Safety Performance of Part-Time Shoulder Use on Freeways, Volume 2: Conduct of Research Report (2021) / Chapter Skim
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56 C H A P T E R 5 - H S M P R E D I C T I V E M O D E L HSM Predictive Model This chapter describes the findings obtained during the development of crash prediction models (CPMs) for freeways with part-time shoulder use (PTSU)
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57 The sections of this chapter provide a description of the predictive model form, an overview of the modeling approach, an overview of the statistical analysis methods, and a discussion of the findings from the model estimation and validation activities. Predictive Model Form The basic structure of the predictive model for freeways with PTSU was described previously in Chapter 3.
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58 day but not during the remaining hours of the day. The following equation was used to compute an equivalent AF for sites with a PTSU operating for a portion of the typical day.
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59 PTSU lane. Similarly, in the downstream zone, vehicles change lanes or adjust speed as they interact with vehicles that have just exited the PTSU lane.
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60 next downstream segment of freeway is also evaluated, it too will have a non-zero value for Ptransition because it includes the remaining portion of the transition zone. In Figure 5c, the site is shown as a freeway segment between two PTSU lanes.
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61 represented in the database. If the coefficient for a given state-specific indicator was found to be statistically significant and if it did not notably alter the magnitude, direction, or significance of any site characteristic variable, then it was retained in the model.
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62 crashes for a group of similar sites can be described by the negative binomial distribution. The variance of this distribution is computed using the following equation.
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63 Statistical Analysis Methods The nonlinear regression procedure (NLMIXED) in the SAS software was used to estimate the proposed model coefficients.
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64 The last measure of model fit is the dispersion-parameter-based coefficient of determination Rk2. This statistic was developed by Miaou (1996)
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65 A If the observation corresponds to a freeway segment, the following model is used.
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66 Equation 36 𝐴𝐹 , , exp 𝑏 , , /𝑛 min 𝑊 , 12 10 Equation 37 𝐴𝐹 | , , 1.0 𝑃 1.0 𝑃 exp 𝑏 , , /𝑛 Equation 38 𝐴𝐹 | , , 1.0 𝑃 exp 𝑏 , , /𝑛 𝑊 𝑊 , 𝐼 , , 𝑊 20 𝑃 exp 𝑏 , , /𝑛 𝑊 20 Equation 39 𝐴𝐹 | , , 1.0 𝑃 1.0 𝑃 exp 𝑏 , , 𝑛/𝑊 Equation 40 𝐴𝐹 | , , 1.0 𝑃 1.0 𝑃 exp 𝑏 , , /𝑛 Equation 41 𝑃 𝐿 , /𝐿 , Equation 42 𝐶 , , exp 𝑏 , , 𝐼 𝑏 , , 𝐼 𝑏 , , 𝐼 𝑏 , , 𝐼 𝑏 , , 𝐼 𝑏 , , 𝐼 𝑏 , , 𝐼 𝑏 , , 𝐼 B If the observation corresponds to a ramp entrance speed-change lane, the following model is used.
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67 Equation 51 𝐴𝐹 | , , 1.0 𝑃 , exp 𝑓 , 𝑃 , exp 𝑓 , 𝑓 , , 𝑓 , Equation 52 𝑓 , , 𝑏 , , 1 𝐼 𝑃 , Equation 53 𝑃 , 𝐿 , /𝐿 , Equation 54 𝐴𝐹 , , exp 𝑏 , , 1𝐿 1 0.071 where AADTfs = one-directional AADT volume of freeway segment (veh/day) ; AADTf = one-directional AADT volume of freeway in speed-change lane site (veh/day)
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68 Ls,fs = length of freeway segment (miles) ; Ls,en = length of ramp entrance speed-change lane site being evaluated (≤ length of ramp entrance speedchange lane, as measured from gore point to taper point)
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69 Length of median barrier: 0.0 miles (i.e., not present) Outside shoulder width: 10 feet Length of rumble strip on outside shoulder: 0.0 miles (i.e., not present)
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70 by Equation 20 to Equation 54) represents separate models for each of the three site types.
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71 Table 32. Predictive model estimation statistics, FI crashes, all site types, four states.
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72 Park 2008)
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73 Table 33. Predictive model validation statistics, FI crashes, all site types, four states.
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74 are described in the next subsection. The subsequent three sections describe the model fit to each of the three site-type-specific regression models that comprise the generalized model.
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75 Table 34. Final predictive model estimation statistics, FI crashes, all site types, five states.
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76 Table 35. Final predictive model estimation statistics, FI crashes, freeway segment, five states.
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77 Table 36. Final predictive model estimation statistics, FI crashes, ramp entrance speed-change lane, five states.
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78 Table 37. Final predictive model estimation statistics, FI crashes, ramp exit speed-change lane, five states.
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79 Horizontal Curve AF The estimated horizontal curve AF is described using the following equation. Equation 58 𝐴𝐹 , , 1.0 exp 4.888 5,730𝑅 The radii used to estimate this AF range from 1,430 to 24,170 feet.
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80 Figure 11. Estimated lane width AF for FI crashes.
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81 Figure 12. Estimated inside shoulder width AF for FI crashes.
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82 Figure 13. Estimated inside shoulder rumble strip AF for FI crashes.
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83 The median width AF is shown in Figure 14 using the thick, solid trend line labeled "proposed, 3 lanes; no barrier." The equivalent CMF from the HSM Supplement (AASHTO 2014) is shown using a thin, dashed trend line labeled "HSM, no barrier." These two trend lines are in good agreement on the relationship between median width and AF value.
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84 Lane Change AF The estimated lane change AF is described for freeway segments using the following equation. Equation 65 𝐴𝐹 , , 1.0 exp 14.34 𝑋 , 1.305 ln 𝐴𝐴𝐷𝑇 , /100014.34 𝐿 , 1.0 exp 14.34 𝐿 , 1.0 exp 14.34 𝑋 , 1.305 ln 𝐴𝐴𝐷𝑇 , /100014.34 𝐿 , 1.0 exp 14.34 𝐿 , This AF is based on five input variables.
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85 subsequent segment. This decline in AF value reflects the decreasing number of lane changes with increasing distance from the ramp gore.
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86 The variable for "number of through traffic lanes" n is included in Equation 66 because it was found to improve the overall model fit to the data. The manner in which it is used (i.e., as a divisor)
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87 Outside Clearance AF The estimated outside clearance AF is described for freeway segments using the following equation. Equation 68 𝐴𝐹 | , , 1.0 𝑃 exp 0.00601/𝑛 𝑊 𝑊 , 𝐼 , , 𝑊 20 𝑃 exp 0.00601/𝑛 𝑊 20 The clear zone width Whc used in this AF is an average for the site.
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88 Outside Barrier AF The estimated median barrier AF is described for freeway segments using the following equation. Equation 69 𝐴𝐹 | , , 1.0 𝑃 1.0 𝑃 exp 0.01664 𝑛/𝑊 The variables Pob and Wocb were described in the previous section.
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89 Figure 19. Estimated ramp entrance AF for FI crashes.
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90 Figure 20. Estimated ramp exit AF for FI crashes.
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91 Figure 21. Estimated turnout presence AF for FI crashes.
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92 and the PTSU lane effectively continues through the site even though it may not be marked as an exclusive PTSU lane (because ramp traffic is permitted to cross this area to enter or exit the freeway through lanes)
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93 Table 38. Estimated PTSU operation AF for FI crashes.
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94 a. Proposed models.
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95 crashes than the HSM model for volumes in excess of about 70,000 veh/day. This difference was investigated for explanation by other model variables and by issues with the reported crash data; however, nothing notable was found.
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96 these coefficients and the associated lane change AF were removed from the model. Similarly, the coefficient for the inside and outside shoulder rumble strip AFs was not statistically significant and very near to 0.0, so the coefficient and the AFs were removed from the model.
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97 Table 39. Final predictive model estimation statistics, PDO crashes, all site types, five states.
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98 than χ2 0.03, 499 (= 560)
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99 Figure 25. Predicted vs.
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100 indicate that the model provides an unbiased estimate of predicted crash frequency for sites experiencing up to 24 PDO crashes during the study period. Figure 26.
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101 The fit of the estimated model is shown in Figure 27. This figure compares the predicted and reported crash frequency in the estimation database.
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102 Figure 28. Estimated horizontal curve AF for PDO crashes.
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103 Inside Shoulder Width AF The inside shoulder width AF is described using the following equation. Equation 86 𝐴𝐹 , , exp 0.02725/𝑛 min 𝑊 , , 12 6 The shoulder width used in this AF represents the paved width.
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104 The median width used in this AF is an average for the site. The AF is derived to be applicable to a site that has median barrier present along some portion of the site.
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105 Median Barrier AF The estimated median barrier AF is described using the following equation. Equation 89 𝐴𝐹 | , , 1.0 𝑃 1.0 𝑃 exp 0.01618 𝑛/𝑊 The variables Pib and Wicb were described in the previous section.
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106 Figure 32. Estimated outside shoulder width AF for PDO crashes.
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107 available. Nevertheless, the trend line is in good agreement on the relationship between clear zone width and AF value for FI crashes, as shown in Figure 18.
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108 Ramp Entrance AF The estimated ramp entrance AF is described using the following equation. Equation 93 𝐴𝐹 , , exp 0.09908 1𝐿 1 0.142 The ramp entrance length Len is measured from the gore to the taper point of the speed-change lane, as defined in Chapter 18 (Figure 18-3)
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109 0.071 miles. This value represents the median ramp exit length in the estimation database.
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110 the traveled way such that the crashes occurring in the middle lanes are less influenced by turnout presence. The turnout AF is shown in Figure 36 using three thick trend lines; one line is shown for each of two, four, and six through traffic lanes.
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111 The variable Wptsu represents the average width of the shoulder that is allocated to vehicular traffic use (i.e., as an additional travel lane) during one or more hours of the typical day.
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112 Table 43. Estimated PTSU operation AF for PDO crashes.
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113 a. Proposed models.
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114 crashes than the HSM model for volumes in excess of about 70,000 veh/day. A similar trend was noted for FI crashes in the discussion associated with Figure 24.
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