National Academies Press: OpenBook

Development of Clear Recovery Area Guidelines (2024)

Chapter: Chapter 7 - Variable Sensitivity and Importance

« Previous: Chapter 6 - Clear Zone Guideline Assistance Program
Page 81
Suggested Citation:"Chapter 7 - Variable Sensitivity and Importance." National Academies of Sciences, Engineering, and Medicine. 2024. Development of Clear Recovery Area Guidelines. Washington, DC: The National Academies Press. doi: 10.17226/27593.
×
Page 81
Page 82
Suggested Citation:"Chapter 7 - Variable Sensitivity and Importance." National Academies of Sciences, Engineering, and Medicine. 2024. Development of Clear Recovery Area Guidelines. Washington, DC: The National Academies Press. doi: 10.17226/27593.
×
Page 82
Page 83
Suggested Citation:"Chapter 7 - Variable Sensitivity and Importance." National Academies of Sciences, Engineering, and Medicine. 2024. Development of Clear Recovery Area Guidelines. Washington, DC: The National Academies Press. doi: 10.17226/27593.
×
Page 83
Page 84
Suggested Citation:"Chapter 7 - Variable Sensitivity and Importance." National Academies of Sciences, Engineering, and Medicine. 2024. Development of Clear Recovery Area Guidelines. Washington, DC: The National Academies Press. doi: 10.17226/27593.
×
Page 84
Page 85
Suggested Citation:"Chapter 7 - Variable Sensitivity and Importance." National Academies of Sciences, Engineering, and Medicine. 2024. Development of Clear Recovery Area Guidelines. Washington, DC: The National Academies Press. doi: 10.17226/27593.
×
Page 85
Page 86
Suggested Citation:"Chapter 7 - Variable Sensitivity and Importance." National Academies of Sciences, Engineering, and Medicine. 2024. Development of Clear Recovery Area Guidelines. Washington, DC: The National Academies Press. doi: 10.17226/27593.
×
Page 86
Page 87
Suggested Citation:"Chapter 7 - Variable Sensitivity and Importance." National Academies of Sciences, Engineering, and Medicine. 2024. Development of Clear Recovery Area Guidelines. Washington, DC: The National Academies Press. doi: 10.17226/27593.
×
Page 87
Page 88
Suggested Citation:"Chapter 7 - Variable Sensitivity and Importance." National Academies of Sciences, Engineering, and Medicine. 2024. Development of Clear Recovery Area Guidelines. Washington, DC: The National Academies Press. doi: 10.17226/27593.
×
Page 88
Page 89
Suggested Citation:"Chapter 7 - Variable Sensitivity and Importance." National Academies of Sciences, Engineering, and Medicine. 2024. Development of Clear Recovery Area Guidelines. Washington, DC: The National Academies Press. doi: 10.17226/27593.
×
Page 89
Page 90
Suggested Citation:"Chapter 7 - Variable Sensitivity and Importance." National Academies of Sciences, Engineering, and Medicine. 2024. Development of Clear Recovery Area Guidelines. Washington, DC: The National Academies Press. doi: 10.17226/27593.
×
Page 90
Page 91
Suggested Citation:"Chapter 7 - Variable Sensitivity and Importance." National Academies of Sciences, Engineering, and Medicine. 2024. Development of Clear Recovery Area Guidelines. Washington, DC: The National Academies Press. doi: 10.17226/27593.
×
Page 91
Page 92
Suggested Citation:"Chapter 7 - Variable Sensitivity and Importance." National Academies of Sciences, Engineering, and Medicine. 2024. Development of Clear Recovery Area Guidelines. Washington, DC: The National Academies Press. doi: 10.17226/27593.
×
Page 92
Page 93
Suggested Citation:"Chapter 7 - Variable Sensitivity and Importance." National Academies of Sciences, Engineering, and Medicine. 2024. Development of Clear Recovery Area Guidelines. Washington, DC: The National Academies Press. doi: 10.17226/27593.
×
Page 93
Page 94
Suggested Citation:"Chapter 7 - Variable Sensitivity and Importance." National Academies of Sciences, Engineering, and Medicine. 2024. Development of Clear Recovery Area Guidelines. Washington, DC: The National Academies Press. doi: 10.17226/27593.
×
Page 94
Page 95
Suggested Citation:"Chapter 7 - Variable Sensitivity and Importance." National Academies of Sciences, Engineering, and Medicine. 2024. Development of Clear Recovery Area Guidelines. Washington, DC: The National Academies Press. doi: 10.17226/27593.
×
Page 95
Page 96
Suggested Citation:"Chapter 7 - Variable Sensitivity and Importance." National Academies of Sciences, Engineering, and Medicine. 2024. Development of Clear Recovery Area Guidelines. Washington, DC: The National Academies Press. doi: 10.17226/27593.
×
Page 96
Page 97
Suggested Citation:"Chapter 7 - Variable Sensitivity and Importance." National Academies of Sciences, Engineering, and Medicine. 2024. Development of Clear Recovery Area Guidelines. Washington, DC: The National Academies Press. doi: 10.17226/27593.
×
Page 97
Page 98
Suggested Citation:"Chapter 7 - Variable Sensitivity and Importance." National Academies of Sciences, Engineering, and Medicine. 2024. Development of Clear Recovery Area Guidelines. Washington, DC: The National Academies Press. doi: 10.17226/27593.
×
Page 98
Page 99
Suggested Citation:"Chapter 7 - Variable Sensitivity and Importance." National Academies of Sciences, Engineering, and Medicine. 2024. Development of Clear Recovery Area Guidelines. Washington, DC: The National Academies Press. doi: 10.17226/27593.
×
Page 99
Page 100
Suggested Citation:"Chapter 7 - Variable Sensitivity and Importance." National Academies of Sciences, Engineering, and Medicine. 2024. Development of Clear Recovery Area Guidelines. Washington, DC: The National Academies Press. doi: 10.17226/27593.
×
Page 100
Page 101
Suggested Citation:"Chapter 7 - Variable Sensitivity and Importance." National Academies of Sciences, Engineering, and Medicine. 2024. Development of Clear Recovery Area Guidelines. Washington, DC: The National Academies Press. doi: 10.17226/27593.
×
Page 101
Page 102
Suggested Citation:"Chapter 7 - Variable Sensitivity and Importance." National Academies of Sciences, Engineering, and Medicine. 2024. Development of Clear Recovery Area Guidelines. Washington, DC: The National Academies Press. doi: 10.17226/27593.
×
Page 102
Page 103
Suggested Citation:"Chapter 7 - Variable Sensitivity and Importance." National Academies of Sciences, Engineering, and Medicine. 2024. Development of Clear Recovery Area Guidelines. Washington, DC: The National Academies Press. doi: 10.17226/27593.
×
Page 103
Page 104
Suggested Citation:"Chapter 7 - Variable Sensitivity and Importance." National Academies of Sciences, Engineering, and Medicine. 2024. Development of Clear Recovery Area Guidelines. Washington, DC: The National Academies Press. doi: 10.17226/27593.
×
Page 104
Page 105
Suggested Citation:"Chapter 7 - Variable Sensitivity and Importance." National Academies of Sciences, Engineering, and Medicine. 2024. Development of Clear Recovery Area Guidelines. Washington, DC: The National Academies Press. doi: 10.17226/27593.
×
Page 105
Page 106
Suggested Citation:"Chapter 7 - Variable Sensitivity and Importance." National Academies of Sciences, Engineering, and Medicine. 2024. Development of Clear Recovery Area Guidelines. Washington, DC: The National Academies Press. doi: 10.17226/27593.
×
Page 106
Page 107
Suggested Citation:"Chapter 7 - Variable Sensitivity and Importance." National Academies of Sciences, Engineering, and Medicine. 2024. Development of Clear Recovery Area Guidelines. Washington, DC: The National Academies Press. doi: 10.17226/27593.
×
Page 107
Page 108
Suggested Citation:"Chapter 7 - Variable Sensitivity and Importance." National Academies of Sciences, Engineering, and Medicine. 2024. Development of Clear Recovery Area Guidelines. Washington, DC: The National Academies Press. doi: 10.17226/27593.
×
Page 108
Page 109
Suggested Citation:"Chapter 7 - Variable Sensitivity and Importance." National Academies of Sciences, Engineering, and Medicine. 2024. Development of Clear Recovery Area Guidelines. Washington, DC: The National Academies Press. doi: 10.17226/27593.
×
Page 109
Page 110
Suggested Citation:"Chapter 7 - Variable Sensitivity and Importance." National Academies of Sciences, Engineering, and Medicine. 2024. Development of Clear Recovery Area Guidelines. Washington, DC: The National Academies Press. doi: 10.17226/27593.
×
Page 110
Page 111
Suggested Citation:"Chapter 7 - Variable Sensitivity and Importance." National Academies of Sciences, Engineering, and Medicine. 2024. Development of Clear Recovery Area Guidelines. Washington, DC: The National Academies Press. doi: 10.17226/27593.
×
Page 111
Page 112
Suggested Citation:"Chapter 7 - Variable Sensitivity and Importance." National Academies of Sciences, Engineering, and Medicine. 2024. Development of Clear Recovery Area Guidelines. Washington, DC: The National Academies Press. doi: 10.17226/27593.
×
Page 112
Page 113
Suggested Citation:"Chapter 7 - Variable Sensitivity and Importance." National Academies of Sciences, Engineering, and Medicine. 2024. Development of Clear Recovery Area Guidelines. Washington, DC: The National Academies Press. doi: 10.17226/27593.
×
Page 113
Page 114
Suggested Citation:"Chapter 7 - Variable Sensitivity and Importance." National Academies of Sciences, Engineering, and Medicine. 2024. Development of Clear Recovery Area Guidelines. Washington, DC: The National Academies Press. doi: 10.17226/27593.
×
Page 114
Page 115
Suggested Citation:"Chapter 7 - Variable Sensitivity and Importance." National Academies of Sciences, Engineering, and Medicine. 2024. Development of Clear Recovery Area Guidelines. Washington, DC: The National Academies Press. doi: 10.17226/27593.
×
Page 115
Page 116
Suggested Citation:"Chapter 7 - Variable Sensitivity and Importance." National Academies of Sciences, Engineering, and Medicine. 2024. Development of Clear Recovery Area Guidelines. Washington, DC: The National Academies Press. doi: 10.17226/27593.
×
Page 116
Page 117
Suggested Citation:"Chapter 7 - Variable Sensitivity and Importance." National Academies of Sciences, Engineering, and Medicine. 2024. Development of Clear Recovery Area Guidelines. Washington, DC: The National Academies Press. doi: 10.17226/27593.
×
Page 117

Below is the uncorrected machine-read text of this chapter, intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text of each book. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

81   Variable Sensitivity and Importance As described in the preceding chapters, a wide array of roadway and roadside design variables were incorporated into the encroachment simulation matrix as well as the various encroachment relationship models. The variables include horizontal curvature, vertical grade, shoulder width, foreslope ratio, foreslope width, ditch bottom width, backslope ratio, and backslope width. While it is desirable to have clear zone guidance expressed in terms of key, significant design variables, the addition of variables with little significance to clear zone risk can unnecessarily complicate the guidelines. Thus, it is important to understand the key variables that have a great impact on the determination of P(K+A) during a vehicle encroachment. A sensitivity analysis was performed to understand the change in P(K+A) for a change in the value of each design variable. The general approach involved defining various design configu- rations and varying the individual variables within the CZ-GAP risk analysis tool to examine the effects of changes in P(K+A) across a range of clear zone distances. If varying a roadway or roadside parameter is found to have little or no influence on P(K+A), it can be removed from the guideline development process and assigned a fixed value representative of common practice. This helps streamline the presentation of the resulting clear zone guidelines without significantly changing the resulting clear zone distance. The fewer the number of variables, the simpler the presentation and implementation of the guidelines. A variable-importance analysis was also performed to provide insight into the impact of each variable. The variable-importance analysis ranks the variables according to their contribution to the prediction of P(K+A). Variable Sensitivity Using the CZ-GAP risk analysis tool, the team performed sensitivity analyses to better under- stand the influence of impact angle percentiles, impact speed percentiles, and tree spacings on P(K+A). The impact speed and angle models developed from the encroachment simulation data and described in Chapter 5 provide distributions for the variable at different lateral and longitu- dinal offset distances. A selection of the percentile value to use in the clear zone risk analysis was part of the overall clear zone analysis plan. For example, for impact speed, a median or 85th percen- tile value could be used, with the 85th percentile representing higher impact speeds and, thus, being more conservative. Similarly, a median or 15th-percentile impact angle could be utilized in the analysis. The 15th-percentile angle would be more conservative because it projects a wider contact envelope onto the tree line at the clear zone edge and, thus, increases the probability of impact. The tree spacing is intended to represent a relative obstacle density at the edge of the clear zone. The intent was to select values of obstacle spacing to represent low, medium, and high hazard levels for the clear zone guidelines. C H A P T E R   7

82 Development of Clear Recovery Area Guidelines Figure 54 through Figure 57 present the P(K+A) relationships for different impact speed and impact angle percentile combinations for different clear zone distances. This analysis was per- formed for a particular roadway and roadside terrain configuration as noted in the figures. As can be observed, the P(K+A) associated with tree impacts at the clear zone edge decreases as the vehicle encroaches further onto the roadside. This is intuitive given that increased lateral offset distances are generally associated with lower impact speed. It can also be observed that P(K+A) due to rollover increases with lateral distance. The P(K+A) due to rollover is computed based on the probability of the rollover for a given terrain configura- tion and lateral offset distance. As a vehicle encroaches further onto the roadside, the probability of rollover increases. It can be further observed that the change of the speed distribution metrics from the mean speed (Figure 54) to the 85th percentile speed (Figure 55) is associated with an increase in the P(K+A) for trees. Similarly, as observed by comparing Figure 54 and Figure 56, a change in the angle distribution metrics from the mean angle (Figure 54) to the 15th percentile angle (Figure 56) results in an increase in the P(K+A) for trees. Figure 57 presents P(K+A) for both 85th percentile speed and 15th percentile angle, which is the most conservative combination and results in the highest P(K+A). The research team also performed a sensitivity analysis for tree spacing. In this analysis, the spacing of trees varied from 20 ft to 500 ft, and the average impact angle and 85th percentile speed were used to develop the P(K+A) curves. As can be observed from Figure 58 through Figure 62, as the spacing between trees increases, the magnitude of P(K+A), due to tree impacts, decreases. As expected, the spacing of trees has a significant influence on the estimate of P(K+A). P( K+ A) NOTE: VGrade (% downgrade) = vertical grade; HCurveR (degree of curvature) = horizontal curvature; ShldW (ft) = shoulder width; FS (H in ratio 1V:H) = foreslope ratio; FSW (ft) = foreslope width; BtW (ft) = ditch bottom width; BS (H in ratio 1V:H) = backslope; and BSW (ft) = backslope width. Figure 54. P(K1A) for the average impact speed and average impact angle.

Variable Sensitivity and Importance 83   P( K+ A) NOTE: VGrade (% downgrade) = vertical grade; HCurveR (degree of curvature) = horizontal curvature; ShldW (ft) = shoulder width; FS (H in ratio 1V:H) = foreslope ratio; FSW (ft) = foreslope width; BtW (ft) = ditch bottom width; BS (H in ratio 1V:H) = backslope; and BSW (ft) = backslope width. Figure 55. P(K1A) for the 85th percentile impact speed and average impact angle. NOTE: VGrade (% downgrade) = vertical grade; HCurveR (degree of curvature) = horizontal curvature; ShldW (ft) = shoulder width; FS (H in ratio 1V:H) = foreslope ratio; FSW (ft) = foreslope width; BtW (ft) = ditch bottom width; BS (H in ratio 1V:H) = backslope; and BSW (ft) = backslope width. P( K+ A) Figure 56. P(K1A) for the average impact speed and 15th percentile impact angle.

84 Development of Clear Recovery Area Guidelines NOTE: VGrade (% downgrade) = vertical grade; HCurveR (degree of curvature) = horizontal curvature; ShldW (ft) = shoulder width; FS (H in ratio 1V:H) = foreslope ratio; FSW (ft) = foreslope width; BtW (ft) = ditch bottom width; BS (H in ratio 1V:H) = backslope; and BSW (ft) = backslope width. P( K+ A) Figure 57. P(K1A) for the 85th percentile impact speed and 15th percentile impact angle. P( K+ A) NOTE: VGrade (% downgrade) = vertical grade; HCurveR (degree of curvature) = horizontal curvature; ShldW (ft) = shoulder width; FS (H in ratio 1V:H) = foreslope ratio; FSW (ft) = foreslope width; BtW (ft) = ditch bottom width; BS (H in ratio 1V:H) = backslope; and BSW (ft) = backslope width. Figure 58. P(K1A) for 20 ft spacing between trees.

Variable Sensitivity and Importance 85   NOTE: VGrade (% downgrade) = vertical grade; HCurveR (degree of curvature) = horizontal curvature; ShldW (ft) = shoulder width; FS (H in ratio 1V:H) = foreslope ratio; FSW (ft) = foreslope width; BtW (ft) = ditch bottom width; BS (H in ratio 1V:H) = backslope; and BSW (ft) = backslope width. P( K+ A) Figure 59. P(K1A) for 50 ft spacing between trees. NOTE: VGrade (% downgrade) = vertical grade; HCurveR (degree of curvature) = horizontal curvature; ShldW (ft) = shoulder width; FS (H in ratio 1V:H) = foreslope ratio; FSW (ft) = foreslope width; BtW (ft) = ditch bottom width; BS (H in ratio 1V:H) = backslope; and BSW (ft) = backslope width. P( K+ A) Figure 60. P(K1A) for 100 ft spacing between trees.

86 Development of Clear Recovery Area Guidelines NOTE: VGrade (% downgrade) = vertical grade; HCurveR (degree of curvature) = horizontal curvature; ShldW (ft) = shoulder width; FS (H in ratio 1V:H) = foreslope ratio; FSW (ft) = foreslope width; BtW (ft) = ditch bottom width; BS (H in ratio 1V:H) = backslope; and BSW (ft) = backslope width. P( K+ A) Figure 61. P(K1A) for 200 ft spacing between trees. NOTE: VGrade (% downgrade) = vertical grade; HCurveR (degree of curvature) = horizontal curvature; ShldW (ft) = shoulder width; FS (H in ratio 1V:H) = foreslope ratio; FSW (ft) = foreslope width; BtW (ft) = ditch bottom width; BS (H in ratio 1V:H) = backslope; and BSW (ft) = backslope width. P( K+ A) Figure 62. P(K1A) for 500 ft spacing between trees.

Variable Sensitivity and Importance 87   The research team also performed a sensitivity analysis on the various roadside and roadway design variables. The sensitivity analysis was based on the probability of a fatal or serious injury crash given a vehicle hit a tree P(K+A). The median impact speed and angle and a tree spacing of 100 ft were used in the analyses. Three roadside configurations were selected to cover the range of terrain variations within the design variable matrix. These configurations generally represent flat, moderate, and steep terrain. The design parameter values selected for each case are presented in Table 49. The key difference for the three terrains relates to the foreslope and backslope values. For the flat terrain condition, the flattest slopes in the simulation design matrix were used. These are a 1V:10H foreslope and a 1V:6H backslope. The moderate terrain used a 1V:6H foreslope and a 1V:4H backslope. The steep terrain used the steepest slope values in the simulation design variable matrix, which were a 1V:3H foreslope and a 1V:2H backslope. For each terrain configuration, each design variable was parametrically varied using the values from the simulation matrix, and the P(K+A) was plotted for a range of clear zone distances. Separate graphs were prepared for 2U and 4D facility types. A high posted-speed-limit condition was used since that is believed to show the most sensitivity to injury probability. A qualitative comparison of the curves was performed for the different terrain configurations and facility types. Additionally, the percentage of change between the maximum and minimum P(K+A) for the different values of the design variable was computed at a selected clear zone distance of 30 ft to provide a quantitative assessment. For instance, if the shoulder width was being assessed, the overall change in P(K+A) for the minimum (2 ft) and maximum (12 ft) shoulder widths was considered. The following sections present the results for each roadway and roadside design variable. Vertical Alignment Figure 63 through Figure 68 present the distribution of the probability of a fatal or serious injury crash [P(K+A)] for varying values (0, 4%, 6%) of vertical downgrades. Note that for pro- gramming purposes, the vertical downgrade (VGrade) is expressed as 1/% grade multiplied by a factor of 100. In the figures, VGrade = 16.667 = 6% of downgrade and VGrade = 25 = 4% of downgrade. Figure 63 presents the P(K+A) curves for a 2U facility type and flat terrain. Figure 64 presents the P(K+A) curves for a 4D facility type on flat terrain. Similar pairs of graphs are pre- sented for moderate and sharp terrain in Figure 65 through Figure 68. Across the facility type, the P(K+A) is higher for the 2U facility than the 4D facility. The observed differences in P(K+A) for different vertical grade values are not significant, irre- spective of the facility type. In general, the difference increases slightly as clear zone distance increases. Table 50 provides the P(K+A) values at a clear zone distance of 30 ft and the percent Variable Case 1 (Flat) Case 2 (Moderate) Case 3 (Steep) Vertical Alignment 0 0 0 Horizontal Alignment 0 0 0 Shoulder Width 2 2 2 Foreslope 1V:10H 1V:6H 1V:3H Foreslope Width 16 16 16 Bottom Ditch Width 0 0 0 Backslope 6:1 4:1 2:1 Backslope Width 8 8 8 Table 49. Roadside configuration for test cases.

88 Development of Clear Recovery Area Guidelines Figure 63. P(K1A) for 2U facility with varying vertical alignments (VGrade) (flat). Figure 64. P(K1A) for 4D facility with varying vertical alignments (VGrade) (flat).

Variable Sensitivity and Importance 89   Figure 65. P(K1A) for 2U facility with varying vertical alignments (VGrade) (moderate). Figure 66. P(K1A) for 4D facility with varying vertical alignments (VGrade) (moderate).

90 Development of Clear Recovery Area Guidelines Figure 67. P(K1A) for 2U facility with varying vertical alignments (VGrade) (steep). Figure 68. P(K1A) for 4D facility with varying vertical alignments (VGrade) (steep).

Variable Sensitivity and Importance 91   Case Facility, Speed, and Configuration P(K+A) Difference Case 1 (Flat) 2U high-speed (VGrade = −4%) 0.0205 9.8% 2U high-speed (VGrade = 0) 0.0187 4D high-speed (VGrade = −4%) 0.0178 11.3% 4D high-speed (VGrade = 0) 0.0160 Case 2 (Moderate) 2U high-speed (VGrade = −4%) 0.0171 10.6% 2U high-speed (VGrade = 0) 0.0155 4D high-speed (VGrade = −4%) 0.0147 11.6% 4D high-speed (VGrade = 0) 0.0132 Case 3 (Steep) 2U high-speed (VGrade = −4%) 0.0123 11.2% 2U high-speed (VGrade = 0) 0.0110 4D high-speed (VGrade = −4%) 0.0106 12.0% 4D high-speed (VGrade = 0) 0.0094 Table 50. Sensitivity of P(K1A) at a 30-ft clear zone with respect to vertical grade (VGrade). difference between the minimum and maximum P(K+A) values for the range of vertical grade values. The maximum percent difference among the various terrain and facility types is only 12%. Horizontal Alignment Figure 69 through Figure 74 present the distribution of P(K+A) for 2U and 4D facilities and various terrain configurations for different values of roadway horizontal curvature. The hori- zontal curvature (HCurve) is commonly expressed in either the degree of curvature or radius of curvature. The values used in the analyses were 4 degrees of curvature (radius of curvature = 1,432 ft) and 6 degrees of curvature (radius of curvature = 1,432 ft). It can be observed that horizontal curvature has a significant impact on the P(K+A) irrespective of the facility and ter- rain type. The segments with the highest horizontal curvature (HCurve = 6 deg = 1,432 ft) were Figure 69. P(K1A) for 2U facility with varying horizontal alignments (HCurve) (flat).

92 Development of Clear Recovery Area Guidelines Figure 70. P(K1A) for 4D facility with varying horizontal alignments (HCurve) (flat). Figure 71. Probability of fatal/injury crash for 2U facility with varying horizontal alignments (HCurve) (moderate).

Variable Sensitivity and Importance 93   Figure 72. P(K1A) for 4D facility with varying horizontal alignments (HCurve) (moderate). Figure 73. P(K1A) for 2U facility with varying horizontal alignments (HCurve) (steep).

94 Development of Clear Recovery Area Guidelines Figure 74. P(K1A) for 4D facility with varying horizontal alignments (HCurve) (steep). associated with the highest P(K+A) across the entire clear zone distance spectrum. On the other hand, the tangent segments have the lowest P(K+A) values. Further, the 2U facilities have a slightly higher P(K+A) compared to 4D facilities, but the sensitivity [range of P(K+A)] is greater for 4D than 2U. Table 51 shows a significant percent difference for all terrain types, with the steep terrain on a 4D facility type having a difference of 76%. Shoulder Width The variation of P(K+A) with changes in shoulder width is presented in Figure 75 through Figure 80. As can be seen in these figures, the change in shoulder width over a range from 2 ft to 12 ft has only a small impact on the P(K+A) irrespective of the facility type or terrain con- figuration. The P(K+A) values are slightly higher for 2U facilities compared to 4D facilities. Case Facility, Speed, and Configuration P(K+A) Difference Case 1 (Flat) 2U high-speed (HCurve = 6 deg/955 ft radius) 0.0264 41.5% 2U high-speed (HCurve = 0) 0.0187 4D high-speed (HCurve = 6 deg/955 ft radius) 0.0246 54.4% 4D high-speed (HCurve = 0) 0.0160 Case 2 (Moderate) 2U high-speed (HCurve = 6 deg/955 ft radius) 0.0231 48.9% 2U high-speed (HCurve = 0) 0.0155 4D high-speed (HCurve = 6 deg/955 ft radius) 0.0217 64.8% 4D high-speed (HCurve = 0) 0.0132 Case 3 (Steep) 2U high-speed (HCurve = 6 deg/955 ft radius) 0.0173 57.0% 2U high-speed (HCurve = 0) 0.0110 4D high-speed (HCurve = 6 deg/955 ft radius) 0.0166 75.9% 4D high-speed (HCurve = 0) 0.0094 Table 51. Sensitivity of P(K1A) at a 30-ft clear zone with respect to horizontal alignment (HCurve).

Variable Sensitivity and Importance 95   Figure 75. P(K1A) for 2U facility with varying shoulder widths (flat). Figure 76. P(K1A) for 4D facility with varying shoulder widths (flat).

96 Development of Clear Recovery Area Guidelines P( K+ A) Figure 77. P(K1A) for 2U facility with varying shoulder widths (moderate). Figure 78. P(K1A) for 4D facility with varying shoulder widths (moderate).

Variable Sensitivity and Importance 97   Figure 79. P(K1A) for 2U facility with varying shoulder widths (steep). Figure 80. P(K1A) for 4D facility with varying shoulder widths (steep).

98 Development of Clear Recovery Area Guidelines Table 52 shows the percent difference in P(K+A) values for the different facility types and terrain configurations at a clear zone distance of 30 ft. The highest variation of 24.8% occurs for the steep terrain. Foreslope Ratio Figure 81 through Figure 86 present the distribution of P(K+A) for varying foreslope ratios. Overall, steeper slopes have a lower impact on P(K+A). It can be observed that foreslope ratios of 1V:10H and 1V:6H have the smallest change, while the largest change in P(K+A) occurs between 1V:4H and 1V:3H slopes. Table 53 shows the largest relative difference (16.6%) is associated with the steep terrain case. Case Facility, Speed, and Configuration P(K+A) Difference Case 1 (Flat) 2U high-speed (shoulder width = 12 ft) 0.0206 10.5% 2U high-speed (shoulder width = 2 ft) 0.0187 4D high-speed (shoulder width = 12 ft) 0.0177 10.6% 4D high-speed (shoulder width = 2 ft) 0.0160 Case 2 (Moderate) 2U high-speed (shoulder width = 12 ft) 0.0177 14.4% 2U high-speed (shoulder width = 2 ft) 0.0155 4D high-speed (shoulder width = 12 ft) 0.0151 14.3% 4D high-speed (shoulder width = 2 ft) 0.0132 Case 3 (Steep) 2U high-speed (shoulder width = 12 ft) 0.0138 24.8% 2U high-speed (shoulder width = 2 ft) 0.0110 4D high-speed (shoulder width = 12 ft) 0.0116 23.3% 4D high-speed (shoulder width = 2 ft) 0.0094 Table 52. Sensitivity of P(K1A) at a 30-ft clear zone with respect to shoulder widths. P( K+ A) Figure 81. P(K1A) for 2U facility with varying foreslope ratio (flat).

Variable Sensitivity and Importance 99   P( K+ A) Figure 82. P(K1A) for 4D facility with varying foreslope ratio (flat). P( K+ A) Figure 83. P(K1A) for 2U facility with varying foreslope ratio (moderate).

100 Development of Clear Recovery Area Guidelines P( K+ A) Figure 84. P(K1A) for 4D facility with varying foreslope ratio (moderate). P( K+ A) Figure 85. P(K1A) for 2U facility with varying foreslope ratio (steep).

Variable Sensitivity and Importance 101   P( K+ A) Figure 86. P(K1A) for 4D facility with varying foreslope ratio (steep). Case Facility, Speed, and Configuration P(K+A) Difference Case 1 (Flat) 2U high-speed (foreslope = 1V:10H) 0.0187 6.3% 2U high-speed (foreslope = 1V:3H) 0.0176 4D high-speed (foreslope = 1V:10H) 0.0160 4.9% 4D high-speed (foreslope = 1V:3H) 0.0152 Case 2 (Moderate) 2U high-speed (foreslope = 1V:10H) 0.0157 9.2% 2U high-speed (foreslope = 1V:3H) 0.0144 4D high-speed (foreslope = 1V:10H) 0.0133 8.1% 4D high-speed (foreslope = 1V:3H) 0.0123 Case 3 (Steep) 2U high-speed (foreslope = 1V:10H) 0.0129 16.6% 2U high-speed (foreslope = 1V:3H) 0.0110 4D high-speed (foreslope = 1V:10H) 0.0109 15.1% 4D high-speed (foreslope = 1V:3H) 0.0094 Table 53. Sensitivity of P(K1A) at a 30-ft clear zone with respect to foreslope ratio. Foreslope Width As shown in Figure 87 through Figure 92, wider foreslopes are associated with higher P(K+A) irrespective of the facility type and terrain configuration. The differences in P(K+A) for the two facility types are relatively similar, but the 2U facility has a higher magnitude of P(K+A) com- pared to 4D facilities. Table 54 shows that 4D facilities have a relatively higher percent change in P(K+A), with the highest difference (27.6%) observed for the steep terrain. Ditch Bottom Width Figure  93 through Figure  98 show that wider ditch bottoms are associated with higher P(K+A) irrespective of facility type or terrain configuration. This is likely attributed to the

102 Development of Clear Recovery Area Guidelines P( K+ A) Figure 87. P(K1A) for 2U facility with varying foreslope widths (FSW) (flat). P( K+ A) Figure 88. P(K1A) for 4D facility with varying foreslope widths (FSW) (flat).

Variable Sensitivity and Importance 103   P( K+ A) Figure 89. P(K1A) for 2U facility with varying foreslope widths (FSW) (moderate). P( K+ A) Figure 90. P(K1A) for 4D facility with varying foreslope widths (FSW) (moderate).

104 Development of Clear Recovery Area Guidelines P( K+ A) Figure 91. P(K1A) for 2U facility with varying foreslope widths (FSW) (steep). P( K+ A) Figure 92. P(K1A) for 4D facility with varying foreslope widths (FSW) (steep).

Variable Sensitivity and Importance 105   Case Facility, Speed, and Configuration P(K+A) Difference Case 1 (Flat) 2U high-speed (FSW = 16 ft) 0.0187 17.5% 2U high-speed (FSW = 8 ft) 0.0159 4D high-speed (FSW = 16 ft) 0.0160 20.6% 4D high-speed (FSW = 8 ft) 0.0132 Case 2 (Moderate) 2U high-speed (FSW = 16 ft) 0.0155 19.9% 2U high-speed (FSW = 8 ft) 0.0129 4D high-speed (FSW = 16 ft) 0.0132 23.1% 4D high-speed (FSW = 8 ft) 0.0107 Case 3 (Steep) 2U high-speed (FSW = 16 ft) 0.0110 24.8% 2U high-speed (FSW = 8 ft) 0.0089 4D high-speed (FSW = 16 ft) 0.0094 27.6% 4D high-speed (FSW = 8 ft) 0.0074 Table 54. Sensitivity of P(K1A) at a 30-ft clear zone with respect to foreslope widths (FSW). P( K+ A) Figure 93. P(K1A) for 2U facility with varying ditch bottom widths (BtW) (flat).

106 Development of Clear Recovery Area Guidelines P( K+ A) Figure 94. P(K1A) for 4D facility with varying ditch bottom widths (BtW) (flat). P( K+ A) Figure 95. P(K1A) for 2U facility with varying ditch bottom widths (BtW) (moderate).

Variable Sensitivity and Importance 107   P( K+ A) Figure 96. P(K1A) for 4D facility with varying ditch bottom widths (BtW) (moderate). P( K+ A) Figure 97. P(K1A) for 2U facility with varying ditch bottom widths (BtW) (steep).

108 Development of Clear Recovery Area Guidelines vehicle maintaining more speed based on the further offset of the backslope. The lowest values of P(K+A) are obtained for the V-ditch profiles (BtW = 0). Table 55 shows a 36.2% difference in P(K+A) values at a 30-ft clear zone distance for the steep terrain case. Backslope Ratio Figure 99 through Figure 104 show that flatter backslope ratios have higher P(K+A) compared to steeper backslopes. This is likely attributed to a steeper backslope producing a greater reduc- tion in vehicle speed prior to impacting an obstacle at the clear zone edge. Additionally, the sen- sitivity results in Table 56 show significant differences in P(K+A) with changes in the backslope ratio with the highest change (61.1%) occurring for the steep terrain case. P( K+ A) Figure 98. P(K1A) for 4D facility with varying ditch bottom widths (BtW) (steep). Case Facility, Speed, and Configuration P(K+A) Difference Case 1 (Flat) 2U high-speed (BtW = 10 ft) 0.0219 17.4% 2U high-speed (BtW = 0) 0.0187 4D high-speed (BtW = 10 ft) 0.0188 17.8% 4D high-speed (BtW = 0) 0.0160 Case 2 (Moderate) 2U high-speed (BtW = 10 ft) 0.0187 20.8% 2U high-speed (BtW = 0) 0.0155 4D high-speed (BtW = 10 ft) 0.0160 21.1% 4D high-speed (BtW = 0) 0.0132 Case 3 (Steep) 2U high-speed (BtW = 10 ft) 0.0150 36.2% 2U high-speed (BtW = 0) 0.0110 4D high-speed (BtW = 10 ft) 0.0127 34.2% 4D high-speed (BtW = 0) 0.0094 Table 55. Sensitivity of P(K1A) at a 30-ft clear zone with respect to ditch bottom widths (BtW).

Variable Sensitivity and Importance 109   P( K+ A) Figure 99. P(K1A) for 2U facility with varying backslope ratio (flat). P( K+ A) Figure 100. P(K1A) for 4D facility with varying backslope ratio (flat).

110 Development of Clear Recovery Area Guidelines P( K+ A) Figure 101. P(K1A) for 2U facility with varying backslope ratio (moderate). P( K+ A) Figure 102. P(K1A) for 4D facility with varying backslope ratio (moderate).

Variable Sensitivity and Importance 111   P( K+ A) Figure 103. P(K1A) for 2U facility with varying backslope ratio (steep). P( K+ A) Figure 104. P(K1A) for 4D facility with varying backslope ratio (steep).

112 Development of Clear Recovery Area Guidelines Case Facility, Speed, and Configuration P(K+A) Difference Case 1 (Flat) 2U high-speed (backslope ratio = 1V:6H) 0.0187 44.9% 2U high-speed (backslope ratio = 1V:2H) 0.0129 4D high-speed (backslope ratio = 1V:6H) 0.0160 46.8% 4D high-speed (backslope ratio = 1V:2H) 0.0109 Case 2 (Moderate) 2U high-speed (backslope ratio = 1V:6H) 0.0184 45.6% 2U high-speed (backslope ratio = 1V:2H) 0.0126 4D high-speed (backslope ratio = 1V:6H) 0.0158 48.5% 4D high-speed (backslope ratio = 1V:2H) 0.0107 Case 3 (Steep) 2U high-speed (backslope ratio = 1V:6H) 0.0176 59.0% 2U high-speed (backslope ratio = 1V:2H) 0.0110 4D high-speed (backslope ratio = 1V:6H) 0.0152 61.1% 4D high-speed (backslope ratio = 1V:2H) 0.0094 Table 56. Sensitivity of P(K1A) at a 30-ft clear zone with respect to backslope ratio. Backslope Width The variation of P(K+A) with changes in backslope width is presented in Figure 105 through Figure 110. As can be seen in these figures, the changes in P(K+A) associated with backslope widths of 8 ft and 16 ft are consistently small. As shown in Table 57, the maximum percent dif- ference in P(K+A) for backslope widths analyzed is less than 10%. Summary An analysis was performed to investigate the relative sensitivity of parameters—such as impact speed percentile, impact angle percentile, and tree spacing—on the risk of a fatal or serious injury crash [P(K+A)]. As anticipated, it was found that the P(K+A) is highly sensitive to these parameters. P( K+ A) Figure 105. P(K1A) for 2U facility with varying backslope widths (BSW) (flat).

Variable Sensitivity and Importance 113   P( K+ A) Figure 106. P(K1A) for 4D facility with varying backslope widths (BSW) (flat). P( K+ A) Figure 107. P(K1A) for 2U facility with varying backslope widths (BSW) (moderate).

114 Development of Clear Recovery Area Guidelines P( K+ A) Figure 108. P(K1A) for 4D facility with varying backslope widths (BSW) (moderate). P( K+ A) Figure 109. P(K1A) for 2U facility with varying backslope widths (BSW) (steep).

Variable Sensitivity and Importance 115   P( K+ A) Figure 110. P(K1A) for 4D facility with varying backslope widths (BSW) (steep). Case Facility, Speed, and Configuration P(K+A) Difference Case 1 (Flat) 2U High-speed (BSW = 8 ft) 0.0187 6.8% 2U High-speed (BSW = 16 ft) 0.0175 4D High-speed (BSW = 8 ft) 0.0160 7.1% 4D High-speed (BSW = 16 ft) 0.0149 Case 2 (Moderate) 2U High-speed (BSW = 8 ft) 0.0155 7.2% 2U High-speed (BSW = 16 ft) 0.0144 4D High-speed (BSW = 8 ft) 0.0132 8.2% 4D High-speed (BSW = 16 ft) 0.0122 Case 3 (Steep) 2U High-speed (BSW = 8 ft) 0.0110 7.7% 2U High-speed (BSW = 16 ft) 0.0103 4D High-speed (BSW = 8 ft) 0.0094 9.3% 4D High-speed (BSW = 16 ft) 0.0086 Table 57. Sensitivity of P(K1A) at a 30-ft clear zone with respect to backslope width (BSW). When selecting values for these parameters for use in the final risk analysis, the researchers wanted to avoid making the guidelines too conservative so that they are no longer practical. Since the weight factors or marginal probabilities determined for the various encroachment variables were based on reported crashes, they tend to be conservative because they do not account for unreported crashes or encroachments. This led the researchers to select the median impact speed and impact angle for use in the guideline development process. Precedence for the use of median or average impact speed and angle percentiles was also found in RSAPv3 (25). When selecting tree spacings to represent different hazard levels at the clear zone edge, consid- eration was given to capturing a reasonable range of conditions from relatively dense to sparse. An initial selection of 100 ft, 200 ft, and 300 ft tree spacings to represent high, medium, and low hazard ratings was later expanded to include tree spacings ranging from 50 ft to 500 ft in the clear

116 Development of Clear Recovery Area Guidelines zone development process. Note that below a certain spacing or density of trees, the projected vehicle envelope (which is a function of the impact angle) ensures an impact will occur if the encroaching vehicle reaches the clear zone edge. A sensitivity analysis was also performed for the different roadway and roadside design vari- ables across different terrain configurations intended to represent relatively flat, moderate, and steep slope conditions. One purpose of the analysis was to identify less-sensitive variables and remove them from the guideline development process given that the risk analysis results will need to be simplified into a practical set of clear zone guidelines. This typically involves reducing the number of variables at some stage in the analysis. The sensitivity analysis permitted some of these decisions to be made prior to the final risk analysis, which simplified the clear zone guide- line development process. Design variables with a high level of sensitivity tend to dominate those with lower sensitivity. Any variable with a relatively low sensitivity is still represented in the analysis but with a single value rather than a variable value. The research team used a 25% variation as the cutoff for design variable inclusion. If the maxi- mum percent change of a design variable across its values in the analysis matrix was less than 25%, the variable was excluded from the guideline development and assigned a mean value in the risk analysis. As presented above, the maximum percent change was typically associated with the steep terrain configuration, which utilized a 1V:3H foreslope and 1V:2H backslope combina- tion. The moderate and flat terrain configurations were generally associated with smaller percent differences in P(K+A). Based on this process, the research team concluded that vertical grade (9.8%–12%), foreslope ratio (6.3%–16.6%), and backslope width (6.8%–9.3%) should be excluded from the guideline development analysis based on their relatively low sensitivity compared to the other design vari- ables. Note that the percent differences shown for each variable represent the range of differences in P(K+A) obtained across the various facility types and terrain configurations. The variables retained for the initial guideline development analysis include horizontal cur- vature (41.5%—75.9%), shoulder width (10.5%—24.8%), foreslope width (17.5%—27.6%), ditch bottom width (17.4%—36.2%), and backslope ratio (44.9%—61.1%). Variable Importance To further aid in the selection of the key variables with significant influence on clear zone estimation, the research team applied the variable-importance approach. In this approach, a linear regression model was prepared, and the capability of the model to predict the P(K+A) was determined. To determine the important variables, the team divided the data into two sets: a training set and a testing set. The training data were used to develop the model, while the testing set was used to examine the prediction capability of the developed model. The training data contained 70% of the entire risk analysis dataset, while the testing data contained the remaining 30%. The team developed linear models for the lower- and higher-posted-speed-limit categories using the training data and tested the accuracy of the model using the testing dataset. The resulting mean square error (MSE) for the lower-posted-speed-limit category was 0.043, while that of the higher-posted-speed-limit category was 0.042. These MSE are small, which implies that the predicted and observed P(K+A) are very similar. The research team then estimated the importance of each variable, which is the relative influ- ence of each variable used in the model in making accurate predictions of P(K+A). Figure 111 presents the relative importance of the various roadway and roadside design variables.

Variable Sensitivity and Importance 117   It can be observed that hazard density and lateral distance are the most important predictors of P(K+A). Horizontal curvature, backslope ratio, ditch bottom width, and foreslope width have the higher importance values. On the other hand, the foreslope ratio and backslope width have low importance in the prediction of P(K+A). Further, facility type, shoulder width, and vertical grade have intermediate importance. It was interesting to note that the importance analysis sup- ported the results of the sensitivity analysis. 0 200 400 600 800 1000 1200 1400 1600 Floreslope ratio Backslope width Vertical grade Shoulder width Facility type Foreslope width Bottom ditch width Backslope Horizontal curve Lateral distance Hazard density Importance Scale V ar ia bl e Medium PSL High PSL Figure 111. Model variable importance. PSL 5 posted speed limit.

Next: Chapter 8 - Recovery Area Guideline Development »
Development of Clear Recovery Area Guidelines Get This Book
×
 Development of Clear Recovery Area Guidelines
Buy Paperback | $97.00
MyNAP members save 10% online.
Login or Register to save!
Download Free PDF

The clear zone concept for roadside design emerged in the mid-1960s as a single distance for lateral clearance that reduced the likelihood of an errant vehicle striking a roadside obstacle. Subsequent recovery area guidance that evolved over the next two decades provided a variable distance expressed in terms of traffic volume, design speed, sideslope, and other roadway and roadside factors.

NCHRP Research Report 1097: Development of Clear Recovery Area Guidelines, from TRB's National Cooperative Highway Research Program, develops updated guidelines for roadside clear zones expressed in terms of key roadway and roadside design parameters. These updated guidelines can aid designers in better understanding the risk associated with roadside encroachments while recognizing and working within the associated design constraints.

READ FREE ONLINE

  1. ×

    Welcome to OpenBook!

    You're looking at OpenBook, NAP.edu's online reading room since 1999. Based on feedback from you, our users, we've made some improvements that make it easier than ever to read thousands of publications on our website.

    Do you want to take a quick tour of the OpenBook's features?

    No Thanks Take a Tour »
  2. ×

    Show this book's table of contents, where you can jump to any chapter by name.

    « Back Next »
  3. ×

    ...or use these buttons to go back to the previous chapter or skip to the next one.

    « Back Next »
  4. ×

    Jump up to the previous page or down to the next one. Also, you can type in a page number and press Enter to go directly to that page in the book.

    « Back Next »
  5. ×

    To search the entire text of this book, type in your search term here and press Enter.

    « Back Next »
  6. ×

    Share a link to this book page on your preferred social network or via email.

    « Back Next »
  7. ×

    View our suggested citation for this chapter.

    « Back Next »
  8. ×

    Ready to take your reading offline? Click here to buy this book in print or download it as a free PDF, if available.

    « Back Next »
Stay Connected!