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Guidelines for Cost-Effective Safety Treatments of Roadside Ditches (2021)

Chapter: CHAPTER 8. EVALUATION OF DITCH DESIGN VARIABLES

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Suggested Citation:"CHAPTER 8. EVALUATION OF DITCH DESIGN VARIABLES." National Academies of Sciences, Engineering, and Medicine. 2021. Guidelines for Cost-Effective Safety Treatments of Roadside Ditches. Washington, DC: The National Academies Press. doi: 10.17226/26127.
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Suggested Citation:"CHAPTER 8. EVALUATION OF DITCH DESIGN VARIABLES." National Academies of Sciences, Engineering, and Medicine. 2021. Guidelines for Cost-Effective Safety Treatments of Roadside Ditches. Washington, DC: The National Academies Press. doi: 10.17226/26127.
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Suggested Citation:"CHAPTER 8. EVALUATION OF DITCH DESIGN VARIABLES." National Academies of Sciences, Engineering, and Medicine. 2021. Guidelines for Cost-Effective Safety Treatments of Roadside Ditches. Washington, DC: The National Academies Press. doi: 10.17226/26127.
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Suggested Citation:"CHAPTER 8. EVALUATION OF DITCH DESIGN VARIABLES." National Academies of Sciences, Engineering, and Medicine. 2021. Guidelines for Cost-Effective Safety Treatments of Roadside Ditches. Washington, DC: The National Academies Press. doi: 10.17226/26127.
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Suggested Citation:"CHAPTER 8. EVALUATION OF DITCH DESIGN VARIABLES." National Academies of Sciences, Engineering, and Medicine. 2021. Guidelines for Cost-Effective Safety Treatments of Roadside Ditches. Washington, DC: The National Academies Press. doi: 10.17226/26127.
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Suggested Citation:"CHAPTER 8. EVALUATION OF DITCH DESIGN VARIABLES." National Academies of Sciences, Engineering, and Medicine. 2021. Guidelines for Cost-Effective Safety Treatments of Roadside Ditches. Washington, DC: The National Academies Press. doi: 10.17226/26127.
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Suggested Citation:"CHAPTER 8. EVALUATION OF DITCH DESIGN VARIABLES." National Academies of Sciences, Engineering, and Medicine. 2021. Guidelines for Cost-Effective Safety Treatments of Roadside Ditches. Washington, DC: The National Academies Press. doi: 10.17226/26127.
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Suggested Citation:"CHAPTER 8. EVALUATION OF DITCH DESIGN VARIABLES." National Academies of Sciences, Engineering, and Medicine. 2021. Guidelines for Cost-Effective Safety Treatments of Roadside Ditches. Washington, DC: The National Academies Press. doi: 10.17226/26127.
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Suggested Citation:"CHAPTER 8. EVALUATION OF DITCH DESIGN VARIABLES." National Academies of Sciences, Engineering, and Medicine. 2021. Guidelines for Cost-Effective Safety Treatments of Roadside Ditches. Washington, DC: The National Academies Press. doi: 10.17226/26127.
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Suggested Citation:"CHAPTER 8. EVALUATION OF DITCH DESIGN VARIABLES." National Academies of Sciences, Engineering, and Medicine. 2021. Guidelines for Cost-Effective Safety Treatments of Roadside Ditches. Washington, DC: The National Academies Press. doi: 10.17226/26127.
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Suggested Citation:"CHAPTER 8. EVALUATION OF DITCH DESIGN VARIABLES." National Academies of Sciences, Engineering, and Medicine. 2021. Guidelines for Cost-Effective Safety Treatments of Roadside Ditches. Washington, DC: The National Academies Press. doi: 10.17226/26127.
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Suggested Citation:"CHAPTER 8. EVALUATION OF DITCH DESIGN VARIABLES." National Academies of Sciences, Engineering, and Medicine. 2021. Guidelines for Cost-Effective Safety Treatments of Roadside Ditches. Washington, DC: The National Academies Press. doi: 10.17226/26127.
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Suggested Citation:"CHAPTER 8. EVALUATION OF DITCH DESIGN VARIABLES." National Academies of Sciences, Engineering, and Medicine. 2021. Guidelines for Cost-Effective Safety Treatments of Roadside Ditches. Washington, DC: The National Academies Press. doi: 10.17226/26127.
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Suggested Citation:"CHAPTER 8. EVALUATION OF DITCH DESIGN VARIABLES." National Academies of Sciences, Engineering, and Medicine. 2021. Guidelines for Cost-Effective Safety Treatments of Roadside Ditches. Washington, DC: The National Academies Press. doi: 10.17226/26127.
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Suggested Citation:"CHAPTER 8. EVALUATION OF DITCH DESIGN VARIABLES." National Academies of Sciences, Engineering, and Medicine. 2021. Guidelines for Cost-Effective Safety Treatments of Roadside Ditches. Washington, DC: The National Academies Press. doi: 10.17226/26127.
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Suggested Citation:"CHAPTER 8. EVALUATION OF DITCH DESIGN VARIABLES." National Academies of Sciences, Engineering, and Medicine. 2021. Guidelines for Cost-Effective Safety Treatments of Roadside Ditches. Washington, DC: The National Academies Press. doi: 10.17226/26127.
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Suggested Citation:"CHAPTER 8. EVALUATION OF DITCH DESIGN VARIABLES." National Academies of Sciences, Engineering, and Medicine. 2021. Guidelines for Cost-Effective Safety Treatments of Roadside Ditches. Washington, DC: The National Academies Press. doi: 10.17226/26127.
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Suggested Citation:"CHAPTER 8. EVALUATION OF DITCH DESIGN VARIABLES." National Academies of Sciences, Engineering, and Medicine. 2021. Guidelines for Cost-Effective Safety Treatments of Roadside Ditches. Washington, DC: The National Academies Press. doi: 10.17226/26127.
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Suggested Citation:"CHAPTER 8. EVALUATION OF DITCH DESIGN VARIABLES." National Academies of Sciences, Engineering, and Medicine. 2021. Guidelines for Cost-Effective Safety Treatments of Roadside Ditches. Washington, DC: The National Academies Press. doi: 10.17226/26127.
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Suggested Citation:"CHAPTER 8. EVALUATION OF DITCH DESIGN VARIABLES." National Academies of Sciences, Engineering, and Medicine. 2021. Guidelines for Cost-Effective Safety Treatments of Roadside Ditches. Washington, DC: The National Academies Press. doi: 10.17226/26127.
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Suggested Citation:"CHAPTER 8. EVALUATION OF DITCH DESIGN VARIABLES." National Academies of Sciences, Engineering, and Medicine. 2021. Guidelines for Cost-Effective Safety Treatments of Roadside Ditches. Washington, DC: The National Academies Press. doi: 10.17226/26127.
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Suggested Citation:"CHAPTER 8. EVALUATION OF DITCH DESIGN VARIABLES." National Academies of Sciences, Engineering, and Medicine. 2021. Guidelines for Cost-Effective Safety Treatments of Roadside Ditches. Washington, DC: The National Academies Press. doi: 10.17226/26127.
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Suggested Citation:"CHAPTER 8. EVALUATION OF DITCH DESIGN VARIABLES." National Academies of Sciences, Engineering, and Medicine. 2021. Guidelines for Cost-Effective Safety Treatments of Roadside Ditches. Washington, DC: The National Academies Press. doi: 10.17226/26127.
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Suggested Citation:"CHAPTER 8. EVALUATION OF DITCH DESIGN VARIABLES." National Academies of Sciences, Engineering, and Medicine. 2021. Guidelines for Cost-Effective Safety Treatments of Roadside Ditches. Washington, DC: The National Academies Press. doi: 10.17226/26127.
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Suggested Citation:"CHAPTER 8. EVALUATION OF DITCH DESIGN VARIABLES." National Academies of Sciences, Engineering, and Medicine. 2021. Guidelines for Cost-Effective Safety Treatments of Roadside Ditches. Washington, DC: The National Academies Press. doi: 10.17226/26127.
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Suggested Citation:"CHAPTER 8. EVALUATION OF DITCH DESIGN VARIABLES." National Academies of Sciences, Engineering, and Medicine. 2021. Guidelines for Cost-Effective Safety Treatments of Roadside Ditches. Washington, DC: The National Academies Press. doi: 10.17226/26127.
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Suggested Citation:"CHAPTER 8. EVALUATION OF DITCH DESIGN VARIABLES." National Academies of Sciences, Engineering, and Medicine. 2021. Guidelines for Cost-Effective Safety Treatments of Roadside Ditches. Washington, DC: The National Academies Press. doi: 10.17226/26127.
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Suggested Citation:"CHAPTER 8. EVALUATION OF DITCH DESIGN VARIABLES." National Academies of Sciences, Engineering, and Medicine. 2021. Guidelines for Cost-Effective Safety Treatments of Roadside Ditches. Washington, DC: The National Academies Press. doi: 10.17226/26127.
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Suggested Citation:"CHAPTER 8. EVALUATION OF DITCH DESIGN VARIABLES." National Academies of Sciences, Engineering, and Medicine. 2021. Guidelines for Cost-Effective Safety Treatments of Roadside Ditches. Washington, DC: The National Academies Press. doi: 10.17226/26127.
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Suggested Citation:"CHAPTER 8. EVALUATION OF DITCH DESIGN VARIABLES." National Academies of Sciences, Engineering, and Medicine. 2021. Guidelines for Cost-Effective Safety Treatments of Roadside Ditches. Washington, DC: The National Academies Press. doi: 10.17226/26127.
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Suggested Citation:"CHAPTER 8. EVALUATION OF DITCH DESIGN VARIABLES." National Academies of Sciences, Engineering, and Medicine. 2021. Guidelines for Cost-Effective Safety Treatments of Roadside Ditches. Washington, DC: The National Academies Press. doi: 10.17226/26127.
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Suggested Citation:"CHAPTER 8. EVALUATION OF DITCH DESIGN VARIABLES." National Academies of Sciences, Engineering, and Medicine. 2021. Guidelines for Cost-Effective Safety Treatments of Roadside Ditches. Washington, DC: The National Academies Press. doi: 10.17226/26127.
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Suggested Citation:"CHAPTER 8. EVALUATION OF DITCH DESIGN VARIABLES." National Academies of Sciences, Engineering, and Medicine. 2021. Guidelines for Cost-Effective Safety Treatments of Roadside Ditches. Washington, DC: The National Academies Press. doi: 10.17226/26127.
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Suggested Citation:"CHAPTER 8. EVALUATION OF DITCH DESIGN VARIABLES." National Academies of Sciences, Engineering, and Medicine. 2021. Guidelines for Cost-Effective Safety Treatments of Roadside Ditches. Washington, DC: The National Academies Press. doi: 10.17226/26127.
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Suggested Citation:"CHAPTER 8. EVALUATION OF DITCH DESIGN VARIABLES." National Academies of Sciences, Engineering, and Medicine. 2021. Guidelines for Cost-Effective Safety Treatments of Roadside Ditches. Washington, DC: The National Academies Press. doi: 10.17226/26127.
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Suggested Citation:"CHAPTER 8. EVALUATION OF DITCH DESIGN VARIABLES." National Academies of Sciences, Engineering, and Medicine. 2021. Guidelines for Cost-Effective Safety Treatments of Roadside Ditches. Washington, DC: The National Academies Press. doi: 10.17226/26127.
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Suggested Citation:"CHAPTER 8. EVALUATION OF DITCH DESIGN VARIABLES." National Academies of Sciences, Engineering, and Medicine. 2021. Guidelines for Cost-Effective Safety Treatments of Roadside Ditches. Washington, DC: The National Academies Press. doi: 10.17226/26127.
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Suggested Citation:"CHAPTER 8. EVALUATION OF DITCH DESIGN VARIABLES." National Academies of Sciences, Engineering, and Medicine. 2021. Guidelines for Cost-Effective Safety Treatments of Roadside Ditches. Washington, DC: The National Academies Press. doi: 10.17226/26127.
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Suggested Citation:"CHAPTER 8. EVALUATION OF DITCH DESIGN VARIABLES." National Academies of Sciences, Engineering, and Medicine. 2021. Guidelines for Cost-Effective Safety Treatments of Roadside Ditches. Washington, DC: The National Academies Press. doi: 10.17226/26127.
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Suggested Citation:"CHAPTER 8. EVALUATION OF DITCH DESIGN VARIABLES." National Academies of Sciences, Engineering, and Medicine. 2021. Guidelines for Cost-Effective Safety Treatments of Roadside Ditches. Washington, DC: The National Academies Press. doi: 10.17226/26127.
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Suggested Citation:"CHAPTER 8. EVALUATION OF DITCH DESIGN VARIABLES." National Academies of Sciences, Engineering, and Medicine. 2021. Guidelines for Cost-Effective Safety Treatments of Roadside Ditches. Washington, DC: The National Academies Press. doi: 10.17226/26127.
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Suggested Citation:"CHAPTER 8. EVALUATION OF DITCH DESIGN VARIABLES." National Academies of Sciences, Engineering, and Medicine. 2021. Guidelines for Cost-Effective Safety Treatments of Roadside Ditches. Washington, DC: The National Academies Press. doi: 10.17226/26127.
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Suggested Citation:"CHAPTER 8. EVALUATION OF DITCH DESIGN VARIABLES." National Academies of Sciences, Engineering, and Medicine. 2021. Guidelines for Cost-Effective Safety Treatments of Roadside Ditches. Washington, DC: The National Academies Press. doi: 10.17226/26127.
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Suggested Citation:"CHAPTER 8. EVALUATION OF DITCH DESIGN VARIABLES." National Academies of Sciences, Engineering, and Medicine. 2021. Guidelines for Cost-Effective Safety Treatments of Roadside Ditches. Washington, DC: The National Academies Press. doi: 10.17226/26127.
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Suggested Citation:"CHAPTER 8. EVALUATION OF DITCH DESIGN VARIABLES." National Academies of Sciences, Engineering, and Medicine. 2021. Guidelines for Cost-Effective Safety Treatments of Roadside Ditches. Washington, DC: The National Academies Press. doi: 10.17226/26127.
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150 CHAPTER 8. EVALUATION OF DITCH DESIGN VARIABLES PROBABILITY-WEIGHTED SIMULATION RESULTS AS A FUNCTION OF LATERAL DISTANCE The simulation outcomes were used to analyze each of the simulated roadway ditch configurations and the design variables of interest. Various exploratory data analysis efforts were performed to better understand the characteristics of the encroachments in aggregate. These analyses included the following: Exceedance probability of the extent of lateral encroachments by encroached vehicles (which can be used to predict the probability that an encroached vehicle would traverse beyond a certain lateral distance). Cumulative rollover probability as a function of the extent of the lateral distance reached by an encroaching vehicle. Cumulative encroachment cost as a function of the extent of the lateral distance reached by an encroaching vehicle. These relationships were plotted for all the simulated baseline configurations on two- lane, two-way undivided highways. A selected number of ditch configurations with a PSL of 55 mph are presented for illustrative purposes. The following abbreviations are used to represent shoulder width and geometric elements of ditches in subsequent discussions and related figures: SHW: Shoulder width. FS: Foreslope ratio. FSW: Foreslope width. BTW: Ditch bottom width. BS: Backslope ratio. BSW: Backslope width. Relationship plots for the selected ditch configurations are arranged into six figures. Two figures are included for each of the three performance measures. Figure 8.1 shows the exceedance probability of lateral extent of encroachment for ditches with various bottom widths. Exceedance probability of lateral extent of encroachment for V-ditches with various shoulder widths is presented in Figure 8.2. Figure 8.3 presents cumulative rollover probability as a function of lateral extent of encroachment for ditches with various bottom widths, while cumulative rollover probability as a function of lateral extent of encroachment for V-ditches with various shoulder widths is presented in Figure 8.4. Figure 8.5 presents cumulative encroachment cost as a function of lateral extent of encroachment for ditches with various bottom widths, while cumulative encroachment cost as a function of lateral extent of encroachment for V-ditches with various shoulder widths is presented in Figure 8.6. All relationships are plotted for a foreslope width and backslope width of 8 ft. Each of these figures (Figures 8.1 through 8.6) contains 12 plots arranged in 4 columns and 3 rows. Different columns show the relationship for ditches with different backslope ratios: 1V:6H (Column 1), 1V:4H (Column 2), 1V:3H (Column 3), and 1V:2H (Column 4). Different rows represent varying ditch bottom widths or shoulder widths, respectively. In each plot, the x- axis is the lateral distance measured from the edgeline of the traveled way, and the y-axis

151 represents one of the three performance measures (i.e., exceedance probability, rollover probability, or cumulative cost). A trapezoidal ditch is depicted as four vertical lines: two thick lines representing the beginning (left line) and end (right line) of the ditch, and two thin lines between them that represent the beginning and end of the ditch bottom. The left thick line coincides with the edge of the shoulder. For V-ditches, there is only a single interior thin line that represents the ditch bottom, which has a width of zero. Each figure represents a particular relationship for 100 different shoulder width-ditch configurations. Some interesting observations regarding how these relationships vary with respect to changes in shoulder width and ditch geometric elements can be made from these plots and are discussed below. Exceedance Probability Exceedance probability can be shown in Figures 8.1 and 8.2. Additional details related to these figures are as follows: In general, ditches with steep foreslopes (e.g., 1V:2H) have a slightly higher exceedance probability than those with a relatively flat foreslope (e.g., 1V:10H) when the lateral distance is within the ditch. However, a complete reverse of the exceedance probability curve occurs when the lateral distance is beyond the ditch. That is, a much higher exceedance probability can be observed for ditches with a relatively flat foreslope than for those with steep foreslopes. In general, except for ditches with a 10-ft BTW, about 30 to 40% of the encroached vehicles climb up and over the backslope of the ditch. For ditches with a 10-ft BTW, about 25 to 30% of the encroached vehicles reach the bottom but do not get to the backslope. The BS serves a significant role in keeping the encroached vehicles from going beyond the ditch, which can be seen from the probability curves in V-ditches (see Figure 8.2). In the curves, about 30 to 40% of the encroached vehicles reach the toe of the backslope but do not go beyond the top of the backslope. By comparing the exceedance probability curves from column to column (and from left to right), it can be observed that the probability for an encroached vehicle to go beyond the entire width of the ditch drops by about 10% as the BS increases from 1V:6H to 1V:2H. For V-ditches with various SHWs (see Figure 8.2), about 13 to 14% of the encroached vehicles do not go beyond the shoulder. Once the encroached vehicles enter the ditch, the great majority of them reach the backslope for V-ditches and trapezoidal BTW of 4 ft. In reference to Figure 8.2, by comparing the probability curves across rows, it can be observed that the exceedance probability decreases slightly faster with lateral distance increases than for ditches with wider shoulders. However, the differences are rather small. Cumulative Rollover Probability Figures 8.3 and 8.4 show cumulative rollover probability. Details related to this are described below: In general, rollover begins to occur after the encroached vehicles reach the backslope area.

152 For V-ditches, a significant percentage of rollovers occur on the backslope. As shown in Figure 8.4, the cumulative probability of rollover curves rises sharply in the backslope area. From all plots, it can be seen that a rather significant percentage of rollovers occur after the encroached vehicles climb up and over the backslope of the ditch. This result often happens in high-speed and angle encroachment conditions due to the vehicle ramping up on a steep backslope and becoming airborne from the ramping effect. V-ditches have a much higher overall rollover probability than trapezoidal ditches with 4-ft bottom width (see Figure 8.4). The increase in rollover probability is more pronounced as the foreslope ratio increases. Increasing BTW from 4 ft to 10 ft reduces the overall rollover probability, but the reduction is not as dramatic. By comparing across columns of Figures 8.3 and 8.4, it can be observed that the rollover probability curve increases as the BS increases. The increase is more pronounced for V- ditches with sharp FSs. Cumulative Encroachment Cost The cumulative encroachment cost curves shown in Figures 8.5 and 8.6 have very similar patterns to the cumulative rollover probability curves. The observations discussed above for the rollover probability curves can be applied to the encroachment cost curves as well.

153 Figure 8.1. Exceedance probability of the extent of lateral encroachments: ditches with various BTWs, SHW = 6 ft, FSW = 8 ft, BSW = 8 ft.

154 Figure 8.2. Exceedance probability of the extent of lateral encroachments: V-ditches with various SHWs, FSW = 8 ft, BSW = 8 ft.

155 Figure 8.3. Cumulative rollover probability as a function of lateral distance: ditches with various BTWs, SHW = 6 ft, FSW = 8 ft, BSW = 8 ft.

156 Figure 8.4. Cumulative rollover probability as function of lateral distance: V-ditches with various SHWs, FSW = 8 ft, BSW = 8 ft.

157 Figure 8.5. Cumulative encroachment cost as a function of lateral distance: ditches with various BTWs, SHW = 6 ft, FSW = 8 ft, BSW = 8 ft.

158 Figure 8.6. Cumulative encroachment cost as a function of lateral distance: V-ditches with various SHWs, FSW = 8 ft, BSW = 8 ft.

159 GUIDELINE DEVELOPMENT The BCA method described in Chapter 5 was used to develop guidelines for the design of roadside ditches. The BCA method takes a large number of roadway, roadside, traffic, and encroachment variables into consideration. Roadway factors include HC and vertical grade. Roadside variables include shoulder width, foreslope ratio, foreslope width, ditch bottom width, backslope ratio, and backslope width. Traffic factors include AADT and traffic growth rate. Encroachment variables include vehicle type, encroachment speed, encroachment angle, and driver input conditions. Details of the computational procedures are provided in Appendix A. The guideline development process involved using crash costs obtained from the BCA to determine preferred design envelopes, in terms of the foreslope and backslope ratios, for different roadway and roadside design conditions and traffic volumes. A set of 80 different design configurations of V-ditches served as a set of baseline conditions. The preferred design envelopes developed for these baseline configurations served as initial guidelines that could then be adjusted for other non-baseline design configurations. The next section illustrates this methodology for a selected default design configuration. Cost Contour Maps with an Equal Contour Interval Figure 8.7 is an illustration of 20 design points representing different foreslope ratio- backslope ratio combinations for a default design configuration (i.e., two-lane, two-way undivided highway with a PSL of 55 mph). The normalized expected crash cost is estimated for each design point. The normalized expected crash cost is the expected crash cost calculated from the crash cost model divided by the real-world per-crash cost presented earlier in Chapter 5. A cost contour line is a curve connecting points where the normalized expected crash cost (per encroachment) has the same value—for example, 1.0, 2.0, or 5.0. A cost contour map consists of cost contour lines representing various normalized crash costs. The contour interval of a cost contour map is the difference in the normalized cost between successive contour lines. A cost contour map with an equal contour interval is a contour map in which the difference in normalized crash cost is the same between any two successive contour lines. Figure 8.8 presents an example contour map with an equal contour interval of 1.0. These contour lines are interpolated from the 20 normalized crash cost points in the design space. In the cost contour maps, the x-axis represents the ditch foreslope ratio, and the y-axis represents the ditch backslope ratio. Each contour line represents the set of foreslope and backslope combinations that are estimated to have the same encroachment cost for the default roadway design configuration. The construction of a cost contour map with an equal contour interval allows assessment of the relative gradient (rate of change) of crash costs. Note that the gradient of the contour lines is the direction of steepest increase in the design space and is perpendicular to the contour lines. When the contour lines are close together, the magnitude of the gradient is large, and the increase in crash cost is steep. The strategy used to select a preferred design envelope for a given design condition is to look for a contour line in the design space prior to the point at which the gradient begins to increase significantly. A steep increase in gradient is an indication that the rollover probability is rapidly increasing, and a relatively small change in ditch configuration can have a significant effect on overall encroachment severity. Figure 8.9 provides an illustration of this

160 selection strategy. The preferred design envelope represents a set of ditch slope combinations for the default design condition beyond which the increase in rollover probability begins to accelerate rapidly as the slopes get steeper. Envelope Adjustment Factors for Baseline Design Condition An envelope adjustment factor (EAF) is developed for each different design configuration to move the preferred design envelope for the default design condition either inward or outward to stay neutral in crash cost. In this manner, the design envelope for each roadway design configuration offers the same level of safety or risk as the default design condition. Figure 8.10 provides an illustration of the EAF. A design configuration that has a higher estimated crash cost than the default design condition will have a higher EAF. In order to reduce the crash cost to the same preferred level selected for the default design condition, the envelope for the new design configuration needs to be moved inward to reduce the crash cost proportionally. Essentially, the permissible foreslope and backslope combinations are more restricted in order to maintain the desired level of safety or risk. On the other hand, a design configuration that has a lower estimated crash cost than the default design condition will have a lower EAF, and its preferred design envelope is allowed to move outward to increase the crash cost proportionally. In other words, steeper foreslope and/or backslope combinations are permissible without increasing encroachment severity. Figure 8.7. An illustration of design points where normalized expected crash costs will be estimated for default design configuration.

161 Figure 8.8. An example cost contour map with equal contour interval. Figure 8.9. An illustration of the strategy to select preferred design envelope based on cost gradient.

162 Figure 8.10. EAF moves preferred envelope for default design condition either inward or outward to stay neutral in crash cost. The EAF concept can be extended to select preferred design envelopes for design variables that include changes in traffic volume (through a change in ER), HC, vertical grade, shoulder width, and ditch bottom width. For example, a condition having a higher EAF, such as a site having a higher ER, will have a contracted design envelope (i.e., the design envelope will move inward and be smaller). A configuration with a lower EAF, such as having a wider shoulder, will have an expanded design envelope that permits consideration of steeper slope combinations (i.e., the preferred envelope will move outward and be larger). This approach enables generation of preferred design envelopes for various design variables and traffic conditions. After analysis of the size, pattern, and sensitivity of these envelopes, they were combined and simplified to develop final ditch design guidelines as described in the sections that follow. Development of Cost Contour Maps This section presents some of the final BCA results for all roadside configurations simulated in this study. It includes rollover probability, encroachment cost, normalized encroachment cost, and cost contour maps for the normalized encroachment costs for the various design configurations. As in the previous section, the results for two-lane, two-way undivided highways with a PSL of 55 mph (2U55) are presented for illustrative purposes. The following abbreviations are used to represent shoulder width and geometric elements of the ditch:

163 SHW: Shoulder width. FS: Foreslope ratio. FSW: Foreslope width. BTW: Ditch bottom width. BS: Backslope ratio. BSW: Backslope width. Two figures are included for each of three performance measures to show how the relationships change as a function of ditch FS for varying BTW and SHW. The plots with varying BTW assume a 6-ft shoulder width, and the plots for different SHW are for V-ditches (i.e., BTW = 0). Figure 8.11 and Figure 8.12 show rollover probability for ditches with various bottom widths and shoulder widths, respectively. Figure 8.13 presents encroachment costs associated with various ditch bottom widths, while encroachment cost for various shoulder widths is presented in Figure 8.14. Figure 8.15 and Figure 8.16 present normalized encroachment cost for ditches with various bottom widths and shoulder widths, respectively. The normalized encroachment cost relationships (shown in Figure 8.15 and Figure 8.16) will be the same as those for cumulative encroachment costs (shown in Figure 8.13 and Figure 8.14). As discussed previously, the normalized encroachment cost is a dimensionless quantity used for ease of understanding and comparison of relationships within the guideline development process. Each of these figures (Figures 8.11 through 8.18) contains 12 plots arranged in 3 columns and 4 rows. Different columns show the performance measures for different ditch BTWs or different SHWs as appropriate. Different rows represent varying combinations of FSW-BSW: FSW = 8 ft and BSW = 8 ft (Row 1), FSW = 16 ft and BSW = 8 ft (Row 2), FSW = 8 ft and BSW = 16 ft (Row 3), and FSW = 16 ft and BSW = 16 ft (Row 4). In each plot, the x-axis is the FS ratio and the y-axis represents one of the three performance measures. In all, 400 different roadside design configurations (shoulder width and ditch combinations) are presented for each performance measure. The rollover probability relationships presented in Figure 8.11 and Figure 8.12 were generated from the simulation data described earlier in Chapter 7. As described in Chapter 5, the crash cost model was then used to calculate the associated expected encroachment cost for each design configurations based on rollover probability. Note that the encroachment cost relationships presented in Figure 8.13 and Figure 8.14 have similar shape to the rollover probability plots. The encroachment cost relationships were then converted to normalized encroachment costs by dividing by the average real-world encroachment cost (i.e., $72,480). In reference to the normalized encroachment cost plots in Figure 8.15 and Figure 8.16, any horizontal line that is parallel to the x-axis represents a certain encroachment cost level. For example, the dotted line shown in each plot in these figures represents a cost level of 1.0. When a horizontal line intersects with more than one encroachment cost curve in the plot, these intersecting points constitute a set of FS-BS combinations with an equal encroachment cost as represented by the line. A cost contour line can be constructed by connecting these intersecting points. A cost contour map with equal contour interval can then be constructed by selecting a set of horizontal lines with equal increment in cost to intersect with the normalized encroachment cost curves.

164 The construction of the cost contour maps presented in Figure 8.17 and Figure 8.18 was based on the selection of 20 horizontal lines representing normalized cost levels from 0.1 to 2.0, with an equal cost increment of 0.1. To smooth out the contour lines, some interpolations and extrapolations were performed. These and similar cost contour maps associated with other design variables of interest were used as a basis to formulate design envelopes, as will be subsequently described. Figure 8.17 and Figure 8.18 provide cost contour maps for varying ditch bottom widths and shoulder widths, respectively. In these cost contour maps, each line represents the set of FS- BS combinations that are estimated to have the same encroachment cost under the specified shoulder width-ditch configuration. A further discussion of cost contour maps and their use in developing design guidelines is presented below.

165 Figure 8.11. Rollover probabilities for varying ditch bottom widths.

166 Figure 8.12. Rollover probabilities for varying shoulder widths.

167 Figure 8.13. Encroachment costs for varying ditch bottom widths.

168 Figure 8.14. Encroachment costs for varying shoulder widths.

169 Figure 8.15. Normalized encroachment costs for varying ditch bottom widths.

170 Figure 8.16. Normalized encroachment costs for varying shoulder widths.

171 Figure 8.17. Cost contour maps for varying ditch bottom widths.

172 Figure 8.18. Cost contour maps for varying shoulder widths.

173 Benefit-Cost Analysis Results and Preliminary Guideline Development This section presents BCA results for all ditch variables considered in the study. It further describes how the BCA results were used to determine the maximum risk level in terms of the expected encroachment cost for developing guidelines for various roadway-roadside configurations. For each roadway-roadside configuration considered, the BCA procedure calculates the expected cost per encroachment (CPE), which is a measure of the level of risk. The CPE is further divided by the average real-world encroachment cost to obtain the normalized cost per encroachment (NCPE). Recall that the NCPE is a dimensionless quantity that is easier to present than the CPE (e.g., 0.84 versus $61,180). As an example, Figure 8.19 shows four NCPE contour maps generated for the baseline ditch configurations (i.e., V-ditches) simulated in this study for two-lane undivided roadways with a PSL of 55 mph. The contour lines in these contour maps have an equal interval of 0.1 in the NCPE, which is equivalent to a difference of $7,248 in the CPE. Recall that the contour line with a value of 1.0 has practical significance in design. It represents a set of ditch configurations with different FS-BS combinations that have a risk level close to the average risk level of ditches currently in the field. As explained earlier in this chapter, the contour map shows the relative gradient of the encroachment cost as the FS-BS combination changes. When the contour lines are close together, the magnitude of the gradient is large, and the increase in encroachment cost is steep. The strategy used to select a preferred design envelope for the baseline ditch condition is to look for a contour line in the map beyond which the gradient begins to increase significantly. For the contour maps in Figure 8.19, the contour line with an NCPE value of 0.6 is a good choice for all four maps, and this is the maximum level of risk (or the default risk) chosen for developing the guidelines. This risk level is equal to about $43,500 per encroachment. For a baseline ditch that has one encroachment per mile per year per side of travelway (per mi-yr-side), this is the design envelope of choice. Note that the contour line representing NCPE = 0.6 falls outside the design envelope for V-ditches currently recommended by the RDG, which is superimposed on the contour maps. Thus, a designer is afforded additional flexibility in the choice of foreslope and backslope combinations for the specified V-ditch conditions.

174 Figure 8.19. NCPE contour maps for base configurations. The contour map can provide a good visual understanding of how the cost varies as the magnitude of certain elements of a ditch is changed. For example, by comparing the contour maps on the left to the map on its immediate right in Figure 8.19, it is possible to see how the

175 cost increases as the FSW increases from 8 ft to 16 ft. It can be seen that when both the FS and BS are steep (the upper right quadrant) the cost increases significantly as the FSW increases (regardless of the BSW). The BCA results are summarized into sets of contour maps that are presented in Figure 8.20 through Figure 8.23. Figure 8.20 presents NCPE contour maps for varying ditch bottom widths, and Figure 8.21 provides NCPE contour maps for varying shoulder widths. Similarly, Figure 8.22 shows NCPE contour maps for varying vertical grades, and Figure 8.23 presents NCPE contour maps for varying HCs. These maps are for 2U55. The effects of these design variables (i.e., ditch bottom width, shoulder width, vertical grade, and HC) on encroachment cost can be evaluated from these figures. This evaluation is accomplished by studying how the contour map changes, with a special focus on the variation of contour line with an NCPE of 0.6. The interactive effects of each of these design variables with FSW and BSW can be similarly examined. A summary of the effect that each design variable has on encroachment severity is as follows: BTW: very significant effect, quite interactive with FSW, and some interaction with BSW. SHW: very weak effect on encroachment severity and vehicle stability. Vertical grade (VG): very weak effect. HC: very significant effect, some interactions with FSW and BSW. The objective was to develop guidelines that incorporate the most significant results from the BCA that are straightforward and easy to use. Based on the above results and observations, the development of the design guidelines focused on the effects of ditch BTW and roadway HC and their interactions with ditch FSW and ditch BSW. The contour lines with an NCPE of 0.6 are pulled together in Figure 8.24 and Figure 8.25 to more clearly see the influence and interaction of these design elements for further guideline development. The same types of relationships were generated for an NCPE of 0.2, 0.3, 0.4, 0.6, 0.9, and 1.2. These results allowed the researchers to generate design envelopes for sites with different ERs (encroachments per mi-yr-side) using the neutral cost strategy described earlier. By careful examination of Figure 8.24 and Figure 8.25 and of similar relationships for the other NCPE values, an initial set of design envelopes was selected and is presented in Figure 8.26 for sites with various ERs (0.3, 0.5, 1.0, 1.5, and 3.0 encroachments per mi-yr-side).

176 Figure 8.20. NCPE contour maps for varying ditch bottom widths.

177 Figure 8.21. NCPE contour maps for varying shoulder widths.

178 Figure 8.22. NCPE contour maps for varying vertical grades.

179 Figure 8.23. NCPE contour maps for varying HCs.

180 Figure 8.24. NCPE = 0.6 for varying BTW, FSW, and BSW.

181 Figure 8.25. NCPE = 0.6 for varying HC, FSW, and BSW.

182 Figure 8.26. Initial design envelopes for sites with ERs of 0.3, 0.5, 1.0, 1.5, and 3.0 per mi-yr-side.

183 Figure 8.26. Initial design envelopes for sites with ERs of 0.3, 0.5, 1.0, 1.5, and 3.0 per mi-yr-side (continued).

184 The same BCA and guideline development process described above for 2U55 was followed for three additional roadway design configurations: Two-lane undivided roadways with a 65-mph PSL (2U65). Four-lane divided roadways with a 55-mph PSL (4D55). Four-lane divided roadways with a 65-mph PSL (4D65). As discussed in Chapter 5, different roadside encroachment conditions, including encroachment speed and angle distributions and ERs, were used to characterize the main differences between these roadways when considering their roadside design needs. As an example of the BCA results, Figure 8.27 shows contour maps of the NCPE for the simulated V- ditches for 4D65 roadways with varying FSWs and BSWs. Figure 8.28 provides a comparison of the contour line with an NCPE of 0.6 for the four roadway design configurations. Recall that an NCPE of 0.6 was selected as the maximum level of risk per encroachment for the guideline development. The design envelopes, as represented by the contour lines (NCPE = 0.6) shown in Figure 8.28, were not different enough to warrant the use of separate guidelines for each roadway-PSL type. Thus, the decision was to simplify the guidelines by using the envelopes developed for the 4D65 roadways for all four roadway-PSL types. The 4D65 roadway configuration represents a conservative selection for FS-BS combinations to maintain the selected risk level. Figure 8.29 presents design envelopes by ER and FSW for relatively straight road sections (i.e., an HC of 3 degrees or less). The figure contains 18 plots. Plots in different rows are for different ERs, which are expressed in number of encroachments per mile per year per side of travelway (enc/mys). The columns are for three different ditch bottom widths (BTW), grouped as follows: Column 1: BTW < 4 ft (i.e., 0–4 ft). Column 2: 4 ft ≤ BTW < 8 ft (i.e., 4–8 ft). Column 3: 8 ft ≤ BTW < 12 ft (i.e., 8–12-) ft). Within each plot, five design envelopes are shown for different FSWs: 4, 8, 12, 16, and 20 ft. In addition to using the strategy of selecting the maximum risk level per encroachment (NCPE = 0.6), these design envelopes were developed using the previously discussed cost- neutral strategy to maintain the same level of expected encroachment costs for sites with different ERs. Note that these curves were smoothed numerically from the originally contour lines and then slightly adjusted manually at some boundary areas where data appeared unreliable. Two similar sets of design envelopes were also developed for sites with HCs greater than or equal to 3 degrees and less than 6 degrees and for those sites with HCs greater than or equal to 6 degrees. These results are presented in Figure 8.30 and Figure 8.31, respectively. Figure 8.29 through Figure 8.31 represent the preferred design envelopes for roadside ditches for roadways with different ranges of HC, namely, <3 degrees, 3 degrees ≤ HC < 6 degrees, and ≥6 degrees, respectively. In addition to HC, these design envelopes are expressed in terms of roadway ERs, ditch bottom width, ditch foreslope width, ditch foreslope ratio, and ditch backslope ratio. As discussed above, these variables were found to have the most influence on the severity of encroachments. However, it is recognized that 54 plots, each with multiple curves,

185 is not ideal for incorporation of design guidance into the AASHTO RDG. Further simplification of the preferred design envelopes into a more practical set of final recommended design guidelines is described in Chapter 10.

186 Figure 8.27. NCPE contour map for simulated V-ditches with varying FSW and BSW: 4D65.

187 Figure 8.28. Comparison of contour lines for NCPE=0.6 for four highway types—PSL combinations.

188 Figure 8.29. Design envelopes for relatively straight sections by ER and foreslope width.

189 Figure 8.29. Design envelopes for relatively straight sections by ER and foreslope width (continued).

190 Figure 8.29. Design envelopes for relatively straight sections by ER and foreslope width (continued).

191 Figure 8.30. Design envelopes for sections with an HC of ≥3 degrees and <6 degrees by ER and foreslope width.

192 Figure 8.30. Design envelopes for sections with an HC of ≥3 degrees and <6 degrees by ER and foreslope width (continued).

193 Figure 8.30. Design envelopes for sections with an HC of ≥3 degrees and <6 degrees by ER and foreslope width (continued).

194 Figure 8.31. Design envelopes for sections with an HC of ≥6 degrees by ER and foreslope width.

195 Figure 8.31. Design envelopes for sections with an HC of ≥6 degrees by ER and foreslope width (continued).

196 Figure 8.31. Design envelopes for sections with an HC of ≥6 degrees by ER and foreslope width (continued).

Next: CHAPTER 9. EVALUATION OF POTENTIAL MITIGATION METHODS »
Guidelines for Cost-Effective Safety Treatments of Roadside Ditches Get This Book
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Run-off-road traffic crashes account for almost one-third of the deaths and serious injuries each year on U.S. highways.

The TRB National Cooperative Highway Research Program's NCHRP Web-Only Document 296: Guidelines for Cost-Effective Safety Treatments of Roadside Ditches provides new proposed design guidance for the configuration of ditches adjacent to the roadway.

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