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

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79 Chapter 4. Development of Models for Use in HSM Crash Prediction Methods: Three-Leg Intersections with Signal Control on Rural Highways This section of the report describes the development of crash prediction models for three-leg intersections with signal control on rural highways and presents the final models recommended for incorporation in the second edition of the HSM. Chapters 10 (Rural Two-Lane, Two-Way Roads) and 11 (Rural Multilane Highways) in the first edition of the HSM do not include crash prediction models for three-leg intersections with signal control. Crash prediction models are recommended for the following intersection types for the second edition of the HSM: • Three-leg intersections with signal control (3SG) on rural two-lane, two-way roads • Three-leg intersections with signal control (3SG) on rural multilane highways Section 4.1 describes the site selection and data collection process for developing the crash prediction models for three-leg intersections with signal control on rural highways. Section 4.2 presents descriptive statistics of the databases used for model development. Section 4.3 presents the statistical analysis and SPFs developed for three-leg intersections with signal control on rural highways. Section 4.4 presents the CMFs recommended for use with the SPFs. Section 4.5 presents the results of an analysis to develop SDFs for use with the SPFs for three-leg intersections with signal control on rural highways, and Section 4.6 summarizes the recommendations for incorporating new crash prediction models for three-leg intersections with signal control on rural highways in the second edition of the HSM. 4.1 Site Selection and Data Collection A list of potential intersections for model development was derived from HSIS or Safety Analyst databases for several states, as well as lists provided by state transportation agencies. The intersections were located in ten states: • California (CA) • Florida (FL) • Illinois (IL) • Kentucky (KY) • Michigan (MI) • Minnesota (MN) • New Hampshire (NH) • Ohio (OH) • Pennsylvania (PA) • Washington (WA) 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:

80 • The traffic control at the intersection was something other than signal control. • The number of intersection legs was not three. • The intersection was in an urban area. • A private driveway was located in close proximity to the intersection. • One or more of the approaches to the intersection was a private/commercial access. • Google Street View® was not available to identify leg specific attributes. • 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 rural three-leg signalized intersections. Table 17 lists all of the intersection attributes collected (and respective definitions and permitted values) for rural three-leg signalized 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 17. Site characteristic variables collected for three-leg intersections with signal control on rural highways Variable/Parameter Definition Range or 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 3SG Area type (urban/rural) Indicates whether the intersection is in a rural or urban area Rural Presence of intersection lighting Indicates if overhead lighting is present at the intersection proper Yes, no Approach Specific Attributes Route name or number Specify the route name or number of the approach Location at intersection Side/quadrant of the intersection the approach is located N, S, E, W, NE, NW, SE, SW 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, 3 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, 3

81 Table 17. Site characteristic variables collected for three-leg intersections with signal control on rural highways (Continued) Variable/Parameter Definition Range or Permitted Values Right-turn channelization Type of right-turn channelization used on the intersection approach Raised or depressed island, painted, none Median width Measured from outside of outer most through lane of approaching lanes to outside of lane in opposing direction Values in feet Median type Type of median separating opposing directions of travel Raised, depressed, flush, barrier, TWLTL Permit right-turn-on-red Indicates if turning right on red is permitted on the intersection approach Yes, no, not applicable 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 and type of supplementary pavement markings on the intersection approach Yes, no, unknown If yes, type of marking: “Signal Ahead”, other Presence of signal ahead warning signs Indicates the presence of signal 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 Horizontal alignment of intersection approach Indicates whether the approaching roadway, within 250 ft of the intersection, is a tangent or curved section of roadway Tangent, curve Horizontal curve radius Indicates the radius of the curve on the intersection approach if a curve is present within 250 ft of the intersection 2,000-ft Maximum Range: 100-2000 ft Posted speed limit Posted speed limit on the intersection approach (mph) 25, 30, 35, 40, 45, 50, 55, 60, 65, 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 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 the appropriate years of data for use in model development. Due to very low intersection totals, Minnesota and Pennsylvania sites were removed from the dataset for model development. Table 18 lists the crash and traffic volume data sources for the eight states included in the study. 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 model development. Table 18. Traffic volume and crash data sources for rural three-leg signalized intersections State Traffic Volume Data Source Crash Data Source California HSIS HSIS Florida State agency State agency Illinois Safety Analyst Safety Analyst Kentucky State agency State agency Michigan Safety Analyst Safety Analyst New Hampshire Safety Analyst Safety Analyst Ohio Safety Analyst Safety Analyst Washington HSIS and Safety Analyst HSIS

82 4.2 Descriptive Statistics of Database A total of 161 sites—89 on two-lane and 72 on multilane highways—were available for development of crash prediction models. The data collections sites were located in eight states: California, Florida, Illinois, Kentucky, Michigan, New Hampshire, Ohio, and Washington. 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 Traffic volume and crash data were available for varying periods but were typically available over a 5- or 6-year period. Table 19 shows the breakdown of all sites by roadway classification and intersection 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. Of the intersection characteristics collected in Google Earth®(see Table 17), most showed no or very little variability across sites within a roadway classification (i.e., most intersections were predominantly of one type for a specific variable). However, the following three intersection characteristics had sufficient variability for inclusion in the development of SPFs using CMFs (percent of “Yes” by roadway classification is indicated in parentheses): • presence of intersection lighting (two-lane: 81%; multilane: 74%) • presence of left-turn lanes on major road (two-lane: 89%; multilane: 93%) • presence of right-turn lanes on major road (two-lane: 65%; multilane: 67%) The use of these site characteristics is discussed later in the SPF model development section. Crashes Of the 161 intersections included in the study, only 11 intersections (6.8%) experienced no crashes over the entire study period; their breakdown by roadway classification is as follows: • Rural three-leg signalized intersections on two-lane highways: 3 out of 89 • Rural three-leg signalized intersections on multilane highways: 8 out of 72 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. Table 20 shows total, FI, and PDO crash counts by roadway classification and crash severity for each state over the entire study period. Counts are also shown for nighttime crashes only. For one of the 10 intersections on two-lane highways and one of the 17 intersections on multilane highways in Florida, crash severity was unknown. Similarly, for eight of the nine intersections on two-lane highways and 13 of the 15 intersections on multilane highways in Kentucky, crash severity was unknown. In those cases, only total crash counts are shown, and thus FI and PDO crashes do not add up to the total crash count.

83 Table 19. Major- and minor road AADT statistics by roadway classification for rural three-leg intersections with signal control State Date Range Number of Sites Number of Site-Years Major Road AADT (veh/day) Minor Road AADT (veh/day) Min Max Mean Median Min Max Mean Median INTERSECTIONS ON RURAL TWO-LANE HIGHWAYS CA 2007-2011 24 112 3,130 23,591 14,521 14,233 100 23,320 3,034 1,166 FL 2007-2010 10 40 6,600 21,425 12,520 11,425 3,650 18,225 6,730 5,560 IL 2008-2012 6 30 2,900 5,300 4,575 4,800 1,900 5,100 3,425 3,375 KY 2010-2014 9 45 6,707 11,800 8,969 9,452 2,330 7,866 4,447 4,106 MI 2008-2013 6 34 7,353 21,058 13,829 12,875 4,005 16,329 9,802 9,523 NH 2009-2013 7 35 10,927 16,000 12,315 11,277 1,400 8,800 4,725 4,600 OH 2009-2013 17 85 3,832 14,930 7,949 8,197 190 10,336 2,772 729 WA 2007-2011 10 42 5,669 18,612 12,259 12,334 1,881 13,068 6,685 6,434 All States 2007-2014 89 423 2,900 23,591 11,334 10,239 100 23,320 4,568 4,106 INTERSECTIONS ON RURAL MULTILANE HIGHWAYS CA 2007-2011 21 77 1,001 56,000 19,675 19,360 101 27,000 4,734 1,500 FL 2007-2010 17 65 7,375 25,000 17,181 16,925 800 17,300 7,188 6,000 KY 2010-2014 15 75 8,249 25,151 15,304 15,241 677 9,108 4,394 3,762 MI 2008-2013 4 24 9,735 11,705 11,077 11,434 6,786 8,547 7,777 7,887 OH 2009-2013 15 73 2,456 28,402 11,182 10,694 156 11,510 2,952 2,620 All States 2007-2014 72 314 1,001 56,000 15,928 15,834 101 27,000 5,040 3,752 Table 20. Crash counts by roadway classification and crash severity for rural three-leg intersections with signal control State Date Range Number of Sites Number of Site-Years Time of Day Total FI PDO INTERSECTIONS ON RURAL TWO-LANE HIGHWAYS CA 2007-2011 24 112 All 98 45 53 Night 25 12 13 FLa 2007-2010 10 40 All 103 68 34 Night 33 25 7 IL 2008-2012 6 30 All 56 15 41 Night 8 3 5 KYa 2010-2014 9 45 All 168 29 10 Night 32 5 2 MI 2008-2013 6 34 All 142 27 115 Night 42 6 36 NH 2009-2013 7 35 All 37 13 24 Night 5 1 4 OH 2009-2013 17 85 All 164 40 124 Night 32 8 24 WA 2007-2011 10 42 All 119 45 74 Night 30 9 21 All Statesa 2007-2014 89 423 All 887 282 475 Night 207 69 112 INTERSECTIONS ON RURAL MULTILANE HIGHWAYS CA 2007-2011 21 77 All 104 45 59 Night 24 10 14 FLa 2007-2010 17 65 All 257 139 117 Night 53 34 18 KYa 2010-2014 15 75 All 356 76 15 Night 71 17 5 MI 2008-2013 4 24 All 95 17 78 Night 10 1 9 OH 2009-2013 15 73 All 163 42 121 Night 33 12 21 All Statesa 2007-2014 72 314 All 975 319 390 Night 191 74 67 a Crash records did not indicate severity level for a number of crashes for some intersections; FI and PDO crashes will not add up to total crashes. Crash counts are tallied by collision type and manner of collision across all states in Table 21 for intersections on rural two-lane highways. Crash counts tallied across all states by collision type and severity at intersections on multilane highways are shown in Table 22.

84 Table 21. Crash counts by collision type and manner of collision and crash severity at three-leg intersections with signal control on rural two-lane highways Collision Type Totala FI PDO SINGLE-VEHICLE CRASHES Collision with animal 16 0 16 Collision with bicycle 3 2 1 Collision with pedestrian 0 0 0 Overturned 16 13 3 Ran off road 1 0 1 Other SV crash 137 35 90 Total SV crashes 173 50 111 MULTIPLE-VEHICLE CRASHES Angle collision 171 74 75 Head-on collision 24 16 8 Rear-end collision 408 120 220 Sideswipe collision 43 7 22 Other MV collision 68 15 39 Total MV crashes 714 232 364 Total Crashes 887 282 475 a Crash records did not indicate severity level for a number of crashes for some intersections in Florida and Kentucky; FI and PDO crashes will not add up to total crashes in some cases. Table 22. Crash counts by collision type and crash severity at three-leg intersections with signal control on rural multilane highways Collision Type Totala FI (KABC) FIb (KAB) PDO Head-on collision 23 13 4 7 Sideswipe collision 78 11 7 42 Rear-end collision 421 117 58 172 Angle collision 273 130 86 86 SV collision 110 31 18 59 Other 70 17 9 24 Total Crashes 975 319 182 390 a Crash records did not indicate severity level for a number of crashes for some intersections in Florida and Kentucky; FI and PDO crashes will not add up to total crashes in some cases. b Using the KABCO scale, these include only KAB crashes. Crashes with severity level C (possible injury) are not included. 4.3 Safety Performance Functions—Model Development SPFs of the form shown in Equation 2 were developed separately for intersections on two-lane and multilane highways, using all crash types combined (single- and MV and pedestrian and bicycle crashes). 𝑵𝒔𝒑𝒇 𝒊𝒏𝒕 = 𝒆𝒙𝒑 𝒂 + 𝒃 × 𝐥𝐧 𝑨𝑨𝑫𝑻𝒎𝒂𝒋 + 𝒄 × 𝐥𝐧(𝑨𝑨𝑫𝑻𝒎𝒊𝒏) (Eq. 2) 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) a, b, and c = estimated regression coefficients

85 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. All SPFs were developed using a NB regression model based on all sites combined within a given area type and intersection type. In all models, state was included as a random blocking effect, with sites nested within their respective state. A significance level of 0.20 for inclusion in a model was selected for an individual parameter. This was based on previous models included in the first edition of the HSM (Harwood et al., 2007). PROC GLIMMIX of SAS 9.3 was used for all modeling (SAS, 2013). For intersections on either highway type, models were developed for total, FI, and PDO crashes. For intersections on multilane highways, a model was also developed for a subset of FI crashes including only KAB crashes (i.e., crashes with severity level C [possible injury] not included) as done in Chapter 11 in the HSM. For comparison, the base conditions in Chapter 10 of the HSM for four-leg intersections with signal control on rural two-lane highways are the absence of intersection lighting and that of left- and right-turn lanes. In Chapter 11 of the HSM, the SPFs for four-leg intersections with signal control on rural multilane highways have no specific base conditions. Considering the absence of intersection lighting and that of left- and right-turn lanes as possible base conditions for three-leg intersections with signal control for both rural two-lane and multilane highways, the distribution of intersections by the three characteristics is as follows: • Intersections on two-lane highways: 72 lighted; 17 unlighted (19% unlighted) • Intersections on multilane highways: 53 lighted; 19 unlighted (26% unlighted) • Intersections on two-lane highways: 58 with right-turn lane on one approach; 31 with none (35% with none) • Intersections on multilane highways: 48 with right-turn lane on one approach; 24 with none (33% with none) • Intersections on two-lane highways: 79 with left-turn lane on one approach; 10 with none (11% with none) • Intersections on multilane highways: 66 with left-turn lane on one approach; 1 with left- turn lane on two approaches; 5 with none (7% with none) In an effort to include all intersections in the models, crashes at intersections that did not meet base conditions for these three characteristics were first adjusted using the following CMFs in reverse (i.e., divide rather than multiply the crashes by the product of the CMFs): • Lighting: use CMF4i, shown in Equation 10-24 in the HSM (same as Equation 11-22 in the HSM) and the proportion of total crashes for unlighted intersections that occurred at night in the current database, shown in Table 23 (similar to Tables 10-15 and 11-24 in the HSM); this CMF was applied to total, FI, and PDO crashes before modeling

86 • Installation of left-turn lanes: use CMF2i shown in Table 30 (same as Tables 10-13 and 11-22 in the HSM with the addition of a CMF for three-leg intersections with signal control) • Installation of right-turn lanes: use CMF3i shown in Table 31 (same as Tables 10-14 and 11-23 in the HSM with the addition of a CMF for three-leg intersections with signal control) Table 23. Nighttime crash counts and proportions for unlighted three-leg intersections with signal control by roadway type used for modeling Roadway Type Number of Sitesa Number of Nighttime Crashes Total Crashes Proportion of Crashes that Occurred at Night (pni) Two-lane 17 58 247 0.235 Multilane 19 50 244 0.205 a Number of unlighted intersections only. The final SPF models for crashes at intersections on rural two-lane highways are shown in Table 24, separately for each crash severity. The table shows the model coefficients and overdispersion parameter (estimate), their standard error, and associated p-values (or significance level) for each severity level. Figures 13-15 graphically present the SPFs shown in Table 24 for various major- and minor approach AADTs. Table 24. SPF coefficients for three-leg intersections with signal control on rural two-lane highways Crash Severity Parameter Estimate Standard Error Pr > F Significance Level INTERSECTIONS ON RURAL TWO-LANE HIGHWAYS Total Crashes Intercept -5.88 1.89 -- -- ln(AADTmaj) 0.54 0.18 <.01 Significant at 99% level ln(AADTmin) 0.23 0.07 <.01 Significant at 99% level Overdispersion 0.31 0.06 -- -- FI Crashes Intercept -9.69 3.22 -- -- ln(AADTmaj) 0.78 0.31 0.01 Significant at 99% level ln(AADTmin) 0.24 0.12 0.04 Significant at 95% level Overdispersion 0.72 0.19 -- -- PDO Crashes Intercept -6.49 2.50 -- -- ln(AADTmaj) 0.50 0.24 0.04 Significant at 95% level ln(AADTmin) 0.26 0.09 <.01 Significant at 99% level Overdispersion 0.49 0.11 -- -- Base Condition: Absence of intersection lighting and absence of left- and right-turn lanes

87 Figure 13. Graphical representation of the SPF for total crashes at three-leg intersections with signal control on rural two-lane highways Figure 14. Graphical representation of the SPF for FI crashes at three-leg intersections with signal control on rural two-lane highways

88 Figure 15. Graphical representation of the SPF for PDO crashes at three-leg intersections with signal control on rural two-lane highways The final SPF models for crashes at three-leg intersections with signal control on rural multilane highways are shown in Table 25, separately for each crash severity. No usable model could be obtained for FI crashes considering KAB severities only. Figures 16-18 graphically present the SPFs shown in Table 25 for various major- and minor approach AADTs. Table 25. SPF coefficients for three-leg intersections with signal control on rural multilane highways Crash Severity Parameter Estimate Standard Error Pr > F Significance Level INTERSECTIONS ON RURAL MULTILANE HIGHWAYS Total Crashes Intercept -6.28 1.97 -- -- ln(AADTmaj) 0.52 0.21 0.02 Significant at 95% level ln(AADTmin) 0.31 0.08 <.01 Significant at 99% level Overdispersion 0.40 0.08 -- -- FI Crashes Intercept -11.03 3.81 -- -- ln(AADTmaj) 0.79 0.39 0.05 Significant at 95% level ln(AADTmin) 0.39 0.14 <.01 Significant at 99% level Overdispersion 1.15 0.26 -- -- FI Crashesa No usable model could be obtained PDO Crashes Intercept -6.40 2.49 -- -- ln(AADTmaj) 0.44 0.27 0.10 Significant at 90% level ln(AADTmin) 0.30 0.10 <.01 Significant at 99% level Overdispersion 0.53 0.13 -- -- a Using the KABCO scale, these include only KAB crashes. Crashes with severity level C (possible injury) are not included. Base Condition: Absence of intersection lighting and absence of left- and right-turn lanes

89 Figure 16. Graphical representation of the SPF for total crashes at three-leg intersections with signal control on rural multilane highways Figure 17. Graphical representation of the SPF for FI crashes at three-leg intersections with signal control on rural multilane highways

90 Figure 18. Graphical representation of the SPF for PDO crashes at three-leg intersections with signal control on rural multilane highways Similar to Tables 10-5 and 10-6 in the HSM, respectively, Tables 26 and 27 provide percentages for crash severity levels and collision types and manner of collision, respectively, for three-leg intersections with signal control on rural two-lane highways. These percentages were calculated based on all crash counts at all intersections in all states combined, excluding those sites in Florida and Kentucky with missing crash severity information. Table 26. Distributions for crash severity level at three-leg intersections with signal control on rural two-lane highways Crash Severity Level Percentage of Total Crashes Fatal 0.1 Incapacitating injury 2.4 Non-incapacitating injury 14.3 Possible injury 20.5 Total fatal plus injury 37.3 Property-damage-only 62.7 Total 100.0

91 Table 27. Distributions for collision type and manner of collision and crash severity at three-leg intersections with signal control on rural two-lane highways Collision Type Percentage of Total Crashes Total FI PDO SINGLE-VEHICLE CRASHES Collision with animal 1.8 0.0 3.4 Collision with bicycle 0.3 0.7 0.2 Collision with pedestrian 0.0 0.0 0.0 Overturned 1.8 4.6 0.6 Ran off road 0.1 0.0 0.2 Other SV crash 15.4 12.4 18.9 Total SV crashes 19.4 17.7 23.3 MULTIPLE-VEHICLE CRASHES Angle collision 19.3 26.2 15.8 Head-on collision 2.7 5.7 1.7 Rear-end collision 46.0 42.6 46.3 Sideswipe collision 4.8 2.5 4.6 Other MV collision 7.7 5.3 8.2 Total MV crashes 80.5 82.3 76.6 Total Crashes 100.0 100.0 100.0 Similar to Table 11-9 in the HSM, Table 28 provides percentages to break down total, FI (both with and without level C injuries), and PDO crash severities into specific collision types for three-leg intersections with signal control on rural multilane highways. These percentages were calculated based on all crash counts at all intersections in all states combined, excluding those sites in Florida and Kentucky with missing crash severity information (for FI and PDO statistics only). Table 28. Distributions of intersection crashes by collision type and crash severity at three-leg intersections with signal control on rural multilane highways Collision Type Percentage of Total Crashes Total FI FIa PDO Head-on collision 2.4 4.1 2.2 1.8 Sideswipe collision 8.0 3.4 3.8 10.8 Rear-end collision 43.2 36.7 31.9 44.1 Angle collision 28.0 40.8 47.3 22.1 SV collision 11.3 9.7 9.9 15.1 Other 7.2 5.3 4.9 6.2 Total Crashes 100.0 100.0 100.0 100.0 a Using the KABCO scale, these include only KAB crashes. Crashes with severity level C (possible injury) are not included. Following the development of the crash prediction models for three-leg intersections with signal control on rural highways, 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 13-18 provide some sense of the reasonableness of the new models for three-leg intersections with signal control on rural highways. Nothing from these figures suggests that the models provide unreasonable results. In addition, the models for three-leg intersections with signal control on rural highways were compared to the corresponding models for intersections on urban and suburban arterials in Chapter 12 of the HSM.

92 Figure 19 illustrates a comparison of the predicted average crash frequency for total crashes based on the 3SG model for rural two-lane roads (Table 24) to the predicted average crash frequency based on the 3SG model in Chapter 12 of the HSM. As previously, the dashed lines in the figure represent the predicted average crash frequency for the new model (i.e., 3SG model for rural two-lane roads), and the solid lines represent the predicted average crash frequency for the 3SG model in the HSM. Similarly, Figure 20 illustrates a comparison of the predicted average crash frequency for total crashes based on the 3SG model for rural multilane highways (Table 25) to the predicted average crash frequency based on the 3SG model in Chapter 12 of the HSM. In both instances, for lower major approach AADTs, higher average crash frequencies were predicted for three-leg signalized intersections on rural highways compared to urban and suburban arterials. As the major road AADT increased the predicted average crash frequencies drew closer together, and in some cases, the predicted average crash frequencies for three-leg intersections with signal control on urban and suburban arterials exceeded the predicted average crash frequencies for three-leg intersections with signal control on rural highways. This seems reasonable as drivers in rural areas during low volume conditions may not be as attentive to the task of driving as they would in an urban area and may be more susceptible to a crash as a result in rural environments given the same traffic volumes. Then, as traffic volumes increase in the rural areas, drivers’ awareness to the driving task may increase to similar levels as in urban and suburban areas, resulting in similar levels of safety performance at three-leg signalized intersections in both rural and urban environments. In summary, the models for three-leg signalized intersections on rural highways 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 19. Comparison of new crash prediction model to existing model in HSM: 3SG for rural two-lane roads vs 3SG for urban and suburban arterials (total crashes)

93 Figure 20. Comparison of new crash prediction model to existing model in HSM: 3SG for rural multilane highways vs 3SG for urban and suburban arterials (total crashes) 4.4 Crash Modification Factors During the development of the crash prediction models for three-leg intersections with signal control on rural highways, 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 intersections with signal control on rural highways • High-quality CMFs applicable to three-leg intersections with signal control on rural highways 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 literature After considering developing CMFs through regression modeling as part of this research and 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, three CMFs were identified for potential use with the crash prediction models for three-leg intersections with signal control on rural highways, including:

94 • 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 and 11 of the first edition of the HSM • The CMFs for providing a left-turn lane on one or two intersection approaches at a rural three-leg signalized intersection based on the work by Harwood et al. (2002), similar to the CMFs identified for use with intersection crash prediction models in Chapters 10 and 11 of the first edition of the HSM and included in HSM Part D • The CMFs for providing a right-turn lane on one or two intersection approaches at a rural three-leg signalized intersection based on the work by Harwood et al. (2002), similar to the CMFs identified for use with intersection crash prediction models in Chapters 10 and 11 of the first edition of the HSM and included in HSM Part D The CMFs recommended for use with the SPFs for three-leg intersections with signal control on rural highways are presented below. Lighting CMF With the CMF for intersection lighting based on the work by Elvik and Vaa (2004), the base condition is the absence of intersection lighting. The CMF for lighted intersections is similar to the CMF in Equation 10-24 (two-lane highways) and Equation 11-22 (multilane highways) in the HSM and has the form (AASHTO, 2010): 𝐶𝑀𝐹 = 1 − 0.38 × 𝑝 (Eq. 39) Where: CMFi = crash modification factor for the effect of lighting on total crashes; and pni = proportion of total crashes for unlighted intersections that occur at night. This CMF applies to total intersection crashes. Table 29 (similar to Table 23; and similar to Tables 10-15 and 11-24 in the HSM) presents default values for the nighttime crash proportion, pni, by roadway type. Table 29. Nighttime crash proportions for unlighted three-leg intersections with signal control Roadway Type Proportion of Crashes that Occur at Night (pni) Rural two-lane 0.235 Rural multilane 0.205 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, we have recommended this CMF for application to three-leg intersections with signal control on rural highways because this CMF has been used in the HSM first edition. If any

95 decision to remove or change the lighting CMFs is made, this should be done consistently for all facility types as part of the development of the HSM second edition. Intersection Approaches with Left-Turn Lanes CMF With the CMF for providing a left-turn lane on one or two intersection approaches at a rural three-leg signalized intersection based on the work by Harwood et al. (2002), the base condition is the absence of left-turn lanes on intersection approaches. The CMFs for providing a left-turn lane on one or two intersection approaches are presented in Table 30. Table 30 is presented in the same format as Table 14-10 in the HSM Part D (AASHTO, 2010). These CMFs apply to all severity levels for three-leg intersections with signal control on both rural two-lane and multilane highways. Table 30. CMF for installation of left-turn lanes on intersection approaches (Harwood et al., 2002; AASHTO, 2010) Treatment Setting (Intersection Type) Traffic Volume AADT (veh/day) Crash Type (Severity) CMF Std. Error One approach Two approaches Installation of left- turn lanes Rural (three-leg intersections with signal control) Unspecified All types (All severities) 0.85 0.72 N/A a a Standard error of CMF is unknown. Intersection Approaches with Right-Turn Lanes CMF With the CMF for providing a right-turn lane on one or two intersection approaches at a rural three-leg signalized intersection based on the work by Harwood et al. (2002), the base condition is the absence of right-turn lanes on intersection approaches. The CMFs for providing a right- turn lane on one or two intersection approaches are presented in Table 31. Table 31 is presented in the same format as Table 14-15 in HSM Part D (AASHTO, 2010). Table 31. CMF for installation of right-turn lanes on intersection approaches (Harwood et al., 2002; AASHTO, 2010) Treatment Setting (Intersection Type) Traffic Volume AADT (veh/day) Crash Type (Severity) CMF Std. Error Installation of right-turn on one intersection approach Rural (three-leg intersections with signal control) Major road 7,000 to 55,100, minor road 550 to 8,400 All types (All severities) 0.96 0.02 All types (Injury) 0.91 0.04 Installation of right-turn on two intersection approaches All types (All severities) 0.92 0.03 All types (Injury) 0.83 N/A a a Standard error of CMF is unknown.

96 4.5 Severity Distribution Functions The development of SDFs was explored for three-leg intersections with signal control on rural two-lane and multilane highways using methods outlined in Section 2.2.3 of this report. SDFs were not used in the development of crash prediction methods in the first edition of the HSM but were subsequently used in the Supplement to the HSM for freeways and ramps (AASHTO, 2014). Due to sample size issues, the data for three-leg intersections with signal control on rural two-lane and multilane highways were combined for development of the SDFs. Therefore, the SDFs that were developed are applicable to three-leg intersections with signal control on both rural two-lane and multilane highways. SDFs were not developed separately for three-leg intersections with signal control on rural two-lane and multilane highways. The database used to explore SDFs consisted of the same crashes and intersections as the databases used to estimate the SPFs, but restructured so that the basic observation unit (i.e., database row) is a crash instead of an intersection. For three-leg intersections with signal control on both rural two-lane and multilane highways, the SDF takes the following form: 𝑃 , , = ( ) ( ) × 𝑃 | , , (Eq. 40) 𝑃 , , = ( 𝑩) ( ) × 𝑃 | , , (Eq. 41) 𝑃 , , = ( 𝑩) ( ) × 1 − 𝑃 | , , − 𝑃 | , , (Eq. 42) 𝑃 , , = 1 − 𝑃 , , + 𝑃 , , + 𝑃 , , (Eq. 43) Where: P3SG,at,K = probability of a fatal crash (given that a fatal or injury crash occurred) for three-leg signalized intersections (3SG) based on all collision types (at) P3SG,at,A = probability of an incapacitating injury crash (given that a fatal or injury crash occurred) for three-leg signalized intersections (3SG) based on all collision types (at) P3SG,at,B = probability of a non-incapacitating injury crash (given that a fatal or injury crash occurred) for three-leg signalized intersections (3SG) based on all collision types (at) P3SG,at,C = probability of a possible injury crash (given that a fatal or injury crash occurred) for three-leg signalized intersections (3SG) based on all collision types (at) VKAB = systematic component of crash severity likelihood for severity KAB

97 PK|KAB,3SG,at = probability of a fatal crash given that the crash has a severity of either fatal, incapacitating injury, or non-incapacitating injury for three-leg signalized intersections (3SG) based on all collision types (at) PA|KAB,3SG,at = probability of an incapacitating injury crash given that the crash has a severity of either fatal, incapacitating injury, or non- incapacitating injury for three-leg signalized intersections (3SG) based on all collision types (at) The basic model form for the systematic components of crash severity likelihood at three-leg intersections with signal control on both rural two-lane and multilane highways is illustrated by Equation 44. 𝑉 = 𝑎 + 𝑏 × 0.001 × 𝐴𝐴𝐷𝑇 + 𝑐 × 𝐼 + 𝑑 × 𝑛 + 𝑒 × 𝑛 (Eq. 44) Where: 𝐴𝐴𝐷𝑇 = AADT on the major road (veh/day) Ilight = intersection lighting indicator variable (1 if lighting is present,0 otherwise) nmajLTL = total number of left-turn lanes on both major road approaches (0, 1, or 2) nmajthru = total number of through lanes on the major road a, b, c, d, and e = estimated SDF coefficients The SDF coefficients for three-leg intersections with signal control on rural two-lane and multilane highways are provided in Table 32. Table 32. SDF coefficients for three-leg intersections with signal control on rural two-lane and multilane highways Severity (z) Variable a b c d e Fatal, incapacitating injury, or non- incapacitating injury (KAB) VKAB 0.368 -0.0639 -0.760 -0.605 0.594 For three-leg intersections with signal control on rural two-lane and multilane highways, values of 0.0259 and 0.159 are used for PK|KAB and PA|KAB, respectively. 4.6 Summary of Recommended Models for Incorporation in the HSM In summary, several crash prediction models were developed for three-leg intersections with signal control on rural two-lane and multilane highways for consideration in the second edition of the HSM, including models for: • Three-leg intersections with signal control (3SG) on rural two-lane highways • Three-leg intersections with signal control (3SG) on rural multilane highways

98 The final predictive model for estimating total crashes at three-leg intersections with signal control on rural two-lane highways presented in Table 24 and the final predictive models for estimating total and FI crashes at three-leg intersections with signal control on multilane highways presented in Table 25 are recommended for inclusion in the second edition of the HSM, consistent with existing methods in HSM Chapters 10 and 11. Logical interpretations do exist for the SDFs reported in Section 4.5. For example, the negative parameter for AADT may be capturing lower (on average) impact speeds of crashes at locations with higher traffic volumes. The negative parameter for number of left-turn lanes on the major road approaches may be capturing the severity impacts of separating through and turning vehicles with high-speed differentials. The positive parameter for number of through lanes may be capturing a compound effect of higher operating speeds plus longer crossing distances resulting in more severe crashes. These interpretations cannot, however, be verified or validated with existing crash databases. Additionally, the types of severity effects found for three-leg intersections with signal control on rural two-lane and multilane highways were not consistently found across other intersection types. More generally, uncovering consistent and statistically significant impacts of intersection characteristics on crash severity proved challenging. These challenges were also implied by the SDF results of NCHRP Project 17-45, where only area type (urban, rural) and presence of protected left-turn phasing were included in crossroad ramp terminal SDFs. With these challenges in mind, ongoing and future research efforts will continue to explore the most promising approaches for addressing crash severity in the HSM predictive methods. Due to the challenges and inconsistencies observed to-date in developing SDFs for three-leg intersections with signal control on rural two-lane and multilane highways, it is recommended for the second edition of the HSM that crash severity for three-leg intersections with signal control on rural two-lane and multilane highways be addressed in a manner consistent with existing methods in Chapters 10 and 11 of the HSM, respectively, without use of SDFs. Appendix A presents recommended text for incorporating the final recommended models for three-leg intersections with signal control on rural two-lane and multilane highways into Chapters 10 and 11 of the HSM.