Crash Modification Factors in the Highway Safety Manual: Resources for Evaluation (2023) / Chapter Skim
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Appendix O HSM Implementation of a Proposed Roadside Design CMF for Rural Two-Lane Two-Way Roads
Appendix O HSM Implementation of a Proposed Roadside Design CMF for Rural Two-Lane Two-Way Roads
Pages 414-456
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Appendix O HSM Implementation of a Proposed Roadside Design CMF for Rural Two-Lane Two-Way Roads O-1
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O-41 SVROR Crash Severity Distribution Worksheet .................................................................................... O-42 Crash Type and Severity Distribution Worksheet ..................................................................................
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Appendix N described the roadside design elements that influence safety, as well as the process used to develop and verify the procedure for estimating the roadside design CMF value. Appendix N also described the development of a procedure for estimating the SVROR and non-SVROR crash severity distribution.
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β Mountainous: Any combination of grades and horizontal and vertical alignment that causes heavy vehicles to operate at crawl speed for significant distances or at frequent intervals. For each segment in the project limits, the roadside design elements are determined separately for each of the two sides of the road.
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Apply the Crash Type Distribution, if Desired The crash type distribution can be used to compute the average crash frequency for each of several crash types (e.g., collision with pedestrian, rollover, head-on collision)
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Section 10.X provides a procedure for updating the crash type distribution and then using it to compute the average crash frequency for specific crash types. Apply the Severity Distribution, if Desired The crash severity distribution can be used to compute the average crash frequency for each of the following severity levels: fatal, incapacitating injury, non-incapacitating injury, and possible injury.
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The crash type distribution values are subsequently used to estimate the "Lane Width" CMF and the "Shoulder Width and Type" CMF.] [Delete the discussion associated with the existing Roadside Design CMF.
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They are identified in the following list. β’ Terrain type β’ Longitudinal barrier type β’ Foreslope width β’ Side slope β’ Narrow object count β’ Average offset to narrow objects β’ Miscellaneous obstacle length β’ Miscellaneous obstacle offset O-8
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, ft/obstacle; and nmo = number of miscellaneous obstacles on the subject roadside. The average effective offset distance to a typical roadside feature is computed using the following equation.
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Equation 5 βοΏ½πΏπΏππππ,ππ Γ π·π·ππππππ,ππππ,ππ οΏ½ π·π·ππππππ,ππππ = βοΏ½πΏπΏππππ,ππ οΏ½ where Doff,lb = average effective offset distance to typical barrier on the subject roadside (measured from edge of traveled way) , ft; Llb,i = length longitudinal barrier piece i adjacent to the subject roadside, ft; and Doff,lb,j = offset distance to barrier piece i on the subject roadside (measured from edge of traveled way)
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For the calculation of the CMF for roadside design, narrow objects and miscellaneous obstacles are combined in Step 1 and represented as a set of "typical roadside features" having a common offset Doff,ob and total length Lob. This step describes the calculation of the proportion of the segment length that is adjacent to longitudinal barrier, to clear slope, and to roadside features.
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on the subject roadside; Lenv = average length of hazard envelope for a feature on the subject roadside (Equation 6) , ft/feature; Lob = average effective length of typical roadside feature on the subject roadside (Equation 3)
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or with a barrier, given that the vehicle has encroached onto the roadside adjacent to a barrier. The Part 2 Roadside Design CMF worksheet (provided in the section Worksheets)
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Equation 17 ππππ,ππππ = π·π·ππππππ,ππππ β πππ π where Wf,lb = width of that portion of the foreslope between the edge of shoulder and face of barrier on the subject roadside, ft; Ws = width of shoulder on the subject roadside, ft; and all other variables are defined previously. The third equation is used to compute the probability of a rollover crash before reaching the barrier.
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Equation 21 ππππ>π·π·π·π·π·π·π·π·,ππππ = 0.01 Γ expοΏ½4.605 β 0.0790 Γ π·π·ππππππ,ππππ οΏ½ where pd>Doff,ob = probability that a vehicle's encroachment distance d on the subject roadside exceeds a given offset distance Doff,ob; and Doff,ob = average effective offset distance to a typical feature on the subject roadside (measured from edge of traveled way) (Equation 4)
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Step 7 β Compute Roadside Design CMF This step describes the calculation of the CMF for roadside design. The Part 2 Roadside Design CMF worksheet (provided in the section Worksheets)
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; and Pob = proportion of the segment length that is adjacent to features (i.e., narrow objects or miscellaneous obstacles) on the subject roadside (Equation 11)
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Equation 29 πΆπΆπΆπΆπΆπΆππππ = πππ π π π π π π π π π ,ππππ Γ πΆπΆπΆπΆπΆπΆπ π π π π π π π π π + οΏ½1 β πππ π π π π π π π π π ,ππππ οΏ½ where CMFrd = crash modification factor for roadside design; Psvror,as = proportion of SVROR crashes of all severities for the subject roadway segment when the roadside design elements present are at base condition values; and CMFsvror = crash modification factor for SVROR crashes. Step 8 β Adjust the Crash Type Distribution if Necessary The guidance provided in Section 10.X is applied in this step to determine if the default crash type distribution should be adjusted to more reliably reflect that for the subject segment.
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or the subject segment's roadside design elements are different from the base condition values in Section 10.6.1 (by a practically significant amount) , then the crash type distribution values in the last column of Table 1 should be adjusted (such that they are a more reliable reflection of the crash distribution for the subject segment)
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β P13,c The following equation can be used to compute the crash frequency associated with a specific crash type. Equation 30 ππππ,ππππ,π¦π¦,ππππ = ππππ,ππππ,ππππ,ππππ Γ πππ¦π¦,ππππ where Np,rs,y,as = predicted average crash frequency of a road segment for crash type y and all severity levels; crashes/yr; Np,rs,at,as = predicted average crash frequency of a road segment for all crash types and severity levels; crashes/yr; and Py,as = proportion of crashes having crash type y for all severity levels combined.
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or the subject segment's roadside design elements are different from the base condition values in Section 10.6.1 (by a practically significant amount) , then the crash severity distribution values in the last row of Table 2 should be adjusted (such that they are a more reliable reflection of the crash distribution for the subject segment)
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7.2 HSM Section 10.Y.2 β Crash Frequency by Crash Type and Severity Base Procedure Table 1 provides the default crash type and severity distribution proportions for the typical rural twolane two-way highway segment. If the proportion of SVROR crashes obtained from Equation 28 is different from the typical value of 0.5399 (by a practically significant amount)
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β’ SVROR Crash Severity Distribution worksheet β’ Crash Type and Severity Distribution worksheet The Roadside Design Element, Roadside Design CMF (Part 1) , the Roadside Design CMF (Part 2)
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. Step 3 β Compute SVROR Crash Severity Distribution This step describes the calculation of the "proportion of SVROR crashes" by severity level for the segment of interest.
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; Psvror,as = proportion of SVROR crashes of all severities for the subject roadway segment when the roadside design elements present are at base condition values (Equation 28) ; pc,P = probability of a SVROR crash, given an encroachment on the primary roadside and based on input variables describing the primary roadside (Equation 26)
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8.2 The Questions What is the predicted average crash frequency of the roadway segment for a particular year? What is the crash severity distribution for the SVROR and non-SVROR crash types?
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ο§ 3.5H:1V side slope ο§ 80 narrow objects ο§ 11.5 average offset to narrow objects (measured from edge of traveled way) ο§ No miscellaneous obstacles 8.4 Assumptions β’ The roadside design elements do not match the base condition values in Section 10.6.1 so the crash type distribution will need to be estimated using the guidance in Section 10.X and the severity distribution for SVROR crashes will need to be estimated using the guidance in Section 10.Y.2.
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Step 1 β Compute Offset to Typical Roadside Elements The average effective length of the typical roadside features (i.e., objects and obstacles) on the primary direction roadside is computed as follows (the value for the opposing direction is the same for this segment)
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The average length of the hazard envelope can be computed using the following equation. πΏπΏππππππ = πΏπΏππππ + πΏπΏππππ = 47.85 + 0.667 = 48.52 ft/feature Step 3 β Compute the Distribution of Segment Length by Roadside Element The proportion of the segment that is adjacent to longitudinal barrier is computed as: βπΏπΏππππ,ππ 975 ππππππ = = = 0.123 5280 Γ πΏπΏ 5280 Γ 1.5 The density of the collective set of features is computed as: ππππππ + ππππππ 80 + 0 ππππππ = = = 60.8 features/mile πΏπΏ β οΏ½βπΏπΏππππ,ππ /5280οΏ½ 1.5 β (975/5280)
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= 0.623 The average effective offset distance to a typical barrier Doff,lb was computed in Step 1 as 6.0 ft. The width of that portion of the foreslope between the edge of shoulder and the face of the barrier is computed as: ππππ,ππππ = π·π·ππππππ,ππππ β πππ π = 6.0 β 4.0 = 2.0 ft The probability of a crash by rollover before reaching the barrier (given an encroachment)
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or with the typical feature (given an encroachment) is computed as: ππππ,ππππ+ππππππππ = ππππ,ππππππππ,ππππ + ππππ,ππππ = 0.146 + 0.344 = 0.490 Step 7 β Compute Roadside Design CMF The probability of a SVROR crash in the primary direction (given an encroachment)
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= 1.061 Step 8 β Adjust the Crash Type Distribution if Necessary The guidance in Section 10.X is to use the default crash type distribution in Table 1 unless one or both of the following conditions is satisfied: 1. The proportion of SVROR crashes Psvror,as from Step 7 is different from 0.5399 (by a practically significant amount)
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Completed Crash Type Distribution worksheet for Sample Problem 1. Segment number (c = 1)
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, severity distribution, and crash type distribution. Apply the Severity Distribution, if Desired It is desired to obtain the severity distribution for the SVROR and non-SVROR crash types.
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This guidance directs the analyst to complete the SVROR Crash Severity Distribution worksheet and the Crash Type and Severity Distribution worksheet, in this order. The proportion of SVROR crashes Psvror,as was previously computed as 0.359.
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for the segment is computed as: ππππππππ,π π π π π π π π π π ,ππππ = ππππππππ,π π π π π π π π π π ,πΎπΎ + ππππππππ,π π π π π π π π π π ,π΄π΄ + ππππππππ,π π π π π π π π π π ,π΅π΅ + ππππππππ,π π π π π π π π π π ,πΆπΆ + ππππππππ,π π π π π π π π π π ,ππππππ = 0.0071 + 0.0295 + 0.0613 + 0.0833 + 0.2141 = 0.3953 Step 4 β Compute Non-SVROR Crash Severity Distribution The crash type and severity distribution in Table 1 is adjusted using the guidance offered in the Crash Type and Severity Distribution worksheet. The completed worksheet is shown in Table 4.
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d β P13,c = P4,c + P5,c e β P14,c = (P1,c +...+ P11,c) β P13,c Equation 32 is used with the values in the last two rows of Table 4 to estimate the crash frequency by severity level for the SVROR and non-SVROR crash types.
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mo,P: Lmo,O: (LβD) mo,O: Obstacle count nmo,P: nmo,O: Roadside Design Element Calculations Primary Opposing Variable Direction Direction Base Condition Average effective length of typical roadside feature Lob (ft/feature)
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Proportion of SVROR crashes when roadside design elements are at base condition values Psvror,as πππ π π π π π π π π π ,ππππ = 2.150 Γ π΄π΄π΄π΄π΄π΄π΄π΄ β0.1797 Γ 1.0068ππππ Γ 0.9820ππππ,ππππ Γ 0.9616ππππ,π’π’π’π’ Γ 0.9539πΉπΉ Γ 0.9935ππ a β Variable is obtained from the Roadside Design Element worksheet.
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or with the typical feature pc,ob+roll 0.400 ππππ,ππππ+ππππππππ = ππππ,ππππππππ,ππππ + ππππ,ππππ Roadside Design CMF Primary Opposing Base Input Variables Direction Direction Condition Proportion of segment length with clear slope Pclear b Proportion of segment length adjacent to longitudinal barrier Plb b Proportion of segment length adjacent to features Pob b Probability of a rollover crash pc,roll b Proportion of SVROR crashes of all severities on segment Psvror,as b -- Calculations Probability of a SVROR crash pc pc,P: pc,O: pc,base: 0.290 ππππ = οΏ½ππππππππππππ Γ ππππ,ππππππππ οΏ½ + οΏ½ππππππ Γ ππππ,ππππ+ππππππππ οΏ½ + οΏ½ππππππ Γ ππππ,ππππ+ππππππππ οΏ½ Crash modification factor for SVROR crashes CMFsvror -- πΆπΆπΆπΆπΆπΆπ π π π π π π π π π = 0.5 Γ οΏ½ππππ,ππ βππππ,ππππππππ οΏ½ + 0.5 Γ οΏ½ππππ,ππ βππππ,ππππππππ οΏ½ Crash modification factor for roadside design CMFrd -- πΆπΆπΆπΆπΆπΆππππ = πππ π π π π π π π π π ,ππππ Γ πΆπΆπΆπΆπΆπΆπ π π π π π π π π π + οΏ½1 β πππ π π π π π π π π π ,ππππ οΏ½ a β Variable is obtained from the Roadside Design Element worksheet. b β Variable is obtained from the Roadside Design CMF worksheet (Part 1)
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a (Pr,2) Guidance for Estimating Adjusted Proportions Pr,2 SINGLE-VEHICLE Collision with animal (r =1)
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of crash with a feature without rolling prior to impact pc,ob c Calculations Proportion of crashes before a feature (by rollover) or with a feature having severity z Pob+roll,z ππππππ+ππππππππ,π§π§ = οΏ½ππππ,ππππππππ,ππππ Γ ππππππππππ,π§π§ + ππππ,ππππ Γ ππππππ,π§π§ οΏ½/οΏ½ππππ,ππππππππ,ππππ + ππππ,ππππ οΏ½ Severity Distribution Primary Direction Opposing Direction Input Variables K A B C PDO K A B C PDO Proportion of segment length with clear slope Pclear b Proportion of segment length adjacent to barrier Plb b Proportion of segment length adjacent to features Pob b Probability of a SVROR crash pc c Proportion of SVROR crashes of all severities on segment Psvror,as b Crash modification factor for roadside design CMFrd c Calculations Proportion of crashes having severity z Pz πππ§π§ = οΏ½ππππππππππππ Γ ππππππππππ,π§π§ οΏ½ + οΏ½ππππππ Γ ππππππ+ππππππππ,π§π§ οΏ½ + οΏ½ππππππ Γ ππππππ+ππππππππ,π§π§ οΏ½ Segment (Both Directions)
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Table 1 /Pr,1; where "(Pr,c) Table 1" is the value of Pr,c in Table 1 and Padj,svror,z is obtained from the SVROR Crash Severity Distribution worksheet.
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