 while exiting I-95 to SR-836 in BDK83-977-11-rpt.pdf Miami. Retrieved June 7, 2017 https://web.archive.org/web/ 20090821192159/http://ww 9 mile road bridge 11-Dec- w.macombdaily.com/articles Tanker accident 15-Jul-09 Michigan - 149 149 Collapsed due to tanker accident at Interstate 75 09 /2009/07/17/news/srv00000 05860485.txt Retrieved June 1, 2017

185

Table C. 1 - continued

Partial Complete Closure Date Date Hazard Event Closed Bridge Location Restorati Restoration Duration Comments Data Source Closed Opened on (days) (days) (days)

1. https://www.thinkreliability. The NTSB said that com/case_studies/root- undersized gusset plates, Minneapolis cause-analysis-of-the-i-35- increased concrete surfacing load, Interstate 35W bridge-collapse/ Retrieved Undersized 18-Sep- and weight of construction bridge over 1-Aug-07 Minnesota - 414 414 June 1, 2017 2. gusset plates 08 supplies/equipment caused this the Mississippi https://www.thinkreliability. collapse. The rebuilt I-35W Saint River com/wp- Anthony Falls Bridge was content/uploads/2016/06/C reopened on 18 September 2008. M-i-35v4.pdf Retrieved June 1, 2017 Barge struck one pier of the http://newsok.com/article/89 bridge causing a partial collapse Barge Collision Interstate 40 26-May-02 29-Jul-02 Oklahoma - 63 63 4007 Retrieved June 1, of a Concrete bridge for vehicle 2017 traffic over Arkansas River http://www.truckinginfo.co A fuel tanker overturned Interstate 285 m/news/story/2001/07/i- Fuel tank underneath the bridge, engulfing bridge over GA- 9-Jun-01 7-Jul-01 Georgia - 28 28 285-to-reopen-this- explosion the bridge in fire. Reopened after 400 weekend.aspx Retrieved four week repair June 1, 2017 The collapse was caused by a southbound semi-trailer https://archive.is/201306151 truck from Canada hauling 93737/www.theprovince.co an oversize load to Vancouver, m/news/bridge+collapses+in Oversize truck Interstate 5 Skagit 19-Jun- Washington, directly damaging 23-May-13 Washington - 27 27 to+Skagit+River+Washingto load River bridge 13 sway struts and, indirectly, the n+motorists+reportedly+wat compression chords in the er/8427876/story.html overhead steel frame (trusswork) Retrieved June 1, 2017 on the northernmost span of the bridge. 1. https://www.usatoday.com/s tory/news/nation/2015/07/19 /i-10-collapse- california/30399815/ Abutment displacement due to 2. Interstate 10 30-Sep- Southern stream meander, which caused Abutment scour 20-Jul-15 - 41 41 http://www.azcentral.com/st bridge 15 California abutment scour. Partial bridge ory/news/local/arizona/2015 collapse of span /09/25/washed-out- interstate-10-bridge-in- california-desert- reopens/72784358/ Retrieved June 1, 2017

186

Table C. 1 - continued

Partial Complete Closure Date Date Hazard Event Closed Bridge Location Restorati Restoration Duration Comments Data Source Closed Opened on (days) (days) (days)

Two tension rods and a crossbeam from a recently installed repair collapsed during the evening commute, causing the bridge to be closed temporarily. During an extended closure as part of the eastern span replacement of the http://www.sfgate.com/baya San Francisco – Tension rods San Francisco Oakland Bay rea/article/Bridge-parts- Oakland Bay and crossbeam 27-Oct-09 2-Nov-09 California - 6 6 Bridge over the 2009 Labor Day couldn-t-take-the-wind- Bridge. Interstate collapse holiday, a critical failure was 3282778.php Retrieved 80 discovered in an eyebar that June 1, 2017 would have been significant enough to cause a closure of the bridge.[47] Emergency repairs took 70 hours and were completed on 9 September 2009. This is the repair that failed. As part of a construction project, a girder twisted, sagged, and fell https://www.ntsb.gov/investi onto I-70. An SUV was driving C-470 overpass 17-May- gations/AccidentReports/Re Girder collapse 15-May-04 Colorado - 3 3 eastbound and struck the fallen over I-70 04 ports/HAB0601.pdf girder; the top of the vehicle was Retrieved June 1,2017 torn off and the three passengers died instantly http://www.constructionequi pmentguide.com/crews- Traffic crash - 31-Mar- Collapse Traffic Crash Caused I-95 Bridge 26-Mar-04 Connecticut 3 6 6 reopen-fire-closed-i-95-in- Fire 04 Fire – Bridgeport, CT six-days/4416 Retrieved June 2, 2017 A loaded gasoline tanker heading north on I-65 slammed into a pier supporting southbound lanes http://aehof.eng.ua.edu/mem 11-Feb- directly overhead. The raging of bers/emergency-i-65-bridge- Fire I-65 Bridge 5-Jan-02 Alabama - 37 37 02 the inevitable fire compromised replacement/ Retrieved the bridge’s steel June 2, 2017 girders. Rebuilding began January 21 Authorities said a tanker carrying http://www.firehouse.com/n fuel overturned in a curve about 7 ews/10516690/fuel-tanker- Intersection I-65 30-Nov- a.m., spilling an estimated 9,000 flips-burns-at-busy- Fire 21-Oct-04 Alabama - 40 40 and I 20/59 04 gallons of fuel that erupted into alabama-interstate- flames and sent a huge column of interchange Retrieved June inky black smoke skyward. 2, 2017

187

Table C. 1 - continued

Partial Complete Closure Date Date Hazard Event Closed Bridge Location Restorati Restoration Duration Comments Data Source Closed Opened on (days) (days) (days)

1. http://www.upi.com/Archive s/1996/03/21/Fire-damaged- The I-95 fire broke out the I-95-reopens-in- morning of March 13, 1996, in an Phila/7439827384400/ Fire I-95 Bridge 13-Mar-96 Sep-96 Pennsylvania 8 180 180 illegal tire dump under the 2. highway in Port Richmond and http://www.philly.com/phill went to eight alarms. y/blogs/real-time/Atlanta- Interstate-fire-recalls-Philly- I-95-fire-21-years-ago.html Retrieved June 2, 2017 http://www.equipmentworld .com/wp- content/uploads/sites/91/201 2/08/U.S.-Bridge-Failure- Oakland Bay Partial Collapse in Earthquake – Earthquake 17-Oct-89 Nov-89 California 30 30 30 Listing-from-Timothy-G.- Bridge San Francisco, CA Galarnyk-CEO-of- Construction-Risk- Management.pdf Retrieved June 2, 2017 1. http://www.equipmentworld .com/wp- content/uploads/sites/91/201 2/08/U.S.-Bridge-Failure- Listing-from-Timothy-G.- Galarnyk-CEO-of- Mianus River Collapse Metal Fatigue – Construction-Risk- Metal Fatigue 28-Jun-83 Nov-83 Connecticut - 150 150 Bridge (I-95) Greenwich, CT Management.pdf Retrieved June 2, 2017 2. https://www.revolvy.com/m ain/index.php?s=Mianus%2 0River%20Bridge&item_ty pe=topic Retrieved June 5, 2017 http://www.nj.com/news/ind I-287 over Bridge Collapses Due to Flood – Morris ex.ssf/2011/09/miracle_on_i Flood 28-Aug-11 1-Sep-11 New Jersey 2 4 4 Rockaway River County, NJ -287_how_crews_put.html Retrieved June 5, 2017

188

Table C. 1 - continued

Partial Complete Closure Date Date Hazard Event Closed Bridge Location Restorati Restoration Duration Comments Data Source Closed Opened on (days) (days) (days)

http://www.sfgate.com/baya MacArthur rea/article/One-MacArthur- Collapse Due to Traffic Crash Fire Bridge/Freeway 29-Apr-07 7-May-07 California - 8 8 freeway-connector-reopens- Fire – Oakland, CA (I-880 connector) 2597008.php Retrieved June 6, 2017 http://www.sfgate.com/baya I-580 connector 24-May- Collapse Due to Traffic Crash rea/article/I-580-connector- Fire 29-Apr-07 California - 26 26 (MacArthur Maze) 07 Fire – Oakland, CA reopens-2573892.php Retrieved June 6, 2017 1. http://mynorthwest.com/150 242/bizarre-lake- washington-disaster-struck- 25-years-ago/ Retrieved Lacey Murrow 29-Nov- Sunk Due to Heavy Flooding – Heavy Flooding 25-Nov-90 Washington - 4 4 June 6, 2017 2. Bridge 90 Seattle, WA http://mynorthwest.com/317 621/feliks-banels-top-10- worst-traffic-jams-in-puget- sound-history/ Retrieved June 6, 2017 A truck carrying a tall load on I- http://fox59.com/2017/05/01 465 smashed into the overpass, /rockville-road-bridge-to- Rockville bridge Truck Collision 9-Jan-17 1-May-17 Indiana 1 112 112 shutting down the interstate and reopen-four-months-after- over I-465 Rockville Road for nearly 30 crash/ Retrieved June 7, hours. 2017 The closed stretch of I-10 east in http://www.wbrz.com/news/ Ascension Parish re-opened interstate-detour-this- 12-Mar- overnight, nearly a day ahead of Repair I-10 bridge 11-Mar-17 Louisiana - 1 1 weekend-on-i-10-east-near- 17 schedule after a weekend-long sorrento/ Retrieved June closure so crews could make 9, 201 repairs to a bridge section. http://wfla.com/2017/05/24/ high-wind-advisory-issued- Sunshine Skyway 24-May- several several High winds 24-May-17 Florida - - for-sunshine-skyway- bridge 17 hours hours bridge-6/ Retrieved June 9, 2017 http://www.newsday.com/ne Triborough ws/weather/all-but-two- Hurricane 30-Oct- Bridge (Suspensio 29-0ct-12 New York - 1 1 - bridges-closed-during- Sandy 12 n Bridge) I-278 sandy-reopen-1.4164914 Retrieved June 9, 2017

189

Table C. 1 - continued

Partial Complete Closure Date Date Hazard Event Closed Bridge Location Restorati Restoration Duration Comments Data Source Closed Opened on (days) (days) (days)

http://www.newsday.com/ne ws/weather/all-but-two- Hurricane Midtown Tunnel 30-Oct- 29-0ct-12 New York - 1 1 - bridges-closed-during- Sandy I-495 12 sandy-reopen-1.4164914 Retrieved June 9, 2017 http://www.newsday.com/ne ws/weather/all-but-two- Hurricane Throgs Neck 30-Oct- 29-0ct-12 New York - 1 1 - bridges-closed-during- Sandy Bridgei I-295 12 sandy-reopen-1.4164914 Retrieved June 9, 2017 http://www.newsday.com/ne Verrazano- ws/weather/all-but-two- Hurricane 30-Oct- Narrows Bridge I- 29-0ct-12 New York - 1 1 - bridges-closed-during- Sandy 12 278 sandy-reopen-1.4164914 Retrieved June 9, 2017 http://www.newsday.com/ne ws/weather/all-but-two- Hurricane Brooklyn–Battery 30-Oct- 29-0ct-12 New York - 1 1 - bridges-closed-during- Sandy Tunnel I-478 12 sandy-reopen-1.4164914 Retrieved June 9, 2017 https://patch.com/florida/bra The Skyway Bridge has reopened denton/skyway-bridge- Hurricane Sunshine Skyway 1-Sep-16 2-Sep-16 Florida - 1 1 after a storm-prompted closing reopens-after-hurricane- Hermine bridge that last for more than a day. hermine Retrieved June 16, 2017 http://www.tampabay.com/n ews/weather/hurricanes/west Skyway 11-Sep- bound-lanes-on-courtney- Hurricane Irma 9-Sep-17 Florida - 2 2 - Bridge 17 campbell-gandy-bridge- close-as-hurricane- irma/2336981 http://www.tampabay.com/n ews/weather/hurricanes/west Howard 11-Sep- bound-lanes-on-courtney- Hurricane Irma Frankland 9-Sep-17 Florida - 2 2 - 17 campbell-gandy-bridge- Bridge close-as-hurricane- irma/2336983

190

Table C. 2 Post-hazard restoration times for non-interstate bridges Partial Complete Closure Date Date Hazard Event Closed Bridge Location Restoratio Restoration Duratio Comments Data Source Closed Opened n (days) (days) n (days)

30 feet of the bridge was destroyed in addition to the approaches. The span opened Bob Sikes Bridge September 22, 2004 for Pensacola http://www.aaroads.com/guid Hurricane Ivan (Santa Rosa 9/16/2004 9/22/2004 Florida - 6 6 Beach residents only. Residents e.php?page=hivanfl County 399) were required to have an official beach decal on their vehicle to cross. Significant structural damage was done to the crossing and it Navarre Beach remained closed until November http://www.aaroads.com/guid Hurricane Ivan Causeway (Santa 16-Sep-04 3-Nov-04 Florida - 48 48 3, 2004. Pedestrian traffic e.php?page=hivanfl Rosa County 399) however was permitted across the span. The three mile long span was closed as storm surge erosion displaced the approaches. The span opened September 21, 2004 U.S. 98 Pensacola http://www.aaroads.com/guid Hurricane Ivan 16-Sep-04 21-Sep-04 Florida - 5 5 to residents and emergency crews. Bay Bridge e.php?page=hivanfl Fishing piers to the east of U.S. 98 were damaged beyond repair and were dismantled completely by 2011. Some structural damage was done to the two-lane span and reopening occurred on September Florida Toll 281 22, 2004. Tolls on the span were http://www.aaroads.com/guid Hurricane Ivan (Garcon Point 16-Sep-04 22-Sep-04 Florida - 6 6 suspended to aid hurricane e.php?page=hivanfl Bridge) recovery efforts and allow emergency vehicles greater access to impacted areas. The span was closed because of structural damage on the Alabama side of Perdido Bay and flooding on the Escambia County side. As of October 5, 2004, all of U.S. 98 U.S. 98 Lillian http://www.aaroads.com/guid Hurricane Ivan 16-Sep-04 19-Feb-05 Florida 17 137 137 between the Alabama state line Highway Bridge e.php?page=hivanfl and Bay County was opened to traffic. Work to restore the highway to four lanes between Fort Walton Beach and Destin took another 120 days.

191

Table C. 2 - continued

Partial Complete Closure Date Date Closed Hazard Event Closed Bridge Opened Location Restoratio Restoration Duratio Comments Data Source n (days) (days) n (days) Hurricane debris and damage rendered the eastbound carriageway of U.S. 90 impassable. The westbound U.S. 90 Escambia http://www.aaroads.com/guid Hurricane Ivan 16-Sep-04 22-Sep-04 Florida 1 6 6 direction accommodated one lane River causeway e.php?page=hivanfl of traffic in each direction until closure and repairs on September 21 and 22, 2004 saw the four-lane causeway completely reopened. The span and roadway was closed due to flooding and structural Florida 292 damage and only open to Perdido Key late emergency personnel. Shuttle http://www.aaroads.com/guid Hurricane Ivan 16-Sep-04 January Florida - 120 120 Bridge / Perdido 2005 service was made available for e.php?page=hivanfl Key Road area residents. Repair work on the highway continued until late January 2005. The innermost lanes of the Cochrane-Africatown Bridge U.S. 90 & U.S. 98 Hurricane 31-Aug- reopened to traffic on August 31, http://www.aaroads.com/guid Truck Cochrane- 29-Aug-05 Alabama - 2 2 Katrina 05 2005. Repair estimates were less e.php?page=hkatrinala Africatown Bridge than $1 million,6 and all work completed by the end of 2005. Bayou Liberty Total repair of pontoon bridge, Hurricane bridge, La. 433, in end of http://www.aaroads.com/guid 29-Aug-05 February, Louisiana - 180 180 Coastal Bridges, estimated six Katrina St. Tammany e.php?page=hkatrinala 2006 months. Parish Hurricane Bayou Barataria, http://www.aaroads.com/guid 29-Aug-05 5-Sep-05 Louisiana - 7 7 Electrical/mechanical repairs Katrina La. 302, Jefferson e.php?page=hkatrinala

Hurricane Rigolets, U.S. 90, Electrical/mechanical repairs, http://www.aaroads.com/guid 29-Aug-05 28-Sep-05 Louisiana - 30 30 Katrina Orleans Parish Coastal Bridges e.php?page=hkatrinala

East Pearl River, U.S. 90, on the Hurricane Mississippi- http://www.aaroads.com/guid 29-Aug-05 28-Sep-05 Louisiana - 30 30 Electrical/mechanical repairs Katrina Louisiana border, e.php?page=hkatrinala St. Tammany Parish

192

Table C. 2 - continued Partial Complete Closure Date Date Closed Hazard Event Closed Bridge Opened Location Restoratio Restoration Duratio Comments Data Source n (days) (days) n (days) The eastbound side of the divided Florida 196 highway was washed out by storm end of http://www.aaroads.com/guid Hurricane Ivan (Bayfront 16-Sep-04 December Florida - 100 100 surge. Reconstruction of the e.php?page=hivanfl Parkway) 2004 roadway was completed by the end of December 2004.

Debris and downed power lines Florida 291 (Davis http://www.aaroads.com/guid Hurricane Ivan 16-Sep-04 17-Sep-04 Florida - 1 1 down on the road. The highway Highway) e.php?page=hivanfl was reopened on 09-17-04.

U.S. 98 from the Okaloosa U.S. 98 in Santa http://www.aaroads.com/guid Hurricane Ivan 16-Sep-04 17-Sep-04 Florida - 1 1 County line to Gulf Breeze was Rosa County e.php?page=hivanfl reopened as of 09-17-04.

State Road 87 reopened on 09-17- http://www.aaroads.com/guid Hurricane Ivan Florida 87 16-Sep-04 17-Sep-04 Florida - 1 1 04. e.php?page=hivanfl

The truss bridge over the Chef Menteur Pass in east New Orleans Hurricane Chef Menteur Pass 30-Nov- http://www.aaroads.com/guid 29-Aug-05 Louisiana - 100 100 remained closed through Katrina Bridge - U.S. 90. 05 e.php?page=hkatrinala November 30, 2005 due to structural damage https://smartech.gatech.edu/bi tstream/handle/1853/9431/Ka Hurricane Bay St. Louis 29-Aug-05 6-Jun-07 Mississippi - 670 670 - trina.pdf?sequence=1&isAllo Katrina wed=y Retrieved on June 5, 2017 https://smartech.gatech.edu/bi tstream/handle/1853/9431/Ka Hurricane Handerson Point 29-Aug-05 24-Jan-07 Mississippi - 172 172 - trina.pdf?sequence=1&isAllo Katrina US-90 wed=y Retrieved on June 5, 2017 https://smartech.gatech.edu/bi tstream/handle/1853/9431/Ka Hurricane 23-Dec- Popps Ferry 29-Aug-05 Mississippi - 176 176 - trina.pdf?sequence=1&isAllo Katrina 05 wed=y Retrieved on June 5, 2017

193

Table C. 2 - continued Partial Complete Closure Date Date Closed Hazard Event Closed Bridge Opened Location Restoratio Restoration Duratio Comments Data Source n (days) (days) n (days)

Complete Replacement with new 6-lane high-rise bridge–Avoid https://smartech.gatech.edu/bi storm surge issues–Increased tstream/handle/1853/9431/Ka Hurricane Biloxi Ocean 29-Aug-05 1-May-07 Mississippi - 550 550 capacity•Contracting–Design- trina.pdf?sequence=1&isAllo Katrina Springs US-90 build–Estimated at $150 million– wed=y Retrieved on June 5, Completion in May, 2007 (1.5 2017 yrs)

Bridge collapse results in 6 hour https://sf.curbed.com/2017/3/ detour to get from one side of Big Massive rain Pfeiffer Canyon 180 - 20/14983602/pfeiffer-canyon- 11-Mar-17 N/A California - 180 - 270 Sur to the other side, effectively and avalanche Bridge 270 bridge-collapse splitting the community in half. Retrieved June 1, 2017 Concrete bridge A Union Pacific train T-boned a Burlington Northern Santa Fe train outside of Scott City, Missouri at approximately 2:30 1. am. The impact caused numerous http://www.cnn.com/2013/05/ rail cars to hit a support pillar of a 25/us/missouri-train- Scott City Collision at 30-Aug- highway overpass, collapsing two collision/index.html?hpt=hp_t roadway bridge 25-May-13 Missouri - 97 97 support pillar 13 sections of the bridge onto the rail 2 Retrieved June 1, 2017 collapse line. Two cars ended up driving http://www.semissourian.com onto the collapsed sections, /story/1998056.html injuring three people in one Retrieved June 1, 2017 vehicle and two in the other. Two people on one of the trains were also injured The MV Delta Marinerstruck the bottom portion of a span of the bridge when travelling in the Eggner Ferry incorrect channel of the river. https://www.explorekentuckyl Vessel collision Bridge over 25-May- Emergency repairs to bridge ake.com/eggners/eggners_ferr 27-Jan-12 Kentucky - 118 118 at bottom span the Tennessee 12 completed on May 25, 2012. y_bridge_collapse2.htm River There were preexisting plans Retrieved June 1, 2017 before the collapse to replace the bridge with a 4-lane bridge over the river.

194

Table C. 2 - continued Partial Complete Closure Date Date Closed Hazard Event Closed Bridge Opened Location Restoratio Restoration Duratio Comments Data Source n (days) (days) n (days)

1. http://samlawpc.com/2017/03 /2008-flood-caused-by-large- man-made-obstructions-in- The Cedar Rapids Three of the bridge's four steel waterloo-cedar-rapids-and- and Iowa City spans were swept into the river Midwest floods 12-Jun-08 29-Sep-09 Iowa - 443 443 iowa-city-cedar-rapids-flood- Railway (CRAND along with 15 CRANDIC rail cars class-action-update/ IC) bridge loaded with rock 2. http://www.ble- t.org/pr/news/pf_headline.asp ?id=27740 Retrieved June 1, 2017

https://www.news- journal.com/news/2010/jun/0 Collapsed When Struck by Truck Truck Collision Texas 322 Bridge 30-Apr-10 9-Jun-10 Texas - 40 40 9/texas-322-bridge-overpass- – Longview, TX reopens/ Retrieved June 5, 2017

http://www.equipmentworld.c om/wp- content/uploads/sites/91/2012 /08/U.S.-Bridge-Failure- Salem Bridge over Collapse During Construction – Construction 15-Jun-10 15-Jun-10 Connecticut - 1 1 Listing-from-Timothy-G.- Naugatuck River Norfolk, CT Galarnyk-CEO-of- Construction-Risk- Management.pdf Retrieved June 2, 2017 http://www.philly.com/philly/ The bridge had been closed since business/transportation/Turnp Jan. 20 after a worker on a ike-bridge-over-the- Observed Crack Delaware River Pennsylvan 20-Jan-17 9-Mar-17 - 48 48 painting crew found a crack in a Delaware-will-reopen- in Truss Turnpike Bridge ia truss on the underside of the tonight-cracked-truss- bridge. repaired.html Retrieved June 5, 2017 http://www.wsbtv.com/news/r Bolton Road Collapsed When Struck by Truck oad-reopens-after-partial- Truck Collision 28-Jun-11 1-Jul-11 Georgia - 3 3 Bridge – Atlanta, GA bridge-collapse/241688319 Retrieved June 5, 2017 http://www.dailybulldog.com/ db/features/carrabassett- Carrabassett River 18-Nov- Collapsed – Flood, Scour – Flood, Scour 28-Aug-11 Maine - 83 83 valley-bridges-officially- Bridge 11 Carrabassett Valley, ME reopen/ Retrieved June 6, 2017

195

Table C. 2 - continued Partial Complete Closure Date Date Closed Hazard Event Closed Bridge Opened Location Restoratio Restoration Duratio Comments Data Source n (days) (days) n (days) http://www.dailybulldog.com/ db/features/carrabassett- Bracket Brook Collapsed Due to Flood – Flood 28-Aug-11 2-Noz-11 Maine - 69 69 valley-bridges-officially- Bridge Carrabassett Valley, ME reopen/ Retrieved June 6, 2017

1. http://www.equipmentworld.c om/wp- content/uploads/sites/91/2012 /08/U.S.-Bridge-Failure- Listing-from-Timothy-G.- Tennessee River 25-May- Collapsed Struck by Barge – Galarnyk-CEO-of- Barge Collision (Eggners Ferry) 26-Jan-12 Kentucky - 120 120 12 Eggner’s Ferry, KY Construction-Risk- Bridge Management.pdf Retrieved June 2, 2017 2. http://www.wlky.com/article/ eggners-ferry-bridge-reopens- after-collapse/3777150 Retrieved June 6, 2017

https://en.wikipedia.org/wiki/ Sabo Pedestrian Cable Failure (Constructed 2007) Cable Failure 20-Feb-12 1-Jun-12 Minnesota - 102 102 Martin_Olav_Sabo_Bridge Bridge – Minneapolis, MN Retrieved June 6, 2017

https://en.wikipedia.org/wiki/ Queen Isabella 21-Nov- Collapse Struck by Barge – South Queen_Isabella_Causeway#2 Barge Collision 15-Sep-01 Texas - 67 67 Causeway 01 Padre Island, TX 001_causeway_collapse Retrieved June 6, 2017

https://en.wikipedia.org/wiki/ Brittle Steel Hoan Bridge Partial Collapse due to Brittle 13-Dec-00 1-Nov-01 Wisconsin 16 291 291 Hoan_Bridge Retrieved Fatigue Partial Collapse Steel Fatigue – Milwaukee, WI June 6, 2017

http://www.upi.com/Archives /1993/09/26/Salvage-crews- Big Bayou Canot Collapsed Struck by Barge – Barge Collision 22-Sep-93 - Alabama - 8 to 14 8 to 14 raise-last-of-wrecked-train- bRIDGE Mobile, AL from-bayou/2613749016000/ Retrieved June 6, 2017 https://en.wikipedia.org/wiki/ Claiborne Avenue Collapse Struck by Barge – New Claiborne_Avenue_Bridge#ci Barge Collision 28-May-93 Jul-93 Louisiana - 60 60 Bridge Orleans, LA te_note-2 Retrieved June 6, 2017

196

Table C. 2 - continued Partial Complete Closure Date Date Closed Hazard Event Closed Bridge Opened Location Restoratio Restoration Duratio Comments Data Source n (days) (days) n (days) http://www.wsiltv.com/story/ 35398719/chester-bridge- 10-May- 4-May-17 Flooding Chester Bridge 17 Missouri - 6 6 Closed as precautionary measure reopens-after-being-closed- due-to-flooding Retrieved June 7, 2017 http://jacksonville.com/news/ public-safety/2017-03- Jacksonville’s Work on the span’s mechanical, 31/main-street-bridge-shut- Electrical work 31-Mar-17 2-Apr-17 Florida - 2 2 Main Street bridge electrical and structural systems weekend-detours-acosta- bridge Retrieved June 7, 2017 http://www.firstcoastnews.co No motorists will be able to m/traffic/hart-bridge-will-be- Repairs Hart Bridge 9-Jun-17 11-Jun-17 Florida - 2 2 access the bridge while crews closed-this-weekend-plan- work to make general repairs. accordingly/446508573 Retrieved June 7, 2017 http://www.actionnewsjax.co Officials announced the closure of m/news/local/shands-bridge- Hurricane Shands Bridge 6-Oct-16 9-Oct-16 Florida - 3 3 the bridge on Saturday after it was closed-until-further- Matthew damaged during the storm. notice/455320864 Retrieved June 7, 2017 http://www.wokv.com/news/l ocal/northeast-florida- bridges-reopening-after- Hurricane Palm Valley 6-Oct-16 8-Oct-16 Florida - 2 2 - matthew- Matthew Bridge closures/HLbjk4du4CfqPS83 AqlWPO/ Retrieved June 7, 2017 http://www.wokv.com/news/l ocal/northeast-florida- bridges-reopening-after- Hurricane Usina Bridge 6-Oct-16 8-Oct-16 Florida - 2 2 - matthew- Matthew closures/HLbjk4du4CfqPS83 AqlWPO/ Retrieved June 7, 2017 http://www.wokv.com/news/l ocal/northeast-florida- bridges-reopening-after- Hurricane Shave Bridge 6-Oct-16 8-Oct-16 Florida - 2 2 - matthew- Matthew closures/HLbjk4du4CfqPS83 AqlWPO/ Retrieved June 7, 2017

197

Table C. 2 - continued Partial Complete Closure Date Hazard Event Closed Bridge Date Closed Location Restoratio Restoration Duratio Comments Data Source Opened n (days) (days) n (days) http://www.wokv.com/news/l ocal/northeast-florida- bridges-reopening-after- Hurricane Bridge of Lions 6-Oct-16 8-Oct-16 Florida - 2 2 - matthew- Matthew closures/HLbjk4du4CfqPS83 AqlWPO/ Retrieved June 7, 2017 http://www.wftv.com/news/lo cal/brevard-county-bridges- Hurricane Pineda Causeway 6-Oct-16 7-Oct-16 Florida - 1 1 - reopen-after-matthew-tears- Matthew through/454554340 Retrieved June 9, 2017

http://www.wftv.com/news/lo cal/brevard-county-bridges- Hurricane Eau Gallie Cause 6-Oct-16 7-Oct-16 Florida - 1 1 - reopen-after-matthew-tears- Matthew way through/454554340 Retrieved June 9, 2017 http://www.wftv.com/news/lo cal/some-bridges-reopen-in- Hurricane daytona-beach-but-sunglow- Dunlawton Bridge 6-Oct-16 8-Oct-16 Florida - 2 2 - Matthew pier-damaged-after- matthew/454943678 Retrieved June 16, 2017 http://www.wftv.com/news/lo cal/some-bridges-reopen-in- Hurricane daytona-beach-but-sunglow- Granada Bridge 6-Oct-16 8-Oct-16 Florida - 2 2 - Matthew pier-damaged-after- matthew/454943678 Retrieved June 16, 2017 http://www.wftv.com/news/lo cal/brevard-county-bridges- Hurricane Melbourne 6-Oct-16 7-Oct-16 Florida - 1 1 - reopen-after-matthew-tears- Matthew Causeway through/454554340 Retrieved June 9, 2017

The bridge was damaged by http://www.fayobserver.com/ Hurricane Hope Mills Road 15-Nov- heavy rains before and during 6f264e16-d075-50c9-990b- 6-Oct-16 Florida - 40 40 Matthew bridge 16 Hurricane Matthew. It reopened 840a73b7352b.html on Tuesday afternoon. Retrieved June 19, 2017

198

Table C. 2 - continued Partial Complete Closure Date Hazard Event Closed Bridge Date Closed Location Restoratio Restoration Duratio Comments Data Source Opened n (days) (days) n (days) Closed in both directions between the intersection of Sheehans Rd in Mehoopany to the https://www.foleyservices.co 11-Nov- Pennsylvan intersection of School House Rd m/news/list-of-hurricane- Hurricane Irene Route 87(PA-087) 27-Aug-11 - 76 76 11 ia in Mehoopany due to flooding irene-road-closures-by-state/ waters that left trees and other Retrieved June 8, 2017 debris on the bridge. Anticipated reopening is November 11, 2011. Closed both directions between the intersection of Gameland Route 3001(SR Package Area Rd in Forkston to https://www.foleyservices.co 3001 SH/Windy Pennsylvan the intersection of (PA-087) in m/news/list-of-hurricane- Hurricane Irene 27-Aug-11 15-Sep-11 - 19 19 Valley RD/Church ia Forkston due to partial road irene-road-closures-by-state/ St) damage. Anticipated reopening of Retrieved June 8, 2017 temporary bridge– September 15, 2011. Closed in both directions between the intersection of Liberty Park Rd in Great Bend to the intersection of New York Ave in https://www.foleyservices.co Route 1037 Pennsylvan Hallstead due to water m/news/list-of-hurricane- Hurricane Irene (Dubois St/ SR 27-Aug-11 6-Sep-11 - 10 10 ia approaching bridge, may have irene-road-closures-by-state/ 1037 SH) cause damage. Temporary closure Retrieved June 8, 2017 until bridge is inspected. Anticipated reopening, September 6, 2011. http://www.mynbc5.com/artic Taftsville Covered le/another-vt-covered-bridge- Hurricane Irene 28-Aug-11 7-Sep-11 Vermont - 10 10 - Bridge to-reopen-after-irene/3311115 Retrieved June 8, 2017

http://www.nj.com/salem/ind East Lake Road ex.ssf/2012/05/east_lake_road Hurricane Irene 28-Aug-11 3-May-12 New Jersey - 249 249 - bridge _bridge_reopened.html Retrieved June 9, 2017 http://www.newsday.com/ne ws/weather/all-but-two- Hurricane Brooklyn Bridge 29-0ct-12 30-Oct-12 New York - 1 1 - bridges-closed-during-sandy- Sandy reopen-1.4164914 Retrieved June 9, 2017

199

Table C. 2 - continued Partial Complete Closure Date Date Closed Hazard Event Closed Bridge Opened Location Restoratio Restoration Duratio Comments Data Source n (days) (days) n (days) http://www.newsday.com/ne ws/weather/all-but-two- Hurricane Manhattan Bridge 29-0ct-12 30-Oct-12 New York - 1 1 - bridges-closed-during-sandy- Sandy reopen-1.4164914 Retrieved June 9, 2017 http://www.newsday.com/ne ws/weather/all-but-two- Hurricane Williamsburg 29-0ct-12 30-Oct-12 New York - 1 1 - bridges-closed-during-sandy- Sandy Bridge reopen-1.4164914 Retrieved June 9, 2017 http://www.newsday.com/ne ws/weather/all-but-two- Hurricane Queensboro 29-0ct-12 30-Oct-12 New York - 1 1 - bridges-closed-during-sandy- Sandy Bridge reopen-1.4164914 Retrieved June 9, 2017 http://www.wjcl.com/article/b lue-moon-cafe-owner-offers- Hurricane Talmadge bridge 7-Oct-16 9-Oct-16 Florida - 2 2 - troops-a-reminder-of-home- Matthew cooking/10042438 Retrieved June 19, 2017

http://www.wjcl.com/article/b lue-moon-cafe-owner-offers- Hurricane Houlihan bridge 7-Oct-16 9-Oct-16 Florida - 2 2 - troops-a-reminder-of-home- Matthew cooking/10042438 Retrieved June 19, 2017 1. http://pittsburgh.cbslocal.com The bridge reopened to weight- /2016/10/06/chief-liberty- limited traffic on September 26th, bridge-contractors-did-not- and full traffic on September 30th. Pennsylvan have-proper-permits-fire- Fire Liberty Bridge 2-Sep-16 30-Sep-16 24 28 28 The Pennsylvania Department of ia suppression/ 2. Transportation assessed the value https://en.wikipedia.org/wiki/ of the damages at over Liberty_Bridge_(Pittsburgh)# $3,000,000. Fire Retrieved June 19, 2017 http://www.wdam.com/story/ The bridge had been closed since 34337402/petal-bridge- Tornado Petal bridge 21-Jan-17 25-Jan-17 Mississippi - 4 4 the storm because of power lines reopens-after-storm that fell across it. Retrieved June 19, 2017

200

Table C. 2 - continued Partial Complete Closure Date Date Closed Hazard Event Closed Bridge Opened Location Restoratio Restoration Duratio Comments Data Source n (days) (days) n (days) http://kstp.com/news/highway -7-minnetonka-boulevard- Construction/R Minnetonka May, 2016 29-Oct-16 Minnesota - ~180 ~180 - bridges-construction-detours- epairs Boulevard bridge mndot/4305244/ Retrieved June 19, 2017

1. https://www.usnews.com/new s/best- states/texas/articles/2017-05- 22/weather-damage-closes- Rains and World Trade 29-May- key-commercial-us-mexico- 21-May-17 Texas - 8 8 - Winds Bridge 17 border-bridge 2. http://www.americanshipper.c om/main/news/world-trade- bridge-to-reopen-memorial- day-67651.aspx#hide Retrieved June 19, 2017

http://okcfox.com/news/local/ May Avenue 26-May- two-lanes-of-may-avenue- Truck Collision 19-May-16 Oklahoma 7 - - - Bridge 16 bridge-to-reopen Retrieved June 19, 2017 The Department of Transportation http://m.washingtontimes.co said in a news release that state m/news/2016/jul/28/major- South Highway 9 bridge that crosses the *Repairs Highway 9 Bridge 18-Jul-18 28-Jul-16 - 10 10 upstate-bridge-reopens-more- Carolina river in Chester and Union than-2-weeks-ear/ Retrieved counties was reopened at 4 p.m. June 19, 2017 Thursday. http://levittownnow.com/2017 *Construction/ Frost Hollow 26-May- Pennsylvan /05/26/frosty-hollow-road- March, 2017 - ~70 ~70 - Repairs Road Bridge 17 ia bridge-reopens/ Retrieved June 20, 2017

https://www.foleyservices.co Route 7 is open except where the m/news/list-of-hurricane- Hurricane Irene Route 7 bridge 28-Aug-11 2-Sep-11 Vermont - 4 4 bridge is out by formula ford. irene-road-closures-by-state/ Retrieved June 8, 2017

201

Table C. 2 - continued Partial Complete Closure Date Date Closed Hazard Event Closed Bridge Opened Location Restoratio Restoration Duratio Comments Data Source n (days) (days) n (days) http://www.scdot- 10/31/201 transfer.org/SCDOTphotos/Se 6 South Floods Old Shoals Road 1-Oct-15 - 350 350 Bridge Replacement cretaryRecoveryMonthlyRep (Projected Carolina ) ortSep2016.pdf Retrieved June 21, 2017

11/14/201 http://www.scdot- 6 South transfer.org/SCDOTphotos/Se Floods Highway 301 1-Oct-15 - 364 364 Bridge Replacement (Projected Carolina cretaryRecoveryMonthlyRep ) ortSep2016.pdf

http://www.scdot- transfer.org/SCDOTphotos/Se 9/23/2016 South Floods Pine Grove Road 1-Oct-15 (Projected - 312 312 Bridge Replacement cretaryRecoveryMonthlyRep Carolina ) ortSep2016.pdf Retrieved June 21, 2017

10/31/201 http://www.scdot- 6 South transfer.org/SCDOTphotos/Se Floods Hope Station Road 1-Oct-15 - 350 350 Bridge Replacement (Projected Carolina cretaryRecoveryMonthlyRep ) ortSep2016.pdf

11/30/201 http://www.scdot- Samuel Padgett 6 South transfer.org/SCDOTphotos/Se Floods 1-Oct-15 - 380 380 Bridge Replacement Road (Projected Carolina cretaryRecoveryMonthlyRep ) ortSep2016.pdf

http://www.scdot- transfer.org/SCDOTPHOTOS 8/4/2016 South Floods Congaree Road 1-Oct-15 (Projected - 262 262 Bridge Replacement /SecretaryRecoveryMonthlyR Carolina ) eportAugust2016.pdf Retrieved June 21, 2017

http://www.scdot- Governor 8/31/2016 South transfer.org/SCDOTPhotos/S Floods 1-Oct-15 (Projected - 289 289 Bridge Replacement Richardson Road ) Carolina ecretarysReport02122016.pdf Retrieved June 21, 2017

http://www.scdot- Plowden Mill 8/31/2016 South transfer.org/SCDOTPhotos/S Floods 1-Oct-15 (Projected - 289 289 Bridge Replacement Road ) Carolina ecretarysReport02122016.pdf Retrieved June 21, 2017

202

Table C. 2 - continued Partial Complete Closure Date Date Closed Hazard Event Closed Bridge Opened Location Restoratio Restoration Duratio Comments Data Source n (days) (days) n (days) http://www.scdot- 4/29/2016 South transfer.org/SCDOTPhotos/S Floods River Road 1-Oct-15 (Projected - 165 165 Bridge Replacement ) Carolina ecretarysReport02122016.pdf Retrieved June 21, 2017

http://www.scdot- South Old River 5/27/2016 South transfer.org/SCDOTPhotos/S Floods 1-Oct-15 (Projected - 193 193 Bridge Replacement Road ) Carolina ecretarysReport02122016.pdf Retrieved June 21, 2017

http://www.scdot- 7/16/2016 South transfer.org/SCDOTPhotos/S Floods Belfast Rd. 1-Oct-15 (Projected - 243 243 Bridge Replacement ) Carolina ecretarysReport02122016.pdf Retrieved June 21, 2017

http://www.scdot- 3/29/2016 South transfer.org/SCDOTPhotos/S Floods US 176 1-Oct-15 (Projected - 134 134 Bridge Replacement ) Carolina ecretarysReport02122016.pdf Retrieved June 21, 2017

http://www.scdot- 4/15/2016 South transfer.org/SCDOTPhotos/S Floods Bluff Road 1-Oct-15 (Projected - 151 151 Bridge Replacement ) Carolina ecretarysReport02122016.pdf Retrieved June 21, 2017

http://www.scdot- 5/15/2016 South transfer.org/SCDOTPhotos/S Floods Congress Road 1-Oct-15 (Projected - 181 181 Bridge Replacement ) Carolina ecretarysReport02122016.pdf Retrieved June 21, 2017

http://www.scdot- 6/15/2016 South transfer.org/SCDOTPhotos/S Floods Rockbridge Road 1-Oct-15 (Projected - 212 212 Bridge Replacement ) Carolina ecretarysReport02122016.pdf Retrieved June 21, 2017

http://www.scdot- 6/15/2016 South transfer.org/SCDOTPhotos/S Floods Battery Park Road 1-Oct-15 (Projected - 212 212 Bridge Replacement ) Carolina ecretarysReport02122016.pdf Retrieved June 21, 2017 http://wavy.com/2016/09/03/r The Wright Memorial Bridge has oads-interstates-in-hampton- Hurricane Wright Memorial North 3-Sep-16 4-Sep-16 - 1 1 reopened to passenger vehicles roads-affected-during- Hermine Bridge Carolina only hermine/ Retrieved June 22, 2017

203

Table C. 2 - continued Partial Complete Closure Date Date Hazard Event Closed Bridge Location Restoratio Restoration Duratio Comments Data Source Closed Opened n (days) (days) n (days) http://wavy.com/2016/09/03/r oads-interstates-in-hampton- Hurricane Dare County North 3-Sep-16 4-Sep-16 - 1 1 - roads-affected-during- Hermine Memorial Bridge Carolina hermine/ Retrieved June 22, 2017 http://wavy.com/2016/09/03/r oads-interstates-in-hampton- Hurricane North Bonner Bridge 3-Sep-16 4-Sep-16 - 1 1 High Winds roads-affected-during- Hermine Carolina hermine/ Retrieved June 22, 2017 http://wavy.com/2016/09/03/r William B. oads-interstates-in-hampton- Hurricane North Umstead/Old 3-Sep-16 4-Sep-16 - 1 1 High Winds roads-affected-during- Hermine Carolina Manns Harbor hermine/ Retrieved June 22, 2017 http://wavy.com/2016/09/03/r oads-interstates-in-hampton- Hurricane Virginia Dare North 3-Sep-16 4-Sep-16 - 1 1 High Winds roads-affected-during- Hermine Bridge Carolina hermine/ Retrieved June 22, 2017 http://jacksonville.com/news/ public-safety/2017-09- Browns Creek Damage to one side of the bridge Hurricane Irma 13-Sep-17 15-Sep-17 Florida - 2 2 13/closure-heckscher-drive- Bridge approaches bridge-damaged-irma-means- long-detours http://www.tampabay.com/ne ws/weather/hurricanes/westbo Hurricane Irma Gandy Bridge 9-Sep-17 11-Sep-17 Florida - 2 2 - und-lanes-on-courtney- campbell-gandy-bridge-close- as-hurricane-irma/2336982

204

Table C. 3 Post-hazard restoration times for interstate roadways Partial Complete Closure Hazard Closed Date Date Location Restoration Restoration Duration Comments Data Source Event Road Closed Opened (days) (days) (days)

Hurricane Interstate North http://www.charlotteobserver.com/news/local/article108768732.html 10-Oct-16 17-Oct-16 - 7 7 Flooding Matthew 95 Carolina Retrieved June 21, 2017

1. http://www.stltoday.com/news/local/aerial-photos-of-meramec- river-flooding/collection_33511d7b-3a0e-55f8-95e5- Interstate 6342359e6876.html 2. Floods 2-May-17 4-May-17 Missouri - 2 2 - 44 http://www.stltoday.com/news/local/metro/eastbound-i--reopens-as- roads-get-back-to-normal/article_40fe56f0-7c9d-5efc-9398- 4081572b6ee7.html Retrieved June 22, 2017 1. http://www.stltoday.com/news/local/aerial-photos-of-meramec- river-flooding/collection_33511d7b-3a0e-55f8-95e5- Interstate 6342359e6876.html 2. Floods 2-May-17 4-May-17 Missouri - 2 2 - 270 http://www.stltoday.com/news/local/metro/eastbound-i--reopens-as- roads-get-back-to-normal/article_40fe56f0-7c9d-5efc-9398- 4081572b6ee7.html Retrieved June 22, 2017 1. http://www.stltoday.com/news/local/aerial-photos-of-meramec- river-flooding/collection_33511d7b-3a0e-55f8-95e5- Interstate 6342359e6876.html 2. Floods 2-May-17 3-May-17 Missouri - 1 1 - 55 http://www.stltoday.com/news/local/metro/eastbound-i--reopens-as- roads-get-back-to-normal/article_40fe56f0-7c9d-5efc-9398- 4081572b6ee7.html Retrieved June 22, 2017

Table C. 4 Post-hazard restoration times for non-interstate roadways Partial Complete Closure Date Date Hazard Event Closed Road Location Restoration Restoration Duration Comments Data Source Closed Opened (days) (days) (days) http://wjtv.com/2016/10/13/som Section of N.C. 12 e-roads-in-north-carolina- Hurricane leading south North 10-Oct-16 13-Oct-16 - 3 3 - reopening-after-hurricane- Matthew toward Cape Carolina matthew/ Retrieved June 21, Hatteras. 2017 http://www.wftv.com/news/local /a1a-coastal-byway-reopens-in- Hurricane A1A coastal 11/7/2016 6-Oct-16 Florida - 32 32 - flagler-beach-after-hurricane- Matthew byway (Projected) damage-repaired/464839150 Retrieved June 21, 2017

205

Table C. 4 - continued Partial Complete Closure Date Date Hazard Event Closed Road Location Restoration Restoration Duration Comments Data Source Closed Opened (days) (days) (days) http://www.scdot- transfer.org/SCDOTphotos/Secr 10/31/2016 South Floods Old Shoals Road 1-Oct-15 - 350 350 Bridge Replacement etaryRecoveryMonthlyReportSe (Projected) Carolina p2016.pdf Retrieved June 21, 2017 http://www.scdot- 11/14/2016 South transfer.org/SCDOTphotos/Secr Floods Highway 301 1-Oct-15 - 364 364 Bridge Replacement (Projected) Carolina etaryRecoveryMonthlyReportSe p2016.pdf http://www.scdot- transfer.org/SCDOTphotos/Secr 9/23/2016 South Floods Pine Grove Road 1-Oct-15 - 312 312 Bridge Replacement etaryRecoveryMonthlyReportSe (Projected) Carolina p2016.pdf Retrieved June 21, 2017 http://www.scdot- 10/31/2016 South transfer.org/SCDOTphotos/Secr Floods Hope Station Road 1-Oct-15 - 350 350 Bridge Replacement (Projected) Carolina etaryRecoveryMonthlyReportSe p2016.pdf http://www.scdot- Samuel Padgett 11/30/2016 South transfer.org/SCDOTphotos/Secr Floods 1-Oct-15 - 380 380 Bridge Replacement Road (Projected) Carolina etaryRecoveryMonthlyReportSe p2016.pdf http://www.scdot- transfer.org/SCDOTPHOTOS/S 8/4/2016 South Floods Congaree Road 1-Oct-15 - 262 262 Bridge Replacement ecretaryRecoveryMonthlyReport (Projected) Carolina August2016.pdf Retrieved June 21, 2017 http://www.scdot- Governor 8/31/2016 South transfer.org/SCDOTPhotos/Secr Floods 1-Oct-15 - 289 289 Bridge Replacement Richardson Road (Projected) Carolina etarysReport02122016.pdf Retrieved June 21, 2017 http://www.scdot- Plowden Mill 8/31/2016 South transfer.org/SCDOTPhotos/Secr Floods 1-Oct-15 - 289 289 Bridge Replacement Road (Projected) Carolina etarysReport02122016.pdf Retrieved June 21, 2017 http://www.scdot- 2/29/2016 South Road/Culvert/Slope transfer.org/SCDOTPhotos/Secr Floods Saint Paul Road 1-Oct-15 - 105 105 (Projected) Carolina Repairs etarysReport02122016.pdf Retrieved June 21, 2017 http://www.scdot- 4/29/2016 South transfer.org/SCDOTPhotos/Secr Floods River Road 1-Oct-15 - 165 165 Bridge Replacement (Projected) Carolina etarysReport02122016.pdf Retrieved June 21, 2017

206

Table C. 4 - continued Partial Complete Closure Date Date Hazard Event Closed Road Location Restoration Restoration Duration Comments Data Source Closed Opened (days) (days) (days) http://www.scdot- 5/31/2016 South transfer.org/SCDOTPhotos/Secr Floods Marion Street 1-Oct-15 - 197 197 Road Repairs (Projected) Carolina etarysReport02122016.pdf Retrieved June 21, 2017 http://www.scdot- South Old River 5/27/2016 South transfer.org/SCDOTPhotos/Secr Floods 1-Oct-15 - 193 193 Bridge Replacement Road (Projected) Carolina etarysReport02122016.pdf Retrieved June 21, 2017 http://www.scdot- 7/16/2016 South transfer.org/SCDOTPhotos/Secr Floods Belfast Rd. 1-Oct-15 - 243 243 Bridge Replacement (Projected) Carolina etarysReport02122016.pdf Retrieved June 21, 2017 http://www.scdot- 3/29/2016 South transfer.org/SCDOTPhotos/Secr Floods US 176 1-Oct-15 - 134 134 Bridge Replacement (Projected) Carolina etarysReport02122016.pdf Retrieved June 21, 2017 http://www.scdot- 4/15/2016 South transfer.org/SCDOTPhotos/Secr Floods Bluff Road 1-Oct-15 - 151 151 Bridge Replacement (Projected) Carolina etarysReport02122016.pdf Retrieved June 21, 2017 http://www.scdot- 5/15/2016 South transfer.org/SCDOTPhotos/Secr Floods Congress Road 1-Oct-15 - 181 181 Bridge Replacement (Projected) Carolina etarysReport02122016.pdf Retrieved June 21, 2017 http://www.scdot- 6/15/2016 South transfer.org/SCDOTPhotos/Secr Floods Rockbridge Road 1-Oct-15 - 212 212 Bridge Replacement (Projected) Carolina etarysReport02122016.pdf Retrieved June 21, 2017 http://www.scdot- 2/29/2016 South transfer.org/SCDOTPhotos/Secr Floods Zeigler Road 1-Oct-15 - 105 105 Road/Culvert Repairs (Projected) Carolina etarysReport02122016.pdf Retrieved June 21, 2017 http://www.scdot- 3/4/2016 South transfer.org/SCDOTPhotos/Secr Floods Hayne Street 1-Oct-15 - 109 109 Road/Culvert Repairs (Projected) Carolina etarysReport02122016.pdf Retrieved June 21, 2017 http://www.scdot- 2/29/2016 South transfer.org/SCDOTPhotos/Secr Floods Pearson Road 1-Oct-15 - 105 105 Road/Culvert Repairs (Projected) Carolina etarysReport02122016.pdf Retrieved June 21, 2017

207

Table C. 4 - continued Partial Complete Closure Date Date Hazard Event Closed Road Location Restoration Restoration Duration Comments Data Source Closed Opened (days) (days) (days) http://www.scdot- 6/15/2016 South transfer.org/SCDOTPhotos/Secr Floods Battery Park Road 1-Oct-15 - 212 212 Bridge Replacement (Projected) Carolina etarysReport02122016.pdf Retrieved June 21, 2017 http://www.scdot- Old Georgetown 5/31/2016 South transfer.org/SCDOTPhotos/Secr Floods 1-Oct-15 - 197 197 Road/Culvert Repairs Road (Projected) Carolina etarysReport02122016.pdf Retrieved June 21, 2017 http://abc11.com/news/manchest Hurricane North er-road-will-finally-reopen-at- Manchester Road 10-Oct-16 24-Feb-17 - 137 137 - Matthew Carolina fort-bragg/1770411/ Retrieved June 21, 2017 http://www.newsobserver.com/n Hurricane North Rogers Road 10-Oct-16 5-Dec-16 - 56 56 - ews/traffic/article118990368.ht Matthew Carolina ml Retrieved June 21, 2017 1. http://www.stltoday.com/news/l ocal/aerial-photos-of-meramec- river- flooding/collection_33511d7b- 3a0e-55f8-95e5- Highway 21 Floods 2-May-17 4-May-17 Missouri - 2 2 - 6342359e6876.html 2. (Tesson Ferry) http://www.stltoday.com/news/l ocal/metro/eastbound-i-- reopens-as-roads-get-back-to- normal/article_40fe56f0-7c9d- 5efc-9398-4081572b6ee7.html Retrieved June 22, 2017 1. http://www.stltoday.com/news/l ocal/aerial-photos-of-meramec- river- flooding/collection_33511d7b- 3a0e-55f8-95e5- Highway 109 Floods 2-May-17 4-May-17 Missouri - 2 2 - 6342359e6876.html 2. north of I-44 http://www.stltoday.com/news/l ocal/metro/eastbound-i-- reopens-as-roads-get-back-to- normal/article_40fe56f0-7c9d- 5efc-9398-4081572b6ee7.html Retrieved June 22, 2017

208

Table C. 4 - continued Partial Complete Closure Date Date Hazard Event Closed Road Location Restoration Restoration Duration Comments Data Source Closed Opened (days) (days) (days) 1. http://www.stltoday.com/news/l ocal/aerial-photos-of-meramec- river- flooding/collection_33511d7b- 3a0e-55f8-95e5- Highway 141 at Floods 2-May-17 4-May-17 Missouri - 2 2 - 6342359e6876.html 2. Romaine Creek http://www.stltoday.com/news/l ocal/metro/eastbound-i-- reopens-as-roads-get-back-to- normal/article_40fe56f0-7c9d- 5efc-9398-4081572b6ee7.html Retrieved June 22, 2017 http://fox2now.com/2017/05/08/ idot-opens-several-area-roads- IL 143 at IL 255 Floods 30-Apr-17 8-May-17 Illinois - 8 8 - as-flood-waters- in Wood River recede/#thumbnail-modal Retrieved June 22, 2017 http://fox2now.com/2017/05/08/ IL 100 between idot-opens-several-area-roads- US 67 and IL 3 Floods 30-Apr-17 8-May-17 Illinois - 8 8 - as-flood-waters- (Alton and recede/#thumbnail-modal Grafton) Retrieved June 22, 2017 http://fox2now.com/2017/05/08/ idot-opens-several-area-roads- IL 3 at Nine Mile Floods 30-Apr-17 8-May-17 Illinois - 8 8 - as-flood-waters- Creek recede/#thumbnail-modal Retrieved June 22, 2017 http://fox2now.com/2017/05/08/ idot-opens-several-area-roads- IL 3 @ IL 100 in Floods 30-Apr-17 8-May-17 Illinois - 8 8 - as-flood-waters- Grafton recede/#thumbnail-modal Retrieved June 22, 2017 http://fox2now.com/2017/05/08/ idot-opens-several-area-roads- IL 100 north of Floods 30-Apr-17 8-May-17 Illinois - 8 8 - as-flood-waters- Kampsville recede/#thumbnail-modal Retrieved June 22, 2017 http://fox2now.com/2017/05/08/ idot-opens-several-area-roads- US 50 at Silver Floods 30-Apr-17 8-May-17 Illinois - 8 8 - as-flood-waters- Creek recede/#thumbnail-modal Retrieved June 22, 2017

209

Table C. 4 - continued Partial Complete Closure Date Date Hazard Event Closed Road Location Restoration Restoration Duration Comments Data Source Closed Opened (days) (days) (days) http://www.newsobserver.com/n Old Milburnie North Floods 23-Apr-17 2-May-17 - 9 9 - ews/traffic/article146592339.ht Road Carolina ml Retrieved June 22, 2017 http://www.newsobserver.com/n North Floods Blue Ridge Road 23-Apr-17 24-Apr-17 - 1 1 - ews/traffic/article146592339.ht Carolina ml Retrieved June 22, 2017 http://www.newsobserver.com/n N.C. 97, West North Floods 23-Apr-17 24-Apr-17 - 1 1 - ews/traffic/article146592339.ht Gannon Avenue Carolina ml Retrieved June 22, 2017 Jonesville Road http://www.newsobserver.com/n North Floods near Upchurch 23-Apr-17 26-Apr-17 - 3 3 - ews/traffic/article146592339.ht Carolina Lane ml Retrieved June 22, 2017 Johnson Pond http://www.newsobserver.com/n Road near Bells North Floods 23-Apr-17 24-Apr-17 - 1 1 - ews/traffic/article146592339.ht Lake Road near Carolina ml Retrieved June 22, 2017 Apex Morphus Bridge http://www.newsobserver.com/n Road at Corbin North Floods 23-Apr-17 24-Apr-17 - 1 1 - ews/traffic/article146592339.ht Road near Carolina ml Retrieved June 22, 2017 Zebulon Country Club http://www.newsobserver.com/n Road near Pecan North Floods 23-Apr-17 26-Apr-17 - 3 3 - ews/traffic/article146592339.ht Grove Road near Carolina ml Retrieved June 22, 2017 Zebulon Grasshopper Road http://www.newsobserver.com/n North Floods at Carl Williamson 23-Apr-17 26-Apr-17 - 3 3 - ews/traffic/article146592339.ht Carolina Road near Raleigh ml Retrieved June 22, 2017 Cornwallis Road http://www.newsobserver.com/n North Floods near N.C. 42, west 23-Apr-17 24-Apr-17 - 1 1 - ews/traffic/article146592339.ht Carolina of Clayton ml Retrieved June 22, 2017 Donny Brook http://www.newsobserver.com/n Road, between North Floods 23-Apr-17 24-Apr-17 - 1 1 - ews/traffic/article146592339.ht Lake Wheeler Carolina ml Retrieved June 22, 2017 Road and U.S. 401 NC 12 closed http://wavy.com/2016/09/03/roa Hurricane between White North ds-interstates-in-hampton-roads- 3-Sep-16 7-Sep-16 - 4 4 - Hermine Avenue and Carolina affected-during-hermine/ Starfish Lane Retrieved June 22, 2017

210

Table C. 4 - continued Partial Complete Closure Date Date Hazard Event Closed Road Location Restoration Restoration Duration Comments Data Source Closed Opened (days) (days) (days) http://www.journalnow.com/ne ws/local/some-roads-reopening- Richmond Hill others-still-closed-after- Church Road North Floods 24-Apr-17 25-Apr-17 - 1 1 - flooding-across- (commonly known Carolina the/article_7c7c63f8-7cec-51a5- as Rockford Road) a715-8f7b9faf7cc5.html Retrieved June 22, 2017 http://www.journalnow.com/ne ws/local/some-roads-reopening- others-still-closed-after- Farmington Road North Floods 24-Apr-17 25-Apr-17 - 1 1 - flooding-across- near East Bend Carolina the/article_7c7c63f8-7cec-51a5- a715-8f7b9faf7cc5.html Retrieved June 22, 2017 http://www.journalnow.com/ne ws/local/some-roads-reopening- others-still-closed-after- Butner Mill Road North Floods 24-Apr-17 25-Apr-17 - 1 1 - flooding-across- near East Bend Carolina the/article_7c7c63f8-7cec-51a5- a715-8f7b9faf7cc5.html Retrieved June 22, 2017 http://www.journalnow.com/ne ws/local/some-roads-reopening- others-still-closed-after- North Floods Myers Road 24-Apr-17 25-Apr-17 - 1 1 - flooding-across- Carolina the/article_7c7c63f8-7cec-51a5- a715-8f7b9faf7cc5.html Retrieved June 22, 2017 http://www.journalnow.com/ne ws/local/some-roads-reopening- others-still-closed-after- Rockford Road in North Floods 24-Apr-17 25-Apr-17 - 1 1 - flooding-across- Surry County Carolina the/article_7c7c63f8-7cec-51a5- a715-8f7b9faf7cc5.html Retrieved June 22, 2017 http://www.journalnow.com/ne ws/local/some-roads-reopening- others-still-closed-after- Reeves Road in North Floods 24-Apr-17 25-Apr-17 - 1 1 - flooding-across- Surry County Carolina the/article_7c7c63f8-7cec-51a5- a715-8f7b9faf7cc5.html Retrieved June 22, 2017

211

Table C. 4 - continued Partial Complete Closure Date Date Hazard Event Closed Road Location Restoration Restoration Duration Comments Data Source Closed Opened (days) (days) (days) http://www.journalnow.com/ne ws/local/some-roads-reopening- others-still-closed-after- Radar Road in North Floods 24-Apr-17 25-Apr-17 - 1 1 - flooding-across- Surry County Carolina the/article_7c7c63f8-7cec-51a5- a715-8f7b9faf7cc5.html Retrieved June 22, 2017 http://www.journalnow.com/ne ws/local/some-roads-reopening- others-still-closed-after- North Floods State Road 2230 24-Apr-17 25-Apr-17 - 1 1 - flooding-across- Carolina the/article_7c7c63f8-7cec-51a5- a715-8f7b9faf7cc5.html Retrieved June 22, 2017

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BIOGRAPHICAL SKETCH

EDUCATION

Florida State University Tallahassee, Florida Doctor of Philosophy in Civil Engineering Summer 2018 Graduate Minor in Statistics Fall 2017

Florida State University Tallahassee, Florida Master of Science in Civil Engineering August 2014

Kwame Nkrumah University of Science and Technology (KNUST) Kumasi, Ghana Bachelor of Science in Civil Engineering June 2011 With Honors

RESEARCH INTERESTS

I have keen interests in transportation engineering, planning, and civil engineering infrastructure management. My research areas include the following: resilience of civil infrastructure, transportation user cost evaluation, transportation network resilience, travel demand modeling and network optimization, spatial modeling and post-hazard evaluation of transportation network performance. Currently, my research emphasis is on measuring transportation network resiliency for regional networks subject to hazard events and network component damages by utilizing quantitative concepts and leveraging GIS-based and demand modeling applications.

WORK EXPERIENCE  Graduate Research Assistant, Florida State University, August 2014 to August 2018.  Graduate Research Assistant, Florida State University, August 2012 to August 2014.  Instructor and Teaching Assistant, Sunyani Technical University, Ghana, October 2011 – August 2012.  Intern, Associated Consultants (ACON), Ghana June 2010 – August 2010.  Intern, Sonitra Construction Limited, Ghana, June 2009 – August 2009.

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