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

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D-1 APPENDIX D. PROPOSED GUIDELINES

D-2 The roadside ditch design guidelines are presented in Figure D.1 through Figure D.6. Following is a list of variables used in the guidelines. HC—Horizontal curvature (degrees). ER—Encroachment rate (encroachments/mile/year). BTW—Ditch bottom width (ft). Foreslope—Slope of the roadside ditch before ditch bottom. Backslope—Slope of the roadside ditch after ditch bottom. VG—Vertical grade (percent) The guidelines are grouped into three horizontal curvature ranges of (1) less than 3 degrees, (2) greater than or equal to 3 degrees but less than 6 degrees, and (3) equal to or greater than 6 degrees. For each horizontal curvature, the guidelines are further grouped into two ditch bottom width ranges of less than 6 ft and equal to or greater than 6 ft. In each of the figures, preferred design threshold curves for combinations of foreslopes and backslopes are presented. A total of six curves, representing six encroachment rates, are plotted on each graph. An appropriate baseline encroachment rate should be determined from Figure D.7 based on roadway type (divided or undivided) and AADT. The baseline encroachment rate relationships are based on the AADT of the primary side of the road. Thus, a bidirectional AADT should be divided by two, or the appropriate AADT for the primary direction of interest should be used if the AADT for the two directions are not equal. It should be noted that the baseline encroachment rate for divided highways in Figure D.7 accounts for right side departures in the primary direction of travel. The baseline encroachment rate for undivided highways includes both primary right and opposite left side departures across the right side edge. If the roadway segment has horizontal curvature, Table D.1 is used to determine the appropriate adjustment factor for the baseline encroachment rate for the direction of interest. Interpolation can be used to determine the adjustment factor for values of horizontal curvature not listed in the table. The previously determined baseline encroachment rate is multiplied by the horizontal curvature adjustment factor to obtain an adjusted encroachment rate for use in the ditch design guidelines. For a roadway segment with horizontal curvature, the adjustment to the encroachment rate may be different for each side of the roadway. If one side (direction of travel) has a left curve, the other side will have a right curve. If the roadway segment has vertical grade, Table D.2 is used to determine the appropriate adjustment factor for the baseline encroachment rate for the direction of interest. The previously determined baseline encroachment rate is multiplied by the vertical grade adjustment factor to obtain an adjusted encroachment rate for use in the ditch design guidelines. For a roadway segment with vertical grade, the adjustment to the encroachment rate may be different for each side of the roadway. If one side (direction of travel) has a downgrade, the other side will have an upgrade. If the roadway has both horizontal curvature and vertical grade, adjustment factors are determined for both and each is multiplied by the previously determined baseline encroachment rate to obtain an adjusted encroachment rate for use in the ditch design guidelines. The applicable horizontal roadway curvature and desired ditch bottom width are used to select the appropriate design chart from Figure D.1 though Figure D.6. A point is plotted for the

D-3 foreslope and backslope combination of interest on the appropriate chart. If the point falls on or inside the curve representing the adjusted encroachment rate, the foreslope and backslope combination is acceptable. If this point falls outside of the curve for the applicable encroachment rate, the ditch configuration being considered is not within the recommended thresholds of the guideline and adjustment of the slopes and/or ditch bottom width should be considered. If the roadside ditch configuration cannot meet the proposed guidelines, the following guidance from RDG section 3.2.4 is suggested: “Channel sections that fall outside the shaded (acceptable) region are considered less desirable and their use should be limited where high-angle encroachments can be expected, such as outside of relatively sharp curves. Channel sections outside the shaded region may be acceptable for projects having one or more of the following characteristics: restrictive right-of-way environmental constraints; rugged terrain: resurfacing restoration, or rehabilitation (3R) projects; low-volume or low-speed roads and streets, particularly if the channel bottom and backslope are free of any fixed objects or located beyond suggested clear-zone distance. If practical, drainage channels with cross-sections outside the shaded regions and located in vulnerable areas may be reshaped and converted to a closed system (culvert or pipe) or, in some cases, shielded by a traffic barrier.” Two examples are presented below to illustrate the use of the guidelines.

D-4 Figure D.1. Roadside ditch design guidelines for ditch bottom width of less than 6 ft and horizontal curvature of less than 3 degrees. 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 a1 : b1 a 2 : b 2 Ba ck slo pe R at io = a 2 / b 2 Foreslope Ratio = a1 / b1 BTW < 6 ft, HC < 3 degrees 1:10 1:8 1:6 1:5 1:4 1:3 1:2 | | | | | | -1:8 -1:6 1:2 -1:3 -1:4 -1:5 -1:10

D-5 Figure D.2. Roadside ditch design guidelines for ditch bottom width of greater than or equal to 6 ft and horizontal curvature of less than 3 degrees. 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 Ba ck slo pe R at io = a 2 / b 2 Foreslope Ratio = a1 / b1 BTW ≥ 6ft, HC < 3 degrees 1:10 1:8 1:6 1:5 1:4 1:3 1:21:2 1:3 1:5 1:10 1:8 1:6 1:4

D-6 Figure D.3. Roadside ditch design guidelines for ditch bottom width of less than 6 ft and horizontal curvature of greater than or equal to 3 degrees and less than 6 degrees. 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 a1 : b1 Ba ck slo pe R at io = a2 / b 2 Foreslope Ratio = a1 / b1 BTW < 6ft, 3 degrees ≤ HC < 6 degrees 1:10 1:8 1:6 1:5 1:4 1:3 1:2 | | | | | | 1:2 -1:3 -1:4 -1:10 -1:6 -1:8 a 2 : b 2 -1:5

D-7 Figure D.4. Roadside ditch design guidelines for ditch bottom width of greater than or equal to 6 ft and horizontal curvature greater than or equal to 3 degrees and less than 6 degrees. 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 Ba ck slo pe R at io = a 2 / b 2 Foreslope Ratio = a1 / b1 BTW ≥ 6ft, 3 degrees ≤ HC < 6 degrees 1:10 1:8 1:6 1:5 1:4 1:3 1:2 | | | | | | a1 : b1 -1:5 -1:4 -1:6 -1:8 a 2 : b 2 -1:10 -1:3 1:2

D-8 Figure D.5. Roadside ditch design guidelines for ditch bottom width of less than 6 ft and horizontal curvature of greater than or equal to 6 degrees. 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 a1 : b1 a 2 : b 2 Ba ck slo pe R at io = a 2 / b 2 Foreslope Ratio = a1 / b1 BTW< 6 ft, HC ≥ 6 degrees 1:10 1:8 1:6 1:5 1:4 1:3 1:2 | | | | | | 1:2 -1:3 -1:5 -1:10 -1:8 -1:6 -1:4

D-9 Figure D.6. Roadside ditch design guidelines for ditch bottom width of greater than or equal to 6 ft and horizontal curvature of greater than or equal to 6 degrees. 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 Ba ck slo pe R at io = a 2 / b 2 Foreslope Ratio = a1 / b1 BTW ≥ 6 ft, HC ≥ 6 degrees 1:10 1:8 1:6 1:5 1:4 1:3 1:2 | | | | | | -1:3 -1:5 -1:10 -1:8 -1:6 -1:4 a1 : b1 a 2 : b 2 1:2

D-10 Figure D.7. Encroachment rate based on AADT for divided and undivided highway types. Table D.1. Adjustment Factors for ER Based on Horizontal Curvature Degree of Curvature* Rural Urban Undivided Divided Undivided Divided -25 3.11 1.00 2.07 1.00 -20 2.13 1.00 1.63 1.00 -15 1.46 1.00 1.28 1.00 -10 1.00 1.00 1.00 1.00 -5 1.00 1.00 1.00 1.00 0 1.00 1.00 1.00 1.00 5 1.00 1.00 1.00 1.00 10 1.00 1.00 1.00 1.00 15 1.11 1.00 1.03 1.00 20 1.23 1.00 1.07 1.00 25 1.36 1.00 1.10 1.00 *(-) curvature to the left, (+) curvature to the right 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 5,000 10,000 15,000 20,000 25,000 30,000 35,000 40,000 45,000 50,000 En cr oa ch m en ts /M ile /Y ea r ( Pr im ar y D ir ec tio n, R ig ht S id e) Average Daily Traffic (vpd) Undivided Divided

D-11 Table D.2. Adjust Factors for ER Based on Vertical Grade Grade* Rural Urban Undivided Divided Undivided Divided -14 1.24 1.93 0.76 0.21 -13 1.21 1.81 0.78 0.24 -12 1.19 1.71 0.80 0.28 -11 1.17 1.61 0.82 0.32 -10 1.15 1.52 0.84 0.37 -9 1.12 1.43 0.86 0.42 -8 1.10 1.35 0.88 0.49 -7 1.08 1.27 0.91 0.56 -6 1.06 1.20 0.93 0.65 -5 1.04 1.13 0.95 0.75 -4 1.02 1.06 0.98 0.87 -3 1.00 1.00 1.00 1.00 0 1.00 1.00 1.00 1.00 3 1.00 1.00 1.00 1.00 4 1.01 1.05 0.97 0.85 5 1.02 1.10 0.94 0.72 6 1.03 1.16 0.91 0.61 7 1.04 1.22 0.89 0.51 8 1.05 1.28 0.86 0.43 9 1.06 1.34 0.83 0.37 10 1.08 1.41 0.81 0.31 11 1.09 1.48 0.78 0.26 12 1.10 1.56 0.76 0.22 13 1.11 1.64 0.74 0.19 14 1.12 1.72 0.72 0.16 *(-) vertical grade down, (+) vertical grade up EXAMPLE A Figure D.8. Example A—Proposed roadside ditch geometry.

D-12 Roadway Details  Roadway type: rural two-lane undivided.  Bidirectional AADT: 3,000 vpd.  Horizontal curvature: 2 degrees curving left.  Vertical grade: N.A. Proposed Ditch Design  Proposed backslope: 1V:4H.  Proposed foreslope: 1V:6H.  Ditch bottom width: 0 ft (i.e., V-ditch). Discussion 1. For single-sided analysis, divide AADT by 2, which equals 1,500 vpd. Using the single- sided AADT and roadway type (2-lane undivided), refer to Figure D.7 to determine the baseline encroachment rate. For this example, the encroachment rate is 0.56. 2. Using Table D.1 and the given roadway information, determine the horizontal curvature encroachment rate adjustment factor. For this example, the adjustment factor is 1.00. 3. To calculate the adjusted encroachment rate, multiply the baseline encroachment rate found in Step 1 by the horizontal curvature adjustment rate factor found in Step 2. For this example, the encroachment rate remains unchanged (0.56 x 1.00 = 0.56). 4. Using the horizontal roadway curvature and ditch bottom width of the proposed channel geometry in Figure D.8, select the appropriate ditch guideline chart. For this example, Figure D.1 (BTW < 6 ft, HC < 3 degrees) is the appropriate guideline chart. Since Figure D.1 does not include an encroachment rate of 0.56, round to the nearest encroachment rate of 0.75. 5. Plot a point on Figure D.1 corresponding to the slopes of the proposed channel in Figure D.9. 6. Since the point plotted in Step 5 falls inside the 0.75 encroachment rate curve, the channel meets the recommended guideline.

D-13 EXAMPLE B Figure D.9. Example B—Proposed roadside ditch geometry. Roadway Details  Roadway type: urban four-lane divided.  Bidirectional AADT: 30,000 vpd.  Horizontal curvature: 5 degree curving left.  Vertical grade: 4% downgrade. Proposed Ditch Design  Proposed backslope: 1V:6H.  Proposed foreslope: 1V:6H.  Ditch bottom width: 8 ft. Discussion 1. For single-sided analysis, divide AADT by 2, which equals 15,000 vpd. Using the single- sided AADT and roadway type (4-lane divided), refer to Figure D.7 to determine the baseline encroachment rate. For this example, the encroachment rate is 1.8. 2. Using Table D.1 and the given roadway horizontal curvature (5 degrees left), determine the horizontal curvature encroachment rate adjustment factor. For this example, the horizontal curvature adjustment factor is 1.00. 3. Using Table D.2 and the given roadway vertical grade (4% down), determine the vertical grade encroachment rate adjustment factor. For this example, the vertical grade adjustment factor is 0.87. 4. To calculate the adjusted encroachment rate, multiply the baseline encroachment rate found in Step 1 by the adjustment rate factors found in Step 2 and Step 3. The adjusted encroachment rate for this example is 1.56 (1.8 x 1.00 x 0.87). 5. Using the horizontal roadway curvature and ditch bottom width of the proposed channel geometry in Figure D.9, select the appropriate ditch guideline chart. For this example, Figure D.4 is the appropriate guideline chart. Since Figure D.4 does not include an encroachment rate of 1.56, round to the nearest encroachment rate of 1.5.

D-14 6. Plot a point on Figure D.4 corresponding to the slopes of the proposed channel in Figure D.9. 7. Since the point plotted in Step 5 falls outside the 1.5 encroachment rate curve, the channel does not meet the recommended guidelines. Consider flattening the slopes, other channel section transformations, or shielding the ditch.