Development of Roundabout Crash Prediction Models and Methods (2019)

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143 Research Findings This chapter presents the research findings from the project. The first section presents the final planning-level, intersection-level, and leg-level crash prediction models. The following sections present the (1) calibration for the crash prediction models; (2) results of the driver learning curve evaluation; (3) findings related to pedestrian and bicycle safety at roundabouts; (4) findings related to predicted speed (i.e., fastest path) and crash frequency at roundabouts; and (5) contributions to the Highway Safety Manual (HSM). 6.1 Crash Prediction Models 6.1.1 Planning-Level Crash Prediction Models This section presents the final planning-level crash pre- diction models. These are exactly as presented in Chapter 5 of the report, which describes the entire model development process. Intersection-level safety performance factors (SPFs) were developed for three groups of roundabouts: rural, urban single-lane, and urban multilane roundabouts. 6.1.1.1 Rural Roundabouts The final models developed for rural roundabouts, which were estimated with the combined estimation and validation datasets, took the model form shown below. For the final models, the variable for major road speed limit was not included because of its low statistical significance. Although the validation sample indicated that including the STATE variable did not significantly improve model performance, it was found that when estimating the models with the combined dataset (initial estimation plus validation data) the exclusion of STATE resulted in a large standard error for the major road AADT variable. For this reason, STATE was included in the model. Equation 6-1 N exp MAJAADT MINAADT exp a STATE b c d NUMBERLEGS e CIRCLANES = ( ) + × + × where N = predicted average crash frequency, crashes/yr; STATE = an additive intercept term dependent on state; MAJAADT = total entering AADT on major road; MINAADT = total entering AADT on minor road; NUMBERLEGS = 1 if a 3-leg roundabout; 0 if 4-legs; CIRCLANES = 1 if a single-lane roundabout; 0 if more than 1 circulating lane; and MAJSPD = posted speed on the major road (mph). Table 6-1 presents the parameter estimates and stan- dard errors (in brackets) for the models developed for each crash type, as well as the negative binomial overdispersion parameters k. 6.1.1.2 Urban Single-Lane Roundabouts The final models developed for urban single-lane round- abouts, which were estimated with the combined estimation and validation datasets, are of the form show in Equation 6-2. Equation 6-2 N exp MAJAADT MINAADT expa b c d NUMBERLEGS= ( )× where N = predicted average crash frequency, crashes/yr; MAJAADT = total entering AADT on major road; MINAADT = total entering AADT on minor road; and NUMBERLEGS = 1 if a 3-leg roundabout; 0 if 4-legs. C H A P T E R 6

144 Table 6-2 presents the parameter estimates and stan- dard errors (in brackets) for the models developed for each crash type, as well as the negative binomial overdispersion parameters k. 6.1.1.3 Urban Multilane Roundabouts The final models developed for urban multilane round- abouts, which were estimated with the combined esti- mation and validation datasets, are of the form shown in Equation 6-3. Equation 6-3 N exp MAJAADT MINAADT expa b c d NUMBERLEGS= ( )× where N = predicted average crash frequency, crashes/yr; MAJAADT = total entering AADT on major road; MINAADT = total entering AADT on minor road; and NUMBERLEGS = 1 if a 3-leg roundabout; 0 if 4-legs. Table 6-3 presents the parameter estimates and stan- dard errors (in brackets) for the models developed for each crash type, as well as the negative binomial overdispersion parameters k. 6.1.2 Intersection-Level Crash Prediction Models for Design This section presents the final version of the intersection- level crash prediction models. The presentation is divided into four subsections. These subsections address one combination of crash severity category and number of circulating lanes. The four subsections are identified in the following list. • FI Crash Frequency Prediction Model, One Circulating Lane; • FI Crash Frequency Prediction Model, Two Circulating Lanes; • PDO Crash Frequency Prediction Model, One Circulating Lane; and • PDO Crash Frequency Prediction Model, Two Circulating Lanes. Within each subsection, the calibrated model is presented using a list of steps that outline the procedure for the model’s application. Then, a sensitivity analysis is provided that illus- trates the relationships between the model predictions and various input variables. Model ID a b c d e k TOT -5.3299 (1.5425) 0.3356 (0.1767) 0.5142 (0.1165) -0.6854 (0.2244) -0.9375 (0.2309) 0.6292 (0.1005) FI -10.4848 (2.2682) 0.7756 (0.2356) 0.4239 (0.1312) -1.0080 (0.2827) -0.5506 (0.2658) 0.4424 (0.1288) PDO -5.4115 (1.6602) 0.2980 (0.1939) 0.5463 (0.1280) -0.7104 (0.2430) -1.0192 (0.2488) 0.7284 (0.1192) Table 6-1. Final planning-level models for rural roundabouts. Model ID a b c d k TOT -5.6049 (1.0533) 0.3274 (0.1479) 0.3960 (0.1157) -0.8681 (0.1489) 0.5030 (0.0727) FI -8.6597 (1.3337) 0.5271 (0.1886) 0.3505 (0.1374) -0.7317 (0.1822) 0.3290 (0.0908) PDO -5.5319 (1.1659) 0.2653 (0.1650) 0.4294 (0.1304) -0.9260 (0.1656) 0.6064 (0.0878) Table 6-2. Final planning-level models for urban single-lane roundabouts. Model ID a b c d k TOT -5.6642 (1.2790) 0.5210 (0.1545) 0.2905 (0.1198) -0.4610 (0.2357) 0.9263 (0.1371) FI -10.3369 (1.7505) 0.9134 (0.2129) 0.1937 (0.1248) -0.5131 (0.2261) 0.5611 (0.1398) PDO -5.7669 (1.3664) 0.4954 (0.1640) 0.3098 (0.1274) -0.4618 (0.2527) 1.0642 (0.1583) Table 6-3. Final planning-level models for urban multilane roundabouts.

145 6.1.2.1 Fatal-and-Injury Crash Frequency Prediction Model, One Circulating Lane This section describes the final version of the predictive models for roundabouts with one circulating lane. These models are not applicable to roundabouts that have two cir- culating lanes conflicting with one or more legs. The models predict fatal-and-injury (FI) crash frequency. One variation of the model is applicable to three-leg roundabouts and a second variation of the model is applicable to four-leg roundabouts. This section consists of two subsections. The first sub- section describes the predictive model. The second subsection offers a sensitivity analysis of selected factors that influence the predicted crash frequency or severity. Calibrated Model. This section presents the calibrated model using a list of steps that outline the procedure for model application. Step 1: Apply SPF. The calibrated SPFs for three- and four-leg roundabouts are shown in Equations 6-4 and 6-5, respectively. These equations are used to compute the pre- dicted crash frequency for base conditions. SPF for three-leg roundabouts. 4.404 1.084 1000 0.206 Equation 6-4 ,3 3N exp LN EntAADT I SPF rural [ ] ( )= − + × + × SPF for four-leg roundabouts. 3.503 0.915 1000 0.206 Equation 6-5 ,4 4N exp LN EntAADT I SPF rural [ ] ( )= − + × + × where NSPF,m = predicted average crash frequency for base conditions on all legs for roundabout with m legs (m = 3, 4), crashes/yr; EntAADTm = entering annual average daily traffic (AADT) for roundabout with m legs (m = 3, 4), veh/d; and Irural = area type indicator variable (= 1.0 if area is rural, 0.0 otherwise). The entering AADT for the roundabout represents the sum of the AADT that enters the roundabout when considering all legs. If a leg serves two-way traffic, then its entering volume can be estimated by multiplying a representative directional distribution factor by the leg AADT. If this factor is unknown, then a default value of 0.5 can be used. If a leg serves one-way traffic inbound to the roundabout, then the leg’s AADT can be included directly in the summation. If a leg serves one-way traffic outbound from the roundabout, then the leg’s AADT should not be included in the summation. Step 2: Apply CMFs. The calibrated crash modification factors (CMFs) that can be used with the SPFs are shown in this section. These equations are used to compute the CMF value that adjusts the SPF prediction when nonbase conditions are of interest to the analyst. The inscribed circle diameter CMF is computed using the following equation. 0.00621 125 Equation 6-6CMF exp ICDICD [ ]( )= − × − where CMFICD = CMF for inscribed circle diameter at urban roundabouts; and ICD = inscribed circle diameter (ICD), ft. This CMF is applicable to roundabouts in urban or sub- urban areas, but it is not applicable to roundabouts in rural areas. The diameters used to calibrate this CMF ranged from 90 to 160 ft. If the ICD exceeds 160 ft, the CMF value computed at 160 ft (0.80) should be used in subsequent steps of the analysis. Values less than 0.80 should not be used for this CMF. The outbound-only leg CMF (CMFoutbd) has a value of 0.426 (= exp[-0.853]). It is applicable to any roundabout in an urban, suburban, or rural area. It is applicable only to inter- change crossroad-ramp terminal roundabouts with one outbound-only leg. It is not applicable to roundabouts with two or more outbound-only legs. The right-turn bypass lane CMF (CMFbypass) has a value of 0.335 (= exp[-1.095]). It is a leg-specific CMF. It is appli- cable to any roundabout in an urban, suburban, or rural area. The sites used to calibrate this CMF have 0, 1, or 2 right-turn bypass lanes. It is rationalized that this CMF can be reason- ably extended to roundabouts with a bypass lane present on every leg given the independent operation of each bypass lane. This CMF is applicable when the bypass lane has add-lane, merge, or yield control. The access point frequency CMF is a leg-specific CMF. It is described using the following equation. 0.0659 Equation 6-7, ,CMF exp nap j ap j[ ]= × where CMFap,j = CMF presence of driveways or unsignalized access points on leg j ( j = 1 to m), and nap,j = number of driveways or unsignalized access points on leg j ( j = 1 to m) (within 250 ft of yield line).

146 This CMF is applicable to a roundabout in an urban, suburban, or rural area. The count of access points on a leg represents the number of driveways or unsignalized access points on the leg (either side) within 250 ft of the yield line. The number of access points in the data used to calibrate this CMF ranged from 0 to 8 access points per leg. Step 3: Aggregate Leg-Specific CMFs. All leg-specific CMFs of interest need to have their effect aggregated to the overall intersection level (and thereby, consistent with the SPFs, which are also applicable to the overall intersection). As a first activity, for each roundabout leg j with one or more leg-specific CMFs, the following equation is used to compute the leg CMF. Equation 6-8, ,CMF CMF CMFj bypass j ap j= × where CMFj is the combined crash modification factor for leg j (j = 1 to m). Then, the aggregated CMFs for three- and four-leg roundabouts are computed using Equations 6-9 and 6-11, respectively. Aggregated CMF for three-leg roundabouts (m = 3): Equation 6-9 1 1 2 2 3 3CMF p CMF p CMF p CMFlegs ( ) ( ) ( )= × + × + × Equation 6-10 1 2 3 p AADT AADT AADT AADT j j= + + Aggregated CMF for four-leg roundabouts (m = 4): Equation 6-11 1 1 2 2 3 3 4 4 CMF p CMF p CMF p CMF p CMF legs ( ) ( ) ( ) ( ) = × + × + × + × Equation 6-12 1 2 3 4 p AADT AADT AADT AADT AADT j j= + + + where CMFlegs = aggregate CMF for all legs; pj = proportion of total leg traffic volume associated with roundabout leg j ( j = 1 to m); CMFj = combined CMF for leg j ( j = 1 to m); and AADTj = AADT volume for roundabout leg j ( j = 1 to m), veh/d. Step 4: Compute Predicted Crash Frequency. The CMF and SPF values from the preceding steps are used in this step to compute the predicted FI crash frequency. Equations 6-13 and 6-14 are provided for three- and four-leg roundabouts, respectively. Predicted crash frequency for three-leg roundabouts: Equation 6-13 , ,3N C N CMF CMF CMFp FI SPF legs outbd ICD= × × × × Predicted crash frequency for four-leg roundabouts: Equation 6-14 , ,4N C N CMF CMF CMFp FI SPF legs outbd ICD= × × × × where Np,FI = predicted FI average crash frequency, crashes/yr; and C = local calibration factor. Step 5: Apply Severity Adjustment Factor (optional). The calibrated adjustment factor is used to adjust the pre- dicted severity distribution as a function of speed limit. It is a leg-specific factor. The speed limit adjustment factor is computed using the following equation. One factor value is computed for each roundabout leg. 3.1187 100 35 100 Equation 6-15, 2 2f exp SLj sl j{ }( ) ( )= × −  where fj,sl = severity adjustment factor for the effect of speed limit on leg j (j = 1 to m), and SLj = speed limit on leg j (j = 1 to m). This adjustment factor is applicable to roundabouts in urban, suburban, and rural areas. The leg speed limit data used to calibrate this factor ranged from 10 to 60 mph. This factor should not be used for speed limits outside of this range. Step 6: Aggregate Leg-Specific Adjustment Factor (optional). The leg-specific adjustment factors need to have their effect aggregated to the overall intersection level. The aggregated adjustment factors for three- and four-leg roundabouts are computed using the following equations. Aggregated CMF for three-leg roundabouts (m = 3): exp 3.4725 Equation 6-16 1 1, 2 2, 3 3,S p f p f p fK sl sl sl[ ][ ]= − × × + × + × exp 1.1752 Equation 6-17 1 1, 2 2, 3 3,S p f p f p fA sl sl sl[ ][ ]= − × × + × + ×

147 exp 0.0415 Equation 6-18 1 1, 2 2, 3 3,S p f p f p fB sl sl sl[ ][ ]= − × × + × + × The proportion of total leg volume pj is computed using Equation 6-10. Aggregated CMF for four-leg roundabouts (m = 4): 4.6216 Equation 6-19 1 1, 2 2, 3 3, 4 4,S exp p f p f p f p fK sl sl sl sl[ ][ ]= − × × + × + × + × 2.3243 Equation 6-20 1 1, 2 2, 3 3, 4 4,S exp p f p f p f p fA sl sl sl sl[ ][ ]= − × × + × + × + × 0.4627 Equation 6-21 1 1, 2 2, 3 3, 4 4,S exp p f p f p f p fB sl sl sl sl[ ][ ]= − × × + × + × + × The proportion of total leg volume pj is computed using Equation 6-12. where Sl = distribution score for severity l (l = K, A, B), and pj = proportion of total leg traffic volume associated with roundabout leg j (j = 1 to m). Step 7: Apply Severity Distribution (optional). The dis- tribution scores computed in the previous step are used in the following equations to compute the predicted distribution of FI crashes. 1 Equation 6-22P S S S S K K K A B = + + + 1 Equation 6-23P S S S S A A K A B = + + + = + + +1 Equation 6-24P S S S S B B K A B 1 Equation 6-25P P P PC K A B( )= − + + where Pl = probability of the occurrence of crash severity l (l = K, A, B, C), and Sl = distribution score for severity l (l = K, A, B). Step 8: Apply Crash-Type Distribution (optional). The crash-type distribution for FI crashes is listed in Table 6-4. The proportion associated with a given crash type Pt is ob- tained from the corresponding column of the table and the row that coincides with the number of roundabout legs. Step 9: Compute Predicted Crash Frequency by Crash Type and Severity (optional). The predicted crash fre- quency for a given severity category is computed using the following equation. Equation 6-26, ,N P Np l l p FI= × where Np,l = predicted average crash frequency for crash severity l (l = K, A, B, C), crashes/yr; Pl = probability of the occurrence of crash severity l (l = K, A, B, C); and Np,FI = predicted FI average crash frequency, crashes/yr. This equation is used once for each severity category (K, A, B, or C) of interest. The probability used in the equa- tion above is obtained from Step 7. The predicted FI average crash frequency is obtained from Step 4. The predicted crash frequency for a given crash-type category is computed using the following equation. Equation 6-27, ,N P Np t t p FI= × where Np,t = predicted average crash frequency for crash type t (see Table 6-4 for types), crashes/yr; Pt = probability of the occurrence of crash type t; and Np,FI = predicted FI average crash frequency, crashes/yr. This equation is used once for each crash type of interest. The crash types are listed in Table 6-4. The probability used Number of Legs Multiple-Vehicle Crash Type Single-Vehicle Crash Type Head On Right Angle Rear End Sideswipe, Same Dir. Other Animal Fixed Object Other Object Parked Vehicle Other 3 0.007 0.168 0.356 0.045 0.139 0.000 0.109 0.000 0.000 0.175 4 0.011 0.115 0.298 0.078 0.071 0.000 0.216 0.000 0.002 0.209 Table 6-4. FI crash-type distribution, one circulating lane.

148 in the equation above is obtained from Step 8. The predicted FI average crash frequency is obtained from Step 4. The predicted crash frequency for a given combination of crash type and severity is computed using the following equation. Equation 6-28, , ,N P P Np t l t l p FI= × × where Np,t,l is the predicted average crash frequency for crash type t and severity l, crashes/yr, and all other variables are as previously defined. This equation is used once for each crash type and severity category of interest. The probabilities used in the equation above are obtained from Step 7 and Step 8. The predicted FI average crash frequency is obtained from Step 4. Sensitivity Analysis. This section illustrates the relation- ships between the model predictions and various input variables. Safety Performance Function. The relationship between crash frequency and traffic demand, as obtained from the calibrated model, is shown in Figure 6-1a for roundabouts with one circulating lane. The inscribed circle diameter, outbound-leg presence, and right-turn bypass lane pres- ence conditions are such that the associated CMFs have a value of 1.0. It was assumed that there was one access point on each leg and that the leg AADT volume was the same on each leg (for the purpose of computing the access point frequency CMF). The trends in Figure 6-1a indicate that roundabout crash frequency increases with entering AADT volume. Round- abouts in rural areas tend to have about 23% more crashes than those in urban or suburban areas with similar volume. The three-leg model was calibrated using sites with entering AADT ranging from 3,000 to 18,000 veh/d. The four-leg model was calibrated using sites with entering AADT ranging from 3,000 to 21,000 veh/d. Figure 6-1b compares the proposed predictive models for urban roundabouts with those discussed previously in Sec- tion 5.2.2.2. The proposed models for urban roundabouts are shown using the two solid trend lines. Trend lines for the reported models are shown using dashed lines. The trends for the proposed models are similar to those of the reported models in the sense that they have an intercept of zero, an upward slope to the right, and a predicted crash frequency that is in the middle of the range of values offered by the collective set of reported models. Differences between the proposed and reported models may be explained by geo- metric differences (e.g., ICD, outbound-only lane presence, right-turn bypass lane presence, and number of access points on each leg) that exist among the databases used to calibrate the models. The general reduction in crashes between the proposed models and the NCHRP Report 572 models may be a result of a larger database and improved roundabout design over time being reflected in the proposed models. ICD CMF. The inscribed circle diameter CMF is shown in Figure 6-2. The trend line shown indicates that the CMF value decreases with increasing diameter. It is rationalized that roundabouts with a larger diameter are more visible to approaching vehicles and require through vehicles to have a larger entry path deflection angle. A larger deflection angle may result in slower speed while negotiating the round- about. It follows that the reduction in crashes associated with increased diameter may be indirectly a result of improved roundabout visibility and slower speed. Outbound-Only Leg CMF. The value of this CMF suggests that a roundabout with one outbound-only leg has a. Proposed models. b. Model comparison. Figure 6-1. Proposed predictive models, FI crashes, one circulating lane.

149 57% fewer crashes than a roundabout at which all legs serve two-way traffic flow. It is rationalized that the presence of an outbound-only leg reduces the number of conflict points be- tween intersecting traffic streams, relative to a leg that serves two-way traffic flow. A reduction in conflict points is likely to result in fewer crashes. Right-Turn Bypass Lane CMF. Illustrative aggregate CMF values that reflect the presence of a bypass lane are listed in Table 6-5. To compute these values, it was assumed that there are no access points on any leg (CMFap = 1.0 for all legs) and that the AADT volume is the same on each roundabout leg. The presence of a bypass lane is indicated by the CMF values to reduce crash frequency. This trend is logical given that the bypass lane is physically separated from the adja- cent entering lane and the circulating lane. This separation eliminates conflicts at several points in the roundabout. Also, a bypass lane is typically associated with a heavy right-turn volume. These characteristics explain the relatively large crash reductions associated with bypass lane presence, as implied by the CMF values in Table 6-5. Access Point Frequency CMF. Illustrative aggregate CMF values that reflect the presence of access points are shown in Figure 6-3. To compute these values, it was assumed that there are no bypass lanes on any leg (CMFbypass = 1.0 for all legs) and that the AADT volume is the same on each roundabout leg. It was also assumed that the number of access points was the same on each leg. The trend line shown in Figure 6-3 indicates that the aggre- gate CMF value increases with increasing number of access points. This trend is consistent with that shown in Table 2-11 for access points on the crossroad legs of an unsignalized crossroad-ramp terminal intersection. For a given number of access points, the CMF values for roundabouts are about 30% smaller than those for ramp terminals. Severity Distribution Function. The predicted severity distribution for roundabouts with a 35-mph speed limit on each leg is shown in Table 6-6. The proportions shown in any one row add to 1.0. The proportions shown in Table 6-6 can be used to exam- ine the predicted trends associated with number of legs. Specifically, the trend associated with the number of legs can be assessed by comparing a pair of rows associated the same number of circulating lanes. The proportions are Figure 6-2. Calibrated ICD CMF, FI crashes, one circulating lane. Number of Legs with a Right-Turn Bypass Lane Aggregate CMF a (CMFlegs) 0 1.000 1 0.834 2 0.667 3 0.501 4 0.335 aCMF values are based on the assumption that there are no access points on any leg, and the AADT volume on each leg is the same as that of the other legs. Table 6-5. Calibrated right-turn bypass lane CMF, FI crashes, one circulating lane. Figure 6-3. Calibrated access point frequency CMF, FI crashes, one circulating lane. Number of Legs Crash Proportion by Severity a K A B C 3 0.014 0.134 0.417 0.435 4 0.006 0.056 0.362 0.576 aProportions are based on a speed limit of 35 mph on each leg. Table 6-6. Comparison of predicted severity distribution for a common speed limit, FI crashes, one circulating lane.

150 smaller for K, A, and B crashes at four-leg roundabouts than for three-leg roundabouts. A similar trend exists for round- abouts with two circulating lanes. These trends are consistent with those noted for K, A, and B crashes in the examination of crash frequency associated with Table 5-61. The predicted severity distribution as a function of speed limit is shown in Table 6-7. The proportions shown in this table are based on the assumption that the speed limit is the same on each leg. The predictive model should be used (instead of the table) when the speed limit varies among the roundabout legs. Speed Limit Adjustment Factor. The speed limit adjust- ment factor is shown in Figure 6-4. It is computed using Equation 6-15. The trend line in the figure shows the adjust- ment factor value for the K, A, and B severity categories. The line shown indicates that the proportion of crashes that have K, A, or B severity increases with increasing leg speed limit. 6.1.2.2 Fatal-and-Injury Crash Frequency Prediction Model, Two Circulating Lanes This section describes the final version of the predictive models for roundabouts with two circulating lanes conflicting with one or more legs. These models are not applicable to roundabouts having one circulating lane conflicting with each leg. The models predict FI crash frequency. One varia- tion of the model is applicable to three-leg roundabouts and a second variation of the model is applicable to four-leg roundabouts. Number of Legs Speed Limit, mph Crash Proportion by Severity A K A B C 3 20 0.012 0.119 0.370 0.499 25 0.012 0.123 0.383 0.481 30 0.013 0.128 0.399 0.460 35 0.014 0.134 0.417 0.435 40 0.014 0.141 0.438 0.406 45 0.015 0.149 0.462 0.375 50 0.016 0.157 0.487 0.341 55 0.017 0.165 0.513 0.305 4 20 0.005 0.048 0.310 0.637 25 0.005 0.050 0.324 0.621 30 0.005 0.053 0.341 0.600 35 0.006 0.056 0.362 0.576 40 0.006 0.060 0.387 0.547 45 0.006 0.065 0.415 0.514 50 0.007 0.069 0.447 0.477 55 0.008 0.075 0.481 0.436 Note: A Proportions listed in the table are based on the assumption that each leg has the same speed limit. Table 6-7. Predicted severity distribution for a range of speed limits, FI crashes, one circulating lane. Figure 6-4. Calibrated speed limit adjustment factor, FI crashes.

151 This section consists of two subsections. The first sub- section describes the predictive model. The second subsection offers a sensitivity analysis of selected factors that influence the predicted crash frequency or severity. Calibrated Model. Step 1: Apply SPF. The calibrated SPFs for three- and four-leg roundabouts are shown in Equations 6-29 and 6-30, respectively. These equations are used to compute the pre- dicted crash frequency for base conditions. SPF for three-leg roundabouts: 3.887 1.306 1000 0.250 Equation 6-29 ,3 3N exp LN EntAADT I SPF rural ( ) ] [= − + × + × SPF for four-leg roundabouts: 3.535 1.276 1000 0.250 Equation 6-30 ,4 4N exp LN EntAADT I SPF rural ( ) ] [= − + × + × where NSPF,m = predicted average crash frequency for base conditions on all legs for roundabout with m legs (m = 3, 4), crashes/yr; EntAADTm = entering AADT for roundabout with m legs (m = 3, 4), veh/d; and Irural = area type indicator variable (= 1.0 if area is rural, 0.0 otherwise). The entering AADT for the roundabout represents the sum of the AADT that enters the roundabout when considering all legs. If a leg serves two-way traffic, then its entering volume can be estimated by multiplying a representative directional distribution factor by the leg AADT. If this factor is unknown, then a default value of 0.5 can be used. If a leg serves one-way traffic inbound to the roundabout, then the leg’s AADT can be included directly in the summation. If a leg serves one-way traffic outbound from the roundabout, then the leg’s AADT should not be included in the summation. Step 2: Apply CMFs. The calibrated CMFs that can be used with the SPFs are shown in this section. These equa- tions are used to compute the CMF value that adjusts the SPF prediction when nonbase conditions are of interest to the analyst. The outbound-only leg CMF (CMFoutbd) has a value of 0.455 (= exp[-0.787]). It is applicable to any roundabout in an urban, suburban, or rural area. It is applicable only to interchange crossroad-ramp terminal roundabouts with one outbound- only leg. It is not applicable to roundabouts with two or more outbound-only legs. The sites used to calibrate this CMF have zero or one outbound-only legs. The right-turn bypass lane CMF (CMFbypass) has a value of 0.432 (= exp[-0.840]). It is a leg-specific CMF. It is appli- cable to any roundabout in an urban, suburban, or rural area. The sites used to calibrate this CMF have zero, one, two, or three right-turn bypass lanes. It is rationalized that this CMF can be reasonably extended to roundabouts with a bypass lane present on every leg given the independent operation of each bypass lane. This CMF is applicable when the bypass lane has add-lane, merge, or yield control. The entry width CMF is a leg-specific CMF. It is described using the following equation. 0.0300 Equation 6-31, , , ,CMF exp W Wew j ew j ew b j[ ]( )= − × − This CMF is applicable to roundabouts in an urban, sub- urban, or rural area. The base entry width, Wew,b, equals 20 ft if there is one entering lane on the subject approach. It equals 29 ft if there are two entering lanes on the subject approach. The entry widths used to calibrate this CMF ranged from 16 to 25 ft for legs with one entering lane, and 24 to 34 ft for legs with two entering lanes. Entry width is measured at the entrance line (i.e., the continuation of the ICD) to the circulating roadway. It is the perpendicular width of all entering lanes and the shoulder (if present). The width is measured from the splitter island curb to the curb face at the outside edge of the travel way. In the absence of a curb on the outside edge of the travel way, the width is measured from the splitter island curb face to the closer of the paved edge of the travel way or the near edge of the bypass lane (if present). The circulating lane CMF is a leg-specific CMF. It is described using the following equation. 0.196 4 Equation 6-32, , ,CMF exp n ncl j cl j el j[ ]( )= × × − This CMF is applicable to a roundabout in an urban, sub- urban, or rural area. The number of circulating lanes, ncl, used to calibrate this CMF ranged from one to two. The number of entering lanes nel ranged from one to two. This CMF is not applicable to outbound-only legs. Step 3: Aggregate Leg-Specific CMFs. All leg-specific CMFs of interest need to have their effect aggregated to the overall intersection level (and thereby, consistent with the SPFs, which are also applicable to the overall intersection). As a first activity, for each roundabout leg j with one or more

152 leg-specific CMFs, the following equation is used to compute the leg CMF. Equation 6-33, , ,CMF CMF CMF CMFj bypass j ew j cl j= × × where CMFj is the combined crash modification factor for leg j ( j = 1 to m). Then, the aggregated CMFs for three- and four-leg roundabouts are computed using Equations 6-34 and 6-36, respectively. Aggregated CMF for three-leg roundabouts (m = 3): Equation 6-34 1 1 2 2 3 3CMF p CMF p CMF p CMFlegs ( ) ( ) ( )= × + × + × Equation 6-35 1 2 3 p AADT AADT AADT AADT j j= + + Aggregated CMF for four-leg roundabouts (m = 4): Equation 6-36 1 1 2 2 3 3 4 4 CMF p CMF p CMF p CMF p CMF legs ( ) ( ) ( ) ( ) = × + × + × + × Equation 6-37 1 2 3 4 p AADT AADT AADT AADT AADT j j= + + + where CMFlegs = aggregate CMF for all legs; pj = proportion of total leg traffic volume associated with roundabout leg j ( j = 1 to m); CMFj = combined CMF for leg j ( j = 1 to m); and AADTj = AADT volume for roundabout leg j ( j = 1 to m), veh/d. Step 4: Compute Predicted Crash Frequency. The CMF and SPF values from the preceding steps are used in this step to compute the predicted FI crash frequency. Equations 6-38 and 6-39 are provided for three- and four-leg roundabouts, respectively. Predicted crash frequency for three-leg roundabouts: Equation 6-38, ,3N C N CMF CMFp FI SPF legs outbd= × × × Predicted crash frequency for four-leg roundabouts: Equation 6-39, ,4N C N CMF CMFp FI SPF legs outbd= × × × where Np,FI = predicted FI average crash frequency, crashes/yr; and C = local calibration factor. Step 5: Apply Severity Adjustment Factor (optional). The calibrated adjustment factor is used to adjust the predicted severity distribution as a function of speed limit. It is a leg- specific factor. The speed limit adjustment factor is computed using Equation 6-40. One factor value is computed for each roundabout leg. 3.1187 100 35 100 Equation 6-40, 2 2f exp SLj sl j{ }( ) ( )= × −  where fj,sl = severity adjustment factor for the effect of speed limit on leg j ( j = 1 to m); and SLj = speed limit on leg j ( j = 1 to m). This adjustment factor is applicable to roundabouts in urban, suburban, and rural areas. The leg speed limit data used to calibrate this factor ranged from 10 to 60 mph. This factor should not be used for speed limits outside of this range. Step 6: Aggregate Leg-Specific Adjustment Factor (optional). The leg-specific adjustment factors need to have their effect aggregated to the overall intersection level. The aggregated adjustment factors for three- and four-leg round- abouts are computed using Equations 6-41 through 6-46. Aggregated CMF for three-leg roundabouts (m = 3): 3.3124 Equation 6-41 1 1, 2 2, 3 3,S exp p f p f p fK sl sl sl[ ][ ]= − × × + × + × 1.0151 Equation 6-42 1 1, 2 2, 3 3,S exp p f p f p fA sl sl sl[ ][ ]= − × × + × + × 0.3639 Equation 6-43 1 1, 2 2, 3 3,S exp p f p f p fB sl sl sl[ ][ ]= − × × + × + × The proportion of total leg volume pj is computed using Equation 6-35. Aggregated CMF for four-leg roundabouts (m = 4): 4.4615 Equation 6-44 1 1, 2 2, 3 3, 4 4,S exp p f p f p f p fK sl sl sl sl[ ][ ]= − × × + × + × + ×

153 2.1642 Equation 6-45 1 1, 2 2, 3 3, 4 4,S exp p f p f p f p fA sl sl sl sl[ ][ ]= − × × + × + × + × 0.7851 Equation 6-46 1 1, 2 2, 3 3, 4 4,S exp p f p f p f p fB sl sl sl sl[ ][ ]= − × × + × + × + × The proportion of total leg volume pj is computed using Equation 6-37. where Sl = distribution score for severity l (l = K, A, B); and pj = proportion of total leg traffic volume associated with roundabout leg j (j = 1 to m). Step 7: Apply Severity Distribution (optional). The distribution scores computed in Step 6 are used in Equa- tions 6-47 through 50 to compute the predicted distribution of FI crashes. 1 Equation 6-47P S S S S K K K A B = + + + 1 Equation 6-48P S S S S A A K A B = + + + 1 Equation 6-49P S S S S A B K A B = + + + 1 Equation 6-50P P P PC K A B( )= − + + where Pl = probability of the occurrence of crash severity l (l = K, A, B, C); and Sl = distribution score for severity l (l = K, A, B). Step 8: Apply Crash-Type Distribution (optional). The crash type distribution for FI crashes is listed in Table 6-8. The proportion associated with a given crash type Pt is obtained from the corresponding column of the table and the row that coincides with the number of roundabout legs. Step 9: Compute Predicted Crash Frequency by Crash Type and Severity (optional). The predicted crash fre- quency for a given severity category is computed using Equation 6-51. Equation 6-51, ,N P Np l l p FI= × where Np,l = predicted average crash frequency for crash severity l (l = K, A, B, C), crashes/yr; Pl = probability of the occurrence of crash severity l (l = K, A, B, C); and Np,FI = predicted FI average crash frequency, crashes/yr. This equation is used once for each severity category (K, A, B, or C) of interest. The probability used in Equa- tion 6-51 is obtained from Step 7. The predicted FI average crash frequency is obtained from Step 4. The predicted crash frequency for a given crash-type category is computed using Equation 6-52. Equation 6-52, ,N P Np t t p FI= × where Np,t = predicted average crash frequency for crash type t (see Table 6-8 for types), crashes/yr; Pt = probability of the occurrence of crash type t; and Np,FI = predicted FI average crash frequency, crashes/yr. This equation is used once for each crash type of interest. The crash types are listed in Table 6-8. The probability used in Equation 6-52 is obtained from Step 8. The predicted FI average crash frequency is obtained from Step 4. The predicted crash frequency for a given combination of crash type and severity is computed using Equation 6-46. Equation 6-53, , ,N P P Np t l t l p FI= × × where Np,t,l is the predicted average crash frequency for crash type t and severity l, crashes/yr; and all other variables are as previously defined. Number of Legs Multiple-Vehicle Crash Type Single-Vehicle Crash Type Head On Right Angle Rear End Sideswipe, Same Dir. Other Animal Fixed Object Other Object Parked Vehicle Other 3 0.000 0.072 0.137 0.109 0.124 0.000 0.325 0.000 0.000 0.233 4 0.008 0.142 0.268 0.177 0.152 0.000 0.127 0.000 0.000 0.126 Table 6-8. FI crash-type distribution, two circulating lanes.

154 This equation is used once for each crash type and severity category of interest. The probabilities used in Equation 6-53 are obtained from Step 7 and Step 8. The predicted FI average crash frequency is obtained from Step 4. Sensitivity Analysis. This section illustrates the rela- tionships between the model predictions and various input variables. Safety Performance Function. The relationship between crash frequency and traffic demand, as obtained from the calibrated model, is shown in Figure 6-5a for roundabouts with two circulating lane. The outbound-leg presence, right- turn bypass lane presence, and entry width conditions are such that the associated CMFs have a value of 1.0. For the three-leg trend lines, it was assumed that there were two legs with one entry lane per leg, each leg having one conflicting circulating lane, and one leg with two entry lanes and two conflicting circulating lanes. For the four-leg trend lines, it was assumed that there were two legs with one entry lane per leg, each leg having one conflicting circulating lane, and two legs with two entry lanes per leg, each leg having two conflicting circulating lanes. The trends in Figure 6-5a indicate that roundabout crash frequency increases with entering AADT volume. Round- abouts in rural areas tend to have about 28% more crashes than those in urban or suburban areas with similar volume. The three-leg model was calibrated using sites with entering AADT ranging from 2,000 to 25,000 veh/d. The four-leg model was calibrated using sites with entering AADT ranging from 6,000 to 31,000 veh/d. Figure 6-5b compares the proposed predictive models for urban roundabouts with those discussed previously in Section 2.6.1. The proposed models for urban roundabouts are shown using the two solid trend lines. Trend lines for the reported models are shown using dashed lines. The trends for the proposed models are similar to those of the models reported in the literature. In general, the predicted values from the proposed models are in the middle of the range of values offered by the collective set of reported models. Differences between the proposed and reported models may be explained by geometric differences (e.g., outbound-only lane presence, right-turn bypass lane presence, entry width, and number of circulating lanes conflicting with each leg) that exist among the databases used to calibrate the models. The proposed models have a convex shape, while those from the literature have a concave shape. It is not possible to explain these differences in shape without looking at the data asso- ciated with each model. Outbound-Only Leg CMF. The value of this CMF sug- gests that a roundabout with one outbound-only leg has 54.5% fewer crashes than a roundabout at which all legs serve two-way traffic flow. It is rationalized that the presence of an outbound-only leg reduces the number of conflict points between intersecting traffic streams, relative to a leg that serves two-way traffic flow. A reduction in conflict points is likely to result in fewer crashes. Right-Turn Bypass Lane CMF. Illustrative aggregate CMF values that reflect the presence of a bypass lane are listed in Table 6-9. To compute these values, it was assumed that the other leg-specific CMFs (CMFew and CMFcl) have a value of 1.0 and that the AADT volume is the same on each round- about leg. The presence of a bypass lane is indicated by the CMF values to reduce crash frequency. This trend is logical given that the bypass lane is physically separated from the adjacent a. Proposed models. b. Model comparison. Figure 6-5. Proposed predictive models, FI crashes, two circulating lanes.

155 entering lane and the circulating lane(s), which eliminates conflicts at several points through the roundabout. Also, a bypass lane is typically associated with a heavy right-turn volume. These characteristics can explain the relatively large crash reductions associated with bypass lane presence, as implied by the CMF values in Table 6-9. Entry Width CMF. Illustrative aggregate CMF values that reflect a range in entry width are shown in Figure 6-6. To compute these values, it was assumed that the other leg- specific CMFs (CMFbypass and CMFcl) have a value of 1.0 and that the AADT volume is the same on each roundabout leg. The x-axis of this figure represents the difference between the entry width for a given leg and the base entry width (deviation = Wew – Wew,b). A positive deviation implies that the entry width on the leg is wider than the base width. The trend line shown in Figure 6-6 indicates that the CMF value decreases as the entry width increases (for a given base width). It is rationalized that roundabouts with a wider entry width provide more lateral separation between the vehicle and roadside objects (e.g., curb). For legs with two entering lanes, a wider lane also increases the lateral separation between vehi- cles in adjacent lanes. The safety benefit associated with larger entry width is likely a result of this increase in lateral separation. Circulating Lane CMF. Illustrative aggregate CMF values that reflect the number of lanes present are listed in Table 6-10. To compute these values, it was assumed that the other leg- specific CMFs (CMFbypass and CMFew) have a value of 1.0 and that the AADT volume is the same on each roundabout leg. The presence of one circulating lane conflicting with the subject leg is indicated to decrease crash frequency, relative to there being two circulating lanes. This trend is logical given that the second circulating lane increases the number of conflict points in the entry area. The CMF values for legs with two entering lanes are larger than those for legs with one entering lane. Again, this trend likely reflects the increase in the number of conflict points associated with the second entering lane. Severity Distribution Function. The predicted severity distribution for roundabouts with a 35-mph speed limit on each leg is shown in Table 6-11. The proportions shown in any one row add to 1.0. Number of Legs with a Right-Turn Bypass Lane Aggregate CMF A (CMFlegs) 0 1.000 1 0.858 2 0.716 3 0.574 4 0.432 NOTE: ACMF values are based on the assumptions that the other leg-speciic CMFs have a value of 1.0 and the AADT volume on each leg is the same as the other legs. Table 6-9. Calibrated right-turn bypass lane CMF, FI crashes, two circulating lanes. Figure 6-6. Calibrated entry width CMF, FI crashes, two circulating lanes. Number of Legs with Two Circulating Lanes Aggregate CMFA (CMFlegs) Based on Number of Entry Lanes One Entering Lane Two Entering Lanes 1 0.586 0.757 2 0.616 0.838 3 0.646 0.919 4 0.676 1.000 NOTE: ACMF values are based on the assumptions that the other leg-speciic CMFs have a value of 1.0 and the AADT volume on each leg is the same as the other legs. Table 6-10. Calibrated circulating lane CMF, FI crashes, two circulating lanes. Number of Legs Crash Proportion by Severity A K A B C 3 0.017 0.173 0.332 0.478 4 0.007 0.073 0.288 0.632 NOTE: A Proportions based on a speed limit of 35 mph on each leg. Table 6-11. Comparison of predicted severity distribution for a common speed limit, FI crashes, two circulating lanes.

156 The proportions shown in Tables 6-6 and 6-11 can be used to examine the predicted trends associated with circulat- ing lanes. For example, the trend associated with circulating lanes can be assessed by comparing one row in each table asso ciated with the same number of legs. A comparison of one- and two-circulating-lanes rows associated with round- abouts with three legs indicates that there is a tendency for the proportions of K and A crashes to increase as the number of lanes increases. In contrast, the proportion of B crashes decreases as the number of lanes increases. Similar trends exist for roundabouts with four legs. These trends are consis- tent with those noted for A and B crashes in the examination of crash frequency associated with Table 5-60. The predicted severity distribution as a function of speed limit is shown in Table 6-12. The proportions shown are based on the assumption that the speed limit is the same on each leg. The predictive model should be used (instead of the table) when the speed limit varies among the roundabout legs. 6.1.2.3 PDO Crash Frequency Prediction Model, One Circulating Lane This section describes the final version of the predictive models for roundabouts with one circulating lane. These models are not applicable to roundabouts that have two cir- culating lanes conflicting with one or more legs. The models predict property damage–only (PDO) crash frequency. One variation of the model is applicable to three-leg roundabouts, and a second variation of the model is applicable to four-leg roundabouts. This section consists of two subsections. The first sub- section describes the predictive model. The second subsection offers a sensitivity analysis of selected factors that influence the predicted crash frequency or severity. Calibrated Model. This section presents the calibrated model using a list of steps that outline the procedure for model application. Step 1: Apply SPF. The calibrated SPFs for three- and four-leg roundabouts are shown in Equations 6-54 and 6-55, respectively. These equations are used to compute the pre- dicted crash frequency for base conditions. SPF for three-leg roundabouts: 1.720 0.486 1000 0.168 Equation 6-54 ,3 3N exp LN EntAADT I SPF rural ( ) ] [= − + × + × Number of Legs Speed Limit, mph Crash Proportion by Severity A K A B C 3 20 0.015 0.152 0.291 0.542 25 0.016 0.158 0.302 0.524 30 0.017 0.165 0.316 0.503 35 0.017 0.173 0.332 0.478 40 0.018 0.183 0.350 0.449 45 0.019 0.193 0.371 0.416 50 0.021 0.205 0.394 0.381 55 0.022 0.218 0.418 0.343 4 20 0.006 0.061 0.243 0.690 25 0.006 0.064 0.255 0.674 30 0.007 0.068 0.270 0.655 35 0.007 0.073 0.288 0.632 40 0.008 0.078 0.310 0.604 45 0.008 0.084 0.335 0.572 50 0.009 0.092 0.364 0.536 55 0.010 0.100 0.396 0.495 NOTE: A Proportions listed in the table are based on the assumption that each leg has the same speed limit. Table 6-12. Predicted severity distribution for a range of speed limits, FI crashes, two circulating lanes.

157 SPF for four-leg roundabouts: 1.475 0.702 1000 0.168 Equation 6-55 ,4 4N exp LN EntAADT I SPF rural ( ) ] [= − + × + × where NSPF,m = predicted average crash frequency for base conditions on all legs for roundabout with m legs (m = 3, 4), crashes/yr; EntAADTm = entering AADT for roundabout with m legs (m = 3, 4), veh/d; and Irural = area type indicator variable (= 1.0 if area is rural, 0.0 otherwise). The entering AADT for the roundabout represents the sum of the AADT that enters the roundabout when considering all legs. If a leg serves two-way traffic, then its entering volume can be estimated by multiplying a representative directional distribution factor by the leg AADT. If this factor is unknown, then a default value of 0.5 can be used. If a leg serves one-way traffic inbound to the roundabout, then the leg’s AADT can be included directly in the summation. If a leg serves one-way traffic outbound from the roundabout, then the leg’s AADT should not be included in the summation. Step 2: Apply CMFs. The calibrated CMFs that can be used with the SPFs are shown in this section. These equations are used to compute the CMF value that adjusts the SPF pre- diction when nonbase conditions are of interest to the analyst. The access point frequency CMF is a leg-specific CMF. It is described using Equation 6-56. 0.0855 Equation 6-56, ,CMF exp nap j ap j[ ]= × where CMFap,j = CMF presence of driveways or unsignalized access points on leg j (j = 1 to m); and nap,j = number of driveways or unsignalized access points on leg j (j = 1 to m) (within 250 ft of yield line). This CMF is applicable to a roundabout in an urban, suburban, or rural area. The count of access points on a leg represents the number of driveways or unsignalized access points on the leg (either side) within 250 ft of the yield line. The number of access points in the data used to calibrate this CMF ranged from 0 to 8 access points per leg. Step 3: Aggregate Leg-Specific CMFs. All leg-specific CMFs of interest need to have their effect aggregated to the overall intersection level (and thereby, consistent with the SPFs that are also applicable to the overall intersection). As a first activity, for each roundabout leg j with one or more leg-specific CMFs, the following equation is used to compute the leg CMF. Equation 6-57,CMF CMFj ap j= where CMFj is the combined CMF for leg j ( j = 1 to m). Then, the aggregated CMFs for three- and four-leg roundabouts are computed using Equations 6-58 and 6-60, respectively. Aggregated CMF for three-leg roundabouts (m = 3): Equation 6-58 1 1 2 2 3 3CMF p CMF p CMF p CMFlegs ( ) ( ) ( )= × + × + × Equation 6-59 1 2 3 p AADT AADT AADT AADT j j= + + Aggregated CMF for four-leg roundabouts (m = 4): Equation 6-60 1 1 2 2 3 3 4 4 CMF p CMF p CMF p CMF p CMF legs ( ) ( ) ( ) ( ) = × + × + × + × Equation 6-61 1 2 3 4 p AADT AADT AADT AADT AADT j j= + + + where CMFlegs = aggregate CMF for all legs; pj = proportion of total leg traffic volume associated with roundabout leg j ( j = 1 to m); CMFj = combined CMF for leg j ( j = 1 to m); and AADTj = AADT volume for roundabout leg j ( j = 1 to m), veh/d. Step 4: Compute Predicted Crash Frequency. The CMF and SPF values from the preceding steps are used in this step to compute the predicted PDO average crash frequency. Equations 6-62 and 6-63 are provided for three- and four-leg roundabouts, respectively. Predicted crash frequency for three-leg roundabouts: Equation 6-62, ,3N C N CMFp PDO SPF legs= × × Predicted crash frequency for four-leg roundabouts: Equation 6-63, ,4N C N CMFp PDO SPF legs= × ×

158 where Np,PDO = predicted PDO average crash frequency, crashes/yr; and C = local calibration factor. Step 5: Apply Crash Type Distribution (optional). The crash-type distribution for PDO crashes is listed in Table 6-13. The proportion associated with a given crash type Pt is obtained from the corresponding column of the table and the row that coincides with the number of roundabout legs. Step 6: Compute Predicted Crash Frequency by Crash Type (optional). The predicted crash frequency for a given crash-type category is computed using the following equation. Equation 6-64, ,N P Np t t p PDO= × where Np,t = predicted average crash frequency for crash type t (see Table 6-13 for types), crashes/yr; Pt = probability of the occurrence of crash type t; and Np,PDO = predicted PDO average crash frequency, crashes/yr. This equation is used once for each crash type of interest. The crash types are listed in Table 6-13. The probability used in the equation above is obtained from Step 5. The predicted PDO average crash frequency is obtained from Step 4. Sensitivity Analysis. This section illustrates the relation- ships between the model predictions and various input variables. Safety Performance Function. The relationship between crash frequency and traffic demand, as obtained from the calibrated model, is shown in Figure 6-7a for roundabouts with one circulating lane. It was assumed that there was one access point on each leg and that the leg AADT volume was the same on each leg (for the purpose of computing the access point frequency CMF). The trends in Figure 6-7a indicate that roundabout crash frequency increases with entering AADT volume. Round- abouts in rural areas tend to have about 18% more crashes Number of Legs Area Type Multiple-Vehicle Crash Type Single-Vehicle Crash Type Head On Right Angle Rear End Sideswipe, Same Dir. Other Animal Fixed Object Other Object Parked Vehicle Other 3 R 0.000 0.070 0.411 0.099 0.151 0.017 0.183 0.000 0.000 0.069 U 0.008 0.121 0.226 0.053 0.241 0.008 0.225 0.002 0.000 0.117 4 R 0.004 0.149 0.248 0.136 0.070 0.014 0.261 0.000 0.003 0.116 U 0.010 0.192 0.263 0.093 0.187 0.002 0.188 0.002 0.009 0.054 NOTE: Area type: R = rural; U = urban or suburban. Table 6-13. PDO crash-type distribution, one circulating lane. a. Proposed models. b. Model comparison. Figure 6-7. Proposed predictive models, PDO crashes, one circulating lane.

159 than those in urban or suburban areas with similar volume. The three-leg model was calibrated using sites with entering AADT ranging from 3,000 to 18,000 veh/d. The four-leg model was calibrated using sites with entering AADT ranging from 3,000 to 21,000 veh/d. Figure 6-7b compares the proposed predictive models for urban roundabouts with those discussed previously in Sec- tion 2.6.1. The predictions from the FI and PDO models have been added to estimate the predicted total crash frequency. The proposed models for urban roundabouts are shown using the two solid trend lines. Trend lines for the reported models are shown using dashed lines. The trends for the proposed models are similar to those of the models reported in the literature. In general, the predicted values from the proposed models are about in the middle of the range of values offered by the collective set of reported models. Differences between the proposed and reported models may be explained by geometric differences (e.g., ICD, outbound-only lane presence, right-turn bypass lane presence, and number of access points on each leg) that exist among the databases used to calibrate the models. Access Point Frequency CMF. Illustrative aggregate CMF values that reflect the presence of access points are shown in Figure 6-8. To compute these values, it was assumed that the AADT volume is the same on each roundabout leg. Also shown in the figure is the corresponding CMF developed for the FI crash model (Equation 6-7). The trend line shown in Figure 6-8 indicates that the aggregate CMF value increases as the number of access points increases. This trend is consistent with that shown in Table 2-11 for access points on the crossroad legs of an unsignalized crossroad-ramp terminal intersection. It is also consistent with the corresponding CMF developed for the FI crash model. 6.1.2.4 PDO Crash Frequency Prediction Model, Two Circulating Lanes This section describes the final version of the predictive models for roundabouts with two circulating lanes conflict- ing with one or more legs. These models are not applicable to roundabouts having one circulating lane conflicting with each leg. The models predict PDO crash frequency. One vari- ation of the model is applicable to three-leg roundabouts, and a second variation of the model is applicable to four-leg roundabouts. This section consists of two subsections. The first sub- section describes the predictive model. The second subsection offers a sensitivity analysis of selected factors that influence the predicted crash frequency or severity. Calibrated Model. Step 1: Apply SPF. The calibrated SPFs for three- and four-leg roundabouts are shown in Equations 6-65 and 6-66, respectively. These equations are used to compute the pre- dicted crash frequency for base conditions. SPF for three-leg roundabouts: 1.565 1.055 1000 0.496 Equation 6-65 ,3 3N exp LN EntAADT I SPF rural ( ) ] [= − + × + × SPF for four-leg roundabouts: 1.536 1.131 1000 0.496 Equation 6-66 ,4 4N exp LN EntAADT I SPF rural ( )[ ] = − + × + × where NSPF,m = predicted average crash frequency for base conditions on all legs for roundabout with m legs (m = 3, 4), crashes/yr; EntAADTm = entering AADT for roundabout with m legs (m = 3, 4), veh/d; and Irural = area type indicator variable (= 1.0 if area is rural, 0.0 otherwise). The entering AADT for the roundabout represents the sum of the AADT that enters the roundabout when considering all legs. If a leg serves two-way traffic, then its entering volume can be estimated by multiplying a representative directional distribution factor by the leg AADT. If this factor is unknown, then a default value of 0.5 can be used. If a leg serves one-way traffic inbound to the roundabout, then the leg’s AADT can be included directly in the summation. If a leg serves one-way Figure 6-8. Calibrated access point frequency CMF, PDO crashes, one circulating lane.

160 traffic outbound from the roundabout, then the leg’s AADT should not be included in the summation. Step 2: Apply CMFs. The calibrated CMFs that can be used with the SPFs are shown in this section. These equations are used to compute the CMF value that adjusts the SPF pre- diction when nonbase conditions are of interest to the analyst. The entry width CMF is a leg-specific CMF. It is described using the following equation. 0.0390 Equation 6-67, , , ,CMF exp W Wew j ew j ew b j[ ]( )= − × − This CMF is applicable to roundabouts in an urban, sub- urban, or rural area. The base entry width Wew,b equals 20 ft if there is one entering lane on the subject approach. It equals 29 ft if there are two entering lanes on the subject approach. The entry widths used to calibrate this CMF ranged from 16 to 25 ft for legs with one entering lane, and 24 to 34 ft for legs with two entering lanes. Entry width is measured at the entrance line (i.e., the continuation of the ICD) to the circulating roadway. It is the perpendicular width of all entering lanes and the shoulder (if present). The width is measured from the splitter island curb to the curb face at the outside edge of the travel way. In the absence of a curb on the outside edge of travel way, the width is measured from the splitter island curb face to the closer of the paved edge of travel way or the near edge of the bypass lane (if present). The circulating lane CMF is a leg-specific CMF. It is described using the following equation. 0.219 4 Equation 6-68, , ,CMF exp n ncl j cl j el j[ ]( )= × × − This CMF is applicable to a roundabout in an urban, suburban, or rural area. The number of circulating lanes ncl used to calibrate this CMF ranged from one to two. The number of entering lanes nel ranged from one to two. This CMF is not applicable to outbound-only legs. Step 3: Aggregate Leg-Specific CMFs. All leg-specific CMFs of interest need to have their effect aggregated to the overall intersection level (and thereby, consistent with the SPFs that are also applicable to the overall intersection). As a first activity, for each roundabout leg j with one or more leg-specific CMFs, the following equation is used to compute the leg CMF. Equation 6-69, ,CMF CMF CMFj ew j cl j= × where CMFj is the combined CMF for leg j ( j = 1 to m). Then, the aggregated CMFs for three- and four-leg round- abouts are computed using Equation 6-70 and Equation 6-72, respectively. Aggregated CMF for three-leg roundabouts (m = 3): Equation 6-70 1 1 2 2 3 3CMF p CMF p CMF p CMFlegs ( ) ( ) ( )= × + × + × Equation 6-71 1 2 3 p AADT AADT AADT AADT j j= + + Aggregated CMF for four-leg roundabouts (m = 4): Equation 6-72 1 1 2 2 3 3 4 4 CMF p CMF p CMF p CMF p CMF legs ( ) ( ) ( ) ( ) = × + × + × + × Equation 6-73 1 2 3 4 p AADT AADT AADT AADT AADT j j= + + + where CMFlegs = aggregate CMF for all legs; pj = proportion of total leg traffic volume associated with roundabout leg j ( j = 1 to m); CMFj = combined CMF for leg j ( j = 1 to m); and AADTj = AADT volume for roundabout leg j ( j = 1 to m), veh/d. Step 4: Compute Predicted Crash Frequency. The CMF and SPF values from the preceding steps are used in this step to compute the predicted PDO average crash frequency. Equation 6-74 and Equation 6-75 are provided for three- and four-leg roundabouts, respectively. Predicted crash frequency for three-leg roundabouts: Equation 6-74, ,3N C N CMFp PDO SPF legs= × × Predicted crash frequency for four-leg roundabouts: Equation 6-75, ,4N C N CMFp PDO SPF legs= × × where Np,PDO = predicted PDO average crash frequency, crashes/yr; and C = local calibration factor. Step 5: Apply Crash-Type Distribution (optional). The crash-type distribution for PDO crashes is listed in Table 6-14.

161 The proportion associated with a given crash type Pt is obtained from the corresponding column of the table and the row that coincides with the number of roundabout legs. Step 6: Compute Predicted Crash Frequency by Crash Type (optional). The predicted crash frequency for a given crash-type category is computed using the following equation. Equation 6-76, ,N P Np t t p PDO= × where Np,t = predicted average crash frequency for crash type t (see Table 6-14 for types), crashes/yr; Pt = probability of the occurrence of crash type t; and Np,PDO = predicted PDO average crash frequency, crashes/yr. This equation is used once for each crash type of interest. The crash types are listed in Table 6-14. The probability used in the equation above is obtained from Step 5. The predicted PDO average crash frequency is obtained from Step 4. Sensitivity Analysis. This section illustrates the relation- ships between the model predictions and various input variables. Safety Performance Function. The relationship between crash frequency and traffic demand, as obtained from the calibrated model, is shown in Figure 6-9a for roundabouts with two circulating lanes. The entry width conditions are such that the associated CMF has a value of 1.0. For the three- leg trend lines, it was assumed that there were two legs with one entry lane per leg, each leg having one conflicting circu- lating lane, and one leg with two entry lanes and two con- flicting circulating lanes. For the four-leg trend lines, it was assumed that there were two legs with one entry lane per leg, each leg having one conflicting circulating lane, and two legs with two entry lanes per leg, each leg having two conflicting circulating lanes. The trends in Figure 6-9a indicate that roundabout crash frequency increases with entering AADT volume. Round- abouts in rural areas tend to have about 62% more crashes Number of Legs Area Type Multiple-Vehicle Crash Type Single-Vehicle Crash Type Head On Right Angle Rear End Sideswipe, Same Dir. Other Animal Fixed Object Other Object Parked Vehicle Other 3 R 0.000 0.147 0.215 0.131 0.262 0.000 0.186 0.000 0.000 0.060 U 0.002 0.072 0.227 0.256 0.131 0.005 0.178 0.000 0.000 0.128 4 R 0.025 0.164 0.216 0.230 0.258 0.005 0.076 0.001 0.000 0.025 U 0.005 0.174 0.178 0.265 0.199 0.003 0.138 0.002 0.000 0.037 NOTE: Area type: R = rural; U = urban or suburban. Table 6-14. PDO crash-type distribution, two circulating lanes. a. Proposed models. b. Model comparison. Figure 6-9. Proposed predictive models, PDO crashes, two circulating lanes.

162 than those in urban or suburban areas with similar volume. The three-leg model was calibrated using sites with entering AADT ranging from 2,000 to 25,000 veh/d. The four-leg model was calibrated using sites with entering AADT ranging from 6,000 to 31,000 veh/d. Figure 6-9b compares the proposed predictive models for urban roundabouts with those discussed previously in Section 2.6.1. The predictions from the FI and PDO models have been added to estimate the predicted total crash frequency. The proposed models for urban roundabouts are shown using the two solid trend lines. Trend lines for the reported models are shown using dashed lines. The trends for the proposed models are similar to those of the models reported in the literature. In general, the predicted values from the proposed models are about in the middle of the range of values offered by the collective set of reported models. Differences between the proposed and reported models may be explained by geometric differences (e.g., entry width and number of circulating lanes conflicting with each leg) that exist among the databases used to calibrate the models. The proposed models have a convex shape, while those from the literature have a concave shape. It is not possible to explain these differences in shape without looking at the data associated with each model. Entry Width CMF. Illustrative aggregate CMF values that reflect a range in entry width are shown in Figure 6-10. To compute these values, it was assumed that the other leg- specific CMF (i.e., CMFcl) has a value of 1.0 and that the AADT volume is the same on each roundabout leg. The x-axis of this figure represents the difference between the entry width for a given leg and the base entry width (deviation = Wew – Wew,b). A positive deviation implies that the entry width on the leg is wider than the base width. Also shown in the figure is the corresponding CMF developed for the FI crash model (Equation 6-31). The trend line shown in Figure 6-10 indicates that the CMF value decreases as the entry width increases (for a given base width). It is rationalized that roundabouts with a wider entry width provide more lateral separation between the vehicle and roadside objects (e.g., curb). For legs with two entering lanes, a wider lane also increases the lateral sepa- ration between vehicles in adjacent lanes. The safety benefit associated with wider entry width is likely a result of this increase in lateral separation. Circulating Lane CMF. Illustrative aggregate CMF values that reflect the number of lanes present are listed in Table 6-15. To compute these values, it was assumed that the other leg-specific CMF (CMFew) has a value of 1.0 and that the AADT volume is the same on each roundabout leg. The presence of one circulating lane conflicting with the subject leg is indicated to decrease crash frequency, relative to there being two circulating lanes. This trend is logical given that the second circulating lane increases the number of conflict points in the entry area. The CMF values for legs with two entering lanes are larger than those for legs with one entering lane. Again, this trend likely reflects the increase in the number of conflict points associated with the second entering lane. The values listed in Table 6-15 can be compared to those in Table 6-10 for FI crashes (at roundabouts with two circu- lating lanes). The CMF values for PDO crashes are 0 to 6% smaller than those for FI crashes, with the amount of decrease dependent on the number of entering lanes. 6.1.3 Leg-Level Crash Prediction Models for Design This section presents the final leg-level crash predic- tion models for design. These models are also presented in Figure 6-10. Calibrated entry width CMF, PDO crashes, two circulating lanes. Number of Legs with Two Circulating Lanes Aggregate CMFA (CMFlegs) based on Number of Entry Lanes One Entering Lane Two Entering Lanes 1 0.550 0.734 2 0.582 0.823 3 0.614 0.911 4 0.645 1.000 NOTE: ACMF values are based on assumptions that the other leg-speciic CMFs have a value of 1.0, and the AADT volume on each leg is the same as the other legs. Table 6-15. Calibrated circulating lane CMF, PDO crashes, two circulating lanes.

163 Section 5 of the report, which describes the model develop- ment process. 6.1.3.1 Entering-Circulating Crash Models Tables 6-16 to 6-20 provide the final models developed. For some combinations of entering and circulating lanes, more than one model is available. Table 6-21 provides the implied CMFs derived from the models for entering-circulating crashes along with the esti- mated standard error of the CMF and the minimum and maximum values of the continuous variables in the data from which the estimates were derived. Table 6-22 provides the same information for KABC crashes. Where multiple models were developed for the same site type the models including circulating width and angle (instead of cosine of angle) were used for deriving the implied CMFs and the standard errors of the CMFs. Equation 6-77 EntCirc exp EntAADT CircAADT expa b c d ICD e Bypass f Statevar= ( )× + × + × Equation 6-78 EntCirc exp EntAADT CircAADT expa b c d ICD e Angle f COS Angle= ( )( )× + × + × Equation 6-79 EntCirc exp EntAADT CircAADT expa b c d ICD g CircWidth= ( )× + × Equation 6-80 EntCirc exp EntAADT CircAADT exp a b c e Angle f COS Angle g CircWidth = ( )( )× + × + × For KABC crashes, there were only 127 crashes, which is not enough to develop separate models by number of cir- culating lane and entering lanes. Therefore, all sites were combined. Equation 6-81 EntCirc exp EntAADT CircAADT exp a b c d ICD e Angle f COS Angle h TwoEnteringLanes = ( )( )× + × + × + × Variable Parameter Estimate (s.e.) Intercept a -7.8580 (1.5714) EntAADT b 0.6091 (0.1281) CircAADT c 0.3020 (0.1062) ICD d -0.0068 (0.0043) Bypass e -0.9982 (0.4845) Statevar f -0.9628 (0.3128) Overdispersion Parameter k 0.7470 (0.2187) Table 6-16. Entering-circulating crash model, one circulating and one entering lanes. Variable Parameter Estimate (s.e.) Option 1 Option 2 Intercept a -9.5763 (2.6693) -11.4943 (2.4136) EntAADT b 0.9636 (0.2696) 0.9609 (0.2701) CircAADT c 0.3917 (0.1786) 0.3633 (0.1722) ICD d -0.0082 (0.0046) -0.0080 (0.0046) Angle e -0.0234 (0.0069) – COSAngle f – 1.6403 (0.4020) Overdispersion Parameter k 0.6232 (0.2151) 0.6018 (0.2131) Table 6-17. Entering-circulating crash model, one circulating and two entering lanes. Variable Parameter Estimate (s.e.) Option 1 Option 2 Intercept a -4.3332 (4.0105) -6.3627 (3.9088) EntAADT b 0.3608 (0.2096) 0.3344 (0.2210) CircAADT c 0.6711 0.6282 (0.3422) (0.3483) ICD d -0.0148 (0.0061) -0.0185 (0.0066) Circulating Width g -0.1041 (0.0652) – Overdispersion Parameter k 1.0734 (0.5316) 1.2891 (0.5771) Table 6-18. Entering-circulating crash model, two circulating and one entering lanes.

164 It should be noted that the CMF estimates often appear very small in that the value is close to 1.0. However, these values are per unit increase, meaning in practice they would likely be larger. For example, a designer selecting the angle to the next leg would not likely be comparing 90 degrees with 91 degrees. The CMFs indicate that entering-circulating crashes decrease with an increasing ICD and angle to the next leg. Crashes also decrease when a bypass lane is present and with increased circulating width on two circulating lane roundabouts. At single-lane roundabouts, entering-circulating crashes are associated with more crashes as the circulating width increases. 6.1.3.2 Exiting-Circulating Crash Models Tables 6-23 and 6-24 provide the final models developed. For two circulating lanes and one exiting lane, more than one model is available. Models were not successfully estimated using only sites with one circulating lane and one exiting lane. For two circulating and two exiting lanes, the model developed did not include any non-AADT variables and are thus not reported here because no CMFs can be derived. Table 6-25 provides the implied CMFs derived from the models for exiting-circulating crashes along with the estimated standard error of the CMF and the minimum and maximum values of the continuous variables in the data from which the estimates were derived. Although models were developed both with and without circulating width for the two circulating lane legs, the CMF estimates were derived from the models including circulating width. Equation 6-82 ExtCirc exp ExtAADT CircAADT expa b c e CircWidth g State= ( )× + × Equation 6-83 ExtCirc exp ExtAADT CircAADT expa b c d ICD e CircWidth g State= ( )× + × + × Variable Parameter Estimate (s.e.) Option 1 Option 2 Option 3 Option 4 Intercept a -8.3493 (3.0338) -15.6743 (3.4922) -9.9541 (3.1785) -17.3375 (3.4243) EntAADT b 0.8054 (0.1783) 0.9868 (0.2033) 0.8221 (0.1798) 0.9987 (0.2049) CircAADT c 0.7398 (0.2216) 0.9455 (0.2684) 0.7623 (0.2222) 0.9673 (0.2705) Angle e -0.0134 (0.0053) -0.0153 (0.0052) – – COSAngle f – – 0.8997 (0.3992) 1.0277 (0.3833) Circulating Width g -0.1375 (0.0578) – -0.1353 (0.0590) – Overdispersion Parameter k 0.7759 (0.2202) 0.8850 (0.2366) 0.7854 (0.2222) 0.8926 (0.2381) Table 6-19. Entering-circulating SPFs, two circulating and two entering lanes. Variable Parameter Estimate (s.e.) Option 1 Option 2 Intercept a -13.0182 (2.4290) -14.6408 (2.2413) EntAADT b 0.9374 (0.1946) 0.9380 (0.1937) CircAADT c 0.4749 (0.1487) 0.4764 (0.1493) ICD d -0.0049 (0.0025) -0.0048 (0.0025) Angle e -0.0177 (0.0082) – COSAngle f – 1.2227 (0.4922) 2 Entering Lanes h 1.1599 (0.2487) 1.1546 (0.2488) Overdispersion Parameter k 0.4337 (0.2874) 0.4201 (0.2841) Table 6-20. Entering-circulating KABC crash model, one or two circulating and one or two entering lanes.

165 Variable Circulating Lanes Entering Lanes Parameter Estimate Variable Min Variable Max CMFs/unit increase CMF s.e. Circulating Width 1 2 0.0319 15 42 1.0324 0.0190 2 1 -0.0141 25 45 0.9860 0.0643 2 2 -0.1375 24 45 0.8715 0.0504 ICD 1 1 -0.0068 65 236 0.9932 0.0043 1 2 -0.0082 110 314 0.9918 0.0046 2 1 -0.0148 135 426 0.9853 0.0060 Angle 1 2 -0.0234 53 182 0.9769 0.0067 2 2 -0.0134 69 182 0.9867 0.0052 Bypass Lane Present 1 1 -0.9982 0.3685 0.1856 Table 6-21. Implied CMFs for entering-circulating crashes. Variable Circulating Lanes Entering Lanes Parameter Estimate Variable Min Variable Max CMFs/unit increase CMF s.e. ICD All All -0.0049 65 426 0.9951 0.0025 Angle All All -0.0177 37 186 0.9825 0.0081 Two Entering Lanes All All 1.1599 3.1896 0.8015 Table 6-22. Implied CMFs for KABC entering-circulating crashes. Variable Parameter Estimate (s.e.) Intercept a -29.7315 (8.4312) ExtAADT b 2.0150 (0.7415) CircAADT c 0.5511 (0.3103) Circulating Width e 0.1808 (0.0368) State g 1.6362 (0.5156) Overdispersion Parameter k 1.8837 (0.5828) Table 6-23. Exiting-circulating crash model, one circulating lane and two exiting lanes. Variable Parameter Estimate (s.e.) Option 1 Option 2 Intercept a -5.8705 (5.4794) -14.0278 (5.1071) ExtAADT b 0.4317 (0.2366) 0.4381 (0.2922) CircAADT c 1.0853 (0.5380) 1.2133 (0.5313) ICD d -0.0148 (0.0049) -0.0194 (0.0055) Circulating Width e -0.2582 (0.0862) - State g 0.9808 (0.5080) 0.8823 (0.4814) Overdispersion Parameter k 0.6159 (0.5465) 0.8564 (0.6767) Table 6-24. Exiting-circulating crash model, two circulating lanes and one exiting lane.

166 A larger ICD is associated with fewer crashes in the model for two circulating lanes and one exiting lane. An increased circulating width is associated with more crashes for the one circulating lane legs and fewer crashes for the two circulating lane legs. 6.1.3.3 Rear-End Approach Crash Models This section describes the development of predictive models for rear-end crashes occurring on the approach. All legs were modeled together. Table 6-26 provides the final model estimates. Equation 6-84 RearEnd Approach exp ApprAADT CircAADT exp a b c d NumberAccess e Luminaires = ( )× + × Table 6-27 provides the implied CMFs derived from the models for rear-end crashes along with the estimated standard error of the CMF and the minimum and maximum values of the continuous variables in the data from which the estimates were derived. The model indicates that rear-end approach crashes increase with the number of access points on the approach. As the number of luminaires increase the number of crashes of this type are associated with a decrease. 6.1.3.4 Single-Vehicle Approach Crash Models This section describes the development of predictive models for single-vehicle crashes occurring on the approach. All legs were modeled together. Table 6-28 provides the final model estimates. Equation 6-85 SV Approach exp ApprAADT expa b c PostedSpeed d AreaType e State= ( )× + × + × Table 6-29 provides the implied CMFs derived from the models for single-vehicle approach crashes along with the estimated standard error of the CMF and the minimum and maximum values of the continuous variables in the data from which the estimates were derived. Two models were developed, one using the posted speed limit on the approach and the other considering the area type (urban or rural). Posted speed limit was not known for all legs, so the model, including this variable, is based on 420 of the 534 legs. The CMFs indicate that single-vehicle approach crashes increase with increasing speed limit and are higher in rural than urban areas. This may reflect the fact that speed limits in rural areas are typically higher. 6.1.3.5 Circulating-Circulating Crash Models This section provides the final model for circulating- circulating crashes. Separate models were pursued for legs with one and two circulating legs, but a model was success- fully estimated for only two circulating lane leg sites. Variable Circulating Lanes Exiting Lanes Parameter Estimate Variable Min Variable Max CMFs/unit increase CMF s.e. Circulating Width 1 2 0.1808 15 42 1.198 0.0441 2 1 -0.2582 25 45 0.772 0.0667 ICD 2 1 -0.0148 110 426 0.985 0.0048 Table 6-25. Implied CMFs for exiting-circulating crashes. Variable Parameter Estimate (s.e.) Intercept a -14.4195 (1.6284) ApprAADT b 1.0978 (0.1555) CircAADT c 0.3034 (0.0921) NumberAccess e 0.0894 (0.0557) Luminaires -0.0652 (0.0421) Overdispersion Parameter k 1.0659 (0.1965) Table 6-26. Rear-end approach crash model. Variable Parameter Estimate Variable Min Variable Max CMFs/unit increase CMF s.e. NumberAccess 0.0894 0 8 1.094 0.0609 Luminaires -0.0652 0 8 0.937 0.0395 Table 6-27. Implied CMFs for rear-end approach crashes.

167 The model form and parameter estimates for the success- fully estimated model is provided in Table 6-30. Equation 6-86 Circulating Circulating exp CircAADT expa b c CircWidth− = ( )× Table 6-31 provides the implied CMFs derived from the models for circulating-circulating crashes along with the estimated standard error of the CMF and the minimum and maximum values of the continuous variables in the data from which the estimates were derived. The CMF indicates that circulating-circulating crashes decrease with an increasing circulating width when two circulating lanes are present. 6.1.3.6 Single-Vehicle Circulating Plus Single-Vehicle Approach Crash Models No models were successfully estimated for single-vehicle circulating crashes. These were combined with single- vehicle approach crashes to estimate a new model. All legs were modeled together. Two models were developed as shown in Table 6-32, one using the posted speed limit on the approach and the other considering the area type (urban or rural). Posted speed limit was not known for all legs, so the model, including this variable, is based on 420 of the 534 legs. Equation 6-87 SV Approach SV Circulating exp ApprAADT exp a b c PostedSpeed d CircWidth e TwoEnteringLanes f AreaType g State + = ( )× + × + × + × + × Table 6-33 provides the implied CMFs derived from the model for single-vehicle circulating plus single-vehicle approach crashes along with the estimated standard error of the CMF and the minimum and maximum values of the continuous variables in the data from which the estimates were derived. Model Option 1 was used to derive the CMFs. The CMFs indicate that single-vehicle crashes increase with increasing speed limit. Single-vehicle crashes are higher at legs with two entering lanes and lower with wider circulat- ing widths. 6.1.3.7 Total Crash Models Total crash models were estimated, but not for the purposes of developing CMFs. If estimates for a crash type are not pro- vided for by the models developed for specific crash types, then those estimates can be subtracted from the estimate for total. Because of the nature of the models, it is possible that in certain ranges of predictive variables the sum of estimates of specific crash types could be more than the estimate for total. In this case, the sum of estimates by crash type should be used as the estimate for total crashes. Tables 6-34 and 6-35 present Variable Parameter Estimate (s.e.) Option 1 Option 2 Intercept a -6.8027 (1.1780) -6.5618 (1.1977) ApprAADT b 0.3392 (0.1195) 0.5031 (0.1273) PostedSpeed c 0.0441 (0.0099) – Rural Area Type d – 0.3628 (0.2373) State e -0.7495 (0.2091) -0.9474 (0.2346) Overdispersion Parameter k 0.8153 (0.2657) 1.1070 (0.2807) Table 6-28. Single-vehicle approach crash model. Variable Parameter Estimate Variable Min Variable Max CMFs/unit increase CMF s.e. PostedSpeed 0.0441 10 60 1.0451 0.0103 Rural Area Type 0.3628 1.4373 0.3443 Table 6-29. Implied CMFs for single-vehicle approach crashes. Variable Parameter Estimate (s.e.) Intercept a -2.8066 (2.5657) CircAADT b 0.3963 (0.2438) Circulating Width c -0.0870 (0.0534) Overdispersion Parameter k 1.4571 (0.4378) Table 6-30. Circulating-circulating crash model, two circulating lanes. Variable Parameter Estimate Variable Min. Variable Max. CMFs/Unit Increase CMF (s.e.) CircWidth -0.0870 24 45 0.917 0.0490 Table 6-31. Implied CMFs for circulating-circulating crashes.

168 the final total leg-level crash models for roundabouts with one circulating lane and two circulating lanes, respectively. Models were estimated separately for single and two cir- culating lane sites. Where successful, variables indicating the area type, number of entering and number of exiting lanes were included. Equation 6-88 Total exp ApprAADT CircAADT expa b c d AreaType e TwoEnteringLanes= ( )× + × Equation 6-89 Total exp ApprAADT CircAADT exp a b c d AreaType e TwoEnteringLanes f TwoExitingLanes = ( )× + × + × 6.2 Calibration of Crash Prediction Models Calibrating the final crash prediction models presented above is critical for their application to be able to inform project decisions. Using the models in an uncalibrated form to compare roundabout safety performance to other inter- section forms (e.g., signals, two-way stop control) could lead to erroneous decisions and incorrect comparisons. If it is not feasible for a practitioner to calibrate the crash predic- tion models above, for comparison alternative intersection controls (e.g., roundabout versus signal) practitioners should use the CMFs presented in the HSM, 1st edition, that capture the effects on crashes of converting a signal or stop-control intersection to a roundabout. If practitioners are using the final models presented above to inform roundabout-specific Variable Parameter Estimate (s.e.) Option 1 Option 2 Intercept a -6.0580 (0.8603) -4.6149 (0.9617) ApprAADT b 0.4055 (0.0925) 0.3694 (0.1078) PostedSpeed c 0.0350 (0.0075) – CircWidth d -0.0232 (0.0100) -0.0157 (0.0114) Two Entering Lanes e 0.5464 (0.1461) 0.6093 (0.1548) Rural AreaType f – 0.3348 (0.1763) State g -0.3624 (0.1712) -0.5768 (0.1959) Overdispersion Parameter k 0.9410 (0.1574) 1.1998 (0.1694) Table 6-32. Single-vehicle circulating plus single-vehicle approach crash model. Variable Parameter Estimate Variable Min. Variable Max. CMFs/Unit Increase CMF (s.e.) PostedSpeed 0.0350 10 60 1.0356 0.0078 CircWidth -0.0232 14 45 0.9771 0.0098 Two Entering Lanes 0.5464 1.7270 0.2532 Table 6-33. Implied CMFs for single-vehicle circulating plus approach crashes. Variable Parameter Estimate (s.e.) Intercept a -10.5458 (1.1847) ApprAADT b 0.8197 (0.0929) CircAADT c 0.2747 (0.0657) Rural Area Type d 0.3673 (0.1820) 2 Entering Lanes e 0.9827 (0.1536) Overdispersion Parameter k 0.6921 (0.0841) Table 6-34. Leg-level total crash model, one circulating lane. Variable Parameter Estimate (s.e.) Intercept a -7.1029 (1.6107) ApprAADT b 0.4443 (0.1039) CircAADT c 0.3306 (0.1421) Rural Area Type d 0.4194 (0.2393) 2 Entering Lanes e 0.2950 (0.1381) 2 Exiting Lanes f 0.3805 (0.1139) Overdispersion Parameter k 0.9429 (0.1437) Table 6-35. Leg-level total crash model, two circulating lanes.

169 design decisions, it is feasible to use an uncalibrated model as a basis for a relative comparison (e.g., a change in a round- about feature results in a certain percent increase or decrease in predicted crashes). The following discusses the calibration procedure for the final models presented above. NCHRP 17-62 has a specific charge to review and enhance the local calibration procedure for the predictive models currently in the HSM. It makes sense that the procedure recommended by that project also be recommended for roundabouts to achieve consistency throughout the HSM. Aspects of the procedure, such as dealing with low calibra- tion sample sizes, are especially relevant to calibration of the NCHRP 17-70 roundabout models. The following describes the draft recommendations from NCHRP 17-62. • For site types, crash types, and crash severities for which there are enough CMFs to apply the HSM algorithm, per- form the calibration for the algorithm as a whole (that is, by applying CMFs to the base models). For other situations, perform the calibration for the base models. For round- abouts, there is a multiple variable SPF approach for design applications instead of the base model-CMF approach in other predictive method chapters. So, the calibration will be performed for these SPFs, and the final text here (as well as in the NCHRP 17-62 final report) will reflect that as well as the possibility to calibrate the planning level SPFs, which are also being delivered in the NCHRP 17-62 final report but not as an HSM update. • Start with an available sample that is desirably random and at least as large as that recommended in the HSM, 1st edition. • Perform the calibration first with a constant calibration fac- tor. The FHWA calibrator tool (Lyon et al., 2016) can be used. • Assess the success of the calibration. The user guide for the FHWA calibrator tool provides guidance on how success can be assessed with CURE plots and the CV of the calibra- tion factor. The latter measure is estimated and assessed in the calibrator tool based on guidance provided in Bahar and Hauer (2014), Appendix B. That guidance can be used instead of the tool. • If the sample is insufficient, then incrementally assemble additional data for additional sites and assess until a success- ful calibration is achieved. • If a successful calibration cannot be achieved with the entire sample available for the crash type of interest, then the cali- bration results for a similar site type (from which a success- ful calibration was achieved) may be assumed to apply. • If a successful calibration cannot be achieved with the entire sample available for a specific crash type or severity, then the calibration results for total crashes, however obtained, may be assumed to apply. • Estimate a calibration function using the approach in Srinivasan et al. (2016) and adopt it in preference to the calibration factor if it is successfully estimated and performs better. • If appropriate skills are available or could be acquired, it is recommended to try to estimate directly a model with the final calibration dataset and adopt it if it is successfully estimated and performs better than the calibration factor and calibration function. The FHWA Calibrator tool can be used in this performance assessment. 6.3 Effect of Driver Learning Curve on Roundabout Safety Performance This section presents the findings of the investigation into a possible driver learning curve effect on safety. To investigate a potential driver learning curve, crashes at roundabouts were modeled using each site-year as an obser- vation and using generalized estimating equation techniques to account for the temporal correlation of crash counts across years for individual sites. A variable representing the year postconstruction was included in each model to assess whether a decreasing trend in crashes was observable when accounting for changes in AADT over time and other site characteristics. Only sites where the opening year was known were used, which included 109 sites. It was determined that because of the limited sample size all sites needed to be combined. Various modeling options were attempted, including allowing or disallowing a separate intercept term by state, whether years postconstruction was treated as a factor or continuous variable, and if the parameter estimate for years postconstruction should differ for single-lane versus multi- lane roundabouts. Separate models were developed for total, KABC, and PDO crashes, including separate intercept terms for each state. The Florida data could not be used, as only a single site was available. Most models used roundabouts that had at least 5 years of postconstruction data and limited the data to the first 5 years. It was felt that 5 years would provide a reasonable time period for a potential driver learning curve to be seen, as well as to ensure a substantial number of sites could be used for model development. This restriction also ensured there was not bias in the model estimates due to each year postconstruction having a different distribution of sites providing data. To summarize the findings, the trend in expected crashes over years of service does not exhibit a clear pattern when the postconstruction year is treated as a factor variable. When the postconstruction year is treated as a continuous variable, whatever trends exist are weak and are not consistent across states. However, there was, over all states combined, a statisti- cally insignificant trend of increasing crashes over time. That trend appears highly influenced by the data from Washington State, where the sites had particularly low crash frequencies in

170 Year 1 postconstruction, an observation that does not seem generalizable. These general observations hold for all crash severity categories modeled and even for multilane and rural roundabouts for which a driver learning curve might arguably be more evident if it indeed exists. Based on the findings, there is not satisfactory evidence of a driver learning curve affecting safety at roundabouts. A caveat to this is that full years of crash data were used start- ing with the first full year of data after construction, meaning it was not feasible to consider the possibility, based on limited anecdotal evidence that, should a driver learning curve exist, it is shorter (e.g., first 3 months postconstruction). For the data available many of the sites could only provide an open- ing year, and thus such an analysis was not possible. Even so, a learning curve of such a short period would not have had any impact of significance on the results related to principal objectives of the research project—to develop SPFs and CMFs that can be used to estimate the severity and number of crashes likely to occur at roundabouts. 6.4 Pedestrian and Bicycle Safety at Roundabouts The project team investigated developing models that would predict pedestrian and bicycle crashes at roundabouts. However, as shown in Table 6-36, there were not enough crashes to develop models that the team would feel confident in. Pedestrian and bicycle crashes at roundabouts are both relatively rare compared to motor vehicle crashes. Bicycle crashes account for approximately 1% of all reported crashes in the project database. Pedestrian crashes represent about 0.4% of all reported crashes in the database. Table 6-37 summarizes bicycle and pedestrian crashes by severity. Most pedestrian and bicycle crashes resulted in a reported injury, with the majority of crashes resulting in an injury level of B or C on the KABCO scale. About 8% of each crash type resulted in an Injury A level crash. There were no reported fatalities. The following subsections provide further information on pedestrian and bicycle crashes by land-use context and geometric features. 6.4.1 Pedestrian and Bicycle Crashes Based on Land-Use Context Table 6-38 presents where pedestrian and bicycle crashes were reported based on the land-use context. More pedestrian and bicycle crashes were reported at urban sites than rural sites, based on total crashes. There were more urban than rural sites in the database and more years of crash data at urban sites as well. Taking into account these factors, the yearly average number of pedestrian crashes is slightly higher at rural sites (approximately 0.014 crashes/yr) than urban sites (0.011 crashes/yr), though the actual number of crashes is relatively small, so there is a fair amount of uncer- tainty in this comparison. This is a counterintuitive finding; without exposure data (i.e., pedestrian counts) it is difficult to analyze the data further. There are a slightly higher number bicycle crashes per year at urban sites than rural sites (0.038 crashes/yr at urban sites compared to 0.028 crashes/yr at rural sites). This finding may be because there may be more people bicycling in urban sites than rural sites, but the project team does not have access to bicycle count data at the sites, so this hypothesis cannot be tested. 6.4.2 Pedestrian and Bicycle Crashes Based on Geometric Characteristics Table 6-39 presents the basic roundabout intersection char- acteristics where pedestrian and bicycle crashes were reported. More bicycle crashes were reported at single-lane sites, as compared to multilane sites; however, this appears to be related to there being more years of data at the single-lane sites. The number of bicycle crashes per year is lower for single-lane sites (approximately 0.030 crashes/yr) than it is for multilane sites (approximately 0.046 crashes/yr). Pedestrian crashes Crash Type Number of Crashes in Database Bicycle 74 Pedestrian 25 All Crashes 6,771 Table 6-36. Total bicycle and pedestrian crashes. Crashes by Severity Crash Type Fatal Injury A Injury B Injury C Injury (ABC)A PDO Bicycle 0 6 36 21 3 8 Pedestrian 0 2 7 8 7 1 A Severity of injury unknown. Table 6-37. Bicycle and pedestrian crashes by severity.

171 exhibit a similar trend on a per year basis (approximately 0.007 crashes/yr at single sites compared to approximately 0.025 crashes/yr at multilane sites). This trend is consistent with what is seen for all crashes. However, without bicycle and pedestrian count data it cannot be determined if this trend is mitigated at all by exposure levels; though the multilane sites do typically have higher motor vehicle volumes, so this level of exposure is known to be higher at these sites. Similarly, bicycle and pedestrian crashes are both reported at higher frequencies at sites with four legs compared to sites with three legs. These sites have more conflict points, but without volume data, it is difficult to say much more. 6.5 Speed and Roundabouts One of the objectives of the project was to better explore the relationship between speed and crashes at roundabouts. Based on the project team’s experience, this is a topic of interest to many agencies. To the extent feasible with project resources, the project team investigated the role that speed may have on crashes. The project team calculated fastest path radii for each approach at 32 roundabouts sites. The fastest path was calcu- lated for the right-turning, left-turning, and through-traveling paths (R1, R2, R3, R4, and R5 from NCHRP Report 672: Round­ abouts: An Informational Guide, 2nd edition). These radii were then used to predict speeds at various points along the path for different movements using the equations presented in NCHRP Report 672. The project team compared the pre- dicted speeds to the reported crash data for each leg at these sites. This preliminary analysis indicated more research is needed to understand the potential relationship. Based on this work, the research team believes that the predicted entering speed from the fastest path methodology would be worth further evaluation, and it does or does not relate to entering-circulating crashes and exiting-circulating crashes. Figure 6-11 shows predicted (theoretical) entering speed versus crashes per MEV. The project team also identified a relationship between posted speed limits and single-vehicle crashes at all sites, as documented in the leg-level crash prediction models docu- mented in Section 6.1.3. Given these findings, future research should focus on fur- ther examining the relationship between predicted entering speed (R1) and crashes at roundabouts. Ideally, this research would include measured speed and theoretical speeds based on R1 measurements, since correlating crashes to the R1 mea- surement would provide a measurement that designers could adjust. There does not appear to be enough of a correlation between the other speeds (R2, R3, R4, and R5) to encourage additional data collection of these predicted or actual speeds for the purpose of crash prediction. 6.6 Contributions to the Highway Safety Manual The findings from this project are proposed to be incor- porated into relevant chapters of the HSM. No new chap- ters are proposed. The full draft HSM text can be found in Appendix E (available online by searching the TRB website for “NCHRP Research Report 888”). Planning-level crash prediction models are recommended for the network screening chapter (Chapter 4) in Part B of the HSM. The intersection-level and leg-level crash pre- diction models are recommended for each chapter of Part C Area Type Crash Type Rural Urban Bicycle 14 60 Pedestrian 7 18 All Crashes 1,938 4,833 No. of Sites 105 250 No. of Study Years 508 1,580 Table 6-38. Pedestrian and bicycle crashes based on land-use context. Table 6-39. Pedestrian and bicycle crashes based on geometric characteristics. No. of Circulating Lanes No. of Legs Crash Type Single Lane Multilane 3 Legs 4 Legs Bicycle 46 28 12 62 Pedestrian 10 15 2 23 All Crashes 2,537 4,234 1,000 5,771 No. of Sites 235 120 104 251 No. of Study Years 1,485 603 606 1,482

172 (Chapters 10, 11, 12, 18, and 19). The revised HSM text in Appendix E shows the models themselves contained in Chapter 12, while the other chapters provide specific refer- ences to the appropriate sections of Chapter 12. The models are provided in only one chapter to avoid redundancy in the HSM, since the roundabout crash prediction models have variables to differentiate between land-use contexts, whereas the previous models included in Part C of the HSM have separate models developed for different land-use and roadway contexts. Accompanying sample problems and crash modification factors for roundabouts are also provided in the updated draft Part C text in Appendix E. Finally, calibration instructions specific to this project’s models are also provided. 6.7 Summary This project has developed crash prediction models for roundabouts. There are three sets of models ranging in scope from planning-level applications to predicting roundabout- specific crash types at the leg level. The planning-level crash prediction models can be used for network screening or intersection control evaluations, while the team expects the intersection-level and leg-level crash prediction models to be useful for practitioners making design decisions. Before these models are used in practice, they should be calibrated to local conditions. This is especially true if results from these models are being compared to results produced by other crash prediction models (e.g., those in the current HSM). Comparing uncalibrated models developed from different datasets can result in misleading outcomes. Instruc- tions on how to calibrate this project’s crash prediction models are provided in Section 6.2. The final crash prediction models and guidance on their use is proposed to be included in Parts B and C of the HSM. Draft HSM text is provided in Appendix E. Areas that the project team was unable to explore to develop sufficient conclusions and that would be good can- didates for future research include (1) the effect of different geometric features on pedestrian and bicycle safety (and a comparison to other intersection control types) and (2) the y = 0.0088x - 0.1286 R² = 0.153 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 10 20 30 40 50 Cr as he s/ M EV Theoretical Entering Speed, V1 (mph) Entering-Circulating Crash Rates (Multilane Sites) y = 0.0082x - 0.1483 R² = 0.074 0 0.1 0.2 0.3 0.4 0.5 0.6 0 10 20 30 40 50 Cr as he s/ M EV Theoretical Entering Speed, V1 (mph) Exiting-Circulating Crash Rates (Multilane Sites) Figure 6-11. Crash types potentially correlated with entering speed.

173 effect of entry speed on crashes (and whether predicted entry speed can be used in lieu of actual measurements). 6.8 References and Bibliography Bahar, G., and E. Hauer. 2014. User’s Guide to Develop Highway Safety Manual Safety Performance Function Calibration Factors. Final Report, NCHRP Project 20-07, Task 332. Lyon, C., B. Persaud, and F. Gross. 2016. The Calibrator—Calibrate, Critique, CURE. An SPF Calibration Tool. FHWA DTFH61-10- D-00022-T-13005. Srinivasan, R., M. Colety, G. Bahar, B. Crowther, and M. Farmen. 2016. Estimation of Calibration Functions for Predicting Crashes on Rural Two-Lane Roads in Arizona. Transportation Research Record: Journal of the Transportation Research Board Annual Meeting, No. 2583, Transportation Research Board, Washington, D.C., pp. 17–24.