DEVELOPMENT OF CRASH MODIFICATION FACTORS FOR BRIDGE RAIL IMPROVEMENTS ROBERT TYLER FIELDS STEVEN JONES, COMMITTEE CHAIR JAY LINDLY JOE WEBER A THESIS

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1 DEVELOPMENT OF CRASH MODIFICATION FACTORS FOR BRIDGE RAIL IMPROVEMENTS by ROBERT TYLER FIELDS STEVEN JONES, COMMITTEE CHAIR JAY LINDLY JOE WEBER A THESIS Submitted in partial fulfillment of the requirements for the degree of Master of Science in the Department of Civil Engineering in the Graduate School of The University of Alabama TUSCALOOSA, ALABAMA 2015

2 Copyright Robert Tyler Fields 2015 ALL RIGHTS RESERVED

3 ABSTRACT Bridge components such as bridge railings are safety features designed to protect drivers. The guidelines for those safety features have recently been updated to accommodate for the increase in vehicle size. One method to bring non-conforming bridges up to current standards is retrofitting. The objective of this research is to determine the safety effectiveness of retrofitted bridges that have been updated to current standards. Bridge data and bridge related crash data from historical data for Alabama were collected. The data was cleaned and processed in a geographic information system. The remaining data was used in the development of Safety Performance Functions (SPFs) and Crash Modification Factors (CMFs). The SPFs used in this study were developed to predict crash frequency and severity in future years based on roadway and geometric characteristics. The SPFs for general crashes were developed using Negative Binomial. The SPFs for severity of single vehicle crashes were developed using both Negative Binomial and Conway-Maxwell-Poisson. The SPFs used in this study were developed in a connected study and used in this study as part of the CMF development. After obtaining the various prediction models for general crashes and for single vehicle severity crashes, the research utilized the information obtained from them in the development of the CMFs. This research employed the empirical Bayes (EB) before-after approach to develop the CMFs. The CMFs were a measure of effectiveness for retrofitting bridge railings to meet current standards. CMFs were determined for both the general crash and for severity of single vehicle crashes. The findings of this research were that retrofitting bridges to conform to the current standards results in a reduction in crashes and a reduction in the severity of crashes. The findings of this research can aid in the decision making process involving bridge railing improvements. ii

4 LIST OF ABBREVIATIONS AND SYMBOLS AADT AASHTO AMF CAPS CARE CG CMF CMP CRF EB FB FHWA GIS HSM MAF MASH NB NBI NCHRP NHS SPF TIGER Annual Average Daily Traffic American Association of State Highway and Transportation Officials Accident Modification Factor Center for Advanced Public Safety Critical Analysis Reporting Environment Comparison Group Crash Modification Factor Conway-Maxwell-Poisson Crash Reduction Factor Empirical Bayes Full Bayes Federal highway Administration Geographic Information System Highway Safety Manual Master Address File Manual for Assessing Safety Hardware Negative Binomial National Bridge Inventory National Cooperative Highway Research Program National Highway System Safety Performance Function Topologically Integrated Geographic Encoding and Referencing iii

5 θ N a N b λi x ij β j β o CMF estimate Expected crash frequency resulting from countermeasure Expected crash frequency without countermeasure Predicted number of crashes The jth explanatory variable for the mean of crash counts at bridge i Corresponding coefficients for each of the explanatory variables Constant to capture other unknown or unobserved factors ε Random term with mean of 1 and variance of 1/α Expected Before Observed Before Predicted Before Expected After Observed After Predicted After Expected number of crashes before treatment Observed number of crashes in the before period for treated sites Predicted number of crashes in the before period for treated sites Expected number of crashes after treatment Observed number of crashes in the after period for treated sites Predicted number of crashes in the after period for treated sites w 1 Weight applied to adjust the Expected Before w 2 k P Var( Expected After ) Weight applied to adjust the Expected Before Dispersion parameter Sum of annual SPF estimates in the before period Variance of the Expected After iv

6 ACKNOWLEDGMENTS I want to take this opportunity to thank the colleagues, friends, and faculty members who have aided me along the way with this research project. I am grateful to Steven Jones, the chairman of my thesis, for sharing his expertise and insight about transportation throughout this research project. I would also like to take the time to thank the other members of my thesis committee, Jay Lindly and Joe Weber, for their support and involvement with my thesis. I would like to thank Yingyan Lou for support and guidance in the initial phases of this research project, Jing Li for assistance in data processing, and Gaurav Mehta for help with the prediction models. v

7 Contents ABSTRACT... ii LIST OF ABBREVIATIONS AND SYMBOLS... iii ACKNOWLEDGMENTS...v LIST OF TABLES... ix CHAPTER 1 INTRODUCTION Problem Statement Structure of the Thesis...2 CHAPTER 2 BACKGROUND HSM Background of CMFs Theoretical Background CRFs Practical Issues Involving CMFs Implementation and Adoption into HSM CMF Clearinghouse Bridge Rail Protection Early Efforts NCHRP Report vi

8 2.4.3 Other CHAPTER 3 LITERATURE REVIEW Safety Performance Function Crash Severity Crash Modification Factor CHAPTER 4 METHODOLOGY Data Preparation Bridge Data Crash Data Data Integration Data Checking Safety Performance Functions General Crash SPF Single Vehicle Crash Severity SPF Crash Modification Factors Data Description Methodology for Empirical Bayes Before-After General Crash CMF Single Vehicle Crash Severity CMF CHAPTER 5 RESULTS vii

9 5.1 SPF Modeling Results General Vehicle Crash Data SPF Model Single Vehicle Crash Severity Data SPF Models Specification of Bridge Rail-Related CMFs General Vehicle Crash Data CMF Single Vehicle Crash Severity Data CMFs CHAPTER 6 CONCLUSIONS AND RECOMMENDATIONS REFERENCES APPENDIX A: SAMPLE DATA FOR CRASHES AND BRIDGES APPENDIX B: SAMPLE EXCEL DATA FOR CMF CALCULATION APPENDIX C: CMF CALCULATION EXAMPLE viii

10 LIST OF TABLES 4-1 Severity groupings for SPF and CMF development Estimated parameters of the NB SPFs for general vehicle crashes Individual severity specified NB SPFs for single vehicle crashes Individual severity specified CMP SPFs for single vehicle crashes Combined severity specified NB SPFs for single vehicle crashes Combined severity specified CMP SPFs for single vehicle crashes General vehicle crash CMFs Severity specified CMFs using CMP SPFs and assumed weights Combined severity specified CMFs using NB SPFs and calculated weights Combined severity specified CMFs using NB SPFs and assumed weights Combined severity specified CMFs using CMP SPFs and assumed weights A-1 Sample General Crash Data for Alabama A-2 Sample Single Vehicle Crash Data for Alabama A-3 Sample Bridge Data for Alabama B-1 Sample Excel Data for CMF Calculation C-1 CMF Calculation Example ix

11 CHAPTER 1 INTRODUCTION Bridge components such as bridge railings are safety features designed to protect drivers. These bridge components keep vehicles from running off the road by safely redirecting the vehicle towards the roadway. The Federal Highway Administration (FHWA) requires the installation of bridge railings on all National Highway System (NHS) roads, but the installation of bridge railings on other roadways is at the discretion of each state (FHWA, 2010). The National Cooperative Highway Research Program (NCHRP) Report 350 provided guidelines about the safety evaluation of safety features such as bridge railings (Ross, Sicking, Zimmer, & Michie, 1993). Recently, the Manual for Assessing Safety Hardware (MASH) has replaced the NCHRP Report 350 as the current state of practice (FHWA, 2014). The MASH was created because vehicle sizes have increased and a new standard was needed to account for the change. However, MASH does not require that the safety features accepted by the NCHRP Report 350 be replaced, but any future improvements must be up to the most current standard. A common practice to address bridge railings that do not conform to the NCHRP Report 350 or MASH standards is to retrofit the bridges. The term conforming refers to a bridge railing that has passed the crash testing standards in the NCHRP Report 350 or the MASH. The practice of retrofitting is a way to bring outdated safety features up to current standards. The retrofitting of bridge railings updates the safety effectiveness of those features which should increases driver safety. There are benefits to retrofitting safety features such as bridge railings, but there are also costs so finding when retrofitting is worthwhile is essential. This study focuses on determining the effect, whether it is positive or negative, that retrofitting has on crash frequency and severity. The Highway Safety Manual (HSM) is a guide published by the American Association of State Highway and Transportation Officials designed to help practitioners make informed decisions about situations such as the one above. The HSM provides information and tools including CMFs that can aid 1

12 in decisions making about the safety aspects of what improvements are being done. The HSM provides information and guidance in the application of CMFs which are used in this study to determine the effectiveness of retrofits. 1.1 Problem Statement The objective of this research is to analyze the safety effectiveness of retrofitted bridges to help determine if retrofitting non-conforming bridges is warranted. One part necessary for this research was the development of safety performance functions (SPFs) in order to understand crash severity and its relationship to roadway and traffic characteristics. The safety performance of both the non-conforming and conforming bridges was first evaluated by estimating SPFs from historical data for the state of Alabama. Crash Modification Factors (CMFs) were developed from before after analysis of retrofitted bridges using Empirical Bayes method to quantify the crash frequency change that results from the safety improvements. Other studies have shown the positive benefits of bridge railings, but the additional costs attributed to those improvements sometimes make the installation a selective process (Bigelow, Hans, & Phares, 2010) (Gates, Noyce, & Stine, 2006). The findings of previous studies warrant this research into the effects of retrofitting bridges that do not meet NCHRP Report 350 or MASH standards. In this research CMFs were developed to analyze the safety effectiveness of retrofits on bridges in Alabama to understand if there is a need to retrofit bridges up to the current MASH standards. 1.2 Structure of the Thesis The thesis research is presented in six chapters including the introductory material presented in Chapter 1. Chapter 2 presents the background of the study and comprises a detailed review of relevant material on the concept behind CMFs. The background of CMFs in the HSM is covered as well as practical issues associated with CMFs. Chapter 3 presents a detailed review of related research literature including the development and applicability of SPFs, crash severity studies, and CMF studies. Chapter 4 provides the methodology used in this research. The methodology contains the preparation of the data, development of SPFs, and the development of CMFs. The data preparation and the SPF methodology is 2

13 covered briefly whereas the CMF methodology is discussed in more depth because it is the primary focus of this research. Chapter 5 provides the analysis results. The analysis results include the SPF models and the CMFs. The results consist of the SPF models developed for the general crash data and the single vehicle crash severity data, the general crash data CMF developed using the Negative Binomial (NB) SPFs, and the single vehicle crash severity data CMFs developed using both NB SPFs and Conway- Maxwell-Poisson (CMP) SPFs. Finally, the conclusion and recommendations of the study are summarized in Chapter 6. 3

14 CHAPTER 2 BACKGROUND The following section covers the background of CMFs. The HSM is discussed including information about the CMFs that are contained in the HSM. The practical issues associated with the use of CMFs are covered in this section. Another source for CMFs called the CMF Clearinghouse is discussed. Finally, there is a discussion about bridge rail protection. 2.1 HSM Background of CMFs The American Association of State Highway and Transportation Officials (AASHTO) published the Highway Safety Manual (HSM) in The HSM integrates new scientific techniques and knowledge to aid practitioners in making informed decisions throughout the project development process. This includes helping in the planning, design, operations, maintenance, and the overall roadway safety management process. The HSM provides information and tools such as SPFs and CMFs to utilize in decision making with careful consideration on the safety aspects. The HSM is organized into four parts and three volumes. Part A of the HSM is an introductory part that explains the scope and the purpose of the manual. Part B of the HSM presents information which aids planners and managers in identifying sites that need improvement, diagnosis, countermeasure selection, economic appraisal, and project prioritization effectiveness evaluation (AASHTO, 2010). Part C of the HSM provides information about predictive methods which estimate expected average crash frequency. The first edition of the HSM includes three facilities types: Two-lane Two Way Rural Roads (TLTWR), Multilane Rural Highways and Urban and Suburban Arterials. Part D of the HSM provides information and guidance in the application of CMFs. The information in Part D of the HSM has passed a screening process or met approval of an expert panel (AASHTO, 2010). The application of CMFs generally occurs within the operations and maintenance activities, but can also occur throughout the 4

15 project development process. The information included in Part D of the HSM is organized into chapters about roadway segments, intersections, interchanges, special facilities and geometric situations, and road networks. Traditionally, roadway safety analysis was performed using techniques such as observed crash frequency and crash rate to determine the safety effectiveness of improvements (Wade, Hammond, & Kim, 2004; AASHTO, 2010). However, the use of these techniques can result in misleading conclusions especially if there is no consideration provided for things such as regression to the mean bias or variations in the environmental and roadway conditions. Those mislead conclusions could result in implementation of an incorrect or less efficient countermeasure. This type of situation justifies the development of HSM to help guide practitioners in conducting quantitative safety analysis, allowing safety to be quantitatively evaluated alongside other transportation performance measures like level of service or construction cost. For instance, Part D of the HSM provides the ability to quantify information about the effects of treatments, geometric characteristics, and operational characteristics for specific locations into CMFs that are included in the manual. There are over 200 crash modification factors and functions included in Part D of the HSM that passed through the six-step selection process (Carter, Srinivasan, Gross, & Council, 2012). The HSM splits the information about CMF development in Part D into chapters about different facility types. The chapters in Part D are roadway segments, intersections, interchanges, special facilities and geometric situations, and road networks. Throughout Part D of the HSM are numerous formulas used to develop CMFs for various aspects in roadway safety. Some of the CMFs in the HSM are a CMF for lane width on rural two-lane roadway segments, a CMF for shoulder width on rural two-lane roadway segments, CMFs for converting a signalized intersection into a modern roundabout, CMFs for converting stop control to signal control, CMFs for converting an at-grade intersection into a grade-separated interchange, CMFs for work zone design treatments, and CMFs for automated speed enforcement. However, the HSM does not contain CMFs related to bridges or bridge railings. 5

16 2.1.1 Theoretical Background This section contains the background for CMFs including the definition of a CMF, the application of CMFs, and other measures related to CMFs. In the past, engineers would rely on engineering judgment alone when it came to selecting countermeasures in highway safety (Carter, Srinivasan, Gross, & Council, 2012). The increasing importance of highway safety in transportation engineering throughout the years has brought progress to the science behind highway safety beyond this reliance on engineering judgment (Carter, Srinivasan, Gross, & Council, 2012). The HSM is one result of this increased focus on highway safety. The HSM provides practitioners with the state of knowledge concerning countermeasure effectiveness through crash modification factors (Carter, Srinivasan, Gross, & Council, 2012). A crash modification factor is a factor that shows how the implementation of a countermeasure affects the number of crashes that are expected at a location (Gross, Persaud, & Lyon, A Guide to Developing Quality Crash Modification Factors, 2010). For a CMF estimate,, there is a comparison made between the expected crash frequency that resulted from the implementation of a countermeasure, N a, and the expected crash frequency had that countermeasure not been implemented, N b in order to determine what kind of affect the countermeasure had on crash frequency (Hauer, Bonneson, Council, Srinivasan, & Zegeer, 2012). This comparison is usually made as a ratio in the form: Na Nb where, is the CMF estimate N a is the expected crash frequency resulting from implementation of a countermeasure N b is the expected crash frequency if the countermeasure had not been implemented The CMF estimate,, is used to predict the safety effect of the implementation in regards to crash frequency (Hauer, Bonneson, Council, Srinivasan, & Zegeer, 2012). This is done using the following equation: 6

17 N a N b However, the safety effect is usually measured by examining the change in crashes that a countermeasure causes after being implemented (Hauer, Bonneson, Council, Srinivasan, & Zegeer, 2012). The expected change in the number of crashes is obtained using the following equation: N b Na Nb 1 A CMF with a value of 1 indicates that the countermeasure resulted in no change to the current situation, whereas a CMF below 1 indicates a decrease in crashes as a result of the countermeasure and vice versa. Transportation professionals can use CMFs in several ways: 1) estimating the impact of various roadway safety countermeasures on roadway safety; 2) comparing safety benefits among various alternatives; and 3) evaluating cost benefit analysis of the counter measures. 2.2 CRFs A Crash Reduction Factor (CRF) is similar to a CMF, but it provides an estimate of the crash reduction as a percentage. When the CRF is positive, the implementation of the countermeasure is expected to cause a decrease in the percentage of crashes and when the CRF is negative that indicates that the countermeasure will be expected to cause an increase in the percentage of crashes. The CRF measures the safety effectiveness of a countermeasure and provides practitioners aid with decision making (U.S. DOT, 2008). However, engineering judgment and other information about each site such as the volume of traffic is still needed when selecting what to implement (U.S. DOT, 2008). The CRF has a mathematical relationship with the CMF. The following equation shows this relationship between the CRF and CMF: CMF CRF 1 ( ) 100 The CRF provides the percentage reduction or increase in crashes whereas the CMF provides a single number that provides the same information just in another form. For example, if a certain countermeasure has a CRF of 15% then the CMF for that same countermeasure would be Other 7

18 studies have discussed that the move from the CRF to the CMF provides a broader application range when considering the use with safety prediction models (Lord & Bonneson, 2005). 2.3 Practical Issues Involving CMFs There are several practical issues related to CMFs to discuss. Evaluations of safety effectiveness use many different performance measures such as a CMF, percentage reduction in crashes, or a benefitcost analysis (AASHTO, 2010). Several study methods exist that are used to evaluate the effectiveness of a treatment. There are several things to consider when selecting a method to evaluate the safety effectiveness of a treatment including the nature of the treatment, the types of sites at which the treatment has been implemented, and the time period for which data is available (AASHTO, 2010). Therefore, all the above information is considered in order to determine how to properly measure the safety effectiveness of a countermeasure. The CMF is the performance measure used in this study, but there are some possible issues related to CMF development that must be avoided. These issues can affect the quality of the CMF that is developed. One of these instances can occur when applying multiple CMFs. When multiple countermeasures are implemented at one location caution should be taken while trying to determine the combined safety effect of the countermeasures. Simple multiplying the CMFs of the various countermeasures implemented to try to determine the combined safety effect could result in overestimating the combined effect (Gross, Persaud, & Lyon, A Guide to Developing Quality Crash Modification Factors, 2010). Another instance to carefully consider involves the use of CMF determined from locations with high crash frequencies. The effectiveness of a countermeasure can be overestimated if a CMF from locations with high crash frequencies is applied to locations with much lower, more average amounts of crashes (Gross, Persaud, & Lyon, A Guide to Developing Quality Crash Modification Factors, 2010). Other considerations for CMFs are related to before-after study methods like the EB before-after used for this study which includes sample size and potential bias (Gross, Persaud, & Lyon, A Guide to Developing Quality Crash Modification Factors, 2010). 8

19 The HSM and the CMF Clearinghouse are two sources for CMFs. Both have screened the CMFs that are included to avoid the issues presented above. The screening process used on the CMFs for both the HSM and CMF Clearinghouse is observed Implementation and Adoption into HSM The HSM contains various CMFs that have been through a six-step screening process (Carter, Srinivasan, Gross, & Council, 2012). Before the six-step process, a literature review is conducted in order to identify potential CMFs that exist in published studies that could be used in the HSM. The sixstep process is then performed on the studies that were examined. The first step was to determine the estimate of the safety effect of the treatment as documented in the study that is examined. The second step is to adjust the estimate of the safety effect to account for potential bias. The potential bias that must be accounted for is regression-to-the-mean and changes in traffic volume (Carter, Srinivasan, Gross, & Council, 2012). The third step in the process is to determine the standard error of the safety effect. The fourth step is to apply a correction factor to the standard error based on the evaluation characteristics of the study. This correction factor that is applied to the standard error is used to adjust the reliability of the standard error (Carter, Srinivasan, Gross, & Council, 2012). The fifth step in this process is to adjust the corrected standard error to account for bias. The final step in the process is to combine CMFs when specific criteria are met. After the six-step process is completed, the CMFs were filtered based on the adjusted standard error (Carter, Srinivasan, Gross, & Council, 2012). The HSM includes all CMFs that have an adjusted standard error of 0.1 or less and also includes CMFs with an adjusted standard error between 0.1 and 0.3if those CMFs came from a study that produced CMFs with an adjusted standard error of 0.1 (AASHTO, 2010). The procedure necessary to implement the CMFs contained in the HSM is discussed when each CMF is identified in the HSM. The HSM covers how to apply the CMFs for various safety treatments. It also identifies what considerations to take when applying the CMFs. 9

20 2.3.2 CMF Clearinghouse The CMF Clearinghouse is a resource available to help transportation officials make decisions about transportation safety. The CMF Clearinghouse provides a comprehensive list of available CMFs (U.S. DOT, 2009). It includes all CMFs that are part of the HSM and many other CMFs that are not part of the HSM. Similar to the HSM, the CMF Clearinghouse has a review process for CMFs. The CMF Clearinghouse review process is based on the study design, sample size, standard error, potential biases, and data source and assigns a star rating between one and five depending on how those five categories are addressed (U.S. DOT, 2009). The CMF Clearinghouse presents all available CMFs, regardless of the quality (Carter, Srinivasan, Gross, & Council, 2012). This allows users to examine all CMFs and select what is most appropriate for each situation. 2.4 Bridge Rail Protection Bridge components such as bridge railings are safety features designed to protect drivers. These bridge components keep vehicles from running off the road by safely redirecting the vehicle towards the roadway. Thus, bridge railings are an important factor in terms of mitigating crashes. FHWA requires the installation of bridge railings on all National Highway System (NHS) roads that have met the appropriate crash test criteria (FHWA, 2010). The guidelines for installation of bridge railings on non- NHS roads is at the discretion of State transportation agencies, but FHWA recommends the use of crashworthy railings on facilities with the chance of run-off-the-road crashes (FHWA, 2010). This study examines how the guidelines for bridge rail safety have changed over the years Early Efforts There have been many changes to the guidelines for bridge railings from early efforts in bridge rail safety. Engineering judgment and the current edition of the Standard Specifications for Highway Bridges (AASHTO, 1973) were the basis of appropriate bridge railing selection until the late 80 s (FHWA, 1997). However, these standards did not require total crash testing for bridge railings to be implemented. The FHWA later required that all bridge railings meet the criteria for crash testing 10

21 established in the National Cooperative Highway Research Program (NCHRP) Report 230 Recommended Procedures for the Safety Performance Evaluation of Highway Appurtenances (Transportation Research Board, 1981) after the determination that many of the currently accepted railings failed the crash testing. Later, AASHTO also presented specific tests in three performance levels in Guide Specifications for Bridge Railings (AASHTO, 1989), but its use by state highway agencies was optional. The next update to bridge railing safety guidelines came in 1993 in the NCHRP Report 350 Recommended Procedures for the Safety Performance Evaluation of Highway Features (Ross, Sicking, Zimmer, & Michie, 1993) NCHRP Report 350 The NCHRP Report 350 Recommended Procedures for the Safety Performance Evaluation of Highway Features provides the guidelines for safety evaluation of features such as bridge rails and guardrails (Ross, Sicking, Zimmer, & Michie, 1993). The NCHRP Report 350 contains crash testing for six different test levels. The first three test levels are based on impact speeds for light vehicles and the other three tests contain additional tests for bridge railings about containing and redirecting heavy vehicles. The FHWA requires that at minimum new railings on NHS roads must meet test level 3 to be accepted. The NCHRP report 350 guidelines remained in effect until it was updated and replaced by the AASHTO Manual for Assessing Safety Hardware (MASH) (AASHTO, 2009) Other The MASH has become the current state of practice for crash testing (FHWA, 2012). The MASH was created because vehicle sizes have increased and a new standard was needed to account for the change. The increase in vehicle size resulted in the bumper of vehicles being raised which made the existing railings less effective at safely redirecting the vehicles back to the roadway. However, the MASH does not require that the safety features accepted by the NCHRP 350 be replaced, but any new railings as of 2011 must be up to MASH standards. 11

22 CHAPTER 3 LITERATURE REVIEW This section of the research contains the review of literature involving safety performance functions, crash severity studies, and crash modification factors. First, the safety performance function literature is reviewed. After that there are some crash severity studies. Finally, the crash modification factors literature is covered. 3.1 Safety Performance Function Safety performance functions are statistical models used to describe the relationship between crash frequencies (or severity) and characteristics of roadways and traffic, such as AADT and facility types. Safety performance functions are used to identify which facilities are candidates for safety improvement. There are three important applications of SPFs listed in the HSM. The first application in the HSM is to determine the safety impacts of design changes at the project level. The second application is to identify sections of roads which have high potential for safety improvements. The third application is to evaluate the safety effects of countermeasures as a part of the empirical Bayes before-after study. The various regression models commonly used in SPF development are covered next. Several methods exist in estimating safety performance functions including lognormal regression and log-linear regression (Tegge, Jo, & Ouyang, 2010). Lognormal regression and log-linear regression are both maximum likelihood estimation methods. Maximum likelihood estimation is a statistical method that estimates the variables in a sample by selecting the values of the parameter that maximizes the probability of obtaining the observed data. Lognormal regression models are used in situations where the distribution of the data is skewed and the natural log of the crash frequency is assumed to be normally distributed. It is ideal to use in modeling for high-volume intersections (Tegge, Jo, & Ouyang, 2010). Log-linear regression models are a specialized case of linear model (Jeansonne, 2002). Log-linear models 12

23 are used to analyze the conditional relationship of two or more response variables by taking the natural logarithm of the dependent variable (Jeansonne, 2002). Poisson models and negative binomial models are two common types of log-linear regression. Poisson models assume that the response variable follows a Poisson distribution, a discrete distribution that portrays the chance, over a certain amount of time, of a given number of independent events occurring. Negative binomial models, which are used in this study, are similar to Poisson models except the response variables are assumed to follow a negative binomial distribution. Negative binomial distribution also allows the variance to exceed the mean which gives it a broader range of application than Poisson distribution. Negative binomial models can also account for variations caused by factors not explicitly included in the model. As a result, negative binomial regression is better for SPF analysis (Tegge, Jo, & Ouyang, 2010). One main advantage of this method is that it is easy to account for overdispersion. However, this regression method performs poorly when the data is under-dispersed or it has low sample mean and sample size (Lord & Mannering, 2010). This study used negative binomial regression as one method to develop safety performance functions for bridges in Alabama. The SPFs developed using NB were for general crash data and for single vehicle crash severity data. Another regression model used in the development of SPFs is Conway-Maxwell-Poisson. This distribution, which is a generalization of the Poisson distribution, was proposed by Conway and Maxwell in 1962 for modeling queue and service rates. In 2005, Shmueli et al. (2005) derived the statistical properties of this distribution. It is a unique distribution with Geometric, Bernoulli and Poisson distributions as its special cases. The main advantage of this distribution over other models discussed above is its capability to handle both over-dispersed and under-dispersed data. Lord et al. (2008) applied this distribution in highway safety research. The results showed that the CMP model perform comparable to NB regression model for over-dispersed data and provide better fit for under-dispersed data. It should be noted that the CMP model does not perform well when the mean of the sample is low or the sample size is very small. The study used CMP to develop SPFs for single vehicle crash severities. 13

24 3.2 Crash Severity A few studies have analyzed the safety performances of bridge railings based on crash severity. For most state departments of transportation the decision to install bridge guardrails on non-nhs roadways follows certain guidelines with recommended threshold values of certain roadway characteristics, such as the annual average daily traffic (AADT), speed limits, and the geometry of the bridge (Bigelow, Hans, & Phares, 2010). Previous studies have tried to determine the appropriate threshold values for some of the characteristics that are effective. A benefit-to-cost ratio analysis is performed to select the appropriate AADT threshold for the installation of bridge rails and guardrails on low volume roads (Gates, Noyce, & Stine, 2006; Bigelow, Hans, & Phares, 2010). In order to determine the benefit of bridge railings one study applied logistic regression to develop a relationship between crash severity and roadway and bridge components including bridge railings (Gates, Noyce, & Stine, 2006). The study concludes that bridges with guardrails are much safer than bridges without guardrails when considering crash severity. Collisions with the roadside are 2.5 times more likely to result in a fatality or A-injury whereas collisions with the railings usually result in no injury or minor injuries (Gates, Noyce, & Stine, 2006). A study in Iowa determined crash frequencies, using Poisson models, for low volume bridges and crash rates for various characteristics including AADT, bridge width, and bridge length to use in their benefit-to-cost analysis (Bigelow, Hans, & Phares, 2010). The benefit of bridge railings is apparent when considering the reduction in crash severity; however, the bridge railings increase installation and maintenance costs. In considering the previous statement, a cost analysis is necessary to determine when the installation of bridge railings is supported. In the cost analysis the savings attributed to bridge railings is calculated by comparing all costs of the railings to the costs of the more severe crashes that occur without the bridge railings (Gates, Noyce, & Stine, 2006). In Iowa the cost analysis obtained the benefit of updating the bridge rails by comparing crash costs with crash reduction factors (CRF) to determine the amount saved due to reduction in crash numbers or severity (Bigelow, Hans, & Phares, 2010). Finally the benefit-to-cost ratios were used to determine the effectiveness of bridge railings in various situations. 14

25 In Minnesota, the benefit-to-cost ratio analysis for a range of traffic volumes led to a recommended threshold of 400 AADT for installing railings on bridges on low volume roads (Gates, Noyce, & Stine, 2006). However, another study found that the benefit-to-cost ratios were very small on low volume bridges in Iowa, due to the rarity of crashes on those bridges (Bigelow, Hans, & Phares, 2010). It was recommended that the installation of bridge railings should be determined on a case-bycase basis (Bigelow, Hans, & Phares, 2010). 3.3 Crash Modification Factor There have numerous studies that examine effectiveness of safety measures through CMF development. There are various approaches, some simple and others using more complex methods, taken in these studies in the development of CMFs. A brief summary of these studies and the approaches taken is discussed below. The approaches covered include the before-after with comparison group method, empirical Bayes before-after method, case-control method, and the full Bayes method. The role and application of Accident Modification Factors (AMFs) is explored in one study conducted by the Texas Transportation Institute. The AMF mentioned in this study is also referred to as a CMF. The study explains the move from Crash Reduction Factors (CRFs) to the more general concept of AMFs because the reduction was a limiting term since not all improvements will lead to accident reduction (Lord & Bonneson, 2005). This study highlights that the extension to the AMF has a broader application when considering the use with safety prediction models than the CRF concept (Lord & Bonneson, 2005). The study also discusses the mathematic relationship between the CRF and AMF. The study provides a few example applications and procedures to follow for AMFs in the highway design process and the study concludes stating the important role that AMFs can play. Another study conducted in Australia sought to determine an improved methodology for computing CMFs. The study examines the strengths and weaknesses of the Comparison Group (CG) method and the Empirical Bayes (EB) method which are the two most commonly utilized approaches to develop CMFs (Goh, Currie, Sarvi, & Logan, 2012). The EB method can account for regression to the 15

26 mean, but needs a sufficient sample size and it can be difficult to properly account for confounding variables (Goh, Currie, Sarvi, & Logan, 2012). The CG method is able to effectively handle confounding variables, but it can be hard to determine comparison sites and it does not account for regression to the mean (Goh, Currie, Sarvi, & Logan, 2012). This study attempts to develop an approach that combines the CG and EB to account for the limitations associated with each approach for a more accurate CMF. The combined CMF is determined by taking a weighted ratio of the resulting CMFs from both methods. The study found that the combined EB and CG can provide a more precise CMF when the standard errors of the EB and CG are comparable. The Case-Control approach is applied in a study about the estimation of the safety effectiveness of lane and shoulder width. The study decided upon the case-control approach to avoid common limitations of the before-after studies and to compare the safety effectiveness estimates of the case-control with safety effectiveness measured by CMFs (Gross & Jovanis, Estimation of the safety Effectiveness of Lane and Shoulder Width: The Case-Control Approach, 2007). The case-control approach determines an odds ratio which by definition is similar to a CMF, but the two differ by some quantification of exposure to risk so the study applied an adjustment to account for it (Gross & Jovanis, Estimation of the safety Effectiveness of Lane and Shoulder Width: The Case-Control Approach, 2007). The study concludes that the results from the case-control approach are generally consistent with CMFs, but there are differences when dealing with extreme values of lane and shoulder width. A study conducted in the state of Iowa discusses the progression from Empirical Bayes to Full Bayes (FB). The study presents the FB approach and its differences to EB. The study discusses that FB may be less costly to implement and may result in safety estimates with more realistic standard errors since all uncertainties are accounted for in the analyses (Carriquiry & Pawlovich, 2004). The conclusion of this study is that the FB approach has the potential for more reliable assessments than EB. 16

27 CHAPTER 4 METHODOLOGY The methodology of the research is covered in this section. The first part of the methodology is the data preparation. The data preparation subsection includes the preparation of the bridge data, the preparation of the crash data, the integration of the data, and the data checking/validation. The next part of the methodology is for the SPF development. The SPFs for this study were obtained from a connected study and used as part of the CMF analysis. However, a brief view into the methodology applied to the SPFs and how the various SPFs were developed is covered. The final part of the methodology involves the primary focus of this study which is the CMFs. 4.1 Data Preparation The three different data sets for Alabama which include the bridge data, the road shapefiles, and the historical crash data used in this study come from a few different sources. The bridge data which contains geometric information and traffic information about bridges in Alabama is obtained from the National Bridge Inventory (NBI) database. The road shapefiles for Alabama are obtained from the U.S. Census Bureau s Master Address File/Topologically Integrated Geographic Encoding and Referencing (MAF/TIGER). The road shapefiles are needed to combine with the bridge data in a Geographic Information System (GIS) called ArcGIS to determine bridge vectors from the point locations of the bridge data contained in the NBI. The historical crash data for Alabama is obtained through the Critical Analysis Reporting Environment (CARE) program from the Center for Advanced Public Safety (CAPS) at the University of Alabama. The collection and processing of the data is covered in the following subsections. 17

28 4.1.1 Bridge Data As stated previously, the bridge data for Alabama is obtained from the NBI database. The NBI database contains raw inventory data for 17,513 bridges in Alabama. However, the raw inventory data for bridges from NBI contains all types of bridges that are located in the state of Alabama including railroad bridges. The focus of this study is on evaluation of the safety effectiveness of bridges located on state highways and interstate highways. This meant that the bridge data had to be processed down to the target data. After processing the data, the study determines that there are 1,032 bridges located on state and interstate highways from the NBI database. 90 additional bridges located on state and interstate highways in Alabama that were not contained in the NBI database were added to the existing 1,032 bridges. The final bridge data list contained 1,122 Alabama bridges and was coded into point shapefiles in ArcGIS. However, the point locations of the bridges had to be adjusted. The locations of the final bridges in the list were then moved to the nearest road using ArcGIS and the road shapefiles obtained from the MAF/TIGER database. The point locations of the bridges and the road shapefiles were then used to convert the bridge data into bridge vectors. The report (Jones, Li, Mehta, & Fields, 2014) can be examined to obtain more detailed information about the process used to create the bridge vectors Crash Data Historical crash data for Alabama is collected from the Critical Analysis Reporting Environment (CARE) software which is maintained by the Center for Advanced Public Safety at the University of Alabama. The crash data used in the SPF analysis is historical data from When performing the CMF analysis, additional years of crash data is obtained in order to increase the likelihood of having crash records available for the bridges considered in the analysis. The crash data used in the CMF analysis is from The information available for the crash data includes the causal factors, the number of vehicles involved, GPS coordinates, etc. The crash data is allocated to the bridge vectors from the previous section using the GPS coordinates of each crash. 18

29 The approach of associating the crashes to bridges requires some processing of the results to only include bridge-related crashes in the final crash data. The outcome of this approach results in 9,958 crashes available for the development of the SPF for the general vehicle crash data. The process is also performed for the single vehicle crash data. However, there was a change in the reporting format for crashes in between the years resulting in the use of only crash data from for the development of the SPF for the single vehicle crash data. The result available for SPF development of the single vehicle crash data is 865 crashes Data Integration The bridge vectors and the crash data are integrated in order to determine the crashes that were related to the bridges. The crash data is associated to the bridge vectors using ArcGIS. The method to relate crashes to bridges in ArcGIS is to accept crashes as bridge-related if the GPS coordinate of the crash was directly on the bridge or within one half of the length of each individual bridge on both sides of the bridge vector. The process through which the crashes are related to bridges using ArcGIS is discussed next. First, the bridge vector data, the crash data, and the road shapefiles are loaded into ArcGIS. Next, the crash data sets, general vehicle crash data and single vehicle crash severity data, are associated with the bridge vectors using the near (analysis) tool which provides the distance from one feature to the nearest feature. For this study that provides the nearest bridge that exists for each crash. The near analysis creates two additional columns in the crash data sets, the near id and the near dist. The near id is the unique id of the bridge that is returned as the nearest feature to that particular crash and the near distance provides the distance that is between the crash and the bridge. The crash data sets are then filtered down to get rid of crashes that did not have a bridge within a certain range. The two columns that are created in the near analysis are then stored on the crash data sets in the attributes table of each. After that the near analysis is repeated for the remaining crashes in the crash data sets with the road shapefiles. Once again the crash data sets are filtered down and the two columns, near id and near distance, are created between the crashes and the road shapefiles. Subsequently, the attribute tables for the bridge 19

30 vector data and the road shapefiles data are joined into the crash data set attribute table based on the two near id columns created through the near analysis. Finally, the crash data sets are filtered down a final time using the selection tool in the attribute table. The crashes are selected when the crashes fall within half the bridge length plus 100 feet of a bridge and if the crashes are within 90 feet of a road. The remaining crash data is the finalized data that is used in the development of the SPFs and CMFs. This method is used to associate crashes to bridges for two main reasons. The first reason is that the coordinates of the crashes might not be exactly accurate due to the fact that generally the vehicles are moved to the side of the road before the crash report is filed. For example, crashes that occur on bridges might result in the vehicle(s) being moved off the bridge to either side to get the vehicle(s) out of the roadway and that results in the GPS coordinate being relocated off from the bridge. If crashes are only accepted as bridge-related when the GPS coordinate is located exactly on the bridge then this would result in the provided example being excluded from analysis. The other reason is to account for the influence area of the bridges. The increased search area around the bridges allows for inclusion of crashes that are in the influence area of the bridges that would otherwise be left out of the analysis. However, this method of associating crashes could also include crashes that should not be associated with bridges. This means that the resulting crashes need to be further examined to ensure that the bridge-related crashes are properly coded and that crashes that did not belong are removed such as a crash that results on the underpass and not the bridge. This process is performed by examining the road name that is associated to the crashes in the crash data and the road name that is associated with the bridges in the bridge vector data. When the road names between the crashes that are associated with bridges through this method and bridges that each crash is associated with does not match then that crash record is removed from the list. The remaining list of crashes after cleaning out the unmatched records includes only the crashes that were bridge-related that are used for the SPF model development and CMF analysis in this study. 20

31 4.1.4 Data Checking Throughout the process of the collection and the preparation of the data sources the data had to be checked and cleaned. The bridge data and the crash data are trimmed down to obtain the target data that is needed for this study. The bridge data requires processing to get the total bridge data down to bridges that exist on state and interstate highways. The crash data is processed as described in the previous subsection to remove all crashes that are not associated with bridges so that the remaining crashes that are used in the SPF development and CMF analysis for bridges are bridge-related. The accuracy of the data sources and a conformity check on the existing bridge rails is included as part of the data checking Accuracy The bridge data and the crash data used in this study are loaded into ArcGIS based on the GPS coordinates available in each data set. The GPS coordinate of the crash data is only used to locate the crashes on the map in ArcGIS and to associate the crashes with bridges. Therefore, the accuracy of the bridge data is determined and improved to ensure that the proper crashes would be associated with the bridges. Two steps are taken to improve the accuracy of the bridge data. First, the bridge data is examined in Google Maps to determine how accurate the bridge GPS coordinates are in respect to the actual location of the bridges. The result of this examination shows that a majority of the coordinates of the bridges in the data were relatively close to the actual location of the bridge. One study found that around 98% of bridge coordinates are within two miles of the actual location of the bridge (Chase, Small, & Nutakor, 1999). This meant that the locations of the bridges had to be adjusted to the nearest road. The road names for each bridge are then checked against the road name of the nearest road in the road shapefiles that the bridge is relocated onto in order to ensure that the bridges are matched with the proper road. That adjustment of the bridges towards the actual location of the bridge provides increased accuracy when assigning crashes to the bridges. Next, the bridge point locations that are adjusted to the roadways are then turned into bridge vectors. However, the study had to determine what point along the bridges that the point location of the 21