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From page 181... ... 181 CHAPTER 6: PREDICTIVE MODEL FOR RAMP SEGMENTS This chapter describes the activities undertaken to calibrate and validate safety predictive models for ramp segments and collector-distributor (C-D) road segments. Read the entire page →
From page 182... ... 182 PLAN VIEW COMPONENT PARTS Collector-Distributor Road Crossroad Ramp Terminal Seg. length = Lcd Type: diagonal, 4-leg 250-ft influence area (note: seg. Read the entire page →
From page 183... ... 183 As indicated in the HSM, road segment boundaries are typically defined by intersections or by a change in the cross section. This guidance also applies to ramp, C-D road, and crossroad segments. Read the entire page →
From page 184... ... 184 The first term in parentheses in Equations 143 and 144 recognizes that the influence of some geometric factors is unique to each crash type. In contrast, the second term in parentheses in these equations recognizes that some geometric factors have a similar influence on all crash types. Read the entire page →
From page 185... ... 185 As discussed in Appendix B, several of the geometry and lane use variables in the study state databases were of unknown accuracy. Also, several variables often had subtly different definitions among states. Read the entire page →
From page 186... ... 186 Aerial photography was used as the source of the enhanced data. These photographs were obtained from the Internet using Google Earth software. Read the entire page →
From page 187... ... 187 Gore point 2 ft Marked edge line Milepost 0.0 Milepost 0.0 Exit Ramp, C-D Road, Entrance Ramp with Speed-Change Lane Entrance Ramp with Intersection Figure 77. Starting milepost location on ramps and C-D roads. Read the entire page →
From page 188... ... 188 m m if v aXvv ×−= (146) where, am = instantaneous deceleration rate at speed m (= 3.5) Read the entire page →
From page 189... ... 189 TABLE 47. Input data for ramp curve speed prediction Variable Description Default Value Applicable Procedure Xi Milepost of the point of change from tangent to curve (PC) Read the entire page →
From page 190... ... 190 where, vent, 1 equals the average entry speed for curve 1, ft/s. The boundary condition on the right side of the equation indicates that the value computed cannot exceed the average freeway speed. Read the entire page →
From page 191... ... 191 Step 3 - Calculate Curve 1 Entry Speed. The average entry speed at curve 1 is computed using the following equation. Read the entire page →
From page 192... ... 192 If 1.47×Vfrwy ≤ vmax, 1 then: frwyent Vv 47.11, = (157) If 1.47×Vfrwy > vmax, 1 then: cdroadfrwyent VXVv 47.15280034.047.1 11, ≥×−= (158) Read the entire page →
From page 193... ... 193 Curve 1* Tangent 2 Tangent 1 Curve 2 Tangent 3 Curve 1 Tangent 2 Tangent 1 Curve 2* Read the entire page →
From page 194... ... 194 TABLE 49. Results for example application Ramp Location X, mi R, ft Lc, mi vmax, ft/s vent, ft/s vext, ft/s Exit Freeway -- -- -- -- -- 102.9 Curve 1 PC 0.12 1,000 0.10 72.9 81.3 63.5 Curve 2 PC 0.25 500 0.05 59.2 58.0 Entrance Begin 0.00 -- -- -- -- 22.1 Curve 1 PC 0.02 500 0.05 59.2 39.8 57.8 Curve 2 PC 0.10 1,000 0.10 72.9 64.8 METHODOLOGY This part of the chapter describes the methodology used to calibrate the ramp and C-D road predictive models. Read the entire page →
From page 195... ... 195 Taper point Exit Ramp with Taper Design Entrance Ramp with Parallel Design Ramp Exit Length, Lex Ramp Entrance Length, Len * Read the entire page →
From page 196... ... 196 ● horizontal curve presence, ● weaving section presence, and ● barrier presence. CMFs are typically developed for application to homogeneous segments. Read the entire page →
From page 197... ... 197 The second term of Equations 164 and 165 recognizes that the influence of some geometric factors is unique to each crash type. In contrast, the third term of Equations 164 and 165 recognizes that some geometric factors have a similar influence on all crash types. Read the entire page →
From page 198... ... 198 Calibration Data The data collection process consisted of a series of activities that culminated in the assembly of a highway safety database suitable for the development of a comprehensive safety prediction methodology for ramp and C-D road segments. These activities are described in Chapter 4. Read the entire page →
From page 199... ... 199 Nsv = predicted average single-vehicle crash frequency, crashes/yr; Imv = crash indicator variable (= 1.0 if multiple-vehicle crash data, 0.0 otherwise) ; Isv = crash indicator variable (= 1.0 if single-vehicle crash data, 0.0 otherwise) Read the entire page →
From page 200... ... 200 ruralruralmvexrexrmvenrenrmvmvmvmv IbIbIbAADTbAADTbb mvspf eLN ,,,2,1,2,0, ) Read the entire page →
From page 201... ... 201 Single-Vehicle Crash Frequency ( ) agghcmvsvspfsvspfsv CMFININN \|,22,,11,, ×+= (183) Read the entire page →
From page 202... ... 202 L L P ilblb = , (190) where, Llb,i = length of left side lane paralleled by barrier i, mi; and Woff,l,i = horizontal clearance from the edge of the traveled way to the face of barrier i on left side of segment, ft. Read the entire page →
From page 203... ... 203 TABLE 50. Ramp FI model statistical description–combined model–two states Model Statistics Value R2: 0.17 Scale parameter φ: 0.98 Pearson χ2: 2,557 (χ20.05, 2603 = 2,723) Read the entire page →
From page 204... ... 204 The findings from an examination of the coefficient values and the corresponding CMF or SPF predictions are documented in a subsequent section. In general, the sign and magnitude of the calibration coefficients in Table 50 are logical and consistent with previous research findings. Read the entire page →
From page 205... ... 205 TABLE 51. Ramp model validation statistics Component Model R 2 Rk2 Scale Parameter φ Pearson χ2 Deg. Read the entire page →
From page 206... ... 206 those in Washington. This trend is consistent with that found in the comparison of summary crash rates for these states in Table 22. Read the entire page →
From page 207... ... 207 Model for Predicting Multiple-Vehicle Non-Ramp-Related Crash Frequency The results of the multiple-vehicle model calibration are presented in Table 53. The Pearson χ2 statistic for the model is 1,327, and the degrees of freedom are 1,494 (= n − p = 1,512 −18) Read the entire page →
From page 208... ... 208 0.0 0.5 1.0 1.5 0.0 0.5 1.0 1.5 2.0 2.5 Predicted Injury + Fatal Crash Frequency, cr/5 yrs R ep or te d C ra sh F re qu en cy , cr /5 y rs Each data point represents an average of 10 sites. 1 1 to form groups of segments with similar crash frequency. Read the entire page →
From page 209... ... 209 0.0 1.0 2.0 3.0 4.0 0 1 2 3 4 5 6 Predicted Injury + Fatal Crash Frequency, cr/5 yrs R ep or te d C ra sh F re qu en cy , cr /5 y rs Each data point represents an average of 10 sites. 1 1 The inverse dispersion parameter is relatively large when compared to that for other models reported in the literature. Read the entire page →
From page 210... ... 210 Many of the CMFs found in the literature are typically derived from (and applied to) the combination of multiple-vehicle and single-vehicle crashes. Read the entire page →
From page 211... ... 211 1.0 1.2 1.4 1.6 1.8 2.0 0 500 1,000 1,500 2,000 2,500 3,000 3,500 Curve Radius, ft C ra sh M od ifi ca tio n Fa ct or . Two-Lane Highway Harwood et al. Read the entire page →
From page 212... ... 212 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 11 12 13 14 15 16 17 18 Lane Width, ft C ra sh M od ifi ca tio n Fa ct or Bauer and Harwood (1998) proposed Figure 83. Read the entire page →
From page 213... ... 213 0.8 0.9 1.0 1.1 1.2 1.3 1.4 3 5 7 9 11 Right Shoulder Width, ft C ra sh M od ifi ca tio n Fa ct or . Rural Access Controlled Highway Urban Access Controlled Highway (Harkey et al., 2008) Read the entire page →
From page 214... ... 214 0.7 0.8 0.9 1.0 1.1 1.2 1.3 2 3 4 5 6 7 8 9 Left Shoulder Width, ft C ra sh M od ifi ca tio n Fa ct or . Rural and Urban Ramps, proposed Frontage Road, Bonneson & Pratt (2009) Read the entire page →
From page 215... ... 215 1.00 1.02 1.04 1.06 1.08 1.10 1.12 1.14 10 15 20 25 Distance from Edge of Traveled Way to Barrier, ft C ra sh M od ifi ca tio n Fa ct or Roadside has barrier for 50 percent of segment 8-ft Right Shoulder Width Roadside has barrier for 100 percent of segment Figure 86. Calibrated ramp right side barrier CMF for FI crashes. Read the entire page →
From page 216... ... 216 1.00 1.02 1.04 1.06 1.08 1.10 1.12 1.14 6 10 14 18 22 Distance from Edge of Traveled Way to Barrier, ft C ra sh M od ifi ca tio n Fa ct or Roadside has barrier for 50 percent of segment 4-ft Left Shoulder Width Roadside has barrier for 100 percent of segment Figure 87. Calibrated ramp left side barrier CMF for FI crashes. Read the entire page →
From page 217... ... 217 1.0 1.1 1.2 1.3 1.4 1.5 1.6 0.10 0.15 0.20 0.25 Weaving Section Length, mi C ra sh M od ifi ca tio n Fa ct or . Pwev = 1.0 Weave Section AADT = 8,000 veh/day, proposed 11,000 veh/day, proposed Freeway Weaving Section, Bonneson and Pratt (2009) Read the entire page →
From page 218... ... 218 0.95 1.00 1.05 1.10 1.15 Rural, 1 Lane Ramp Urban, 1 Lane Ramp Urban, 2 Lane Ramp Presence of Ramp Speed-Change Lane C ra sh M od ifi ca tio n Fa ct or Pen-ex = 1.0 Figure 89. Calibrated ramp speed-change lane CMF for FI crashes. Read the entire page →
From page 219... ... 219 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Drop No change Add Change in Lane Count C ra sh M od ifi ca tio n Fa ct or Ptpr = 1.0 Figure 90. Calibrated ramp lane add or drop CMF for FI crashes. Read the entire page →
From page 220... ... 220 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0 4 8 12 16 20 24 28 Average Daily Traffic Demand (1000s) , veh/day FI M ul tip le -V eh ic le C ra sh Fr eq ue nc y, c ra sh es /y r 0.2-mile segment length, no barrier, no curves 1 lane 2 lanes Rural Ramp Urban Ramp Exit Ramp 0.00 0.05 0.10 0.15 0 4 8 12 16 20 24 28 Average Daily Traffic Demand (1000s) Read the entire page →
From page 221... ... 221 The trend lines shown in Figure 92 also indicate that crash frequency is lower on urban entrance ramps and C-D roads with one lane, relative to those with two lanes. In fact, the models indicate that single-lane urban entrance ramp segments have about 10 percent fewer crashes than two-lane urban entrance ramp segments. Read the entire page →
From page 222... ... 222 TABLE 56. Ramp PDO model statistical description–combined model–three states Model Statistics Value R2: 0.29 Scale parameter φ: 1.0 Pearson χ2: 3,044 (χ20.05, 3031 = 3,160) Read the entire page →
From page 223... ... 223 0.0 1.0 2.0 3.0 4.0 0 1 2 3 4 5 6 Predicted PDO Crash Frequency, cr/5 yrs R ep or te d C ra sh F re qu en cy , cr /5 y rs Each data point represents an average of 10 sites. 1 1 The coefficients in Table 56 were combined with the regression model to obtain the calibrated SPFs for multiple-vehicle crashes. Read the entire page →
From page 224... ... 224 0.0 1.0 2.0 3.0 4.0 5.0 6.0 0 2 4 6 8 Predicted PDO Crash Frequency, cr/5 yrs R ep or te d C ra sh F re qu en cy , cr /5 y rs Each data point represents an average of 10 sites. Read the entire page →
From page 225... ... 225 Calibrated CMFs Several CMFs were calibrated in conjunction with the SPFs. All of them were calibrated using PDO crash data. Read the entire page →
From page 226... ... 226 1.0 1.2 1.4 1.6 1.8 2.0 0 500 1,000 1,500 2,000 2,500 3,000 3,500 Curve Radius, ft C ra sh M od ifi ca tio n Fa ct or . Curve speed = 50 mi/h 40 mi/h 20 mi/h 30 mi/h Urban, Single-Lane Ramp 0.8 0.9 1.0 1.1 1.2 1.3 1.4 3 5 7 9 11 Right Shoulder Width, ft C ra sh M od ifi ca tio n Fa ct or . Read the entire page →
From page 227... ... 227 0.7 0.8 0.9 1.0 1.1 1.2 1.3 2 3 4 5 6 7 8 9 Left Shoulder Width, ft C ra sh M od ifi ca tio n Fa ct or . Rural and Urban Ramps Urban Ramps Rural Ramps Left Shoulder Width CMF. Read the entire page →
From page 228... ... 228 1.00 1.02 1.04 1.06 1.08 1.10 1.12 1.14 10 15 20 25 Distance from Edge of Traveled Way to Barrier, ft C ra sh M od ifi ca tio n Fa ct or Roadside has barrier for 50 percent of segment 8-ft Right Shoulder Width Roadside has barrier for 100 percent of segment This CMF is applicable to multiple- and single-vehicle crashes. Guidance for computing the variables Prb and Wrcb was provided previously in the subsection titled Barrier Variable Calculations. Read the entire page →
From page 229... ... 229 1.00 1.02 1.04 1.06 1.08 1.10 1.12 1.14 6 10 14 18 22 Distance from Edge of Traveled Way to Barrier, ft C ra sh M od ifi ca tio n Fa ct or Roadside has barrier for 50 percent of segment 4-ft Left Shoulder Width Roadside has barrier for 100 percent of segment Figure 99. Calibrated ramp left side barrier CMF for PDO crashes. Read the entire page →
From page 230... ... 230 1.0 1.2 1.4 1.6 1.8 0.10 0.15 0.20 0.25 Weaving Section Length, mi C ra sh M od ifi ca tio n Fa ct or . Pwev = 1.0 Weave Section AADT = 8,000 veh/day 11,000 veh/day Figure 100. Read the entire page →
From page 231... ... 231 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0 4 8 12 16 20 24 28 Average Daily Traffic Demand (1000s) , veh/day PD O M ul tip le -V eh ic le C ra sh Fr eq ue nc y, c ra sh es /y r 0.2-mile segment length, no barrier, no curves 1 lane 2 lanes Rural and Urban Ramps Exit Ramp 0.0 0.1 0.2 0.3 0.4 0.5 0 4 8 12 16 20 24 28 Average Daily Traffic Demand (1000s) Read the entire page →
From page 232... ... 232 0.0 0.2 0.4 0.6 0.8 1.0 0 4 8 12 16 20 24 28 Average Daily Traffic Demand (1000s) , veh/day To ta l P D O C ra sh F re qu en cy , cr as he s/ yr 1 lane 0.2-mile segment length, no barrier, no curves 2 lanesRural Ramp Urban Ramp Exit Ramp 1 lane 0.0 0.2 0.4 0.6 0.8 1.0 0 4 8 12 16 20 24 28 Average Daily Traffic Demand (1000s) Read the entire page →
From page 233... ... 233 Iadd = lane add indicator variable (= 1.0 if one or more lanes are added, 0.0 otherwise) ; Ica = California indicator variable (= 1.0 if segment in California, 0.0 otherwise) Read the entire page →
From page 234... ... 234 vi = initial speed, ft/s; vm = speed associated with acceleration rate am, ft/s vmax,i = limiting speed for curve i, ft/s; Vxroad = average speed at point where ramp connects to crossroad, mi/h; V[X] = crash frequency variance for a group of similar locations, crashes2; Wl = lane width, ft; Wlcb = distance from edge of left shoulder to barrier face, ft; Wls = left shoulder width, ft; Woff, l,i = horizontal clearance from the edge of the traveled way to the face of barrier i on left side of segment, ft; Woff, r,i = horizontal clearance from the edge of the traveled way to the face of barrier i on right side of segment, ft; Wrcb = distance from edge of right shoulder to barrier face, ft; Wrs = right shoulder width, ft; X = distance traveled, ft; X = reported crash count for y years, crashes; Xi = milepost of the point of change from tangent to curve (PC) Read the entire page →

From page 181...

... 181 CHAPTER 6: PREDICTIVE MODEL FOR RAMP SEGMENTS This chapter describes the activities undertaken to calibrate and validate safety predictive models for ramp segments and collector-distributor (C-D) road segments.