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

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156 Chapter 7. Development of Models for Use in HSM Crash Prediction Methods: Three-Leg Intersections Where the Through Movements Make Turning Maneuvers at the Intersections This section describes the development of crash prediction models for three-leg intersections, where the through movement makes a turning maneuver at the intersection, and presents the final models recommended for incorporation in the second edition of the HSM. Three-leg turning intersections (3STT) are implemented in both rural and urban areas; and due to the characteristics of this intersection type, they are almost always located on two-lane undivided roadways. Stop control can be used on only the minor road approach, or also on one of the major road approaches with a “Stop Except Right Turn” sign. These two configurations are shown in Figure 56. Figure 56. Three-leg turning intersection traffic control configurations Section 7.1 describes the site selection and data collection processes for developing crash prediction models for three-leg turning intersections. Section 7.2 provides descriptive statistics of the databases used for model development. Section 7.3 presents the statistical analysis and resulting SPFs for three-leg turning intersections. Section 7.4 discusses the CMFs recommended for use with the SPFs. Section 7.5 addresses SDFs for three-leg turning intersections, and Section 7.6 provides recommendations for incorporating the new crash prediction models for three-leg turning intersections in the second edition of the HSM. 7.1 Site Selection and Data Collection A list of potential three-leg intersections, where the through movement makes a turning maneuver at the intersection, was developed by searching databases and satellite imagery in three states: • Kentucky (KY) • Ohio (OH) • Pennsylvania (PA) Each intersection in the list was initially screened using Google Earth® to determine if the site was suitable for inclusion in model development. Several reasons a site could be deemed inappropriate for use in model development were:

157 • The traffic control at the intersection was something other than stop control or stop except right turn • The number of intersection legs was not three • A private driveway was located at the intersection • One or more of the approaches to the intersection was a private/commercial access • One or more of the intersection legs was a one-way street Each intersection that was initially deemed appropriate for inclusion in model development was given a unique identification code and included in a refined database for detailed data collection. Three types of data were collected for each intersection during detailed data collection: site characteristic, crash, and traffic volume data. Google Earth® was used to collect detailed site characteristics of the intersections. To reduce potential errors during data collection and to streamline data entry, a data collection tool was created using Visual Basic for Applications, very similar to the tool shown in Figure 4. The data collection tool was suited to only collect data relevant to three-leg intersections where the through movements make turning maneuvers at the intersections. Table 71 lists all of the intersection attributes collected (and respective definitions and permitted values) for three-leg intersections using the data collection tool. Once all necessary data were entered into the data collection tool and saved for a given intersection, the data collection tool was used to validate the inputs for that particular intersection, consistent with the range and/or permitted values for the respective variables/parameters. Table 71. Site characteristic variables collected for three-leg intersections where the through movements make turning maneuvers at the intersections Variable Definition Range or Permitted Values General Intersection Attributes Area type (urban/rural) Indicates whether the intersection is in a rural or urban area Rural, urban Presence of intersection lighting Indicates if overhead lighting is present at the intersection proper Yes, no Presence of flashing beacons Indicates if overhead flashing beacons are present at the intersection proper Yes, no Curve length The horizontal curve length of the through movement at the intersection Range: 40 to 383 ft Curve radius The horizontal curve radius of the through movement at the intersection Range: 25 to 438 ft Specific Approach Attributes Route name or number Specify the route name or number of the approach Traffic control The type of traffic control used on the approach Uncontrolled, stop, stop except right turn, other Number of through lanes This includes dedicated through lanes and any lanes with shared movements. On the minor approach of a 3-leg intersection, if there is only one lane, then it should be classified as a through lane 0, 1, 2, 3 Presence/number of left-turn lanes The number of lanes in which only a left-turn movement can be made 0, 1, 2 Left-turn channelization Type of left-turn channelization used on the intersection approach Raised or depressed island, painted, none Presence/number of right-turn lanes The number of lanes in which only a right-turn movement can be made 0, 1, 2

158 Table 71. Site characteristic variables collected for three-leg intersections where the through movements make turning maneuvers at the intersections (Continued) Variable Definition Range or Permitted Values Right-turn channelization Type of right-turn channelization used on the intersection approach Raised or depressed island, painted, none Presence of transverse rumble strips Indicates the presence of transverse rumble strips on the intersection approach Yes, no, unknown Presence/type of supplementary pavement markings Indicates the presence of supplementary pavement markings on the intersection approach Yes, no, unknown Presence of stop ahead warning signs Indicates the presence of stop ahead warning signs on the intersection approach Yes, no, unknown Presence of advance warning flashers Indicates the presence of advance warning flashers on the intersection approach Yes, no, unknown Posted speed limit Posted speed limit on the intersection approach 15, 20, 25, 30, 35, 40, 45, 50, 55, unknown Presence of crosswalk Indicates the presence of a crosswalk perpendicular to the intersection approach Yes, no, unknown Presence of bike lane Indicates the presence of a marked bike lane parallel to the intersection approach Yes, no, unknown Presence of railroad crossing Indicates the presence of a railroad crossing on the intersection approach within 250 ft of the intersection Yes, no, unknown Approach heading Heading of the approach in the direction towards the intersection 0 to 359.99 degrees During detailed data collection, to the extent possible, the research team reviewed historical aerial images to determine if a site had recently been reconstructed or improved to determine which years of data should be used in model development. Crash and traffic volume data were obtained from the Kentucky Transportation Cabinet, the Ohio DOT, and the Pennsylvania DOT. The goal was to obtain the most recent four to six years of crash and traffic volume data for each site for model development. All of the data (i.e., site characteristics, crash, and traffic volume) were assembled into one database for the purposes of model development. 7.2 Descriptive Statistics of Database Data for 242 sites—195 rural and 47 urban three-leg intersections—were initially available for development of crash prediction models for three-leg turning intersections. The data collection sites were located in three states—Kentucky, Ohio, and Pennsylvania. To remain consistent with the standards for development of the intersection predictive models in the first edition of the HSM, the goal of this research was to develop crash prediction models with a minimum of 200 site-years of data, and preferably 450 site-years of data or more. Traffic Volumes and Site Characteristics Of the intersection characteristics collected in Google Earth® (see Table 71), many showed no or very little variability across sites within a category (i.e., most intersections were predominantly of one type for a specific variable) and were thus excluded from modeling. The remaining variables (percent of “Yes” by area type indicated in parentheses) of potential interest in modeling were: • Presence of intersection lighting (rural: 16%; urban: 51%) • Presence of stop ahead warning signs (rural: 45%; urban: 36%)

159 Curve length and radius were also of potential interest for model development. The use of some of these site characteristics is discussed later in the SPF model development section (Section 7.3). As explained in more detail in Section 7.3, a decision was made to use only unlighted intersections in rural areas and use both unlighted and lighted intersections in urban areas. Therefore, the summary statistics throughout this section are based on the 164 unlighted intersections in rural areas and the 47 unlighted and lighted intersections in urban areas. Traffic volume and crash data were available for varying periods but were typically collected over a five- to ten-year period. Table 72 shows the breakdown of all sites by area type. Study period (date range), number of sites and site-years, and basic traffic volume statistics are shown by state in each category and across all states within a category.

160 Table 72. Major- and minor road AADT and total entering volume statistics for three-leg intersections where the through movements make turning maneuvers at the intersections Major Road AADT (veh/day) Minor Road AADT (veh/day) Total Entering Volume (veh/day) State Date Range Number of Sites Number of Site-Years Min Max Mean Median Min Max Mean Median Min Max Mean Median RURALa KY 2014-2018 41 205 46.0 7,663.0 890.6 391.0 50.0 1,362.0 161.2 92.0 71.0 8,344.0 971.2 508.5 OH 2008-2017 56 560 90.0 5,700.0 1,377.5 1,090.0 45.0 4,020.0 424.6 280.0 112.5 7,710.0 1,589.8 1,326.0 PA 2013-2017 67 335 95.5 2,727.0 636.8 402.0 16.0 2,797.0 390.6 273.0 118.0 3,042.0 832.1 539.0 All states 2008-2018 164 1100 46.0 7,663.0 1,061.2 680.1 16.0 4,020.0 365.1 255.0 71.0 8,344.0 1,243.8 873.6 URBAN KY 2014-2018 19 95 642.0 17,688.0 4,587.8 2,610.0 50.0 4,181.0 506.7 129.0 673.0 17,752.5 4,841.2 2,663.5 OH 2008-2017 7 70 492.0 6,840.0 2,616.5 2,020.0 226.0 3,503.0 1,042.1 535.0 615.0 8,591.5 3,137.6 2,389.5 PA 2013-2017 21 105 795.0 11,431.5 4,120.8 3,468.5 93.0 5,787.0 2,535.3 2,281.0 1,086.0 14,325.0 5,388.5 4,671.0 All states 2008-2018 47 270 492.0 17,688.0 3,895.1 2,976.0 50.0 5,787.0 1,434.4 636.0 615.0 17,752.5 4,612.3 3,151.5 a Unlighted intersections only

161 Crash Counts Intersection crashes were defined as those crashes that occurred within 250 ft of the intersection and were classified as “at intersection” or intersection-related, consistent with recommended practice in the HSM for assigning crashes to an intersection. Of the 211 intersections used in model development, 87 intersections (41.2%) experienced no crashes over the entire study period. Tables 73 (rural intersections) and 74 (urban intersections) show total, FI, and PDO crash counts by crash severity for each state over the entire study period. Counts are also shown for nighttime crashes only. Table 73. Crash counts by crash severity for unlighted rural three-leg intersections where the through movements make turning maneuvers at the intersections State Date Range Number of Sites Number of Site-Years Time of Day All Crashes Combined SV Crashesa Multiple-Vehicle Crashes Total FI PDO Total FI PDO Total FI PDO KY 2014-2018 41 205 All 29 5 24 18 4 14 11 1 10 Night 16 3 13 14 3 11 2 0 2 OH 2008-2017 56 560 All 301 116 185 214 82 132 87 34 53 Night 147 54 93 129 48 81 18 6 12 PA 2013-2017 67 335 All 34 10 24 30 8 22 4 2 2 Night 20 4 16 18 4 14 2 0 2 All states 2008-2018 164 1100 All 364 131 233 262 94 168 102 37 65 Night 183 61 122 161 55 106 22 6 16 a Total and FI SV crashes include pedestrian and bicycle crashes.

162 Table 74. Crash counts by crash severity for urban three-leg intersections where the through movements make turning maneuvers at the intersections State Date Range Number of Sites Number of Site Years Time of Day All Crashes Combined SV Crashes Multiple-Vehicle Crashes Pedestrian Crashes Bicycle Crashes Total FI PDO Total FI PDO Total FI PDO FI FI KY 2014-2018 19 95 All 49 5 44 15 4 11 34 1 33 0 0 Night 11 3 8 7 3 4 4 0 4 0 0 OH 2008-2017 7 70 All 67 21 46 34 11 23 33 10 23 0 0 Night 17 4 13 15 4 11 2 0 2 0 0 PA 2013-2017 21 105 All 61 26 35 29 11 18 32 15 17 2 0 Night 32 13 19 19 8 11 13 5 8 2 0 All States 2008-2018 47 270 All 177 52 125 78 26 52 99 26 73 2 0 Night 60 20 40 41 15 26 19 5 14 2 0

163 Crash counts are tallied by collision type and manner of collision across all states in Table 75 for rural three-leg turning intersections and in Table 76 for urban three-leg turning intersections. Table 75. Crash counts by collision type and manner of collision and crash severity at unlighted rural three- leg intersections where the through movements make turning maneuvers at the intersections Collision Type Total FI PDO SINGLE-VEHICLE CRASHES Collision with animal 26 0 26 Collision with bicycle 0 0 0 Collision with pedestrian 0 0 0 Overturned 14 9 5 Ran off road 208 80 128 Other SV crash 14 5 9 Total SV crashes 262 94 168 MULTIPLE-VEHICLE CRASHES Angle collision 66 26 40 Head-on collision 10 5 5 Rear-end collision 8 2 6 Sideswipe collision 14 3 11 Other MV collision 4 1 3 Total MV crashes 102 37 65 Total crashes 364 131 233 Table 76. Crash counts by collision type and manner of collision and crash severity at urban three-leg intersections where the through movements make turning maneuvers at the intersections Collision Type Total FI PDO SINGLE-VEHICLE CRASHES Collision with parked vehicle 0 0 0 Collision with animal 2 0 2 Collision with fixed object 62 18 44 Collision with other object 3 0 3 Collision with pedestrian 2 2 0 Collision with bicycle 0 0 0 Other SV crash 7 4 3 Noncollision 2 2 0 Total SV crashes 78 26 52 MULTIPLE-VEHICLE CRASHES Angle collision 45 15 30 Head-on collision 8 3 5 Rear-end collision 16 3 13 Sideswipe collision 24 3 21 Other MV collision 6 2 4 Total MV crashes 99 26 73 Total crashes 177 52 125 7.3 Safety Performance Functions—Model Development Intersection SPFs were developed in the forms illustrated by Equations 2, 53, and 54. 𝑁 = 𝑒𝑥𝑝 𝑎 + 𝑏 × ln 𝐴𝐴𝐷𝑇 + 𝑐 × ln(𝐴𝐴𝐷𝑇 ) (Eq. 2) 𝑁 = 𝑒𝑥𝑝 𝑎 + 𝑑 × ln(𝑇𝐸𝑉) (Eq. 53) 𝑇𝐸𝑉 = 0.5 × 𝐴𝐴𝐷𝑇 , + 𝐴𝐴𝐷𝑇 , + 𝐴𝐴𝐷𝑇 (Eq. 54)

164 Where: Nspf int = predicted average crash frequency for an intersection with base conditions (crashes/year) AADTmaj = AADT on the major road (veh/day) AADTmin = AADT on the minor road (veh/day) AADTmaj,1 = AADT on major road approach 1 (veh/day) AADTmaj,2 = AADT on major road approach 2 (veh/day) TEV = total entering volume at intersection (veh/day) a, b, c, and d = estimated regression coefficients For consistency with Chapters 10 and 12 in the HSM, an attempt was made to develop SPFs for the following crash severity levels and collision types: • Rural three-leg turning intersections: total crashes, including pedestrian and bicycle crashes (similar to Equations 10-8 and 10-9 in the HSM) • Urban three-leg turning intersections: total, FI, and PDO crashes (excluding pedestrian and bicycle crashes), separately for single- and MV crashes (similar to Equations 12-21 and 12-24 in the HSM) For three-leg turning intersections on urban and suburban arterials, the SPFs were developed in a manner consistent with the methodology used in Chapter 12 of the HSM for predicting intersection crashes in urban and suburban areas. This methodology is illustrated in Equation 4 and Equation 5. 𝑁 = 𝑁 + 𝑁 + 𝑁 × 𝐶 (Eq. 4) 𝑁 = 𝑁 × 𝐶𝑀𝐹 × 𝐶𝑀𝐹 × … × 𝐶𝑀𝐹 (Eq. 5) Where: Npredicted int = predicted average crash frequency for an individual intersection for the selected year (crashes/year) Nbi = predicted average crash frequency of an intersection (excluding vehicle-pedestrian and vehicle-bicycle crashes) (crashes/year) Npedi = predicted average crash frequency of vehicle-pedestrian crashes of an intersection (crashes/year) Nbikei = predicted average crash frequency of vehicle-bicycle crashes of an intersection (crashes/year) Nspf int = predicted total average crash frequency of intersection-related crashes for base conditions (excluding vehicle-pedestrian and vehicle-bicycle collisions) (crashes/year) CMF1i…CMFyi = crash modification factors specific to intersection type i and specific geometric design and traffic control features y Ci = calibration factor to adjust the SPF for intersection type i to local conditions

165 The SPF portion of Nbi, Nspf int, is the sum of two more disaggregate predictions by collision type, as shown in Equation 6. 𝑁 = 𝑁 + 𝑁 (Eq. 6) Where: Nbimv = predicted average crash frequency of MV crashes of an intersection for base conditions (crashes/year) Nbisv = predicted average crash frequency of SV crashes of an intersection for base conditions (crashes/year) Separate model structures are used to estimate the yearly number of vehicle-pedestrian (Npedi) and vehicle-bicycle (Nbikei) crashes at three-leg turning intersections on urban and suburban arterials. The average number of annual vehicle-pedestrian and vehicle-bicycle crashes are estimated with Equations 9 and 12, respectively. 𝑁 = 𝑁 × 𝑓 (Eq. 9) Where: fpedi = pedestrian crash adjustment factor for intersection type i 𝑁 = 𝑁 × 𝑓 (Eq. 12) Where: fbikei = bicycle crash adjustment factor for intersection type i All of the vehicle-pedestrian and vehicle-bicycle crashes predicted with Equations 9 and 12 are assumed to be FI crashes (none as PDO). All SPFs were developed using a NB regression model based on all sites combined. Based on a review of the number of states, sites, site-years, and crashes for the database assembled, data for all sites were used for model development to maximize the sample size rather than using a portion of the data for model development and a portion for model validation. A significance level of 0.2 was used to assess the individual, estimated regression parameters. During model development, several intersection characteristics were initially tested in the models to develop CMFs for use with the SPFs. These characteristics included traffic control configuration, presence of intersection lighting, presence of stop ahead warning signs, and curve length and radius of the through movement at the intersection. Presence of stop ahead warning signs and traffic control configuration showed no consistent or statistically significant relationships to expected crash frequency. For both rural and urban three-leg turning intersections, minor road AADT was not found to be statistically significant. Thus, total entering volume was used as an exposure variable in the models, which was estimated as half of the sum of the AADTs for the three intersection legs.

166 For the rural three-leg turning intersection model, presence of intersection lighting was found to be the only intersection characteristic that was statistically significant. Since there was an abundance of site-years, it was decided to exclude all intersections with lighting and derive a model based only on unlighted intersections. The CMF for presence of lighting in Chapter 10 of the HSM then could be used to adjust for lighted intersections (see discussion in Section 7.4). For the urban three-leg turning intersection models, presence of intersection lighting was not found to be a statistically significant predictor of intersection crashes. However, horizontal curve length and radius were found to be statistically significant predictors in the models for total, FI, and PDO severity levels for MV crashes. Curve length was also found to be a statistically significant predictor of SV crashes for total, FI, and PDO severity levels. The effect that curve length and radius has on predicting crashes at urban three-leg turning intersections was converted into CMFs, which are presented in Section 7.4. The statistical software known as “R” was used for developing models for SV and multi-vehicle FI crashes at three-leg turning intersections on urban and suburban arterials. SAS® Version 9 was used for all other modeling. The final SPF for three-leg turning intersections in rural areas is provided in Table 77, for total severity using Equation 53. Table 77 shows the estimated model coefficients and overdispersion parameter (estimate), their standard errors, and associated p-values (and significance level). Figure 57 graphically presents the SPF in Table 77 for various major- and minor approach AADTs. Table 77. SPF coefficients for three-leg turning intersections on rural two-lane roadways Intersection Type Parameter Estimate Standard Error Pr > F Significance Level TOTAL CRASHESa Three-Leg Turning Intersection Intercept -6.501 0.782 -- -- ln(TEV) 0.703 0.099 <.001 Significant at 99% level Overdispersion 0.24 0.11 -- -- a Includes SV, MV, pedestrian, and bicycle crashes. Base condition: absence of lighting.

167 Figure 57. Graphical representation of the SPF for total crashes at three-leg turning intersections on rural two-lane roadways (based on model for total crashes in Equation 53) Similar to Tables 10-5 and 10-6 in the first edition of the HSM, Tables 78 and 79 provide percentages for crash severity levels and for collision types and manner of collision, respectively, for rural three-leg turning intersections. These percentages were calculated based on all crash counts at all unlighted intersections in all states combined. Table 78. Distributions for crash severity level at three-leg turning intersections on rural two-lane roadways Crash Severity Level Percentage of Total Crashes Fatal 0.3 Incapacitating injury 6.0 Non-incapacitating injury 17.3 Possible injury 12.4 Total fatal plus injury 36.0 Property-damage-only 64.0 Total 100.0

168 Table 79. Distributions for collision type and manner of collision and crash severity at three-leg turning intersections on rural two-lane roadways Collision Type Percentage of Total Crashes by Collision Type Total FI PDO Single-Vehicle Crashes Collision with animal 7.1 0.0 11.2 Collision with bicycle 0.0 0.0 0.0 Collision with pedestrian 0.0 0.0 0.0 Overturned 3.8 6.9 2.1 Ran off road 57.1 61.1 54.9 Other SV crash 3.9 3.8 3.9 Total SV crashes 71.9 71.8 72.1 Multiple-Vehicle Crashes Angle collision 18.1 19.8 17.2 Head-on collision 2.8 3.8 2.1 Rear-end collision 2.2 1.5 2.6 Sideswipe collision 3.9 2.3 4.7 Other MV collision 1.1 0.8 1.3 Total MV crashes 28.1 28.2 27.9 Total crashes 100.0 100.0 100.0 Table 80 shows the coefficients and associated statistics of the final SPFs for urban three-leg turning intersections. Usable models were developed for multiple- and SV crashes separately for total, FI and PDO severity levels. Figures 58-63 graphically present the SPFs shown in Table 80 for various major- and minor approach AADTs. SPFs for vehicle-pedestrian and vehicle-bicycle crashes at three-leg turning intersections on urban and suburban arterials could not be developed as pedestrian and bicycle volumes were not available. Table 80. SPF coefficients for three-leg turning intersections on urban and suburban arterials Crash Severity Parameter Estimate Standard Error Pr > F Significance Level Multiple-Vehicle Crashes Total Crashes Intercept -8.49 1.95 -- -- ln(TEV) 0.87 0.22 < .01 Significant at 99% level Overdispersion 0.32 0.22 -- -- FI Crashes Intercept -9.53 3.04 -- -- ln(TEV) 0.81 0.33 0.01 Significant at 99% level Overdispersion 0.02 0.01 -- -- PDO Crashes Intercept -8.12 2.05 -- -- ln(TEV) 0.79 0.23 < .01 Significant at 99% level Overdispersion 0.14 0.22 -- -- Single-Vehicle Crashesa Total Crashes Intercept -5.40 1.93 -- -- ln(TEV) 0.46 0.23 0.05 Significant at 95% level Overdispersion 0.50 0.29 -- -- FI Crashes Intercept -4.69 3.29 -- -- ln(TEV) 0.19 0.38 0.61 Not significant Overdispersion 0.00 0.00 -- -- PDO Crashes Intercept -6.68 2.21 -- -- ln(TEV) 0.57 0.26 0.03 Significant at 95% level Overdispersion 0.61 0.44 -- -- a (i.e., pedestrian and bicycle crashes are excluded). Base condition is 100-ft long curve with a radius of 84 ft for the through route making a turning maneuver.

169 Figure 58. Graphical representation of the SPF for total MV crashes at three-leg turning intersections on urban and suburban arterials (based on model for total crashes in Equation 53) Figure 59. Graphical representation of the SPF for FI multiple-vehicle crashes at three-leg turning intersections on urban and suburban arterials (based on model for total crashes in Equation 53)

170 Figure 60. Graphical representation of the SPF for PDO multiple-vehicle crashes at three-leg turning intersections on urban and suburban arterials (based on model for total crashes in Equation 53) Figure 61. Graphical representation of the SPF for total SV crashes at three-leg turning intersections on urban and suburban arterials (based on model for total crashes in Equation 53)

171 Figure 62. Graphical representation of the SPF for FI SV crashes at three-leg turning intersections on urban and suburban arterials (based on model for total crashes in Equation 53) Figure 63. Graphical representation of the SPF for PDO single-vehicle crashes at three-leg turning intersections on urban and suburban arterials (based on model for total crashes in Equation 53)

172 Table 81 (similar to Table 79 for rural intersections) provides percentages of total crashes by collision type and severity level for urban three-leg turning intersections. These percentages were calculated based on all crash counts at all intersections—lighted and unlighted—in all states combined. Table 81. Distributions for collision type and manner of collision and crash severity at three-leg turning intersections on urban and suburban arterials Collision Type Percentage of Total Crashes by Collision Type Total FI PDO Single-Vehicle Crashes Collision with parked vehicle 0.0 0.0 0.0 Collision with animal 1.1 0.0 1.6 Collision with fixed object 35.4 36.0 35.2 Collision with other object 1.7 0.0 2.4 Other SV collision 4.0 8.0 2.4 Noncollision 1.1 4.0 0.0 Total SV crashes 42.4 48.0 41.6 Multiple-Vehicle Crashes Angle collision 25.7 30.0 24.0 Head-on collision 4.6 6.0 4.0 Rear-end collision 9.1 6.0 10.4 Sideswipe collision 13.7 6.0 16.8 Other MV collision 3.4 4.0 3.2 Total MV crashes 56.6 52.0 58.4 Total crashes 100.0 100.0 100.0 For urban intersections, the predicted average crash frequency excludes vehicle-pedestrian and vehicle-bicycle crashes. To calculate a predicted average crash frequency of an intersection that includes vehicle-pedestrian and vehicle-bicycle crashes, the predictive model is given by 𝑵𝒑𝒓𝒆𝒅𝒊𝒄𝒕𝒆𝒅 𝒊𝒏𝒕 = 𝑪𝒊 × 𝑵𝒃𝒊 + 𝑵𝒑𝒆𝒅𝒊 + 𝑵𝒃𝒊𝒌𝒆𝒊 (Eq. 4) Where: Npredicted int = predicted average crash frequency for an individual intersection for the selected year (crashes/year) Nbi = predicted average crash frequency of an intersection (excluding vehicle- pedestrian and vehicle-bicycle crashes) (crashes/year) Npedi = predicted average crash frequency of vehicle-pedestrian crashes of an intersection (crashes/year) Nbikei = predicted average crash frequency of vehicle-bicycle crashes of an intersection (crashes/year) Ci = calibration factor to adjust the SPF for intersection type i to local conditions Similar to Table 12-16 in the HSM, Table 82 provide a pedestrian crash adjustment factor for three-leg turning intersections on urban and suburban arterials. The number of vehicle-pedestrian crashes per year for a three-leg turning intersection is estimated as: 𝑁 = 𝑁 × 𝑓 (Eq. 9)

173 Where: fpedi = pedestrian crash adjustment factor for intersection type i Table 82. Pedestrian crash adjustment factor for three-leg turning intersections on urban and suburban arterials Intersection Type Pedestrian Crash Adjustment Factor (fpedi) Three-Leg Turning 0.011 Similar to Table 12-17 in the first edition of the HSM, Table 83 provides a bicycle crash adjustment factor for three-leg turning intersections on urban and suburban arterials. The number of vehicle-bicycle crashes per year for a three-leg turning intersection is estimated as: 𝑁 = 𝑁 × 𝑓 (Eq. 12) Where: fbikei = bicycle crash adjustment factor for intersection type i Table 83. Bicycle crash adjustment factor for three-leg turning intersections on urban and suburban arterials Intersection Type Bicycle Crash Adjustment Factor (fbikei) Three-Leg Turning 0.000 Following the development of the crash prediction models for three-leg turning intersections in rural and urban areas, compatibility testing of the new models was conducted 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 57-63 provide some sense of the reasonableness of the new models for three-leg turning intersections. Nothing from these figures suggests that the models provide unreasonable results. In addition, the new models for three-leg turning intersections were compared to the associated minor road stop-controlled intersection SPFs in the HSM. Figure 64 illustrates a comparison of the predicted average crash frequency for total crashes based on the rural 3STT model (Table 77) to the predicted average crash frequency based on the 3ST model in Chapter 10 of the HSM. In the figure, the dashed lines represent the predicted average crash frequency for the 3STT model, and the solid lines represent the predicted average crash frequency for the 3ST model in the HSM. Similarly, Figures 65-68 illustrate a comparison of the predicted average crash frequency for MV total crashes, MV FI crashes, SV total crashes, and SV FI crashes, respectively, based on the 3STT model for urban and suburban arterials (Table 80) to the predicted average crash frequency based on the 3ST models in Chapter 12 of the HSM. In all instances, as major road AADT increases, the 3STT multi-vehicle SPFs predict fewer crashes than the 3ST multi-vehicle SPFs in the HSM. It seems reasonable to expect fewer multi-vehicle crashes at 3STT intersections than 3ST intersections. Vehicle speeds on uncontrolled approaches of the intersection must slow down to navigate the horizontal curve. This gives vehicles on stop-controlled approaches

174 potentially more time to assess gaps once vehicles on the uncontrolled approach(es) are seen. Also, slower speeds allow for longer reaction times to potentially avoid a collision at the intersection. The SV total SPF for 3STT intersections tends to predict more crashes than the similar model for 3ST intersections from the HSM, especially as major approach volume increases. This may be due to the fact that the major road curves at the intersection, which may potentially lead to more crashes. The SV FI SPF for 3STT intersections follow a similar trend to the 3ST SV FI model from the HSM. In summary, the models for three-leg turning intersections appear to provide reasonable results over a broad range of input conditions and can be integrated seamlessly with existing intersection crash prediction models in the first edition of the HSM. Figure 64. Comparison of new crash prediction model to existing model in HSM: 3STT vs 3ST on rural two-lane roads (total crashes)

175 Figure 65. Comparison of new crash prediction model to existing model in HSM: 3STT vs 3ST on urban and suburban arterials (MV-total crashes)

176 Figure 66. Comparison of new crash prediction model to existing model in HSM: 3STT vs 3ST on urban and suburban arterials (MV FI crashes)

177 Figure 67. Comparison of new crash prediction model to existing model in HSM: 3STT vs 3ST on urban and suburban arterials (SV-total crashes)

178 Figure 68. Comparison of new crash prediction model to existing model in HSM: 3STT vs 3ST on urban and suburban arterials (SV FI crashes) 7.4 Crash Modification Factors During the development of the crash prediction models for three-leg turning intersections, three potential sources of CMFs for use with the SPFs were considered: • CMFs developed as part of this research based on a cross-sectional study design and regression modeling • CMFs already incorporated into the first edition of the HSM and applicable to three-leg turning intersections • High-quality CMFs applicable to three-leg turning intersections developed using defensible study designs (e.g., observational before-after evaluation studies using SPFs— the EB method), as referenced in FHWA’s CMF Clearinghouse with four- or five-star quality ratings or based on a review of relevant intersection safety literatures Based on a review of the CMFs already incorporated in the first edition of the HSM and other potential high-quality CMFs developed using defensible study designs, the only CMF that was

179 identified for potential use with the crash prediction models for rural three-leg turning intersections was the CMF for intersection lighting based on the work by Elvik and Vaa (2004), which is identified for use with the intersection crash prediction models in Chapters 10, 11, and 12 of the first edition of the HSM. Thus, the only CMF recommended for use with the final SPF for rural three-leg turning intersections is the CMF for intersection lighting based on the work by Elvik and Vaa (2004). With this CMF, the base condition is the absence of intersection lighting. The CMF for lighted intersections is similar to the CMF in Equation 10-24 in the HSM and has the form: 𝐶𝑀𝐹 = 1 − 0.38 × 𝑝 (Eq. 39) Where: CMFi = crash modification factor for the effect of lighting on total crashes pni = proportion of total crashes for unlighted intersections that occur at night This CMF applies to total intersection crashes. Table 10-15 in the HSM presents values for the nighttime crash proportion, pni, by intersection type. Based on crash data used in this research, pni for rural three-leg turning intersections is 0.503. Recent research by Washington State DOT has raised concerns about whether use of the lighting CMF in the HSM is appropriate. Based on their research, van Schalkwyk et al. (2016) concluded that the contribution of continuous illumination to nighttime crash reduction is negligible. However, this CMF is recommended for application to rural three-leg turning intersections because this CMF has been used in the first edition of the HSM. If any decision to remove or change the lighting CMFs is made, it should be done consistently for all facility types as part of the development of the second edition of the HSM. Based on the regression modeling as part of this research, curve length and radius were also identified for CMF development for three-leg turning intersections on urban and suburban arterials. Therefore, a CMF was developed as part of this research for curve length and radius. The curve to which this CMF applies is the turn for the through movement. Curve length and radius are measured along the centerline of the roadway. The base condition of this CMF is a curve length equal to 100 ft, and a curve radius equal to 84 ft. This CMF was developed based on curves with radii ranging from 25 to 270 ft and lengths ranging from 40 to 240 ft. The CMF is presented in Equation 55 with accompanying coefficients shown in Table 84. 𝐶𝑀𝐹 = 𝑒 ( ) ( ) (Eq. 55) Where: CMFi = crash modification factor for the effect of curve length and radius on crashes R = curve radius (ft) Lc = curve length (ft) a, b = regression coefficients Table 84 presents the values of the coefficients a and b used in applying Equation 55.

180 Table 84. CMF coefficients for curve CMF at three-leg turning intersections on urban and suburban arterials SPF to which the CMF applies Coefficients used in Equation 55 A b MV-Total -0.014 0.017 MV FI -0.014 0.019 MV PDO -0.017 0.020 SV-Total 0a 0.009 SV FI 0a 0.013 SV PDO 0a 0.008 a Curve radius was not found to be statistically significant in predicting SV crashes Tables 85-90 show computed curve CMF values for various crash types and severities by various levels of curve length and radius. There are certain combinations of curve length and radius that are not realistic for this intersection type and are not shown in these tables. Table 85. Curve CMF values for MV total crashes Curve Radius (ft) Curve Length (ft) 50 75 100 125 150 175 200 225 25 0.976 -- -- -- -- -- -- -- 50 0.688 1.052 1.610 2.462 -- -- -- -- 75 0.485 0.742 1.134 1.735 2.654 4.059 -- -- 100 0.342 0.523 0.799 1.223 1.870 2.861 4.375 6.693 125 -- 0.368 0.563 0.862 1.318 2.016 3.083 4.716 150 -- 0.259 0.397 0.607 0.929 1.420 2.173 3.323 175 -- -- 0.280 0.428 0.654 1.001 1.531 2.342 200 -- -- 0.197 0.301 0.461 0.705 1.079 1.650 225 -- -- -- 0.212 0.325 0.497 0.760 1.163 250 -- -- -- 0.150 0.229 0.350 0.536 0.820 Table 86. Curve CMF values for MV FI crashes Curve Radius (ft) Curve Length (ft) 50 75 100 125 150 175 200 225 25 0.883 -- -- -- -- -- -- -- 50 0.623 1.001 1.610 2.588 -- -- -- -- 75 0.439 0.705 1.134 1.824 2.933 4.716 -- -- 100 0.309 0.497 0.799 1.285 2.067 3.323 5.344 8.593 125 -- 0.350 0.563 0.906 1.456 2.342 3.766 6.056 150 -- 0.247 0.397 0.638 1.026 1.650 2.654 4.267 175 -- -- 0.280 0.450 0.723 1.163 1.870 3.007 200 -- -- 0.197 0.317 0.510 0.820 1.318 2.119 225 -- -- -- 0.223 0.359 0.578 0.929 1.493 250 -- -- -- 0.157 0.253 0.407 0.654 1.052 Table 87. Curve CMF values for MV PDO crashes Curve Radius (ft) Curve Length (ft) 50 75 100 125 150 175 200 225 25 1.003 -- -- -- -- -- -- -- 50 0.656 1.081 1.782 2.939 -- -- -- -- 75 0.429 0.707 1.165 1.921 3.168 5.223 -- -- 100 0.280 0.462 0.762 1.256 2.071 3.414 5.629 9.281 125 -- 0.302 0.498 0.821 1.354 2.232 3.680 6.068 150 -- 0.198 0.326 0.537 0.885 1.459 2.406 3.967 175 -- -- 0.213 0.351 0.579 0.954 1.573 2.593 200 -- -- 0.139 0.229 0.378 0.624 1.028 1.696 225 -- -- -- 0.150 0.247 0.408 0.672 1.108 250 -- -- -- 0.098 0.162 0.267 0.440 0.725

181 Table 88. Curve CMF values for SV total crashes Curve Radius (ft) Curve Length (ft) 50 75 100 125 150 175 200 225 25 0.638 -- -- -- -- -- -- -- 50 0.638 0.799 1.000 1.252 -- -- -- -- 75 0.638 0.799 1.000 1.252 1.568 1.964 -- -- 100 0.638 0.799 1.000 1.252 1.568 1.964 2.460 3.080 125 -- 0.799 1.000 1.252 1.568 1.964 2.460 3.080 150 -- 0.799 1.000 1.252 1.568 1.964 2.460 3.080 175 -- -- 1.000 1.252 1.568 1.964 2.460 3.080 200 -- -- 1.000 1.252 1.568 1.964 2.460 3.080 225 -- -- -- 1.252 1.568 1.964 2.460 3.080 250 -- -- -- 1.252 1.568 1.964 2.460 3.080 Table 89. Curve CMF values for SV FI crashes Curve Radius (ft) Curve Length (ft) 50 75 100 125 150 175 200 225 25 0.522 -- -- -- -- -- -- -- 50 0.522 0.723 1.000 1.384 -- -- -- -- 75 0.522 0.723 1.000 1.384 1.916 2.651 -- -- 100 0.522 0.723 1.000 1.384 1.916 2.651 3.669 5.078 125 -- 0.723 1.000 1.384 1.916 2.651 3.669 5.078 150 -- 0.723 1.000 1.384 1.916 2.651 3.669 5.078 175 -- -- 1.000 1.384 1.916 2.651 3.669 5.078 200 -- -- 1.000 1.384 1.916 2.651 3.669 5.078 225 -- -- -- 1.384 1.916 2.651 3.669 5.078 250 -- -- -- 1.384 1.916 2.651 3.669 5.078 Table 90. Curve CMF values for SV PDO crashes Curve Radius (ft) Curve Length (ft) 50 75 100 125 150 175 200 225 25 0.670 -- -- -- -- -- -- -- 50 0.670 0.819 1.000 1.221 -- -- -- -- 75 0.670 0.819 1.000 1.221 1.492 1.822 -- -- 100 0.670 0.819 1.000 1.221 1.492 1.822 2.226 2.718 125 -- 0.819 1.000 1.221 1.492 1.822 2.226 2.718 150 -- 0.819 1.000 1.221 1.492 1.822 2.226 2.718 175 -- -- 1.000 1.221 1.492 1.822 2.226 2.718 200 -- -- 1.000 1.221 1.492 1.822 2.226 2.718 225 -- -- -- 1.221 1.492 1.822 2.226 2.718 250 -- -- -- 1.221 1.492 1.822 2.226 2.718 7.5 Severity Distribution Functions Based on previous results of attempting to develop SDFs for intersections, it was decided not to explore the development of SDFs for three-leg turning intersections.

182 7.6 Summary of Recommended Models for Incorporation in the HSM In summary, several crash prediction models were developed for three-leg intersections where the through movements make turning maneuvers at the intersections for consideration in the second edition of the HSM, including models for: • Three-leg turning intersections on rural two-lane roadways • Three-leg turning intersections on urban and suburban arterials The final models recommended for inclusion in the second edition of the HSM are for total crashes on three-leg turning intersections on rural two-lane roadways (as shown in Table 77) and MV total, MV FI, MV PDO, SV total, and SV PDO crashes at three-leg turning intersections on urban and suburban arterials (as shown in Table 80). The model for SV FI crashes for three-leg turning intersections on urban and suburban arterials in Table 80 is not recommended for inclusion in the second edition of the HSM because the parameter for total entering volume is not statistically significant in the model. In addition, SDFs were not developed for three-leg turning intersections. Therefore, it is recommended for the second edition of the HSM that crash severity for three-leg turning intersections on rural two-lane highways and urban and suburban arterials be addressed in a manner consistent with existing methods in Chapter 10 and Chapter 12 of the HSM, respectively, without use of SDFs. Appendix A presents recommended text for incorporating the final recommended models for three-leg turning intersections into Chapters 10 and 12 of the HSM.