Intersection Crash Prediction Methods for the Highway Safety Manual (2021)

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197 Chapter 9. Development of Models for Use in HSM Crash Prediction Methods: Crossroad Ramp Terminals at Tight Diamond Interchanges This section describes the development of crash prediction models for crossroad ramp terminals at tight diamond interchanges (TDs). Tight diamond interchanges are implemented in urban areas. Their crossroad ramp terminals are characterized by two at-grade intersections spaced between 200 and 400 ft apart, through which all at-grade traffic movements are made (Leisch, 2005, Hughes et al., 2010, Sellinger and Sharp, 2000). An additional characteristic of the tight diamond interchange is exclusive left-turn lanes, for movements from the crossroad to the freeway, in advance of the upstream ramp terminal (Leisch, 2005). The two intersections of the tight diamond interchange are signalized to operate as one (Leisch, 2005). Section 9.1 describes the site selection and data collection processes for developing crash prediction models for crossroad ramp terminals at tight diamond interchanges. Section 9.2 provides descriptive statistics of the databases used for model development. Section 9.3 presents the statistical analysis and resulting SPFs for crossroad ramp terminals at tight diamond interchanges. Section 9.4 discusses CMF development for use with the SPFs. Section 9.5 addresses the outcomes of the analysis to develop SDFs for crossroad ramp terminals of tight diamond interchanges. Section 9.6 provides recommendations for incorporating the new crash prediction models for crossroad ramp terminals at tight diamond interchanges in the second edition of the HSM. 9.1 Site Selection and Data Collection A list of potential tight diamond interchanges was developed by searching databases and satellite imagery in six states: • Arizona (AZ) • California (CA) • Florida (FL) • Minnesota (MN) • Ohio (OH) • Utah (UT) Data collection activities for these sites included gathering geometric design attributes of the interchanges as well as traffic and crash data. Geometric attributes were collected from aerial imagery in Google Earth®, as well as Google Street View®. Table 99 lists the geometric attributes collected (and respective definitions and permitted values) for each tight diamond interchange.

198 Table 99. Site characteristic variables collected for crossroad ramp terminals at tight diamond interchanges Variable Definition Range of Permitted Values General Intersection Attributes Intersection configuration (i.e., number of legs and type of traffic control) Indicates the number of legs and type of traffic control 4SG Area type Indicates whether the intersection is in a rural or urban area Urban Presence of intersection lighting Indicates if overhead lighting is present at the intersection proper Yes, no Crossroad over or under freeway Indicates whether the crossroad passes over or under the freeway Over or under Construction year Estimated year when the interchange was constructed Range: 2005 to 2018 Approach Specific Attributes Route name or number Specifies the route name or number of the approach Location at intersection Side of the intersection the approach is located Primary, secondary Presence of left-turn lanes The number of approaches with one or more left-turn lanes 2,3,4 Left-turn protected only Number of approaches with protected only left-turn operations 0,1,2 Number of left-turn lanes Number of left-turn lanes provided for turning movements to/from each freeway ramp 0, 1, 2 Presence of right-turn lane Number of approaches with one or more right-turn lanes 0,1,2 Number of right-turn lanes Number of right-turn lanes provided for turning movements to/from each freeway ramp 0, 1, 2 Number of through lanes Number of through lanes present on each crossroad approach to each crossroad ramp terminal 1, 2 Presence of frontage roads Indicates the presence of frontage roads at the interchange, where a through movement is added between the exit and entrance ramps Yes, no Presence of crosswalk Indicates the presence of crosswalks at the crossroad ramp terminal Yes, no Presence of bike lane Indicates the presence of a bike lane on the crossroad at each crossroad ramp terminal Yes, no Median width Width of median (in feet) on each crossroad approach to each crossroad ramp terminal Range: 0 to 32 Median type Type of median present on each crossroad approach to the crossroad ramp terminal Raised, flush, none Number of driveways Number of driveways located within 250 ft of the crossroad stop bars/lines Range: 0 to 2 Number of intersections Number of intersections with public streets located within 250 ft of the stop bars/lines Range: 0 to 4 Presence of railroad crossing Indicates the presence of a railroad crossing on the crossroad Yes, no Traffic control type for right turns Type of traffic control for right-turn movements Signal, stop, yield, none Number of channelized right turns Number of right-turn movements from the crossroad to ramps and from the ramps to the crossroad with raised or painted island 0, 1, 2, 3, 4 U-turns allowed Indicates if a U-turn is allowed between exit ramps and entrance ramps Yes, no The “construction year” was estimated using the “Clock” feature in Google Earth® as the earliest year with the interchange present in aerial imagery. Some tight diamond interchanges in the database were built during the study period and, therefore, had fewer years of data available for analysis. Additional information about the interchange configuration was used to exclude sites with uncommon or inconsistent geometric conditions, such as the lack of a left-turn lane on a crossroad approach. Speed limits on freeways and crossroads were not collected because they were not statistically significant in single-point interchange models.

199 Traffic data collection activities primarily involved accessing publicly available traffic volumes and statistics. Crash data were obtained from state DOTs. The crash data generally included details about the crash location (geographic coordinates), as well as attributes describing the crash, people involved in the crash, and the road and environmental conditions at the location and time of the crash. Identifying crashes associated with the ramp terminal required a clear definition of a ramp terminal-related crash based on geographic location and crash attributes. To maintain a level of consistency with the ramp terminal models in NCHRP Project 17-45 and in the single-point diamond chapter of this report, these crashes were selected using the following criteria: • Crashes occurring on the crossroad within the ramp terminal boundary, defined as a point 100 ft from the gore or curb return of the outermost ramp connection, and having one of the following attributes: - at intersection - intersection-related - at driveway - driveway-related - involving a pedestrian or bicyclist • Crashes occurring on a ramp with at least one of the following attributes: - at intersection - intersection-related - involving a pedestrian or bicyclist - located on an exit ramp and manner of collision is rear-end This definition departs from the NCHRP 17-45 ramp terminal definition, using a different distance reference to define the crossroad ramp terminal boundary. The NCHRP 17-45 definition used 250 ft from the crossroad ramp terminal, measured from the center of the intersection. The definition implemented for the crossroad ramp terminals of tight diamond interchanges (as well as single-point diamond interchanges) is based on the ANSI D16.1-2007 (Manual on Classification of Motor Vehicle Traffic Accidents) definition of an interchange crash. According to the ANSI definition, an interchange crash is a crash in which the first harmful event occurs within a boundary defined by a point 100 ft from the gore or curb return of the outermost ramp connection. Figure 74 shows an example of a tight diamond interchange with the boundaries for identifying interchange-related crashes. Crossroad crashes were identified using the yellow boundary, while ramp crashes were identified using the white boundaries.

200 Figure 74. Example of a tight diamond interchange with the ramp boundaries definition All of the collected data (i.e., site characteristics, crashes, and traffic volumes) were assembled into one database for the purpose of model development. After initial database development and quality assessments, interchanges in Arizona and Utah were selected for model development due to a higher level of confidence in accurately and reliably locating and identifying terminal- related crashes in those states. This decision resulted in 57 potential crossroad ramp terminals for model development. This list of interchanges was further reduced due to lack of available or compatible data. Specifically, one interchange was removed because it was not striped as a tight diamond interchange until 2015, one was removed because crossroad traffic volumes were not available, and three were removed because ramp traffic volumes were either questionable or nonexistent. With 52 potential sites remaining for model development, CURE plots for preliminary models indicated one potential outlier was present in the database. This location had an exceptionally low number of crashes compared to the traffic volume in the interchange. The final database excluded this site, resulting in 51 crossroad ramp terminals at tight diamond interchanges for model development. 9.2 Descriptive Statistics of Database A total of 51 crossroad ramp terminals at tight diamond interchanges were used for crash prediction model development. The selected sites were from two states: Arizona and Utah.

201 Traffic Volumes and Site Characteristics Traffic volumes and crash data from years 2011 through 2015 were used for analysis. Table 100 provides summary statistics for traffic volumes at the study sites used for model development. Study period (date range), number of sites and site-years, and traffic volume descriptive statistics are shown by state. Table 100. Crossroad and ramp AADT statistics at tight diamond interchange crossroad ramp terminals State Date Range Number of Sites Number of Site- Years Crossroad AADT Ramp AADT (sum of all four ramps) Min Max Mean Median Min Max Mean Median AZ 2011-2015 45 225 8,921 51,438 27,467 26,357 9,955 74,656 38,827 38,386 UT 2011-2015 6 28 14,600 34,200 24,322 25,200 20,416 72,179 35,842 31,523 All states 2011- 2015 51 253 8,921 51,438 27,097 26,357 9,955 74,656 38,476 37,049 Interchange geometric characteristics were collected using Google Earth® and Google Street View® (Table 99). The key variables of interest for modeling were: • Distance between terminals - Min = 174.5 ft, Max = 387 ft, Mean = 307.9 ft • Number of through lanes on crossroad approaches - Min = 0, Max = 4, Mean = 2.20 • Number of left-turn lanes - Exit (from freeway) and entrance (to freeway) movements: Min = 0, Max = 2, Mean = 1.30 • Number of right-turn lanes - Entrance (to freeway) movements: Min = 0, Max = 2, Mean = 0.82 - Exit (from freeway) movements: Min = 0, Max = 2, Mean = 1.05 - All movements: Min = 0, Max = 2, Mean = 0.94 • Traffic control type for right turns - To entrance ramp: • Both signalized: 47 sites • Both yield control: 1 site • 1 signalized, 1 no control (free right): 2 sites • 1 yield, 1 no control: 1 site - From exit ramp • Both signalized: 44 sites • Both yield control: 3 site • 1 signalized, 1 no control: 3 sites • 1 yield control, 1 no control: 1 site

202 The findings with respect to some of these site characteristics are discussed in Section 9.3 on SPF development. Crash Counts All 51 interchanges included in the study experienced crashes. The average number of SV and MV crashes per terminal was 92.8 crashes (approximately 18.7 crashes per terminal per year), and the average number of vehicle-pedestrian plus vehicle-bicycle crashes per intersection was 1.4 over the entire study period (approximately 0.3 pedestrian and bicycle crashes per terminal per year). Table 101 shows all, SV, and MV crash counts by crash severity and time of day for each state over the entire study period. Crash counts are tallied by collision type and manner of collision across all states in Table 102. Table 101. All crashes combined, single- and MV, and pedestrian and bicycle crash counts by crash severity—tight diamond interchange crossroad ramp terminals State Date Range Number of Sites Number of Site- Years Time of Day All Crashes SV Crashes Multiple-Vehicle Crashes Pedestrian Crashes Bicycle Crashes Total FI PDO Total FI PDO Total FI PDO Total FI PDO Total FI PDO AZ 2011-2015 45 225 All 4185 1215 2970 144 30 114 3974 1125 2849 23 22 1 44 38 6 UT 2011-2015 6 28 All 621 199 422 14 3 11 601 190 411 2 2 0 4 4 0 All states 2011- 2015 51 253 All 4806 1414 3392 158 33 125 4575 1315 3260 25 24 1 48 42 6 Table 102. Crash counts by collision type and manner of collision and crash severity at tight diamond interchange crossroad ramp terminals Collision Type Total FI PDO Single-Vehicle Crashes Collision with animal 1 0 1 Collision with fixed object 128 19 109 Collision with other object 2 0 2 Collision with parked vehicle 0 0 0 Other SV collision 27 14 13 Total SV crashes 158 33 125 Multiple-Vehicle Crashes Head-on collision 31 14 17 Angle collision 1428 617 811 Rear-end collision 2592 628 1964 Sideswipe collision 461 39 422 Other MV collision 63 17 46 Total MV crashes 4575 1315 3260 Nonmotorized Crashes Pedestrian 25 24 1 Bicycle 48 42 6 Total nonmotorized crashes 73 66 7 Total Crashes 4806 1414 3392

203 9.3 Safety Performance Functions—Model Development SPFs for the crossroad ramp terminal of a tight diamond interchange were developed using Equation 57: 𝑁 = 𝑒𝑥𝑝 𝑎 + 𝑏 × ln(𝐴𝐴𝐷𝑇 ) + 𝑐 × ln 𝐴𝐴𝐷𝑇 (Eq. 57) Where: Nspf int = predicted average crash frequency of a crossroad ramp terminal at a tight diamond interchange with base condition (crashes/year); AADTxrd = AADT on the crossroad (veh/day); AADTramp = sum of ramp AADTs (veh/day); and a, b, c = estimated regression coefficients. The SPFs were developed using NB regression. All data from AZ and UT were used in developing the SPFs to maximize the sample size. However, separate models for AZ and UT were first compared and showed consistency between the models, which increased confidence that combining the data was appropriate. STATA 14.2 was used for modeling. The final SPF models for tight diamond interchange crossroad ramp terminals are shown in Table 103, and separate SPFs are provided for different crash severity levels—total, FI, and PDO crashes. Table 103 displays the overdispersion parameter (estimate), standard error, and significance level (p-value) for the model variables for each severity level. SPFs for vehicle-pedestrian and vehicle-bicycle collisions at crossroad ramp terminals of tight diamond interchanges could not be developed as pedestrian and bicycle volumes were not available. The SPFs predict the average crash frequency at the crossroad ramp terminal for all crash types (i.e., multi-vehicle, SV, pedestrian, and bicyclist) of different injury severities. Table 103. SPF coefficients for tight diamond interchange cross ramp terminals Crash Severity Parameter Estimate Standard Error Pr > F Significance Level Total Crashes Intercept -11.46 2.03 -- -- ln(AADTxrd) 0.68 0.26 0.008 Significant at 99% level ln(AADTramp) 0.71 0.22 0.002 Significant at 99% level Overdispersion 0.25 0.05 -- -- FI Crashes Intercept -11.90 2.09 -- -- ln(AADTxrd) 0.50 0.26 0.05 Significant at 95% level ln(AADTramp) 0.81 0.22 <0.001 Significant at 99% level Overdispersion 0.23 0.06 -- -- PDO Crashes Intercept -11.99 2.19 -- -- ln(AADTxrd) 0.77 0.28 0.006 Significant at 99% level ln(AADTramp) 0.63 0.24 0.009 Significant at 99% level Overdispersion 0.29 0.06 -- -- No base conditions The estimated SPFs use both the crossroad AADT and sum of AADTs on all ramps connected to the interchange. The natural log of the years of data was included as an offset in all models. The coefficients for these terms are positive and statistically significant (at greater than or equal to 95% confidence level) in each SPF, although their magnitudes fluctuate between the FI and PDO models. The crossroad and ramp volume coefficients indicate that as the volumes increase, the predicted crash frequency increases.

204 Before finalizing the models in Table 103, multiple models were developed testing other variables, such as traffic control type for right turns, number of left-turn lanes, number of right- turn lanes, number of channelized right turns, distance between terminals, number of driveways, and number of intersections. However, none of the parameters associated with the tested variables were statistically significant in the models. The only statistically significant variables, which were included in the final models, were the crossroad and ramp AADT. In addition, CURE plots were developed for the SPFs to determine and analyze the functional form of the models. Separate CURE plots were created for each SPF (i.e., total, FI, and PDO crashes) and for each independent variable (crossroad AADT and ramp AADT). The CURE plots indicated the model functional forms in Table 103 are fitting based on the fluctuations of the residuals around the zero cumulative residuals line and based on the cumulative residuals within the upper and lower bounds. Figures 78-80 present graphical representations of the SPFs for the different crash severity levels and crossroad and ramp AADTs. Figure 75. Graphical representation of the SPF for total crashes at crossroad ramp terminals at tight diamond interchanges

205 Figure 76. Graphical representation of the SPF for FI crashes at crossroad ramp terminals at tight diamond interchanges Figure 77. Graphical representation of the SPF for PDO crashes at crossroad ramp terminals at tight diamond interchanges

206 Following the development of the crash prediction models for crossroad ramp terminals at tight diamond interchanges, the research team conducted compatibility testing of the new models to confirm that the new models provide reasonable results over a broad range of input conditions and that the new models integrate seamlessly with existing intersection crash prediction models in the first edition of the HSM. The graphical representations of the crash prediction models in Figures 75-77 provide some sense of the reasonableness of the new models for crossroad ramp terminals at tight diamond interchanges. Nothing from these figures suggests that the models provide unreasonable results. Figures 78-80 compare the crash prediction models for crossroad ramp terminals at tight diamond interchanges to the crash prediction models from Section 8.3 for crossroad ramp terminals at single-point diamond interchanges when there are no free-flow right turns from the exit ramps to the crossroads. In general, the SPFs for single-point diamond ramp terminals predict more crashes than the SPFs for tight diamond ramp terminals in higher volume conditions, and the differences are primarily driven by the PDO models. In summary, the comparisons show that the two sets of models appear compatible and provide reasonable results over the range of applicable traffic volume conditions. The figures do not display the general ranges of prediction error and therefore readers should not put too much emphasis on the relative positions of predicted average crash frequencies when predictions are close. Figure 78. Comparison of crash prediction models for total crashes at crossroad ramp terminals at tight diamond interchanges and single-point diamond interchanges

207 Figure 79. Comparison of crash prediction models for FI crashes at crossroad ramp terminals at tight diamond interchanges and single-point diamond interchanges Figure 80. Comparison of crash prediction models for PDO crashes at crossroad ramp terminals at tight diamond interchanges and single-point diamond interchanges

208 Table 104 displays the distribution of crashes at tight diamond interchange crossroad ramp terminals by severity level. Table 105 displays the distribution of crashes at tight diamond interchange crossroad ramp terminals by collision type and manner of collision. The data from all states combined were used to calculate the proportions. Table 104. Distributions for crash severity level at tight diamond interchange crossroad ramp terminals Crash Severity Level Percentage of Total Crashes Percentage of FI Crashes Fatal 0.08 0.28 Incapacitating injury 1.81 6.15 Non-incapacitating injury 9.68 32.89 Possible injury 17.85 60.68 Total fatal plus injury 29.42 Property-damage-only 70.58 Total 100.0 100.0 Table 105. Distributions for collision type and manner of collision at tight diamond interchange crossroad ramp terminals Collision Type Percentage of Total Crashes FI PDO SV Crashes Collision with animal 0.0 0.0 Collision with fixed object 1.3 3.2 Collision with other object 0.0 0.1 Collision with parked vehicle 0.0 0.0 Other SV collision 1.0 0.4 Multiple-Vehicle Crashes Head-on collision 1.0 0.5 Angle collision 43.6 23.9 Rear-end collision 44.4 57.9 Sideswipe collision 2.8 12.4 Other MV collision 1.2 1.4 Nonmotorized Crashes Pedestrian 1.7 0.0 Bicycle 3.0 0.2 Total Crashes 100.0 100.0 9.4 Crash Modification Factors There were no CMFs in the literature that were adaptable to the predictive models for tight diamond interchange crossroad ramp terminals. New potential CMFs were explored during this analysis using regression modeling; however, none showed statistically significant safety effects. As with the single-point diamond models, the lack of other effects is not necessarily surprising. Crossroad ramp terminals at tight diamond interchanges are relatively similar in some of their major features and operation (e.g., left-turn lanes for crossroad to freeway movements developed in advance of upstream terminal, signalized to operate as single intersection). Sample sizes, collinearity, and use of aggregate traffic volumes (i.e., AADT) did not allow any differences in safety performance to be detected at final levels of detail (e.g., number of lanes by movement).

209 9.5 Severity Distribution Functions Development of SDFs was explored for tight diamond interchange crossroad ramp terminals using methods outlined in Section 2.2.3 of this report. The database used to explore SDFs consisted of the same crashes and crossroad ramp terminals as the database used to estimate the SPFs but restructured so that the basic observation unit (i.e., database row) was a crash instead of a ramp terminal. No traffic or geometric variables showed consistent, interpretable, and statistically significant effects in the SDFs for tight diamond interchange crossroad ramp terminals. 9.6 Summary of Recommended Models for Incorporation in the HSM In summary, crash prediction models were developed for tight diamond interchange crossroad ramp terminals for consideration in the second edition of the HSM. The final models presented in Table 103 for FI and PDO crashes are recommended for inclusion in the second edition of the HSM. Attempts to develop SDFs for tight diamond interchange crossroad ramp terminals proved unsuccessful. The SPFs by severity for tight diamond interchange crossroad ramp terminals provided in Table 103, combined with the severity distributions provided in Table 104, are recommended for addressing crash severity at these intersection types. The SPFs predict FI and PDO crashes separately. Additional disaggregation of FI crashes into fatal, incapacitating injury, non-incapacitating injury, and possible injury crashes can be accomplished using the severity distributions provided in Table 104.