Safety Prediction Methodology and Analysis Tool for Freeways and Interchanges (2021)

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235 CHAPTER 7: PREDICTIVE MODEL FOR CROSSROAD RAMP TERMINALS This chapter describes the activities undertaken to calibrate and validate safety predictive models for both signalized and unsignalized crossroad ramp terminals. Each model consists of a SPF and a family of CMFs. The SPF is derived to estimate the crash frequency for crossroad ramp terminals with specified design elements and operating conditions. The CMFs are used to adjust the SPF estimate whenever one or more elements or conditions deviate from those that are specified. The calibrated safety predictive models were used to develop a safety predictive method for crossroad ramp terminals. This method will describe how to use the models to evaluate terminal safety, as may be influenced by road geometry, roadside features, and traffic volume. This method is documented in Appendix D. Collectively, the predictive models for crossroad ramp terminals address the following area type and traffic control modes: ● rural ramp terminal with stop control ● rural ramp terminal with signal control, ● urban ramp terminal with stop control, and ● urban ramp terminal with signal control. Several typical ramp terminal configurations were identified in Figure 37. Other configurations exist but they are less common than those shown in the figure. Based on the conclusions reached during the prioritization process (as described in Chapter 3), it was determined that the predictive model would address the configurations shown in Figure 37. This chapter is divided into six parts. The first part provides some background information on the topic of predictive models for crossroad ramp terminals. The second part describes the theoretic development of selected CMFs. The third part describes the method used to calibrate the proposed models. The fourth part describes the calibration of the models to predict FI crash frequency. The fifth part describes the calibration of the models to predict PDO crash frequency. The sixth part provides a list of the variables defined in this chapter.

236 BACKGROUND This part of the chapter consists of three sections. The first section describes the crossroad ramp terminal analysis units (i.e., sites). The second section provides a brief overview of the predictive model structure. The last part reviews the highway safety data assembled for model calibration. Crossroad Ramp Terminals For analysis purposes, an interchange is considered to consist of a set of ramp segments, crossroad ramp terminals, and, possibly, one or more C-D road segments. These components are also referred to as “sites.” The more common crossroad ramp terminal configurations are identified in the list below; they are illustrated in Figure 37. ● three-leg ramp terminal with diagonal exit ramp (D3ex), ● three-leg ramp terminal with diagonal entrance ramp (D3en), ● four-leg ramp terminal with diagonal ramps (D4), ● four-leg ramp terminal at four-quadrant parclo A (A4), ● four-leg ramp terminal at four-quadrant parclo B (B4), ● three-leg ramp terminal at two-quadrant parclo A (A2), and ● three-leg ramp terminal at two-quadrant parclo B (B2). Figure 103 illustrates two crossroad ramp terminals with the D4 configuration. Each terminal represents a separate site. The two terminals are shown in the context of a diamond interchange. The arrangement shown is intended to illustrate the ramp terminal boundaries used for safety evaluation–it is not necessarily typical ramp terminal geometry. In the context of the predictive method, the free-flow loop ramp associated with the four- quadrant parclos (i.e., the A4 and B4 configurations) is not considered to be part of the ramp terminal. All subsequent discussions where “ramp AADT” is identified for these two configurations are referring to the volume of the diagonal entrance ramp or the diagonal exit ramp. With one exception, the loop ramp of the A4 and B4 configuration is not explicitly addressed by the models described in this chapter. The one exception is that the right-turn channelization that serves traffic entering the loop ramp at the A4 configuration can be part of the ramp terminal design, and its associated crashes are addressed by the predictive models.

237 Crossroad Left-Side Ramp Right-Side Ramp 250 ft 250 ft 250 ft 250 ft - Ramp terminal boundary Figure 103. Illustrative crossroad ramp terminal boundary. Safety Predictive Models The predicted average crash frequency for an interchange is computed as the sum of the predicted average crash frequency of all sites that comprise the facility. This calculation is described by Equation 217. ( ) ( ) ++= segmentsall inalstermall rtsvmvnterchangei NNNN (217) where, Ninterchange = predicted average crash frequency within the limits of an interchange, crashes/yr; Nmv = predicted average multiple-vehicle crash frequency, crashes/yr; Nsv = predicted average single-vehicle crash frequency, crashes/yr; and Nrt = predicted average crossroad ramp terminal crash frequency, crashes/yr. The predicted average crash frequency for each site is computed using a predictive model. Each model represents the combination of an SPF and several CMFs. The SPF is used to estimate the average crash frequency for a generic site whose attributes are consistent with the SPF’s stated base conditions. The CMFs are used to adjust the SPF estimate when the attributes of the subject site are not consistent with the base conditions. The general form of the safety predictive models for crossroad ramp terminals is shown as Equations 218 to 221. The general form of the model for ramp and C-D road segments is described in Chapter 6. ( ) ( )kwBABABAspfBABArt CMFCMFCMFCMFNCN ×××××××= ...... 1,221,2222,2222, (218) ( ) ( )kxexDAexDAexDAspfexDAexDArt CMFCMFCMFCMFNCN ×××××××= ...... 1,341,3434,3434, (219)

238 ( ) ( )kyenDBenDBenDBspfenDBenDBrt CMFCMFCMFCMFNCN ×××××××= ...... 1,341,3434,3434, (220) ( ) ( )kzDDDspfDDrt CMFCMFCMFCMFNCN ×××××××= ...... 1,41,44,44, (221) where, Nspf, A2B2 = predicted average crash frequency for A2 and B2 configurations for base conditions, crashes/yr; Nspf, A4D3ex = predicted average crash frequency for A4 and D3ex configurations for base conditions, crashes/yr; Nspf, B4D3en = predicted average crash frequency for B4 and D3en configurations for base conditions, crashes/yr; Nspf, D4 = predicted average crash frequency for D4 configuration for base conditions, crashes/yr; CA2B2 = local calibration factor for A2 and B2 configurations; CA4D3ex = local calibration factor for A4 and D3ex configurations; CB4D3en = local calibration factor for B4 and D3en configurations; CD4 = local calibration factor for D4 configuration; CMFA2B2, 1 ... CMFA2B2, w = crash modification factors for crashes at an A2 or B2 site with specific geometric design features w; CMFA4D3ex, 1 ... CMFA4D3ex, x = crash modification factors for crashes at an A4 or D3ex site with specific geometric design features x; CMFB4D3en, 1 ... CMFB4D3en, y = crash modification factors for crashes at a B4 or D3en site with specific geometric design features y; CMFD4, 1 ... CMFD4, z = crash modification factors for crashes at a D4 site with specific geometric design features z; and CMF1 ... CMFk = crash modification factors for ramp terminal crashes at a site with specific geometric design features k. The subscript for the dependent variables indicates the ramp terminal configuration to which the predictive model applies. Four configuration groups are identified using this nomenclature. The four groups were developed to overcome limitations in the sample size for the component ramp terminal configurations. Three of the four groups include two configurations. The configurations that were paired for each group have the same turn movement orientation and very similar conflicting movements. For these reasons, they are rationalized to have a similar relationship between traffic volume and crash frequency. The first term in parentheses in Equations 218 to 221 recognizes the influence of some geometric factors is unique to each ramp terminal configuration group. In contrast, the second term in parentheses in these equations recognizes that some geometric factors have a similar influence on all groups. Highway Safety Database The HSIS was used as the primary source of data for model calibration and validation. The “HSIS” states California, Maine, and Washington were identified as including ramp volume data, which is of fundamental importance to all aspects of this project. These data were not

239 available from the other HSIS states. Hence, the database assembly focused on these three states. They are called the “study states” in this report. In addition to ramp volume data, each study state database included a range of data describing the location, area type, traffic characteristics, geometry, and lane use for crossroad ramp terminals. The data acquired from these databases is summarized in Table 60. TABLE 60. Terminal variables from HSIS database Category Variable Description Descriptive state Source of data (CA, ME, WA) rte_nbr State route number rte_suf State route suffix county County number (established by state DOT) begmp Begin milepost (established by state DOT in CA, WA; by researchers for ME) endmp End milepost (established by state DOT in CA, WA; by researchers for ME) rururb Area type (urban, rural) Traffic ave_adt_xrd Crossroad segment AADT volume averaged for a three-year period ave_adt_ramp1 Ramp segment AADT volume averaged for a three-year period ave_adt_ramp2 Ramp segment AADT volume averaged for a three-year period Crash nk_mv Count of reported fatal during three-year period na_mv Count of reported incapacitating injury crashes during three-year period nb_mv Count of reported non-incapacitating injury crashes during three-year period nc_mv Count of reported possible-injury crashes during three-year period no_mv Count of reported PDO crashes during three-year period The data identified as “Descriptive” in Table 60 were obtained directly from the HSIS database for each study state. The data identified as “Traffic” or “Crash Data” were derived from the HSIS data. SAS software was used to manipulate the HSIS data to compute the desired variables. As discussed in Appendix B, several of the geometry and lane use variables in the study state databases were of unknown accuracy. Also, several variables often had subtly different definitions among states. Moreover, the study state databases often did not include variables that describe road-related factors known to be associated with crash frequency. To overcome these limitations, the study-state databases were enhanced using data from other sources. These variables are listed in Table 61. The collection of these data required the location of each ramp using geographic coordinates and aerial photography, based on the freeway milepost reference system in HSIS. Aerial photography was used as the source of the enhanced data. These photographs were obtained from the Internet using Google Earth software. The data collected include the ramp terminal configuration, number of lanes, bay presence, type of control, and median width. A description of the variables acquired from aerial photography is provided in Table 61.

240 TABLE 61. Variables from supplemental data sources Category Variable Description Descriptive problem_flag Code to identify issues that make segment unsuitable for analysis lat_lon_coord Latitude and longitude of ramp terminal center term_type Terminal configuration (diamond, spui, parclo A, etc.; see discussion) frontage Presence of frontage road movement RR_crossing Presence of a railroad crossing on one or more ramp terminal legs offsys_legs Number of intersecting legs that are “off-system” skew Skew angle of the exit ramp at the ramp terminal Roadway xrd_th_lanes Number of through lanes on the crossroad xrd_lt_bays Number of crossroad legs with a left-turn bay (or lane) xrd_rt_bays Number of crossroad legs with a right-turn bay (or lane) xrd_rt_chan Number of crossroad approaches with a right-turn channelizing island xrd_med_width Width of crossroad median (excluding width of left-turn bays) ent_lanes Number of lanes on the ramp leg serving as a freeway entrance ramp exit_lanes Number of lanes on the ramp leg serving as a freeway exit ramp exit_rt_bay Presence of a right-turn bay (or lane) on the exit ramp approach exit_rt_chan Presence of right-turn channelizing island on the exit ramp approach Traffic control control_type Type of control for conflicting movements at the ramp terminal xrd_prot_lt Presence of protected left-turn phasing on crossroad (if signal) xrd_rt_cntl Type of control for right turn entering ramp from crossroad exit_rt_cntl Type of control for right turn entering crossroad from ramp adj_ramp_cntl Type of control for nearest ramp terminal nonramp_cntl Type of control for nearest non-ramp intersection Other xrd_int_dist Distance between centers of subject and nearest ramp intersections xrd_ext_dist Distance between centers of subject and nearest non-ramp intersections xrd_dway Number of driveways on the crossroad within 250 ft of stop line offsys_st Presence of public street approach on the crossroad within 250 ft of stop line The “frontage” and “RR_crossing” variables were used to identify ramp terminals with a frontage road approach or a railroad crossing in the ramp terminal boundary. Quantifying the safety influence of these conditions was not ranked high in the prioritization process, as documented in Chapter 3. Hence, these variables were used to screen ramp terminals having either attribute from the database. CMF DEVELOPMENT This part of the chapter describes the development of several CMFs. The first section describes the development of a general CMF model for quantifying the relationship between intersection safety and some geometric characteristic of one of the intersecting roads. This model was developed because most of the CMFs in the literature that address a road-specific treatment (e.g., widen major road median) are used to adjust the prediction of total intersection crashes, as opposed to just that portion that occur on the treated road.

241 The second section describes the development of a general CMF model for quantifying the relationship between safety and some geometric characteristic of an intersection leg. Most of the CMFs in the literature that address a leg-specific treatment (e.g., add turn bay) are used to adjust the prediction of total intersection crashes, as opposed to just that portion that occur on the treated leg. The third and subsequent sections describe the development of a CMF for specific geometric elements at intersections. These elements include: add turn bay, widen median, change exit ramp capacity, and change intersection skew angle. General CMF Model for Street Treatments The general CMF model is developed for the situation where a CMF is developed to estimate the relationship between “intersection crash frequency” and a change that is made to one of the two intersecting streets. In this context, “intersection crash frequency” is meant to include all crashes that occur at the intersection plus those that occur in the immediate vicinity of the intersection and which are identified as “intersection related.” Intuitively, a treatment applied to one street (e.g., increase lane width) should not have an influence on crashes associated with the intersecting street. Consider the situation where a treatment is applied to one intersecting street at an intersection. The magnitude of its safety effect can be quantified using a CMF that is based on just the crashes associated with the treated street (i.e., CMFstr). This effect can then be extended to an estimate of the CMF for total intersection crashes (i.e., CMFint) using the following equation. ( )iistrinti RRCMFCMF −+= 0.10.1, (222) where, CMFint, i = CMF for a specified treatment to street i, quantified in terms of intersection crashes (i = 1 for major street or 2 for minor street); CMFstr = CMF for a specified treatment to any street, quantified in terms of the crashes that occur on the subject street; and Ri = proportion of intersection crashes that occur on treated street i. By using a simple crash rate relationship, Bonneson and Pratt (2008) suggest that the value of Rstr, i can be estimated as the ratio of traffic volume on the subject street to that on both intersecting streets. The following equation can be used to compute this estimate. 21 AADTAADT AADTPR iii + =≈ (223) where, Pi = proportion of total leg AADT on street i; and AADTi = AADT volume for street i (i = 1 for major street or 2 for minor street), veh/day. If Equation 223 is applied to a crossroad ramp terminal then the word “crossroad” is substituted for “major-street” in the variable definitions (with i = xrd or rmp, as appropriate), and the minor street AADT volume is computed using Equation 224.

242 exenrmp AADTAADTAADTAADT 5.05.02 +== (224) where, AADTex = AADT volume for the exit ramp, veh/day (= 0 if ramp does not exist); and AADTen = AADT volume for the entrance ramp, veh/day (= 0 if ramp does not exist). Equation 222 (with Equation 223) represents the “General CMF Model for Street Treatments.” It recognizes that the effect of a treatment on intersection crashes is a function of the AADT volume on the treated street. If both streets are treated, then the intersection CMF for the combined treatment (i.e., CMFint,1,2) is computed using the following equation. [ ] [ ])0.1(0.1)0.1(0.1 22112,1, PPCMFPPCMFCMF strstrnti −+×−+= (225) The general model is appropriate for treatments that occur along an intersecting street, on both sides of the intersection. Changes in lane width or shoulder width are examples of such treatments. A model is described in the next section that is applicable to treatments that occur on a specific intersection leg. General CMF Model for Leg Treatments The framework developed in the previous section is extended in this section to the development of a general CMF model when the treatment is specific to an intersection leg (as opposed to one of the intersecting streets). The form of this model is described in the following equation. ( )kklegknti RRCMFCMF −+= 0.10.1, (226) with, 4321 AADTAADTAADTAADT AADTPR kkk +++ =≈ (227) where, CMFint, k = CMF for a specified treatment to leg k, quantified in terms of intersection crashes (k = 1 for one major-street leg, 2 for the other major-street leg, 3 for one minor-street leg, and 4 for the other minor-street leg); CMFleg = CMF for a specified treatment to any leg, quantified in terms of the crashes that occur on the subject leg; R k = proportion of intersection crashes that occur on treated leg k; Pk = proportion of total leg AADT on leg k; and AADTk = AADT volume for leg k, veh/day. Equations 226 and 227 are equally applicable to three- or four-leg intersections. However, if applied to a three-leg intersection, AADT4 is set equal to zero. If these equations are applied to a ramp terminal, then AADT3 is set equal to AADTex, AADT4 is set equal to AADTen, and the word “crossroad” is substituted for “major-street” in the variable definitions (with k = in, out, ex, or en, as appropriate). The subscript “in” corresponds to the crossroad leg is that located between the two ramp terminals of the interchange. The subscript “out” is the other crossroad leg.

243 Equation 226 is used in a multiplicative manner to address treatments made to any number of legs. For example, if two legs are treated, then the intersection CMF (i.e., CMFint,k,l) is computed using the following equation. [ ] [ ])0.1(0.1)0.1(0.1,, lllegkkleglknti PPCMFPPCMFCMF −+×−+= (228) The general model is appropriate for treatments that occur on an intersection leg. The installation of a turn lane, a channelized right-turn, or the addition of a driveway are examples of such treatments. Turn Lane CMF - Total Crashes This section describes the development of the leg-specific turn lane CMFs using the intersection- and street-specific turn lane CMFs developed by Harwood et al. (2002). They developed CMFs for left-turn lanes and right-turn lanes installed individually and in pairs at signalized and unsignalized intersections. The intersections were located in urban and rural areas. Some intersections had three legs and others had four legs. Finally, some intersections had signal control installed at the time of the lane installation (they were referred to as “newly signalized” intersections). The database assembled by Harwood et al. (2002) represents 280 treated intersections (143 rural and 137 urban intersections) collectively located in eight states. At these intersections, 392 left-turn lanes were added and 182 right-turn lanes were added. They used the crash data for these intersections to develop FI crash CMFs and total-crash CMFs. The total-crash CMFs are the focus of this section. The objective of the analysis described in the remainder of this section is to quantify leg- specific total-crash CMFs for the left-turn lane and right-turn lane treatments at signalized, newly signalized, and unsignalized intersections in urban and rural settings using the data reported by Harwood et al. (2002). These combinations represent a maximum of 12 CMFs (= 2×3×2). A series of regression equations were developed that related the CMFs reported by Harwood et al. (2002) to leg-specific CMFs. In each equation, the leg-specific CMF represented the regression coefficient. The regression model structure is described in the report by Bonneson and Pratt (2008). The regression equations were calibrated using the crash reduction factors (CRFs) for total crashes provided in Appendix C of the report by Harwood et al. (2002). The CRFs were converted into CMFs using the following equation. 100 0.1 CRFCMF += (229) The CMFs obtained from Equation 229 were used as the dependent variable in the regression analysis. A search algorithm was used to simultaneously evaluate all of the regression equations and find the value of the leg-specific CMFs (i.e., CMFleg,m,n) that minimized the sum of the squared error. This algorithm was automated using the nonlinear regression (NLIN) procedure in the SAS software (SAS, 2009). The SAS procedure was coded to minimize the

244 weighted squared error, where the weight for each CMF observation was equal to the reciprocal of its squared standard error. The results of the model calibration are presented in Table 62. Calibration of this model focused on CMFs for total crash frequency. The R2 for the model is 0.45. TABLE 62. Turn lane CMF model statistical description - total crashes Model Statistics Value R2: 0.45 Observations no: 78 CMFs (from 248 intersections and 440 legs) Standard deviation se: ±0.083 Calibrated Coefficient Values Variable Definition Value Std. Dev. t-statistic 1 b0 Rural CMF exponent 1.397 0.136 -2.9 CMFleg,sig,left Leg-specific CMF for left-turn lane installation at signalized urban intersection 0.672 0.007 47.0 CMFleg,sig,right Leg-specific CMF for right-turn lane installation at signalized urban intersection 0.868 0.015 8.7 CMFleg,new,left Leg-specific CMF for left-turn lane installation at newly signalized urban intersection 0.694 0.021 14.6 CMFleg,new,right Leg-specific CMF for right-turn lane installation at newly signalized urban intersection 0.941 0.067 0.9 CMFleg,unsig,left Leg-specific CMF for left-turn lane installation at unsignalized urban intersection (uncontrolled) 0.586 0.028 14.8 CMFleg,unsig,right Leg-specific CMF for right-turn lane installation at unsignalized urban intersection (uncontrolled) 0.758 0.035 6.9 Note: 1 - Test of null hypothesis that coefficient value is equal to 1.0. Figure 104 provides a graphical indication of the fit of the model to the reported CMFs. The figure compares the residual error of the predicted CMF over the range of predicted CMFs. Each residual error was “standardized” by dividing it by its standard error. Each data point represents one of the 78 CMFs reported by Harwood et al. (2002). The data are centered on “0” which indicates that there is no bias in the predicted CMFs. The scatter in the data indicates that almost all observations are within three standard deviations. The CMFs reported in Table 62 for urban intersections are repeated in Table 63. The rural CMF exponent was used to compute the CMFs for rural intersections, as described in the footnote to the table. The CMFs in this table are applicable to leg-specific total crashes. They can be used with Equation 226 to estimate the relationship between turn lane presence on a leg and overall intersection crash frequency.

245 -5 -4 -3 -2 -1 0 1 2 3 4 5 0.0 0.2 0.4 0.6 0.8 1.0 Predicted CMFs St an da rd iz ed R es id ua ls Figure 104. Comparison of predicted turn lane CMFs with standardized residuals - total crashes. TABLE 63. Leg-specific turn lane CMFs - total crashes Area Type Control Type Left-Turn Lane Right-Turn Lane Rural 1 Unsignalized 2 0.47 0.68 Signalized 0.57 0.82 Newly signalized 0.60 0.92 Urban (and suburban) Unsignalized 2 0.59 0.76 Signalized 0.67 0.87 Newly signalized 0.69 0.94 Notes: 1 - Rural CMFs computed from urban CMFs for common control type and turn lane configuration using the following equation CMFrural = (CMFurban)1.397. 2 - CMFs listed are for the uncontrolled approach at an unsignalized intersection. To illustrate the use of the CMFs in Table 63, consider the installation of a left-turn lane on one approach of a four-leg urban intersection with the same AADT volume on all legs. The intersection is signal controlled. Table 63 indicates the CMF for leg-specific crashes is 0.67. Thus, if there are 10 crashes/yr on the leg before the lane is installed, the expected crash frequency after installation is 6.7 crashes/yr (= 10 ×0.67), which corresponds to a reduction of 3.3 crashes/yr. Continuing with the same example, the leg-specific CMF of 0.67 can be converted into an equivalent CMF for intersection crashes using Equation 226. Based on Equation 227, the proportion of intersection crashes for the treated leg Pk is equal to 0.25 because each leg has the same AADT volume in this example. This calculation yields a CMF of 0.91 (= 0.67 ×0.25 + 1.0

246 [1 - 0.25]). Thus, if the intersection experiences 40 crashes/yr, the expected crash frequency after installation is 36.5 crashes/yr (= 40 ×0.91), which corresponds to a reduction of 3.5 crashes/yr. Consider the installation of a left-turn lane and a right-turn lane on one approach of a four-leg urban intersection with the same AADT volume on all legs. The intersection is signal controlled. Table 63 indicates the CMF for leg-specific crashes is 0.67 and 0.87 for left-turn and right-turn lanes, respectively. The combined CMF for both lanes is equal to the product of these two CMFs, or 0.58. Thus, if there are 10 crashes/yr on the leg before the lanes are installed, the expected crash frequency after installation is 5.8 crashes/yr (= 10 ×0.58), which corresponds to a reduction of 4.2 crashes/yr. Continuing with the same example, the leg-specific CMFs of 0.67 and 0.87 can be converted into an equivalent CMF for intersection crashes using Equation 228. Based on Equation 227, the proportion of intersection crashes for the treated leg Pk is equal to 0.25 because each leg has the same AADT volume in this example. This calculation yields a CMF of 0.88 (={0.67 ×0.25 + 1.0 [1 - 0.25]} ×{0.87 ×0.25 + 1.0 [1 - 0.25]}). Thus, if the intersection experiences 40 crashes/yr, the expected crash frequency after installation is 35.3 crashes/yr (= 40 × 0.88), which corresponds to a reduction of 4.7 crashes/yr. This same result would be realized if the lanes were implemented on opposing approaches, provided that the leg AADT volumes were the same. If they are not the same, then Equation 227 would be used to compute Pk for each leg, and these two proportions would be used in Equation 228 to obtain the combined CMF. Turn Lane CMF - FI Crashes This section describes the development of leg-specific turn lane CMFs for FI crashes. The development process is the same as that described in the previous section. However, it is based on a regression analysis of the FI-based CMFs reported by Harwood et al. (2002). Details of the statistical analysis are reported by Bonneson and Pratt (2008). The R2 for the model is 0.53. The converted CMFs are listed in Table 64. The CMFs in this table are applicable to leg- specific, FI crashes. They can be used with Equations 226 or 227 to estimate the relationship between turn lane presence and intersection crash frequency. TABLE 64. Leg-specific turn lane CMFs - FI crashes Area Type Control Type Left-Turn Lane CMF Right-Turn Lane CMF Rural Unsignalized 1 0.36 0.76 Signalized 0.44 0.59 Newly signalized 0.34 0.62 Urban (and suburban) Unsignalized 1 0.59 0.87 Signalized 0.65 0.76 Newly signalized 0.57 0.78 Note: 1 - CMFs listed are for the uncontrolled approach at an unsignalized intersection.

247 Turn Lane CMF - PDO Crashes This section describes the development of leg-specific turn lane CMFs for PDO crashes. The total-crash CMFs in Table 63 and the FI crash CMFs in Table 64 were combined for this purpose. Specifically, they were used with Equation 230 to compute the equivalent PDO CMFs for each combination of area type, control type, and turn movement. ( )FIPDOFIFItot PCMFPCMFCMF −+= 0.1 (230) where, CMFtot = CMF for total crashes; CMFFI = CMF for FI crashes; CMFPDO = CMF for PDO crashes; and PFI = proportion of intersection crashes that have a fatal or injury severity. The average proportion of FI crashes in the database assembled by Harwood et al. (2002) is 0.40. This proportion was used in Equation 230 to compute the leg-specific PDO crash CMFs for turn lane treatments. The computed CMFs are listed in Table 65. TABLE 65. Leg-specific turn lane CMFs - PDO crashes Area Type Control Type Left-Turn Lane Right-Turn Lane Rural 1 Unsignalized 1 0.55 0.63 Signalized 0.66 0.97 Urban (and suburban) Unsignalized 1 0.58 0.69 Signalized 0.68 0.94 Note: 1 - CMFs listed are for the uncontrolled approach at an unsignalized intersection. Median-Width CMF Chapter 14 of the HSM indicates that median presence at an intersection can influence crash frequency, provided that its width is 14 ft or more (Highway, 2010). The HSM indicates that, at rural unsignalized intersections, an increase in median width is associated with a decrease in crash frequency. In contrast, at urban intersections (unsignalized and signalized), an increase in median width is associated with an increase in crash frequency. This latter trend is contrary to segment-based safety research that shows crash frequency decreases with an increase in median width. Although this trend is not discussed in the HSM, the referenced sources describe conflict studies that confirm a tendency for improper use of wide median areas within intersections that, when complicated by high traffic volume, results in an increased propensity for multiple-vehicle crashes (Harwood et al., 1995). Based on the discussion in the previous paragraph, the median-width CMF is defined using the following equation.

248 [ ] [ ])0.1(0.1 )0.1(0.1 ,, ,, )000,1/( )000,1/( outout WAADTbb inin WAADTbb mw PPe PPeCMF outmeoutmeAADTme inmeinmeAADTme −+ ×−+= + + (231) with, exenoutin in in AADTAADTAADTAADT AADTP +++ = (232) 0.0,, ≥−= kmbmkme WWW (233) ( )14;,, kbkmb WMaxW = (234) where, CMFmw = median-width crash modification factor; AADTin = AADT volume for crossroad leg between ramps, veh/day; Pin = proportion of total leg AADT on crossroad leg between ramps; AADTout = AADT volume for crossroad leg outside of interchange, veh/day; Pout = proportion of total leg AADT on crossroad leg outside of interchange; AADTen = AADT volume for the entrance ramp, veh/day (= 0 if ramp does not exist); AADTex = AADT volume for the exit ramp, veh/day (= 0 if ramp does not exist); Wb, k = left-turn lane (or bay) width for crossroad leg k (k = in or out) (= 0.0 if no lane present on leg), ft; Wmb, k = base median width for crossroad leg k (k = in or out), ft; Wme, k = width of median adjacent to turn lane (or bay) for crossroad leg k (k = in or out), ft; Wm = median width, ft; and bi = calibration coefficient for condition i The base median width represents the larger of the left-turn lane (or bay) width or 14 ft. It will typically have a value of 14 ft, but it could be larger if there are two or more lanes to serve left-turning traffic. Guidelines for measuring median width and left-turn lane width are provided in the next part of this chapter. The AADT volume of the loop exit ramp at a B4 terminal configuration is not included in AADTex. Similarly, the AADT volume of the loop entrance ramp at an A4 configuration is not included in AADTen. Equation 231 is applicable to ramp terminals with 0, 1, or 2 left-turn lanes (or bays) present on the crossroad. The two exponential terms in Equation 231 represent the leg-specific CMFs for median width on the two crossroad approaches. The proportions Pin and Pout are based on Equation 227; its application to the calculation of Pin is shown in Equation 232. The CMF described by Equation 231 yields a value of 1.0 when the median width is 14 ft, which is consistent with the guidance described in the HSM. If the regression coefficient bme is negative and bAADT, me is positive, then the trend described in the HSM can be replicated for urban and rural unsignalized intersections. This trend is shown in Figure 105 using hypothetical coefficients and values of Pin and Pout equal to 0.39. The thick solid lines correspond to the CMFs described in the HSM. The thin dashed lanes illustrate Equation 231 using the hypothetical coefficients. These coefficients suggest that a major road AADT volume of about 9,000 veh/day yields a CMF value of 1.0, regardless of median width.

249 0.0 0.5 1.0 1.5 2.0 2.5 10 20 30 40 50 60 Median Width, ft C ra sh M od ifi ca tio n Fa ct or Major-road AADT = 14,000 veh/day Rural, 4 Legs (Highway, 2010) Urban, 4 Legs (Highway, 2010) Major-road AADT = 5,000 veh/day Figure 105. Relationship between median width and CMF value at unsignalized intersections. Exit Ramp Capacity CMF Excessively long queues on exit ramps are recognized as sometimes creating unsafe operating conditions. Crash risk tends to increase as the length of ramp available for deceleration to the back of queue is reduced due to long queues from the downstream ramp terminal. The exit ramp capacity CMF is derived to capture this trend. It is described using the following equation. ( )exexn AADTb rc PPeCMF effex ex rc −+= 0.10.1,000,1 (235) with, ( )    − −+− = turnrightcontrolledyieldorstopsignaln turnrightflowfreeormergen n ex ex effex ,,:5.0 :0.10.15.0 , (236) exenoutin ex ex AADTAADTAADTAADT AADTP +++ = (237) where, CMFrc = exit ramp capacity crash modification factor; Pex = proportion of total leg AADT on exit ramp leg; nex, eff = effective number of lanes serving exit ramp traffic, lanes; and nex = number of lanes serving exit ramp traffic; lanes. The number of lanes serving the exit ramp is based on the count of lanes taken at the last point where all exiting movements are joined (i.e., at the channelization gore point if right-turn channelization is provided). All lanes counted need to be fully developed for 100 ft or more upstream from the point at which their respective movement intersects with the crossroad. The

250 nex = 2, nex,ef f = 1 nex = 1, nex,ef f = 0.5 nex = 2, nex,ef f = 1 nex = 1, nex,ef f = 0.5 Lbay > 100 ft Lbay < 100 ft nex = 2, nex,ef f = 1 nex = 1, nex,ef f = 0.5 Lbay > 100 ft Lbay < 100 ft nex = 2, nex,ef f = 1.5 nex = 1, nex,ef f = 1 Lbay > 100 ft Lbay < 100 ft lane (or lanes) associated with the loop exit ramp at a B4 terminal configuration are not included in this count. Similarly, the AADT volume of the loop exit ramp is not included in AADTex and the AADT volume of the loop entrance ramp at an A4 configuration is not included in AADTen. This CMF is applicable to any ramp terminal with an exit ramp. The exponential term in Equation 235 represents the leg-specific CMF for ramp capacity. The proportion Pex is based on Equation 227; its application to the calculation of Pex is shown in Equation 237. It is likely the calibration coefficient will vary, depending on whether the intersection is signalized or unsignalized. The effective number of lanes is based on the number of lanes on the exit ramp and the type of control used for the exit ramp right-turn movement. The constant “0.5” in Equation 236 approximately represents the ratio of capacity for a signal, stop, or yield controlled lane to the capacity of a free-flow lane. Figure 106 illustrates the use of Equation 236 to calculate the effective number of lanes for various exit ramp configurations. Figure 106. Effective number of lanes for various exit ramp configurations.

251 1.0 1.1 1.2 1.3 0 5 10 15 20 Average Daily Traffic Demand (1000s), veh/day C ra sh M od ifi ca tio n Fa ct or 1 lane, right turn is signal or yield control 2 lanes, right turn is signal or yield control 2 lanes, right turn is merge or free-flow with accepting lane The trend in CMF values suggested by Equation 235 is shown in Figure 107 using a hypothetical coefficient and a value of Pex equal to 0.12. The trend lines correspond to three relatively common combinations of ramp lanes and right-turn control for exit ramps. They suggest that, for a given ramp AADT volume, crash risk increases as ramp capacity decreases. The inference from this trend is that the associated ramp queues are reducing the length of ramp available for deceleration. Figure 107. Relationship between exit ramp volume, control, and CMF value at signalized terminals. Skew Angle CMF Chapter 14 of the HSM describes several CMFs for skew angle at rural unsignalized intersections (Highway, 2010). All of the CMFs are continuous functions of the skew angle. The CMF value increases above 1.0 as the skew angle increases above 0.0 degrees. Intersection skew angle is defined as 0.0 degrees when the two roadways intersect at a right angle (i.e., are perpendicular). The HSM does not provide a similar CMF for signalized intersections and suggests that this angle may have little influence on signalized intersection safety. The CMFs in the HSM provide much larger CMF values for multilane highway intersections, relative to two-lane highway intersections. This difference is not acknowledged or discussed. It is likely a reflection of the volume differences that exist among the two intersection types. Based on the discussion in the previous paragraph, the skew angle CMF is defined using the following equation. ( )exexAADTISinbsk PPeCMF exsksk −+= 0.10.1000,1/)( (238) where, CMFsk = skew angle crash modification factor;

252 0.8 1.0 1.2 1.4 1.6 1.8 0 10 20 30 40 50 60 70 Skew Angle, degrees C ra sh M od ifi ca tio n Fa ct or Minor-Road AADT = 3,500 veh/day Rural Multilane Highways, 3 Legs (Highway, 2010) Minor-Road AADT = 6,000 veh/day Rural Two-Lane Highways, 3 Legs (Highway, 2010) Isk = skew angle between exit ramp and crossroad, degrees; and Sin(x) = sine of angle x. The sine function is added to Equation 238 in recognition of the trends observed in the HSM CMFs. The sine of an angle has a relatively small change in value for angle changes in the range of 0 to 10 degrees and 80 to 90 degrees. In contrast, it has a relatively large change for angle changes between 30 and 60 degrees. These trends are logical when extended to the relationship between safety and skew angle. This CMF is applicable to any unsignalized ramp terminal with an exit ramp. The exponential term in Equation 238 represents the leg-specific CMF for skew angle. At a B4 ramp terminal, the skew angle represents that for the diagonal exit ramp (not the loop exit ramp). The AADT volume of the loop exit ramp at a B4 terminal configuration is not included in AADTex. The CMF described by Equation 238 yields a value of 1.0 when the skew angle is 0.0 degrees, which is consistent with the guidance described in the HSM. If the regression coefficient bsk is positive, then the trend described in the HSM relative to multilane and two-lane highway intersections can be replicated. This trend is shown in Figure 108 using a hypothetical coefficient. The thick solid lines correspond to the CMFs described in the HSM. The thin dashed lanes illustrate Equation 238 using a hypothetical coefficient and a value of Pex equal to 0.12. Figure 108. Relationship between skew angle and CMF value at unsignalized intersections. METHODOLOGY This part of the chapter describes the methodology used to calibrate the crossroad ramp terminal predictive models. It is divided into two sections. The first section describes several supplemental variables used to calibrate the predictive models. The second section provides an overview of the approach used to calibrate the predictive models.

253 Crossroad Left-Side Ramp Right-Side Ramp - Intersection boundary Lch,ex 10 ft 2.0 ft 2.0 ft 2.0 ft 2.0 ft Lch,en Lch,en Lch,en Supplemental Variables As noted in a previous part of this chapter, several variables in the database were obtained from aerial photographs of the ramp terminals represented in the study state databases. Of these variables, two of the more complex ones are defined in this section. Right-Turn Channelization Length Channelizing islands are frequently provided for the right-turn movements at crossroad ramp terminals. This treatment provides a larger radius for the right-turn movement which accommodates the swept path of large trucks that frequently use these terminals. A useful characteristic that describes the geometry of the channelization is the length of the channelizing island, as measured along the side of the island adjacent to the non-turning traffic stream. This length is measured from the gore point (i.e., the point where the painted gore, or its equivalent, is 2.0 ft wide) to the point where the non-turning traffic stream intersects with the near edge of the crossing traffic stream’s traveled way. This length is shown in Figure 109 for two ramp terminals with the D4 configuration. The length of interest is identified by the variables Lch,ex and Lch,en. Figure 109. Right-turn channelization length.

254 Crossroad Left-Side Ramp Right-Side Ramp - Intersection boundary Median width Median width Left-turn bay width Median Width The crossroad median width at an intersection is measured between the near edges of the traveled way associated with the opposing through traffic streams. It includes the width of the left shoulder and any left-turn lanes that are present. It is measured in an identical manner for road segments. The median width at a ramp terminal is shown in Figure 110. Figure 110. Crossroad median width. The left-turn bay width is also shown in Figure 110 for the one approach with a left-turn bay. This width is measured from the near edge of the traveled way of the adjacent through lane to the lane marking (or curb face) that delineates the median. Modeling Approach This section describes the regression modeling approach and the rationale for using a cross-sectional database. Details of the methods used for PDO model calibration are provided in Chapter 5 in the subsection titled Prediction of PDO Crash Frequency. Combined Regression Models The calibration activity used SAS that employs maximum-likelihood methods and a negative binomial distribution of crash frequency. Four models were calibrated. The form of each model is shown in the following equations. ( ) ( )kwBABABAspfBArt CMFCMFCMFCMFNN ××××××= ...... 1,221,2222,22, (239) ( ) ( )kxexDAexDAexDAspfexDArt CMFCMFCMFCMFNN ××××××= ...... 1,341,3434,34, (240)

255 ( ) ( )kyenDBenDBenDBspfenDBrt CMFCMFCMFCMFNN ××××××= ...... 1,341,3434,34, (241) ( ) ( )kzDDDspfDrt CMFCMFCMFCMFNN ××××××= ...... 1,41,44,4, (242) where all variables were defined previously. The SPFs associated with these models are defined as: )000,1/000,1/ln()000,1/ln( 22, 22,22,22,0 enexBArmpxrdBAxrdBA AADTAADTbAADTbb BAspf eN +++= (243) )000,1/000,1/ln()000,1/ln( 34, 34,34,34,0 enexexDArmpxrdexDAxrdexDA AADTAADTbAADTbb exDAspf eN +++= (244) )000,1/000,1/ln()000,1/ln( 34, 34,34,34,0 enexenDBrmpxrdenDBxrdenDB AADTAADTbAADTbb enDBspf eN +++= (245) )000,1/000,1/ln()000,1/ln( 4, 4,4,4,0 enexDrmpxrdDxrdD AADTAADTbAADTbb Dspf eN +++= (246) where all variables were defined previously. The second term of Equations 239 to 242 recognizes that the influence of some geometric factors is unique to each crash type. In contrast, the third term of Equations 239 to 242 recognizes that some geometric factors have a similar influence on all crash types. The use of common CMFs in multiple models required the use of a combined-model approach. With this approach, the regression analysis evaluated all four models simultaneously and used the total log-likelihood statistic for all models to determine the best-fit calibration coefficients. The regression analysis is described in more detail in the next part of this chapter. Cross-Sectional Database The database is described as cross-sectional (as opposed to panel). It represents a common three-year study period for all observations. Study duration in “years” is represented as an offset variable in the regression model. The rationale for using this type of database is provided in Chapter 5 in the section titled Cross-Sectional Database. Inverse Dispersion Parameter It was assumed that ramp terminal crash frequency is Poisson distributed, and that the distribution of the mean crash frequency for a group of similar ramp terminals is gamma distributed. In this manner, the distribution of crashes for a group of similar terminals can be described by the negative binomial distribution. The variance of this distribution is computed using the following equation. ( ) K NyNyXV 2 ][ += (247) where,

256 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 0.0 0.5 1.0 1.5 2.0 2.5 True Inverse Dispersion Parameter, K t Es tim at ed In ve rs e D is pe rs io n Pa rm et er , K < 50 crashes >1,000 crashes V[X] = crash frequency variance for a group of similar locations, crashes2; N = predicted average crash frequency, crashes/yr; X = reported crash count for y years, crashes; y = time interval during which X crashes were reported, yr; and K = inverse dispersion parameter (= 1/k, where k = overdispersion parameter). Research by Lord (2006) has indicated that databases with low sample mean values and small sample size may not exhibit the variability associated with crash data of similar sites, as described by Equation 247. Rather, the regression model may “over-explain” some of the random variability in a small database, or the low sample mean may introduce an instability in the model coefficients. Lord (2006) explored the effect of sample size on the variability of crash data through the use of simulation. Specifically, he simulated the crash frequency for three database sizes (i.e., 50, 100, and 1,000 sites), each with three different average crash frequencies (i.e., 0.5, 1.0, and 10 crashes per site), and three inverse dispersion parameters (i.e., 0.5, 1, and 2). One complete set of simulations consisted of the nine combinations of average crash frequency and dispersion parameter, each simulated once for each site yielding a total of 10,350 (= 3×3×[50 + 100 + 1,000]) site crash frequency estimates. A total of 30 replications was conducted yielding 310,500 site estimates. A maximum-likelihood technique was used to estimate the dispersion parameter for each of the 27 combinations. This process was repeated 30 times to yield 30 estimates of K for each of the 27 combinations. The average value of K for each combination is shown in Figure 111. Figure 111. Simulation results for the inverse dispersion parameter. As shown in Figure 111, the estimated inverse dispersion parameter for a given database was about equal to the specified (i.e., true) overdispersion parameter, provided that there were 1,000 or more crashes in the database. However, the estimated dispersion parameter was larger

257 than the true value when the number of crashes was less than 1,000. The following relationship was derived to relate the estimated and true dispersion parameters based on observed trends in the data: mpn KKK ttr )( 2.17 2 − += (248) where, Kr = estimated inverse dispersion parameter obtained from database analysis; Kt = true inverse dispersion parameter; n = number of observations (i.e., segments or intersections in database); p = number of model variables; and m = average number of crashes per observation (= total crashes in database / n). The constant “17.2” in Equation 248 represents an empirical adjustment derived through weighted regression analysis (sk = 2.45, p = 0.0001). Equation 248 was algebraically manipulated to yield the following relationship for estimating the true inverse dispersion parameter, given the other variables as input values. 5.34 )()(8.68)( 22 mpnmpnKmpn K rt −−−+− = (249) Equation 249 was used to estimate the true inverse dispersion parameter for each of the ramp terminal models described in this chapter. The ramp terminal databases tend to have a relatively small sample size. In contrast, the freeway and ramp segment databases were relatively large and did not require adjustment using Equation 249. All subsequent references to the inverse dispersion parameter K for ramp terminals show the estimated true parameter obtained from Equation 249 (i.e., hereafter, K = Kt for ramp terminals). MODEL CALIBRATION FOR FI CRASHES This part of the chapter describes the calibration and validation of the crossroad ramp terminal predictive models based on FI crashes. The first section identifies the data used for model calibration. The second section summarizes statistical analysis methods used for model calibration. The third section describes the results leading to the development of predictive models for signalized ramp terminals. The last section describes the results leading to the development of predictive models for unsignalized ramp terminals. Calibration Data The data collection process consisted of a series of activities that culminated in the assembly of a highway safety database suitable for the development of a comprehensive safety prediction methodology for crossroad ramp terminals. These activities are described in Chapter 4. Crash data were identified for each crossroad ramp terminal using the most recently available data from the HSIS. Three years of crash data were identified for each ramp terminal. The analysis period is 2005, 2006, and 2007 for the California and Washington segments. It is

258 2004, 2005, and 2006 for the Maine segments. The AADT volume for each year was merged into the assembled database. A total of 2,177 FI crashes and 4,172 PDO crashes are represented in the database. Additional information about the database is provided in Chapter 4. Statistical Analysis Methods The nonlinear regression procedure (NLMIXED) in the SAS software was used to estimate the proposed model coefficients. This procedure was used because the proposed predictive model is both nonlinear and discontinuous. The log-likelihood function for the negative binomial distribution was used to determine the best-fit model coefficients. Equation 247 was used to define the variance function for all models. The procedure was set up to estimate model coefficients based on maximum-likelihood methods. The statistics used to assess model fit to the data are described in Chapter 5. Signalized Ramp Terminal Models This section describes the development of predictive models for signalized ramp terminals. The first subsection describes the structure of the predictive models as used in the regression analysis. The second subsection describes the regression statistics for each of the calibrated models. The third subsection describes a validation of the calibrated models. The fourth subsection describes the proposed predictive models. The fifth section describes the calibrated CMFs. The last subsection provides a sensitivity analysis of the predictive models over a range of traffic demands. Model Development This subsection describes the proposed predictive models and the methods used to calibrate them. The regression models are generalized to accommodate a wide range of ramp terminal geometry and right-turn control modes. The generalized form shows all the CMFs in the model, even though some CMFs are applicable only to some ramp terminal configurations. Indicator variables are used to determine which CMFs are applicable to each ramp terminal observation in the database. Those CMFs that are not applicable to a given ramp terminal are set to 1.0 using an indicator variable. The generalized form includes intersection CMFs that include leg-specific terms for both crossroad legs, even when the associated treatment is only applicable to one leg. For example, a left-turn lane is typically added to the “inside” crossroad leg for a D4 configuration, where the inside leg is that leg located between the two ramp terminals of the interchange. In contrast, a left-turn lane is typically added to the outside crossroad leg for an A2 configuration. The generalized form of the left-turn lane CMF includes terms for both left-turn bays, where indicator variables are used to determine which terms are applicable (and which should be set to 1.0) for each observation. The following regression model form was used to facilitate the combined regression analysis of the four models for signalized ramp terminals.

259 ( ) mwslnd rtbayltbayrcpsexchxrdchltp DDspfenDBenDBspfexDAexDAspfBABAspfcajrt CMFCMFCMF CMFCMFCMFCMFCMFCMFCMF ININININCN ××× ××××××× +++×= ,,,,, 44,3434,3434,2222,, (250) with, )000,1/000,1/ln()000,1/ln( 22, 22,22,ln22,0 enexBArmpxrdBAxrdthBA AADTAADTbAADTbnbb BAspf eN ++++= (251) )000,1/000,1/ln()000,1/ln( 34, 34,34,ln34,0 enexexDArmpxrdexDAxrdthexDA AADTAADTbAADTbnbb exDAspf eN ++++= (252) )000,1/000,1/ln()000,1/ln( 34, 34,34,ln34,0 enexenDBrmpxrdenDBxrdthenDB AADTAADTbAADTbnbb enDBspf eN ++++= (253) )000,1/000,1/ln()000,1/ln( 4, 4,4,ln4,0 enexDrmpxrdDxrdthD AADTAADTbAADTbnbb Dspf eN ++++= (254) [ ] [ ] outltpoutoltp inltpinoltp I xrdxrd nb I xrdxrd nb ltp PPe PPeCMF ,,,, ,,,, )0.1(0.1 )0.1(0.1, −+ ×−+= (255) exenoutin outin xrd AADTAADTAADTAADT AADTAADTP +++ += (256) [ ] [ ] outchxrdch inchxrdch I outout b I inin b xrdch PPe PPeCMF ,, ,, )0.1(0.1 )0.1(0.1, −+ ×−+= (257) [ ] exchexch Iexexbexch PPeCMF ,, )0.1(0.1, −+= (258) psps Ib ps eCMF = (259) ( )[ ] ( )[ ] outltbay inltbay I outoutruralrural I ininruralruralltbay PPII PPIICMF ,, ,, )0.1(0.1]0.1[65.044.0 )0.1(0.1]0.1[65.044.0, −+−+ ×−+−+= (260) ( )[ ] ( )[ ] outrtbay inrtbay I outoutruralrural I ininruralruralrtbay PPII PPIICMF ,, ,, )0.1(0.1]0.1[76.059.0 )0.1(0.1]0.1[76.059.0, −+−+ ×−+−+= (261) )0.1(0.1)( outout nnb ap PPeCMF psdwnd −+= + (262) )333.0/0.1/0.1( −+= strrmpsl LLbsl eCMF (263) caca Ib ca eC = (264)

260 where, Nrt, j = predicted average crossroad ramp terminal crash frequency for model j (j = A2B2 if IA2B2 = 1.0; j = A4D3ex if IA4D3ex = 1.0; j = B4D3en if IB4D3en = 1.0; j = D4 if ID4 = 1.0;); crashes/yr; Nrt, A2B2 = predicted average crash frequency for A2 and B2 configurations, crashes/yr; Nrt, A4D3ex = predicted average crash frequency for A4 and D3ex configurations, crashes/yr; Nrt, B4D3en = predicted average crash frequency for B4 and D3en configurations, crashes/yr; Nrt, D4 = predicted average crash frequency for D4 configuration, crashes/yr; AADTxrd = AADT volume for crossroad (= 0.5 AADTin + 0.5 AADTout), veh/day; IA2B2 = crash indicator variable (= 1.0 if A2 or B2 crash data, 0.0 otherwise); IA4D3ex = crash indicator variable (= 1.0 if A4 or D3ex crash data, 0.0 otherwise); IB4D3en = crash indicator variable (= 1.0 if B4 or D3en crash data, 0.0 otherwise); ID4 = crash indicator variable (= 1.0 if D4 crash data, 0.0 otherwise); Cca = calibration factor for California; CMFp, lt = protected left-turn operation crash modification factor; CMFch, xrd = channelized right turn from crossroad crash modification factor; CMFch, ex = channelized right turn from exit ramp crash modification factor; CMFps = non-ramp public street leg crash modification factor; CMFbay, lt = crossroad left-turn lane crash modification factor; CMFbay, rt = crossroad right-turn lane crash modification factor; CMFap = access point frequency crash modification factor; CMFsl = segment length crash modification factor; nth = number of through traffic lanes on the crossroad at the ramp terminal (total of both directions), lanes; no, k = number of through traffic lanes that oppose the left-turn movement on crossroad leg k (k = in or out), lanes; Pxrd = proportion of total leg AADT on the crossroad; Ip, lt, k = protected left-turn operation indicator variable for crossroad leg k (k = in or out) (= 1.0 if protected operation exists, 0.0 otherwise); Pin = proportion of total leg AADT on crossroad leg between ramps; Pout = proportion of total leg AADT on crossroad leg outside of interchange; Ich, k = right-turn channelization indicator variable for leg k (k = in, out, or ex) (= 1.0 if right-turn channelization exists, 0.0 otherwise); Ips = non-ramp public street leg indicator variable (= 1.0 if leg is present, 0.0 otherwise); Irural = area type indicator variable (= 1.0 if area is rural, 0.0 if it is urban); Ibay, lt, k = left-turn lane (or bay) indicator variable for crossroad leg k (k = in or out) (= 1.0 if left-turn lane (or bay) present, 0.0 otherwise); Ibay, rt, k = right-turn lane (or bay) indicator variable for crossroad leg k (k = in or out) (= 1.0 if right-turn lane (or bay) present, 0.0 otherwise); ndw = number of unsignalized driveways on the crossroad leg outside of the interchange and within 250 ft of the ramp terminal; nps = number of unsignalized public street approaches to the crossroad leg outside of the interchange and within 250 ft of the ramp terminal; Lrmp = distance between subject ramp terminal and adjacent ramp terminal (measured along the crossroad from terminal center to terminal center), mi;

261 Lstr = distance between subject ramp terminal and nearest public road intersection in a direction away from freeway (measured along the crossroad from terminal center to intersection center), mi; and bi = calibration coefficient for condition i The final form of the regression model is described here, before the discussion of regression analysis results. However, this form reflects the findings from several preliminary regression analyses where alternative model forms were examined. The form that is described represents that which provided the best fit to the data, while also having coefficient values that are logical and constructs that are theoretically defensible and properly bounded. Equation 255 describes a CMF that quantifies the relationship between left-turn control mode and crash frequency. The CMF is specific to protected left-turn operation. If a ramp terminal has permissive or protected-permissive operation then it does not have protected operation. This focus on protected operation is based partly on the guidance in Chapter 14 of the HSM that indicates a change from permissive to protected-permissive operation has a negligible effect on safety. The number of opposing through traffic lanes is included in this CMF because most traffic engineering guidelines for left-turn mode selection indicate that protected operation is more effective when there are many opposing lanes. Equations 260 and 261 describe CMFs for left- and right-turn lane (or bay) presence, respectively. These CMFs are not associated with a regression coefficient. Rather, these CMFs are considered to be fairly definitive based on the extensive nature of the research that produced them (Harwood et al., 2002). The derivation of the leg-specific CMF values that are used in Equations 260 and 261 is described in the discussion associated with Table 64. Equation 263 describes the relationship between ramp terminal crash frequency and the distance to the adjacent ramp and nearest public street intersection. The preliminary examination of the data indicated that crash frequency tends to increase as this distance increases. The CMF for median-width CMFmw was described previously using Equation 231. Similarly, the CMF for exit ramp capacity CMFrc was described using Equation 235. The indicator variables used in several of the CMFs are identified in Table 66 for typical ramp terminal configurations. A value of 1.0 is shown in the table to indicate that the associated CMF can apply to the configuration, approach, and movement; whether the CMF does apply at a specific ramp terminal is based on whether the condition the CMF defines is present at that terminal.

262 TABLE 66. Indicator variable values for typical ramp terminal configurations CMF Indicator Variable Value by Ramp Terminal Configuration 1 D3ex A4 D3en B4 A2 B2 D4 Protected left turn operation Ip,lt,in = 0.0 Ip,lt,out = 0.0 Ip,lt,in = 0.0 Ip,lt,out = 0.0 Ip,lt,in = 1.0 Ip,lt,out = 0.0 Ip,lt,in = 1.0 Ip,lt,out = 0.0 Ip,lt,in = 0.0 Ip,lt,out = 1.0 Ip,lt,in = 1.0 Ip,lt,out = 0.0 Ip,lt,in = 1.0 Ip,lt,out = 0.0 Chan. right turn from crossroad Ich,in = 0.0 Ich,out = 0.0 Ich,in = 1.0 Ich,out = 1.0 Ich,in = 0.0 Ich,out = 1.0 Ich,in = 0.0 Ich,out = 1.0 Ich,in = 1.0 Ich,out = 0.0 Ich,in = 0.0 Ich,out = 1.0 Ich,in = 0.0 Ich,out = 1.0 Chan. right turn from exit ramp Ich,ex = 1.0 Ich,ex = 1.0 Ich,ex = 0.0 Ich,ex = 0.0 Ich,ex = 1.0 Ich,ex = 1.0 Ich,ex = 1.0 Crossroad left- turn lane Ibay,lt,in = 0.0 Ibay,lt,out = 0.0 Ibay,lt,in = 0.0 Ibay,lt,out = 0.0 Ibay,lt,in = 1.0 Ibay,lt,out = 0.0 Ibay,lt,in = 1.0 Ibay,lt,out = 0.0 Ibay,lt,in = 0.0 Ibay,lt,out = 1.0 Ibay,lt,in = 1.0 Ibay,lt,out = 0.0 Ibay,lt,in = 1.0 Ibay,lt,out = 0.0 Crossroad right- turn lane Ibay,rt,in = 0.0 Ibay,rt,out = 0.0 Ibay,rt,in = 1.0 Ibay,rt,out = 1.0 Ibay,rt,in = 0.0 Ibay,rt,out = 1.0 Ibay,rt,in = 0.0 Ibay,rt,out = 1.0 Ibay,rt,in = 1.0 Ibay,rt,out = 0.0 Ibay,rt,in = 0.0 Ibay,rt,out = 1.0 Ibay,rt,in = 0.0 Ibay,rt,out = 1.0 Note: 1 - An indicator value of 1.0 in this table only indicates that such a value is possible for the associated configuration. The actual indicator value can still be 0.0 if the condition it defines is not satisfied at the subject terminal (e.g., a left-turn lane is not provided). Values indicated as “0.0” can, in fact, be 1.0 if there is a non-ramp public street leg present at the ramp terminal. Model Calibration The predictive model calibration process was based on a combined-model approach, as discussed in the section titled Modeling Approach. With this approach, the combined ramp terminal models and the CMFs (represented by Equations 250 to 264) are calibrated using a common database. This approach is needed because several CMFs are common to two or more of the ramp terminal models. The models were calibrated using the California and Washington data. The Maine data were reserved for model validation. The discussion in this section focuses on the findings from the model calibration. The findings from model validation are provided in the next section. The results of the combined regression model calibration are presented in Table 67. The Pearson χ2 statistic for the model is 226, and the degrees of freedom are 202 (= n − p = 225 −23). As this statistic is less than χ2 0.05, 202 (= 236), the hypothesis that the model fits the data cannot be rejected. The t-statistic for each coefficient is listed in the last column of Table 67. These statistics describe a test of the hypothesis that the coefficient value is equal to 0.0. Those t-statistics with an absolute value that is larger than 2.0 indicate that the hypothesis can be rejected with the probability of error in this conclusion being less than 0.05. For those few variables where the absolute value of the t-statistic is smaller than 2.0, it was decided that the variable was important to the model and its trend was found to be intuitive and, where available, consistent with previous research findings (even if the specific value was not known with a great deal of certainty as applied to this database).

263 TABLE 67. Terminal FI model statistical description–combined model–two states– signalized Model Statistics Value R2: 0.56 Scale parameter φ: 1.01 Pearson χ2: 226 (χ20.05, 202 = 236) Observations no: 225 terminals (1,615 injury or fatal crashes in 3 years) Calibrated Coefficient Values Variable Inferred Effect of... Value Std. Dev. t-statistic bp, lt Protected left-turn operation -0.414 0.093 -4.5 bch, xrd Right-turn channelization on crossroad 0.524 0.191 2.7 bch, ex Right-turn channelization on exit ramp 1.014 0.278 3.6 bnd Driveways or unsignalized public street approaches 0.133 0.081 1.6 bps Public street leg at ramp terminal 0.663 0.289 2.3 bsl Distance to adjacent ramp terminal and intersection -0.0211 0.0048 -4.4 brc Exit ramp capacity 0.0684 0.0277 2.5 bme Width of median adjacent to left-turn lane (or bay) 0.0283 0.0104 2.7 bAADT, me AADT on median width -0.00072 0.0004 -1.8 b0, A2B2 A2 and B2 ramp terminal configuration -0.623 0.664 -0.9 bxrd, A2B2 Crossroad AADT 0.320 0.267 1.2 brmp, A2B2 Ramp AADT 0.195 0.243 0.8 b0, A4D3ex A4 and D3ex ramp terminal configuration -1.538 0.595 -2.6 bxrd, A4D3ex Crossroad AADT 0.355 0.185 1.9 brmp, A4D3ex Ramp AADT 0.385 0.132 2.9 b0, B4D3en B4 and D3en ramp terminal configuration -2.331 1.578 -1.5 bxrd, B4D3en Crossroad AADT 0.257 0.344 0.7 brmp, B4D3en Ramp AADT 0.922 0.675 1.4 b0, D4 D4 ramp terminal configuration -3.044 0.421 -7.2 bxrd, D4 Crossroad AADT 1.255 0.177 7.1 brmp, D4 Ramp AADT 0.114 0.162 0.7 bln Number of through lanes 0.156 0.044 3.6 bca Location in California -0.438 0.095 -4.6 The findings from an examination of the coefficient values and the corresponding CMF or SPF predictions are documented in a subsequent section. In general, the sign and magnitude of the calibration coefficients in Table 67 are logical and consistent with previous research findings. An indicator variable for the state of California was included in the regression model. The coefficient for this variable is shown in the last row of Table 67. It is statistically significant. Its value indicates that the ramp terminals in California have about 35 percent fewer crashes than those in Washington. This trend is consistent with that found in the comparison of summary crash rates for these two states in Table 25. The trend could not be explained by differences in ramp terminal design among the two states. It is likely due to differences between states that are due to unobserved variables such as approach grade, signing, pavement condition, weather, and speed limit.

264 Model Validation Model validation was a two-step process. The first step required using the calibrated models to predict the crash frequency for sites from a third state (i.e., Maine). The objective of this step was to demonstrate the robustness of the model structure and its transferability to another state. The second step required comparing the calibrated CMFs with similar CMFs reported in the literature, where such information was available. The objective of this step was to demonstrate that the calibrated CMFs were consistent with previous research findings. The findings from the first step of the validation process are described in this section. Those from the second step are described in the next section. The first step of the validation process consisted of several tasks. The first task was to quantify the local calibration factor for each of the four ramp terminal models, which would be the first step for any agency using the HSM methodology. However, only a single, overall calibration factor could be computed because there are only 11 signalized ramp terminals in the Maine database. This overall calibration factor was used to produce a “re-calibrated” set of models (i.e., the models with the coefficients from Table 67 plus the local calibration factors). The local calibration factor value for the Maine data Cme was computed as 1.30. The second task was to apply the re-calibrated models to the Maine data to compute the predicted average crash frequency for each ramp terminal. The predicted crash frequency was then compared to the reported crash frequency for each site. The third task was to compute the fit statistics and assess the robustness of the calibrated model. These statistics are listed in Table 68. The Pearson χ2 statistic for combined model is less than χ20.05 so the hypothesis that the model fits the validation data cannot be rejected. TABLE 68. Terminal model validation statistics–signalized R 2 Rk2 Scale Parameter φ Pearson χ2 Deg. of Freedom χ20.05, n - 1 0.40 0.53 1.46 14.6 10 18.3 The findings from this validation step indicate that the trends in the Maine data are not significantly different from those in the California and Washington data. These findings also suggest that the model structure is transferable to other states (when locally calibrated) for the prediction of FI crash frequency. Based on these findings, the data for the three states were combined and used in a second regression model calibration. The larger sample size associated with the combined database reduced the standard error of several calibration coefficients. Bared and Zhang (2007) also used this approach in their development of predictive models for urban freeways. Combined Model The data from the three study states were combined and the predictive models were calibrated a second time using the combined data. The calibration coefficients for the combined

265 ramp terminal models are described first. Then, the fit statistics and inverse dispersion parameter for each ramp terminal model are described. The results of the combined regression model calibration are presented in Table 69. The Pearson χ2 statistic for the model is 239, and the degrees of freedom are 212 (= n − p = 236 −24). As this statistic is less than χ2 0.05, 212 (= 247), the hypothesis that the model fits the data cannot be rejected. Several terminals were removed as a result of outlier analysis such that the calibration database included only 1,708 of the 1,740 crashes identified in Chapter 4. TABLE 69. Terminal FI model statistical description–combined model–three states– signalized Model Statistics Value R2: 0.56 Scale parameter φ: 1.02 Pearson χ2: 239 (χ20.05, 212 = 247) Observations no: 236 terminals (1,708 injury or fatal crashes in 3 years) Calibrated Coefficient Values Variable Inferred Effect of... Value Std. Dev. t-statistic bp, lt Protected left-turn operation -0.363 0.084 -4.3 bch, xrd Right-turn channelization on crossroad 0.466 0.190 2.5 bch, ex Right-turn channelization on exit ramp 0.992 0.270 3.7 bnd Driveways or unsignalized public street approaches 0.158 0.076 2.1 bps Public street leg at ramp terminal 0.592 0.285 2.1 bsl Distance to adjacent ramp terminal and intersection -0.0185 0.0046 -4.0 brc Exit ramp capacity 0.0668 0.0276 2.4 bme Width of median adjacent to left-turn lane (or bay) 0.0287 0.0102 2.8 bAADT, me AADT on median width -0.00074 0.0004 -1.9 b0, A2B2 A2 and B2 ramp terminal configuration -0.778 0.643 -1.2 bxrd, A2B2 Crossroad AADT 0.325 0.263 1.2 brmp, A2B2 Ramp AADT 0.212 0.242 0.9 b0, A4D3ex A4 and D3ex ramp terminal configuration -1.672 0.580 -2.9 bxrd, A4D3ex Crossroad AADT 0.379 0.182 2.1 brmp, A4D3ex Ramp AADT 0.394 0.131 3.0 b0, B4D3en B4 and D3en ramp terminal configuration -2.388 1.577 -1.5 bxrd, B4D3en Crossroad AADT 0.265 0.345 0.8 brmp, B4D3en Ramp AADT 0.905 0.674 1.3 b0, D4 D4 ramp terminal configuration -2.975 0.405 -7.4 bxrd, D4 Crossroad AADT 1.191 0.172 6.9 brmp, D4 Ramp AADT 0.131 0.158 0.8 bln Number of through lanes 0.160 0.043 3.7 bme Location in Maine 0.305 0.160 1.9 bca Location in California -0.477 0.093 -5.1

266 The t-statistic for each coefficient is listed in the last column of Table 69. These statistics have generally increased, relative to their counterparts in Table 67, as a result of the increased sample size. With a few exceptions, these statistics have an absolute value that is larger than 2.0, which indicates that the null hypothesis can be rejected with the probability of error in this conclusion being less than 0.05. For those few variables where the absolute value of the t- statistic is smaller than 2.0, it was decided that the variable was important to the model and its trend was found to be intuitive and, where available, consistent with previous research findings (even if the specific value was not known with a great deal of certainty as applied to this database). This consistency is demonstrated in a subsequent section. Indicator variables were included for the states of California and Maine in the regression model. These coefficients are shown in the last two rows of Table 69. The value for California is statistically significant. The value for California indicates that the ramp terminals in California have fewer crashes than those in Washington. The opposite trend is suggested for Maine ramp terminals. This trend is consistent with that found in the comparison of summary crash rates for these states in Table 25. The trend could not be explained by differences in ramp terminal design among the two states. It is likely due to differences between states that are due to unobserved variables such as approach grade, signing, pavement condition, weather, and speed limit. Model for A2 and B2 Configurations. The statistics describing the calibrated model for A2 and B2 ramp terminal configurations are presented in Table 70. The Pearson χ2 statistic for the model is 33.2, and the degrees of freedom are 31 (= n − p = 32 −1). As this statistic is less than χ20.05,31 (= 45), the hypothesis that the model fits the data cannot be rejected. The R2 for the model is 0.43. The Rk2 for the calibrated model is 0.63. The inverse dispersion parameter was adjusted using Equation 249. TABLE 70. Terminal FI model statistical description–A2 and B2 configuration–signalized Model Statistics Value R2 (Rk2): 0.43 (0.63) Scale parameter φ: 1.07 Pearson χ2: 33.2 (χ20.05, 31 = 45) Inverse dispersion parameter K: 2.17 Observations no: 32 terminals (168 injury or fatal crashes in 3 years) Standard deviation se: ±1.37 crashes/yr The coefficients in Table 69 were combined with Equation 251 to obtain the calibrated SPF for the A2 and B2 configuration. The form of the model is described in the following equation. )000,1/000,1/ln(212.0)000,1/ln(325.0160.0778.0 22, enexxrdth AADTAADTAADTn BAspf eN ++++−= (265) The calibrated CMFs used with this SPF are described in a subsequent section.

267 0 4 8 12 16 0 5 10 15 20 Predicted Injury + Fatal Crash Frequency, cr/3 yrs R ep or te d C ra sh F re qu en cy , cr /3 y rs 1 1 The fit of the calibrated model is shown in Figure 112. This figure compares the predicted and reported crash frequency in the calibration database. The trend line shown represents a “y = x” line. A data point would lie on this line if its predicted and reported crash frequency were equal. The data points shown represent the reported crash frequency for the ramp terminals used to calibrate the corresponding component model. In general, the data shown in the figure indicate that the model provides an unbiased estimate of expected crash frequency for ramp terminals experiencing up to 12 crashes in a three-year period. Figure 112. Predicted vs. reported FI crashes at signalized A2 and B2 configurations. Model for A4 and D3ex Configurations. The statistics describing the calibrated model for A4 and D3ex ramp terminal configurations are presented in Table 71. The Pearson χ2 statistic for the model is 67.1, and the degrees of freedom are 59 (= n − p = 60 −1). As this statistic is less than χ20.05,59 (= 78), the hypothesis that the model fits the data cannot be rejected. The R2 for the model is 0.45. The Rk2 for the calibrated model is 0.73. The inverse dispersion parameter was adjusted using Equation 249. TABLE 71. Terminal FI model statistical description–A4 and D3ex configuration– signalized Model Statistics Value R2 (Rk2): 0.45 (0.73) Scale parameter φ: 1.14 Pearson χ2: 67.1 (χ20.05, 59 = 78) Inverse dispersion parameter K: 8.72 Observations no: 60 terminals (422 injury or fatal crashes in 3 years) Standard deviation se: ±1.13 crashes/yr

268 0 5 10 15 20 25 0 5 10 15 20 25 30 Predicted Injury + Fatal Crash Frequency, cr/3 yrs R ep or te d C ra sh F re qu en cy , cr /3 y rs 1 1 The coefficients in Table 69 were combined with Equation 252 to obtain the calibrated SPF for the A4 and D3ex configuration. The form of the model is described in the following equation. )000,1/000,1/ln(394.0)000,1/ln(379.0160.0672.1 34, enexxrdth AADTAADTAADTn exDAspf eN ++++−= (266) The calibrated CMFs used with this SPF are described in a subsequent section. The AADT volume of the loop entrance ramp at an A4 configuration is not included in AADTen. Also, AADTen equals 0.0 when the SPF is applied to a D3ex configuration. The fit of the calibrated model is shown in Figure 113. In general, the data shown in the figure indicate that the model provides an unbiased estimate of expected crash frequency for ramp terminals experiencing up to 17 crashes in a three-year period. Figure 113. Predicted vs. reported FI crashes at signalized A4 and D3ex configurations. Model for B4 and D3en Configurations. The statistics describing the calibrated model for B4 and D3en ramp terminal configurations are presented in Table 72. The Pearson χ2 statistic for the model is 2.67, and the degrees of freedom are 3 (= n − p = 4 −1). As this statistic is less than χ20.05,3 (= 7.8), the hypothesis that the model fits the data cannot be rejected. The R2 for the model is 0.51. The Rk2 for the calibrated model is 0.57. The inverse dispersion parameter was adjusted using Equation 249. TABLE 72. Terminal FI model statistical description–B4 and D3en configuration– signalized Model Statistics Value R2 (Rk2): 0.51 (0.57) Scale parameter φ: 0.88 Pearson χ2: 2.67 (χ20.05, 3 = 7.8) Inverse dispersion parameter K: 5.37 Observations no: 4 terminals (34 injury or fatal crashes in 3 years) Standard deviation se: ±1.58 crashes/yr

269 0 5 10 15 20 25 0 5 10 15 20 25 30 Predicted Injury + Fatal Crash Frequency, cr/3 yrs R ep or te d C ra sh F re qu en cy , cr /3 y rs 1 1 The coefficients in Table 69 were combined with Equation 253 to obtain the calibrated SPF for the B4 and D3en configuration. The form of the model is described in the following equation. )000,1/000,1/ln(905.0)000,1/ln(265.0160.0388.2 34, enexxrdth AADTAADTAADTn enDBspf eN ++++−= (267) The calibrated CMFs used with this SPF are described in a subsequent section. The AADT volume of the loop exit ramp at a B4 configuration is not included in AADTex. Also, AADTex equals 0.0 when the SPF is applied to a D3en configuration. The fit of the calibrated SPF is shown in Figure 114. The small number of observations for this configuration limits the ability to make broad claims about the transferability of the SPF. The fit is adequate and the SPF predictions compare favorably with the other SPFs (see Figure 118). Local calibration will be very important for this SPF to ensure that it provides an acceptable level of accuracy. Figure 114. Predicted vs. reported FI crashes at signalized B4 and D3en configurations. Model for D4 Configuration. The statistics describing the calibrated model for D4 ramp terminal configuration are presented in Table 73. The Pearson χ2 statistic for the model is 139, and the degrees of freedom are 139 (= n − p = 140 −1). As this statistic is less than χ20.05,139 (= 167), the hypothesis that the model fits the data cannot be rejected. The R2 for the model is 0.60. The Rk2 for the calibrated model is 0.82. The inverse dispersion parameter was adjusted using Equation 249.

270 0 10 20 30 40 0 5 10 15 20 25 30 35 40 45 50 Predicted Injury + Fatal Crash Frequency, cr/3 yrs R ep or te d C ra sh F re qu en cy , cr /3 y rs 1 1 TABLE 73. Terminal FI model statistical description–D4 configuration–signalized Model Statistics Value R2 (Rk2): 0.60 (0.82) Scale parameter φ: 1.00 Pearson χ2: 139 (χ20.05, 139 = 167) Inverse dispersion parameter K: 11.5 Observations no: 140 terminals (1,084 injury or fatal crashes in 3 years) Standard deviation se: ±1.28 crashes/yr The coefficients in Table 69 were combined with Equation 254 to obtain the calibrated SPF for the D4 configuration. The form of the model is described in the following equation. )000,1/000,1/ln(131.0)000,1/ln(191.1160.0975.2 4, enexxrdth AADTAADTAADTn Dspf eN ++++−= (268) The calibrated CMFs used with this SPF are described in a subsequent section. The fit of the calibrated model is shown in Figure 115. In general, the data shown in the figure indicate that the model provides an unbiased estimate of expected crash frequency for ramp terminals experiencing up to 30 crashes in a three-year period. Figure 115. Predicted vs. reported FI crashes at signalized D4 configurations. Calibrated CMFs Several CMFs were calibrated in conjunction with the SPFs. All of them were calibrated using FI crash data. Collectively, they describe the relationship between various geometric factors and crash frequency. These CMFs are described in this section and, where possible, compared with the findings from previous research as means of model validation.

271 Many of the CMFs found in the literature are typically derived from (and applied to) “intersection” crashes. That is, one CMF is used to indicate the influence of a leg-specific geometric factor on total crashes. In contrast, the models developed for this research project include several CMFs that are calibrated for leg-specific conditions. In these instances, Equations 222 and 226 were used to convert the leg-specific CMF to an intersection CMF. The converted CMFs are compared in this subsection with the intersection CMFs reported in the literature using typical values for the leg AADT distribution at intersections (as opposed to that found at ramp terminals). The following CMFs were described previously in this chapter and are not discussed in this section. The figure provided for the last CMF listed is based on the calibration coefficients in Table 69. ● crossroad left-turn lane CMF (Equation 260, Table 64); ● crossroad right-turn lane CMF (Equation 261, Table 64); and ● exit ramp capacity CMF (Equation 235, Figure 107). Protected Left-Turn Operation CMF. The protected left-turn operation CMF is described using the following equation. [ ] [ ] outltpouto inltpino I xrdxrd n I xrdxrd n ltp PPe PPeCMF ,,, ,,, )0.1(0.1 )0.1(0.1 363.0 363.0 , −+ ×−+= − − (269) This CMF is applicable to any crossroad leg with protected left-turn operation. It is not applicable to any leg that has permissive or protected-permissive operation. The values obtained from this CMF are listed in Table 74 for both ramp terminals and for intersections. The CMF values for ramp terminals reflect a proportion of total leg AADT on the crossroad Pxrd of 0.78, which is a typical value for ramp terminals. The CMF values for intersections are based on AADT proportions that are more consistent with those found at the intersection of a major and minor street. Chapter 14 of the HSM recommends a CMF value of 0.94 for the conversion from permissive or protected-permissive left-turn operation to protected operation on one intersection leg (Highway, 2010). This value compares with the values of 0.91 and 0.79 in Table 74 for minor and major street legs, respectively. One of the references cited in the HSM as a source of the recommended value is a report by Davis and Aul (2007). Consultation of this report indicates that they derived a CMF value of 0.82 for intersections where both minor-street legs were converted. This value compares favorably with the value of 0.83 in Table 74 (second row from bottom). Davis and Aul reported a CMF value of 0.58 for an intersection where both major street legs were converted. This value compares favorably with the values of 0.41 and 0.62 in Table 74 (last row).

272 TABLE 74. Calibrated protected left-turn operation CMF for FI crashes Junction Location Legs with Protected Operation Leg Location Proportion AADT CMF Value by Number of Opposing Lanes 1 lane 2 lanes Ramp terminal 1 Crossroad 0.78 0.76 0.60 2 Crossroad 0.78 0.58 0.36 Intersection 1 Minor street 1 0.30 0.91 0.85 Major street 1 0.70 0.79 0.64 2 Minor street 1 0.30 0.83 0.71 Major street 1 0.70 0.62 0.41 Note: 1 - Intersection CMFs are computed using Equation 269 and the AADT proportion shown in the table. Channelized Right-Turn CMFs. Two CMFs are discussed in this section. One is the CMF for channelized right turns from the crossroad and the other is the CMF for right turns from the exit ramp. These two CMFs are described using the following equations. [ ] [ ] outch inch I outout I ininxrdch PPe PPeCMF , , )0.1(0.1 )0.1(0.1 466.0 466.0 , −+ ×−+= (270) [ ] exchIexexexch PPeCMF ,)0.1(0.1992.0, −+= (271) The first CMF listed is applicable to any ramp terminal with right-turn channelization on one or both crossroad legs, where the associated right-turn movement is turning from the crossroad. This CMF can be applied to channelization associated with the loop entrance ramp of the A4 configuration. The second CMF listed is applicable to any ramp terminal with a diagonal exit ramp that has right-turn channelization, where the associated right-turn movement is turning from the exit ramp. This CMF is not applicable to the loop exit ramp of the B4 configuration. The values obtained from these CMFs are listed in Table 75 for both ramp terminals and intersections. The values for ramp terminals reflect the proportion of total leg AADT on the subject legs that are typical for ramp terminals. The values for intersections are based on leg AADT proportions that are more consistent with those found at the intersection of a major and minor street. A channelized right-turn CMF derived by Bonneson and Pratt (2008) for four-leg urban signalized intersections indicates a value of 1.04 when one minor leg has channelization. This value compares with the value of 1.09 in Table 75 (second row from bottom). Similarly, this source indicates a value of 1.10 with one major leg has channelization. This value compares with the value of 1.21 in Table 75 (last row).

273 TABLE 75. Calibrated right-turn channelization CMF for FI crashes–signalized Junction Location Leg Location Proportion AADT on Leg CMF Value by Number of Legs with Channelization 1 leg 2 legs Ramp terminal Exit ramp 0.12 1.20 1.45 Crossroad 1 0.39 1.23 1.52 Intersection Minor street 1, 2 0.15 1.09 1.19 Major street 1, 2 0.35 1.21 1.46 Notes: 1 - For Equation 270, Pin is assumed to equal Pout. 2 - Intersection CMFs are computed using Equation 270 and the AADT proportion shown in the table. The value of this CMF implies that channelized right turns are less safe than right turns made at the intersection (without channelization). This finding is consistent with that of Dixon et al.(2000) (and later confirmed by Fitzpatrick et al. [2006]) who found a higher right-turn-related crash frequency for channelized right turns than for right turns made at the intersection (without channelization). It likely reflects the fact that the channelized right turn driver’s check of the merge gap requires a relatively large head rotation coupled with a lengthy diversion of attention from the road ahead. Sometimes this gap check occurs while the vehicle is still moving forward, all of which can be problematic if the right-turning driver just ahead decides to yield. Non-Ramp Public Street Leg CMF. The non-ramp public street CMF is described using the following equation. psI ps eCMF 592.0= (272) This CMF is applicable to any ramp terminal that has a fourth leg that: (1) is a public street serving two-way traffic and (2) intersects with the crossroad at the terminal. Public street legs are fairly rare (i.e., they were found at about 2 percent of the terminals in the database). At most ramp terminals, the public street leg will be on the opposite side of the crossroad from the exit ramp. At the B4 and A4 ramp terminals, the public street leg will be opposite from the diagonal exit ramp (the diagonal entrance ramp will intersect with the crossroad at some distance from the ramp terminal such that it is not part of the ramp terminal). At the D3en configuration, the public street leg will be on the opposite side of the crossroad from the entrance ramp. This CMF has a value of 1.81 when a public street approach is present at a ramp terminal. The corresponding increase in the predicted number of crashes is likely a reflection of the increased number of conflicting movements created at the ramp terminal by a two-way traffic leg. Access Point Frequency CMF. The access point frequency CMF is described using the following equation. )0.1(0.1)(158.0 outout nn ap PPeCMF psdw −+= + (273) This CMF applies to any ramp terminal with unsignalized driveways or unsignalized public street approaches on the crossroad leg that is outside of the interchange. Driveways and

274 approaches on both sides of the leg should be counted when they are within 250 ft of the ramp terminal. The count of driveways should only include active driveways (i.e., those driveways with an average daily volume of 10 veh/day or more). The values obtained from this CMF are listed in Table 76 for ramp terminals and for intersections. The CMF values for ramp terminals reflect the proportion of total leg AADT on crossroad legs that are typical for ramp terminals. The CMF values for intersections are based on leg AADT proportions that are more consistent with those found on the major street at the intersection of a major and minor street. TABLE 76. Calibrated access point frequency CMF for FI crashes–signalized Junction Location Proportion AADT on Leg CMF Value by Number of Driveways or Public Street Approaches 1 2 3 4 Ramp terminal 0.39 1.07 1.14 1.24 1.34 Intersection 1 0.35 1.06 1.13 1.21 1.31 Note: 1 - Intersection CMFs are computed using Equation 273 and the AADT proportion shown in the table. A driveway frequency CMF derived by Bonneson et al. (2005) for rural signalized intersections indicates a value of 1.05 when one driveway is present. This value compares with the value of 1.06 in Table 76 (last row). Similarly, this source indicates a value of 1.20 when four driveways are present. This value compares with the value of 1.31 in Table 76 (last row). Segment Length CMF. The segment length CMF is described using the following equation. )333.0/0.1/0.1(0185.0 −+−= strrmp LLsl eCMF (274) This CMF is applicable to all ramp configurations. It describes the relationship between ramp terminal crash frequency and the distance to the adjacent ramp or nearest public street intersection. The adjacent ramp or intersection can be signalized or unsignalized. The distances used to calibrate this CMF were as small as 100 ft. The base condition for this CMF is no adjacent ramp or public street intersection (i.e., Lrmp = Lstr = 6.0 mi). The segment length CMF is shown in Figure 116. The trend line shown indicates that the CMF value increases with increasing distance. It is rationalized that the distance between the subject ramp and its adjacent ramp and intersection is correlated with crossroad operating speed. This speed is likely to increase as distance increases, and an increase in speed is likely to increase the risk of a crash.

275 0.0 0.2 0.4 0.6 0.8 1.0 0 500 1,000 1,500 2,000 Distance to Adjacent Intersection, ft C ra sh M od ifi ca tio n Fa ct or Distance to adjacent ramp terminal = 0.15 mi Figure 116. Calibrated segment length CMF for FI crashes–signalized. Median-Width CMF. The median-width CMF is described using the following equation. [ ] [ ])0.1(0.1 )0.1(0.1 , , )000,1/00074.00287.0( )000,1/00074.00287.0( outout WAADT inin WAADT mw PPe PPeCMF outmeout inmein −+ ×−+= − − (275) with, 0.0,, ≥−= kmbmkme WWW (276) ( )12;,, kbkmb WMaxW = (277) Guidance for using this CMF was provided in the CMF Development part of this chapter (in the section titled Median-Width CMF). The constant “12” represents the minimum median width below which the CMF value is 1.0. This value is decreased from the 14 ft value stated in the HSM based on the trends found in the ramp terminal safety database. The applicable AADT volumes range from 14,000 to 60,000 veh/day. AADT volumes smaller than 14,000 should be set to 14,000 in Equation 275. The median-width CMF is shown in Figure 117. The trend line shown indicates that the CMF value increases with increasing median width. This trend is consistent with the CMF described in the HSM for urban four-leg signalized intersections. By interpolation, the HSM CMF is consistent with a crossroad AADT volume of about 23,000 veh/day. Other CMF values are obtained for other AADT volumes. A CMF value of about 1.0 is obtained for an AADT volume of 40,000 veh/day.

276 1.0 1.1 1.2 1.3 1.4 1.5 1.6 10 20 30 40 50 Median Width, ft C ra sh M od ifi ca tio n Fa ct or Ramp Terminal, 30,000 veh/day, proposed Urban, 4 Legs (Highway, 2010) Ramp Terminal, 15,000 veh/day, proposed Figure 117. Calibrated median-width CMF for FI crashes–signalized. The AADT coefficient is negative indicating that the CMF value decreases with increasing AADT volume. This trend is opposite to that for unsignalized intersections, as suggested previously by the trends in Figure 105. For AADT volumes in the range of 14,000 to 15,000, Equation 275 yields about the same CMF value as that shown in Figure 105 for unsignalized intersections. This trend suggests that the CMF value is largest for AADT volumes in this range and lower for larger or smaller AADT volumes. It is likely that the negative AADT coefficient value in Equation 275 reflects a tendency for drivers to be more cautious as the intersection becomes busier. Also, busier intersections may have long queues present for more cycles, which could reduce the likelihood of errant vehicles in middle or outside lanes that have sufficient speed to cross the median. Sensitivity Analysis The relationship between crash frequency and traffic demand, as obtained from the combined calibrated models, is shown in Figure 118 for signalized ramp terminals. The distance between ramps is 0.15 mi and the distance to the nearest public street intersection is also 0.15 mi. The ramp terminal has protected left-turn operation for the crossroad left-turn movement. All other geometric and control conditions are such that the associated CMF has a value of 1.0. The axis scale for each graph in Figure 118 is the same. This technique is used to facilitate comparison among ramp configurations. Figure 118a shows the SPF for urban three-leg signalized intersections that is described in the HSM. Similarly, Figure 118f shows the SPF for urban four-leg signalized intersections that is described in the HSM. The trend lines in Figure 118a indicate that three-leg ramp terminals have about the same number of crashes as three-leg intersections. In contrast, the trend lines in Figure 118f suggest that four-leg ramp terminals have up to 30 percent more crashes than four- leg intersections.

277 0 2 4 6 8 10 0 10 20 30 40 50 60 Crossroad AADT (1000s), veh/day Fl C ra sh F re qu en cy , c ra sh es /y r Terminal Types: A2, B2 Ramp AADT = 0.32 x Crossroad AADT 6-lane crossroad, 2-lane exit ramp4-lane crossroad, 1-lane exit ramp 2-lane crossroad, 1-lane exit ramp 0.15 miles to adjacent intersection Exit ramp right turn: signal controlled Protected crossroad left turn phase All other CMFs = 1.00 Urban, 3 Legs (Highw ay, 2010) 0 2 4 6 8 10 0 10 20 30 40 50 60 Crossroad AADT (1000s), veh/day Fl C ra sh F re qu en cy , c ra sh es /y r Terminal Type: A4 Ramp AADT = 0.32 x Crossroad AADT 6-lane crossroad, 2-lane exit ramp 4-lane crossroad, 1-lane exit ramp 2-lane crossroad, 1-lane exit ramp 0.15 miles to adjacent intersection Exit ramp right turn: signal controlled All other CMFs = 1.00 0 2 4 6 8 10 0 10 20 30 40 50 60 Crossroad AADT (1000s), veh/day FI C ra sh F re qu en cy , c ra sh es /y r Terminal Type: D3 with exit ramp Ramp AADT = 0.32 x Crossroad AADT 6-lane crossroad, 2-lane exit ramp 4-lane crossroad, 1-lane exit ramp 2-lane crossroad, 1-lane exit ramp 0.15 miles to adjacent intersection Exit ramp right turn: signal controlled All other CMFs = 1.00 0 2 4 6 8 10 0 10 20 30 40 50 60 Crossroad AADT (1000s), veh/day FI C ra sh F re qu en cy , c ra sh es /y r Terminal Type: B4 Ramp AADT = 0.32 x Crossroad AADT 6-lane crossroad, 2-lane exit ramp 4-lane crossroad, 1-lane exit ramp 2-lane crossroad, 1-lane exit ramp 0.15 miles to adjacent intersection Exit ramp right turn: signal controlled Protected crossroad left turn phase All other CMFs = 1.00 0 2 4 6 8 10 0 10 20 30 40 50 60 Crossroad AADT (1000s), veh/day FI C ra sh F re qu en cy , c ra sh es /y r Terminal Type: D3 with entrance ramp Ramp AADT = 0.32 x Crossroad AADT 6-lane crossroad 4-lane crossroad 2-lane crossroad 0.15 miles to adjacent intersection Protected crossroad left turn phase All other CMFs = 1.00 0 2 4 6 8 10 0 10 20 30 40 50 60 Crossroad AADT (1000s), veh/day FI C ra sh F re qu en cy , c ra sh es /y r Terminal Type: D4 Ramp AADT = 0.32 x Crossroad AADT 6-lane crossroad, 2-lane exit ramp 4-lane crossroad, 1-lane exit ramp 2-lane crossroad, 1-lane exit ramp 0.15 miles to adjacent intersection Exit ramp right turn: signal controlled Protected crossroad left turn phase All other CMFs = 1.00 Urban, 4 Legs (Highw ay, 2010) a. Terminal types A2 and B2. b. Terminal type A4. c. Terminal Type D3 with exit ramp. d. Terminal type B4. e. Terminal Type D3 with entrance ramp. f. Terminal type D4. Figure 118. Terminal FI models–signalized.

278 The A2, B2, and D3 configurations are shown in Figure 118 to have fewer crashes than the other configurations, for a given AADT volume. This trend is likely due to the fact that these configurations have only three legs, while the other configurations have four legs. The number of conflict points increases significantly with the number of legs. The D4 configuration is shown in Figure 118f to have more crashes for a given AADT volume than the other configurations. This trend is likely a reflection of the fact that it has four legs, two left-turn movements, and a higher “sum of conflicting volumes” than the other configurations. Although the D3en and B4 configurations are represented collectively by only four observations, the trends shown in Figure 118d and 118e are consistent with those of the other configurations shown and provide some evidence of the validity of the associated SPF. Unsignalized Ramp Terminal Models This section describes the development of predictive models for unsignalized ramp terminals. An unsignalized ramp terminal has either one-way stop control (with stop control for the exit ramp) or all-way stop control. The first subsection describes the structure of the predictive models as used in the regression analysis. The second subsection describes the regression statistics for each of the calibrated models. The third subsection describes a validation of the calibrated models. The fourth subsection describes the proposed predictive models. The fifth section describes the calibrated CMFs. The last subsection provides a sensitivity analysis of the predictive models over a range of traffic demands. Model Development This subsection describes the proposed predictive models and the methods used to calibrate them. The regression models are generalized to accommodate a wide range of ramp terminal geometry and right-turn control modes. The generalized form shows all the CMFs in the model, even though some CMFs are applicable only to some ramp terminal configurations. Indicator variables are used to determine which CMFs are applicable to each ramp terminal observation in the database. Those CMFs that are not applicable to a given ramp terminal are set to 1.0 using an indicator variable. The generalized form includes intersection CMFs that include leg-specific terms for both crossroad legs, even when the associated treatment is only applicable to one leg. For example, a left-turn lane is typically added to the “inside” crossroad leg for a D4 configuration, where the inside leg is that leg located between the two ramp terminals of the interchange. In contrast, a left-turn lane is typically added to the outside crossroad leg for an A2 configuration. The generalized form of the left-turn lane CMF includes terms for both left-turn bays, where indicator variables are used to determine which terms are applicable (and which should be set to 1.0) for each observation.

279 The following regression model form was used to facilitate the combined regression analysis of the four models for unsignalized ramp terminals. ( ) awscmwslns rtbayltbayrcsk DDspfenDBenDBspfexDAexDAspfBABAspfjrt CMFCMFCMFCMF CMFCMFCMFCMF ININININN ×××× ×××× +++= ,, 44,3434,3434,2222,, (278) with, )000,1/000,1/ln()000,1/ln( 22, 22,22,22,0 enexBArmpxrdBAxrdruralruralBA AADTAADTbAADTbIbb BAspf eN ++++= (279) )000,1/000,1/ln()000,1/ln( 34, 34,34,34,0 enexexDArmpxrdexDAxrdruralruralexDA AADTAADTbAADTbIbb exDAspf eN ++++= (280) )000,1/000,1/ln()000,1/ln( 34, 34,34,34,0 enexenDBrmpxrdenDBxrdruralruralenDB AADTAADTbAADTbIbb enDBspf eN ++++= (281) )000,1/000,1/ln()000,1/ln( 4, 4,4,4,0 enexDrmpxrdDxrdruralruralD AADTAADTbAADTbIbb Dspf eN ++++= (282) ( )[ ] ( )[ ] outltbay inltbay I outoutruralrural I ininruralruralltbay PPII PPIICMF ,, ,, )0.1(0.1]0.1[59.036.0 )0.1(0.1]0.1[59.036.0, −+−+ ×−+−+= (283) ( )[ ] ( )[ ] outrtbay inrtbay I outoutruralrural I ininruralruralrtbay PPII PPIICMF ,, ,, )0.1(0.1]0.1[87.076.0 )0.1(0.1]0.1[87.076.0, −+−+ ×−+−+= (284) )0.1(0.1 outout nb ap PPeCMF psns −+= (285) )333.0/0.1/0.1( −+= strrmpsl LLbsl eCMF (286) awscawsc Ib awsc eCMF = (287) where, CMFap = access point frequency crash modification factor; CMFawsc = all-way stop control crash modification factor; and Iawsc = all-way stop control indicator variable (= 1.0 if ramp terminal has all-way stop controlled, 0.0 if it has one-way stop control for the exit ramp). All other variables are defined previously. The final form of the regression model is described here, before the discussion of regression analysis results. However, this form reflects the findings from several preliminary regression analyses where alternative model forms were examined. The form that is described represents that which provided the best fit to the data, while also having coefficient values that are logical and constructs that are theoretically defensible and properly bounded.

280 Equations 283 and 284 describe CMFs for left- and right-turn lane (or bay) presence, respectively. These CMFs are not associated with a regression coefficient. Rather, these CMFs are considered to be fairly definitive based on the extensive nature of the research that produced them (Harwood et al., 2002). The derivation of the leg-specific CMF values that are used in Equations 283 and 284 is described in the discussion associated with Table 64. Equation 286 describes the relationship between ramp terminal crash frequency and the distance to the adjacent ramp and nearest public street intersection. The preliminary examination of the data indicated that crash frequency tends to increase as this distance increases. Equation 287 describes the relationship between ramp terminal crash frequency and the presence of all-way stop control. If the ramp terminal has one-way stop control (with stop control for the exit ramp), then this CMF equals 1.0. The CMF for median-width CMFmw was described previously using Equation 231. Similarly, the CMF for exit ramp capacity CMFrc was described using Equation 235 and the CMF for skew was described using Equation 238. The indicator variables used in several of the CMFs were previously identified in Table 66 for typical ramp terminal configurations. Model Calibration The predictive model calibration process was based on a combined-model approach, as discussed in the section titled Modeling Approach. With this approach, the combined ramp terminal models and the CMFs (represented by Equations 278 to 287) are calibrated using a common database. This approach is needed because several CMFs are common to two or more of the ramp terminal models. The models were calibrated using the California and Washington data. The Maine data were reserved for model validation. The discussion in this section focuses on the findings from the model calibration. The findings from model validation are provided in the next section. The results of the combined regression model calibration are presented in Table 77. The Pearson χ2 statistic for the model is 273, and the degrees of freedom are 240 (= n − p = 260 −20). As this statistic is less than χ2 0.05, 240 (= 277), the hypothesis that the model fits the data cannot be rejected. The t-statistic for each coefficient is listed in the last column of Table 77. These statistics describe a test of the hypothesis that the coefficient value is equal to 0.0. Those t-statistics with an absolute value that is larger than 2.0 indicate that the hypothesis can be rejected with the probability of error in this conclusion being less than 0.05. For those few variables where the absolute value of the t-statistic is smaller than 2.0, it was decided that the variable was important to the model and its trend was found to be intuitive and, where available, consistent with previous research findings (even if the specific value was not known with a great deal of certainty as applied to this database).

281 TABLE 77. Terminal FI model statistical description–combined model–two states– unsignalized Model Statistics Value R2: 0.41 Scale parameter φ: 1.05 Pearson χ2: 273 (χ20.05, 240 = 277) Observations no: 260 terminals (325 injury or fatal crashes in 3 years) Calibrated Coefficient Values Variable Inferred Effect of... Value Std. Dev. t-statistic bsk Skew angle between exit ramp and crossroad 0.487 0.333 1.5 bns Unsignalized public street approaches 0.588 0.304 1.9 bsl Distance to adjacent ramp terminal and intersection -0.0178 0.0079 -2.3 brc Exit ramp capacity 0.162 0.046 3.5 bme Width of median adjacent to left-turn lane (or bay) -0.0410 0.040 -1.0 bAADT, me AADT on median width 0.00411 0.0029 1.4 bawsc All-way stop control -0.422 0.300 -1.4 b0, A2B2 A2 and B2 ramp terminal configuration -2.410 0.597 -4.0 bxrd, A2B2 Crossroad AADT 0.232 0.389 0.6 brmp, A2B2 Ramp AADT 0.876 0.384 2.3 b0, A4D3ex A4 and D3ex ramp terminal configuration -2.545 0.842 -3.0 bxrd, A4D3ex Crossroad AADT 0.369 0.374 1.0 brmp, A4D3ex Ramp AADT 0.854 0.239 3.6 b0, B4D3en B4 and D3en ramp terminal configuration -4.202 1.731 -2.4 bxrd, B4D3en Crossroad AADT 0.805 0.532 1.5 brmp, B4D3en Ramp AADT 1.111 0.456 2.4 b0, D4 D4 ramp terminal configuration -3.049 0.355 -8.6 bxrd, D4 Crossroad AADT 1.054 0.178 5.9 brmp, D4 Ramp AADT 0.140 0.157 0.9 bln Rural area type 0.355 0.161 2.2 The findings from an examination of the coefficient values and the corresponding CMF or SPF predictions are documented in a subsequent section. In general, the sign and magnitude of the calibration coefficients in Table 77 are logical and consistent with previous research findings. Model Validation Model validation was a two-step process. The first step required using the calibrated models to predict the crash frequency for sites from a third state (i.e., Maine). The objective of this step was to demonstrate the robustness of the model structure and its transferability to another state. The second step required comparing the calibrated CMFs with similar CMFs reported in the literature, where such information was available. The objective of this step was to demonstrate that the calibrated CMFs were consistent with previous research findings.

282 The findings from the first step of the validation process are described in this section. Those from the second step are described in the next section. The first step of the validation process consisted of several tasks. The first task was to quantify the local calibration factor for each of the four ramp terminal models, which would be the first step for any agency using the HSM methodology. However, only a single, overall calibration factor could be computed because there are only 41 unsignalized ramp terminals in the Maine database. This overall calibration factor was used to produce a “re-calibrated” set of models (i.e., the models with the coefficients from Table 77 plus the local calibration factors). The local calibration factor value for the Maine data Cme was computed as 0.81. The second task was to apply the re-calibrated models to the Maine data to compute the predicted average crash frequency for each ramp terminal. The predicted crash frequency was then compared to the reported crash frequency for each site. The third task was to compute the fit statistics and assess the robustness of the combined calibrated model. These statistics are listed in Table 78. The Pearson χ2 statistic for combined model is less than χ20.05 so the hypothesis that the model fits the validation data cannot be rejected. TABLE 78. Terminal model validation statistics–unsignalized R 2 Rk2 Scale Parameter φ Pearson χ2 Deg. of Freedom χ20.05, n - 1 0.28 0.39 1.14 45.7 40 55.8 The findings from this validation step indicate that the trends in the Maine data are not significantly different from those in the California and Washington data. These findings also suggest that the model structure is transferable to other states (when locally calibrated) for the prediction of FI crash frequency. Based on these findings, the data for the three states were combined and used in a second regression model calibration. The larger sample size associated with the combined database reduced the standard error of several calibration coefficients. Bared and Zhang (2007) also used this approach in their development of predictive models for urban freeways. Combined Model The data from the three study states were combined and the predictive models were calibrated a second time using the combined data. The calibration coefficients for the combined ramp terminal models are described first. Then, the fit statistics and inverse dispersion parameter for each ramp terminal model are described. The results of the combined regression model calibration are presented in Table 79. The Pearson χ2 statistic for the model is 311, and the degrees of freedom are 281 (= n − p = 301 −20). As this statistic is less than χ2 0.05, 281 (= 321), the hypothesis that the model fits the data cannot be rejected. Several terminals were removed as a result of outlier analysis such that the calibration database included only 365 of the 420 crashes identified in Chapter 4.

283 TABLE 79. Terminal FI model statistical description–combined model–three states– unsignalized Model Statistics Value R2: 0.40 Scale parameter φ: 1.04 Pearson χ2: 311 (χ20.05, 281 = 321) Observations no: 301 terminals (365 injury or fatal crashes in 3 years) Calibrated Coefficient Values Variable Inferred Effect of... Value Std. Dev. t-statistic bsk Skew angle between exit ramp and crossroad 0.341 0.404 0.8 bns Unsignalized public street approaches 0.522 0.309 1.7 bsl Distance to adjacent ramp terminal and intersection -0.0141 0.0075 -1.9 brc Exit ramp capacity 0.151 0.046 3.3 bme Width of median adjacent to left-turn lane (or bay) -0.0322 0.036 -0.9 bAADT, me AADT on median width 0.00354 0.0027 1.3 bawsc All-way stop control -0.377 0.295 -1.3 b0, A2B2 A2 and B2 ramp terminal configuration -2.687 0.588 -4.6 bxrd, A2B2 Crossroad AADT 0.260 0.357 0.7 brmp, A2B2 Ramp AADT 0.947 0.348 2.7 b0, A4D3ex A4 and D3ex ramp terminal configuration -3.223 0.847 -3.8 bxrd, A4D3ex Crossroad AADT 0.582 0.376 1.5 brmp, A4D3ex Ramp AADT 0.899 0.228 4.0 b0, B4D3en B4 and D3en ramp terminal configuration -3.141 0.992 -3.2 bxrd, B4D3en Crossroad AADT 0.709 0.384 1.8 brmp, B4D3en Ramp AADT 0.730 0.323 2.3 b0, D4 D4 ramp terminal configuration -3.064 0.331 -9.2 bxrd, D4 Crossroad AADT 1.008 0.171 5.9 brmp, D4 Ramp AADT 0.177 0.149 1.2 bln Rural area type 0.324 0.147 2.2 The t-statistic for each coefficient is listed in the last column of Table 79. These statistics have generally increased, relative to their counterparts in Table 77, as a result of the increased sample size. With a few exceptions, these statistics have an absolute value that is larger than 2.0, which indicates that the null hypothesis can be rejected with the probability of error in this conclusion being less than 0.05. For those few variables where the absolute value of the t- statistic is smaller than 2.0, it was decided that the variable was important to the model and its trend was found to be intuitive and, where available, consistent with previous research findings (even if the specific value was not known with a great deal of certainty as applied to this database). This consistency is demonstrated in a subsequent section. Model for A2 and B2 Configurations. The statistics describing the calibrated model for A2 and B2 ramp terminal configurations are presented in Table 80. The Pearson χ2 statistic for the model is 32.9, and the degrees of freedom are 39 (= n − p = 40 −1). As this statistic is less

284 than χ20.05,39 (= 55), the hypothesis that the model fits the data cannot be rejected. The R2 for the model is 0.55. The Rk2 for the calibrated model is 1.00. TABLE 80. Terminal FI model statistical description–A2 and B2 configuration– unsignalized Model Statistics Value R2 (Rk2): 0.55 (1.00) Scale parameter φ: 0.84 Pearson χ2: 32.9 (χ20.05, 39 = 55) Inverse dispersion parameter K: 99 (3.40 recommended for EB applications) Observations no: 40 terminals (61 injury or fatal crashes in 3 years) Standard deviation se: ±0.34 crashes/yr The fit of the model to the data was sufficiently good that the inverse overdispersion factor was infinitely large such that the error distribution converged to a Poisson distribution. However, this result is likely an aberration of the data (i.e., relatively small sample coupled with too much similarity among ramp terminals). The true error distribution for these configurations is undoubtedly negative binomial and the inverse dispersion parameter is likely to be much lower than 99. It is desirable to have an estimate of the inverse dispersion parameter K for EB applications of the predictive method. A lower bound on this parameter was obtained by conducting a regression analysis using the null model (i.e., N = b0) with a negative binomial distribution. The parameter for this model knull was 3.40. The true value of K for the calibrated model is likely to be larger than 3.40 but less than 99. Hence, for the EB application a conservatively small value of K equal to 3.40 is recommended. The coefficients in Table 79 were combined with Equation 279 to obtain the calibrated SPF for the A2 and B2 configuration. The form of the model is described in the following equation. )000,1/000,1/ln(947.0)000,1/ln(260.0324.0687.2 22, enexxrdrural AADTAADTAADTI BAspf eN ++++−= (288) The calibrated CMFs used with this SPF are described in a subsequent section. The fit of the calibrated model is shown in Figure 119. This figure compares the predicted and reported crash frequency in the calibration database. In general, the data shown in the figure indicate that the model provides an unbiased estimate of expected crash frequency for ramp terminals experiencing up to 5 crashes in a three-year period.

285 0 1 2 3 4 5 6 0 2 4 6 8 Predicted Injury + Fatal Crash Frequency, cr/3 yrs R ep or te d C ra sh F re qu en cy , cr /3 y rs 1 1 Figure 119. Predicted vs. reported FI crashes at unsignalized A2 and B2 configurations. Model for A4 and D3ex Configurations. The statistics describing the calibrated model for A4 and D3ex ramp terminal configurations are presented in Table 81. The Pearson χ2 statistic for the model is 35.1, and the degrees of freedom are 36 (= n − p = 37 −1). As this statistic is less than χ20.05,36 (= 51), the hypothesis that the model fits the data cannot be rejected. The R2 for the model is 0.55. The Rk2 for the calibrated model is 0.88. The inverse dispersion parameter was adjusted using Equation 249. TABLE 81. Terminal FI model statistical description–A4 and D3ex configuration– unsignalized Model Statistics Value R2 (Rk2): 0.55 (0.88) Scale parameter φ: 0.88 Pearson χ2: 31.5 (χ20.05, 36 = 51) Inverse dispersion parameter K: 2.16 Observations no: 37 terminals (58 injury or fatal crashes in 3 years) Standard deviation se: ±0.51 crashes/yr The coefficients in Table 79 were combined with Equation 280 to obtain the calibrated SPF for the A4 and D3ex configuration. The form of the model is described in the following equation. )000,1/000,1/ln(899.0)000,1/ln(582.0324.0223.3 34, enexxrdrural AADTAADTAADTI exDAspf eN ++++−= (289)

286 0 2 4 6 8 10 0 2 4 6 8 10 12 Predicted Injury + Fatal Crash Frequency, cr/3 yrs R ep or te d C ra sh F re qu en cy , cr /3 y rs 1 1 The calibrated CMFs used with this SPF are described in a subsequent section. The AADT volume of the loop entrance ramp at an A4 configuration is not included in AADTen. Also, AADTen equals 0.0 when the SPF is applied to a D3ex configuration. The fit of the calibrated model is shown in Figure 120. In general, the data shown in the figure indicate that the model provides an unbiased estimate of expected crash frequency for ramp terminals experiencing up to 8 crashes in a three-year period. Figure 120. Predicted vs. reported FI crashes at unsignalized A4 and D3ex configurations. Model for B4 and D3en Configurations. The statistics describing the calibrated model for B4 and D3en ramp terminal configurations are presented in Table 82. The Pearson χ2 statistic for the model is 17.8, and the degrees of freedom are 21 (= n − p = 22 −1). As this statistic is less than χ20.05,21 (= 33), the hypothesis that the model fits the data cannot be rejected. The R2 for the model is 0.22. The Rk2 for the calibrated model is 0.81. The inverse dispersion parameter was adjusted using Equation 249. TABLE 82. Terminal FI model statistical description–B4 and D3en configuration– unsignalized Model Statistics Value R2 (Rk2): 0.22 (0.81) Scale parameter φ: 0.85 Pearson χ2: 17.8 (χ20.05, 21 = 33) Inverse dispersion parameter K: 0.918 Observations no: 22 terminals (40 injury or fatal crashes in 3 years) Standard deviation se: ±0.61 crashes/yr The coefficients in Table 79 were combined with Equation 281 to obtain the calibrated SPF for the B4 and D3en configuration. The form of the model is described by the following equation.

287 0 2 4 6 8 0 2 4 6 8 10 Predicted Injury + Fatal Crash Frequency, cr/3 yrs R ep or te d C ra sh F re qu en cy , cr /3 y rs 1 1 )000,1/000,1/ln(730.0)000,1/ln(709.0324.0141.3 34, enexxrdrural AADTAADTAADTI enDBspf eN ++++−= (290) The calibrated CMFs used with this SPF are described in a subsequent section. The AADT volume of the loop exit ramp at a B4 configuration is not included in AADTex. Also, AADTex equals 0.0 when the SPF is applied to a D3en configuration. The fit of the calibrated model is shown in Figure 121. In general, the data shown in the figure indicate that the model provides an unbiased estimate of expected crash frequency for ramp terminals experiencing up to 8 crashes in a three-year period. Figure 121. Predicted vs. reported FI crashes at unsignalized B4 and D3en configurations. Model for D4 Configuration. The statistics describing the calibrated model for D4 ramp terminal configuration are presented in Table 83. The Pearson χ2 statistic for the model is 214, and the degrees of freedom are 201 (= n − p = 202 −1). As this statistic is less than χ20.05,201 (= 235), the hypothesis that the model fits the data cannot be rejected. The R2 for the model is 0.31. The Rk2 for the calibrated model is 0.74. The inverse dispersion parameter was adjusted using Equation 249. TABLE 83. Terminal FI model statistical description–D4 configuration–unsignalized Model Statistics Value R2 (Rk2): 0.31 (0.74) Scale parameter φ: 1.06 Pearson χ2: 214 (χ20.05, 201 = 235) Inverse dispersion parameter K: 2.58 Observations no: 202 terminals (206 injury or fatal crashes in 3 years) Standard deviation se: ±0.41 crashes/yr

288 0 1 2 3 4 0 1 2 3 4 5 Predicted Injury + Fatal Crash Frequency, cr/3 yrs R ep or te d C ra sh F re qu en cy , cr /3 y rs 1 1 Each data point represents an average of 10 sites. The coefficients in Table 79 were combined with Equation 282 to obtain the calibrated SPF for the D4 configuration. The form of the model is described in the following equation. )000,1/000,1/ln(177.0)000,1/ln(008.1324.0064.3 4, enexxrdrural AADTAADTAADTI Dspf eN ++++−= (291) The calibrated CMFs used with this SPF are described in a subsequent section. The fit of the calibrated model is shown in Figure 122. In general, the data shown in the figure indicate that the model provides an unbiased estimate of expected crash frequency for ramp terminals experiencing up to 4 crashes in a three-year period. Figure 122. Predicted vs. reported FI crashes at unsignalized D4 configurations. Each data point shown in Figure 122 represents the average predicted and average reported crash frequency for a group of 10 ramp terminals. The data were sorted by predicted crash frequency to form groups of terminals with similar crash frequency. The purpose of this grouping was to reduce the number of data points shown in the figure and, thereby, to facilitate an examination of trends in the data. The individual terminal observations were used for model calibration. Calibrated CMFs Several CMFs were calibrated in conjunction with the SPFs. All of them were calibrated using FI crash data. Collectively, they describe the relationship between various geometric factors and crash frequency. These CMFs are described in this section and, where possible, compared with the findings from previous research as means of model validation. Many of the CMFs found in the literature are typically derived from (and applied to) “intersection” crashes. That is, one CMF is used to indicate the influence of a leg-specific

289 1.0 1.1 1.2 1.3 0 1 2 3 4 5 Average Daily Traffic Demand (1000s), veh/day C ra sh M od ifi ca tio n Fa ct or 1 lane, right turn is stop or yield control 2 lanes, right turn is stop or yield control 2 lanes, right turn is merge or free-f low w ith accepting lane geometric factor on total crashes. In contrast, the models developed for this research project include several CMFs that are calibrated for leg-specific conditions. In these instances, Equations 222 and 226 were used to convert the leg-specific CMF to an intersection CMF. The converted CMFs are compared in this subsection with the intersection CMFs reported in the literature using typical values for the leg AADT distribution at intersections (as opposed to that found at ramp terminals). The following CMFs were described previously in this chapter and are not discussed in this section. The figure provided for the last CMF listed is based on the calibration coefficients in Table 79. ● crossroad left-turn lane CMF (Equation 283, Table 64); ● crossroad right-turn lane CMF (Equation 284, Table 64); and ● skew angle CMF (Equation 238, Figure 108). Exit Ramp Capacity CMF. The exit ramp capacity CMF is described using the following equation. ( )exexn AADT rc PPeCMF effex ex −+= 0.10.1,000,1 151.0 (292) Guidance for using this CMF was provided in the CMF Development part of this chapter (in the section titled exit ramp capacity CMF). The exit ramp capacity CMF is shown in Figure 123. The trend line shown indicates that the CMF value increases with increasing exit ramp AADT volume. For a given AADT volume, the CMF value is lower with a two-lane ramp than a one-lane ramp. For a given AADT volume on a two-lane ramp, the CMF value is lower for the ramp with right-turn merge operation than the ramp with right-turn stop control. This trend is consistent with the exit ramp capacity CMF described previously for signalized ramp terminals. Figure 123. Calibrated exit ramp capacity CMF for FI crashes–unsignalized.

290 Access Point Frequency CMF. The access point frequency CMF is described using the following equation. )0.1(0.1522.0 outout n ap PPeCMF ps −+= (293) This CMF applies to any ramp terminal with one or more unsignalized public street approaches on the crossroad leg that is outside of the interchange. Approaches on both sides of the leg should be counted when they are within 250 ft of the ramp terminal. The values obtained from this CMF are listed in Table 84 for ramp terminals and for intersections. The CMF values for ramp terminals reflect the proportion of total leg AADT on crossroad legs that are typical for ramp terminals. The CMF values for intersections are based on leg AADT proportions that are more consistent with those found on the major street at the intersection of a major and minor street. TABLE 84. Calibrated access point frequency CMF for FI crashes–unsignalized Junction Location Proportion AADT on Leg CMF Value by Number of Public Street Approaches 1 2 Ramp terminal 0.39 1.26 1.71 Intersection 1 0.35 1.24 1.64 Note: 1 - Intersection CMFs are computed using Equation 293 and the AADT proportion shown in the table. Segment Length CMF. The segment length CMF is described using the following equation. )333.0/0.1/0.1(0141.0 −+−= strrmp LLsl eCMF (294) This CMF is applicable to all ramp configurations. It describes the relationship between ramp terminal crash frequency and the distance to the adjacent ramp or nearest public street intersection. The adjacent ramp or intersection can be signalized or unsignalized. The distances used to calibrate this CMF were as small as 100 ft. The base condition for this CMF is no adjacent ramp or public street intersection (i.e., Lrmp = Lstr = 6.0 mi). The segment length CMF is shown in Figure 124. The trend line shown indicates that the CMF value increases with increasing distance. It is rationalized that the distance between the subject ramp and its adjacent ramp and intersection is correlated with crossroad operating speed. This speed is likely to increase as distance increases, and an increase in speed is likely to increase the risk of a crash.

291 0.0 0.2 0.4 0.6 0.8 1.0 0 500 1,000 1,500 2,000 Distance to Adjacent Intersection, ft C ra sh M od ifi ca tio n Fa ct or Distance to adjacent ramp terminal = 0.19 mi Figure 124. Calibrated segment length CMF for FI crashes–unsignalized. All-Way Stop Control CMF. The all-way stop control CMF is described using the following equation. awscI awsc eCMF 377.0−= (295) This CMF is applicable to any ramp terminal where an engineering study has determined that all-way stop control is appropriate. The base condition is one-way stop control for the ramp terminal with stop control for the exit ramp left-turn movement. The regression coefficient indicates that the CMF has a value of 0.686 when applied to all- way stop-controlled ramp terminals. Chapter 14 of the HSM identifies a CMF value of 0.30 for urban intersections converted from minor road stop control to all-way stop control. It identifies a CMF value of 0.52 for rural intersections undergoing this conversion. Median-Width CMF. The median-width CMF is described using the following equation. [ ] [ ])0.1(0.1 )0.1(0.1 , , )000,1/00354.00322.0( )000,1/00354.00322.0( outout WAADT inin WAADT mw PPe PPeCMF outmeout inmein −+ ×−+= +− +− (296) with, 0.0,, ≥−= kmbmkme WWW (297) ( )12;,, kbkmb WMaxW = (298) Guidance for using this CMF was provided in the CMF Development part of this chapter (in the section titled Median-Width CMF). The constant “12” represents the minimum median

292 width below which the CMF value is 1.0. This value is decreased from the 14 ft value stated in the HSM based on the trends found in the ramp terminal safety database. The applicable AADTs range from 0 to 14,000 veh/day. AADT volumes larger than 14,000 should be set to 14,000 in Equation 296. The median-width CMF is shown in Figure 105. Sensitivity Analysis The relationship between crash frequency and traffic demand, as obtained from the combined calibrated models, is illustrated in Figure 125 for unsignalized ramp terminals. The distance between ramps is 0.19 mi and the distance to the nearest public street intersection is also 0.19 mi. The ramp terminal is located in an urban area. All other geometric and control conditions are such that the associated CMF has a value of 1.0. The axis scale for each graph in Figure 125 is the same. This technique is used to facilitate comparison among ramp configurations. Figure 125a also shows the SPF for urban three-leg unsignalized intersections that is described in the HSM. Similarly, Figure 125f shows the SPF for urban four-leg unsignalized intersections that is described in the HSM. The trend lines shown in Figure 125a indicate that three- leg ramp terminals have about the same number of crashes as three-leg intersections. In contrast, the trend lines in Figure 125f suggest that four-leg ramp terminals can have up to 25 percent fewer crashes than four-leg intersections. The A2, B2, and D3 configurations are shown in Figure 125 to have fewer crashes than the other configurations, for a given AADT volume. This trend is likely due to the fact that these configurations have only three legs, while the other configurations have four legs. The number of conflict points increases significantly with the number of legs. MODEL CALIBRATION FOR PDO CRASHES This part of the chapter describes the calibration of the crossroad ramp terminal predictive models based on PDO crashes. The methodology used to calibrate the models is described in the part titled Methodology. The calibration data, model development, and statistical analysis methods are described in the part titled Model Calibration for FI Crashes. Signalized Ramp Terminal Models This section describes the calibrated PDO crash prediction models for signalized ramp terminals. The regression model used had the same form as used to develop the FI crash prediction model (i.e., Equation 250). The turn bay CMFs were obtained from Table 65. An initial regression analysis was undertaken with county and state variable combinations treated as fixed effects and as random effects. The Hausman test was performed using the covariance matrix to determine whether the fixed-effect model was appropriate. The null hypothesis is that the regression coefficients from the two model treatments are consistent. This hypothesis was rejected (p = 0.0001) indicating that the coefficients are different (i.e., inconsistent) among the two treatments. In this case, it is concluded that the regression coefficient values are influenced by county so a fixed-effect treatment is needed to remove the county effect.

293 0.0 0.4 0.8 1.2 1.6 2.0 0 5 10 15 20 25 Crossroad AADT (1000s), veh/day FI C ra sh F re qu en cy , c ra sh es /y r Terminal Types: A2, B2 Ramp AADT = 0.32 x Crossroad AADT 4-lane crossroad, 2-lane exit ramp 2-lane crossroad, 1-lane exit ramp Urban area 0.19 miles to adjacent intersection Exit ramp right turn: stop controlled All other CMFs = 1.00 Urban, 3 Legs (Highw ay, 2010) 0.0 0.4 0.8 1.2 1.6 2.0 0 5 10 15 20 25 Crossroad AADT (1000s), veh/day FI C ra sh F re qu en cy , c ra sh es /y r Terminal Type: A4 Ramp AADT = 0.32 x Crossroad AADT 4-lane crossroad, 2-lane exit ramp 2-lane crossroad, 1-lane exit ramp Urban area 0.19 miles to adjacent intersection Exit ramp right turn: stop controlled All other CMFs = 1.00 0.0 0.4 0.8 1.2 1.6 2.0 0 5 10 15 20 25 Crossroad AADT (1000s), veh/day FI C ra sh F re qu en cy , c ra sh es /y r Terminal Type: D3 with exit ramp Ramp AADT = 0.32 x Crossroad AADT 4-lane crossroad, 2-lane exit ramp 2-lane crossroad, 1-lane exit ramp Urban area 0.19 miles to adjacent intersection Exit ramp right turn: stop controlled All other CMFs = 1.00 0.0 0.4 0.8 1.2 1.6 2.0 0 5 10 15 20 25 Crossroad AADT (1000s), veh/day FI C ra sh F re qu en cy , c ra sh es /y r Terminal Type: B4 Ramp AADT = 0.32 x Crossroad AADT 4-lane crossroad, 2-lane exit ramp 2-lane crossroad, 1-lane exit ramp Urban area 0.19 miles to adjacent intersection Exit ramp right turn: stop controlled All other CMFs = 1.00 0.0 0.4 0.8 1.2 1.6 2.0 0 5 10 15 20 25 Crossroad AADT (1000s), veh/day FI C ra sh F re qu en cy , c ra sh es /y r Terminal Type: D3 with entrance ramp Ramp AADT = 0.32 x Crossroad AADT 4-lane crossroad 2-lane crossroad Urban area 0.19 miles to adjacent intersection All other CMFs = 1.00 0.0 0.4 0.8 1.2 1.6 2.0 0 5 10 15 20 25 Crossroad AADT (1000s), veh/day FI C ra sh F re qu en cy , c ra sh es /y r Terminal Type: D4 Ramp AADT = 0.32 x Crossroad AADT 4-lane crossroad, 2-lane exit ramp 2-lane crossroad, 1-lane exit ramp Urban area 0.19 miles to adjacent intersection Exit ramp right turn: stop controlled All other CMFs = 1.00 Urban, 4 Legs (Highw ay, 2010) a. Terminal types A2 and B2. b. Terminal type A4. c. Terminal Type D3 with exit ramp. d. Terminal type B4. e. Terminal Type D3 with entrance ramp. f. Terminal type D4. Figure 125. Terminal FI models–unsignalized.

294 Model Calibration The results of the regression model calibration are presented in Table 85. The Pearson χ2 statistic for the model is 219, and the degrees of freedom are 215 (= n − p = 236 −21). As this statistic is less than χ2 0.05, 215 (= 250), the hypothesis that the model fits the data cannot be rejected. Several segments were removed as a result of outlier analysis such that the calibration database included only 3,245 of the 3,349 crashes identified in Chapter 4. TABLE 85. Terminal PDO model statistical description–combined model–three states– signalized Model Statistics Value R2: 0.53 Scale parameter φ: 0.93 Pearson χ2: 219 (χ20.05, 215 = 250) Observations no: 236 terminals (3,245 PDO crashes in 3 years) Calibrated Coefficient Values Variable Inferred Effect of... Value Std. Dev. t-statistic bp, lt Protected left-turn operation -0.223 0.089 -2.5 bch, xrd Right-turn channelization on crossroad 0.465 0.210 2.2 bch, ex Right-turn channelization on exit ramp 1.429 0.231 6.2 bnd Driveways or unsignalized public street approaches 0.203 0.079 2.6 bps Public street leg at ramp terminal 0.520 0.277 1.9 bsl Distance to adjacent ramp terminal and intersection -0.0186 0.0049 -3.8 bme Width of median adjacent to left-turn lane (or bay) 0.0610 0.0242 2.5 bAADT, me AADT on median width -0.00246 0.0010 -2.4 b0, A2B2 A2 and B2 ramp terminal configuration -2.309 0.886 -2.6 bxrd, A2B2 Crossroad AADT 0.592 0.304 1.9 brmp, A2B2 Ramp AADT 0.516 0.217 2.4 b0, A4D3ex A4 and D3ex ramp terminal configuration -2.755 0.801 -3.4 bxrd, A4D3ex Crossroad AADT 0.797 0.227 3.5 brmp, A4D3ex Ramp AADT 0.384 0.119 3.2 b0, B4D3en B4 and D3en ramp terminal configuration -3.543 1.725 -2.1 bxrd, B4D3en Crossroad AADT 0.741 0.411 1.8 brmp, B4D3en Ramp AADT 0.845 0.655 1.3 b0, D4 D4 ramp terminal configuration -3.058 0.522 -5.9 bxrd, D4 Crossroad AADT 0.879 0.186 4.7 brmp, D4 Ramp AADT 0.545 0.182 3.0 bln Number of through lanes 0.0879 0.055 1.6 The t-statistic for each coefficient is listed in the last column of Table 85. These statistics describe a test of the hypothesis that the coefficient value is equal to 0.0. Those t-statistics with an absolute value that is larger than 2.0 indicate that the hypothesis can be rejected with the probability of error in this conclusion being less than 0.05. For those few variables where the absolute value of the t-statistic is smaller than 2.0, it was decided that the variable was important to the model and its trend was found to be intuitive and, where available, consistent with

295 previous research findings (even if the specific value was not known with a great deal of certainty as applied to this database). The coefficients for 43 county indicator variables are not shown in Table 85 because their individual significance is not directly relevant to model fit assessment or its application. However, it is recognized that the “intercept” variables in Table 85 (i.e., b0, A2Bs, b0, A4D3ex, b0, B4D3en, b0, D4) correspond to only one state and county combination. Desirably, the intercept would represent an average value for all states and counties in the database. To this end, the predicted crash frequencies from the model described by Table 85 were submitted to a second regression analysis using Equation 115 (in Chapter 5). The regression coefficient co was determined to be 0.596 for the A2B2 intercept, 0.332 for the A4D3ex intercept, 0.436 for the B4D3en intercept, and 0.634 for the D4 intercept. Each of these values is added to the appropriate intercept variables to compute an average intercept value for the overall database. This addition is shown in the models described in the next section. Calibrated Models This section describes the fit statistics and inverse dispersion parameter for each of the four ramp terminal models. It also shows the model form with the calibration coefficients from Table 85. Model for A2 and B2 Configurations. The statistics describing the calibrated model for A2 and B2 ramp terminal configurations are presented in Table 86. The Pearson χ2 statistic for the model is 27.0, and the degrees of freedom are 31 (= n − p = 32 −1). As this statistic is less than χ20.05,31 (= 45.0), the hypothesis that the model fits the data cannot be rejected. The R2 for the model is 0.62. The Rk2 for the calibrated model is 0.77. The inverse dispersion parameter was adjusted using Equation 249. TABLE 86. Terminal PDO model statistical description–A2 and B2 configuration– signalized Model Statistics Value R2 (Rk2): 0.62 (0.77) Scale parameter φ: 0.87 Pearson χ2: 27.0 (χ20.05, 31 = 45) Inverse dispersion parameter K: 4.27 Observations no: 32 terminals (321 PDO crashes in 3 years) Standard deviation se: ±2.12 crashes/yr The coefficients in Table 85 were combined with the regression model to obtain the calibrated SPF for the A2 and B2 configuration. The form of the model is described in the following equation. )000,1/000,1/ln(516.0)000,1/ln(592.00879.0596.0309.2 22, enexxrdth AADTAADTAADTn BAspf eN +++++−= (299) The calibrated CMFs used with this SPF are described in a subsequent section.

296 0 4 8 12 16 20 24 0 5 10 15 20 25 30 Predicted PDO Crash Frequency, cr/3 yrs R ep or te d C ra sh F re qu en cy , cr /3 y rs 1 1 The fit of the calibrated model is shown in Figure 126. This figure compares the predicted and reported crash frequency in the calibration database. In general, the data shown in the figure indicate that the model provides an unbiased estimate of expected crash frequency for ramp terminals experiencing up to 20 crashes in a three-year period. Figure 126. Predicted vs. reported PDO crashes at signalized A2 and B2 configurations. Model for A4 and D3ex Configurations. The statistics describing the calibrated model for A4 and D3ex ramp terminal configurations are presented in Table 87. The Pearson χ2 statistic for the model is 55.1, and the degrees of freedom are 59 (= n − p = 60 −1). As this statistic is less than χ20.05,59 (= 78), the hypothesis that the model fits the data cannot be rejected. The R2 for the model is 0.48. The Rk2 for the calibrated model is 0.56. The inverse dispersion parameter was adjusted using Equation 249. TABLE 87. Terminal PDO model statistical description–A4 and D3ex configuration– signalized Model Statistics Value R2 (Rk2): 0.48 (0.56) Scale parameter φ: 0.93 Pearson χ2: 55.1 (χ20.05, 59 = 78) Inverse dispersion parameter K: 4.05 Observations no: 60 terminals (814 PDO crashes in 3 years) Standard deviation se: ±2.48 crashes/yr The coefficients in Table 85 were combined with the regression model to obtain the calibrated SPF for the A4 and D3ex configuration. The form of the model is: )000,1/000,1/ln(384.0)000,1/ln(797.00879.0332.0755.2 34, enexxrdth AADTAADTAADTn exDAspf eN +++++−= (300)

297 0 10 20 30 40 50 0 5 10 15 20 25 30 35 40 45 50 55 60 Predicted PDO Crash Frequency, cr/3 yrs R ep or te d C ra sh F re qu en cy , cr /3 y rs 1 1 The calibrated CMFs used with this SPF are described in a subsequent section. The AADT volume of the loop entrance ramp at an A4 configuration is not included in AADTen. Also, AADTen equals 0.0 when the SPF is applied to a D3ex configuration. The fit of the calibrated model is shown in Figure 127. In general, the data shown in the figure indicate that the model provides an unbiased estimate of expected crash frequency for ramp terminals experiencing up to 30 crashes in a three-year period. Figure 127. Predicted vs. reported PDO crashes at signalized A4 and D3ex configurations. Model for B4 and D3en Configurations. The statistics describing the calibrated model for B4 and D3en ramp terminal configurations are presented in Table 88. The Pearson χ2 statistic for the model is 2.50, and the degrees of freedom are 3 (= n − p = 4 −1). As this statistic is less than χ20.05,3 (= 7.8), the hypothesis that the model fits the data cannot be rejected. The R2 for the model is 0.27. The Rk2 for the calibrated model is 0.63. The inverse dispersion parameter was adjusted using Equation 249. TABLE 88. Terminal PDO model statistical description–B4 and D3en configuration– signalized Model Statistics Value R2 (Rk2): 0.27 (0.63) Scale parameter φ: 0.83 Pearson χ2: 2.50 (χ20.05, 3 = 7.8) Inverse dispersion parameter K: 3.72 Observations no: 4 terminals (61 PDO crashes in 3 years) Standard deviation se: ±3.75 crashes/yr

298 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 45 50 Predicted PDO Crash Frequency, cr/3 yrs R ep or te d C ra sh F re qu en cy , cr /3 y rs 1 1 The coefficients in Table 85 were combined with the regression model to obtain the calibrated SPF for the B4 and D3en configuration. The form of the model is described in the following equation. )000,1/000,1/ln(845.0)000,1/ln(741.00879.0436.0543.3 34, enexxrdth AADTAADTAADTn enDBspf eN +++++−= (301) The calibrated CMFs used with this SPF are described in a subsequent section. The AADT volume of the loop exit ramp at a B4 configuration is not included in AADTex. Also, AADTex equals 0.0 when the SPF is applied to a D3en configuration. The fit of the calibrated SPF is shown in Figure 128. The small number of observations for this configuration limits the ability to make broad claims about the transferability of the SPF. The fit is adequate and the SPF predictions compare favorably with the other SPFs (see Figure 132). Local calibration will be very important for this SPF to ensure that it provides an acceptable level of accuracy. Figure 128. Predicted vs. reported PDO crashes at signalized B4 and D3en configurations. Model for D4 Configuration. The statistics describing the calibrated model for D4 ramp terminal configuration are presented in Table 89. The Pearson χ2 statistic for the model is 135, and the degrees of freedom are 139 (= n − p = 140 −1). As this statistic is less than χ20.05,139 (= 167), the hypothesis that the model fits the data cannot be rejected. The R2 for the model is 0.53. The Rk2 for the calibrated model is 0.69. The inverse dispersion parameter was adjusted using Equation 249.

299 0 10 20 30 40 50 60 0 10 20 30 40 50 60 70 80 Predicted PDO Crash Frequency, cr/3 yrs R ep or te d C ra sh F re qu en cy , cr /3 y rs 1 1 TABLE 89. Terminal PDO model statistical description–D4 configuration–signalized Model Statistics Value R2 (Rk2): 0.53 (0.69) Scale parameter φ: 0.97 Pearson χ2: 135 (χ20.05, 139 = 167) Inverse dispersion parameter K: 7.21 Observations no: 140 terminals (2,049 PDO crashes in 3 years) Standard deviation se: ±2.47 crashes/yr The coefficients in Table 85 were combined with the regression model to obtain the calibrated SPF for the D4 configuration. The form of the model is described by the following equation. )000,1/000,1/ln(545.0)000,1/ln(879.00879.0634.0058.3 4, enexxrdth AADTAADTAADTn Dspf eN +++++−= (302) The calibrated CMFs used with this SPF are described in a subsequent section. The fit of the calibrated model is shown in Figure 129. In general, the data shown in the figure indicate that the model provides an unbiased estimate of expected crash frequency for ramp terminals experiencing up to 55 crashes in a three-year period. Figure 129. Predicted vs. reported PDO crashes at signalized D4 configurations. Calibrated CMFs Several CMFs were calibrated in conjunction with the SPFs. All of them were calibrated using PDO crash data. Collectively, they describe the relationship between various geometric factors and crash frequency.

300 Many of the CMFs found in the literature are typically derived from (and applied to) “intersection” crashes. That is, one CMF is used to indicate the influence of a leg-specific geometric factor on total crashes. In contrast, the models developed for this research project include several CMFs that are calibrated for leg-specific conditions. In these instances, Equations 222 and 226 were used to convert the leg-specific CMF to an intersection CMF for the purpose of illustrating the overall trend. Left-Turn Lane CMF. The left-turn lane CMF is described using the following equation. ( )[ ] ( )[ ] outltbay inltbay I outoutruralrural I ininruralruralltbay PPII PPIICMF ,, ,, )0.1(0.1]0.1[68.066.0 )0.1(0.1]0.1[68.066.0, −+−+ ×−+−+= (303) Equation 303 is not associated with one of the regression coefficients in Table 85. Rather, it is based on a fairly definitive set of CMFs developed by Harwood et al. 2002. The derivation of the leg-specific CMF values that are used in Equation 303 is described in the discussion associated with Table 65. This CMF is applicable to turn bay presence on one or both of the crossroad legs at the ramp terminal. The values obtained from this CMF are listed in Table 90. The CMF values reflect a proportion of total leg AADT on the crossroad Pin and Pout of 0.39, which is a typical value for ramp terminals. TABLE 90. Calibrated left-turn CMF for PDO crashes–signalized Junction Location Legs with Turn Lane Leg Location Proportion AADT on Leg CMF Value by Area Type Urban Rural Ramp terminal 1 Crossroad 1 0.39 0.88 0.87 2 Crossroad 1 0.39 0.77 0.75 Note: 1 - For Equation 303, Pin is assumed to equal Pout. Right-Turn Lane CMF. The right-turn lane CMF is described using the following equation. ( )[ ] ( )[ ] outrtbay inrtbay I outoutruralrural I ininruralruralrtbay PPII PPIICMF ,, ,, )0.1(0.1]0.1[94.097.0 )0.1(0.1]0.1[94.097.0, −+−+ ×−+−+= (304) Equation 304 is not associated with one of the regression coefficients in Table 85. Rather, it is based on a fairly definitive set of CMFs developed by Harwood et al. (2002). The derivation of the leg-specific CMF values that are used in Equation 304 is described in the discussion associated with Table 65. This CMF is applicable to turn bay presence on one or both of the crossroad legs at the ramp terminal.

301 The values obtained from this CMF are listed in Table 91. The CMF values reflect a proportion of total leg AADT on the crossroad Pin and Pout of 0.39, which is a typical value for ramp terminals. TABLE 91. Calibrated right-turn CMF for PDO crashes–signalized Junction Location Legs with Turn Lane Leg Location Proportion AADT on Leg CMF Value by Area Type Urban Rural Ramp terminal 1 Crossroad 1 0.39 0.98 0.99 2 Crossroad 1 0.39 0.95 0.98 Note: 1 - For Equation 304, Pin is assumed to equal Pout. Protected Left-Turn Operation CMF. The protected left-turn operation CMF is described using the following equation. [ ] [ ] outltpouto inltpino I xrdxrd n I xrdxrd n ltp PPe PPeCMF ,,, ,,, )0.1(0.1 )0.1(0.1 223.0 223.0 , −+ ×−+= − − (305) This CMF is applicable to any crossroad leg with protected left-turn operation. It is not applicable to any leg that has permissive or protected-permissive operation. The values obtained from this CMF are listed in Table 92. The CMF values reflect a proportion of total leg AADT on the crossroad Pxrd of 0.78, which is a typical value for ramp terminals. TABLE 92. Calibrated protected left-turn operation CMF for PDO crashes Junction Location Legs with Protected Operation Leg Location Proportion AADT CMF Value by Number of Opposing Lanes 1 lane 2 lanes Ramp terminal 1 Crossroad 0.78 0.84 0.72 2 Crossroad 0.78 0.71 0.52 Channelized Right-Turn CMFs. Two CMFs are discussed in this section. One is the CMF for channelized right turns from the crossroad and the other is the CMF for right turns from the exit ramp. These two CMFs are described using the following equations. [ ] [ ] outch inch I outout I ininxrdch PPe PPeCMF , , )0.1(0.1 )0.1(0.1 465.0 465.0 , −+ ×−+= (306)

302 [ ] exchIexexexch PPeCMF ,)0.1(0.1429.1, −+= (307) The first CMF listed is applicable to any ramp terminal with right-turn channelization on one or both crossroad legs, where the associated right-turn movement is turning from the crossroad. This CMF can be applied to channelization associated with the loop entrance ramp of the A4 configuration. The second CMF listed is applicable to any ramp terminal with a diagonal exit ramp that has right-turn channelization, where the associated right-turn movement is turning from the exit ramp. This CMF is not applicable to the loop exit ramp of the B4 configuration. The values obtained from these CMFs are listed in Table 93. The values reflect the proportion of total leg AADT on the subject legs that are typical for ramp terminals. TABLE 93. Calibrated right-turn channelization CMF for PDO crashes–signalized Junction Location Leg Location Proportion AADT on Leg CMF Value by Number of Legs with Channelization 1 leg 2 legs Ramp terminal Exit ramp 0.12 1.38 1.91 Crossroad 1 0.39 1.23 1.52 Note: 1 - For Equation 306, Pin is assumed to equal Pout. The value of this CMF implies that channelized right turns are less safe than right turns made at the intersection (without channelization). This finding is consistent with that of Dixon et al.(2000) (and later confirmed by Fitzpatrick et al. [2006]) who found a higher right-turn-related crash frequency for channelized right turns than for right turns made at the intersection (without channelization). It likely reflects the fact that the channelized right turn driver’s check of the merge gap requires a relatively large head rotation coupled with a lengthy diversion of attention from the road ahead. Sometimes this gap check occurs while the vehicle is still moving forward, all of which can be problematic if the right-turning driver just ahead decides to yield. Non-Ramp Public Street Leg CMF. The non-ramp public street CMF is described using the following equation. psI ps eCMF 520.0= (308) This CMF is applicable to any ramp terminal that has a fourth leg that: (1) is a public street serving two-way traffic and (2) intersects with the crossroad at the terminal. Public street legs are fairly rare (i.e., they were found at about 2 percent of the terminals in the database). At most ramp terminals, the public street leg will be on the opposite side of the crossroad from the exit ramp. At the B4 and A4 ramp terminals, the public street leg will be opposite from the diagonal exit ramp (the diagonal entrance ramp will intersect with the crossroad at some distance

303 from the ramp terminal such that it is not part of the ramp terminal). At the D3en configuration, the public street leg will be on the opposite side of the crossroad from the entrance ramp. This CMF has a value of 1.68 when a public street approach is present at a ramp terminal. The corresponding increase in the predicted number of crashes is likely a reflection of the increased number of conflicting movements created at the ramp terminal by a two-way traffic leg. Access Point Frequency CMF. The access point frequency CMF is described using the following equation. )0.1(0.1)(203.0 outout nn ap PPeCMF psdw −+= + (309) This CMF applies to any ramp terminal with unsignalized driveways or unsignalized public street approaches on the crossroad leg that is outside of the interchange. Driveways and approaches on both sides of the leg should be counted when they are within 250 ft of the ramp terminal. The count of driveways should only include active driveways (i.e., those driveways with an average daily volume of 10 veh/day or more). The values obtained from this CMF are listed in Table 94. The CMF values reflect the proportion of total leg AADT on crossroad legs that are typical for ramp terminals. TABLE 94. Calibrated access point frequency CMF for PDO crashes–signalized Junction Location Proportion AADT on Leg CMF Value by Number of Driveways or Public Street Approaches 1 2 3 4 Ramp terminal 0.39 1.09 1.19 1.33 1.49 Segment Length CMF. The segment length CMF is described using the following equation. )333.0/0.1/0.1(0186.0 −+−= strrmp LLsl eCMF (310) This CMF is applicable to all ramp configurations. It describes the relationship between ramp terminal crash frequency and the distance to the adjacent ramp or nearest public street intersection. The adjacent ramp or intersection can be signalized or unsignalized. The distances used to calibrate this CMF were as small as 100 ft. The base condition for this CMF is no adjacent ramp or public street intersection (i.e., Lrmp = Lstr = 6.0 mi). The segment length CMF is shown in Figure 130. The trend line shown indicates that the CMF value increases with increasing distance. It is rationalized that the distance between the subject ramp and its adjacent ramp and intersection is correlated with crossroad operating speed. This speed is likely to increase as distance increases, and an increase in speed is likely to increase the risk of a crash.

304 0.0 0.2 0.4 0.6 0.8 1.0 0 500 1,000 1,500 2,000 Distance to Adjacent Intersection, ft C ra sh M od ifi ca tio n Fa ct or Distance to adjacent ramp terminal = 0.15 mi Figure 130. Calibrated segment length CMF for PDO crashes–signalized. Median-Width CMF. The median-width CMF is described using the following equation. [ ] [ ])0.1(0.1 )0.1(0.1 , , )000,1/00246.00610.0( )000,1/00246.00610.0( outout WAADT inin WAADT mw PPe PPeCMF outmeout inmein −+ ×−+= − − (311) with, 0.0,, ≥−= kmbmkme WWW (312) ( )12;,, kbkmb WMaxW = (313) Guidance for using this CMF was provided in the CMF Development part of this chapter (in the section titled Median-Width CMF). The constant “12” represents the minimum median width below which the CMF value is 1.0. This value is decreased from the 14 ft value stated in the HSM based on the trends found in the ramp terminal safety database. The applicable AADT volumes range from 14,000 to 60,000 veh/day. AADT volumes smaller than 14,000 should be set to 14,000 in Equation 311. The median-width CMF is shown in Figure 131. The trend line shown indicates that the CMF value increases with increasing median width, provided that the AADT volume is less than 25,000 veh/day. The reverse trend occurs for AADT volumes in excess of about 25,000 veh/day. A CMF value of about 1.0 is obtained for an AADT volume of 25,000 veh/day.

305 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 10 20 30 40 50 Median Width, ft C ra sh M od ifi ca tio n Fa ct or Ramp Terminal, 30,000 veh/day Ramp Terminal, 15,000 veh/day Figure 131. Calibrated median-width CMF for PDO crashes–signalized. The AADT coefficient is negative indicating that the CMF value decreases with increasing AADT volume. It is likely that the negative AADT coefficient value in Equation 311 reflects a tendency for drivers to be more cautious as the intersection becomes busier. Also, busier intersections may have long queues present for more cycles, which could reduce the likelihood of errant vehicles in middle or outside lanes that have sufficient speed to cross the median. Sensitivity Analysis The relationship between crash frequency and traffic demand, as obtained from the combined calibrated models, is shown in Figure 132 for signalized ramp terminals. The distance between ramps is 0.15 mi and the distance to the nearest public street intersection is also 0.15 mi. The ramp terminal has protected left-turn operation for the crossroad left-turn movement. All other geometric and control conditions are such that the associated CMF has a value of 1.0. The axis scale for each graph in Figure 132 is the same. This technique is used to facilitate comparison among ramp configurations. The A2, B2, and D3 configurations are shown in Figure 132 to have fewer crashes than the other configurations, for a given AADT volume. This trend is likely due to the fact that these configurations have only three legs, while the other configurations have four legs. The number of conflict points increases significantly with the number of legs. The D4 configuration is shown in Figure 132f to have more crashes for a given AADT volume than the other configurations. This trend is likely a reflection of the fact that it has four legs, two left-turn movements, and a higher “sum of conflicting volumes” than the other configurations. Although the D3en and B4 configurations are represented collectively by only four observations, the trends shown in Figure 132d and 132e are consistent with those of the other configurations shown and provide some evidence of the validity of the associated SPF.

306 0 2 4 6 8 10 0 10 20 30 40 50 60 Crossroad AADT (1000s), veh/day PD O C ra sh F re qu en cy , cr as he s/ yr Terminal Types: A2, B2 Ramp AADT = 0.32 x Crossroad AADT 6-lane crossroad, 2-lane exit ramp 4-lane crossroad, 1-lane exit ramp 2-lane crossroad, 1-lane exit ramp 0.15 miles to adjacent intersection Protected crossroad left turn phase All other CMFs = 1.00 0 2 4 6 8 10 0 10 20 30 40 50 60 Crossroad AADT (1000s), veh/day PD O C ra sh F re qu en cy , cr as he s/ yr Terminal Type: A4 Ramp AADT = 0.32 x Crossroad AADT 6-lane crossroad, 2-lane exit ramp 4-lane crossroad, 1-lane exit ramp 2-lane crossroad, 1-lane exit ramp 0.15 miles to adjacent intersection All other CMFs = 1.00 0 2 4 6 8 10 0 10 20 30 40 50 60 Crossroad AADT (1000s), veh/day PD O C ra sh F re qu en cy , cr as he s/ yr Terminal Type: D3 with exit ramp Ramp AADT = 0.32 x Crossroad AADT 6-lane crossroad, 2-lane exit ramp 4-lane crossroad, 1-lane exit ramp 2-lane crossroad, 1-lane exit ramp 0.15 miles to adjacent intersection All other CMFs = 1.00 0 2 4 6 8 10 0 10 20 30 40 50 60 Crossroad AADT (1000s), veh/day PD O C ra sh F re qu en cy , cr as he s/ yr Terminal Type: B4 Ramp AADT = 0.32 x Crossroad AADT 6-lane crossroad, 2-lane exit ramp 4-lane crossroad, 1-lane exit ramp 2-lane crossroad, 1-lane exit ramp 0.15 miles to adjacent intersection Protected crossroad left turn phase All other CMFs = 1.00 0 2 4 6 8 10 0 10 20 30 40 50 60 Crossroad AADT (1000s), veh/day PD O C ra sh F re qu en cy , cr as he s/ yr Terminal Type: D3 with entrance ramp Ramp AADT = 0.32 x Crossroad AADT 6-lane crossroad 4-lane crossroad 2-lane crossroad 0.15 miles to adjacent intersection Protected crossroad left turn phase All other CMFs = 1.00 0 2 4 6 8 10 0 10 20 30 40 50 60 Crossroad AADT (1000s), veh/day PD O C ra sh F re qu en cy , cr as he s/ yr Terminal Type: D4 Ramp AADT = 0.32 x Crossroad AADT 6-lane crossroad, 2-lane exit ramp 4-lane crossroad, 1-lane exit ramp 2-lane crossroad, 1-lane exit ramp 0.15 miles to adjacent intersection Protected crossroad left turn phase All other CMFs = 1.00 a. Terminal types A2 and B2. b. Terminal type A4. c. Terminal Type D3 with exit ramp. d. Terminal type B4. e. Terminal Type D3 with entrance ramp. f. Terminal type D4. Figure 132. Terminal PDO models–signalized.

307 Unsignalized Ramp Terminal Models This section describes the calibrated PDO crash prediction models for signalized ramp terminals. The regression model used had the same form as used to develop the FI crash prediction model (i.e., Equation 278). The turn bay CMFs were obtained from Table 65. An initial regression analysis was undertaken with county and state variable combinations treated as fixed effects and as random effects. The Hausman test was performed using the covariance matrix to determine whether the fixed-effect model was appropriate. The null hypothesis is that the regression coefficients from the two model treatments are consistent. This hypothesis was rejected (p = 0.02) indicating that the coefficients are different (i.e., inconsistent) among the two treatments. In this case, it is concluded that the regression coefficient values are influenced by county so a fixed-effect treatment is needed to remove the county effect. Model Calibration The results of the combined regression model calibration are presented in Table 95. The Pearson χ2 statistic for the model is 297, and the degrees of freedom are 289 (= n − p = 301 −12). As this statistic is less than χ2 0.05, 289 (= 330), the hypothesis that the model fits the data cannot be rejected. Several terminals were removed as a result of outlier analysis such that the calibration database included only 656 of the 786 crashes identified in Chapter 4. TABLE 95. Terminal PDO model statistical description–combined model–three states– unsignalized Model Statistics Value R2: 0.61 Scale parameter φ: 0.99 Pearson χ2: 297 (χ20.05, 289 = 330) Observations no: 301 terminals (656 PDO crashes in 3 years) Calibrated Coefficient Values Variable Inferred Effect of... Value Std. Dev. t-statistic b0, A2B2 A2 and B2 ramp terminal configuration -3.595 0.652 -5.5 bxrd, A2B2 Crossroad AADT 0.773 0.350 2.2 brmp, A2B2 Ramp AADT 0.878 0.331 2.7 b0, A4D3ex A4 and D3ex ramp terminal configuration -3.164 0.704 -4.5 bxrd, A4D3ex Crossroad AADT 0.595 0.309 1.9 brmp, A4D3ex Ramp AADT 0.937 0.199 4.7 b0, B4D3en B4 and D3en ramp terminal configuration -2.961 0.706 -4.2 bxrd, B4D3en Crossroad AADT 0.885 0.302 2.9 brmp, B4D3en Ramp AADT 0.350 0.264 1.3 b0, D4 D4 ramp terminal configuration -2.953 0.309 -9.6 bxrd, D4 Crossroad AADT 0.845 0.144 5.9 brmp, D4 Ramp AADT 0.476 0.133 3.6

308 The t-statistic for each coefficient is listed in the last column of Table 95. These statistics describe a test of the hypothesis that the coefficient value is equal to 0.0. Those t-statistics with an absolute value that is larger than 2.0 indicate that the hypothesis can be rejected with the probability of error in this conclusion being less than 0.05. For those few variables where the absolute value of the t-statistic is smaller than 2.0, it was decided that the variable was important to the model and its trend was found to be intuitive and, where available, consistent with previous research findings (even if the specific value was not known with a great deal of certainty as applied to this database). The coefficients for 43 county indicator variables are not shown in Table 95 because their individual significance is not directly relevant to model fit assessment or its application. However, it is recognized that the “intercept” variables in Table 95 (i.e., b0, A2Bs, b0, A4D3ex, b0, B4D3en, b0, D4) correspond to only one state and county combination. Desirably, the intercept would represent an average value for all states and counties in the database. To this end, the predicted crash frequencies from the model described by Table 95 were submitted to a second regression analysis using Equation 115 (in Chapter 5). The regression coefficient co was determined to be 0.540 for the A2B2 intercept, 0.494 for the A4D3ex intercept, 0.603 for the B4D3en intercept, and 0.521 for the D4 intercept. Each of these values is added to the appropriate intercept variables to compute an average intercept value for the overall database. This addition is shown in the models described in the next section. Table 95 includes only coefficients associated with the SPF models. It does not include any coefficients associated with geometric elements. Coefficients for several geometric variables were found to be significant in the examination of FI crash data (as documented in Table 79). However, none of the coefficients for these variables were significant in the examination of PDO crash data. This result is partially due to the inclusion of county indicator variables and likely a reflection of correlation between county and geometric design. The potential for this result was discussed in a previous section titled Prediction of PDO Crash Frequency. Calibrated Models This section describes the fit statistics and inverse dispersion parameter for each of the four ramp terminal models. It also shows the model form with the calibration coefficients from Table 95. Model for A2 and B2 Configurations. The statistics describing the calibrated model for A2 and B2 ramp terminal configurations are presented in Table 96. The Pearson χ2 statistic for the model is 45.5, and the degrees of freedom are 39 (= n − p = 40 −1). As this statistic is less than χ20.05,39 (= 55), the hypothesis that the model fits the data cannot be rejected. The R2 for the model is 0.69. The Rk2 for the calibrated model is 0.93. The inverse dispersion parameter was adjusted using Equation 249. The coefficients in Table 95 were combined with the regression model to obtain the calibrated SPF for the A2 and B2 configuration. The form of the model is described in the following equation.

309 0 2 4 6 8 10 12 0 2 4 6 8 10 12 14 16 Predicted PDO Frequency, cr/3 yrs R ep or te d C ra sh F re qu en cy , cr /3 y rs 1 1 )000,1/000,1/ln(878.0)000,1/ln(773.0540.0595.3 22, enexxrd AADTAADTAADT BAspf eN ++++−= (314) The calibrated CMFs used with this SPF are described in a subsequent section. TABLE 96. Terminal PDO model statistical description–A2 and B2 configuration– unsignalized Model Statistics Value R2 (Rk2): 0.69 (0.93) Scale parameter φ: 1.17 Pearson χ2: 45.5 (χ20.05, 39 = 55) Inverse dispersion parameter K: 5.49 Observations no: 40 terminals (109 PDO crashes in 3 years) Standard deviation se: ±0.60 crashes/yr The fit of the calibrated model is shown in Figure 133. This figure compares the predicted and reported crash frequency in the calibration database. In general, the data shown in the figure indicate that the model provides an unbiased estimate of expected crash frequency for ramp terminals experiencing up to 11 crashes in a three-year period. Figure 133. Predicted vs. reported PDO crashes at unsignalized A2 and B2 configurations. Model for A4 and D3ex Configurations. The statistics describing the calibrated model for A4 and D3ex ramp terminal configurations are presented in Table 97. The Pearson χ2 statistic for the model is 28.9, and the degrees of freedom are 36 (= n − p = 37 −1). As this statistic is less than χ20.05,36 (= 51), the hypothesis that the model fits the data cannot be rejected. The R2 for the model is 0.78. The Rk2 for the calibrated model is 0.96. The inverse dispersion parameter was adjusted using Equation 249.

310 0 2 4 6 8 10 0 2 4 6 8 10 12 Predicted PDO Crash Frequency, cr/3 yrs R ep or te d C ra sh F re qu en cy , cr /3 y rs 1 1 TABLE 97. Terminal PDO model statistical description–A4 and D3ex configuration– unsignalized Model Statistics Value R2 (Rk2): 0.78 (0.96) Scale parameter φ: 0.80 Pearson χ2: 28.9 (χ20.05, 36 = 51) Inverse dispersion parameter K: 6.57 Observations no: 37 terminals (91 PDO crashes in 3 years) Standard deviation se: ±0.61 crashes/yr The coefficients in Table 95 were combined with the regression model to obtain the calibrated SPF for the A4 and D3ex configuration. The form of the model is described in the following equation. )000,1/000,1/ln(937.0)000,1/ln(595.0494.0164.3 34, enexxrd AADTAADTAADT exDAspf eN ++++−= (315) The calibrated CMFs used with this SPF are described in a subsequent section. The AADT volume of the loop entrance ramp at an A4 configuration is not included in AADTen. Also, AADTen equals 0.0 when the SPF is applied to a D3ex configuration. The fit of the calibrated model is shown in Figure 134. In general, the data shown in the figure indicate that the model provides an unbiased estimate of expected crash frequency for ramp terminals experiencing up to 10 crashes in a three-year period. Figure 134. Predicted vs. reported PDO crashes at unsignalized A4 and D3ex configurations. Model for B4 and D3en Configurations. The statistics describing the calibrated model for B4 and D3en ramp terminal configurations are presented in Table 98. The Pearson χ2 statistic

311 0 2 4 6 8 10 12 0 2 4 6 8 10 12 14 Predicted PDO Crash Frequency, cr/3 yrs R ep or te d C ra sh F re qu en cy , cr /3 y rs 1 1 for the model is 20.5, and the degrees of freedom are 21 (= n − p = 22 −1). As this statistic is less than χ20.05,21 (= 33), the hypothesis that the model fits the data cannot be rejected. The R2 for the model is 0.65. The Rk2 for the calibrated model is 0.92. The inverse dispersion parameter was adjusted using Equation 249. TABLE 98. Terminal PDO model statistical description–B4 and D3en configuration– unsignalized Model Statistics Value R2 (Rk2): 0.65 (0.92) Scale parameter φ: 0.98 Pearson χ2: 20.5 (χ20.05, 21 = 33) Inverse dispersion parameter K: 3.90 Observations no: 22 terminals (68 PDO crashes in 3 years) Standard deviation se: ±0.71 crashes/yr The coefficients in Table 95 were combined with the regression model to obtain the calibrated SPF for the B4 and D3en configuration. The form of the model is described by the following equation. )000,1/000,1/ln(350.0)000,1/ln(885.0603.0961.2 34, enexxrd AADTAADTAADT enDBspf eN ++++−= (316) The calibrated CMFs used with this SPF are described in a subsequent section. The AADT volume of the loop exit ramp at a B4 configuration is not included in AADTex. Also, AADTex equals 0.0 when the SPF is applied to a D3en configuration. The fit of the calibrated model is shown in Figure 135. In general, the data shown in the figure indicate that the model provides an unbiased estimate of expected crash frequency for ramp terminals experiencing up to 12 crashes in a three-year period. Figure 135. Predicted vs. reported PDO crashes at unsignalized B4 and D3en configurations.

312 0 1 2 3 4 5 0 1 2 3 4 5 6 Predicted PDO Crash Frequency, cr/3 yrs R ep or te d C ra sh F re qu en cy , cr /3 y rs 1 1 Each data point represents an average of 10 sites. Model for D4 Configuration. The statistics describing the calibrated model for D4 ramp terminal configuration are presented in Table 99. The Pearson χ2 statistic for the model is 200, and the degrees of freedom are 201 (= n − p = 202 −1). As this statistic is less than χ20.05,201 (= 235), the hypothesis that the model fits the data cannot be rejected. The R2 for the model is 0.48. The Rk2 for the calibrated model is 0.85. The inverse dispersion parameter was adjusted using Equation 249. TABLE 99. Terminal PDO model statistical description–D4 configuration–unsignalized Model Statistics Value R2 (Rk2): 0.48 (0.85) Scale parameter φ: 0.99 Pearson χ2: 200 (χ20.05, 201 = 235) Inverse dispersion parameter K: 4.27 Observations no: 202 terminals (388 PDO crashes in 3 years) Standard deviation se: ±0.62 crashes/yr The coefficients in Table 95 were combined with the regression model to obtain the calibrated SPF for the D4 configuration. The form of the model is described in the following equation. )000,1/000,1/ln(476.0)000,1/ln(845.0521.0953.2 4, enexxrd AADTAADTAADT Dspf eN ++++−= (317) The calibrated CMFs used with this SPF are described in a subsequent section. The fit of the calibrated model is shown in Figure 136. In general, the data shown in the figure indicate that the model provides an unbiased estimate of expected crash frequency for ramp terminals experiencing up to 5 crashes in a three-year period. Figure 136. Predicted vs. reported PDO crashes at unsignalized D4 configurations.

313 Each data point shown in Figure 136 represents the average predicted and average reported crash frequency for a group of 10 ramp terminals. The data were sorted by predicted crash frequency to form groups of terminals with similar crash frequency. The purpose of this grouping was to reduce the number of data points shown in the figure and, thereby, to facilitate an examination of trends in the data. The individual terminal observations were used for model calibration. Calibrated CMFs This section describes two CMFs that were derived from the literature. Both CMFs relate to turn bay presence on the crossroad legs of the ramp terminal. Their derivation was previously described in the discussion associated with Table 65. Left-Turn Lane CMF. The left-turn lane CMF is described using the following equation. ( )[ ] ( )[ ] outltbay inltbay I outoutruralrural I ininruralruralltbay PPII PPIICMF ,, ,, )0.1(0.1]0.1[58.055.0 )0.1(0.1]0.1[58.055.0, −+−+ ×−+−+= (318) Equation 318 is not associated with one of the regression coefficients in Table 95. Rather, it is based on a fairly definitive set of CMFs developed by Harwood et al. (2002). The derivation of the leg-specific CMF values that are used in Equation 318 is described in the discussion associated with Table 65. This CMF is applicable to turn bay presence on one or both of the crossroad legs at the ramp terminal, provided that the leg is uncontrolled. If the leg is stop- controlled, then this CMF is not applicable. The values obtained from this CMF are listed in Table 100. The CMF values reflect a proportion of total leg AADT on the crossroad Pin and Pout of 0.39, which is a typical value for ramp terminals. TABLE 100. Calibrated left-turn CMF for PDO crashes–unsignalized Junction Location Legs with Turn Lane Leg Location Proportion AADT on Leg CMF Value by Area Type Urban Rural Ramp terminal 1 Crossroad 1 0.39 0.84 0.82 2 Crossroad 1 0.39 0.70 0.68 Note: 1 - For Equation 318, Pin is assumed to equal Pout. Right-Turn Lane CMF. The right-turn lane CMF is described using the following equation. ( )[ ] ( )[ ] outrtbay inrtbay I outoutruralrural I ininruralruralrtbay PPII PPIICMF ,, ,, )0.1(0.1]0.1[69.063.0 )0.1(0.1]0.1[69.063.0, −+−+ ×−+−+= (319)

314 Equation 319 is not associated with one of the regression coefficients in Table 95. Rather, it is based on a fairly definitive set of CMFs developed by Harwood et al. (2002). The derivation of the leg-specific CMF values that are used in Equation 319 is described in the discussion associated with Table 65. This CMF is applicable to turn bay presence on one or both of the crossroad legs at the ramp terminal, provided that the leg is uncontrolled. If the leg is stop- controlled, then this CMF is not applicable. The values obtained from this CMF are listed in Table 101. The CMF values reflect a proportion of total leg AADT on the crossroad Pin and Pout of 0.39, which is a typical value for ramp terminals. TABLE 101. Calibrated right-turn CMF for PDO crashes–unsignalized Junction Location Legs with Turn Lane Leg Location Proportion AADT on Leg CMF Value by Area Type Urban Rural Ramp terminal 1 Crossroad 1 0.39 0.88 0.86 2 Crossroad 1 0.39 0.77 0.73 Note: 1 - For Equation 319, Pin is assumed to equal Pout. Sensitivity Analysis The relationship between crash frequency and traffic demand, as obtained from the combined calibrated models, is illustrated in Figure 137 for unsignalized ramp terminals. The axis scale for each graph in Figure 137 is the same. This technique is used to facilitate comparison among ramp configurations. The D3 configurations are shown in Figure 137 to have fewer crashes than the other configurations, for a given AADT volume. This trend is likely due to the fact that these configurations have only three legs, while the other configurations have four legs. The number of conflict points increases significantly with the number of legs.

315 0.0 1.0 2.0 3.0 4.0 0 5 10 15 20 25 Crossroad AADT (1000s), veh/day PD O C ra sh F re qu en cy , cr as he s/ yr Terminal Types: A2, B2 Ramp AADT = 0.32 x Crossroad AADT 0.0 1.0 2.0 3.0 4.0 0 5 10 15 20 25 Crossroad AADT (1000s), veh/day PD O C ra sh F re qu en cy , cr as he s/ yr Terminal Type: A4 Ramp AADT = 0.32 x Crossroad AADT 0.0 1.0 2.0 3.0 4.0 0 5 10 15 20 25 Crossroad AADT (1000s), veh/day PD O C ra sh F re qu en cy , cr as he s/ yr Terminal Type: D3 with exit ramp Ramp AADT = 0.32 x Crossroad AADT 0.0 1.0 2.0 3.0 4.0 0 5 10 15 20 25 Crossroad AADT (1000s), veh/day PD O C ra sh F re qu en cy , cr as he s/ yr Terminal Type: B4 Ramp AADT = 0.32 x Crossroad AADT 0.0 1.0 2.0 3.0 4.0 0 5 10 15 20 25 Crossroad AADT (1000s), veh/day PD O C ra sh F re qu en cy , cr as he s/ yr Terminal Type: D3 with entrance ramp Ramp AADT = 0.32 x Crossroad AADT 0.0 1.0 2.0 3.0 4.0 0 5 10 15 20 25 Crossroad AADT (1000s), veh/day PD O C ra sh F re qu en cy , cr as he s/ yr Terminal Type: D4 Ramp AADT = 0.32 x Crossroad AADT a. Terminal types A2 and B2. b. Terminal type A4. c. Terminal Type D3 with exit ramp. d. Terminal type B4. e. Terminal Type D3 with entrance ramp. f. Terminal type D4. Figure 137. Terminal PDO models–unsignalized.

316 NOMENCLATURE AADTen = AADT volume for the entrance ramp, veh/day (= 0 if ramp does not exist); AADTex = AADT volume for the exit ramp, veh/day (= 0 if ramp does not exist); AADTi = AADT volume for street i, veh/day; AADTin = AADT volume for crossroad leg between ramps, veh/day; AADTk = AADT volume for leg k, veh/day. AADTout = AADT volume for crossroad leg outside of interchange, veh/day; AADTxrd = AADT volume for crossroad (= 0.5 AADTin + 0.5 AADTout), veh/day; CA2B2 = local calibration factor for A2 and B2 configurations; CA4D3ex = local calibration factor for A4 and D3ex configurations; CB4D3en = local calibration factor for B4 and D3en configurations; Cca = calibration factor for California; CD4 = local calibration factor for D4 configuration; CMF1 ... CMFk = crash modification factors for ramp terminal crashes at a site with specific geometric design features k; CMFA2B2, 1 ... CMFA2B2, w = crash modification factors for crashes at an A2 or B2 site with specific geometric design features w; CMFA4D3ex, 1 ... CMFA4D3ex, x = crash modification factors for crashes at an A4 or D3ex site with specific geometric design features x; CMFap = access point frequency crash modification factor; CMFawsc = all-way stop control crash modification factor; CMFB4D3en, 1 ... CMFB4D3en, y = crash modification factors for crashes at a B4 or D3en site with specific geometric design features y; CMFbay, rt = crossroad right-turn lane crash modification factor; CMFbay, lt = crossroad left-turn lane crash modification factor; CMFch, xrd = channelized right turn from crossroad crash modification factor; CMFch, ex = channelized right turn from exit ramp crash modification factor; CMFD4, 1 ... CMFD4, z = crash modification factors for crashes at a D4 site with specific geometric design features z; CMFint, k = CMF for a specified treatment to leg k, quantified in terms of intersection crashes (k = 1 for one major-street leg, 2 for the other major-street leg, 3 for one minor- street leg, and 4 for the other minor-street leg); CMFint, i = CMF for a specified treatment to street i, quantified in terms of intersection crashes (i = 1 for major street or 2 for minor street); CMFleg = CMF for a specified treatment to any leg, quantified in terms of the crashes that occur on the subject leg; CMFmw = median-width crash modification factor; CMFp, lt = protected left-turn operation crash modification factor; CMFps = non-ramp public street leg crash modification factor; CMFrc = exit ramp capacity crash modification factor; CMFsk = skew angle crash modification factor; CMFsl = segment length crash modification factor; CMFstr = CMF for a specified treatment to any street, quantified in terms of the crashes that occur on the subject street; IA2B2 = crash indicator variable (= 1.0 if A2 or B2 crash data, 0.0 otherwise); IA4D3ex = crash indicator variable (= 1.0 if A4 or D3ex crash data, 0.0 otherwise);

317 Iawsc = all-way stop control indicator variable (= 1.0 if ramp terminal has all-way stop controlled, 0.0 if it has one-way stop control for the exit ramp); and IB4D3en = crash indicator variable (= 1.0 if B4 or D3en crash data, 0.0 otherwise); Ibay, rt, k = right-turn lane (or bay) indicator variable for crossroad leg k (k = in or out) (= 1.0 if right-turn lane (or bay) present, 0.0 otherwise); Ibay, lt, k = left-turn lane (or bay) indicator variable for crossroad leg k (k = in or out) (= 1.0 if left-turn lane (or bay) present, 0.0 otherwise); Ich, k = right-turn channelization indicator variable for leg k (k = in, out, or ex) (= 1.0 if right-turn channelization exists, 0.0 otherwise); ID4 = crash indicator variable (= 1.0 if D4 crash data, 0.0 otherwise); Ip, lt, k = protected left-turn operation indicator variable for crossroad leg k (k = in or out) (= 1.0 if protected operation exists, 0.0 otherwise); Ips = non-ramp public street leg indicator variable (= 1.0 if leg is present, 0.0 otherwise); Irural = area type indicator variable (= 1.0 if area is rural, 0.0 if it is urban); Isk = skew angle between exit ramp and crossroad, degrees; K = inverse dispersion parameter (= 1/k, where k = overdispersion parameter). Lrmp = distance between subject ramp terminal and adjacent ramp terminal (measured along the crossroad from terminal center to terminal center), mi; Lstr = distance between subject ramp terminal and nearest public road intersection in a direction away from freeway (measured along the crossroad from terminal center to intersection center), mi; N = predicted average crash frequency, crashes/yr; ndw = number of unsignalized driveways on the crossroad leg outside of the interchange and within 250 ft of the ramp terminal; nex = number of lanes serving exit ramp traffic; lanes; nex, eff = effective number of lanes serving exit ramp traffic, lanes; Ninterchange = predicted average crash frequency within the limits of an interchange, crashes/yr; Nmv = predicted average multiple-vehicle crash frequency, crashes/yr; no, k = number of through traffic lanes that oppose the left-turn movement on crossroad leg k (k = in or out), lanes; nps = number of unsignalized public street approaches to the crossroad leg outside of the interchange and within 250 ft of the ramp terminal; Nrt, D4 = predicted average crash frequency for D4 configuration, crashes/yr; Nrt = predicted average crossroad ramp terminal crash frequency, crashes/yr; Nrt, j = predicted average crossroad ramp terminal crash frequency for model j; crashes/yr; Nrt, A4D3ex = predicted average crash frequency for A4 and D3ex configurations, crashes/yr; Nrt, A2B2 = predicted average crash frequency for A2 and B2 configurations, crashes/yr; Nrt, j = predicted average crossroad ramp terminal crash frequency for model j (j = A2B2 if IA2B2 = 1.0; j = A4D3ex if IA4D3ex = 1.0; j = B4D3en if IB4D3en = 1.0; j = D4 if ID4 = 1.0;); crashes/yr; Nrt, B4D3en = predicted average crash frequency for B4 and D3en configurations, crashes/yr; Nspf, A2B2 = predicted average crash frequency for A2 and B2 configurations for base conditions, crashes/yr; Nspf, B4D3en = predicted average crash frequency for B4 and D3en configurations for base conditions, crashes/yr;

318 Nspf, A4D3ex = predicted average crash frequency for A4 and D3ex configurations for base conditions, crashes/yr; Nspf, D4 = predicted average crash frequency for D4 configuration for base conditions, crashes/yr; Nsv = predicted average single-vehicle crash frequency, crashes/yr; nth = number of through traffic lanes on the crossroad at the ramp terminal (total of both directions), lanes; Pex = proportion of total leg AADT on exit ramp leg; Pi = proportion of total leg AADT on street i; Pin = proportion of total leg AADT on crossroad leg between ramps; Pk = proportion of total leg AADT on leg k; Pout = proportion of total leg AADT on crossroad leg outside of interchange; Pxrd = proportion of total leg AADT on the crossroad; R k = proportion of intersection crashes that occur on treated leg k; Ri = proportion of intersection crashes that occur on treated street i; Sin(x) = sine of angle x; V[X] = crash frequency variance for a group of similar locations, crashes2; Wb, k = left-turn lane (or bay) width for crossroad leg k (k = in or out) (= 0.0 if no lane present on leg), ft; Wm = median width, ft; Wmb, k = base median width for crossroad leg k (k = in or out), ft; Wme, k = width of median adjacent to turn lane (or bay) for crossroad leg k (k = in or out), ft; X = reported crash count for y years, crashes; y = time interval during which X crashes were reported, yr.