Safety Performance of Part-Time Shoulder Use on Freeways, Volume 1: Informational Guide and Safety Evaluation Guidelines (2021)

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31 Chapter 2 – Draft Highway Safety Manual Text 2.1 Overview This chapter presents the predictive method for urban freeways with part-time shoulder use (PTSU). It includes the following information: 1. Overview of the Predictive Method: Section 2.3 provides a general description of the predictive method’s analytic framework and application scope. 2. Definitions and Predictive Model Overview: Section 2.4 provides the information needed to determine whether a freeway facility of interest is addressed by the predictive method. It describes the different site types to which the predictive method can be applied. These site types include basic segments and speed-change lanes. This section also introduces the predictive model for each site type. 3. Predictive Method Overview and Data Needs: Section 2.5 provides a step-by-step overview of the predictive method. It also describes the data needed to apply the predictive method. 4. Segmentation and Crash Assignment: Section 2.6 provides guidance on dividing the freeway facility into one or more study sites. It also describes how to assign crashes to individual site types. 5. Safety Prediction Model for Freeway Segments: Section 2.7 describes the safety prediction model for freeway segments with PTSU. The model components addressed in this section include safety performance functions (SPFs), SPF adjustment factors (AFs), severity distributions, and crash type distributions. 6. Safety Prediction Model for Speed-Change Lanes: Section 2.8 describes the safety prediction model for freeway speed-change lanes with PTSU. The model components addressed in this section include SPFs, AFs, severity distribution functions (SDFs), and crash type distributions. 7. Calibration of Models: Section 2.10 provides information about the calibration factors in the predictive models and the need for practitioners to calibrate these models to local conditions. 8. Limitations of Predictive Method: Limitations of the predictive method are presented in Section 2.11. This information is intended to help the analyst identify site conditions for which the method is most applicable. 9. Sample Problems: Section 2.15 presents two sample problems that illustrate the use of the models in a range of situations. 2.2 Introduction The predictive method for urban freeways with PTSU provides a structured methodology to estimate the average crash frequency (in total, by crash type, or by crash severity) for a freeway with PTSU and other known characteristics. It can be applied to an existing freeway, a design alternative for an existing freeway, or a new freeway whenever PTSU operation is present (or being considered for implementation). An estimate can be made of average crash frequency for a prior time period (i.e., what did or would have occurred) or a future time period (i.e., what is expected to occur). The development of the predictive method described in this chapter is documented by Jenior et al. (1). The predictive method described in this chapter is used to evaluate sites serving one direction of travel along the freeway. This approach is in contrast to that used in HSM Chapter 18 – Freeways. The method in Chapter 18 is used to evaluate sites that serve both directions of travel along the freeway. If an analyst desires to evaluate both directions of travel using the method described in this chapter, they will need to initially use it to evaluate the sites serving one direction of travel and then subsequently use it to evaluate the sites serving the opposing direction of travel.

32 The predictive method described in this chapter is used to evaluate a freeway facility with a PTSU lane serving the subject direction of travel. This facility can represent an existing freeway, a design alternative for an existing freeway, or a new freeway. 2.3 Overview of the Predictive Method 2.3.1 General Description The predictive method includes one or more predictive models and an 18-step procedure for estimating the average crash frequency for a roadway network, facility, or site. A site is either (a) one direction of travel on a freeway segment or (b) a freeway speed-change lane (inclusive of the adjacent freeway lanes). A freeway speed-change lane is an uncontrolled terminal between a ramp and one side of a freeway (Error! Reference source not found., p. 10-103). For evaluation purposes, a facility can be considered to consist of a contiguous set of individual sites. Similarly, for evaluation purposes, a roadway network can be considered to consist of a number of contiguous facilities. The predictive method includes a predictive model for freeway segments and a predictive model for freeway speed-change lanes. Each predictive model typically consists of an SPF, one or more AFs, a calibration factor, a severity distribution, and a crash type distribution. The severity distribution is computed using a severity distribution function. The predictive model is used to compute the predicted average crash frequency of a specified crash type and severity level. The predictive model equation consists of the SPF, AFs, and calibration factor. The predictive method is used to estimate the average number of crashes for an individual site. This estimate can be summed for all sites to compute the average number of crashes for an entire facility or network. The estimate represents a given time period of interest (in years) during which the geometric design and traffic control features are unchanged and traffic volumes are known or forecasted. The average crash frequency is obtained by dividing the average number of crashes by the number of years during the time period of interest. The prediction from the predictive model can be combined with observed crash data using the empirical Bayes (EB) method. This combination produces a more reliable estimate of the average crash frequency than is obtained from the predictive model alone. This estimate is referred to as the “expected” average crash frequency. Guidance for applying the EB method is provided in the appendix for Part C of the Highway Safety Manual (HSM) (3). 2.3.2. Predictive Model Framework The predictive model equations are of the general form shown in Equation 12. Equation 12 𝑁 , , , 𝑁 , , , 𝐴𝐹 , , , 𝐴𝐹 , , , … 𝐴𝐹 , , , 𝐶 , , where Np,w,y,z = predicted average crash frequency for a specific year; for site type w, crash type y, and severity z (crashes/year); Nspf,w,y,z = predicted average crash frequency determined for base conditions of the SPF developed for site type w, crash type y, and severity z (crashes/year); AFm,w,y,z = adjustment factors specific to site type w, crash type y, and severity z for geometric design or traffic control feature m; and Cw,y,z = calibration factor to adjust SPF for local conditions; for site type w, crash type y, and severity z. The crash type distribution can be used with the predictive model equations to quantify the crash frequency for each of several crash types. Similarly, the severity distribution can be used to quantify crash frequency by the following severity levels: fatal K, incapacitating injury A, non-incapacitating injury B,

33 and possible injury C. In this document, a “FI crash” is any crash designated has having a K, A, B, or C severity level. The variables that comprise the predictive models include a series of subscripts to describe precisely the conditions to which they apply. These subscripts are described in detail in later sections of this chapter. For this section, it is sufficient to use “placeholder” subscripts such as w, y, z, and m. The meaning of each subscript is described in the following list.  w is a placeholder for specific site-type subscripts that define the equation’s application (e.g., it is replaced with “fs” when needed to indicate that the equation applies to a freeway segment).  y is a placeholder for crash type subscripts.  z is a placeholder for crash severity level.  m is a placeholder for a specific geometric design or traffic control feature. An overview of the predictive models is provided in Section 2.4. 2.3.3 Application Scope Applicable to Urban Freeways with PTSU. The predictive method described in this chapter is applicable to an urban freeway with part-time use of a shoulder for vehicular travel. The shoulder that is used can be either the inside shoulder or the outside shoulder (but not both shoulders). The method can also be applied to urban freeways without PTSU but at which PTSU implementation is being considered. The predictive method provided in Chapter 18 of the 2014 supplement to the HSM (4) can also be used to evaluate urban freeways without PTSU. However, the predictive models in Chapter 18 and those described in this chapter were developed using data from freeways in different states. When the predictions from these models are to be compared or combined, both sets of models must be calibrated for the region of interest to ensure that the results are reliable. Bus-on-Shoulder (BOS) Operation. The predictive models include variables that describe PTSU operational features and design elements. More precisely, these variables address the case where the shoulder is used by all vehicles and it is allowed on a static (i.e., fixed time schedule; S-PTSU) or dynamic (i.e., traffic responsive; D-PTSU) basis during the day. This type of shoulder use is referred to herein as “PTSU operation.” BOS operation is a special type of operation where only buses are allowed to use the shoulder. Any reference in this document to “PTSU” is referring to shoulder use by all vehicle types; it is not referring to BOS operation. BOS operation was implemented on some of the segments used to develop the predictive models. However, the association between BOS operation and crash frequency was found to be relatively small (and inconclusive from a statistical perspective) (1). Therefore, the predictive model provided herein can be used to evaluate freeways with BOS operation; however, the model cannot be used to evaluate the potential safety influence of BOS operation. High-Occupancy Vehicle (HOV) Lanes. An HOV lane (separated by lane line from the adjacent general-purpose lane) was present on a few of the segments used to estimate the model coefficients. However, the association between HOV lane presence and crash frequency was found to be relatively small (and inconclusive from a statistical perspective) (1). Therefore, the predictive method described in this chapter can be used to evaluate freeways with lane-line-separated HOV lanes; however, the model cannot be used to evaluate the potential safety influence of HOV lane presence. Not Applicable to Left-Side Ramps. The predictive method described in this chapter cannot be used to evaluate the safety influence of speed-change lanes that provide left-side access to the freeway. Weaving Section Analysis. The predictive method described in this chapter can be used to evaluate freeway weaving sections where all weaving vehicles make one lane change to enter or exit the freeway. This lane change occurs across the lane line that connects from the entrance gore point to the exit gore

34 point (as shown in Figure 8b). The method cannot be used to evaluate the safety influence of other weaving section configurations. 2.4 Definitions and Predictive Model Overview This section provides the definitions of the facility and site types addressed by the predictive method. It also describes the predictive models for each of the site types. 2.4.1. Definition of PTSU Freeway Facility and Site Types The predictive method applies to sites that comprise an urban freeway facility (a) with PTSU or (b) at which PTSU implementation is being considered. Freeway facilities have fully-restricted access control and grade separation with all intersecting roads. Freeways are accessed only through grade-separated interchanges. Roads having at-grade access should be analyzed as rural highways, suburban arterials, or urban arterials. These facility types are addressed in HSM Chapters 10, 11, and 12 (3). The freeway site types addressed by the predictive method are identified in the following list.  Basic segment with two to seven lanes in the subject travel direction.  Speed-change lane site (and adjacent through lanes) providing right-side freeway access for an entrance ramp or an exit ramp. In the predictive method, a freeway segment is defined as a length of freeway consisting of two or more through lanes with a continuous cross section providing one direction of travel that is separated from the opposing travel lanes by a median. In the predictive method, a speed-change lane site is defined as the one-directional length of freeway located (a) between the marked gore and taper points of the speed-change lane associated with a ramp merge or diverge, and (b) on the same side of the freeway as the merge or diverge area (the location of the gore and taper points are identified in subsequent figures; e.g., Figure 5). In other words, a speed-change lane site has a length that is less than or equal to that of the speed-change lane and a lateral extent that includes the speed-change lane, adjacent shoulders, adjacent through lanes serving the same travel direction as the speed-change lane, and median. A site with PTSU allocates a portion of one of its shoulders (i.e., the inside shoulder or the outside shoulder, but not both) for use by during specified hours of the day. The portion that is used by vehicles is referred to herein as the PTSU lane. The remaining portion of the shoulder actually functions as shoulder for all hours of the day. The width of this remaining portion is referred to in this document as the “shoulder width.” Both portions are paved. A through lane is defined as a lane that serves all vehicles of all types passing through the site during all hours of the day. A lane that is dropped by ramp within (or just beyond) the site is not a through lane. A PTSU lane is not considered to be a through lane. A managed lane is not considered to be a through lane.

35 Table 3 identifies the site, crash type, and severity configurations for which SPFs have been developed. Table 3. SPFs for urban freeways with PTSU. Site Type (w) Crash Type (y) Crash Severity (z) SPF Freeway segments (fs) All types (at) Fatal and injury (fi) Nspf,fs,at,fi Property damage only (pdo) Nspf,fs,at,pdo Ramp entrance speed-change lane (en) All types (at) Fatal and injury (fi) Nspf,en,at,fi Property damage only (pdo) Nspf,en,at,pdo Ramp exit speed-change lane (ex) All types (at) Fatal and injury (fi) Nspf,ex,at,fi Property damage only (pdo) Nspf,ex,at,pdo 2.4.2. Predictive Model for Freeway Segments with PTSU The predictive model for freeway segments is used to estimate the predicted average crash frequency of a freeway segment (the prediction does not include crashes that occur in a speed-change lane site). The SPFs for freeway segments are presented in Section 2.7.1. The associated AFs are presented in Section 2.7.2, the associated severity distributions are presented in Section 2.7.3, and the associated crash type distributions are presented in Section 2.7.4. Guidance for establishing the value of the calibration factor is described in Section 2.10. The predictive model equation for freeway segments is presented in Equation 13. This equation consists of two terms, where Equation 14 and Equation 15 each correspond to one term. Equation 13 𝑁 , , , 𝑁 , , , 𝑁 , , , Equation 14 𝑁 , , , 𝐶 , , 𝑁 , , , 𝐴𝐹 , , , … 𝐴𝐹 , , , Equation 15 𝑁 , , , 𝐶 , , 𝑁 , , , 𝐴𝐹 , , , … 𝐴𝐹 , , , where Np,fs,at,z = predicted average crash frequency of a freeway segment; for all crash types at and severity z (z = fi: fatal and injury, pdo: property damage only, as: all severities) (crashes/year); Nspf,fs,at,z = predicted average crash frequency of a freeway segment with base conditions; for all crash types at and severity z (z = fi: fatal and injury, pdo: property damage only) (crashes/year); AFm,fs,at,z = adjustment factor associated with feature m in a freeway segment, all crash types at, and severity z (z = fi: fatal and injury, pdo: property damage only); and Cfs,ac,y,z = calibration factor for freeway segments; for all crash types at and severity z (z = fi: fatal and injury, pdo: property damage only). Equation 13 shows that freeway segment crash frequency is estimated as the sum of components: FI crash frequency and PDO crash frequency. Equation 14 is used to estimate the FI crash frequency and Equation 15 is used to estimate the PDO crash frequency. 2.4.3. Predictive Model for Freeway Speed-Change Lanes with PTSU The predictive model for speed-change lane sites is used to estimate the predicted average crash frequency of a speed-change lane site (the prediction does not include crashes that occur in a segment). The SPFs for speed-change lanes are presented in Section 2.8.1. The associated AFs are presented in Section 2.8.2, the associated severity distributions are presented in Section 2.8.3, and the associated crash

36 type distributions are presented in Section 2.8.4. Guidance for establishing the value of the calibration factor is described in Section 2.10. The predictive model equation for ramp entrance speed-change lanes is presented in Equation 16. This equation consists of two terms, where Equation 17 and Equation 18 each correspond to one term. Equation 16 𝑁 , , , 𝑁 , , , 𝑁 , , , Equation 17 𝑁 , , , 𝐶 , , 𝑁 , , , 𝐴𝐹 , , , … 𝐴𝐹 , , , Equation 18 𝑁 , , , 𝐶 , , 𝑁 , , , 𝐴𝐹 , , , … 𝐴𝐹 , , , where Np,en,at,z = predicted average crash frequency of a ramp entrance speed-change lane site; for all crash types at and severity z (z = fi: fatal and injury, pdo: property damage only, as: all severities) (crashes/year); Nspf,en,at,z = predicted average crash frequency of a ramp entrance speed-change lane site with base conditions; for all crash types at and severity z (z = fi: fatal and injury, pdo: property damage only) (crashes/year); AFm,w,at,z = adjustment factor associated with feature m for site type w (w = en: ramp entrance speed-change lane, ex: ramp exit speed-change lane), all crash types at, and severity z (z = fi: fatal and injury, pdo: property damage only); and Cen,ac,y,z = calibration factor for ramp entrance speed-change lanes; for all crash types at and severity z (z = fi: fatal and injury, pdo: property damage only). Equation 16 shows that ramp entrance speed-change lane crash frequency is estimated as the sum of components: FI crash frequency and PDO crash frequency. Equation 17 is used to estimate the FI crash frequency and Equation 18 is used to estimate the PDO crash frequency. The predictive model equation for ramp exit speed-change lanes is the same as for ramp entrance speed-change lanes except that the subscript “ex” is substituted for “en” in each variable. 2.5. Predictive Method for Freeways with PTSU This section describes the predictive method for freeways with PTSU. It consists of two sections. The first section provides a step-by-step description of the predictive method. The second section describes the geometric design features, traffic control features, and traffic volume data needed to apply the predictive method. 2.5.1. Step-by-Step Description of the Predictive Method The predictive method for freeways with PTSU is shown in Figure 3. It consists of the same 18 steps as used in the HSM Part C predictive methods (3). The project limits are identified, site boundaries established, and site data assembled in Steps 1 to 6. The predictive models are applied to all sites in Steps 7 to 12. If desired, the EB method is applied in Steps 13 to 15. Step 16 summarizes the results for the facility. These steps can be repeated for each design alternative being considered. The information needed to apply each step is provided in this section.

37 Figure 3. The HSM predictive method. Step 1—Define the limits of the project. A project can be a freeway network, a freeway facility, or a site. A site is either a speed-change lane or a freeway segment. Both site types represent one direction travel. Section 2.4.1 defines freeway segments and speed-change lane sites. The project limits are defined in this step. They will depend on the purpose of the study. The study may be limited to one specific site or to a group of contiguous sites. Alternatively, the limits can be expanded

38 to include a very long corridor for the purposes of network screening (as discussed in HSM Chapter 4). For comparative analysis of design alternatives, the project limits should be the same for all alternatives. The analyst should identify (or establish) a “reference line” for the freeway in the subject direction of travel. For this predictive method, the reference line is defined as the inside edge of traveled way for the subject direction of travel, where the edge of traveled way is the line separating a through lane and its adjacent shoulder (or PTSU lane). The location of the reference line is shown in subsequent figures (e.g., Figure 7). Locations along the reference line are specified using a linear referencing system, and are identified using the label “milepost X,” where the number for X has units of miles (e.g., milepost 1.4). Step 2—Define the period of interest. The study period is defined as the consecutive years for which an estimate of the average crash frequency is desired. The crash period is defined as the consecutive years for which observed crash data are available. The evaluation period is defined as the combined set of years represented by the study period and crash period. Every year in the evaluation period is evaluated using the predictive method. All periods are measured in years. If the EB method is not used, then the study period is the same as the evaluation period. The EB method is discussed in more detail in Step 3. If the EB method is used and the crash period is not fully included in the study period, then the predictive models need to be applied to the study years plus each year of the crash period not represented in the study period. In this situation, the evaluation period includes the study period and any additional years represented by the crash data but not in the study period. For example, let the study period be defined as the years 2010, 2011, and 2012. If crash data are available for 2008, 2009, and 2010, then the evaluation period is 2008, 2009, 2010, 2011, and 2012. The study period can represent either a past time period or a future time period. Whether the predictive method is used for a past or future period depends upon the purpose of the study. The study period may be:  A past period for:  An existing freeway network, facility, or site. If observed crash data are available, the study period is the period of time for which the observed crash data are available and the site geometric design features, traffic control features, and traffic volumes are known.  An existing freeway network, facility, or site for which alternative geometric design or traffic control features are proposed (for near-term conditions) and site traffic volumes are known.  A future period for:  An existing freeway network, facility, or site for a future period where forecast traffic volumes are available.  An existing freeway network, facility, or site for which alternative geometric design or traffic control features are proposed and forecast traffic volumes are available.  A new freeway network, facility, or site that does not currently exist but is proposed for construction and for which forecast traffic volumes are available. Step 3—For the period of interest, determine the availability of AADT volumes and crash data. Traffic volume data are acquired in this step. Also, a decision is made whether the EB method will be applied. If it will be applied, then it must also be decided whether the site-specific or project-level EB method will be applied. If the EB method will be applied, then the observed crash data are also acquired in this step. Determining Traffic Volumes The SPFs used in Step 9 (and some AFs in Step 10) include annual average daily traffic (AADT) volume as a variable. For a past period, the AADT volume may be determined by using automated

39 recorder data or estimated by a sample survey. For a future period, the AADT volume may be a forecast estimate based on appropriate land use planning and traffic volume forecasting models. For each freeway segment, the following three AADT values are required:  Directional AADT volume of the freeway segment.  AADT volume of the nearest entrance ramp upstream of the segment for the subject travel direction.  AADT volume of the nearest exit ramp downstream of the segment for the subject travel direction. For each ramp entrance speed-change lane site, two values are required: (a) the directional AADT volume of the freeway segment and (b) the AADT volume of the ramp. For each ramp exit speed-change lane site, only the AADT volume of the freeway segment is required; the AADT volume of the ramp is not needed. The AADT volumes are needed for each year of the evaluation period. The AADT volume for a given year represents an annual average daily 24-hour traffic volume. The freeway segment AADT volume is a one-way volume (i.e., the volume in the subject travel direction). In many cases, it is expected that AADT data will not be available for all years of the evaluation period. In that case, an estimate of AADT volume for each missing year is interpolated or extrapolated, as appropriate. If there is not an established procedure for doing this, the following rules may be applied within the predictive method to estimate the AADT volumes for years when such data are not available. If these rules are applied, the fact that some AADT volumes are estimated should be documented with the analysis results.  If AADT volume is available for only a single year, that same volume is assumed to apply to all years of the evaluation period.  If two or more years of AADT data are available, the AADT volumes for intervening years are computed by interpolation.  The AADT volumes for years before the first year for which data are available are assumed to be equal to the AADT volume for that first year.  The AADT volumes for years after the last year for which data are available are assumed to be equal to the AADT volume for that last year. Determining Availability of Observed Crash Data Where an existing site (or an alternative condition for an existing site) is being considered, the EB method can be used to obtain a more reliable estimate of the average crash frequency. The EB method is applicable when crash data are available for the entire project, or for its individual sites. Crash data may be obtained directly from the jurisdiction’s crash report system. At least two years of crash data are desirable to apply the EB Method. The EB method can be used with the predictive method to evaluate a freeway with or without PTSU operation. However, if it is used to evaluate the addition (or removal) of a PTSU lane then the number of through lanes on the freeway must remain the same for both scenarios. Additional criteria to determine whether the EB method is applicable are presented in the appendix to HSM Part C (3). The EB method can be applied at the site-specific level or at the project level. At the site-specific level, crash data are assigned to specific sites in Step 6. The site-specific EB method is applied in Step 13. At the project level, crash data are assigned to a group of sites (typically because they cannot be assigned to individual sites). The project-level EB method is applied in Step 15. The site-specific EB method will provide the best results if the crash data can be accurately assigned to the sites. Guidance to determine whether the site-specific or project-level EB method is applicable is presented in the appendix to HSM Part C (3).

40 Step 4—Determine geometric design features, traffic control features, and site characteristics for all sites in the project limits. A range of data is needed to apply a predictive model. These data are used in the SPFs and AFs to estimate the predicted average crash frequency for the selected site and year. These data represent the geometric design features, traffic control features, and traffic demand characteristics that have been found to have some relationship to crash potential. These data are needed for each site in the project limits. They are needed for the study period and, if applicable, the crash period. These data, and the means by which they are measured or obtained, are described in Section 2.5.2. Step 5—Divide the freeway into sites. Divide the freeway into individual sites (i.e., freeway segments and speed-change lanes) using the information from Step 1 and Step 4. The procedure for dividing the freeway into individual sites is provided in Section 2.6. Step 6—Assign observed crashes to the individual sites (if applicable). Step 6 applies if it was determined in Step 3 that the site-specific EB method is applicable. If the site- specific EB method is not applicable, then proceed to Step 7. In this step, the observed crash data are assigned to the individual sites. Guidance for assigning crashes to individual sites is outlined in Section 2.6.3. Step 7—Select the first or next individual site in the project limits. If there are no more sites to be evaluated, proceed to Step 15. Steps 7 through 14 are repeated for each site within the project limits. Any site can be selected for evaluation because each site is considered to be independent of the other sites. However, good practice is to select the sites in an orderly manner, such as in the order of their physical occurrence in the subject direction of travel. Step 8—For the selected site, select the first or next year in the period of interest. If there are no more years to be evaluated for that site, proceed to Step 13. Steps 8 through 12 are repeated for each year in the evaluation period for the selected site. The individual years of the evaluation period are analyzed one year at a time because the SPFs and some AFs are dependent on AADT volume, which may change from year to year. Step 9—For the selected site, determine and apply the appropriate SPF. The SPF determines the predicted average crash frequency for a site with features that match the SPF’s base conditions. The SPFs (and their base conditions) are described in Sections 2.7.1 and 2.8.1. Determine the appropriate SPF for the selected site based on its site type. This SPF is then used to compute the crash frequency for the selected year using the AADT volume for that year, as determined in Step 3. Step 10—Multiply the result obtained in Step 9 by the appropriate AFs. Collectively, the AFs are used in the predictive model to adjust the SPF estimate from Step 9 so that the resulting predicted average crash frequency accurately reflects the geometric design and traffic control features of the selected site. The available AFs are described in Sections 2.7.2 and 2.8.2. All AFs presented in this chapter have the same base conditions as the SPFs in this chapter. Only the AFs presented in Sections 2.7.2 and 2.8.2 may be used as part of the predictive method described in this chapter. For the selected site, determine the appropriate AFs for the site type, geometric design features, and traffic control features present. The AF’s designation by crash type and severity must match that of the

41 SPF with which it is used (unless indicated otherwise in the AF description). The AFs for the selected site are calculated using the geometric design and traffic control features determined in Step 4. Multiply the result from Step 9 by the appropriate AFs. Step 11—Multiply the result obtained in Step 10 by the appropriate calibration factor. The SPFs and AFs in this chapter have each been developed with data from specific jurisdictions and time periods. Calibration to local conditions will account for any differences between these conditions and those present at the selected sites. A calibration factor is applied to each SPF in the predictive method. Detailed guidance for the development of calibration factors is included in the appendix to HSM Part C (3). Multiply the result from Step 10 by the calibration factor to obtain the predicted average crash frequency. Step 12—If there is another year to be evaluated in the evaluation period for the selected site, return to Step 8. Otherwise, proceed to Step 13. This step creates a loop from Step 8 through Step 12 that is repeated for each year of the evaluation period for the selected site. Step 13—Apply the site-specific EB method (if applicable) and apply crash distributions. The site-specific EB method combines the predicted average crash frequency computed in Step 11 with the observed crash frequency of the selected site to produce an estimate of the expected average crash frequency. The expected average crash frequency is more statistically reliable than the predicted average crash frequency obtained in Step 11. The procedure for applying the site-specific EB method is provided in the appendix to HSM Part C (3). If the EB method is used, then an estimate of expected average crash frequency is obtained for each year of the crash period (i.e., the period for which the observed crash data are available). The individual years of the crash period are analyzed one year at a time because the SPFs and some AFs are dependent on AADT volume, which may change from year to year. Apply the site-specific EB method to a future time period, if appropriate. The appendix to HSM Part C (3) provides a procedure for converting the estimates from the EB method to any years in the study period that are not represented in the crash period (e.g., future years). This approach gives consideration to any differences in traffic volume, geometry, or traffic control between the study period and the crash period. This procedure yields the expected average crash frequency for each year of the study period. Apply the severity distribution, if desired. The severity distribution function (SDF) is used to compute the average crash frequency for each of the following severity levels: fatal K, incapacitating injury A, non-incapacitating injury B, and possible injury C. An SDF is used to compute the severity distribution proportions. Each SDF includes variables that describe the geometric design and traffic control features of a site. In this manner, the computed distribution gives consideration to the features present at the selected site. The SDFs are described in Sections 2.7.3 and 2.8.3. They can benefit from being calibrated to local conditions as part of the calibration process. Guidance for the development of the SDF calibration factor is included in the appendix to HSM Part C (3). Apply the crash type distribution, if desired. Each predictive model includes a default distribution of crash type. These distributions can be used to compute the average crash frequency for each of ten crash types (e.g., head-on, fixed object). The

42 distributions are presented in Sections 2.7.4 and 2.8.4. The distributions can provide a more reliable indication of local crash characteristics if they are updated based on local data as part of the calibration process. Step 14—If there is another site to be evaluated, return to Step 7; otherwise, proceed to Step 15. This step creates a loop from Step 7 through Step 14 that is repeated for each site of interest. Step 15—Apply the project-level EB method (if applicable) and apply crash distributions. The activities undertaken during this step are the same as undertaken for Step 13 but they occur at the project level (i.e., network or facility). They are based on estimating the project-level predicted average crash frequency. This crash frequency is computed for each year during the crash period. It is computed as the sum of the predicted average crash frequency for all sites (as computed in Step 11). The project-level EB method combines the project-level predicted average crash frequency with the observed crash frequency for all sites within the project limits to produce an estimate of the project-level expected average crash frequency. The project-level expected average crash frequency is more statistically reliable than the project-level predicted average crash frequency. The procedure for applying the project-level EB method is provided in the appendix to HSM Part C (3). If the EB method is used, then an estimate of the project-level expected crash frequency is obtained for each year of the crash period (i.e., the period for which the observed crash data are available). The individual years of the crash period are analyzed one year at a time because the SPFs and some AFs are dependent on AADT volume, which may change from year to year. Apply the project-level EB method to a future time period, if appropriate. Follow the same guidance as provided in Step 13 using the estimate from the project-level EB method. Apply the severity distribution, if desired. Follow the same guidance as provided in Step 13 using the estimate from the project-level EB method. Apply the crash type distribution, if desired. Follow the same guidance as provided in Step 13 using the estimate from the project-level EB method. Step 16—Sum all sites and years in the study to estimate the total crash frequency. One outcome of the predictive method is the total (predicted or expected) average crash frequency. The term “total” indicates that the estimate includes all crash types and severities. It is computed from an estimate of the total number of crashes, which represents the sum of the total average crash frequency for each site and for each year in the study period. The total expected number of crashes during the study period is calculated using Equation 19. The same equation can be used to calculate the total predicted number of crashes by substituting the subscript “p” for the subscript “e”. Equation 19 𝑁 , , ,∗ 𝑁 , , , , all sites 𝑁 , , , , all sites 𝑁 , , , , all sites where N*e,aS,at,as = total expected number of crashes for all sites aS and all years in the study period (includes all crash types at, and all severities as) (crashes); ns = number of years in the study period (yr); Ne,fs(i),at,as,j = expected average crash frequency of freeway segment i for year j (includes all crash types at and all severities as) (crashes/year);

43 Ne,en(i),at,as,j = expected average crash frequency of ramp entrance speed-change lane site i for year j (includes all crash types at and all severities as) (crashes/year); and Ne,ex(i),at,as,j = expected average crash frequency of ramp exit speed-change lane site i for year j (includes all crash types at and all severities as) (crashes/year). Equation 19 is used to compute the total expected number of crashes estimated to occur in the project limits during the study period. The summation of crashes for each site type by type and severity for each site and year is not shown in mathematic terms, but is implied by the subscripts at and as. Equation 20 is used to estimate the overall expected average crash frequency within the project limits during the study period. The same equation is used to calculate the overall predicted average crash frequency by substituting the subscript “p” for the subscript “e”. Equation 20 𝑁 , , , 𝑁 , , , ∗ 𝑛 where Ne,aS,ac,at,as = overall expected average crash frequency for all sites aS and all years in the study period (includes all crash types at, and all severities as) (crashes/year); and ns = number of years in the study period (yr). Step 17—Determine if there is an alternative design, treatment, or forecast AADT to be evaluated. Steps 3 through 17 are repeated as appropriate for the same project limits but for alternative conditions, treatments, periods of interest, or forecast AADT volumes. Step 18—Evaluate and compare results. The crash frequency estimates obtained from the previous steps represent statistically reliable estimates of the (expected or predicted) average crash frequency for each configuration (e.g., existing condition, alternative design) that is evaluated. The estimates are based on the configuration’s specified project limits, study period, geometric design, traffic control features, and AADT volume. The estimates can be used to assess the safety associated with each site and the overall project based on consideration of crash type and severity. The estimates can be used to identify treatments or design changes that have the potential for reducing crash frequency, severity, or both. The estimates can also be used to compare the relative safety of alternative designs. 2.5.2. Data Needed to Apply the Predictive Method The input data needed for the predictive models are identified in this section. These data represent the geometric design features, traffic control features, and traffic demand characteristics that have been found to have some relationship to crash potential. The input data are needed for each one-directional site of interest in the project limits. Criteria for defining site boundaries are described in Section 2.6. There are several data elements identified in this section that describe a length along the roadway (e.g., segment length, curve length, etc.). All of these lengths are measured along the reference line established in Step 1 of the predictive method. Points that do not lie on the reference line must be projected onto the reference line (along a perpendicular line if the alignment is straight, or along a radial line if the alignment is curved) to facilitate length determination. These dimensions can be obtained from field measurements, a plan set, or aerial photographs. The input data needed for each one-directional site of interest are identified in the following list.  Number of through lanes—For a freeway segment, use the total number of through lanes in the subject direction of travel. For a speed-change lane site, use the number of through lanes in the portion of

44 freeway adjacent to the speed-change lane. The predictive models are limited to freeways with two to seven lanes. A segment with a lane-add (or lane-drop) taper is considered to have the same number of through lanes as the roadway just downstream of the lane-add (or lane-drop) taper. This guidance is shown in Figure 4. The definition of “through lane” is provided in Section 2.4.1. Figure 4. Through-lane count in segments with a lane added or dropped. Do not include any auxiliary lanes that are associated with a weaving section, unless the weaving section length exceeds 0.85 mi (4,500 ft). If this length is exceeded, then the auxiliary lane is counted as a through lane that starts as a lane-add ramp entrance and ends as a lane-drop ramp exit. Do not include the speed-change lane that is associated with a ramp that merges with (or diverges from) the freeway, unless its length exceeds 0.30 mi (1,600 ft). If this length is exceeded, then the speed-change lane is counted as a through lane that starts as a lane-add ramp entrance and ends as a lane drop by taper (or starts as a lane add by taper and ends as a lane-drop ramp exit). For this predictive method, an HOV lane can be considered as a through lane if (a) the HOV lane volume is reasonably similar to that of the general-purpose lanes and (b) the HOV lane is separated from the adjacent general-purpose lanes by a single dashed lane line (such that the HOV lane has continuous access).  Length of freeway segment, length of speed-change lane site, and length of speed-change lane (if present)—As discussed in Section 2.4.1, a speed-change lane site has a length that is less than or equal to that of the associated speed-change lane. The speed-change lane length is measured from the gore point to the taper point. Figure 5 illustrates these measurement points for a ramp entrance and a ramp exit speed-change lane with the parallel and taper design, respectively.

45 Figure 5. Freeway speed-change lane length.  Radius of curve—Radius is measured using the reference line established in Step 1 of the predictive method. If the curve has spiral transitions, then use the radius of the central circular portion of the curve.  Widths of through lanes, PTSU lane, outside shoulders, inside shoulders, and median—The values assigned to these data elements should be representative of the overall site. They should not be measured where one or more edges are discontinuous or tapered. Rather, they should be measured where the cross section is constant, such as along line A or B in Figure 6. If a width varies along the segment or speed-change lane (but not enough to justify beginning a new site), then compute the length-weighted average width. The definition of “PTSU lane” is provided in Section 2.4.1.  Width of PTSU lane—The width of that portion of the paved shoulder allocated for use by vehicles during specified hours of the day. If the opposing travel direction has a PTSU lane adjacent to the opposing inside shoulder, then the width of the opposing PTSU lane is also needed. If this width varies along the length of the site (e.g., as in the case where it the PTSU lane is tapered to add or drop the PTSU lane), then an average width is used for the subject site.  Shoulder width—This width represents the portion of the paved shoulder that functions as shoulder for all hours of the day (i.e., it does not include the portion of the shoulder used as a PTSU lane). The inside shoulder width is needed for the subject site and for the opposing direction of travel.  Through lane width—This width is computed as an average for all through lanes. The PTSU lane is not considered to be a “through” lane.  Median width—This width is measured between the edges of the traveled way for the two opposing directions of travel. The median width includes the width of the inside shoulders and any PTSU lanes that are present in the subject and opposing travel directions.  Length of rumble strips on the inside (or median) shoulder and on the outside (or roadside) shoulder—Measured separately for each shoulder. Do not include rumble strips on the outside shoulder adjacent to a speed-change lane.

46 Figure 6. Measurement of cross section data elements.  Length of (and offset to) the barrier in the median and the barrier on the roadside—Length and offset are measured for each piece of barrier “associated” with the subject site (i.e., freeway segment or speed-change lane). A barrier is associated with the site if its offset from the near edge of traveled way is 30 ft or less. Barrier adjacent to a ramp (as shown in Figure 6) but also within 30 ft of the freeway traveled way should also be associated with the subject site. Each piece of barrier is represented once for a site. Barrier length is measured along the reference line. Offset is measured from the nearest edge of traveled way to the barrier face. Offset is also measured for barrier that continues for the length of the segment or speed-change lane (and beyond). Figure 7 illustrates these measurements for a barrier element protecting a sign support in a median with width Wm, inside shoulders with width Wis,s and Wis,o, and PTSU lane with width Wptsu,s. The barrier element directly adjacent to the subject direction of travel has a portion of its length that is parallel to the roadway and a portion of its length that is tapered from the roadway. The appropriate way to evaluate this barrier element is to separate it into two pieces, as shown in Figure 7. Each piece is represented by its average offset Woff,in,i and length Lib,i. Figure 7. Barrier variables.  Distance to nearest upstream entrance ramp—The value assigned to this data element represents the distance from the segment boundary to the ramp gore point, as measured along the reference line. The distance to the nearest upstream entrance ramp is shown in Figure 8 using the variable Xb,ent. If the ramp entrance is located at the start of the subject segment (as in Figure 8b), then the corresponding

47 distance is equal to 0.0 mi. If the ramp does not exist or is located more than 0.5 mi from the segment, then this distance can be set to a large value (e.g., 999) in the predictive method to obtain the correct results. The gore point is located where the pair of solid white pavement edge markings that separate the ramp from the freeway main lanes are 2.0 ft apart (as shown in Figure 6). If the markings do not extend to a point where they are 2.0 ft apart, then the gore point is found by extrapolating both markings until the extrapolated portion is 2.0 ft apart. Figure 8a shows a freeway segment with an upstream exit ramp serving travel in the subject direction of travel. Upstream exit ramps are not of interest to the evaluation of the subject segment and data are not needed for these ramps if they exist in the vicinity of the segment.  Distance to nearest downstream exit ramp—The measurement technique is the same as for upstream entrance ramps. This distance is shown in Figure 8 using the variable Xe,ext. Downstream entrance ramps are not of direct interest, and their data are not needed. a. All ramps external to the segment. b. One ramp at beginning and one ramp external to segment. Figure 8. Distance to nearest ramp.

48  Clear zone width—This width is measured from the edge of traveled way to the typical limits of vertical obstruction (e.g., non-traversable slope, fence line, utility poles) along the roadway. The Roadside Design Guide (5) provides information about roadside features that define this width. The clear zone width includes the outside shoulder. It is measured for the subject travel direction. If this width varies along the site, then use the estimated length-weighted average clear zone width (excluding the portion of the site with barrier). Do not consider outside (roadside) barrier when determining the clear zone width for the predictive method (because barrier location and influence is addressed in other AFs). If the site has outside barrier for its entire length, then the clear zone width will not influence the model prediction, and any value can be used for the clear zone width value (e.g., 30 ft). This guidance is illustrated in Figure 9 for a freeway segment. The clear zone is shown to be established by a fence line that varies in offset from the edge of traveled way. A length-weighted width is appropriate for this situation. The lone tree and the guardrail are not considered in the determination of clear zone width. Figure 9. Clear zone width considerations.  Proportion of freeway AADT volume that occurs during hours where the lane volume exceeds 1,000 vehicles per hour per lane (veh/h/ln)—The lane volume for hour i (LVi) is computed as LVi = HVi/n where HVi is the volume during hour i (i = 1, 2, 3, ... , 24) and n is the number of through lanes. The desired proportion Phv is computed as Phv = (Σ HVi*)/AADT where Σ HVi* is the sum of the volume during each hour where the lane volume exceeds 1,000 veh/h/ln. The AADT, HV, and n variables represent the subject travel direction (i.e., they are one-directional values). These data will typically be obtained from the continuous traffic counting station that (a) is nearest to the subject freeway and (b) has similar traffic demand and peaking characteristics. A default value can be computed using the following equation. Equation 21 𝑃 1.0 exp 1.45 0.000124 𝐴𝐴𝐷𝑇𝑛 0.0 where Phv = proportion of subject direction AADT during hours where volume exceeds 1,000 veh/h/ln; AADT = one-directional AADT volume of the freeway (veh/day); and n = number of through lanes in the subject travel direction, lanes.  Freeway AADT volume—The freeway AADT volume represents the subject travel direction (i.e., it is a one-directional value). If a one-directional AADT is not available, it can be estimated as one-half of the two-directional value.

49  Entrance ramp AADT volume, Exit Ramp AADT volume—The annual average daily traffic volume of the ramp. The evaluation of a freeway segment requires the nearest upstream entrance ramp AADT volume (if within 0.5 miles of the segment) and the nearest downstream exit ramp volume (if within 0.5 miles of the segment). The evaluation of a ramp entrance speed-change lane requires the entrance ramp AADT volume. The evaluation of a ramp exit speed-change lane requires the exit ramp AADT volume.  Length of PTSU transition zone present upstream, downstream, or both—The PTSU lane is always preceded and succeeded by a transition zone. In the upstream transition zone, vehicles change lanes or adjust speed as they interact with vehicles preparing to enter the forthcoming PTSU lane. Similarly, in the downstream zone, vehicles change lanes or adjust speed as they interact with vehicles that have just exited the PTSU lane. This transition zone is defined to be 800 ft (0.152 mi) in length. A transition zone can exist entirely within the length of one site or a portion of the zone can be located in two or more sites. In special cases, two separate transition zones can be located in the same site. These points are illustrated in Figure 10. a. Upstream transition zone. b. Downstream transition zone. c. Transition zones between PTSU lanes. Figure 10. Determination of the length of transition zone within a site. In Figure 10a, the site is shown as a freeway segment located upstream of a PTSU lane. The segment’s length is shown to exceed that of the transition zone (which always equals 0.152 miles). As a result, the length of the PTSU transition zone Ltransition,site is computed to be 0.152 miles. In Figure 10b, the site is shown as a freeway segment located downstream of a PTSU lane. The segment’s length is shown to be less than that of the transition zone. As a result, the variable Ltransition,site is equal to the segment length Ls,fs. If the next downstream segment of freeway is also evaluated, it too will have a non-zero value for Ltransition,site because it includes the remaining portion of the transition zone.

50 In Figure 10c, the site is shown as a freeway segment between two PTSU lanes. Its length is shown to include two transition zones. As a result, the value of Ltransition,site is equal to the sum of the two lengths.  Length of turnout within segment—With PTSU operation, turnouts are periodically provided beyond the shoulder to serve as emergency refuge spaces for disabled vehicles. A turnout can exist entirely within the length of one segment or a portion of the turnout can be located in two or more segments. If a segment is long, then two separate turnouts can be located in the same segment. These points are illustrated in Figure 11. The length of the turnout is measured from the begin taper to the end taper. In Figure 11a, the turnout is located fully within the segment. The segment’s length is shown to exceed that of the turnout. As a result, the length of the length of the turnout within the segment Lturnout,fs is equal to the length of the turnout. In Figure 11b, the turnout is located partly within the segment. As a result, the length of the turnout within the segment Lturnout,fs is less than the length of the turnout. If the next upstream segment of freeway is also evaluated, it too will have a non-zero value for Lturnout,fs because it includes the remaining portion of the turnout. a. Turnout fully within segment. b. Turnout partially within segment. Figure 11. Determination of the length of turnout within a segment.  Proportion of time during the average day that PTSU operates—Expressed as the number of hours during which the shoulder is available for part-time use each day of year divided 24 hours per day. If PTSU operating hours vary by weekday and weekend during the year, then the following equation can be used to compute a representative value for the proportion of time the PTSU operates. Variations of this equation can be used if PTSU operating hours vary by day of week or month of year. Equation 22 𝑃 , ∑ 5𝑑𝑎𝑦𝑤𝑘 1 ℎ𝑟 𝑃 , 2 𝑑𝑎𝑦 𝑤𝑘 1 ℎ𝑟 𝑃 , , 7𝑑𝑎𝑦𝑤𝑘 24 ℎ𝑟 where Pt,ptsu = proportion of time during the average day that PTSU operates;

51 Popen, wkday,j = proportion of hour j that PTSU is operating during typical weekday of year; and Popen, wkend,j = proportion of hour j that PTSU is operating during typical weekend day of year. 2.6. Freeway Segments and Speed-Change Lanes with PTSU This section consists of three subsections. The first subsection describes how the freeway facility is represented as a contiguous set of sites. The second subsection provides guidelines for segmenting the freeway facility. The assignment of crashes to sites is discussed in the last subsection. 2.6.1. Representing the Freeway Facility as a Set of Sites For analysis purposes, a freeway facility is considered to consist of a contiguous set of freeway segments, ramp entrance speed-change lane sites, and ramp exit speed-change lane sites. These components are generally referred to as “sites.” Each site type is defined in Section 2.4.1. Figure 12 illustrates the three site types in the context of a short length of freeway near an interchange. The figure shows five sites (with grey shading) for the right-to-left direction of travel. Three freeway segments are labeled Fr1, Fr2, and Fr3 in the figure. The speed-change lane site associated with the entrance ramp is labeled SCen and that associated with the exit ramp is labeled SCex. Figure 12. Illustrative sites for one-directional freeway facility evaluation.

52 The predictive model for speed-change lane sites estimates the average frequency of crashes that are associated with the presence and operation of the speed-change lane. These crashes occur in Region A of Figure 13 (this region is defined by the gore point and the taper point). Crashes that occur outside of Region A (i.e., in Region B) are associated with a freeway segment. Figure 13. Definition of freeway segments and speed-change lane sites. 2.6.2. Segmentation Process As a first step of the segmentation process, the freeway in the subject direction of travel is subdivided into sites. A speed-change lane site begins at the gore (or taper) point and ends at the associated taper (or gore) point. These points are shown in Figure 13. Any site that is not a speed-change lane site is a freeway segment. A freeway segment or a speed-change lane site can be subdivided into two or more sites if dictated by the segmentation guidelines described in subsequent paragraphs. As a second step of the segmentation process, the sites identified in the first step are further subdivided (if needed) to ensure that they are homogeneous with respect to characteristics such as traffic volume, key geometric design features, and traffic control features. A new site begins where there is a change in at least one of the characteristics identified in the following list. The phrases “through lanes” and “PTSU lane” are defined in Section 2.4.1. The listed characteristics are described in Section 2.5.2.  Number of through lanes—Begin a site at the gore point if the lane is added or dropped at a ramp or C-D road. Begin a segment at the upstream start of taper if the lane is added or dropped by taper. Guidance in this regard is described in the text accompanying Figure 4. If a lane is added or dropped by taper, then avoid ending the segment within the length of the taper.  Through lane width—Measure the lane width at successive points along the roadway. Compute an average lane width for each point and round this average to the nearest 0.5 ft. Begin a new site if the rounded value for the current point changes from that of the previous point (e.g., from 11.5 to 12.0 ft).  Outside shoulder width—Measure the outside shoulder width at successive points along the roadway. Compute an average shoulder width for each point and round this average to the nearest 1.0 ft. Begin a

53 new site if the rounded value for the current point changes from that of the previous point (e.g., from 6 to 7 ft).  Inside shoulder width—Measure the inside shoulder width at successive points along the roadway. Compute an average shoulder width for each point and round this average to the nearest 1.0 ft. Begin a new site if the rounded value for the current point changes from that of the previous point (e.g., from 6 to 5 ft).  Median width—Measure the median width at successive points along the roadway. Round the measured median width at each point to the nearest 10 ft. If the rounded value exceeds 90 ft, then set it to 90 ft. Begin a new site if the rounded value for the current point changes from that of the previous point (e.g., from 30 to 20 ft).  Horizontal curve—Begin the site at the beginning or end of a horizontal curve. The curve begins at the point where the reference line changes from straight to curved (i.e., the PC). The curve ends at the point where the reference line changes from curved to straight (i.e., the PT). If the curve has spiral transitions, then begin the site at the “effective” PC or end it at the “effective” PT. The effective PC point is located midway between the TS and SC, where the TS is the point of change from tangent to spiral and the SC is the point of change from spiral to circular curve. The effective PT is located midway between the CS and ST, where CS is the point of change from circular curve to spiral and ST is the point of change from spiral to tangent.  Clear zone width—Measure the clear zone width at successive points along the roadway. Compute an average clear zone width for each point and round this average to the nearest 5 ft. Begin a new site if the rounded value for the current point changes from that of the previous point (e.g., from 25 to 30 ft).  PTSU lane—Begin a segment at the start (or end) of a PTSU lane. If the PTSU lane is added by taper, then begin a segment at the upstream start of taper. If the PTSU lane is dropped by taper, then end the segment at the end of taper. Guidance in this regard is described in the text accompanying Figure 14. If a PTSU lane is added or dropped by taper, then avoid ending the segment within the length of the taper.

54 a. Add PTSU lane. b. Drop PTSU lane. c. PTSU lane accommodation near a speed-change lane. Figure 14. Segment boundaries based on PTSU lane presence. The width-related characteristics in the preceding list indicate that the width should be measured at “successive” points along the roadway. The distance between these points should be established by the analyst and then consistently used for all width measurements. Shorter distances are desirable because they will provide a more reliable indication of the location of a detected change. The analyst should choose a distance that is judged to provide a reasonable balance between site location accuracy and data collection effort. In this regard, a distance of 0.05 miles between successive points may provide the desired balance for typical evaluations. Application of the “median width” segmentation criterion is shown in Figure 15. The freeway section in this figure is shown to consist of five segments. Segment 1 has a rounded median width of 70 ft. Segment 2 starts where the rounded median width first changes to 80 ft. Segment 3 begins at the point where the rounded median width first changes to 90 ft. Segment 4 begins where the rounded median width first changes to 80 ft. Segment 5 begins where the rounded median width first changes to 70 ft. Figure 15. Segmentation for varying median width.

55 Guidance regarding the location of the lane, shoulder, and median width measurement points is provided in the text associated with Figure 6. Each width represents an average for the site. Similarly, guidance associated with Figure 9 is used to determine the clear zone width for the segment. The rounded lane, shoulder, median, and clear zone width values are used solely to determine site boundaries. Once these boundaries are determined, the unrounded values for the site are then used for all subsequent calculations in the predictive method. If an alternatives analysis is undertaken, the number (and location) of sites should be the same (or nearly so) for all design configurations being compared. This approach minimizes possible differences in results due to differences in facility segmentation and ensures that the observed differences in results are attributable to design changes. To illustrate this guidance, consider an existing segment that is proposed to have its lane width increased by 1.0 foot at its mid-point. The analyst desires to compare the existing and proposed designs to determine the safety effect of the lane width increase. The segmentation criteria require the proposed design to be evaluated as two segments (with the end of the first segment and start of the second segment to occur where the lane width changes). To ensure that the observed differences in results between the one-segment existing design and two-segment proposed design are attributable to the change in lane width, the existing design should also be evaluated as two segments where the first segment ends (and the second segment begins) at the same mid-point location as for the proposed design. 2.6.3. Crash Assignment to Sites Observed crash counts are needed if the analyst desires to apply the EB method. These crashes are assigned to the individual sites if the site-specific EB method is applied. The following paragraphs describe the criteria for assigning crashes to the freeway in the subject travel direction and its individual sites. All crashes that occur on the freeway are assigned to the subject or opposing travel direction. Crashes assigned to the subject travel direction that (a) occur in the freeway lanes or roadside associated with the subject travel direction (excluding those involving a vehicle from the opposing direction that has crossed over the median), or (b) occur in the median by a vehicle traveling in the subject travel direction prior to the occurrence of events leading to the crash, or (c) occur beyond the median and include a vehicle traveling in the subject travel direction prior to the occurrence of events leading to the crash. All crashes that are not assigned to the subject travel direction are assigned to the opposing travel direction. All crashes that are assigned to the subject direction of travel are classified as either a speed-change- lane-related crash or a segment-related crash. Speed-change-related crashes include all crashes that are located between the gore point and the taper point of a speed-change lane and that (a) involve vehicles in the speed-change lane, (b) involve vehicles in the freeway lanes on the same side of the freeway as the speed-change lane, or (c) occur in the median by a vehicle traveling in a lane on the same side of the freeway as the speed-change lane and in the same basic direction as vehicles in the speed-change lane. All freeway crashes that are not classified as speed-change-related crashes are considered to be freeway segment crashes. 2.7. Predictive Model for Freeway Segments with PTSU The predictive models for freeways segments are described in this section. Each model typically consists of a safety performance function (SPF), one or more SPF adjustment factors (AFs), a calibration factor, a severity distribution, and crash type distribution. All variables in this section that describe SPF or AF input values are defined in Section 2.5.2. The SPFs are used to estimate the predicted average crash frequency of a site with base conditions. The SPFs, like all regression models, estimate the value of the dependent variable as a function of a set of independent variables. The independent variables for the freeway segment SPFs include the segment’s AADT volume and length. The freeway segment SPFs are summarized in Table 4.

56 Table 4. SPFs for freeway segments. Crash Type (y) Crash Severity (z) SPF Variable SPF Equation All types (at) Fatal and injury (fi) Nspf,fs,at,fi Equation 23 Property damage only (pdo) Nspf,fs,at,pdo Equation 23 Each SPF has an associated overdispersion parameter k. The overdispersion parameter provides an indication of the statistical reliability of the SPF. The closer the overdispersion parameter is to zero, the more statistically reliable the SPF. This parameter is used in the EB method that is discussed in the appendix to HSM Part C (3). The AFs applicable to the SPFs presented in Table 4 are summarized in Table 5. Table 5. SPF adjustment factors for freeway segments. AF Variable AF Description AF Equation AF1,fs,at,z Horizontal curve Equation 25 AF2,fs,at,z Lane width Equation 26 AF3,fs,at,z Inside shoulder width Equation 27 AF4,fs,at,z Median width Equation 28 AF5,fs,at,z Median barrier Equation 30 AF6,fs,at,fi Inside shoulder rumble strip Equation 31 AF7,fs,at,fi Lane change Equation 32 AF8,fs,at,z Outside shoulder width Equation 33 AF9,fs,at,fi Outside shoulder rumble strip Equation 34 AF10,fs,at,z Outside clearance Equation 35 AF11,fs,at,z Outside barrier Equation 36 AF12,fs,at,z Turnout presence Equation 37 AF13,fs,at,z PTSU operation Equation 39 Note: Subscripts to the AF variables use the following notation:  Site type w (w = fs: freeway segment, en: ramp entrance speed-change lane, ex: ramp exit speed-change lane)  Crash type y (y = at: all crash types)  Severity z (z = fi: fatal and injury, pdo: property damage only, as: all severities) Many of the AFs in Table 5 are developed for specific site types and crash severities. This approach was undertaken to make the predictive model sensitive to the geometric design and traffic control features of specific sites, in terms of their influence on specific crash severities. The subscripts for each AF variable indicate the sites and severities to which each AF is applicable. The subscript definitions are provided in the table footnote. In some cases, an AF is applicable to several severity levels. In these cases, the subscript retains the generic letter z. The discussion of these AFs in Section 2.7.2 identifies the specific severity levels to which they apply. For some of the AFs, supplemental calculations must be performed before the AF value can be computed. For example, to apply the median width AF, the proportion of the segment length having inside barrier and the length-weighted average barrier offset (as measured from the edge of the inside shoulder) must be computed. Procedures for supplemental calculations are described in Section 2.9. 2.7.1. Safety Performance Functions for Freeway Segments with PTSU The SPFs for freeway segments are presented in this section. Specifically, SPFs are provided for one- directional freeway segments with two to seven through lanes. The range of freeway AADT volume for

57 which these SPFs are applicable is shown in Table 6. Application of the SPFs to segments with AADT volume substantially outside these ranges may not provide reliable results. Table 6. Applicable AADT volume ranges for freeway segment and speed-change lanes. Through Lanes Applicable AADT Volume Range (veh/day) 2 0 to 46,000 3 0 to 92,000 4 0 to 115,000 5 0 to 121,000 6 0 to 137,000 7 0 to 149,000 The base conditions for the SPFs for freeway segments are presented in the following list of variables (these variables are described in Section 2.5.2):  Horizontal curve presence: not present  Through lane width: 12 feet  Inside shoulder width (paved): 6 feet  Median width: 60 feet  Length of median barrier: 0.0 miles (i.e., not present)  Length of rumble strip on inside shoulder: 0.0 miles (i.e., not present)  Distance to nearest upstream ramp entrance: more than 0.5 miles from segment  Distance to nearest downstream ramp exit: more than 0.5 miles from segment  Outside shoulder width: 10 feet  Length of rumble strip on outside shoulder: 0.0 miles (i.e., not present)  Clear zone width: 30 feet  Length of outside (roadside) barrier: 0.0 miles (i.e., not present)  PTSU operation: no PTSU operation during any hour of the day  PTSU lane width: 0 feet  Turnout length in segment: 0.0 miles (i.e., not present) The SPFs for freeway segments are represented using the following equation: Equation 23 𝑁 , , , 𝐿 , exp 𝑎 𝑏 ln 𝑐 𝐴𝐴𝐷𝑇 where Nspf,fs,at,z = predicted average crash frequency of a freeway segment with base conditions, for all crash types at and severity z (z = fi: fatal and injury, pdo: property damage only) (crashes/year); Ls,fs = length of freeway segment (mi); AADTfs = one-directional AADT volume of freeway segment (veh/day); a, b = regression coefficients; and c = AADT scale coefficient. The regression coefficients and the coefficient for computing the overdispersion parameter are provided in Table 7. The SPFs are illustrated in Figure 16.

58 Table 7. SPF coefficients for freeway segments. Crash Severity (z) SPF Coefficient Dispersion Coefficient Kfs,at,z (mi-1) a b c Fatal and injury (fi) −4.556 1.406 0.001 10.10 Property damage only (pdo) −3.133 1.295 0.001 9.57 a. Fatal-and-injury crash frequency. b. Property-damage-only crash frequency. Figure 16. Graphical form of the SPFs for freeway segments. The value of the overdispersion parameter associated with the SPFs for freeway segments is determined as a function of segment length. This value is computed using Equation 24. Equation 24 𝑘 , , 1.0𝐾 , , 𝐿 , where kfs,at,z = overdispersion parameter for freeway segments and crash severity z; Kfs,at,z = dispersion coefficient for freeway segments and crash severity z (mi–1); and Ls,fs = length of freeway segment (mi). 2.7.2. SPF Adjustment Factors for Freeway Segments with PTSU The AFs for geometric design and traffic control features of freeway segments are presented in this section. Several AFs described in this section include a variable defining the proportion of the segment’s length along which a particular feature (e.g., rumble strip, barrier) is present. Guidance is offered herein for computing each proportion. The concept underlying this guidance is that the computed proportion should equal the total length of the feature divided by the length of the segment. AF1,fs,at,z—Horizontal Curve Two AFs are used to describe the relationship between horizontal curve radius and predicted crash frequency. The SPFs to which they apply are identified in the following list:

59  SPF for fatal-and-injury crashes (fs, at, fi)  SPF for property-damage-only crashes (fs, at, pdo) The base condition is an uncurved (i.e., tangent) alignment. The AFs for horizontal curvature are described using the following equation: Equation 25 𝐴𝐹 , , , 1.0 exp 𝑎 5,730𝑅 where AF1,fs,at,z = adjustment factor for horizontal curvature in a freeway segment; for all crash types and severity z; and R = radius of curve (ft). The values of coefficient a for Equation 25 are provided in Table 8. The AF is applicable to curves with a radius of 1,400 ft or larger. Table 8. Coefficients for horizontal curve AF—freeway segments. Crash Severity (z) AF Variable AF Coefficient (a) Fatal and injury (fi) AF1,fs,at,fi −4.89 Property damage only (pdo) AF1,fs,at,pdo −5.47 AF2,fs,at,z—Lane Width Two AFs are used to describe the relationship between average lane width and predicted crash frequency. The SPFs to which they apply are identified in the following list:  SPF for fatal-and-injury crashes (fs, at, fi)  SPF for property-damage-only crashes (fs, at, pdo) The base condition is a 12-ft lane width. The AFs are described using the following equation: Equation 26 𝐴𝐹 , , , exp 𝑎 min 𝑊 , 13 12 where AF2,fs,at,z = adjustment factor for lane width in a freeway segment; for all crash types and severity z; and Wl = through lane width (ft); The values of coefficient a for Equation 26 are provided in Table 9. The AF is discontinuous, breaking at a lane width of 13 ft. The AF value does not change for lane width in excess of 13 ft. The AF is applicable to lane widths in the range of 10.5 to 14.4 ft. Table 9. Coefficients for lane width AF—freeway segments. Crash Severity (z) AF Variable AF Coefficient (a) Fatal and injury (fi) AF2,fs,at,fi −0.0411 Property damage only (pdo) AF2,fs,at,pdo −0.0273

60 AF3,fs,at,z—Inside Shoulder Width Two AFs are used to describe the relationship between average inside shoulder width and predicted crash frequency. The SPFs to which they apply are identified in the following list:  SPF for fatal-and-injury crashes (fs, at, fi)  SPF for property-damage-only crashes (fs, at, pdo) The base condition is a 6-ft inside shoulder width. The AFs are described using the following equation: Equation 27 𝐴𝐹 , , , exp 𝑎𝑛 min 𝑊 , , 12 6 where AF3,fs,at,z = adjustment factor for inside shoulder width in a freeway segment; for all crash types and severity z; n = number of through lanes within site; and Wis,s = paved inside shoulder width for the subject travel direction (does not include the portion of the shoulder used as a PTSU lane) (ft). The values of coefficient a for Equation 27 are provided in Table 10. The AF is discontinuous such that its value does not change for shoulder widths in excess of 12 ft. The AF is applicable to inside shoulder widths in the range of 0.7 to 11.0 ft. The number of through lanes range from 2 to 7. Table 10. Coefficients for inside shoulder width AF—freeway segments. Crash Severity (z) AF Variable AF Coefficient (a) Fatal and injury (fi) AF3,fs,at,fi −0.0411 Property damage only (pdo) AF3,fs,at,pdo −0.0273 AF4,fs,at,z—Median Width Two AFs are used to describe the relationship between average median width and predicted crash frequency. The SPFs to which they apply are identified in the following list:  SPF for fatal-and-injury crashes (fs, at, fi)  SPF for property-damage-only crashes (fs, at, pdo) The base condition is a 60-ft median width, a 6-ft inside shoulder width, no PTSU lane, and no barrier present in the median. The AFs are described using the following equation: Equation 28 𝐴𝐹 , , , 1.0 𝑃 exp 𝑎𝑛 𝑊 48 𝑃 exp 𝑎𝑛 min 𝑊 , 2 𝑊 48 with Equation 29 𝑊 𝑊 𝑊 , 𝑊 , 𝑊 , 𝐼 , , 𝑊 , 𝐼 , , where AF4,fs,at,z = adjustment factor for median width in a freeway segment; for all crash types and severity z; Iptsu,s,in = indicator variable for PTSU lane location in the subject travel direction (= 1.0 if inside shoulder is allocated to part-time vehicular traffic use at any time of the day; otherwise 0.0) (ft); Iptsu,o,in = indicator variable for PTSU lane location in the opposing travel direction (= 1.0 if inside shoulder is allocated to part-time vehicular traffic use at any time of the day; otherwise 0.0) (ft); n = number of through lanes within site;

61 Pib = proportion of site length with a barrier present in the median (i.e., inside); Wicb = distance from edge of inside shoulder to barrier face (ft); Wis,s = paved inside shoulder width for the subject travel direction (does not include the portion of the shoulder used as a PTSU lane) (ft); Wis,o = paved inside shoulder width for the opposing travel direction (does not include the portion of the shoulder used as a PTSU lane) (ft); Wm = median width (measured from near edges of traveled way in both directions) (ft); Wptsu,s = width of shoulder allocated to part-time vehicular traffic use in the subject travel direction (i.e., as an additional travel lane) (if PTSU is not provided at any time, this width equals 0.0) (ft); Wptsu,o = width of shoulder allocated to part-time vehicular traffic use in the opposing travel direction (i.e., as an additional travel lane) (if PTSU is not provided at any time, this width equals 0.0) (ft); and Wum = non-shoulder part of median width (measured from near edges of shoulder in both directions) (ft). The values of coefficient a for Equation 28 are provided in Table 11. This AF is applicable to a segment with no median barrier and to a segment that has median barrier present along some portion of its length. However, it does not describe the relationship between barrier presence and predicted crash frequency. This latter relationship is described using the median barrier AF. Guidance for computing the variables Pib and Wicb is provided in Section 2.9. Table 11. Coefficients for median width AF—freeway segments. Crash Severity (z) AF Variable AF Coefficient (a) Fatal and injury (fi) AF4,fs,at,fi −0.00601 Property damage only (pdo) AF4,fs,at,pdo −0.00407 The AF is applicable to median widths of 5 ft or more. The number of through lanes range from 2 to 7. The variable Pib ranges from 0.0 to 1.0. The inside shoulder width ranges from 0.7 to 11.0 ft. The variable Wicb ranges from 0.75 to 20 ft. The width of the PTSU lane is 16.8 ft or less. If the median width exceeds 90 ft, then 90 ft should be used for Wm in Equation 29. AF5,fs,at,z—Median Barrier Two AFs are used to describe the relationship between median barrier presence and predicted crash frequency. The SPFs to which they apply are identified in the following list:  SPF for fatal-and-injury crashes (fs, at, fi)  SPF for property-damage-only crashes (fs, at, pdo) The base condition is “no barrier present in the median” (i.e., Pib = 0.0). The AFs are described using the following equation: Equation 30 𝐴𝐹 , , , 1.0 𝑃 1.0 𝑃 exp 𝑎 𝑛/𝑊 where AF5,fs,at,z = adjustment factor for median barrier in a freeway segment; for all crash types and severity z; and n = number of through lanes within site; Pib = proportion of site length with a barrier present in the median (i.e., inside); and Wicb = distance from edge of inside shoulder to barrier face (ft). The values of coefficient a for Equation 30 are provided in Table 12. Guidance for computing the variables Pib and Wicb is provided in Section 2.9.

62 Table 12. Coefficients for median barrier AF—freeway segments. Crash Severity (z) AF Variable AF Coefficient (a) Fatal and injury (fi) AF5,fs,at,fi 0.0166 Property damage only (pdo) AF5,fs,at,pdo 0.0162 This AF is applicable to a “number of through lanes” ranging from 2 to 7. The variable Wicb ranges from 0.75 to 20 ft. The variable Pib ranges from 0.0 to 1.0. AF6,fs,at,fi—Inside Shoulder Rumble Strip One AF is used to describe the relationship between inside shoulder rumble strip presence and predicted crash frequency. The SPF to which it applies is identified in the following list:  SPF for fatal-and-injury crashes (fs, at, fi) The base condition is “no inside shoulder rumble strips present” (i.e., Pir = 0.0). The AF is described using the following equation: Equation 31 𝐴𝐹 , , , 1.0 𝑃 1.0 𝑃 exp 0.516/𝑛 where AF6,fs,at,fi = adjustment factor for rumble strips on the inside shoulder of a freeway segment; for all crash types and fatal-and-injury fi crashes; n = number of through lanes within site; and Pir = proportion of site length with a rumble strips present on the inside shoulder. The proportion Pir represents the proportion of the segment length with rumble strips present on the inside shoulders. It is computed by summing the length of roadway with rumble strips on the inside shoulder (do not include rumble strips within the PTSU lane, if present) and dividing by the segment length. This AF is applicable to values of Pir that range from 0.0 to 1.0. The number of through lanes range from 2 to 7. AF7,fs,at,fi—Lane Change One AF is used to describe the relationship between lane change activity and predicted crash frequency. The SPF to which it applies is identified in the following list:  SPF for fatal-and-injury crashes (fs, at, fi) The base condition is “no significant lane changing due to ramp entry or exit.” More specifically, the base condition is no ramp entrance or ramp exit within 0.5 mi of the segment. The AF is described using the following equation: Equation 32 𝐴𝐹 , , , 1.0 exp 14.34 𝑋 , 1.30 ln 0.001 𝐴𝐴𝐷𝑇 ,14.34 𝐿 , 1.0 exp 14.34 𝐿 , 1.0 exp 14.34 𝑋 , 1.30 ln 0.001 𝐴𝐴𝐷𝑇 ,14.34 𝐿 , 1.0 exp 14.34 𝐿 , where AF7,fs,at,fi = adjustment factor for lane changes in a freeway segment; for all crash types and fatal-and-injury fi crashes; AADTb,ent = AADT volume of entrance ramp located at distance Xb,ent upstream of the subject segment (veh/day);

63 AADTe,ext = AADT volume of exit ramp located at distance Xe,ext downstream of the subject segment (veh/day); Xb,ent = distance from segment begin milepost to nearest upstream entrance ramp gore point (mi); Xe,ext = distance from segment end milepost to nearest downstream exit ramp gore point (mi); and Ls,fs = length of freeway segment (mi). The X and AADT variables describe the distance to (and volume of) the nearest upstream entrance ramp and the nearest downstream exit ramp. Only those ramps that contribute volume to the subject segment are of interest. Hence, a downstream entrance ramp is not of interest. For similar reasons, an upstream exit ramp is not of interest. The lane change AF is applicable to any segment in the vicinity of one or more ramps. These ramps can access the freeway from the left or right side. The AF is equally applicable to segments in a weaving section (regardless of the weaving section type) and segments in a non-weaving section (i.e., segments between an entrance ramp and an exit ramp where both ramps have a speed-change lane). The AF is applicable to weaving section lengths between 0.10 and 0.85 mi. It is applicable to any value for the distance variable X and to ramp AADTs up to 30,700 veh/day. AF8,fs,at,z—Outside Shoulder Width Two AFs are used to describe the relationship between average outside shoulder width and predicted crash frequency. The SPFs to which they apply are identified in the following list:  SPF for fatal-and-injury crashes (fs, at, fi)  SPF for property-damage-only crashes (fs, at, pdo) The base condition is a 10-ft outside shoulder width. The AFs are described using the following equation: Equation 33 𝐴𝐹 , , , exp 𝑎𝑛 min 𝑊 , 12 10 where AF8,fs,at,z = adjustment factor for outside shoulder width in a freeway segment; for all crash types and severity z; n = number of through lanes within site; and Ws = paved outside shoulder width (does not include the portion of the shoulder used as a PTSU lane) (ft). The values of coefficient a for Equation 33 are provided in Table 13. The AF is discontinuous such that its value does not change for shoulder widths in excess of 12 ft. The AF is applicable to outside shoulder widths in the range of 0.7 to 14.0 ft. The number of through lanes range from 2 to 7. Table 13. Coefficients for outside shoulder width AF—freeway segments. Crash Severity (z) AF Variable AF Coefficient (a) Fatal and injury (fi) AF8,fs,at,fi −0.0411 Property damage only (pdo) AF8,fs,at,pdo −0.0273 AF9,fs,at,fi—Outside Shoulder Rumble Strip One AF is used to describe the relationship between outside shoulder rumble strip presence and predicted crash frequency. The SPF to which it applies is identified in the following list:  SPF for fatal-and-injury crashes (fs, at, fi)

64 The base condition is “no outside shoulder rumble strips present” (i.e., Por = 0.0). The AF is described using the following equation: Equation 34 𝐴𝐹 , , , 1.0 𝑃 1.0 𝑃 exp 0.516/𝑛 where AF9,fs,at,fi = adjustment factor for rumble strips on the outside shoulder of a freeway segment; for all crash types and fatal-and-injury fi crashes; n = number of through lanes within site; and Por = proportion of site length with a rumble strips present on the outside shoulder. The proportion Por represents the proportion of the segment length with rumble strips present on the outside shoulders. It is computed by summing the length of roadway with rumble strips on the outside shoulder (do not include rumble strips within the PTSU lane, if present) and dividing by the segment length. This AF is applicable to values of Por that range from 0.0 to 1.0. The number of through lanes range from 2 to 7. AF10,fs,at,z—Outside Clearance Two AFs are used to describe the relationship between average outside clearance and predicted crash frequency. The SPFs to which they apply are identified in the following list:  SPF for fatal-and-injury crashes (fs, at, fi)  SPF for property-damage-only crashes (fs, at, pdo) The base condition is a 30-ft clear zone, a 10-ft outside shoulder width, no PTSU lane, and no barrier present in the clear zone. The AFs are described using the following equation: Equation 35 𝐴𝐹 , , , 1.0 𝑃 exp 𝑎𝑛 𝑊 𝑊 , 𝐼 , , 𝑊 20 𝑃 exp 𝑎𝑛 𝑊 20 where AF10,fs,at,z = adjustment factor for outside clearance in a freeway segment; for all crash types and severity z; Iptsu,s,o = indicator variable for PTSU lane location in the subject travel direction (= 1.0 if outside shoulder is allocated to part-time vehicular traffic use at any time of the day; otherwise 0.0) (ft); n = number of through lanes within site; Pob = proportion of site length with a barrier present on the outside (roadside); Whc = clear zone width (ft); Wocb = distance from edge of outside shoulder to barrier face (ft); Ws = paved outside shoulder width (does not include the portion of the shoulder used as a PTSU lane) (ft); Wptsu,s = width of shoulder allocated to part-time vehicular traffic use in the subject travel direction (i.e., as an additional travel lane) (if PTSU is not provided at any time, this width equals 0.0) (ft). The values of coefficient a for Equation 35 are provided in Table 14. This AF is applicable to a segment with no outside (roadside) barrier and to a segment that has outside barrier present along some portion of its length. However, it does not describe the relationship between barrier presence and predicted crash frequency. This latter relationship is described using the outside barrier AF. Guidance for computing the variables Pob and Wocb is provided in Section 2.9. The text associated with Figure 9 describes how to quantify the clear zone width used in Equation 35.

65 Table 14. Coefficients for outside clearance AF—freeway segments. Crash Severity (z) AF Variable AF Coefficient (a) Fatal and injury (fi) AF10,fs,at,fi −0.00601 Property damage only (pdo) AF10,fs,at,pdo −0.00407 The AF is applicable to clear zone widths of 30 ft or less. The number of through lanes range from 2 to 7. The variable Pob ranges from 0.0 to 1.0. The values of Wocb range from 0.75 to 20 ft. The outside shoulder width Ws ranges from 0.7 to 14.0 ft. AF11,fs,at,z—Outside Barrier Two AFs are used to describe the relationship between outside barrier presence and predicted crash frequency. The SPFs to which they apply are identified in the following list:  SPF for fatal-and-injury crashes (fs, at, fi)  SPF for property-damage-only crashes (fs, at, pdo) The base condition is “no barrier present in the clear zone” (i.e., Pob = 0.0). The AFs are described using the following equation: Equation 36 𝐴𝐹 , , , 1.0 𝑃 1.0 𝑃 exp 𝑎 𝑛/𝑊 where AF11,fs,at,z = adjustment factor for outside (roadside) barrier in a freeway segment; for all crash types and severity z; n = number of through lanes within site; Pob = proportion of site length with a barrier present on the outside (roadside); and Wocb = distance from edge of outside shoulder to barrier face (ft). The values of coefficient a for Equation 36 are provided in Table 15. Guidance for computing the variables Pob and Wocb is provided in Section 2.9. Table 15. Coefficients for outside barrier AF—freeway segments. Crash Severity (z) AF Variable AF Coefficient (a) Fatal and injury (fi) AF11,fs,at,fi 0.0166 Property damage only (pdo) AF11,fs,at,pdo 0.0162 This AF is applicable to a “number of through lanes” ranging from 2 to 7. The variable Wocb ranges from 0.75 to 20 ft. The variable Pib ranges from 0.0 to 1.0. AF12,fs,at,z—Turnout Presence Two AFs are used to describe the relationship between turnout presence and predicted crash frequency. The SPFs to which they apply are identified in the following list:  SPF for fatal-and-injury crashes (fs, at, fi)  SPF for property-damage-only crashes (fs, at, pdo) The base condition is “no turnout present” (i.e., Pturnout = 0.0). The AFs are described using the following equation:

66 Equation 37 𝐴𝐹 , , , 1.0 𝑃 1.0 𝑃 exp 𝑎/𝑛 with Equation 38 𝑃 𝐿 , /𝐿 , where AF12,fs,at,z = adjustment factor for turnout presence in a freeway segment; for all crash types and severity z; Ls,fs = length of freeway segment (mi); Lturnout,fs = length of turnout within segment (i.e., between segment begin and end mileposts) (mi); n = number of through lanes within site; and Pturnout = proportion of segment length with a turnout present on the outside (roadside). The values of coefficient a for Equation 37 are provided in Table 16. The proportion Pturnout represents the proportion of the segment length adjacent to a turnout. Guidance for determining the length used in Equation 38 to compute this proportion is provided in Section 2.5.2 (see Figure 11). Table 16. Coefficients for turnout presence AF—freeway segments. Crash Severity (z) AF Variable AF Coefficient (a) Fatal and injury (fi) AF12,fs,at,fi −0.787 Property damage only (pdo) AF12,fs,at,pdo −1.091 This AF is applicable to a “number of through lanes” ranging from 2 to 7. The variable Pturnout ranges from 0.0 to 1.0. This AF is applicable to freeway segments with a marked PTSU lane. AF13,fs,at,z—PTSU Operation Two AFs are used to describe the relationship between PTSU operation and predicted crash frequency. The SPFs to which they apply are identified in the following list:  SPF for fatal-and-injury crashes (fs, at, fi)  SPF for property-damage-only crashes (fs, at, pdo) The base condition is “no PTSU operation during any hour of the day” (i.e., Pt,ptsu = 0.0) and no PTSU lane or transition present. The AFs are described using the following equation: Equation 39 𝐴𝐹 , , , 1.0 𝑃 , exp 𝑓 , 𝑃 , exp 𝑓 , 𝑓 , , 𝑓 , with Equation 40 𝑓 , 𝑎/𝑛 min 𝑊 , , 12 𝐼 Equation 41 𝑓 , 𝑎 min 𝑊 , , 13 12 𝐼 Equation 42 𝑓 , 𝑏 𝐼 Equation 43 𝑓 , , 𝑑 1 𝐼 𝑃 , Equation 44 𝑃 , 𝐿 , /𝐿 , where

67 AF13,fs,at,z = adjustment factor for PTSU operation in a freeway segment; for all crash types and severity z; IptsuLane = indicator variable for PTSU lane presence (= 1.0 if PTSU lane is present [Wptsu,s > 0], 0.0 otherwise); Ls,fs = length of freeway segment (mi); Ltransition,site = total length of PTSU transition zones within site (i.e., between site begin and end mileposts) (mi); n = number of through lanes within site; Pt,ptsu = proportion of time during the average day that PTSU operates; Ptransition,fs = proportion of segment length with PTSU transition zone present upstream, downstream, or both; and Wptsu,s = width of shoulder allocated to part-time vehicular traffic use in the subject travel direction (i.e., as an additional travel lane) (if PTSU is not provided at any time, this width equals 0.0) (ft); The values of coefficients a, b, and d for Equation 40 to Equation 43 are provided in Table 17. The variable Ptransition,fs represents the proportion of the segment length that is adjacent to a PTSU transition zone. Guidance for determining the length Ltransition,site is provided in Section 2.5.2 (see Figure 10). Table 17. Coefficients for PTSU operation AF—freeway segments. Crash Severity (z) AF Variable AF Coefficients a b d Fatal and injury (fi) AF13,fs,at,fi −0.0411 1.318 1.305 Property damage only (pdo) AF13,fs,at,pdo −0.0273 1.567 1.515 The proportion Pt,ptsu represents the number of hours during which the shoulder is available for part- time use each day of year divided 24 hours per day. It has a nonzero value if (a) the segment has a full- width PTSU lane or the tapered portion of a PTSU lane, or (b) the segment does not have a PTSU lane but a portion of the segment is within 0.152 miles of a PTSU lane (i.e., just upstream or downstream). Case “a” is referred herein to as a PTSU lane and case “b” is referred to as a PTSU transition zone. The text associated with Equation 22 describes how to compute the proportion Pt,ptsu. This AF is applicable to values of Pt,ptsu that range from 0.0 to 0.45. The number of through lanes range from 2 to 7. The width of the PTSU lane is 16.8 ft or less. This AF is applicable to freeway segments with existing (or proposed) PTSU operation during some portion of the typical day. 2.7.3. Severity Distribution for Freeway Segments with PTSU The severity distribution for freeway segments is presented in this section. The severity distribution is used in the predictive model to estimate the average crash frequency for the following severity levels: fatal K, incapacitating injury A, non-incapacitating injury B, and possible injury C. The severity distribution proportions are computed using a severity distribution function (SDF). Each SDF was developed as a logistic regression model using observed crash data. The SDF, like all regression models, estimates the distribution value as a function of a set of independent variables. The independent variables include various geometric design and traffic control features. There is one SDF associated with each severity level in the predictive model. The SDF for level j predicts the proportion of crashes with severity level j, based on various geometric design and traffic control features at the subject site. Each SDF also contains a calibration factor that is used to calibrate the SDF to local conditions. The distribution value for severity level j is multiplied by the fatal-and-injury crash frequency to obtain the average crash frequency for the specified severity level. This crash frequency estimate is obtained from Equation 2 as a predicted value. However, its expected value equivalent should be used if the EB method is applied.

68 The general form for the severity distribution prediction equation for freeway segments is shown in the following equation. Equation 45 𝑁 , , , 𝑁 , , , 𝑃 , , where Np,fs,at,j = predicted average crash frequency of a freeway segment; for all crash types at and severity level j (j = K: fatal, A: incapacitating injury, B: non-incapacitating injury, C: possible injury) (crashes/year); Np,fs,at,fi = predicted average crash frequency of a freeway segment; for all crash types at and fatal-and-injury crashes fi (crashes/year); and Pfs,at,j = proportion of crashes with severity level j (j = K: fatal, A: incapacitating injury, B: non- incapacitating injury, C: possible injury) for all crash types at on a freeway segment. The SDFs for freeway segments are described by the following equations. Equation 46 𝑃 , , 𝑆 , ,1/𝐶 , 𝑆 , . 𝑆 , , 𝑆 , , Equation 47 𝑃 , , 𝑆 , ,1/𝐶 , 𝑆 , . 𝑆 , , 𝑆 , , Equation 48 𝑃 , , 𝑆 , ,1/𝐶 , 𝑆 , . 𝑆 , , 𝑆 , , Equation 49 𝑃 , , 1 𝑃 , , 𝑃 , , 𝑃 , , with Equation 50 𝑆 , , exp 4.493 𝑓 , , , 𝑓 , , 𝑓 , , Equation 51 𝑆 , , exp 2.128 𝑓 , , , 𝑓 , , 𝑓 , , Equation 52 𝑆 , , exp 0.126 𝑓 , , , 𝑓 , , 𝑓 , , Equation 53 𝑓 , , , exp 0.460 𝑃 𝑃 /2 Equation 54 𝑓 , , exp 0.993 𝑃 Equation 55 𝑓 , , exp 4.313 𝑃 , Equation 56 𝑓 , , exp 0.718 𝑃 , Equation 57 𝑓 , , exp 0.101 𝑃 , where Pfs,at,j = proportion of crashes with severity level j (j = K: fatal, A: incapacitating injury, B: non- incapacitating injury, C: possible injury) for all crash types at on a freeway segment; Csdf,fs = calibration factor to adjust SDF for local conditions for freeway segments; Phv = proportion of AADT during hours where volume exceeds 1,000 veh/h/ln; Pib = proportion of site length with a barrier present in the median (i.e., inside); Pt,ptsu = proportion of time during the average day that PTSU operates; and Pob = proportion of site length with a barrier present on the outside (roadside).

69 This SDF is applicable to Phv, Pib, and Pob values in the range of 0.0 to 1.0. Guidance for computing the variables Pib and Pob is provided in Section 2.9. Additional discussion of the variable Phv is provided in the text associated with Equation 21. The SDF is applicable to values of Pt,ptsu that range from 0.0 to 0.45. The sign of the constant in Equation 53 to Equation 57 indicates the direction of the change in the proportion of crashes associated with a change in the corresponding variable. For example, the negative coefficient associated with barrier presence indicates that the proportion of crashes with K, A, and B severity decreases with an increase in the proportion of barrier present in the segment. 2.7.4. Crash Type Distribution for Freeway Segments with PTSU The crash type distributions for freeway segments are presented in this section. They are used in the predictive model to estimate the average crash frequency for typical crash types in each of two crash severity categories: fatal-and-injury and property-damage-only. The two crash frequency estimates that are used to compute the crash type distribution are identified in the following table.  Fatal-and-injury crashes Np,fs,at,fi (from Equation 14); and  Property-damage-only crashes Np,fs,at,pdo (from Equation 15). The estimates needed to compute the crash type distribution are obtained from the aforementioned equations as predicted values; however, their expected value equivalents should be used if the EB method is applied. The general form of the crash type distribution prediction equation for freeway segments is shown in the following equation. Equation 58 𝑁 , , , 𝑁 , , , 𝑃 , , where Np,fs,j,z = predicted average crash frequency of a freeway segment; for crash type j and severity z (z = fi: fatal and injury, pdo: property damage) (crashes/year); Np,fs,at,z = predicted average crash frequency of a freeway segment; for all crash types at and severity z (z = fi: fatal and injury, pdo: property damage) (crashes/year); and Pfs,,j,z = proportion of crashes with crash type j and severity z (z = fi: fatal and injury, pdo: property damage) on a freeway segment. Each application of Equation 58 requires one crash type distribution value (i.e., proportion) for each crash type j. These values are shown in Table 18. The first column of the table indicates whether PTSU operation occurs on the subject segment. The distribution values associated with “No” are applicable to segments that have no PTSU operation during any hour of the day. These segments could be within the project limits but upstream or downstream of the sites with PTSU operation (and their associated transition zones). These segments could also represent the existing condition of an urban freeway for which PTSU operation is being considered for implementation.

70 Table 18. Default distribution of crashes by crash type for freeway segments. PTSU Operation Crash Type Category Crash Type (j) Proportion of Crashes by Severity Fatal and Injury Property Damage Only No a Multiple- vehicle Head-on 0.002 0.002 Right-angle 0.033 0.027 Rear-end 0.598 0.538 Sideswipe 0.122 0.190 Other multiple-vehicle crashes 0.022 0.023 Single- vehicle Crash with animal 0.005 0.022 Crash with fixed object 0.154 0.156 Crash with other object 0.006 0.017 Crash with parked vehicle 0.010 0.006 Other single-vehicle crashes 0.048 0.019 Total 1.000 1.000 Yes b Multiple- vehicle Head-on 0.001 0.001 Right-angle 0.061 0.053 Rear-end 0.712 0.699 Sideswipe 0.080 0.139 Other multiple-vehicle crashes 0.014 0.010 Single- vehicle Crash with animal 0.001 0.004 Crash with fixed object 0.098 0.075 Crash with other object 0.007 0.007 Crash with parked vehicle 0.003 0.003 Other single-vehicle crashes 0.023 0.009 Total 1.000 1.000 a – Proportions based on data from Georgia, Hawaii, Minnesota, Ohio, and Virginia (2011 to 2018). b – Proportions based on data from Georgia, Hawaii, Minnesota, and Virginia (2011 to 2018). 2.8. Predictive Model for Freeway Speed-Change Lanes with PTSU The predictive models for speed-change lane sites are described in this section. Each model typically consists of a safety performance function (SPF), one or more SPF adjustment factors (AFs), a calibration factor, a severity distribution, and a crash type distribution. All variables in this section that describe SPF or AF input values are defined in Section 2.5.2. The SPFs are used to estimate the predicted average crash frequency of a site with base conditions. The SPFs, like all regression models, estimate the value of the dependent variable as a function of a set of independent variables. The independent variables for the speed-change lane SPFs include the site’s AADT volume and length. The speed-change lane SPFs are summarized in Table 19.

71 Table 19. SPFs for speed-change lanes. Site Type (w) Crash Type (y) Crash Severity (z) SPF Variable SPF Equation Ramp entrance (en) All types (at) Fatal and injury (fi) Nspf,en,at,fi Equation 59 Property damage only (pdo) Nspf,en,at,pdo Equation 59 Ramp exit (ex) All types (at) Fatal and injury (fi) Nspf,ex,at,fi Equation 61 Property damage only (pdo) Nspf,ex,at,pdo Equation 61 Each SPF has an associated overdispersion parameter k. The overdispersion parameter provides an indication of the statistical reliability of the SPF. The closer the overdispersion parameter is to zero, the more statistically reliable the SPF. This parameter is used in the EB method that is discussed in the appendix to HSM Part C (3). The AFs applicable to the SPFs presented in Table 19 are summarized in Table 20. Table 20. SPF adjustment factors for speed-change lanes. AF Variable AF Description AF Equation AF1,w,at,z Horizontal curve Equation 63 AF2,w,at,z Lane width Equation 64 AF3,w,at,z Inside shoulder width Equation 65 AF4,w,at,z Median width Equation 66 AF5,w,at,z Median barrier Equation 68 AF6,w,at,fi Inside shoulder rumble strip Equation 69 AF13,w,at,z PTSU operation Equation 70 AF14,en,at,z Ramp entrance length Equation 76 AF15,ex,at,z Ramp exit length Equation 77 Note: Subscripts to the AF variables use the following notation:  Site type w (w = fs: freeway segment, en: ramp entrance speed-change lane, ex: ramp exit speed-change lane)  Crash type y (y = at: all crash types)  Severity z (z = fi: fatal and injury, pdo: property damage only, as: all severities) Many of the AFs in Table 20 are developed for specific site types and crash severities. This approach was undertaken to make the predictive model sensitive to the geometric design and traffic control features of specific sites, in terms of their influence on specific crash severities. The subscripts for each AF variable indicate the sites and severities to which each AF is applicable. The subscript definitions are provided in the table footnote. In some cases, an AF is applicable to several severity levels. In these cases, the subscript retains the generic letter z. The discussion of these AFs in Section 2.7.2 identifies the specific severity levels to which they apply. For some of the AFs, supplemental calculations must be performed before the AF value can be computed. For example, to apply the median width AF, the proportion of the site length having inside barrier and the length-weighted average barrier offset (as measured from the edge of the inside shoulder) must be computed. Procedures for supplemental calculations are described in Section 2.9. 2.8.1. Safety Performance Functions for Speed-Change Lanes with PTSU The SPFs for speed-change lanes sites are presented in this section. Specifically, SPFs are provided for speed-change lane sites with 2 to 7 through lanes. A speed-change lane can be represented as one site or it can be subdivided into two or more sites if needed to comply with the guidelines provided in Section 2.6.2. The range of freeway AADT volume for which these SPFs are applicable is shown in Table

72 6. The SPFs are applicable to ramp AADT volume up to 30,700 veh/day. Application of the SPFs to sites with AADT volume substantially outside these ranges may not provide reliable results. Ramp Entrance Speed-Change Lanes The base conditions for the SPFs for ramp entrance speed-change lanes sites are presented in the following list of variables (these variables are described in Section 2.5.2):  Horizontal curve presence: not present  Through lane width: 12 feet  Inside shoulder width (paved): 6 feet  Median width: 60 feet  Length of median barrier: 0.0 miles (i.e., not present)  Length of rumble strip on inside shoulder: 0.0 miles (i.e., not present)  PTSU operation: no PTSU operation during any hour of the day  PTSU lane width: 0 feet  Ramp entrance speed-change lane length: 0.142 miles The SPFs for ramp entrance speed-change lanes sites are represented using the following equation: Equation 59 𝑁 , , , 𝐿 , exp 𝑎 𝑏 ln 𝑐 𝐴𝐴𝐷𝑇 𝑑 𝑐 𝐴𝐴𝐷𝑇 where Nspf,en,at,z = predicted average crash frequency of a ramp entrance speed-change lane site with base conditions, for all crash types at and severity z (z = fi: fatal and injury, pdo: property damage only) (crashes/year); AADTen = AADT volume of entrance ramp (veh/day); AADTf = one-directional AADT volume of freeway in speed-change lane site (veh/day); Ls,en = length of ramp entrance speed-change lane site (≤ length of ramp entrance speed-change lane, as measured from gore point to taper point) (mi); a, b, d = regression coefficients; and c = AADT scale coefficient. The length of the ramp entrance speed-change lane Len is shown in Figure 5. The length of the subject speed-change lane site being evaluated Ls,en can equal length Len. However, Ls,en may be less than length Len if needed to comply with the segmentation guidelines described in Section 2.6.2. The regression coefficients and the coefficient for computing the overdispersion parameter are provided in Table 21. The SPFs are illustrated in Figure 17. Table 21. SPF coefficients for ramp entrance speed-change lanes. Crash Severity (z) SPF Coefficient Dispersion Coefficient Ken,at,z (mi-1) a b c d Fatal and injury (fi) −4.250 1.406 0.001 −0.0499 10.10 Property damage only (pdo) −3.043 1.295 0.001 −0.0202 9.57

73 a. Fatal-and-injury crash frequency. b. Property-damage-only crash frequency. Figure 17. Graphical form of the SPFs for ramp entrance speed-change lanes. The value of the overdispersion parameter associated with the SPFs for ramp entrance speed-change lane sites is determined as a function of site length. This value is computed using Equation 60. Equation 60 𝑘 , , 1.0𝐾 , , 𝐿 , where ken,at,z = overdispersion parameter for ramp entrance speed-change lane sites and crash severity z; Ken,at,z = dispersion coefficient for ramp entrance speed-change lanes and crash severity z (mi–1); and Ls,en = length of ramp entrance speed-change lane site (≤ length of ramp entrance speed-change lane, as measured from gore point to taper point) (mi). Ramp Exit Speed-Change Lanes The base conditions for the SPFs for ramp exit speed-change lanes sites are presented in the following list of variables (these variables are described in Section 2.5.2):  Horizontal curve presence: not present  Through lane width: 12 feet  Inside shoulder width (paved): 6 feet  Median width: 60 feet  Length of median barrier: 0.0 miles (i.e., not present)  Length of rumble strip on inside shoulder: 0.0 miles (i.e., not present)  PTSU operation: no PTSU operation during any hour of the day  PTSU lane width: 0 feet  Ramp exit speed-change lane length: 0.071 miles The SPFs for ramp exit speed-change lanes sites are represented using the following equation: Equation 61 𝑁 , , , 𝐿 , exp 𝑎 𝑏 ln 𝑐 𝐴𝐴𝐷𝑇 𝑑 𝑛 2 . where Nspf,ex,at,z = predicted average crash frequency of a ramp exit speed-change lane site with base conditions, for all crash types at and severity z (z = fi: fatal and injury, pdo: property damage only) (crashes/year);

74 AADTf = one-directional AADT volume of freeway in speed-change lane site (veh/day); Ls,ex = length of ramp exit speed-change lane site (≤ length of ramp exit speed-change lane, as measured from gore point to taper point) (mi); n = number of through lanes within site; a, b, d = regression coefficients; and c = AADT scale coefficient. The length of the ramp exit speed-change lane Lex is shown in Figure 5. The length of the subject speed-change lane site being evaluated Ls,ex can equal length Lex. However, Ls,ex may be less than length Lex if needed to comply with the segmentation guidelines described in Section 2.6.2. The regression coefficients and the coefficient for computing the overdispersion parameter are provided in Table 22. The SPFs are illustrated in Figure 18. Table 22. SPF coefficients for ramp exit speed-change lanes. Crash Severity (z) SPF Coefficient Dispersion Coefficient Kex,at,z (mi-1) a b c d Fatal and injury (fi) −5.374 1.406 0.001 0.930 10.10 Property damage only (pdo) −3.413 1.295 0.001 0.598 9.57 a. Fatal-and-injury crash frequency. b. Property-damage-only crash frequency. Figure 18. Graphical form of the SPFs for ramp exit speed-change lanes. The value of the overdispersion parameter associated with the SPFs for ramp exit speed-change lane sites is determined as a function of site length. This value is computed using Equation 62. Equation 62 𝑘 , , 1.0𝐾 , , 𝐿 , where kex,at,z = overdispersion parameter for ramp exit speed-change lane sites and crash severity z; Kex,at,z = dispersion coefficient for ramp exit speed-change lanes and crash severity z (mi–1); and Ls,ex = length of ramp exit speed-change lane site (≤ length of ramp exit speed-change lane, as measured from gore point to taper point) (mi).

75 2.8.2. SPF Adjustment Factors for Speed-Change Lanes with PTSU The AFs for geometric design and traffic control features of speed-change lane sites are presented in this section. Several AFs described in this section include a variable defining the proportion of the site’s length along which a particular feature (e.g., rumble strip, barrier) is present. Guidance is offered herein for computing each proportion. The concept underlying this guidance is that the computed proportion should equal the total length of the feature divided by the length of the site. AF1,w,at,z—Horizontal Curve Four AFs are used to describe the relationship between horizontal curve radius and predicted crash frequency. The SPFs to which they apply are identified in the following list:  SPF for fatal-and-injury crashes, ramp entrance (en, at, fi)  SPF for property-damage-only crashes, ramp entrance (en, at, pdo)  SPF for fatal-and-injury crashes, ramp exit (ex, at, fi)  SPF for property-damage-only crashes, ramp exit (ex, at, pdo) The base condition is an uncurved (i.e., tangent) alignment. The AFs for horizontal curvature are described using the following equation: Equation 63 𝐴𝐹 , , , 1.0 exp 𝑎 5,730𝑅 where AF1,w,at,z = adjustment factor for horizontal curvature at a speed-change lane site; for site type w (w = en: ramp entrance speed-change lane; ex: ramp exit speed-change lane), all crash types, and severity z; R = radius of curve (ft). The values of coefficient a for Equation 63 are provided in Table 23. The AF is applicable to curves with a radius of 1,400 ft or larger. Table 23. Coefficients for horizontal curve AF—speed-change lanes. Crash Severity (z) AF Variable AF Coefficient (a) Fatal and injury (fi) AF1,w,at,fi −4.89 Property damage only (pdo) AF1,w,at,pdo −5.47 AF2,w,at,z—Lane Width Four AFs are used to describe the relationship between average lane width and predicted crash frequency. The SPFs to which they apply are identified in the following list:  SPF for fatal-and-injury crashes, ramp entrance (en, at, fi)  SPF for property-damage-only crashes, ramp entrance (en, at, pdo)  SPF for fatal-and-injury crashes, ramp exit (ex, at, fi)  SPF for property-damage-only crashes, ramp exit (ex, at, pdo) The base condition is a 12-ft lane width. The AFs are described using the following equation: Equation 64 𝐴𝐹 , , , exp 𝑎 min 𝑊 , 13 12 where

76 AF2,w,at,z = adjustment factor for lane width at a speed-change lane site; for site type w (w = en: entrance ramp speed-change lane; ex: exit ramp speed-change lane), all crash types, and severity z; and Wl = through lane width (ft); The values of coefficient a for Equation 64 are provided in Table 24. The AF is discontinuous, breaking at a lane width of 13 ft. The AF value does not change for lane width in excess of 13 ft. The AF is applicable to lane widths in the range of 10.5 to 14.4 ft. Table 24. Coefficients for lane width AF—speed-change lanes. Crash Severity (z) AF Variable AF Coefficient (a) Fatal and injury (fi) AF2,w,at,fi −0.0411 Property damage only (pdo) AF2,w,at,pdo −0.0273 AF3,w,at,z—Inside Shoulder Width Four AFs are used to describe the relationship between average inside shoulder width and predicted crash frequency. The SPFs to which they apply are identified in the following list:  SPF for fatal-and-injury crashes, ramp entrance (en, at, fi)  SPF for property-damage-only crashes, ramp entrance (en, at, pdo)  SPF for fatal-and-injury crashes, ramp exit (ex, at, fi)  SPF for property-damage-only crashes, ramp exit (ex, at, pdo) The base condition is a 6-ft inside shoulder width. The AFs are described using the following equation: Equation 65 𝐴𝐹 , , , exp 𝑎𝑛 min 𝑊 , , 12 6 where AF3,w,at,z = adjustment factor for inside shoulder width at a speed-change lane site; for site type w (w = en: ramp entrance speed-change lane; ex: ramp exit speed-change lane), all crash types, and severity z; n = number of through lanes within site; and Wis,s = paved inside shoulder width for the subject travel direction (does not include the portion of the shoulder used as a PTSU lane) (ft). The values of coefficient a for Equation 65 are provided in Table 25. The AF is discontinuous such that its value does not change for shoulder widths in excess of 12 ft. The AF is applicable to inside shoulder widths in the range of 0.7 to 11.0 ft. The number of through lanes range from 2 to 7. Table 25. Coefficients for inside shoulder width AF—speed-change lanes. Crash Severity (z) AF Variable AF Coefficient (a) Fatal and injury (fi) AF3,w,at,fi −0.0411 Property damage only (pdo) AF3,w,at,pdo −0.0273 AF4,w,at,z—Median Width Four AFs are used to describe the relationship between average median width and predicted crash frequency. The SPFs to which they apply are identified in the following list:

77  SPF for fatal-and-injury crashes, ramp entrance (en, at, fi)  SPF for property-damage-only crashes, ramp entrance (en, at, pdo)  SPF for fatal-and-injury crashes, ramp exit (ex, at, fi)  SPF for property-damage-only crashes, ramp exit (ex, at, pdo) The base condition is a 60-ft median width, a 6-ft inside shoulder width, no PTSU lane, and no barrier present in the median. The AFs are described using the following equation: Equation 66 𝐴𝐹 , , , 1.0 𝑃 exp 𝑎𝑛 𝑊 48 𝑃 exp 𝑎𝑛 min 𝑊 , 2 𝑊 48 with Equation 67 𝑊 𝑊 𝑊 , 𝑊 , 𝑊 , 𝐼 , , 𝑊 , 𝐼 , , where AF4,w,at,z = adjustment factor for median width at a speed-change lane site; for site type w (w = en: ramp entrance speed-change lane; ex: ramp exit speed-change lane), all crash types, and severity z; Iptsu,s,in = indicator variable for PTSU lane location in the subject travel direction (= 1.0 if inside shoulder is allocated to part-time vehicular traffic use at any time of the day; otherwise 0.0) (ft); Iptsu,o,in = indicator variable for PTSU lane location in the opposing travel direction (= 1.0 if inside shoulder is allocated to part-time vehicular traffic use at any time of the day; otherwise 0.0) (ft); n = number of through lanes within site; Pib = proportion of site length with a barrier present in the median (i.e., inside); Wicb = distance from edge of inside shoulder to barrier face (ft); Wis,s = paved inside shoulder width for the subject travel direction (does not include the portion of the shoulder used as a PTSU lane) (ft); Wis,o = paved inside shoulder width for the opposing travel direction (does not include the portion of the shoulder used as a PTSU lane) (ft); Wm = median width (measured from near edges of traveled way in both directions) (ft); Wptsu,s = width of shoulder allocated to part-time vehicular traffic use in the subject travel direction (i.e., as an additional travel lane) (if PTSU is not provided at any time, this width equals 0.0) (ft); Wptsu,o = width of shoulder allocated to part-time vehicular traffic use in the opposing travel direction (i.e., as an additional travel lane) (if PTSU is not provided at any time, this width equals 0.0) (ft); and Wum = non-shoulder part of median width (measured from near edges of shoulder in both directions) (ft). The values of coefficient a for Equation 66 are provided in Table 26. This AF is applicable to a site with no median barrier and to a site that has median barrier present along some portion of its length. However, it does not describe the relationship between barrier presence and predicted crash frequency. This latter relationship is described using the median barrier AF. Guidance for computing the variables Pib and Wicb is provided in Section 2.9. Table 26. Coefficients for median width AF—speed-change lanes. Crash Severity (z) AF Variable AF Coefficient (a) Fatal and injury (fi) AF4,w,at,fi −0.00601 Property damage only (pdo) AF4,w,at,pdo −0.00407 The AF is applicable to median widths of 5 ft or more. The number of through lanes range from 2 to 7. The variable Pib ranges from 0.0 to 1.0. The inside shoulder width ranges from 0.7 to 11.0 ft. The variable

78 Wicb ranges from 0.75 to 20 ft. The width of the PTSU lane is 16.8 ft or less. If the median width exceeds 90 ft, then 90 ft should be used for Wm in Equation 29. AF5,w,at,z—Median Barrier Four AFs are used to describe the relationship between median barrier presence and predicted crash frequency. The SPFs to which they apply are identified in the following list:  SPF for fatal-and-injury crashes, ramp entrance (en, at, fi)  SPF for property-damage-only crashes, ramp entrance (en, at, pdo)  SPF for fatal-and-injury crashes, ramp exit (ex, at, fi)  SPF for property-damage-only crashes, ramp exit (ex, at, pdo) The base condition is “no barrier present in the median” (i.e., Pib = 0.0). The AFs are described using the following equation: Equation 68 𝐴𝐹 , , , 1.0 𝑃 1.0 𝑃 exp 𝑎 𝑛/𝑊 where AF5,w,at,z = adjustment factor for median barrier at a speed-change lane site; for site type w (w = en: ramp entrance speed-change lane; ex: ramp exit speed-change lane), all crash types, and severity z; n = number of through lanes within site; Pib = proportion of site length with a barrier present in the median (i.e., inside); and Wicb = distance from edge of inside shoulder to barrier face (ft). The values of coefficient a for Equation 68 are provided in Table 27. Guidance for computing the variables Pib and Wicb is provided in Section 2.9. Table 27. Coefficients for median barrier AF—speed-change lanes. Crash Severity (z) AF Variable AF Coefficient (a) Fatal and injury (fi) AF5,w,at,fi 0.0166 Property damage only (pdo) AF5,w,at,pdo 0.0162 This AF is applicable to a “number of through lanes” ranging from 2 to 7. The variable Wicb ranges from 0.75 to 20 ft. The variable Pib ranges from 0.0 to 1.0. AF6,w,at,fi—Inside Shoulder Rumble Strip Two AFs are used to describe the relationship between inside shoulder rumble strip presence and predicted crash frequency. The SPFs to which they apply are identified in the following list:  SPF for fatal-and-injury crashes, ramp entrance (en, at, fi)  SPF for fatal-and-injury crashes, ramp exit (ex, at, fi) The base condition is “no inside shoulder rumble strips present” (i.e., Pir = 0.0). The AF is described using the following equation: Equation 69 𝐴𝐹 , , , 1.0 𝑃 1.0 𝑃 exp 0.516/𝑛 where

79 AF6,w,at,fi = adjustment factor for rumble strips on the inside shoulder of a speed-change lane site; for site type w (w = en: ramp entrance speed-change lane; ex: ramp exit speed-change lane), all crash types, and fatal-and-injury fi crashes; n = number of through lanes within site; and Pir = proportion of site length with a rumble strips present on the inside shoulder. The proportion Pir represents the proportion of the site length with rumble strips present on the inside shoulders. It is computed by summing the length of roadway with rumble strips on the inside shoulder (do not include rumble strips within the PTSU lane, if present) and dividing by the site length. This AF is applicable to values of Pir that range from 0.0 to 1.0. The number of through lanes range from 2 to 7. AF13,w,at,z—PTSU Operation Two AFs are used to describe the relationship between PTSU operation and predicted crash frequency. The SPFs to which they apply are identified in the following list:  SPF for fatal-and-injury crashes, ramp entrance (en, at, fi)  SPF for property-damage-only crashes, ramp entrance (en, at, pdo)  SPF for fatal-and-injury crashes, ramp exit (ex, at, fi)  SPF for property-damage-only crashes, ramp exit (ex, at, pdo) The base condition is “no PTSU operation during any hour of the day” (i.e., Pt,ptsu = 0.0) and no PTSU lane or transition present. The AFs are described using the following equation: Equation 70 𝐴𝐹 , , , 1.0 𝑃 , exp 𝑓 , 𝑃 , exp 𝑓 , 𝑓 , , 𝑓 , with Equation 71 𝑓 , 𝑎/𝑛 min 𝑊 , , 12 𝐼 Equation 72 𝑓 , 𝑎 min 𝑊 , , 13 12 𝐼 Equation 73 𝑓 , 𝑏 𝐼 Equation 74 𝑓 , , 𝑑 1 𝐼 𝑃 , Equation 75 𝑃 , 𝐿 , /𝐿 , where AF13,w,at,z = adjustment factor for PTSU operation in a speed-change lane site; for site type w (w = en: ramp entrance speed-change lane; ex: ramp exit speed-change lane), all crash types, and severity z; IptsuLane = indicator variable for PTSU lane presence (= 1.0 if PTSU lane is present [Wptsu,s > 0], 0.0 otherwise); Ls,w = length of site (w = en: ramp entrance speed-change lane; ex: ramp exit speed-change lane) (mi); Ltransition,site = total length of PTSU transition zones within site (i.e., between site begin and end mileposts) (mi); n = number of through lanes within site; Pt,ptsu = proportion of time during the average day that PTSU operates; Ptransition,w = proportion of site length with PTSU transition zone present upstream, downstream, or both; for site type w; and Wptsu,s = width of shoulder allocated to part-time vehicular traffic use in the subject travel direction (i.e., as an additional travel lane) (if PTSU is not provided at any time, this width equals 0.0) (ft); The values of the coefficients a, b, and d for Equation 71 to Equation 74 are provided in Table 28. The variable Ptransition,w represents the proportion of the site length that is adjacent to a PTSU transition zone. Guidance for determining the length Ltransition,site is provided in Section 2.5.2 (see Figure 10).

80 Table 28. Coefficients for PTSU operation AF—speed-change lanes. Crash Severity (z) AF Variable AF Coefficients a b d Fatal and injury (fi) AF13,fs,at,fi −0.0411 1.318 1.305 Property damage only (pdo) AF13,fs,at,pdo −0.0273 1.567 1.515 The proportion Pt,ptsu represents the number of hours during which the shoulder is available for part- time use each day of year divided 24 hours per day. It has a nonzero value if (a) the site has a full-width PTSU lane or the tapered portion of a PTSU lane, (b) the site does not have a PTSU lane but a portion of the site is within 0.152 miles of a PTSU lane (i.e., just upstream or downstream), or (c) the PTSU lane effectively continues through the site even though it may not be marked as an exclusive PTSU lane (because ramp traffic is permitted to cross this area to enter or exit the freeway through lanes). Cases “a” and “c” are referred herein to as a PTSU lane and case “b” is referred to as a PTSU transition zone. The text associated with Equation 22 describes how to compute the proportion Pt,ptsu. This AF is applicable to values of Pt,ptsu that range from 0.0 to 0.45. The number of through lanes range from 2 to 7. The width of the PTSU lane is 16.8 ft or less. This AF is applicable to sites with existing (or proposed) PTSU operation during some portion of the typical day. AF14,en,at,z—Ramp Entrance Length Two AFs are used to describe the relationship between ramp entrance length and predicted crash frequency. The SPFs to which they apply are identified in the following list:  SPF for fatal-and-injury crashes, ramp entrance (en, at, fi)  SPF for property-damage-only crashes, ramp entrance (en, at, pdo) The base condition is a ramp entrance speed-change lane length of 0.142 mi. The AFs are described using the following equation: Equation 76 𝐴𝐹 , , , exp 𝑎 1𝐿 1 0.142 where AF14,en,at,z = adjustment factor for ramp entrance speed-change lane length; for severity z; Len = length of ramp entrance speed-change lane (as measured from gore point to taper point) (mi). The values of coefficient a for Equation 76 are provided in Table 29. This AF is applicable to a ramp entrance speed-change lanes ranging from 0.06 to 0.32 miles. Table 29. Coefficients for ramp entrance length AF—speed-change lanes. Crash Severity (z) AF Variable AF Coefficient (a) Fatal and injury (fi) AF14,en,at,fi 0.0690 Property damage only (pdo) AF14,en,at,pdo 0.0991 AF15,ex,at,z—Ramp Exit Length Two AFs are used to describe the relationship between ramp exit length and predicted crash frequency. The SPFs to which they apply are identified in the following list:

81  SPF for fatal-and-injury crashes, ramp exit (ex, at, fi)  SPF for property-damage-only crashes, ramp exit (ex, at, pdo) The base condition is a ramp exit speed-change lane length of 0.071 mi. The AFs are described using the following equation: Equation 77 𝐴𝐹 , , , exp 𝑎 1𝐿 1 0.071 where AF15,ex,at,z = adjustment factor for ramp exit speed-change lane length; for severity z; Lex = length of ramp exit speed-change lane (as measured from gore point to taper point) (mi). The values of coefficient a for Equation 77 are provided in Table 30. This AF is applicable to a ramp exit speed-change lanes ranging from 0.02 to 0.27 miles. Table 30. Coefficients for ramp exit length AF—speed-change lanes. Crash Severity (z) AF Variable AF Coefficient (a) Fatal and injury (fi) AF15,ex,at,fi 0.0323 Property damage only (pdo) AF15,ex,at,pdo 0.0433 2.8.3. Severity Distribution for Speed-Change Lanes with PTSU The severity distribution for speed-change lane sites is presented in this section. The severity distribution is used in the predictive model to estimate the average crash frequency for the following severity levels: fatal K, incapacitating injury A, non-incapacitating injury B, and possible injury C. The severity distribution proportions are computed using a severity distribution function (SDF). The SDF was developed as a logistic regression model using observed crash data. The SDF, like all regression models, estimates the distribution value as a function of a set of independent variables. The independent variables include various geometric features and traffic control features. There is one SDF associated with each severity level in the predictive model. The SDF for level j predicts the proportion of crashes with severity level j, based on various geometric design and traffic control features at the subject site. The SDF also contains a calibration factor that is used to calibrate the SDF to local conditions. The distribution value for severity level j is multiplied by the fatal-and-injury crash frequency to obtain the average crash frequency for the specified severity level. This crash frequency estimate is obtained from Equation 17 as a predicted value. However, its expected value equivalent should be used if the EB method is applied. The general form for the severity distribution prediction equation for speed-change lane sites is shown in the following equation. Equation 78 𝑁 , , , 𝑁 , , , 𝑃 , , where Np,w,at,j = predicted average crash frequency of a speed-change lane site; for site type w (w = en: ramp entrance speed-change lane; ex: ramp exit speed-change lane), all crash types, and severity level j (j = K: fatal, A: incapacitating injury, B: non-incapacitating injury, C: possible injury) (crashes/year); Np,w,at,fi = predicted average crash frequency of a speed-change lane site; for site type w (w = en: ramp entrance speed-change lane; ex: ramp exit speed-change lane), all crash types at, and fatal-and-injury crashes fi (crashes/year); and

82 Pw,at,j = proportion of crashes with severity level j (j = K: fatal, A: incapacitating injury, B: non- incapacitating injury, C: possible injury) for all crash types at on site type w (w = en: ramp entrance speed-change lane; ex: ramp exit speed-change lane). The SDFs for speed-change lane sites are described by the following equations. Equation 79 𝑃 , , 𝑆 , ,1/𝐶 , 𝑆 , . 𝑆 , , 𝑆 , , Equation 80 𝑃 , , 𝑆 , ,1/𝐶 , 𝑆 , . 𝑆 , , 𝑆 , , Equation 81 𝑃 , , 𝑆 , ,1/𝐶 , 𝑆 , . 𝑆 , , 𝑆 , , Equation 82 𝑃 , , 1 𝑃 , , 𝑃 , , 𝑃 , , with Equation 83 𝑆 , , exp 𝑘 𝑓 , , , 𝑓 , , 𝑓 , , Equation 84 𝑆 , , exp 𝑎 𝑓 , , , 𝑓 , , 𝑓 , , Equation 85 𝑆 , , exp 𝑏 𝑓 , , , 𝑓 , , 𝑓 , , Equation 86 𝑓 , , , exp 0.460 𝑃 Equation 87 𝑓 , , exp 0.993 𝑃 Equation 88 𝑓 , , exp 4.313 𝑃 , Equation 89 𝑓 , , exp 0.718 𝑃 , Equation 90 𝑓 , , exp 0.101 𝑃 , where Pw,at,j = proportion of crashes with severity level j (j = K: fatal, A: incapacitating injury, B: non- incapacitating injury, C: possible injury) for all crash types at on site type w (w = en: ramp entrance speed-change lane; ex: ramp exit speed-change lane) ; Csdf,w = calibration factor to adjust SDF for local conditions for site type w (w = en: ramp entrance speed- change lane; ex: ramp exit speed-change lane); Phv = proportion of AADT during hours where volume exceeds 1,000 veh/h/ln; Pib = proportion of site length with a barrier present in the median (i.e., inside); Pt,ptsu = proportion of time during the average day that PTSU operates; and Pob = proportion of site length with a barrier present on the outside (roadside). The values of the coefficients in Equation 83 to Equation 85 are provided in Table 31. This SDF is applicable to Phv, Pib, and Pob values in the range of 0.0 to 1.0. Guidance for computing the variables Pib and Pob is provided in Section 2.9. Additional discussion of the variable Phv is provided in the text associated with Equation 21. The SDF is applicable to values of Pt,ptsu that range from 0.0 to 0.45.

83 Table 31. Coefficients for severity distribution function—speed-change lanes. Site Type (w) SDF Coefficients k a b Ramp entrance speed-change lane (en) −4.493 −2.575 −0.270 Ramp exit speed-change lane (ex) −4.493 −2.180 −0.204 The sign of the constant in Equation 86 to Equation 90 indicates the direction of the change in the proportion of crashes associated with a change in the corresponding variable. For example, the negative coefficient associated with barrier presence indicates that the proportion of crashes with K, A, and B severity decreases with an increase in the proportion of barrier present in the site. 2.8.4. Crash Type Distribution for Speed-Change Lanes with PTSU The crash type distributions for speed-change lane sites are presented in this section. They are used in the predictive model to estimate the average crash frequency for typical crash types in each of two crash severity categories: fatal-and-injury and property-damage-only. The two crash frequency estimates that are used to compute the crash type distribution are identified in the following table.  Fatal-and-injury crashes Np,w,at,fi (from Equation 17); and  Property-damage-only crashes Np,w,at,pdo (from Equation 18). The estimates needed to compute the crash type distribution are obtained from the aforementioned equations as predicted values; however, their expected value equivalents should be used if the EB method is applied. The general form of the crash type distribution prediction equation for speed-change lane sites is shown in the following equation. Equation 91 𝑁 , , , 𝑁 , , , 𝑃 , , where Np,w,j,z = predicted average crash frequency of a speed-change lane site; for site type w (w = en: ramp entrance speed-change lane; ex: ramp exit speed-change lane), crash type j, and severity z (z = fi: fatal and injury, pdo: property damage) (crashes/year); Np,w,at,z = predicted average crash frequency of a speed-change lane site; for site type w (w = en: ramp entrance speed-change lane; ex: ramp exit speed-change lane), all crash types at, and severity z (z = fi: fatal and injury, pdo: property damage) (crashes/year); and Pw,,j,z = proportion of crashes with crash type j and severity z (z = fi: fatal and injury, pdo: property damage) on site type w (w = en: ramp entrance speed-change lane; ex: ramp exit speed-change lane). Each application of Equation 91 requires one crash type distribution value (i.e., proportion) for each crash type j. These values are shown in Table 32. The second column of the table indicates whether PTSU operation occurs on the subject site. The distribution values associated with “No” are applicable to sites that have no PTSU operation during any hour of the day. These sites could be within the project limits but upstream or downstream of the sites with PTSU operation (and their associated transition zones). These sites could also represent the existing condition of an urban freeway for which PTSU operation is being considered for implementation.

84 Table 32. Default distribution of crashes by crash type for speed-change lanes. Site Type (w) PTSU Operation Crash Type Category Crash Type (j) Proportion of Crashes by Severity Fatal and Injury Property Damage Only Ramp entrance (en) No a Multiple- vehicle Head-on 0.019 0.003 Right-angle 0.037 0.054 Rear-end 0.606 0.468 Sideswipe 0.094 0.207 Other multiple-vehicle crashes 0.019 0.024 Single-vehicle Crash with animal 0.000 0.020 Crash with fixed object 0.122 0.187 Crash with other object 0.014 0.015 Crash with parked vehicle 0.019 0.002 Other single-vehicle crashes 0.070 0.020 Total 1.000 1.000 Yes b Multiple- vehicle Head-on 0.000 0.000 Right-angle 0.100 0.077 Rear-end 0.616 0.708 Sideswipe 0.097 0.106 Other multiple-vehicle crashes 0.023 0.004 Single-vehicle Crash with animal 0.000 0.007 Crash with fixed object 0.117 0.089 Crash with other object 0.008 0.005 Crash with parked vehicle 0.000 0.004 Other single-vehicle crashes 0.039 0.000 Total 1.000 1.000 Ramp exit (ex) No a Multiple- vehicle Head-on 0.006 0.000 Right-angle 0.020 0.030 Rear-end 0.525 0.499 Sideswipe 0.189 0.214 Other multiple-vehicle crashes 0.012 0.028 Single-vehicle Crash with animal 0.000 0.027 Crash with fixed object 0.175 0.150 Crash with other object 0.014 0.016 Crash with parked vehicle 0.012 0.007 Other single-vehicle crashes 0.047 0.029 Total 1.000 1.000 Yes b Multiple- vehicle Head-on 0.000 0.003 Right-angle 0.028 0.060 Rear-end 0.808 0.718 Sideswipe 0.100 0.118 Other multiple-vehicle crashes 0.014 0.010 Single-vehicle Crash with animal 0.000 0.010 Crash with fixed object 0.050 0.076 Crash with other object 0.000 0.000 Crash with parked vehicle 0.000 0.000 Other single-vehicle crashes 0.000 0.005 Total 1.000 1.000 a – Proportions based on data from Georgia, Hawaii, Minnesota, Ohio, and Virginia (2011 to 2018). b – Proportions based on data from Georgia, Hawaii, Minnesota, and Virginia (2011 to 2018).

85 2.9. Supplemental Calculations to Apply SPF Adjustment Factors Some of the AFs in Section 2.7.2 and Section 2.8.2 require the completion of supplemental calculations before they can be applied. Specifically, these AFs include variables that describe the barrier located in the median or on the roadside (i.e., barrier offset and barrier length). Barrier offset represents a lateral distance measured from the near edge of the shoulder to the face of the barrier (i.e., it does not include the width of the shoulder). Barrier length represents the length of lane paralleled by a barrier. For example, if the outside barrier extends for the length of the subject freeway segment, then the outside barrier length equals the segment length. Two key variables that are needed for the evaluation of barrier presence are the inside barrier offset distance Wicb and the outside barrier offset distance Wocb. As indicated in Equation 30, Equation 36, and Equation 68, this distance is included as a divisor in the exponential term. This relationship implies that the correlation between barrier offset distance and crash frequency is an inverse one (i.e., crash frequency decreases with increasing distance to the barrier). When multiple sections of barrier exist along the segment, a length-weighted average of the reciprocal of the individual distances is needed to properly reflect this inverse relationship. The length used to weight the average is the barrier length. Additional key variables include the proportion of site length with a barrier present in the median Pib and the proportion of site length with a barrier present on the outside Pob. Equations for calculating these proportions and the aforementioned distances are described in the following paragraphs. The length Ls,w used in the following equations is equal to the freeway segment Ls,fs or speed-change lane length Ls,ex or Ls,en, as appropriate for the AF to which the calculated value will be applied. 2.9.1. Sites with Continuous Median Barrier For segments or speed-change lanes with a continuous median barrier, the following equations should be used to compute Wicb and Pib: Equation 92 𝑊 𝐿 , ∑ 𝐿 ,𝑊 , , 𝑊 , 𝐼 , , 𝑊 , 𝐿 , ∑ 𝐿 ,𝑊 , , 𝑊 , 𝐼 , , 𝑊 , Equation 93 𝑃 1.0 where Wicb = distance from edge of inside shoulder to barrier face (ft); Iptsu,s,in = indicator variable for PTSU lane location in the subject travel direction (= 1.0 if inside shoulder is allocated to part-time vehicular traffic use at any time of the day; otherwise 0.0) (ft); Lib,i = length of lane paralleled by median (i.e., inside) barrier i (mi); Ls,w = length of site; for site type w (w = fs: freeway segment, en: ramp entrance speed-change lane, ex: ramp exit speed-change lane) (mi); Pib = proportion of site length with a barrier present in the median (i.e., inside); Wis,s = paved inside shoulder width for the subject travel direction (does not include the portion of the shoulder used as a PTSU lane) (ft); Woff,in,i = horizontal clearance from the edge of the nearest through lane to the face of inside barrier i (ft); Woff,in,c = horizontal clearance from the edge of the nearest through lane to the face of continuous median barrier i (ft); and Wptsu,s = width of shoulder allocated to part-time vehicular traffic use in the subject travel direction (i.e., as an additional travel lane) (if PTSU is not provided at any time, this width equals 0.0) (ft). The width Woff,in,i is measured from the edge of the nearest through lane. If the subject site has PTSU operation on the inside shoulder, the width Woff,in,i includes the width of the PTSU lane.

86 The summation term “∑” in parentheses in Equation 92 applies to short lengths of barrier in the median that are located between the shoulder and continuous barrier. It indicates that the ratio of barrier length Lib,i to clearance distance (= Woff,in,i –Wptsu,s –Wis,s) should be computed for each individual length of barrier that is found in the median along the site (e.g., a barrier protecting a sign support). The continuous median barrier is not considered in this summation. Any clearance distance that is less than 0.75 ft should be set to 0.75 ft. Similarly, if the distance “Woff,in,c –Wptsu,s –Wis,s” is less than 0.75, this distance should be set to 0.75 ft. 2.9.2. Sites with Depressed Median For segments or speed-change lanes with a depressed median and some short sections of barrier in the median (e.g., a barrier protecting a bridge bent), the following equations should be used to compute Wicb and Pib: Equation 94 𝑊 ∑ 𝐿 , ∑ 𝐿 ,𝑊 , , 𝑊 , 𝐼 , , 𝑊 , Equation 95 𝑃 ∑ 𝐿 ,𝐿 , where all variables are previously defined. The width Woff,in,i is measured from the edge of the nearest through lane. If the subject site has PTSU operation on the inside shoulder, the width Woff,in,i includes the width of the PTSU lane. Any clearance distance (= Woff,in,i –Wptsu,s –Wis,s) that is less than 0.75 ft should be set to 0.75 ft. When a site is being evaluated, the proportion Pib represents the proportion of the site length with barrier present in the median. It is computed by summing the length of lane paralleled by median barrier and dividing by the site length Ls. For segments or speed-change lanes with depressed medians and without a continuous barrier or short section of barrier in the median, the following equation should be used to estimate Pib: Equation 96 𝑃 0.0 When Pib equals 0.0, the calculation of Wicb is not required and its value is not needed to compute the related AFs. 2.9.3. Sites with Roadside Barrier For segments with a barrier on the outside (roadside), the following equations should be used to compute Wocb and Pob: Equation 97 𝑊 ∑ 𝐿 , ∑ 𝐿 ,𝑊 , , 𝑊 , 𝐼 , , 𝑊 Equation 98 𝑃 ∑ 𝐿 ,𝐿 , where Wocb = distance from edge of outside shoulder to barrier face (ft);

87 Iptsu,s,o = indicator variable for PTSU lane location in the subject travel direction (= 1.0 if outside shoulder is allocated to part-time vehicular traffic use at any time of the day; otherwise 0.0) (ft); Lob,i = length of lane paralleled by outside (roadside) barrier i (mi); Ls,fs = length of freeway segment (mi); Pob = proportion of site length with a barrier present on the outside (roadside); Ws = paved outside shoulder width (does not include the portion of the shoulder used as a PTSU lane) (ft); Woff,o,i = horizontal clearance from the edge of the nearest through lane to the face of outside barrier i (ft); and Wptsu,s = width of shoulder allocated to part-time vehicular traffic use in the subject travel direction (i.e., as an additional travel lane) (if PTSU is not provided at any time, this width equals 0.0) (ft). The width Woff,o,i is measured from the edge of the nearest through lane. If the subject site is in a weaving section, the width Woff,o,i includes the width of the auxiliary lane. If the site has PTSU operation on the outside shoulder, the width Woff,o,i includes the width of the PTSU lane. Any clearance distance (= Woff,o,i –Wptsu,s –Wis,s) that is less than 0.75 ft should be set to 0.75 ft. When a site is being evaluated, the proportion Pob represents the proportion of the site length with barrier present on the outside. It is computed by summing the length of lane paralleled by outside barrier and dividing by the site length Ls. For speed-change lanes and for segments without a short section of barrier on the outside (roadside), the following equation should be used to estimate Pob: Equation 99 𝑃 0.0 When Pob equals 0.0, the calculation of Wocb is not required and its value is not needed to compute the related AFs. 2.10. Calibration of the SPFs and SDFs to Local Conditions Crash frequencies, even for nominally similar freeway segments or speed-change lanes, can vary widely from one jurisdiction to another. Geographic regions differ markedly in climate, animal population, driver populations, crash-reporting threshold, and crash-reporting practices. These variations may result in some jurisdictions experiencing a different number of traffic crashes on freeways than others. Calibration factors are included in the methodology to allow transportation agencies to adjust the SPFs and SDFs to match actual local conditions. The calibration procedures for SPFs and SDFs are presented in the appendix to HSM Part C (3). Default values are provided for the crash type distributions used in the methodology. These values can also be replaced with locally derived values. The derivation of local values is addressed in HSM Part C (3). Calibration is performed separately for each predictive model equation described in this chapter. Table 33 identifies the combinations of site type and severity level represented in each predictive model equation and for which calibration factors can be derived. Similarly, Table 34 identifies the combinations represented in each severity distribution function (SDF) and for which calibration factors can be derived. Note that there are only three unique SDF calibration factors shown in this table (i.e., the same factor is used for all severity levels of a given site type).

88 Table 33. Crash frequency predictive models with a calibration factor. Site Type (w) Crash Type (y) Crash Severity (z) Calibration Factor Symbol Equation Freeway segment (fs) All types (at) Fatal and injury (fi) Cfs,at,fi Equation 14 Property damage only (pdo) Cfs,at,pdo Equation 15 Ramp entrance speed- change lane (en) All types (at) Fatal and injury (fi) Cen,at,fi Equation 17 Property damage only (pdo) Cen,at,pdo Equation 18 Ramp exit speed-change lane (ex) All types (at) Fatal and injury (fi) Cex,at,fi see note a Property damage only (pdo) Cex,at,pdo see note a a – The equations for ramp exit speed-change lanes are not shown in this document. However, these equations are the same as Equation 17 and Equation 18 except that the subscript “ex” is substituted for “en” in each variable. Table 34. Severity distribution functions with a calibration factor. Site Type (w) Crash Type (y) Crash Severity (j) Calibration Factor Symbol Equation Freeway segment (fs) All types (at) Fatal (K) Csdf,fs Equation 46 Incapacitating injury (A) Csdf,fs Equation 47 Non-incapacitating injury (B) Csdf,fs Equation 48 Ramp entrance speed- change lanes (en) All types (at) Fatal (K) Csdf,en Equation 79 Incapacitating injury (A) Csdf,en Equation 80 Non-incapacitating injury (B) Csdf,en Equation 81 Ramp exit speed-change lanes (ex) All types (at) Fatal (K) Csdf,ex Equation 79 Incapacitating injury (A) Csdf,ex Equation 80 Non-incapacitating injury (B) Csdf,ex Equation 81 The sites selected to quantify any one of the calibration factors listed in Table 33 and Table 34 should equal or exceed the minimum site sample size needed for local calibration. This minimum number is specified in the appendix to HSM Part C (3). The sites used to calibrate the predictive models must be obtained from one or both of the urban freeway types identified in the following list:  Freeways with PTSU on one shoulder.  Freeways without PTSU but at which PTSU implementation is being considered. The sites selected should be located on an urban freeway with part-time use of either the inside shoulder or outside shoulder (but not both shoulders). If the number of sites with part-time shoulder use (PTSU) does not equal or exceed the minimum site sample size, then sites located on an urban freeway at which the implementation of PTSU is considered feasible can be used for calibration. In general, the site characteristics data needed to apply the predictive model equations or the SDFs should be acquired for each site in the calibration database. However, if information on shoulder rumble strip presence or clear zone width is not available, then an assumed value can be substituted (where the substituted value is based on agency policy or typical practice). Similarly, if data are not available to compute the “proportion of AADT that occurs during hours where lane volume exceeds 1,000 veh/h/ln,” then a default value (computed with Equation 21) can be used to calibrate the models.

89 2.11. Limitations of Predictive Method This section discusses limitations of the predictive models described in this chapter. The predictive method does not account for the influence of the following conditions on freeway crash potential:  Freeways with eight or more through lanes in the subject direction of travel  Freeways in rural areas  Freeways with managed lanes (e.g., high-occupancy-vehicle [HOV], high-occupancy-toll [HOT], truck-restricted lanes, truck-only lanes, or bus-only lanes)  Ramp metering  Toll plazas  Reversible lanes  Work zone presence  Speed-change lanes that provide left-side access to the freeway The predictive method does not distinguish between barrier types (i.e., cable barrier, concrete barrier, guardrail, and bridge rail) in terms of their possible unique influence on crash severity. The crash prediction models (CPMs) presented in this document are intended for analysis of freeways with part-time shoulder use (PTSU) or freeways on which PTSU is being considered. Models in the current HSM Supplement should continue to be used for projects not involving PTSU. The HSM Supplement model is applicable to both urban and rural area types, and the models in this document were developed entirely from urban data. The HSM Supplement freeway model was developed from the same states as the current HSM ramp model; freeways and ramps are often analyzed together and Project 17-89 did not analyze ramps. 2.12. Application of Predictive Method The predictive method presented in this chapter is applied to a freeway facility by following the 18 steps presented in Section 2.5. All computations of average crash frequency are conducted with values expressed to three decimal places. This level of precision is needed only for consistency in computations. In the last stage of computations, rounding the final estimates of average crash frequency to one decimal place is appropriate. 2.12.1. Freeways with Barrier-Separated Managed Lanes The predictive method can be used to evaluate freeways with barrier-separated managed lanes. The managed lanes are considered to be part of the median (i.e., the median width is measured between the near edges of the traveled way for the general purpose lanes) and the managed lane’s entry or exit points are treated as entrance or exit ramps, respectively, on the adjacent freeway. The average lane width is based on the general purpose lanes (i.e., the managed lanes are not considered). The shoulder width is measured from the edge of the traveled way of the general-purpose lanes. The barrier between the general purpose lanes and managed lanes is treated as median barrier. The average crash frequency of the managed lanes cannot be addressed by this technique. The computed average crash frequency represents only those crashes that occur in the general purpose lanes. 2.12.2. Freeways with Toll Facilities The predictive method can be used to evaluate a freeway section that is part of toll facility provided that the section is sufficiently distant from the toll plaza that the plaza does not influence vehicle operation. The predictive method is not directly applicable to any portion of the freeway that (a) is in the

90 immediate vicinity of a toll plaza, (b) is widened to accommodate vehicle movements through the toll plaza, (c) experiences toll-related traffic queues, or (d) experiences toll-related speed changes. 2.13. Summary The predictive method presented in this chapter is applied by following the 18 steps of the predictive method presented in Section 2.5. It is used to estimate the average crash frequency for a series of contiguous sites, or a single individual site. If a freeway facility is being evaluated, it is divided into a series of sites in Step 5 of the predictive method. Predictive models are applied in Steps 9, 10, and 11 of the method. Each predictive model typically consists of a safety performance function (SPF), one or more SPF adjustment factors (AFs), a calibration factor, a severity distribution, and a crash type distribution. The SPF is selected in Step 9. It is used to estimate the predicted average crash frequency for a site with base conditions. AFs are selected in Step 10. They are combined with the estimate from the SPF to produce the predicted average crash frequency the subject site. When observed crash data are available, the EB method is applied in Step 13 or 15 of the predictive method to estimate the expected average crash frequency. The EB method can be applied at the site- specific level in Step 13 or at the project level in Step 15. The choice of level will depend on (a) the required reliability of the estimate and (b) the accuracy with which each observed crash can be associated with an individual site. As an evaluation option, the severity distribution can be selected in Step 13 and used to estimate the average crash frequency for one or more crash severity levels (i.e., fatal, incapacitating injury, non- incapacitating injury, or possible injury crash). Also as an option, the crash type distribution can be used in Step 13 to estimate the average crash frequency for one or more crash types (e.g., head-on, fixed object). The SPF should be calibrated to the specific state or geographic region in which the project is located. Calibration accounts for differences in state or regional crash frequencies, relative to the states and regions represented in the data used to define the predictive models described in this chapter. The process for determining calibration factors for the predictive models is described in the appendix to HSM Part C (3). Section 2.15 presents several sample problems that detail the application of the predictive method. 2.14. References 1. Jenior, P., J. Bonneson, L. Zhao, W. Kittelson, E. Donnell, and V. Gayah. 2021. NCHRP Web-Only Document 309: Safety Performance of Part-Time Shoulder Use on Freeways, Volume 2: Conduct of Research Report, Transportation Research Board, Washington, D.C. 2. American Association of State Highway and Transportation Officials (AASHTO). 2011. A Policy on Geometric Design of Highways and Streets. 6th Edition. Washington D.C. 3. American Association of State Highway and Transportation Officials (AASHTO). 2010. Highway Safety Manual. Washington D.C. 4. American Association of State Highway and Transportation Officials (AASHTO). 2014. Highway Safety Manual Supplement. Washington D.C. 5. American Association of Highway Transportation Officials (AASHTO). 2011. Roadside Design Guide. Washington, D.C. 2.15. Sample Problems In this section, two sample problems are presented using the predictive method described in this chapter. Sample Problem 1 illustrates how to calculate the predicted average crash frequency for a

91 freeway segment. Sample Problem 2 illustrates how to calculate the predicted average crash frequency for a ramp entrance speed-change lane. Note: In the following sample problems, the text shows results of calculations copied from a spreadsheet used to obtain these results. In some cases, there are small differences between the results shown and those that may be obtained using a calculator. These differences occur because the results shown in the text were rounded to the third decimal whereas the values from the spreadsheet were not rounded. Table 35. List of sample problems. Problem No. Description 1 Predicted average crash frequency for a one-directional three-lane urban freeway segment with PTSU operation 2 Predicted average crash frequency for a urban freeway ramp entrance speed-change lane 2.15.1. Sample Problem 1 The Site/Facility The urban freeway segment of interest has three through lanes in the subject travel direction, a PTSU lane on the outside shoulder, and a turnout on the outside. The Question What is the predicted average crash frequency of the segment for the specified study year? The Facts The study period is one year in duration (i.e., Year 2020). The conditions present during this year are provided in the following list:  3 through lanes.  0.50-mi length.  No horizontal curvature.  6.0 ft paved inside shoulder width (both travel directions).  No PTSU lane in inside shoulder (both travel directions).  40.0-ft median width.  11.0-ft average through lane width.  11.0-ft PTSU lane in outside shoulder.  1.0-ft paved outside shoulder width.  30.0-ft clear zone width.  Rumble strips on outside shoulder (except at the turnout).  Rumble strips on inside shoulder.  Continuous median barrier; 10-ft offset from edge of traveled way to barrier face.  No outside (roadside) barrier.  0.10-mi long turnout on outside (roadside) (measured from start of taper to end of taper).  PTSU operation allowed between 4:30 pm and 6:30 pm each weekday; not allowed on the weekend.  No PTSU transition zone in segment.  Upstream entrance ramp is 0.20 miles from the segment and has an AADT volume of 1500 veh/day (Xb,ent = 0.20; AADTb,ent = 1500); as shown in Figure 19.

92  Downstream exit ramp is 0.30 miles from the segment and has an AADT volume of 7600 veh/day (Xe,ext = 0.30; AADTe,ext = 7600); as shown in Figure 19.  10 percent of AADT volume occurs during high-volume hours.  60,000 veh/day (one directional AADT).  Calibration factors for the crash frequency prediction models are: FI: 0.95; PDO: 1.10. Assumptions  The crash type distribution is described by the default values presented in Table 18.  The calibration factor for the severity distribution function is 1.00. Figure 19. Ramp access data for sample problem 1. Results Using the predictive method steps as outlined below, the predicted average fatal-and-injury crash frequency for the freeway segment in this sample problem is determined to be 1.5 crashes per year, and the predicted average property-damage-only crash frequency is determined to be 6.2 crashes per year (rounded to one decimal place). The sequence of calculations undertaken to obtain these results are described in the following sections. Steps 1 Through 8 The information obtained for steps 1 through 8 are listed in the previous sections. Observed crash data are not obtained because the EB method will not be applied. Step 9—For the selected site, determine and apply the appropriate SPF. The SPF for fatal-and-injury (FI) crashes (i.e., Equation 23) is used to compute the predicted FI crash frequency for base conditions. 𝑁 , , , 𝐿 , exp 𝑎 𝑏 ln 𝑐 𝐴𝐴𝐷𝑇 0.50 exp 4.556 1.406 ln 0.001 60,000 1.661 crashes/year Similarly, the SPF for property-damage-only (PDO) crashes is used to compute the predicted PDO crash frequency for base conditions. 𝑁 , , , 4.376 crashes/year

93 Step 10—Multiply the result obtained in Step 9 by the appropriate AFs. The AF’s in the predictive model equation for freeway segments are described in this step. AF1,fs,at,z—Horizontal Curve The subject segment does not have horizontal curvature, which is the base condition for the horizontal curve AF. Hence, so the AF1,fs,at,fi and AF1,fs,at,pdo are equal to 1.000. AF2,fs,at,z—Lane Width The lane width AF is computed using Equation 26. This equation is repeated below. 𝐴𝐹 , , , exp 𝑎 min 𝑊 , 13 12 The segment has an average through lane width of 11.0 feet. From Table 9, the coefficient a equals −0.0411 for FI crashes. The AF value for FI crashes is computed as: 𝐴𝐹 , , , exp 0.0411 min 11.0,13 12 1.042 The AF for PDO crashes is computed using the same equation but with a different coefficient. This AF is computed as AF2,fs,at,pdo = 1.028. AF3,fs,at,z—Inside Shoulder Width The subject segment has 6.0-ft paved inside shoulders, which is the base condition for the inside shoulder width AF. Hence, AF3,fs,at,fi and AF3,fs,at,pdo are equal to 1.000. AF4,fs,at,z—Median Width The median width AF is computed using Equation 28. This equation is repeated below. 𝐴𝐹 , , , 1.0 𝑃 exp 𝑎𝑛 𝑊 48 𝑃 exp 𝑎𝑛 min 𝑊 , 2 𝑊 48 The variable Wum needed for this equation is computed using Equation 29 as follows: 𝑊 𝑊 𝑊 , 𝑊 , 𝑊 , 𝐼 , , 𝑊 , 𝐼 , , 40.0 6.0 6.0 0 0 0 0 28.0 feet The subject segment has continuous median barrier but no short lengths of barrier in the median. As a result, Equation 92 reduces to the following: 𝑊 𝑊 , , 𝑊 , 𝐼 , , 𝑊 , 10.0 0 0 6.0 4.0 feet As indicated by Equation 93, Pib equals 1.0 for continuous median barrier. The segment has 3 through lanes. The coefficient a is obtained from Table 11. It equals −0.00601 for FI crashes. The AF value for FI crashes is computed as: 𝐴𝐹 , , , 1.0 1.0 exp 0.006013 28.0 48 1.0 exp 0.006013 min 28.0, 2 4.0 48 1.083

94 The AF for PDO crashes is computed using the same equation but with a different coefficient. This AF is computed as AF4,fs,at,pdo = 1.056. AF5,fs,at,z—Median Barrier The median barrier AF is computed using Equation 30. This equation is repeated below. 𝐴𝐹 , , , 1.0 𝑃 1.0 𝑃 exp 𝑎 𝑛/𝑊 The variables Pib and Wicb were computed for the median width AF. The segment has 3 through lanes. The coefficient a is obtained from Table 12. It equals 0.0166 for FI crashes. The AF value for FI crashes is computed as: 𝐴𝐹 , , , 1.0 1.0 1.0 1.0 exp 0.0166 34.0 1.013 The AF for PDO crashes is computed using the same equation but with a different coefficient. This AF is computed as AF5,fs,at,pdo = 1.012. AF6,fs,at,fi—Inside Shoulder Rumble Strip The inside shoulder rumble strip AF is computed using Equation 31. This equation is repeated below. 𝐴𝐹 , , , 1.0 𝑃 1.0 𝑃 exp 0.516/𝑛 The variable Pir represents the proportion of the site length with a rumble strip present on the inside shoulder. For the subject segment, a rumble strip is present on the inside shoulder for the length of the segment so Pir equals 1.0. The AF value for FI crashes is computed as follows: 𝐴𝐹 , , , 1.0 1.0 1.0 1.0 exp 0.516/3 0.842 This AF is not applicable to PDO crashes. AF7,fs,at,fi—Lane Change The lane change AF is computed using Equation 32. This equation is repeated below. 𝐴𝐹 , , , 1.0 exp 14.34 𝑋 , 1.30 ln 0.001 𝐴𝐴𝐷𝑇 ,14.34 𝐿 , 1.0 exp 14.34 𝐿 , 1.0 exp 14.34 𝑋 , 1.30 ln 0.001 𝐴𝐴𝐷𝑇 ,14.34 𝐿 , 1.0 exp 14.34 𝐿 , The length of the segment Ls,fs is 0.50 miles. The AF value for FI crashes is computed as: 𝐴𝐹 , , , 1.0 exp 14.34 0.20 1.30 ln 0.001 150014.34 0.50 1.0 exp 14.34 0.50 1.0 exp 14.34 0.30 1.30 ln 0.001 760014.34 0.50 1.0 exp 14.34 0.50 1.005 This AF is not applicable to PDO crashes. AF8,fs,at,z—Outside Shoulder Width The outside shoulder width AF is computed using Equation 33. This equation is repeated below.

95 𝐴𝐹 , , , exp 𝑎𝑛 min 𝑊 , 12 10 The segment has 3 through lanes. The coefficient a is obtained from Table 13. It equals −0.0411 for FI crashes. The AF value for FI crashes is computed as: 𝐴𝐹 , , , exp 0.04113 min 1.0,12 10 1.131 The AF for PDO crashes is computed using the same equation but with a different coefficient. This AF is computed as AF8,fs,at,pdo = 1.085. AF9,fs,at,fi—Outside Shoulder Rumble Strip The outside shoulder rumble strip AF is computed using Equation 34. This equation is repeated below. 𝐴𝐹 , , , 1.0 𝑃 1.0 𝑃 exp 0.516/𝑛 The variable Por represents the proportion of the site length with a rumble strip present on the outside shoulder. For the subject segment, a rumble strip is present on the outside shoulder for the length of the segment (Ls,fs = 0.50 miles) with the exception that it does not extend through the length of the 0.10-mi turnout. As a result, Por equals 0.80 (= [0.50 −0.10]/0.50). The AF value for FI crashes is computed as follows: 𝐴𝐹 , , , 1.0 0.80 1.0 0.80 exp 0.516/3 0.874 This AF is not applicable to PDO crashes. AF10,fs,at,z—Outside Clearance The outside clearance AF is computed using Equation 35. This equation is repeated below. 𝐴𝐹 , , , 1.0 𝑃 exp 𝑎𝑛 𝑊 𝑊 , 𝐼 , , 𝑊 20 𝑃 exp 𝑎𝑛 𝑊 20 The segment has a 30.0-ft clear zone, no outside barrier, a 1.0-ft paved outside shoulder, an 11.0-ft PTSU lane in the outside shoulder, and 3 through lanes. Hence, Pob equals 0.0 and the calculation of Wocb does not apply. The coefficient a is obtained from Table 14. It equals −0.00601 for FI crashes. The AF value for FI crashes is computed as: 𝐴𝐹 , , , 1.0 0.0 exp 0.006013 30.0 11.0 1 1.0 20 0.0 exp 0.006013 𝑊 20 1.004 The AF for PDO crashes is computed using the same equation but with a different coefficient. This AF is computed as AF10,fs,at,pdo = 1.003. AF11,fs,at,z—Outside Barrier The segment has no barrier on the outside (roadside), which is the base condition for the outside barrier AF. Hence, AF11,fs,at,fi and AF11,fs,at,pdo are equal to 1.000. AF12,fs,at,z—Turnout Presence The turnout presence AF is computed using Equation 37. This equation is repeated below. 𝐴𝐹 , , , 1.0 𝑃 1.0 𝑃 exp 𝑎/𝑛

96 The 0.10-mi turnout is located wholly within the length of the 0.50-mi segment. Based on the guidance in Figure 11, “length of turnout within the segment” Lturnout,fs is equal to the total turnout length. The variable Pturnout needed for this equation is computed using Equation 38 as follows: 𝑃 𝐿 ,𝐿 , 0.10 0.50 0.20 The segment has 3 through lanes. The coefficient a is obtained from Table 16. It equals −0.787 for FI crashes. The AF value for FI crashes is computed as: 𝐴𝐹 , , , 1.0 0.20 1.0 0.20 exp 0.7873 0.954 The AF for PDO crashes is computed using the same equation but with a different coefficient. This AF is computed as AF12,fs,at,pdo = 0.939. AF13,fs,at,z—PTSU Operation The PTSU operation AF is computed using Equation 39. This equation is repeated below. 𝐴𝐹 , , , 1.0 𝑃 , exp 𝑓 , 𝑃 , exp 𝑓 , 𝑓 , , 𝑓 , The variable Pt,ptsu needed for this equation is computed using Equation 22. This equation requires the proportion of each hour of the day that is opened Pj. For the subject facility, the PTSU operation is closed on the weekends so Pj = 0.0 for all hours of the weekend days. On the weekdays, the PTSU operation opens at 4:30 pm and ends at 6:30 pm so the hours from midnight to 4:00 pm have P1 = P16 = 0.0; P17 (i.e., 4:00 to 5:00 pm) = 0.5; P18 (i.e., 5:00 to 6:00 pm) = 1.0; P19 (i.e., 6:00 to 7:00 pm) = 0.5; and the hours P20 = P24 = 0.0. Using this information, the variable Pt,ptsu is computed as follows: 𝑃 , 5𝑑𝑎𝑦𝑤𝑘 1 ℎ𝑟 ⋯ 0.5 1.0 0.5 ⋯ 2 𝑑𝑎𝑦 𝑤𝑘 1 ℎ𝑟 0.0 7𝑑𝑎𝑦𝑤𝑘 24 ℎ𝑟 0.0595 The width of the PTSU lane is 11.0 feet. The segment has 3 through lanes. The coefficient a is obtained from Table 17. It equals −0.0411 for FI crashes. The factors fw,closed and fw,open are computed as follows: 𝑓 , 𝑎𝑛 min 𝑊 , , 12 𝐼 0.0411 3 min 11.0, 12 1.0 0.1507 𝑓 , 𝑎 min 𝑊 , , 13 12 𝐼 0.0411 min 11.0, 13 12 1.0 0.0411 The coefficient b is obtained from Table 17. It equals 1.318 for FI crashes. The factor fptsu,open is computed as follows: 𝑓 , 𝑏 𝐼 1.318 1.0

97 1.318 The coefficient d is obtained from Table 17. It equals 1.305 for FI crashes. However, the proportion of the segment length with a transition present Ptransition,fs equals 0.0. As a result, the factor fnear,open,fs is equal to 0.0. Using the values computed in the preceding paragraphs, the PTSU operation AF for FI crashes can be computed as: 𝐴𝐹 , , , 1.0 0.0595 exp 0.1507 0.0595 exp 1.318 0.0 0.0411 1.041 The AF for PDO crashes is computed using the same equation but with a different coefficient. This AF is computed as AF13,fs,at,pdo = 1.144. Computed Crash Frequency The AFs are applied to the results obtained in Step 9. For FI crashes, they are applied as follows: 𝑁 , , ,∗ 𝑁 , , , 𝐴𝐹 , , , … 𝐴𝐹 , , , 1.661 1.000 1.042 1.000 1.083 1.013 0.842 1.005 1.131 0.874 1.004 1.000 0.954 1.041 1.582 crashes/year For PDO crashes, they are applied as follows (note that AFs 6, 7, and 9 do not apply to PDO crashes): 𝑁 , , ,∗ 𝑁 , , , 𝐴𝐹 , , , … 𝐴𝐹 , , , 4.376 1.000 1.028 1.000 1.056 1.012 … … 1.085 … 1.003 1.000 0.939 1.144 5.618 crashes/year Step 11—Multiply the result obtained in Step 10 by the appropriate calibration factor. The calibration factor for the FI model is 0.95. It is used to compute the predicted FI crash frequency as follows: 𝑁 , , , 𝐶 , , 𝑁 , , ,∗ 0.95 1.582 1.503 crashes/year The calibration factor for the PDO model is 1.10. It is used to compute the predicted PDO crash frequency as follows: 𝑁 , , , 𝐶 , , 𝑁 , , ,∗ 1.10 5.618 6.180 crashes/year Step 12—If there is another year to be evaluated in the evaluation period for the selected site, return to Step 8. Otherwise, proceed to Step 13. The study period is one year (i.e., 2020), so steps 8 through 11 do not need to be repeated for another year. Step 13—Apply the site-specific EB method (if applicable) and apply crash distributions. This step consists of three optional sets of calculations—site-specific EB method, severity distribution, and crash type distribution.

98 Apply the site-specific EB method to a future time period, if appropriate. The site-specific EB method is not applied in this sample problem. Apply the severity distribution, if desired. The first step in applying the severity distribution functions (SDFs) is to compute the severity adjustment factor for the relationship between barrier presence and severity fbar,fs,at,KAB. This factor is computed using Equation 53. This equation is repeated below. 𝑓 , , , exp 0.460 𝑃 𝑃 /2 The proportions Pib and Pob were computed in Step 10. The value of Pib is 1.0. The value of Pob is 0.0. The factor is computed as: 𝑓 , , , exp 0.460 1.0 0.0 /2 0.795 The second step in applying the SDFs is to compute the severity adjustment factor for the relationship between “proportion of AADT during hours with high volume” and severity fphv,fs,at,KAB. This factor is computed using Equation 54. This equation is repeated below. 𝑓 , , exp 0.993 𝑃 The “proportion of AADT during hours with high volume” is given as 0.10. The factor is computed as: 𝑓 , , exp 0.993 0.10 0.905 The third step in applying the SDFs is to compute the severity adjustment factors for the relationship between PTSU operation and severity level j, fphv,fs,at,j. This factor is computed using Equation 55 to Equation 57. These equations are repeated below. 𝑓 , , exp 4.313 𝑃 , 𝑓 , , exp 0.718 𝑃 , 𝑓 , , exp 0.101 𝑃 , The proportion Pt,ptsu was computed in Step 10. The value of Pt,ptsu is 0.0595. The factors are computed as: 𝑓 , , exp 4.313 0.0595 0.774 𝑓 , , exp 0.718 0.0595 0.958 𝑓 , , exp 0.101 0.0595 1.006 The fourth step is to compute the distribution score for each severity level j. The scores are computed using Equation 50 to Equation 52. These equations are repeated below with the computed scores. 𝑆 , , exp 4.493 𝑓 , , , 𝑓 , , 𝑓 , , 0.011 0.795 0.905 0.774 0.0062

99 𝑆 , , exp 2.128 𝑓 , , , 𝑓 , , 𝑓 , , 0.119 0.795 0.905 0.958 0.0821 𝑆 , , exp 0.126 𝑓 , , , 𝑓 , , 𝑓 , , 0.882 0.795 0.905 1.006 0.6381 The fifth step is to compute the proportion of crashes with severity level j. The proportions are computed using Equation 46 to Equation 49. These equations are repeated below with the computed scores. 𝑃 , , 𝑆 , ,1 𝐶 , 𝑆 , . 𝑆 , , 𝑆 , , 0.0062 1 1.0 0.0062 0.0821 0.6381 0.0036 𝑃 , , 𝑆 , ,1 𝐶 , 𝑆 , . 𝑆 , , 𝑆 , , 0.0475 𝑃 , , 𝑆 , ,1 𝐶 , 𝑆 , . 𝑆 , , 𝑆 , , 0.3696 𝑃 , , 1 𝑃 , , 𝑃 , , 𝑃 , , 1 0.0036 0.0475 0.3696 0.5792 The sixth step is to compute the predicted average crash frequency associated with severity level j. Equation 45 is used for this purpose. It is repeated below. 𝑁 , , , 𝑁 , , , 𝑃 , , The predicted average FI crash frequency Np,fs,at,fi was computed in Step 11. It is used compute the predicted average crash frequency for the K severity level as follows: 𝑁 , , , 𝑁 , , , 𝑃 , , 1.503 0.0036 0.005 crashes/year The predicted average crash frequency for the A, B, and C severity levels is 0.071, 0.556, 0.871 crashes/year, respectively. Note that the sum of the estimates by severity level equals the total FI crash frequency (i.e., 1.503 = 0.005 + 0.071 + 0.556 + 0.871).

100 Apply the crash type distribution, if desired. The first step in applying the crash type distribution proportions is to select the desired crash type proportion from Table 18. The distributions of interest to this sample problem are the FI and PDO distributions for segments having PTSU operation. For example, the proportion of FI crashes having a rear-end manner of collision is 0.712. The proportion of PDO crashes having a rear-end manner of collision is 0.699. The second step is to compute the predicted average crash frequency associated with the crash type of interest. Equation 58 is used for this purpose. It is repeated below. 𝑁 , , , 𝑁 , , , 𝑃 , , The predicted average FI crash frequency Np,fs,at,fi was computed in Step 11. It is used compute the predicted average FI rear-end crash frequency as follows: 𝑁 , , , 𝑁 , , , 𝑃 , , 1.503 0.712 1.070 crashes/year Using the same equation, the predicted average PDO rear-end crash frequency is computed as 4.320 crashes/year (= 6.180 × 0.699). Similar calculations can be performed for other crash types of interest by using the distribution values in Table 18. Step 14—If there is another site to be evaluated, return to Step 7; otherwise, proceed to Step 15. There is only one site to be evaluated so the sample problem continues with Step 15. Step 15—Apply the project-level EB method (if applicable) and apply crash distributions. The project-level EB method does not apply to this sample problem because there is only one site. Step 16—Sum all sites and years in the study to estimate the total crash frequency. There is only one segment and year to be evaluated for this sample problem so the total predicted average crash frequency equals to the sum of the predicted average FI crash frequency and the predicted average PDO crash frequency. These two crash frequencies were computed in Step 11. The total predicted average crash frequency is computed as follows: 𝑁 , , , 𝑁 , , , 𝑁 , , , 1.503 6.180 7.683 crashes/year Step 17—Determine if there is an alternative design, treatment, or forecast AADT to be evaluated. There are no alternative conditions to be evaluated. Step 18—Evaluate and compare results. The AF values computed in Step 10 can be used to evaluate the relative influence of the associated design elements and traffic control features on crash potential. Those AFs with a value in excess of 1.000 indicate that the element or feature is associated with an increase in crash potential, relative to sites with base conditions. For example, the PTSU operation AF value of 1.041 suggests that FI crash frequency is 4.1 percent higher on this segment, relative to a segment without PTSU operation. The turnout presence

101 AF value of 0.954 suggests that FI crash frequency is 4.6 percent lower on a segment with a turnout present, relative to a segment without a turnout. The outside shoulder width AF value of 1.131 suggests that the 1-ft outside shoulder is associated with a 13.1 percent increase in FI crash frequency, relative to a segment with a 10-ft outside shoulder. The 1-ft outside shoulder resulted when most of the shoulder’s original 12-ft width was allocated to PTSU. When the three AFs are combined, their product has a value of 1.123 (= 1.041 × 0.954 × 1.131). This value suggests that the PTSU operation increases FI crash frequency by 12.3 percent on the subject segment. 2.15.2. Sample Problem 2 The Site/Facility The 0.15-mi ramp entrance speed-change lane site of interest provides access to an urban freeway that has three through lanes in the subject travel direction. The site is shorter than the length of the speed- change lane because a horizontal curve begins and requires the subject site to end and a new site to begin. A marked PTSU lane is provided on the outside shoulder upstream and downstream of the speed-change lane. The PTSU lane effectively continues through the speed-change lane even though it is not marked as an exclusive PTSU lane (because ramp traffic is permitted to cross this area to enter or exit the freeway through lanes). A plan view of the subject site is shown in Figure 20 (horizontal curvature not shown). Figure 20. Plan view of speed-change lane site evaluated for sample problem 2. The Question What is the predicted average crash frequency of the subject site for the specified study year? The Facts The study period is one year in duration (i.e., Year 2020). The conditions present during this year are provided in the following list:  3 through lanes.  0.25-mi speed-change lane length.  0.15-mil speed-change lane site length.  No horizontal curvature.  6.0 ft paved inside shoulder width (both travel directions).  No PTSU lane in inside shoulder (both travel directions).  40.0-ft median width.  12.0-ft average through lane width.  11.0-ft PTSU lane in outside shoulder.

102  No rumble strips on inside shoulder.  Continuous median barrier; 10-ft offset from edge of traveled way to barrier face.  PTSU operation allowed between 4:30 pm and 6:30 pm each weekday; not allowed on the weekend.  No PTSU transition zone in site.  10 percent of AADT volume occurs during high-volume hours.  60,000 veh/day one directional freeway AADT.  6800 veh/day entrance ramp AADT volume.  Calibration factors for the crash frequency prediction models are: FI: 1.05; PDO: 1.15. Assumptions  The crash type distribution is described by the default values presented in Table 32.  The calibration factor for the severity distribution function is 1.00. Results Using the predictive method steps as outlined below, the predicted average fatal-and-injury crash frequency for the speed-change lane site in this sample problem is determined to be 0.5 crashes per year, and the predicted average property-damage-only crash frequency is determined to be 1.3 crashes per year (rounded to one decimal place). The sequence of calculations undertaken to obtain these results are described in the following sections. Steps 1 Through 8 The information obtained for steps 1 through 8 are listed in the previous sections. Observed crash data are not obtained because the EB method will not be applied. Step 9—For the selected site, determine and apply the appropriate SPF. The SPF for fatal-and-injury (FI) crashes (i.e., Equation 59) is used to compute the predicted FI crash frequency for base conditions. 𝑁 , , , 𝐿 , exp 𝑎 𝑏 ln 𝑐 𝐴𝐴𝐷𝑇 𝑑 𝑐 𝐴𝐴𝐷𝑇 0.15 exp 4.250 1.406 ln 0.001 60,000 0.0499 0.001 6800 0.482 crashes/year Similarly, the SPF for property-damage-only (PDO) crashes is used to compute the predicted PDO crash frequency for base conditions. 𝑁 , , , 1.252 crashes/year Step 10—Multiply the result obtained in Step 9 by the appropriate AFs. The AF’s in the predictive model equation for speed-change lane sites are described in this step. AF1,en,at,z—Horizontal Curve The subject site does not have horizontal curvature, which is the base condition for the horizontal curve AF. Hence, so the AF1,en,at,fi and AF1,en,at,pdo are equal to 1.000. AF2,en,at,z—Lane Width The subject site has a 12-ft average through lane width, which is the base condition for the lane width AF. Hence, so the AF2,en,at,fi and AF2,en,at,pdo are equal to 1.000.

103 AF3,en,at,z—Inside Shoulder Width The subject site has 6.0-ft paved inside shoulders, which is the base condition for the inside shoulder width AF. Hence, AF3,en,at,fi and AF3,en,at,pdo are equal to 1.000. AF4,ens,at,z—Median Width The median width AF is computed using Equation 66. This equation is repeated below. 𝐴𝐹 , , , 1.0 𝑃 exp 𝑎𝑛 𝑊 48 𝑃 exp 𝑎𝑛 min 𝑊 , 2 𝑊 48 The variable Wum needed for this equation is computed using Equation 67 as follows: 𝑊 𝑊 𝑊 , 𝑊 , 𝑊 , 𝐼 , , 𝑊 , 𝐼 , , 40.0 6.0 6.0 0 0 0 0 28.0 feet The subject site has continuous median barrier but no short lengths of barrier in the median. As a result, Equation 92 reduces to the following: 𝑊 𝑊 , , 𝑊 , 𝐼 , , 𝑊 , 10.0 0 0 6.0 4.0 feet As indicated by Equation 93, Pib equals 1.0 for continuous median barrier. The site has 3 through lanes. The coefficient a is obtained from Table 26. It equals −0.00601 for FI crashes. The AF value for FI crashes is computed as: 𝐴𝐹 , , , 1.0 1.0 exp 0.006013 28.0 48 1.0 exp 0.006013 min 28.0, 2 4.0 48 1.083 The AF for PDO crashes is computed using the same equation but with a different coefficient. This AF is computed as AF4,en,at,pdo = 1.056. AF5,en,at,z—Median Barrier The median barrier AF is computed using Equation 68. This equation is repeated below. 𝐴𝐹 , , , 1.0 𝑃 1.0 𝑃 exp 𝑎 𝑛/𝑊 The variables Pib and Wicb were computed for the median width AF. The site has 3 through lanes. The coefficient a is obtained from Table 27. It equals 0.0166 for FI crashes. The AF value for FI crashes is computed as: 𝐴𝐹 , , , 1.0 1.0 1.0 1.0 exp 0.0166 34.0 1.013 The AF for PDO crashes is computed using the same equation but with a different coefficient. This AF is computed as AF5,en,at,pdo = 1.012. AF6,en,at,fi—Inside Shoulder Rumble Strip The subject site does not have rumble strips on the inside shoulder, which is the base condition for the lane width AF. Hence, so the AF6,en,at,fi is equal to 1.000.

104 AF13,en,at,z—PTSU Operation The PTSU operation AF is computed using Equation 70. This equation is repeated below. 𝐴𝐹 , , , 1.0 𝑃 , exp 𝑓 , 𝑃 , exp 𝑓 , 𝑓 , , 𝑓 , The variable Pt,ptsu needed for this equation is computed using Equation 22. This equation requires the proportion of each hour of the day that is opened Pj. For the subject facility, the PTSU operation is closed on the weekends so Pj = 0.0 for all hours of the weekend days. On the weekdays, the PTSU operation opens at 4:30 pm and ends at 6:30 pm so the hours from midnight to 4:00 pm have P1 = P16 = 0.0; P17 (i.e., 4:00 to 5:00 pm) = 0.5; P18 (i.e., 5:00 to 6:00 pm) = 1.0; P19 (i.e., 6:00 to 7:00 pm) = 0.5; and the hours P20 = P24 = 0.0. Using this information, the variable Pt,ptsu is computed as follows: 𝑃 , 5𝑑𝑎𝑦𝑤𝑘 1 ℎ𝑟 ⋯ 0.5 1.0 0.5 ⋯ 2 𝑑𝑎𝑦 𝑤𝑘 1 ℎ𝑟 0.0 7𝑑𝑎𝑦𝑤𝑘 24 ℎ𝑟 0.0595 The width of the PTSU lane is 11.0 feet. The site has 3 through lanes. The coefficient a is obtained from Table 28. It equals −0.0411 for FI crashes. The factors fw,closed and fw,open are computed as follows: 𝑓 , 𝑎𝑛 min 𝑊 , , 12 𝐼 0.0411 3 min 11.0, 12 1.0 0.1507 𝑓 , 𝑎 min 𝑊 , , 13 12 𝐼 0.0411 min 11.0, 13 12 1.0 0.0411 The coefficient b is obtained from Table 28. It equals 1.318 for FI crashes. The factor fptsu,open is computed as follows: 𝑓 , 𝑏 𝐼 1.318 1.0 1.318 The coefficient d is obtained from Table 28. It equals 1.305 for FI crashes. However, the proportion of the site length with a transition present Ptransition,em equals 0.0. As a result, the factor fnear,open,en is equal to 0.0. Using the values computed in the preceding paragraphs, the PTSU operation AF for FI crashes can be computed as: 𝐴𝐹 , , , 1.0 0.0595 exp 0.1507 0.0595 exp 1.318 0.0 0.0411 1.041 The AF for PDO crashes is computed using the same equation but with a different coefficient. This AF is computed as AF13,en,at,pdo = 1.144. AF14,en,at,z—Ramp Entrance Length The ramp entrance length AF is computed using Equation 76. This equation is repeated below. 𝐴𝐹 , , , exp 𝑎 1𝐿 1 0.142

105 The site is located within a 0.25-mi speed-change lane. The coefficient a is obtained from Table 29. It equals 0.0690 for FI crashes. The AF value for FI crashes is computed as: 𝐴𝐹 , , , exp 0.0690 10.25 1 0.142 0.811 The AF for PDO crashes is computed using the same equation but with a different coefficient. This AF is computed as AF14,en,at,pdo = 0.740. Computed Crash Frequency The AFs are applied to the results obtained in Step 9. For FI crashes, they are applied as follows (note that AFs 7 to 12 do not apply: 𝑁 , , ,∗ 𝑁 , , , 𝐴𝐹 , , , … 𝐴𝐹 , , , 0.482 1.000 1.000 1.000 1.083 1.013 1.000 … … … … … … 1.041 0.811 0.446 crashes/year For PDO crashes, they are applied as follows (note that AFs 6 to 12 do not apply to PDO crashes): 𝑁 , , ,∗ 𝑁 , , , 𝐴𝐹 , , , … 𝐴𝐹 , , , 1.252 1.000 1.000 1.000 1.056 1.012 … … … … … … … 1.144 0.740 1.132 crashes/year Step 11—Multiply the result obtained in Step 10 by the appropriate calibration factor. The calibration factor for the FI model is 1.05. It is used to compute the predicted FI crash frequency as follows: 𝑁 , , , 𝐶 , , 𝑁 , , ,∗ 1.05 0.446 0.468 crashes/year The calibration factor for the PDO model is 1.15. It is used to compute the predicted PDO crash frequency as follows: 𝑁 , , , 𝐶 , , 𝑁 , , ,∗ 1.15 1.132 1.302 crashes/year Step 12—If there is another year to be evaluated in the evaluation period for the selected site, return to Step 8. Otherwise, proceed to Step 13. The study period is one year (i.e., 2020), so steps 8 through 11 do not need to be repeated for another year. Step 13—Apply the site-specific EB method (if applicable) and apply crash distributions. This step consists of three optional sets of calculations—site-specific EB method, severity distribution, and crash type distribution. Apply the site-specific EB method to a future time period, if appropriate. The site-specific EB method is not applied in this sample problem.

106 Apply the severity distribution, if desired. The severity distribution is not needed for this evaluation. Apply the crash type distribution, if desired. The crash type distribution is not needed for this evaluation. Step 14—If there is another site to be evaluated, return to Step 7; otherwise, proceed to Step 15. There is only one site to be evaluated so the sample problem continues with Step 15. Step 15—Apply the project-level EB method (if applicable) and apply crash distributions. The project-level EB method does not apply to this sample problem because there is only one site. Step 16—Sum all sites and years in the study to estimate the total crash frequency. There is only one site and year to be evaluated for this sample problem so the total predicted average crash frequency equals to the sum of the predicted average FI crash frequency and the predicted average PDO crash frequency. These two crash frequencies were computed in Step 11. The total predicted average crash frequency is computed as follows: 𝑁 , , , 𝑁 , , , 𝑁 , , , 0.468 1.302 1.770 crashes/year Step 17—Determine if there is an alternative design, treatment, or forecast AADT to be evaluated. There are no alternative conditions to be evaluated. Step 18—Evaluate and compare results. The AF values computed in Step 10 can be used to evaluate the relative influence of the associated design elements and traffic control features on crash potential. Those AFs with a value in excess of 1.000 indicate that the element or feature is associated with an increase in crash potential, relative to sites with base conditions. For example, the median width AF value of 1.083 suggests that FI crash frequency is 8.3 percent higher on this site (with a 40-ft median), relative to a site with a 60-ft median. The ramp entrance length AF has a value of 0.811. This value suggests that the site’s 0.25-mi speed-change lane length is associated with about 19 percent fewer crashes, relative to a site with a 0.142-mi speed-change lane length.