**Suggested Citation:**"CHAPTER 9. EVALUATION OF POTENTIAL MITIGATION METHODS." 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.

**Suggested Citation:**"CHAPTER 9. EVALUATION OF POTENTIAL MITIGATION METHODS." 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.

**Suggested Citation:**"CHAPTER 9. EVALUATION OF POTENTIAL MITIGATION METHODS." 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.

**Suggested Citation:**"CHAPTER 9. EVALUATION OF POTENTIAL MITIGATION METHODS." 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.

**Suggested Citation:**"CHAPTER 9. EVALUATION OF POTENTIAL MITIGATION METHODS." 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.

**Suggested Citation:**"CHAPTER 9. EVALUATION OF POTENTIAL MITIGATION METHODS." 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.

**Suggested Citation:**"CHAPTER 9. EVALUATION OF POTENTIAL MITIGATION METHODS." 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.

**Suggested Citation:**"CHAPTER 9. EVALUATION OF POTENTIAL MITIGATION METHODS." 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.

**Suggested Citation:**"CHAPTER 9. EVALUATION OF POTENTIAL MITIGATION METHODS." 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.

**Suggested Citation:**"CHAPTER 9. EVALUATION OF POTENTIAL MITIGATION METHODS." 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.

**Suggested Citation:**"CHAPTER 9. EVALUATION OF POTENTIAL MITIGATION METHODS." 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.

**Suggested Citation:**"CHAPTER 9. EVALUATION OF POTENTIAL MITIGATION METHODS." 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.

**Suggested Citation:**"CHAPTER 9. EVALUATION OF POTENTIAL MITIGATION METHODS." 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.

**Suggested Citation:**"CHAPTER 9. EVALUATION OF POTENTIAL MITIGATION METHODS." 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.

**Suggested Citation:**"CHAPTER 9. EVALUATION OF POTENTIAL MITIGATION METHODS." 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.

**Suggested Citation:**"CHAPTER 9. EVALUATION OF POTENTIAL MITIGATION METHODS." 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.

**Suggested Citation:**"CHAPTER 9. EVALUATION OF POTENTIAL MITIGATION METHODS." 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.

**Suggested Citation:**"CHAPTER 9. EVALUATION OF POTENTIAL MITIGATION METHODS." 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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197 CHAPTER 9. EVALUATION OF POTENTIAL MITIGATION METHODS INTRODUCTION Ditch-initiated crashes are currently costing American society about $6.6 billion annually (in 2010 dollars) and, on average, a ditch-initiated crash costs about $127,000 per crash under the current ditch configurations in the field, in which a rollover crash costs about $312,000 and a non-rollover crash costs about $48,000. It is recognized that limited ROW often dictates the configuration of ditches, and in many cases providing an optimal or preferred configuration is not practical. Enclosed drainage systems are expensive and may result in additional requirements for treatment and discharge of the runoff. Other drainage elements, such as culvert ends, inlets, headwalls, and holding basins, may themselves become roadside obstacles. Installing a barrier to shield a ditch reduces the available clear zone, is not cost effective in many cases, and presents maintenance and operational issues. Two strategies identified for mitigating the severity of ditch-related crashes are slope rounding and surface treatment, or ditch paving. These strategies can be applicable to new design or retrofit of existing ditch profiles when crash experience warrants them. However, slope rounding is not a common practice among the states and provinces. Of the states surveyed, only 21% round the top break point, and only 26% round the bottom of the ditch more than 50% of the time. These design options are discussed individually in the following sections. SLOPE ROUNDING Roadside ditches are required in order to accommodate parallel drainage needs along rural highways. However, roadside terrain features such as ditches can be hazardous for errant motorists to traverse. Depending on the encroachment conditions, even cross-sections considered traversable can lead to vehicle instability and overturn. The hazard potential increases with slope steepness. Flattening roadside slopes may enhance safety. However, this is not always possible due to ROW restrictions, cost, and hydraulic demand. One potential mitigation strategy in lieu of slope flattening or shielding is slope rounding. Slope rounding involves rounding the hinge and/or toe of the slope. This practice is believed to provide enhanced safety for motorists who errantly traverse onto the roadside. Risk is reduced because the vehicle maintains contact with the ground for a longer distance, thereby providing the driver greater opportunity to control the vehicle. The AASHTO Guide for Selecting, Locating, and Designing Traffic Barriers defines optimum rounding as the minimum rounding required to keep all tires of a vehicle in contact with the ground. For optimum rounding, the lateral extent of rounding needed varies as a function of shoulder slope, sideslope, and encroachment speed and angle. This guidance was developed primarily from vehicle dynamics and encroachment simulations using the HVOSM. Rounded slope breaks can be more costly to provide depending on the degree of rounding, amount of fill required, and extent of additional ROW needed. When additional ROW is not economical to acquire, the steepness of the backslope can be increased to offset the additional lateral distance required to achieve the desired slope rounding. However, the steeper backslope can offset some of the safety benefits associated with the slope rounding.

198 Rounded slope break points can also be more expensive to maintain, particularly the toe of the slope. Maintaining a well-rounded toe may be difficult due to ditch erosion resulting from hydraulic flow. Maintaining rounding of the slope hinge point is not as problematic but may still require periodic maintenance in some areas depending on factors such as type of soil, vegetation cover, amount of rainfall, and the like. The benefits of slope rounding are not fully understood, and research in this area is limited. In 1993, Ross and Bligh conducted a research study for the Minnesota Department of Transportation to investigate the benefits of rounding the slope hinges at the intersections of shoulders and sideslopes (20). HVOSM simulations were performed to investigate the dynamics of a vehicle as it traversed different roadside shoulder and sideslope configurations. Vehicle encroachment speeds of 45 and 65 mph (72 and 105 km/h) at encroachment angles of 5, 15, 25, 35, and 45 degrees were investigated. Sideslopes of 6H:1V, 4H:1V, and 3H:1V were investigated with a shoulder and roadway cross slope of 25H:1V and 50H:1V, respectively. All simulations were performed using a model of a small passenger car with a return-to-the-road steering input of 8 degrees at the wheels. It was determined that the body-to- terrain contact was an important factor for this analysis. Therefore, a TTI version of the HVOSM (V-3), which provided this type of contact, was used. Curved roadways and V-ditches were not considered in this research, and all roadside ditches were assumed to have flat bottoms. Vehicle overturn was predicted for rounded and unrounded sideslopes for several combinations of encroachment speeds, angles, and ditch configurations. It was determined that high cornering forces due to panic steering, in combination with body-to-terrain contact, resulted in significant vehicular instability. In many cases, this instability led to vehicle overturn. Occupant risk, measured in terms of vehicular accelerations and vehicular stability, was used to estimate an SI for input into a BCA. Results of the BCA were used to develop recommended slope rounding guidelines for freeways and rural arterial roadways as a function of sideslope and AADT (see Table 9.1). While this earlier study provides valuable insight on the benefits of slope rounding, limited resources narrowed the scope of the analyses with regard to cross-sectional parameters, design vehicles, encroachment conditions, and driver response. Roadway curvature was not considered, the ditch was assumed to have a flat bottom with a depth of 5 ft, there was no- rounding at the toe of the slope, and there was no braking as part of the driver response upon leaving the travel way. A more comprehensive study was needed to better understand vehicle response and quantify the benefits of slope rounding. Slope rounding was one of the key mitigation strategies investigated.

199 Table 9.1. AADT range for recommended slope rounding (20). Slope Rounding Parameters Two types of rounding were studied: optimum rounding and constant rounding. As mentioned previously, optimum rounding is defined in the AASHTO Guide for Selecting, Locating, and Designing Traffic Barriers (Barrier Guide) as the minimum rounding required to keep all tires of a vehicle in contact with the ground. Therefore, the lateral extent of rounding needed to achieve this condition varies as a function of the roadside geometry and the encroachment conditions. This condition is contrary to constant rounding, which (as the name implies) has a fixed lateral extent of rounding independent of roadway, roadside, or encroachment variables. The lateral extent of optimum rounding and the rounding curve equations are given in Equations 9.1 and 9.2, respectively, as taken from the AASHTO Guide for Selecting, Locating, and Designing Traffic Barriers. Thirty percent of the states and provinces surveyed stated they use the formula found in the AASHTO Barrier Guide for slope rounding. Formulas developed by the individual states and provinces are used 72% of the time. The AASHTO formula is as follows: (9.1) (9.2) with y, x, and dx in ft, where, e = shoulder slope (ft/ft), positive sloping upward; b/a = reciprocal of embankment slope (ft/ft), positive sloping upward; V = vehicular velocity (ft/sec); ð = vehicular encroachment angle (deg.); and dx = lateral extent of slope rounding (ft).

200 One can see from this formulation that the lateral extent of optimum rounding is a function of shoulder slope, sideslope, and encroachment speed and angle. For example, given a 4% shoulder slope, a 4H:1V sideslope, and design encroachment conditions of 60 mph (97 km/h) and 20 degrees, the lateral extent of optimum rounding is calculated to be 13.8 ft (4.2 m). For the same encroachment conditions and shoulder slope, the lateral extent of optimum rounding for a 6H:1V slope is 8.3 ft (2.5 m). By definition, the lateral extent of rounding, dx, is fixed for constant rounding. To match the curve type used for optimum rounding and provide a relatively smooth transition from shoulder to sideslope, an equal-tangent parabolic curve is proposed for constant rounding. Figure 9.1 illustrates the geometry of the equal-tangent parabolic curve. The general equation for the constant rounding curve is given in Equation 9.3. Figure 9.1. Equal-tangent parabolic rounding. (9.3) where, e = shoulder slope (ft/ft), positive if sloping upward; g = b/a = reciprocal of embankment slope (ft/ft), positive if sloping upward; r = a constant that is the rate of change of grade, (e-g)/L; it is positive for sag curve, negative for crest curve; and L = length of the curve (ft); y and x in ft. The researchers used a lateral extent of rounding of 6 ft (1.8 m) for the evaluation of constant rounding. Ross et al. (20) found that 2-ft (0.6-m) constant rounding was not cost beneficial for the range of conditions investigated. A 6-ft (1.8-m) lateral extent of rounding is more discerning and provides a reasonable variation from the optimal rounding condition, particularly for steeper slopes.

201 Simulated Ditch Configurations As previously discussed, to evaluate the effect slope rounding has on vehicle stability, overturn and the benefit to cost, the two types of slope rounding treatments were simulated and studied: Constant slope rounding: 6 ft (3 ft along shoulder + 3 ft along foreslope). Optimum slope rounding: per AASHTO equation for 60-mph design speed and 15-degree encroachment angle. For each type of slope rounding, simulations were conducted for 16 different ditch configurations as follows: SHW = 6 ft (4% cross slope). FS = 4:1 and 3:1. FSW = 8 and 16 ft. BTW = 4 ft. BS = 4:1 and 2:1. BSW = 8 and 16 ft. That is, all simulated configurations have a 6 ft SHW and 4 ft BTW, and there are 4 FS- BS combinations (2 FS Ã 2 BS), 4 FSW-BSW combinations (2 FSW Ã 2 BSW), and thus a total of 16 FS-FSW-BS-BSW combinations all together. Benefit-Cost Analysis Figure 9.2 shows the NCPE for simulated ditch configurations with and without slope rounding treatments for 4D65. There are 12 plots arranged in 4 rows and 3 columns in the figure. Column 1 contains plots of the NCPEs for no-rounding treatment, Column 2 for constant rounding treatment, and Column 3 for optimum rounding treatment. Different rows show the NCPEs for different FSW-BSW combinations: Row 1 for the 8 ft-8 ft combination, Row 2 for the 16 ft-8 ft combination, Row 3 for the 8 ft-16 ft combination, and Row 4 for the 16 ft-16 ft combination. For the no-rounding scenario in Column 1, the figure shows NCPE values of 20 FS-BS combinations for each of the four FSW-BSW combinations, which are obtained from the analysis of baseline simulation results conducted earlier. For each FSW-BSW combination, contour lines of NCPEs with an equal interval of 0.1 constructed from the 20 NCPE values are presented in the figure as well. Values of several contour lines are labeled, such as 0.2, 0.4, 0.6, 1.2, 2.0, 3.0, and 4.0. In addition, contour lines, as well as their labels, for NCPE values of 0.2, 0.6, and 1.2, are drawn in blue. Note that under the cost-neutral strategy used in this study to develop guidelines, contour lines for NCPE values of 0.2, 0.6, and 1.2 correspond to the design envelopes for sites with ERs of 4.5, 1.5, and 0.75 enc/mys. Similarly, for the constant and optimum rounding plots in Columns 2 and 3, NCPE values for the four simulated FS-BS combinations are shown (in red) for each of the four FSW-BSW combinations. For example, in the constant rounding scenario in Row 1, in which FSW and BSW are both 8 ft, the NCPE value is 0.74 for the 4:1-4:1 FS-BS combination, 1.04 for the 4:1-3:1 combination, 1.54 for the 4:1-2:1 combination, and 2.08 for the 3:1-2:1 combination. The corresponding values for the same set of FS-BS combinations are 0.66, 0.88, 1.49, and 1.87, respectively, for the optimum rounding scenario. In contrast, the NCPE values for the no-

202 rounding scenario are 0.68, 1.14, 1.70, and 2.75, respectively. Note that the NCPE values for the 6:1-6:1 FS-BS combination with no-rounding treatment are also shown in each plot (in gray), which are 0.31 for the two FSW-BSW combinations in Row 1 and Row 2, and 0.27 and 0.32 in Row 3 and Row 4, respectively. The use of these NCPE values to estimate values of those FS-BS combinations that are not simulated will be explained later. Values in parentheses under each NCPE value in the constant and optimum rounding scenarios in Figure 9.2 represent changes in the NCPE value when compared to the same configuration under the no-rounding scenario. These changes are calculated as percentages of the NCPE values in the no-rounding scenario. Taking the 4:1-4:1 (FS-BS) combination in Row 1 as an example, the NCPE value increases from 0.68 in the no-rounding scenario to 0.74 in the constant rounding scenario, an increase of about 8.7% (â(0.74-0.68)*100/0.68%, shown with a positive sign to indicate an increase). For the same configuration, the value decreases from 0.68 to 0.66 in the optimum rounding scenario, a decrease of about 2.4% (â(0.66-0.68)*100/0.68%, shown in negative value to indicate a decrease). These changes are also summarized in Table 9.2. Out of the 32 ditch configurations simulated with slope rounding treatments, 29 of the configurations show some decreases in the NCPE value, and 3 of the configurations show some increases. Overall, both types of slope rounding treatments appear to reduce the encroachment costs and the optimum rounding treatment appears to perform relatively better than the constant rounding treatment for most of the simulated configurations. In addition, the reduction is most significant when FS is 1:3 and BS is 1:2, which is the steepest FS-BS simulated combination. Table 9.2. Change in NCPE value by ditch configuration and slope rounding type (constant rounding, optimum rounding). FS-FSW-BS-BSW Combinations BSW = 8 ft BSW =16 ft BS = 1V:4H BS = 1V:2H BS = 1V:4H BS = 1V:2H FSW=8 ft FS=1V:4H (+8.7%, â2.4%) (â9.5%, â12.2%) (â4.9%, â18.3%) (â0.1%, â6.6%) FS=1V:3H (â8.9%, â22.9%) (â24.6%, â32.2%) (â1.1%, â12.9%) (â13.9%, â18.5%) FSW=16 ft FS=1V:4H (â1.7%, +3.0%) (â12.3%, â11.8%) (â13.1%, â11.2%) (+5.6%, â20.3%) FS=1V:3H (â8.2%, â20.9%) (â23.3%, â24.2%) (â9.5%, â21.0%) (â8.4%, â16.8%) Note: The two values in each parentheses are changes in NCPE values for constant rounding (first value) and optimum rounding (second value) when compared to the values from no-rounding treatment. A positive value indicates an increase and a negative value indicates a decrease. Estimation Procedure and Assumptions To allow for a broader assessment of the effects of slope rounding treatments on encroachment costs beyond the simulated configurations, an estimation procedure is developed to estimate the NCPE values of the 16 FS-BS combinations that are not simulated using the NCPE values from the simulated configurations with the same FSW and BSW. Specifically, for each slope rounding treatment type and FSW-BSW combination, the estimates are made numerically from the 20 NCPE values in the no-rounding scenario and the 4 NCPE values from the slope rounding simulations. The estimation procedure is devised to maximize the use of known information and to preserve the nonlinear property of the NCPE contour lines exhibited in the no-rounding scenarios (see plots in Column 1 of Figure 9.2). An explanation of the notations used in the description of the procedure follows.

203 NCPEno(FSW, BSW, FS, BS) is used to represent the NCPE value of a configuration with FSW, BSW, FS, and BS, and with the no-rounding treatment. Similarly, NCPEcr(FSW, BSW, FS, BS) and NCPEor(FSW, BSW, FS, BS) are used for configurations with constant and optimum rounding treatments, respectively. That is, the subscripts âno,â âcr,â and âorâ are used to distinguish treatment types. The following are some example NCPE values taken from Row 1 of Figure 9.2: No-Rounding: o NCPEno(8ft, 8ft, 6:1, 6:1) = 0.31. o NCPEno(8ft, 8ft, 4:1, 4:1) = 0.68. o NCPEno(8ft, 8ft, 3:1, 4:1) = 1.14. o NCPEno(8ft, 8ft, 4:1, 2:1) = 1.70. o NCPEno(8ft, 8ft, 3:1, 2:1) = 2.75. Constant Rounding: o NCPEcr(8ft, 8ft, 4:1, 4:1) = 0.74. o NCPEcr(8ft, 8ft, 3:1, 4:1) = 1.04. o NCPEcr(8ft, 8ft, 4:1, 2:1) = 1.54. o NCPEcr(8ft, 8ft, 3:1, 2:1) = 2.08. Optimum Rounding: o NCPEor(8ft, 8ft, 4:1, 4:1) = 0.66. o NCPEor(8ft, 8ft, 3:1, 4:1) = 0.88. o NCPEor(8ft, 8ft, 4:1, 2:1) = 1.49. o NCPEor(8ft, 8ft, 3:1, 2:1) = 1.87. For a particular configuration, the change in the NCPE value due to constant and optimum rounding treatments is represented by fcr(FSW, BSW, FS, BS) and for(FSW, BSW, FS, BS), respectively. They are defined as the ratio of the NCPE value of the treatment case over the NCPE value of the none-treatment case, as follows: fcr(FSW, BSW, FS, BS) = NCPEcr(FSW, BSW, FS, BS)/ NCPEno (FSW, BSW, FS, BS). for(FSW, BSW, FS, BS) = NCPEor(FSW, BSW, FS, BS)/ NCPEno (FSW, BSW, FS, BS). The ratio is referred to as the NCPE ratio in the following discussion. It is equal to 1 if no change takes place, less than 1 if a reduction occurs, and greater than 1 if an increase occurs. From the NCPE values discussed above or those percentage changes presented in Table 9.1, users can calculate the ratio for each simulated configuration. Some example NCPE ratios are listed below (again taken from Row 1 of Figure 9.2): Constant Rounding: o fcr(8ft, 8ft, 4:1, 4:1) = 0.74/0.68 = 1.09 (= 1 + 8.7%). o fcr(8ft, 8ft, 3:1, 4:1) = 1.04/1.14 = 0.91 (= 1 â 8.9%). o fcr(8ft, 8ft, 4:1, 2:1) = 1.54/1.70 = 0.91 (= 1 â 9.5%). o fcr(8ft, 8ft, 3:1, 2:1) = 2.08/2.75 = 0.75 (= 1 â 24.6%). Optimum Rounding: o for(8ft, 8ft, 4:1, 4:1) = 0.66/0.68 = 0.97 (= 1 â 2.4%). o for(8ft, 8ft, 3:1, 4:1) = 0.88/1.14 = 0.77 (= 1 â 22.9%). o for(8ft, 8ft, 4:1, 2:1) = 1.49/1.70 = 0.88 (= 1 â 12.2%). o for(8ft, 8ft, 3:1, 2:1) = 1.87/2.75 = 0.68 (= 1 â 32.2%).

204 The objective of the estimation procedure is to estimate the NCPE ratios, fcr(FSW, BSW, FS, BS) and for(FSW, BSW, FS, BS), for those 16 FS-BS combinations that are not simulated. Once these ratios are estimated, NCPEcr(FSW, BSW, FS, BS) and NCPEor(FSW, BSW, FS, BS) can be calculated directly by definition. The following assumptions are used to estimate the NCPE ratios: fcr(FSW, BSW, FS, BS) = for(FSW, BSW, FS, BS) = 1 if NCPEno (FSW, BSW, FS, BS) â¤ NCPEno (FSW, BSW, 6:1, 6:1). That is, no change in NCPE values for those FS-BS combinations that have NCPEno (FSW, BSW, FS, BS) â¤ NCPEno (FSW, BSW, 6:1, 6:1). fcr(FSW, BSW, FS, BS) = fcr(FSW, BSW, 3:1, 2:1) and for(FSW, BSW, FS, BS) = for(FSW, BSW, 3:1, 2:1) if NCPEno (FSW, BSW, FS, BS) â¥ NCPEno (FSW, BSW, 3:1, 2:1). That is, for those combinations that have NCPEno (FSW, BSW, FS, BS) â¥ NCPEno (FSW, BSW, 3:1, 2:1), the ratios fcr(FSW, BSW, 3:1, 2:1) and for(FSW, BSW, 3:1, 2:1) are used as estimates for constant and optimum rounding treatments, respectively. If the NCPE value of a combination is between the NCPE values of two simulated combinations, a linear interpolation of the two NCPE ratios associated with the two simulated combinations is performed to estimate its NCPE ratio. The two simulated combinations need to have the closest NCPE values among all qualified pairs of the simulated combinations. The second assumption limits the maximum reduction in encroachment costs to the level obtained for the 3:1-2:1 FS-BS combination. This assumption produces conservative estimates for more aggressive FS-BS combinations since the actual reductions are likely higher than what are assumed. Based on the estimation procedure, NCPE values for the 16 FS-BS combinations that are not simulated are estimated and presented in Figure 9.3. By using the same interpolation and extrapolation methods as in the no-rounding case, contour maps of NCPE values are then constructed from the estimated NCPE values for the slope rounding cases, which are also shown in Figure 9.3. To take a closer look at the effects of slope rounding, contour lines for NCPE values of 0.2, 0.6, and 1.2 under different slope rounding types are gathered into a single plot for each FSW-BSW combination, as shown in Figure 9.4. Black lines are for no-rounding, red lines are for constant rounding, and blue lines are for optimum rounding. As discussed earlier, under the cost-neutral strategy, contour lines for NCPE values of 0.2, 0.6, and 1.2 correspond to the design envelopes for sites with ERs of 4.5, 1.5, and 0.75 enc/mys. The figure reveals that the effects of slope rounding on the NCPE contour lines of these 3 levels are rather small. The discussion so far is on trapezoidal ditches with a 4-ft bottom width (BTW = 4 ft). Applying the NCPE ratios obtained above for the trapezoidal ditches to estimate the NCPE values for V-ditches (BTW = 0 ft) reveals the estimated NCPE values and associated contour maps, as shown in Figure 9.5, and a comparison of contour lines for the estimated NCPE values of 0.2, 0.6, and 1.2, as shown in Figure 9.6. For comparison purposes, contour lines for the estimated NCPE values of 0.2, 0.6, and 1.2, similar to those in Figures 9.4 and 9.6 for trapezoidal ditches with a 4-ft bottom and V-ditches, are also prepared for 2U55 and presented in Figures 9.7 and 9.8. Again, as revealed in these figures, the effects of slope rounding on the NCPE contour lines of the 3 NCPE levels of interest appear rather small.

205 Summary for Guideline Development In general, both types of slope rounding treatments appear to reduce the encroachment cost in most of the design configurations simulated in this study (29 out of the 32 configurations simulated), and the optimum rounding appears to perform better than the constant rounding for most of the simulated configurations. However, the reductions in cost are not high enough to require a modification of the recommended design envelopes.

206 Figure 9.2. NCPE for simulated ditch configurations with and without slope rounding treatments: 4D65, BTW = 4 ft.

207 Figure 9.3. NCPE contour maps constructed from simulated configurations with and without slope rounding treatments: 4D65, BTW = 4 ft.

208 Figure 9.4. Contour lines for NCPE values of 0.2, 0.6, and 1.2 for ditches with and without slope rounding treatments: 4D65, BTW = 4 ft.

209 Figure 9.5. NCPE contour maps constructed from simulated configurations with and without slope rounding treatments: 4D65, BTW = 0 ft.

210 Figure 9.6. NCPE contour lines of 0.2, 0.6, and 1.2 for ditches with and without slope rounding treatments: 4D65, BTW = 0 ft.

211 Figure 9.7. NCPE contour lines of 0.2, 0.6, and 1.2 for ditches with and without slope rounding treatments: 2U55, BTW = 4 ft.

212 Figure 9.8. NCPE contour lines of 0.2, 0.6, and 1.2 for ditches with and without slope rounding treatments: 2U55, BTW = 0 ft.

213 SURFACE TREATMENTS As determined from the survey of participating states, the most common surface treatment used is vegetation, followed by turf. The least used surface treatments are road base, ditch paving, and gravel. The two surface treatments investigated were pavement and roadbase treatments. The BCA results for these two surface treatment are presented in Figure 9.9. The first column in this figure represents the untreated condition. Pavement and roadbase treatments are presented Columns 2 and 3, respectively. These maps are for 2U55. Row by row, it can be seen how the contour map changes from one column to another, with a special focus on the variation of the contour line with a NCPE of 0.6. The interactive effects of each of these variables with FSW and BSW can be similarly examined by comparing the maps between rows. Examination of Figure 9.9, with an emphasis on the contour line of interest (NCPE = 0.6), indicates that the effects of the analyzed surface treatments are very small. In fact, for some ditch configurations, there is an actual increase in encroachment cost compared to the untreated ditch surface. Consequently, it is not cost effective to incorporate surface treatments into the ditch design guidelines.

214 Figure 9.9. NCPE contour maps for varying surface treatments.