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From page 35...
... 35   Encroachment Relationships The simulation results generated from the large vehicle encroachment simulation matrix were weighted using the marginal probabilities developed in Chapter 4. This methodology permitted the probability of a discrete simulation to be determined through the application of observed crash data.
From page 36...
... 36 Development of Clear Recovery Area Guidelines variable (rollover -- yes/no, and reaching a clear zone distance -- yes/no)
From page 37...
... Encroachment Relationships 37   Estimate Standard Error z-Value P-Value Intercept 0.292 0.068 4.31 0.000 Degree of Horizontal Curvature 0.843 0.027 31.20 <0.001 Shoulder Width 0.008 0.003 2.97 0.003 Foreslope Width 0.028 0.003 9.77 <0.001 Backslope 0.131 0.008 16.73 <0.001 Backslope Width −0.014 0.003 −4.99 0.000 Bottom Ditch Width 0.022 0.003 7.89 0.000 Clear Zone Distance −0.043 0.001 −69.03 <0.001 Model Summary Number of Observations 3,628,800 AIC 18 NOTE: AIC = Akaike information criteria. Table 13.
From page 38...
... 38 Development of Clear Recovery Area Guidelines NOTE: AIC = Akaike information criteria. Estimate StandardError z-Value P-Value Intercept −0.459 0.070 −6.56 0.000 Degree of Horizontal Curvature 0.983 0.029 34.46 <0.001 Shoulder Width 0.020 0.003 6.94 0.000 Foreslope Width 0.035 0.003 11.63 <0.001 Backslope 0.151 0.008 18.68 <0.001 Backslope Width −0.008 0.003 −2.57 0.010 Bottom Ditch Width 0.037 0.003 12.79 <0.001 Clear Zone Distance −0.051 0.001 −76.08 <0.001 Model Summary Number of Observations 3,628,800 AIC 18 Table 16.
From page 39...
... Encroachment Relationships 39   backslope ratio is also associated with a greater probability of reaching a given lateral distance, while a larger backslope width results in a lower likelihood of reaching that lateral distance. An increase in the degree of horizontal curvature (i.e., a sharper curve)
From page 40...
... 40 Development of Clear Recovery Area Guidelines can be seen that, in general, these distributions start with an accentuated spike on their leftmost side and then quickly decay as the longitudinal distance increases. A key feature observed in the data is that the spread of the longitudinal distance distribution increases with increasing lateral distances.
From page 41...
... Encroachment Relationships 41   backslope ratio, and backslope width. Shoulder width, foreslope ratio, and foreslope width have only a mild impact on the shape of the distribution.
From page 42...
... 42 Development of Clear Recovery Area Guidelines Variable Estimate StandardError z-Value P-Value Intercept 4.63E+00 2.32E-02 199.791 < 2e-16 Lateral Distance 3.04E-02 2.02E-04 150.714 < 2e-16 Lateral Distance Squared −1.40E-04 1.21E-06 −115.709 < 2e-16 Vertical Grade 4.13E-05 1.81E-04 0.228 0.81927 Degree of Horizontal Curvature −1.89E-01 4.29E-03 −44.108 < 2e-16 Shoulder Width −8.32E-04 4.56E-04 −1.826 0.06785 Foreslope Squared 9.42E-04 3.43E-04 2.748 0.00599 Foreslope −1.50E-02 5.33E-03 −2.815 0.00488 Foreslope Width −3.57E-03 4.25E-04 −8.391 < 2e-16 Bottom Ditch Width −3.79E-03 4.09E-04 −9.265 < 2e-16 Backslope 5.72E-03 3.07E-03 1.864 0.06239 Backslope Width −1.74E-03 1.03E-03 −1.681 0.09273 Lateral Distance* Vertical Grade 1.64E-05 2.13E-06 7.680 1.59E-14 Lateral Distance*
From page 43...
... Encroachment Relationships 43   Pr ob ab ilit y D en si ty longitudinal distance (ft) Pr ob ab ilit y D en si ty longitudinal distance (ft)
From page 44...
... 44 Development of Clear Recovery Area Guidelines distribution and made a histogram and quantile-to-quantile (q-q) plot.
From page 45...
... Encroachment Relationships 45   3. To try to address the kurtosis and left-tail issues, the algorithm also searched for a truncation point of the predicted distributions at a given flat percentile (defined as parameter trun)
From page 46...
... 46 Development of Clear Recovery Area Guidelines Next, the research team refitted the distributional model to the complete dataset of pickup simulations, with the expectation that a more comprehensive database would yield a better prediction. The results are shown in Figure 28.
From page 47...
... Encroachment Relationships 47   facility types of interest after confirming very similar trends from the raw data. The following sections document the performance of the adjusted distributional predictions.
From page 48...
... 48 Development of Clear Recovery Area Guidelines a = 44.844 b = 0.011 c = -18.71 trun = 0.155 Sum.Sq.Res = 3.72597 a = 44.844 b = 0.011 c = -18.71 trun = 0.155 Sum.Sq.Res = 10.60382 a = 47.935 b = 0.011 c = 2.703 trun = 0.204 Sum.Sq.Res = 5.58145 a = 47.935 b = 0.011 c = 2.703 trun = 0.204 Sum.Sq.Res = 4.00706 a = 47.935 b = 0.011 c = 2.703 trun = 0.204 Sum.Sq.Res = 1.25847 Predicted percentiles Predicted percentiles Predicted percentiles Predicted percentiles Predicted percentiles O bs er ve d pe rc en til es O bs er ve d pe rc en til es O bs er ve d pe rc en til es O bs er ve d pe rc en til es O bs er ve d pe rc en til es Figure 30. Q-q plots for observed versus adjusted predicted longitudinal distance distributions (sample model)
From page 49...
... Encroachment Relationships 49   a = 42.564 b = 0.043 c = 23.295 trun = 0.229 Sum.Sq.Res = 10.07684 a = 42.564 b = 0.043 c = 23.295 trun = 0.229 Sum.Sq.Res = 10.95607 a = 42.564 b = 0.043 c = 23.295 trun = 0.229 Sum.Sq.Res = 10.18595 a = 42.564 b = 0.043 c = 23.295 trun = 0.229 Sum.Sq.Res = 11.31545 a = 42.564 b = 0.043 c = 23.295 trun = 0.229 Sum.Sq.Res = 12.15359 Predicted percentilesPredicted percentiles Predicted percentiles Predicted percentiles Predicted percentiles O bs er ve d pe rc en til es O bs er ve d pe rc en til es O bs er ve d pe rc en til es O bs er ve d pe rc en til es O bs er ve d pe rc en til es Figure 31. Q-q plots for observed versus adjusted predicted longitudinal distance distributions (sample model)
From page 50...
... 50 Development of Clear Recovery Area Guidelines a = 88.925 b = 0.038 c = 39.381 trun = 0.101 Sum.Sq.Res = 16.39958 a = 88.925 b = 0.038 c = 39.381 trun = 0.101 Sum.Sq.Res = 7.6189 a = 88.925 b = 0.038 c = 39.381 trun = 0.101 Sum.Sq.Res = 8.27455 a = 88.925 b = 0.038 c = 39.381 trun = 0.101 Sum.Sq.Res = 9.42885 a = 88.925 b = 0.038 c = 39.381 trun = 0.101 Sum.Sq.Res = 8.98358 Predicted percentiles Predicted percentiles Predicted percentilesPredicted percentilesPredicted percentiles O bs er ve d pe rc en til es O bs er ve d pe rc en til es O bs er ve d pe rc en til es O bs er ve d pe rc en til es O bs er ve d pe rc en til es Figure 32. Q-q plots for observed versus adjusted predicted longitudinal distance distributions (sample model)
From page 51...
... Encroachment Relationships 51   a = 7.295 b = 0.005 c = 39.879 trun = 0.23 Sum.Sq.Res = 5.35658 a = 7.295 b = 0.005 c = 39.879 trun = 0.23 Sum.Sq.Res = 5.99412 a = 7.295 b = 0.005 c = 39.879 trun = 0.23 Sum.Sq.Res = 6.07357 a = 7.295 b = 0.005 c = 39.879 trun = 0.23 Sum.Sq.Res = 5.24419 a = 7.295 b = 0.005 c = 39.879 trun = 0.23 Sum.Sq.Res = 5.56634 Predicted percentiles Predicted percentiles Predicted percentiles Predicted percentiles Predicted percentiles O bs er ve d pe rc en til es O bs er ve d pe rc en til es O bs er ve d pe rc en til es O bs er ve d pe rc en til es O bs er ve d pe rc en til es Figure 33. Q-q plots for observed versus adjusted predicted longitudinal distance distributions (sample model)
From page 52...
... 52 Development of Clear Recovery Area Guidelines a = 85.977 b = 0.02 c = 24.485 trun = 0.187 Sum.Sq.Res = 6.97588 a = 85.977 b = 0.02 c = 24.485 trun = 0.187 Sum.Sq.Res = 6.18441 a = 85.977 b = 0.02 c = 24.485 trun = 0.187 Sum.Sq.Res = 7.91525 a = 85.977 b = 0.02 c = 24.485 trun = 0.187 Sum.Sq.Res = 7.59335 a = 85.977 b = 0.02 c = 24.485 trun = 0.187 Sum.Sq.Res = 7.16276 Predicted percentilesPredicted percentiles Predicted percentiles Predicted percentiles Predicted percentiles O bs er ve d pe rc en til es O bs er ve d pe rc en til es O bs er ve d pe rc en til es O bs er ve d pe rc en til es O bs er ve d pe rc en til es Figure 34. Q-q plots for observed versus adjusted predicted longitudinal distance distributions (sample model)
From page 53...
... Encroachment Relationships 53   a = 71.859 b = 0.05 c = 39.889 trun = 0.156 Sum.Sq.Res = 7.87364 a = 71.859 b = 0.05 c = 39.889 trun = 0.156 Sum.Sq.Res = 6.83467 a = 71.859 b = 0.05 c = 39.889 trun = 0.156 Sum.Sq.Res = 6.8945 a = 71.859 b = 0.05 c = 39.889 trun = 0.156 Sum.Sq.Res = 6.4468 a = 71.859 b = 0.05 c = 39.889 trun = 0.156 Sum.Sq.Res = 6.7219 Predicted percentiles O bs er ve d pe rc en til es Predicted percentiles Predicted percentiles Predicted percentilesPredicted percentiles O bs er ve d pe rc en til es O bs er ve d pe rc en til es O bs er ve d pe rc en til es O bs er ve d pe rc en til es Figure 35. Q-q plots for observed versus adjusted predicted longitudinal distance distributions (sample model)
From page 54...
... 54 Development of Clear Recovery Area Guidelines Impact Speed Models The Impact Speed Models determine the speed at which an encroaching vehicle would hit an object at different clear zone distances. This information is subsequently used within the severity module to determine the severity of the impact.
From page 55...
... Encroachment Relationships 55   two-fold: improve the prediction of impact speeds for the analysis and provide sensitivity to speed limit ranges in the risk calculations. A total of 373 right-departure, fixed-object crashes was used to estimate the corresponding model presented in Table 21.
From page 56...
... 56 Development of Clear Recovery Area Guidelines into three categories of speed limits: low speed limit (less than 45 mph) , medium speed limit (45–55 mph)
From page 57...
... Fixed Effects Estimate StandardError z-Value Intercept 6.38E+01 1.48E-01 431.552 Vertical Grade 5.35E-02 2.36E-03 22.673 Horizontal Curve Radius −1.33E+00 5.82E-02 −22.841 Shoulder Width −1.69E+00 1.48E-02 −114.647 Foreslope 4.65E-02 1.73E-02 2.688 Foreslope Width 3.02E-02 6.13E-03 4.925 Bottom Ditch Width 2.63E-02 5.96E-03 4.415 Lateral Distance −1.68E-01 6.29E-04 −267.679 Longitudinal Distance −5.65E-02 2.59E-04 −217.810 Simulated Speed Limit 45–55 mph 2.59E+01 5.66E-02 456.937 Simulated Speed Limit ≥ 60 mph 3.16E+01 6.80E-02 464.491 Shoulder Width* Foreslope −4.75E-03 2.24E-03 −2.118 Lateral Distance*
From page 58...
... NOTE: * indicates interaction between the variables.
From page 59...
... Encroachment Relationships 59   NOTE: * indicates interaction between the variables.
From page 60...
... NOTE: * indicates interaction between the variables.
From page 61...
... NOTE: * indicates interaction between the variables.
From page 62...
... 62 Development of Clear Recovery Area Guidelines NOTE: * indicates interaction between the variables.
From page 63...
... Encroachment Relationships 63   NOTE: AIC = Akaike information criteria. Fixed Effects Estimate StandardError z-Value P-Value Intercept −1.711 0.204 −8.37 <0.001 Shoulder Width −0.082 0.005 −15.35 <0.001 Foreslope −0.642 0.058 −11.03 <0.001 Foreslope Squared 0.035 0.004 7.71 <0.001 Foreslope Width −0.062 0.005 −11.75 <0.001 Backslope −0.276 0.015 −17.98 <0.001 Bottom Ditch Width −0.111 0.005 −20.54 <0.001 Lateral Distance 0.264 0.007 37.43 <0.001 Lateral Distance Squared −0.003 0.0001 −33.03 <0.001 Model Summary Number of Observations 3,628,800 AIC 18 Table 39.
From page 64...
... 64 Development of Clear Recovery Area Guidelines NOTE: AIC = Akaike information criteria. Fixed Effects Estimate StandardError z-Value P-Value Intercept −0.525 0.3050 −1.72 0.085 Shoulder Width −0.068 0.0080 −8.83 <0.001 Foreslope −1.005 0.0910 −11.01 <0.001 Foreslope Squared 0.055 0.0070 7.59 <0.001 Foreslope Width −0.069 0.0080 −9.01 <0.001 Backslope −0.579 0.0270 −21.39 <0.001 Bottom Ditch Width −0.162 0.0080 −19.12 <0.001 Lateral Distance 0.267 0.0100 25.66 <0.001 Lateral Distance Squared −0.003 0.0001 −22.59 <0.001 Model Summary Number of Observations 3,628,800 AIC 18 Table 42.
From page 65...
... Encroachment Relationships 65   for 2U and 4D roadways. Overall, results suggest that the probability of rollover increases as the lateral distance increases as indicated by the positive coefficients associated with the lateral distance variable in Table 39 through Table 46.

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