Safety Prediction Methodology and Analysis Tool for Freeways and Interchanges (2021) / Chapter Skim
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From page 100... ...
100 CHAPTER 5: PREDICTIVE MODEL FOR FREEWAY SEGMENTS This chapter describes the activities undertaken to calibrate and validate safety predictive models for freeway segments and for freeway speed-change lanes. Each model consists of a SPF and a family of CMFs.
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101 BACKGROUND This part of the chapter consists of three sections. The first section describes the decomposition of a freeway facility into analysis units (i.e., sites)
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102 PLAN VIEW COMPONENT PARTS Speed-Change Lane Speed-Change Lane Crossroad Ramp Terminal Type: ramp entrance Type: ramp exit Type: diagonal, 4-leg Seg. length = Len Seg.
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104 TABLE 29. Freeway variables from HSIS database Category Variable Description Descriptive state Source of data (CA, ME, WA)
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105 definitions among states. Moreover, the study state databases often did not include variables that describe road-related factors known to be associated with crash frequency.
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106 TABLE 30. Freeway variables from supplemental data sources (continued)
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107 to have "high volume" and the proportion of daily traffic using the segment during these highvolume hours. Aerial photography was used as a second source of enhanced data.
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108 A review of the literature (documented in Chapter 2) confirmed an association between time of day and crash frequency, as well as between volume-to-capacity ratio and crash frequency.
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109 0.00 0.02 0.04 0.06 0.08 1 3 5 7 9 11 13 15 17 19 21 23 Hour of Day Pr op or tio n A A D T du rin g H ou r Route 51, Sacramento Co., Calif. Route 5, Shasta Co., Calif.
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110 0.0 0.2 0.4 0.6 0.8 1.0 0 10,000 20,000 30,000 40,000 Average Daily Traffic Demand per Lane, veh/day/ln Pr op or tio n A A D T du rin g H ig hVo lu m e H ou rs Pv = 1 - e[1.45 - 0.124 x AADT/lanes/1000] Figure 40.
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From page 111... ...
111 0.0 1.0 2.0 3.0 4.0 0.00 0.10 0.20 0.30 0.40 Side Friction Demand C ra sh R at e, c ra sh es /m vm 85th% tangent speed = 65 mph Fatal + Injury + PDO Fatal + Injury idc b curve CMFfIAADTaN = (18)
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112 Equations 16 through 19 can be combined to yield the following horizontal curve CMF.
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113 ramp for a common travel direction. These definitions are consistent with the ramp entrance and exit sites identified in Figure 38.
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114 Lwev = w eaving section length 2' Lwev 2' It is generally recognized that the length of the weaving section has an important influence on the operation of the freeway segment. This influence relates to the degree to which the weaving activity is concentrated along the freeway.
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115 end at some point along the length of a segment. When this occurs, the length of the segment associated with the element's initial condition and the length associated with its changed condition were recorded in the database.
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117 Thus, there are accuracy implications associated with this temporal and spatial extrapolation. Moreover, State DOT practice when a current count is not available for a segment is sometimes to adjust the AADT volume from the last year it was counted (which could be several years previous)
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From page 118... ...
118 It is widely-recognized that PDO crash counts vary widely on a regional basis due to significant variation in the reporting threshold. This issue was discussed in Chapter 4 where it was noted that there was wide variation in the representation of PDO crashes in the study-state databases.
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119 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 freeways and speed-change lanes. These activities are described Chapter 4.
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120 Pib = proportion of segment length with a barrier present in the median (i.e., inside) ; Wicb = distance from edge of inside shoulder to barrier face, ft; bi = calibration coefficient for condition i (see Table 31)
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122 AADTe, ent = AADT volume of entrance ramp located at distance Xe, ent, veh/day; AADTe, ext = AADT volume of exit ramp located at distance Xe, ext, veh/day; Wm = median width (measured from near edges of traveled way in both travel directions) , ft; Ri = radius of curve i, ft; Pc,i = proportion of segment length with curve i; Phv = proportion of AADT during hours where volume exceeds 1,000 veh/h/ln; bi = calibration coefficient for condition i (see Table 31)
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From page 124... ...
124 This model is derived to predict the total number of ramp-entrance-related crashes on a segment with one or more ramp entrances. This form is dictated by the non-homogeneous character of most freeway segments in the database.
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125 ( ) ibism iib isiinoff iib icb WWW LL WW L LW −− − + − = 25.0 2 2 , ,, , (63)
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126 For segments with depressed medians without a continuous barrier or short sections of barrier in the median, the following equation should be used to estimate Pib.
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127 This statistic follows the χ2 distribution with n-p degrees of freedom, where n is the number of observations (i.e., segments) and p is the number of model variables (McCullagh and Nelder, 1983)
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128 obtained using a null model formulation (i.e., a model with no independent variables but with the same error distribution, link function, and offset in years y)
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129 TABLE 31. Freeway FI model statistical description–combined model–two states Model Statistics Value R2: 0.66 Scale parameter φ: 1.01 Pearson χ2: 4,069 (χ20.05, 4036 = 4,185)
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130 The findings from an examination of the coefficient values on the corresponding CMF or SPF predictions are documented in a subsequent section. In general, the sign and magnitude of the calibration coefficients in Table 31 are logical and consistent with previous research findings.
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131 TABLE 32. Freeway model validation statistics Component Model R 2 Rk2 Scale Parameter φ Pearson χ2 Deg.
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132 TABLE 33. Freeway FI model statistical description–combined model–three states Model Statistics Value R2: 0.65 Scale parameter φ: 1.00 Pearson χ2: 4,574 (χ20.05, 4568 = 4,726)
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From page 133... ...
133 Indicator variables were included for the states of California and Maine in the regression model. The coefficient for each variable was very small and not statistically significant.
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From page 134... ...
134 0 5 10 15 20 25 30 35 40 0 10 20 30 40 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 Each data point represents an average of 10 sites. 1 1 An additional reason for the relatively large inverse dispersion parameter value stems from this project's development of a "full"model (i.e., one with multiple variables)
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From page 135... ...
135 to form groups of segments with similar crash frequency. The purpose of this grouping was to reduce the number of data points shown in the figure and, thereby, to facilitate an examination of trends in the data.
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136 0 2 4 6 8 10 12 14 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 Each data point represents an average of 10 sites. 1 1 Figure 45.
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From page 137... ...
137 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 0.0 2.0 4.0 6.0 8.0 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 Each data point represents an average of 10 sites. 1 1 The fit of the calibrated model is shown in Figure 46.
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From page 138... ...
138 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.0 1.0 2.0 3.0 4.0 5.0 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 Each data point represents an average of 10 sites. 1 1 The coefficients in Table 33 were combined with Equation 61 to obtain the calibrated SPF for ramp-exit-related crashes.
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From page 139... ...
139 instances, Equation 86 is used to facilitate a comparison of the CMFs reported in the literature with those developed for this project. Specifically, this equation is used to convert the CMFs developed for a specific crash type to one that applies to total crashes.
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140 1.0 1.1 1.2 1.3 1.4 1,500 2,000 2,500 3,000 3,500 4,000 4,500 5,000 Curve Radius, ft C ra sh M od ifi ca tio n Fa ct or . Two-Lane Highway Harwood et al.
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141 0.90 0.95 1.00 1.05 1.10 1.15 10 11 12 13 14 Lane Width, ft C ra sh M od ifi ca tio n Fa ct or Urban, Bonneson and Pratt (2009) Rural, Bonneson and Pratt (2009)
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142 0.9 1.0 1.1 1.2 6 7 8 9 10 11 12 Outside 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)
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143 0.8 0.9 1.0 1.1 1.2 2 4 6 8 10 Inside Shoulder Width, ft C ra sh M od ifi ca tio n Fa ct or . Principal Arterial Highways Milton and Mannering (1998)
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144 0.90 0.95 1.00 1.05 1.10 1.15 1.20 20 30 40 50 60 70 80 Median Width, ft C ra sh M od ifi ca tio n Fa ct or . Barrier in center of median, proposed - No barrier, rural multilane divided highway (Highway, 2010)
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145 Texas freeways. In contrast, the other barrier-related trend line is based on a mixture of rigid, semi-rigid, and cable barrier types in the study states.
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146 1.00 1.02 1.04 1.06 1.08 1.10 10 15 20 25 30 Clear Zone Width, ft C ra sh M od ifi ca tio n Fa ct or . Rural 4-lane, Bonneson and Pratt (2009)
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147 The combined outside barrier CMF is shown in Figure 53. The relevant trend lines are labeled "Roadside has barrier...".
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148 1.0 1.1 1.2 1.3 0.05 0.15 0.25 0.35 0.45 Distance from Gore (x) , mi C ra sh M od ifi ca tio n Fa ct or Rural 6-lane freeway Ramp AADT = 6,000 veh/day Segment Length = 0.1 mi Average CMF for 0.5-mi road section = 1.05 x contribute volume to the subject segment are of interest.
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149 1.0 1.1 1.2 1.3 0.05 0.15 0.25 0.35 0.45 Distance from Left-Side Gore (x) , mi C ra sh M od ifi ca tio n Fa ct or Rural 6-lane freeway Ramp AADT = 6,000 veh/day Segment Length = 0.1 mi Average CMF for 0.5-mi road section = 1.10 x Figure 55.
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From page 150... ...
150 1.0 1.1 1.2 1.3 1.4 1.5 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Weaving Section Length, mi A ve ra ge C ra sh M od ifi ca tio n Fa ct or Bonneson and Pratt (2008) Full cloverleaf, Cirillo (1970)
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From page 151... ...
151 0.8 1.0 1.2 1.4 1.6 1.8 300 500 700 900 Ramp Entrance Length, ft C ra sh M od ifi ca tio n Fa ct or . HSM (Highway, 2010)
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From page 152... ...
152 0.8 1.0 1.2 1.4 1.6 1.8 200 400 600 800 1,000 Ramp Exit Length, ft C ra sh M od ifi ca tio n Fa ct or . HSM (Highway, 2010)
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153 1.00 1.05 1.10 1.15 1.20 0.0 0.2 0.4 0.6 0.8 1.0 Proportion AADT during High-Volume Hours C ra sh M od ifi ca tio n Fa ct or Rural 6-lane, proposed Urban, proposed Rural 4-lane proposed Multiple-vehicle crashes 0.94 0.96 0.98 1.00 0.0 0.2 0.4 0.6 0.8 1.0 Proportion AADT during High-Volume Hours C ra sh M od ifi ca tio n Fa ct or Rural 6-lane, proposed Urban, proposed Rural 4-lane proposed Single-vehicle crashes The proportion of AADT during hours where volume exceeds 1,000 veh/h/ln Phv is computed using the average hourly volume distribution associated with the subject segment. This distribution will typically be computed using the data obtained from the nearest continuous traffic counting station (on a freeway of similar character)
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154 0 3 6 9 12 15 0 50 100 150 200 250 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 1.0-mile segment length, no barrier 4 lanes 6 8 Rural Freeway Urban Freeway 6 10 8 0 1 2 3 4 5 0 50 100 150 200 250 Average Daily Traffic Demand (1000s)
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155 0 5 10 15 20 25 0 50 100 150 200 250 Average Daily Traffic Demand (1000s) , veh/day To ta l F I C ra sh F re qu en cy , cr as he s/ yr 1.0-mile segment length, no barrier 2 entrance ramps, 2 exit ramps 4 lanes 8 Rural Freeway Urban Freeway 6 10 4, 6, 8 lanes Figure 61.
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156 One situation that could not be addressed in the SPF development was a segment with an unbalanced daily traffic demand. The AADT volumes in the study state database represent both travel directions and it is commonly assumed that the daily directional distribution is balanced (i.e., the same in each direction)
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157 segment be evaluated twice. One evaluation would be conducted where the number of lanes is equal to 2Y and one evaluation would be conducted where the number of lanes is equal to 2Z.
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158 TABLE 39. Freeway PDO model statistical description–combined model –three states Model Statistics Value R2: 0.66 Scale parameter φ: 1.07 Pearson χ2: 4,888 (χ20.05, 4557 = 4,715)
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159 would represent an average value for all states and counties in the database. To this end, the predicted crash frequencies from the model described by Table 39 were submitted to a second regression analysis using Equation 115.
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160 0 5 10 15 20 25 30 35 40 0 10 20 30 40 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 Each data point represents an average of 10 sites.
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162 0 5 10 15 20 25 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 Each data point represents an average of 10 sites. 1 1 Figure 63.
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From page 163... ...
163 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 0.0 2.0 4.0 6.0 8.0 10.0 Predicted PDO Crash Frequency, cr/3 yrs R ep or te d C ra sh F re qu en cy , cr /3 y rs Each data point represents an average of 10 sites. 1 1 The fit of the calibrated model is shown in Figure 64.
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From page 164... ...
164 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 0.0 1.0 2.0 3.0 4.0 5.0 Predicted PDO Crash Frequency, cr/3 yrs R ep or te d C ra sh F re qu en cy , cr /3 y rs Each data point represents an average of 10 sites. 1 1 The coefficients in Table 39 were combined with Equation 61 to obtain the calibrated SPF for ramp-exit-related crashes.
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165 these instances, Equation 86 is used to convert the CMFs developed for this project into equivalent total-crash CMFs for the purpose of illustrating the overall trend. The proportion of multiple-vehicle crashes used in this equation is obtained from Table 44.
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166 1.0 1.1 1.2 1.3 1.4 1,500 2,000 2,500 3,000 3,500 4,000 4,500 5,000 Curve Radius, ft C ra sh M od ifi ca tio n Fa ct or . Rural 4-lane Urban 4-lane Rural 6-lane Urban 6-lane Figure 66.
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From page 167... ...
167 0.9 1.0 1.1 1.2 6 7 8 9 10 11 12 Outside Shoulder Width, ft C ra sh M od ifi ca tio n Fa ct or . Rural 4-lane (curve)
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168 0.90 0.95 1.00 1.05 1.10 1.15 1.20 20 30 40 50 60 70 80 Median Width, ft C ra sh M od ifi ca tio n Fa ct or . Barrier in center of median No barrier Median-Width CMF.
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From page 169... ...
169 Guidance for computing the variables Pib and Wicb was provided previously in the subsection titled Barrier Variable Calculations. The variable Wicb (representing the distance from the edge of inside shoulder to median barrier face)
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170 1.00 1.02 1.04 1.06 1.08 10 15 20 25 30 Distance from Edge of Traveled Way to Barrier, ft C ra sh M od ifi ca tio n Fa ct or Rural, 4 Lanes Rural, 6 Lanes Urban 4 Lanes 10-ft Outside Shoulder Width Barrier or Bridge Rail for 100% of Segment Urban 6 Lanes The combined outside barrier CMF is shown in Figure 70. Equation 86 was used to create this CMF (with CMFmv, ob = 1.0)
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171 The variables for weaving section length (i.e., Lwev, inc, Lwev, dec) in Equations 134 and 135 are intended to reflect the degree to which the weaving activity is concentrated along the freeway.
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172 1.0 1.1 1.2 1.3 1.4 1.5 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Weaving Section Length, mi A ve ra ge C ra sh M od ifi ca tio n Fa ct or Ramp AADT = 6,000 veh/day Urban, 6-lane Rural 6-lane Rural 4-lane Urban, 4-lane Figure 71. Average CMF value for PDO crashes as a function of weaving section length.
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173 1.00 1.05 1.10 1.15 1.20 1.25 1.30 300 500 700 900 Ramp Entrance Length, ft C ra sh M od ifi ca tio n Fa ct or . with that of Moon and Hummer (2009)
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174 1.00 1.05 1.10 1.15 1.20 0.0 0.2 0.4 0.6 0.8 1.0 Proportion AADT during High-Volume Hours C ra sh M od ifi ca tio n Fa ct or Rural 6-lane Urban 6-lane Rural 4-lane Multiple-vehicle crashes Urban 4-lane 0.80 0.85 0.90 0.95 1.00 0.0 0.2 0.4 0.6 0.8 1.0 Proportion AADT during High-Volume Hours C ra sh M od ifi ca tio n Fa ct or Rural 6-lane Urban 6-lane Rural 4-lane Single-vehicle crashes Urban 4-lane The CMF for single-vehicle crashes is described using the following equation. hvP hvsv eCMF 611.0 , −= (141)
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From page 175... ...
175 0 10 20 30 40 50 0 50 100 150 200 250 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 1.0-mile segment length, no barrier 4 lanes 6 8 Rural Freeway Urban Freeway 6 10 8 0 2 4 6 8 10 0 50 100 150 200 250 Average Daily Traffic Demand (1000s)
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From page 176... ...
176 0 10 20 30 40 50 60 70 0 50 100 150 200 250 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 1.0-mile segment length, no barrier 2 entrance ramps, 2 exit ramps 4 lanes 8 Rural Freeway Urban Freeway 6 10 4, 6, 8 lanes Figure 75.
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From page 177... ...
177 CMF1 ... CMFk = crash modification factors for freeway segment crashes at a site with specific geometric design features k; CMFen = ramp entrance crash modification factor; CMFen|agg = aggregated ramp entrance crash modification factor; CMFen,1 ...
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From page 178... ...
178 ftan = factor for rumble strip presence on tangent portions of the segment; fwev, dec = weaving section adjustment factor for travel in decreasing milepost direction; fwev, inc = weaving section adjustment factor for travel in increasing milepost direction; Ic = curve deflection angle, degrees; Ien = crash indicator variable (= 1.0 if ramp-entrance-related crash data, 0.0 otherwise) ; Iex = crash indicator variable (= 1.0 if ramp-exit-related crash data, 0.0 otherwise)
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From page 179... ...
179 Nspf, mv = predicted average multiple-vehicle non-entrance/exit crash frequency for base conditions, crashes/yr; Nspf, sv = predicted average single-vehicle non-entrance/exit crash frequency for base conditions, crashes/yr; Nsv = predicted average single-vehicle non-entrance/exit crash frequency, crashes/yr; P1 = proportion of AADT in travel direction 1; P2 = proportion of AADT in travel direction 2 (= 1.0 - P1) ; Pc = proportion of the segment length with curvature; Pc,i = proportion of segment length with curve i; Phv = proportion of AADT during hours where volume exceeds 1,000 veh/h/ln; Pi = proportion of AADT in travel direction i that corresponds to subject speed-change lane; Pib = proportion of segment length with a barrier present in the median (i.e., inside)
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From page 180... ...
180 xb= distance from ramp gore to start of segment, mi; Xe, ent = distance from segment end milepost to nearest upstream entrance ramp gore point, for travel in decreasing milepost direction, mi; Xe, ext = distance from segment end milepost to nearest downstream exit ramp gore point, for travel in increasing milepost direction, mi; xe= distance from ramp gore to end of segment (xe > xb) , mi; y = time interval during which X crashes were reported, yr;
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