Superelevation Criteria for Sharp Horizontal Curves on Steep Grades (2014)

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157 S E C T I O N 5 An analysis of the crashes that occurred at the field data collection sites was conducted to determine the statistical correlation between crash frequency/rate and margin of safety against skidding (i.e., lateral friction margin) and mar- gin of safety against rollover (i.e., rollover margin) estimated from the vehicle dynamic simulation models. In theory, it was assumed that as margin of safety increases, crash frequency decreases. The questions that remain, however, are what is the rate of decrease and is there a threshold value for the mar- gin of safety beyond which the decrease in crash frequency is negligible? These are the primary questions to be answered through the analysis of the crash data. The crash analysis focused on determining the relationship between (1) margin of safety against skidding and single- vehicle run-off-road (SVROR) crashes and (2) margin of safety against rollover and single-vehicle rollover (SVROLL) crashes. The analysis did not include crashes involving multi- ple vehicles. Passenger vehicles and trucks were analyzed sepa- rately. The analysis was limited to crashes that occurred in the immediate vicinity of the horizontal curve at the field data col- lection sites. In most cases, the analysis was limited to crashes that occurred within the limits of the curve, but in some cases, crashes were also included if they occurred slightly upstream or downstream of the curve; it seemed reasonable to assume that these crashes could be curve related. Crashes that occurred further upstream from the curve on the tangent portion of the downgrade or upgrade were not included in the analysis. The analysis was also limited to crashes that occurred in the direc- tion of travel corresponding to the speed and vehicle maneuver studies. The remainder of this section provides descriptive sta- tistics of the data, describes the overall analysis approach, and presents the results. 5.1 Data Description Site geometrics, margin of safety (MOS) data, 5-year crash data, and traffic volumes were available for 19 sites (16 down- grade and 3 upgrade) in five states. (Note: crash data were not available for site WA1, and therefore, this site was excluded from the analysis.) Basic site characteristics considered in the analysis (e.g., curve length, curve radius, superelevation, percent grade, and length of grade) are shown in Table 4 in Section 3.1. Three separate margins of safety were considered in the analysis. Two margins of safety against skidding were esti- mated from the simulation models. One margin of safety estimate against skidding was based on the mean friction supply [MOS skid (mean supply)], and the second margin of safety estimate against skidding was based on the 2nd per- centile friction supply (i.e., mean friction minus two stan- dard deviations) [MOS skid (minimum supply)] measured at the site (see Section 3.4). A margin of safety against roll- over (MOS rollover) was also estimated from the simulation models. For passenger vehicles, the estimated margins of safety are based upon simulations of an SUV, and for trucks the estimated margins of safety are based upon simulations of a tractor semi-trailer. The estimated margins of safety are also based upon the assumption that the passenger vehicle and truck were traveling at the mean speed for the respec- tive vehicle type at the given site as measured in the field (Section 3.2). The estimated margins of safety against skidding and roll over considered in the analysis for each site are shown separately for passenger vehicles and trucks in Table 26. The margins of safety against skidding (i.e., lateral friction mar- gins) were calculated using the multibody model. The margins of safety against rollover were calculated using the methodol- ogy described in Section 4.6, with lateral acceleration obtained from the multibody model, or more specifically, the rollover margin was calculated using RMay. Traffic volume—expressed as an average of the average annual daily traffic (AADT) and in million vehicle miles trav- eled (MVMT)—and curve length of each site and SVROR and SVROLL crash frequencies, all based on 5 years of data, are shown for each site in Table 27, separately for passenger Crash Analysis

State Site No. MOS for passenger vehicles MOS for trucks Skid (mean supply) Skid (minimum supply) Rollover Skid (mean supply) Skid (minimum supply) Rollover CA CA1 0.46 0.33 0.94 0.45 0.31 0.38 CA2 0.39 0.26 0.71 0.47 0.34 0.25 CA3 0.41 0.28 0.77 0.44 0.30 0.30 MD MD1 0.47 0.37 0.93 0.42 0.33 0.33 MD2a 0.38 0.35 0.91 0.49 0.45 0.42 MD3 0.51 0.48 0.92 0.52 0.48 0.33 PA PA1 0.48 0.34 0.86 0.26 0.11 0.18 PA2 0.50 0.37 0.90 0.47 0.33 0.31 WA WA2 0.44 0.31 0.84 0.46 0.32 0.30 WA3 0.52 0.39 0.95 0.55 0.42 0.38 WA4 0.42 0.30 0.87 0.44 0.31 0.32 WA5a 0.47 0.34 0.94 0.59 0.45 0.45 WA6 0.55 0.42 0.98 0.57 0.44 0.39 WA7a 0.44 0.30 0.78 0.49 0.35 0.32 WV WV1 0.35 0.26 0.81 0.22 0.13 0.29 WV2 0.58 0.47 0.94 0.53 0.40 0.33 WV3 0.35 0.26 0.84 0.22 0.12 0.27 WV4 0.49 0.32 0.88 0.52 0.32 0.38 WV5 0.46 0.33 0.91 0.39 0.25 0.32 Minimum MOSb 0.35 0.26 0.71 0.22 0.11 0.18 Maximum MOSb 0.58 0.48 0.98 0.57 0.48 0.39 a Upgrade sites. b Range for 16 downgrade sites only. Table 26. Margins of safety by vehicle type and study site. State Site no. Passenger vehicles Trucks 5-yr Average directional AADT (veh/day) MVMT ROR crash frequency Rollover crash frequency 5-year Average directional AADT (veh/day) MVMT ROR crash frequency Rollover crash frequency CA CA1 35,520 31.764 36 7 1,480 1.323 5 6 CA2 27,160 10.409 6 6 840 0.322 6 6 CA3 27,645 6.559 0 0 855 0.203 0 0 MD MD1 4,348 3.174 3 3 1,776 1.297 3 3 MD2 7,288 6.650 0 0 2,695 2.460 0 0 MD3 7,288 5.985 4 4 2,695 2.214 4 4 PA PA1 6,222 2.157 5 5 468 0.162 5 5 PA2 8,171 4.026 3 3 6,420 3.164 3 3 WA WA2 5,700 2.497 3 4 1,800 0.788 4 4 WA3 5,700 1.976 2 2 1,800 0.624 2 2 WA4 5,700 3.433 4 4 1,800 1.084 4 4 WA5 1,944 0.674 1 1 456 0.158 1 1 WA6 4,810 2.897 1 1 1,690 1.018 1 1 WA7 1,957 1.678 4 4 194 0.166 4 4 WV WV1 11,357 9.327 16 5 2,493 2.047 5 5 WV2 7,846 10.452 13 7 1,494 1.991 7 7 WV3 11,942 2.179 1 1 498 0.091 1 1 WV4 9,570 6.113 12 6 4,930 3.149 6 6 WV5 31,029 28.314 15 11 4,231 3.861 11 11 Table 27. Traffic volumes and ROR and rollover crash frequencies by vehicle type and study site (5 years of data).

159 vehicles and trucks. The years for which the traffic volume and crash data were obtained for each state are as follows: • CA (2004-2008) • MD (2007-2011) • PA (2006-2010) • WA (2004-2008) • WV (2007-2011) 5.2 Analysis Approach A crash prediction model was developed separately for each crash type and vehicle type based on the observed 5-year crash frequency, traffic volume (AADT), and site characteristics. Ini- tially, both downgrade and upgrade sites were used in the crash prediction models, but after further investigation it was decided to only include downgrade sites in the analysis. A simple rela- tionship of the following functional form was assumed: ( ) = + + + + +     exp ln . . . (100)VT,CT 0 1 VT 2 VT,CT 3 3 n n N b b AADT b MOS b Var b Var where: NVT,CT = number of crashes/mi/year for given vehi- cle type (passenger vehicles or truck) and collision type (SVROR or SVROLL) MOSVT,CT = MOS for given vehicle type and collision type AADTVT = vehicles/day of given vehicle type Var3, . . . ,Varn = roadway characteristics (see list of param- eters below) ln = natural logarithm function b0, . . . ,bn = regression coefficients In addition to AADT and MOS, the roadway characteristics (Var3, . . . , Varn) considered in each model included: • Superelevation • Percent grade • Length of grade • Curve radius • Shoulder width The parameters in Equation 100 were estimated using a generalized linear model (GLM) approach with a negative binomial (NB) distribution and a log link using the com- bined crash data from all 5 years and average AADT across all 5 years. SVROR and SVROLL crashes were modeled sepa- rately for each vehicle type. A stepwise approach was used where first all parameters were included and then the least significant parameter(s) were eliminated, one at a time, until all remaining parameters were significant. This is known as backward stepwise selection. In general, a 10% significance level associated with the Type 3 c2-statistic was selected. However, in all cases, AADT and MOS were retained in the models. All analyses were performed using PROC GENMOD of SAS Version 9.3 (SAS, 2011). In all, six models were investigated based on the following combinations: • Passenger vehicles, SVROR crashes, and MOS skid (mean supply) • Passenger vehicles, SVROR crashes, and MOS skid (mini- mum supply) • Passenger vehicles, SVROLL crashes, and MOS rollover • Trucks, SVROR crashes, and MOS skid (mean supply) • Trucks, SVROR crashes, and MOS skid (minimum supply) • Trucks, SVROLL crashes, and MOS rollover 5.3 Analysis Results The NB regression analyses yielded mixed results. In some cases, the coefficients of model parameters, including AADT, were not statistically significant; the sign of the coefficient would be counterintuitive (e.g., the coefficient of MOS would be positive); and/or the model would experience convergence problems. A plausible explanation is that the number of sites is too small and the number of parameters too large and thus they could not provide sufficient evidence for a significant safety effect of one or more parameters. A case also can be made that the range of MOS values of a given type for the 16 downgrade sites is too narrow (see Table 26) to predict with confidence a relationship between margin of safety and crash frequency. Of the six models considered, four were deemed usable, each based on only AADT and either MOS skid (minimum supply) or MOS rollover. The final analysis of variance results are shown in Table 28 for passenger vehicles and in Table 29 for trucks. The last column in these tables indicates whether the parameter is statistically significant at the 10% level. As shown, either AADT or MOS is statistically significant (if one includes the p-value of 0.1111), but never both. Predicted crashes/mi/year and their 95% confidence limits were estimated over an MOS range of 0 to 1 using the four models shown in Tables 28 and 29. The median AADT (pas- senger vehicles or trucks) and median curve length from the 16 downgrade sites were used in the calculations. The four plots are shown in Figures 166 through 169. The vertical lines indicate the MOS range from the study sites on which the models are based; therefore, predictions outside that range are extrapolated and should be used with caution. In general, the crash analysis indicates that as margins of safety against skidding and rollover increase, the predicted crash frequency decreases.

160 Parameter Coefficient estimate Standard error Wald 95% confidence limits Wald chi-square Chi-square p-value Significant at 10% level? MOS Skid (minimum supply) Intercept −4.2109 2.3960 −8.9069 0.4851 3.09 0.0788 — ln(AADTPV) 0.6601 0.2100 0.2484 1.0717 9.88 0.0017 Yes MOS Skid (minimum supply) −1.5664 2.2580 −5.9919 2.8591 0.48 0.4879 No Dispersion 0.1418 0.1145 0.0291 0.6905 MOS Rollover Intercept 0.3988 2.5144 −4.5294 5.3270 0.03 0.8740 — ln(AADTPV) 0.2724 0.1709 −0.0626 0.6074 2.54 0.1111 No (borderline) MOS Rollover −2.2449 1.7768 −5.7274 1.2376 1.60 0.2064 No Dispersion 0.0000 0.0053 — — Table 28. Regression results for passenger vehicle SVROR and SVROLL crashes. Parameter Coefficient estimate Standard error Wald 95% confidence limits Wald Chi-square Chi-square p-value Significant at 10% level? MOS Skid (minimum supply) Intercept 1.0257 1.4512 −1.8187 3.8700 0.50 0.4797 — ln(AADTTruck) 0.0734 0.1918 −0.3026 0.4493 0.15 0.7021 No MOS Skid (minimum supply) −2.1414 1.1872 −4.4683 0.1855 3.25 0.0713 Yes Dispersion 0.0000 0.0115 — — MOS Rollover Intercept 1.2242 1.3655 −1.4521 3.9005 0.80 0.3700 — ln(AADTTruck) 0.2342 0.2100 −0.1773 0.6458 1.24 0.2647 No MOS Rollover −6.4837 2.8890 −12.1460 −0.8213 5.04 0.0248 Yes Dispersion 0.0000 0.0000 0.0000 0.0000 Table 29. Regression results for truck SVROR and SVROLL crashes. Pr ed ic te d SV RO R Cr as he s/ m i/y r 0 1 2 3 4 5 6 7 8 9 10 Passenger vehicle MOS Skid (minimum supply) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Vertical lines indicate interval of MOS values from 16 downgrade study sites Dashed lines represent 95% confidence limits Passenger vehicle AADT = 7,300 veh/day (median); Curve Length = 0.34 mi (median) Figure 166. Passenger vehicles—predicted SVROR crashes versus MOS skid (minimum supply).

Pr ed ic te d SV RO LL C ra sh es /m i/y r 0 1 2 3 4 5 6 7 8 9 10 Passenger vehicle MOS Rollover 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Vertical lines indicate interval of MOS values from 16 downgrade study sites Dashed lines represent 95% confidence limits Passenger vehicle AADT = 7,300 veh/day (median); Curve Length = 0.34 mi (median) Figure 167. Passenger vehicles—predicted SVROLL crashes versus MOS rollover. Pr ed ic te d SV RO R Cr as he s/ m i/y r 0 1 2 3 4 5 6 7 8 9 10 Truck MOS Skid (minimum supply) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Vertical lines indicate interval of MOS values from 16 downgrade study sites Dashed lines represent 95% confidence limits Truck AADT = 1,800 veh/day (median); Curve Length = 0.34 mi (median) Figure 168. Trucks—predicted SVROR crashes versus MOS skid (minimum supply). Figure 169. Trucks—predicted SVROLL crashes versus MOS rollover. Pr ed ic te d SV RO LL C ra sh es /m i/y r 0 1 2 3 4 5 6 7 8 9 10 Truck MOS Rollover 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Vertical lines indicate interval of MOS values from 16 downgrade study sites Dashed lines represent 95% confidence limits Truck AADT = 1,800 veh/day (median); Curve Length = 0.34 mi (median)