Skip to main content

Currently Skimming:


Pages 235-318

The Chapter Skim interface presents what we've algorithmically identified as the most significant single chunk of text within every page in the chapter.
Select key terms on the right to highlight them within pages of the chapter.


From page 235...
... 235 CHAPTER 7: PREDICTIVE MODEL FOR CROSSROAD RAMP TERMINALS This chapter describes the activities undertaken to calibrate and validate safety predictive models for both signalized and unsignalized crossroad ramp terminals. Each model consists of a SPF and a family of CMFs.
From page 236...
... 236 BACKGROUND This part of the chapter consists of three sections. The first section describes the crossroad ramp terminal analysis units (i.e., sites)
From page 237...
... 237 Crossroad Left-Side Ramp Right-Side Ramp 250 ft 250 ft 250 ft 250 ft - Ramp terminal boundary Figure 103. Illustrative crossroad ramp terminal boundary.
From page 239...
... 239 available from the other HSIS states. Hence, the database assembly focused on these three states.
From page 240...
... 240 TABLE 61. Variables from supplemental data sources Category Variable Description Descriptive problem_flag Code to identify issues that make segment unsuitable for analysis lat_lon_coord Latitude and longitude of ramp terminal center term_type Terminal configuration (diamond, spui, parclo A, etc.; see discussion)
From page 241...
... 241 The second section describes the development of a general CMF model for quantifying the relationship between safety and some geometric characteristic of an intersection leg. Most of the CMFs in the literature that address a leg-specific treatment (e.g., add turn bay)
From page 242...
... 242 exenrmp AADTAADTAADTAADT 5.05.02 +== (224) where, AADTex = AADT volume for the exit ramp, veh/day (= 0 if ramp does not exist)
From page 243...
... 243 Equation 226 is used in a multiplicative manner to address treatments made to any number of legs. For example, if two legs are treated, then the intersection CMF (i.e., CMFint,k,l)
From page 244...
... 244 weighted squared error, where the weight for each CMF observation was equal to the reciprocal of its squared standard error. The results of the model calibration are presented in Table 62.
From page 245...
... 245 -5 -4 -3 -2 -1 0 1 2 3 4 5 0.0 0.2 0.4 0.6 0.8 1.0 Predicted CMFs St an da rd iz ed R es id ua ls Figure 104. Comparison of predicted turn lane CMFs with standardized residuals - total crashes.
From page 247...
... 247 Turn Lane CMF - PDO Crashes This section describes the development of leg-specific turn lane CMFs for PDO crashes. The total-crash CMFs in Table 63 and the FI crash CMFs in Table 64 were combined for this purpose.
From page 249...
... 249 0.0 0.5 1.0 1.5 2.0 2.5 10 20 30 40 50 60 Median Width, ft C ra sh M od ifi ca tio n Fa ct or Major-road AADT = 14,000 veh/day Rural, 4 Legs (Highway, 2010) Urban, 4 Legs (Highway, 2010)
From page 250...
... 250 nex = 2, nex,ef f = 1 nex = 1, nex,ef f = 0.5 nex = 2, nex,ef f = 1 nex = 1, nex,ef f = 0.5 Lbay > 100 ft Lbay < 100 ft nex = 2, nex,ef f = 1 nex = 1, nex,ef f = 0.5 Lbay > 100 ft Lbay < 100 ft nex = 2, nex,ef f = 1.5 nex = 1, nex,ef f = 1 Lbay > 100 ft Lbay < 100 ft lane (or lanes) associated with the loop exit ramp at a B4 terminal configuration are not included in this count.
From page 251...
... 251 1.0 1.1 1.2 1.3 0 5 10 15 20 Average Daily Traffic Demand (1000s) , veh/day C ra sh M od ifi ca tio n Fa ct or 1 lane, right turn is signal or yield control 2 lanes, right turn is signal or yield control 2 lanes, right turn is merge or free-flow with accepting lane The trend in CMF values suggested by Equation 235 is shown in Figure 107 using a hypothetical coefficient and a value of Pex equal to 0.12.
From page 252...
... 252 0.8 1.0 1.2 1.4 1.6 1.8 0 10 20 30 40 50 60 70 Skew Angle, degrees C ra sh M od ifi ca tio n Fa ct or Minor-Road AADT = 3,500 veh/day Rural Multilane Highways, 3 Legs (Highway, 2010) Minor-Road AADT = 6,000 veh/day Rural Two-Lane Highways, 3 Legs (Highway, 2010)
From page 253...
... 253 Crossroad Left-Side Ramp Right-Side Ramp - Intersection boundary Lch,ex 10 ft 2.0 ft 2.0 ft 2.0 ft 2.0 ft Lch,en Lch,en Lch,en Supplemental Variables As noted in a previous part of this chapter, several variables in the database were obtained from aerial photographs of the ramp terminals represented in the study state databases. Of these variables, two of the more complex ones are defined in this section.
From page 254...
... 254 Crossroad Left-Side Ramp Right-Side Ramp - Intersection boundary Median width Median width Left-turn bay width Median Width The crossroad median width at an intersection is measured between the near edges of the traveled way associated with the opposing through traffic streams. It includes the width of the left shoulder and any left-turn lanes that are present.
From page 256...
... 256 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 0.0 0.5 1.0 1.5 2.0 2.5 True Inverse Dispersion Parameter, K t Es tim at ed In ve rs e D is pe rs io n Pa rm et er , K < 50 crashes >1,000 crashes V[X] = crash frequency variance for a group of similar locations, crashes2; N = predicted average crash frequency, crashes/yr; X = reported crash count for y years, crashes; y = time interval during which X crashes were reported, yr; and K = inverse dispersion parameter (= 1/k, where k = overdispersion parameter)
From page 257...
... 257 than the true value when the number of crashes was less than 1,000. The following relationship was derived to relate the estimated and true dispersion parameters based on observed trends in the data: mpn KKK ttr )
From page 258...
... 258 2004, 2005, and 2006 for the Maine segments. The AADT volume for each year was merged into the assembled database.
From page 259...
... 259 ( ) mwslnd rtbayltbayrcpsexchxrdchltp DDspfenDBenDBspfexDAexDAspfBABAspfcajrt CMFCMFCMF CMFCMFCMFCMFCMFCMFCMF ININININCN ××× ××××××× +++×= ,,,,, 44,3434,3434,2222,, (250)
From page 260...
... 260 where, Nrt, j = predicted average crossroad ramp terminal crash frequency for model j (j = A2B2 if IA2B2 = 1.0; j = A4D3ex if IA4D3ex = 1.0; j = B4D3en if IB4D3en = 1.0; j = D4 if ID4 = 1.0;) ; crashes/yr; Nrt, A2B2 = predicted average crash frequency for A2 and B2 configurations, crashes/yr; Nrt, A4D3ex = predicted average crash frequency for A4 and D3ex configurations, crashes/yr; Nrt, B4D3en = predicted average crash frequency for B4 and D3en configurations, crashes/yr; Nrt, D4 = predicted average crash frequency for D4 configuration, crashes/yr; AADTxrd = AADT volume for crossroad (= 0.5 AADTin + 0.5 AADTout)
From page 261...
... 261 Lstr = distance between subject ramp terminal and nearest public road intersection in a direction away from freeway (measured along the crossroad from terminal center to intersection center) , mi; and bi = calibration coefficient for condition i The final form of the regression model is described here, before the discussion of regression analysis results.
From page 262...
... 262 TABLE 66. Indicator variable values for typical ramp terminal configurations CMF Indicator Variable Value by Ramp Terminal Configuration 1 D3ex A4 D3en B4 A2 B2 D4 Protected left turn operation Ip,lt,in = 0.0 Ip,lt,out = 0.0 Ip,lt,in = 0.0 Ip,lt,out = 0.0 Ip,lt,in = 1.0 Ip,lt,out = 0.0 Ip,lt,in = 1.0 Ip,lt,out = 0.0 Ip,lt,in = 0.0 Ip,lt,out = 1.0 Ip,lt,in = 1.0 Ip,lt,out = 0.0 Ip,lt,in = 1.0 Ip,lt,out = 0.0 Chan.
From page 263...
... 263 TABLE 67. Terminal FI model statistical description–combined model–two states– signalized Model Statistics Value R2: 0.56 Scale parameter φ: 1.01 Pearson χ2: 226 (χ20.05, 202 = 236)
From page 264...
... 264 Model Validation Model validation was a two-step process. The first step required using the calibrated models to predict the crash frequency for sites from a third state (i.e., Maine)
From page 265...
... 265 ramp terminal models are described first. Then, the fit statistics and inverse dispersion parameter for each ramp terminal model are described.
From page 266...
... 266 The t-statistic for each coefficient is listed in the last column of Table 69. These statistics have generally increased, relative to their counterparts in Table 67, as a result of the increased sample size.
From page 267...
... 267 0 4 8 12 16 0 5 10 15 20 Predicted Injury + Fatal Crash Frequency, cr/3 yrs R ep or te d C ra sh F re qu en cy , cr /3 y rs 1 1 The fit of the calibrated model is shown in Figure 112. This figure compares the predicted and reported crash frequency in the calibration database.
From page 268...
... 268 0 5 10 15 20 25 0 5 10 15 20 25 30 Predicted Injury + Fatal Crash Frequency, cr/3 yrs R ep or te d C ra sh F re qu en cy , cr /3 y rs 1 1 The coefficients in Table 69 were combined with Equation 252 to obtain the calibrated SPF for the A4 and D3ex configuration. The form of the model is described in the following equation.
From page 269...
... 269 0 5 10 15 20 25 0 5 10 15 20 25 30 Predicted Injury + Fatal Crash Frequency, cr/3 yrs R ep or te d C ra sh F re qu en cy , cr /3 y rs 1 1 The coefficients in Table 69 were combined with Equation 253 to obtain the calibrated SPF for the B4 and D3en configuration. The form of the model is described in the following equation.
From page 270...
... 270 0 10 20 30 40 0 5 10 15 20 25 30 35 40 45 50 Predicted Injury + Fatal Crash Frequency, cr/3 yrs R ep or te d C ra sh F re qu en cy , cr /3 y rs 1 1 TABLE 73. Terminal FI model statistical description–D4 configuration–signalized Model Statistics Value R2 (Rk2)
From page 271...
... 271 Many of the CMFs found in the literature are typically derived from (and applied to) "intersection" crashes.
From page 272...
... 272 TABLE 74. Calibrated protected left-turn operation CMF for FI crashes Junction Location Legs with Protected Operation Leg Location Proportion AADT CMF Value by Number of Opposing Lanes 1 lane 2 lanes Ramp terminal 1 Crossroad 0.78 0.76 0.60 2 Crossroad 0.78 0.58 0.36 Intersection 1 Minor street 1 0.30 0.91 0.85 Major street 1 0.70 0.79 0.64 2 Minor street 1 0.30 0.83 0.71 Major street 1 0.70 0.62 0.41 Note: 1 - Intersection CMFs are computed using Equation 269 and the AADT proportion shown in the table.
From page 273...
... 273 TABLE 75. Calibrated right-turn channelization CMF for FI crashes–signalized Junction Location Leg Location Proportion AADT on Leg CMF Value by Number of Legs with Channelization 1 leg 2 legs Ramp terminal Exit ramp 0.12 1.20 1.45 Crossroad 1 0.39 1.23 1.52 Intersection Minor street 1, 2 0.15 1.09 1.19 Major street 1, 2 0.35 1.21 1.46 Notes: 1 - For Equation 270, Pin is assumed to equal Pout.
From page 274...
... 274 approaches on both sides of the leg should be counted when they are within 250 ft of the ramp terminal. The count of driveways should only include active driveways (i.e., those driveways with an average daily volume of 10 veh/day or more)
From page 275...
... 275 0.0 0.2 0.4 0.6 0.8 1.0 0 500 1,000 1,500 2,000 Distance to Adjacent Intersection, ft C ra sh M od ifi ca tio n Fa ct or Distance to adjacent ramp terminal = 0.15 mi Figure 116. Calibrated segment length CMF for FI crashes–signalized.
From page 276...
... 276 1.0 1.1 1.2 1.3 1.4 1.5 1.6 10 20 30 40 50 Median Width, ft C ra sh M od ifi ca tio n Fa ct or Ramp Terminal, 30,000 veh/day, proposed Urban, 4 Legs (Highway, 2010) Ramp Terminal, 15,000 veh/day, proposed Figure 117.
From page 277...
... 277 0 2 4 6 8 10 0 10 20 30 40 50 60 Crossroad AADT (1000s) , veh/day Fl C ra sh F re qu en cy , c ra sh es /y r Terminal Types: A2, B2 Ramp AADT = 0.32 x Crossroad AADT 6-lane crossroad, 2-lane exit ramp4-lane crossroad, 1-lane exit ramp 2-lane crossroad, 1-lane exit ramp 0.15 miles to adjacent intersection Exit ramp right turn: signal controlled Protected crossroad left turn phase All other CMFs = 1.00 Urban, 3 Legs (Highw ay, 2010)
From page 278...
... 278 The A2, B2, and D3 configurations are shown in Figure 118 to have fewer crashes than the other configurations, for a given AADT volume. This trend is likely due to the fact that these configurations have only three legs, while the other configurations have four legs.
From page 279...
... 279 The following regression model form was used to facilitate the combined regression analysis of the four models for unsignalized ramp terminals.
From page 280...
... 280 Equations 283 and 284 describe CMFs for left- and right-turn lane (or bay) presence, respectively.
From page 281...
... 281 TABLE 77. Terminal FI model statistical description–combined model–two states– unsignalized Model Statistics Value R2: 0.41 Scale parameter φ: 1.05 Pearson χ2: 273 (χ20.05, 240 = 277)
From page 282...
... 282 The findings from the first step of the validation process are described in this section. Those from the second step are described in the next section.
From page 283...
... 283 TABLE 79. Terminal FI model statistical description–combined model–three states– unsignalized Model Statistics Value R2: 0.40 Scale parameter φ: 1.04 Pearson χ2: 311 (χ20.05, 281 = 321)
From page 284...
... 284 than χ20.05,39 (= 55) , the hypothesis that the model fits the data cannot be rejected.
From page 285...
... 285 0 1 2 3 4 5 6 0 2 4 6 8 Predicted Injury + Fatal Crash Frequency, cr/3 yrs R ep or te d C ra sh F re qu en cy , cr /3 y rs 1 1 Figure 119. Predicted vs.
From page 286...
... 286 0 2 4 6 8 10 0 2 4 6 8 10 12 Predicted Injury + Fatal Crash Frequency, cr/3 yrs R ep or te d C ra sh F re qu en cy , cr /3 y rs 1 1 The calibrated CMFs used with this SPF are described in a subsequent section. The AADT volume of the loop entrance ramp at an A4 configuration is not included in AADTen.
From page 287...
... 287 0 2 4 6 8 0 2 4 6 8 10 Predicted Injury + Fatal Crash Frequency, cr/3 yrs R ep or te d C ra sh F re qu en cy , cr /3 y rs 1 1 )
From page 288...
... 288 0 1 2 3 4 0 1 2 3 4 5 Predicted Injury + Fatal Crash Frequency, cr/3 yrs R ep or te d C ra sh F re qu en cy , cr /3 y rs 1 1 Each data point represents an average of 10 sites. The coefficients in Table 79 were combined with Equation 282 to obtain the calibrated SPF for the D4 configuration.
From page 289...
... 289 1.0 1.1 1.2 1.3 0 1 2 3 4 5 Average Daily Traffic Demand (1000s) , veh/day C ra sh M od ifi ca tio n Fa ct or 1 lane, right turn is stop or yield control 2 lanes, right turn is stop or yield control 2 lanes, right turn is merge or free-f low w ith accepting lane geometric factor on total crashes.
From page 290...
... 290 Access Point Frequency CMF. The access point frequency CMF is described using the following equation.
From page 291...
... 291 0.0 0.2 0.4 0.6 0.8 1.0 0 500 1,000 1,500 2,000 Distance to Adjacent Intersection, ft C ra sh M od ifi ca tio n Fa ct or Distance to adjacent ramp terminal = 0.19 mi Figure 124. Calibrated segment length CMF for FI crashes–unsignalized.
From page 292...
... 292 width below which the CMF value is 1.0. This value is decreased from the 14 ft value stated in the HSM based on the trends found in the ramp terminal safety database.
From page 293...
... 293 0.0 0.4 0.8 1.2 1.6 2.0 0 5 10 15 20 25 Crossroad AADT (1000s) , veh/day FI C ra sh F re qu en cy , c ra sh es /y r Terminal Types: A2, B2 Ramp AADT = 0.32 x Crossroad AADT 4-lane crossroad, 2-lane exit ramp 2-lane crossroad, 1-lane exit ramp Urban area 0.19 miles to adjacent intersection Exit ramp right turn: stop controlled All other CMFs = 1.00 Urban, 3 Legs (Highw ay, 2010)
From page 294...
... 294 Model Calibration The results of the regression model calibration are presented in Table 85. The Pearson χ2 statistic for the model is 219, and the degrees of freedom are 215 (= n − p = 236 −21)
From page 295...
... 295 previous research findings (even if the specific value was not known with a great deal of certainty as applied to this database)
From page 296...
... 296 0 4 8 12 16 20 24 0 5 10 15 20 25 30 Predicted PDO Crash Frequency, cr/3 yrs R ep or te d C ra sh F re qu en cy , cr /3 y rs 1 1 The fit of the calibrated model is shown in Figure 126. This figure compares the predicted and reported crash frequency in the calibration database.
From page 297...
... 297 0 10 20 30 40 50 0 5 10 15 20 25 30 35 40 45 50 55 60 Predicted PDO Crash Frequency, cr/3 yrs R ep or te d C ra sh F re qu en cy , cr /3 y rs 1 1 The calibrated CMFs used with this SPF are described in a subsequent section. The AADT volume of the loop entrance ramp at an A4 configuration is not included in AADTen.
From page 298...
... 298 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 45 50 Predicted PDO Crash Frequency, cr/3 yrs R ep or te d C ra sh F re qu en cy , cr /3 y rs 1 1 The coefficients in Table 85 were combined with the regression model to obtain the calibrated SPF for the B4 and D3en configuration. The form of the model is described in the following equation.
From page 299...
... 299 0 10 20 30 40 50 60 0 10 20 30 40 50 60 70 80 Predicted PDO Crash Frequency, cr/3 yrs R ep or te d C ra sh F re qu en cy , cr /3 y rs 1 1 TABLE 89. Terminal PDO model statistical description–D4 configuration–signalized Model Statistics Value R2 (Rk2)
From page 300...
... 300 Many of the CMFs found in the literature are typically derived from (and applied to) "intersection" crashes.
From page 301...
... 301 The values obtained from this CMF are listed in Table 91. The CMF values reflect a proportion of total leg AADT on the crossroad Pin and Pout of 0.39, which is a typical value for ramp terminals.
From page 302...
... 302 [ ] exchIexexexch PPeCMF ,)
From page 303...
... 303 from the ramp terminal such that it is not part of the ramp terminal)
From page 304...
... 304 0.0 0.2 0.4 0.6 0.8 1.0 0 500 1,000 1,500 2,000 Distance to Adjacent Intersection, ft C ra sh M od ifi ca tio n Fa ct or Distance to adjacent ramp terminal = 0.15 mi Figure 130. Calibrated segment length CMF for PDO crashes–signalized.
From page 305...
... 305 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 10 20 30 40 50 Median Width, ft C ra sh M od ifi ca tio n Fa ct or Ramp Terminal, 30,000 veh/day Ramp Terminal, 15,000 veh/day Figure 131. Calibrated median-width CMF for PDO crashes–signalized.
From page 306...
... 306 0 2 4 6 8 10 0 10 20 30 40 50 60 Crossroad AADT (1000s) , veh/day PD O C ra sh F re qu en cy , cr as he s/ yr Terminal Types: A2, B2 Ramp AADT = 0.32 x Crossroad AADT 6-lane crossroad, 2-lane exit ramp 4-lane crossroad, 1-lane exit ramp 2-lane crossroad, 1-lane exit ramp 0.15 miles to adjacent intersection Protected crossroad left turn phase All other CMFs = 1.00 0 2 4 6 8 10 0 10 20 30 40 50 60 Crossroad AADT (1000s)
From page 307...
... 307 Unsignalized Ramp Terminal Models This section describes the calibrated PDO crash prediction models for signalized ramp terminals. The regression model used had the same form as used to develop the FI crash prediction model (i.e., Equation 278)
From page 308...
... 308 The t-statistic for each coefficient is listed in the last column of Table 95. These statistics describe a test of the hypothesis that the coefficient value is equal to 0.0.
From page 309...
... 309 0 2 4 6 8 10 12 0 2 4 6 8 10 12 14 16 Predicted PDO Frequency, cr/3 yrs R ep or te d C ra sh F re qu en cy , cr /3 y rs 1 1 )
From page 310...
... 310 0 2 4 6 8 10 0 2 4 6 8 10 12 Predicted PDO Crash Frequency, cr/3 yrs R ep or te d C ra sh F re qu en cy , cr /3 y rs 1 1 TABLE 97. Terminal PDO model statistical description–A4 and D3ex configuration– unsignalized Model Statistics Value R2 (Rk2)
From page 311...
... 311 0 2 4 6 8 10 12 0 2 4 6 8 10 12 14 Predicted PDO Crash Frequency, cr/3 yrs R ep or te d C ra sh F re qu en cy , cr /3 y rs 1 1 for the model is 20.5, and the degrees of freedom are 21 (= n − p = 22 −1)
From page 312...
... 312 0 1 2 3 4 5 0 1 2 3 4 5 6 Predicted PDO Crash Frequency, cr/3 yrs R ep or te d C ra sh F re qu en cy , cr /3 y rs 1 1 Each data point represents an average of 10 sites. Model for D4 Configuration.
From page 313...
... 313 Each data point shown in Figure 136 represents the average predicted and average reported crash frequency for a group of 10 ramp terminals. The data were sorted by predicted crash frequency to form groups of terminals with similar crash frequency.
From page 314...
... 314 Equation 319 is not associated with one of the regression coefficients in Table 95. Rather, it is based on a fairly definitive set of CMFs developed by Harwood et al.
From page 315...
... 315 0.0 1.0 2.0 3.0 4.0 0 5 10 15 20 25 Crossroad AADT (1000s) , veh/day PD O C ra sh F re qu en cy , cr as he s/ yr Terminal Types: A2, B2 Ramp AADT = 0.32 x Crossroad AADT 0.0 1.0 2.0 3.0 4.0 0 5 10 15 20 25 Crossroad AADT (1000s)
From page 316...
... 316 NOMENCLATURE AADTen = AADT volume for the entrance ramp, veh/day (= 0 if ramp does not exist) ; AADTex = AADT volume for the exit ramp, veh/day (= 0 if ramp does not exist)
From page 317...
... 317 Iawsc = all-way stop control indicator variable (= 1.0 if ramp terminal has all-way stop controlled, 0.0 if it has one-way stop control for the exit ramp) ; and IB4D3en = crash indicator variable (= 1.0 if B4 or D3en crash data, 0.0 otherwise)
From page 318...
... 318 Nspf, A4D3ex = predicted average crash frequency for A4 and D3ex configurations for base conditions, crashes/yr; Nspf, D4 = predicted average crash frequency for D4 configuration for base conditions, crashes/yr; Nsv = predicted average single-vehicle crash frequency, crashes/yr; nth = number of through traffic lanes on the crossroad at the ramp terminal (total of both directions) , lanes; Pex = proportion of total leg AADT on exit ramp leg; Pi = proportion of total leg AADT on street i; Pin = proportion of total leg AADT on crossroad leg between ramps; Pk = proportion of total leg AADT on leg k; Pout = proportion of total leg AADT on crossroad leg outside of interchange; Pxrd = proportion of total leg AADT on the crossroad; R k = proportion of intersection crashes that occur on treated leg k; Ri = proportion of intersection crashes that occur on treated street i; Sin(x)

Key Terms



This material may be derived from roughly machine-read images, and so is provided only to facilitate research.
More information on Chapter Skim is available.