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

Chapter: CHAPTER 3: FRAMEWORK FOR SAFETY PREDICTION

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Suggested Citation:"CHAPTER 3: FRAMEWORK FOR SAFETY PREDICTION." National Academies of Sciences, Engineering, and Medicine. 2021. Safety Prediction Methodology and Analysis Tool for Freeways and Interchanges. Washington, DC: The National Academies Press. doi: 10.17226/26367.
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Suggested Citation:"CHAPTER 3: FRAMEWORK FOR SAFETY PREDICTION." National Academies of Sciences, Engineering, and Medicine. 2021. Safety Prediction Methodology and Analysis Tool for Freeways and Interchanges. Washington, DC: The National Academies Press. doi: 10.17226/26367.
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Suggested Citation:"CHAPTER 3: FRAMEWORK FOR SAFETY PREDICTION." National Academies of Sciences, Engineering, and Medicine. 2021. Safety Prediction Methodology and Analysis Tool for Freeways and Interchanges. Washington, DC: The National Academies Press. doi: 10.17226/26367.
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Suggested Citation:"CHAPTER 3: FRAMEWORK FOR SAFETY PREDICTION." National Academies of Sciences, Engineering, and Medicine. 2021. Safety Prediction Methodology and Analysis Tool for Freeways and Interchanges. Washington, DC: The National Academies Press. doi: 10.17226/26367.
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Suggested Citation:"CHAPTER 3: FRAMEWORK FOR SAFETY PREDICTION." National Academies of Sciences, Engineering, and Medicine. 2021. Safety Prediction Methodology and Analysis Tool for Freeways and Interchanges. Washington, DC: The National Academies Press. doi: 10.17226/26367.
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Suggested Citation:"CHAPTER 3: FRAMEWORK FOR SAFETY PREDICTION." National Academies of Sciences, Engineering, and Medicine. 2021. Safety Prediction Methodology and Analysis Tool for Freeways and Interchanges. Washington, DC: The National Academies Press. doi: 10.17226/26367.
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Suggested Citation:"CHAPTER 3: FRAMEWORK FOR SAFETY PREDICTION." National Academies of Sciences, Engineering, and Medicine. 2021. Safety Prediction Methodology and Analysis Tool for Freeways and Interchanges. Washington, DC: The National Academies Press. doi: 10.17226/26367.
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Suggested Citation:"CHAPTER 3: FRAMEWORK FOR SAFETY PREDICTION." National Academies of Sciences, Engineering, and Medicine. 2021. Safety Prediction Methodology and Analysis Tool for Freeways and Interchanges. Washington, DC: The National Academies Press. doi: 10.17226/26367.
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Suggested Citation:"CHAPTER 3: FRAMEWORK FOR SAFETY PREDICTION." National Academies of Sciences, Engineering, and Medicine. 2021. Safety Prediction Methodology and Analysis Tool for Freeways and Interchanges. Washington, DC: The National Academies Press. doi: 10.17226/26367.
×
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Suggested Citation:"CHAPTER 3: FRAMEWORK FOR SAFETY PREDICTION." National Academies of Sciences, Engineering, and Medicine. 2021. Safety Prediction Methodology and Analysis Tool for Freeways and Interchanges. Washington, DC: The National Academies Press. doi: 10.17226/26367.
×
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Page 67
Suggested Citation:"CHAPTER 3: FRAMEWORK FOR SAFETY PREDICTION." National Academies of Sciences, Engineering, and Medicine. 2021. Safety Prediction Methodology and Analysis Tool for Freeways and Interchanges. Washington, DC: The National Academies Press. doi: 10.17226/26367.
×
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Suggested Citation:"CHAPTER 3: FRAMEWORK FOR SAFETY PREDICTION." National Academies of Sciences, Engineering, and Medicine. 2021. Safety Prediction Methodology and Analysis Tool for Freeways and Interchanges. Washington, DC: The National Academies Press. doi: 10.17226/26367.
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57 CHAPTER 3: FRAMEWORK FOR SAFETY PREDICTION This chapter describes a framework for freeway and interchange safety prediction. The framework includes the SPFs and CMFs. These SPFs and CMFs are needed to support safety- based decision making for the planning and designing of freeways and interchanges. The chapter consists of two parts. The first part provides an overview of the safety prediction methodology in the HSM (Highway, 2010). The second part describes the prioritized lists of recommended SPFs and CMFs. OVERVIEW OF HSM METHODOLOGY The methodology for evaluating freeway or interchange safety is envisioned to mirror the chapters described in Part C of the HSM (Highway, 2010). Each chapter is considered to describe a methodology for safety evaluation that is focused on describing a safety predictive method but also describes the scope, limitations, and applications of the method. A safety predictive method represents a process for evaluating the safety of a road facility for a specified time period. A facility is defined to consist of two or more contiguous sites and site is defined as either a homogeneous road segment or an intersection. HSM Predictive Method The HSM predictive method consists of 18 procedural steps. These steps are shown in Figure 36. The method is generic enough to be applied to the evaluation of rural highways and urban streets. With slight modification, it may also be tailored to the evaluation of freeway segments and interchanges. The key attributes of the HSM method are summarized in the following paragraphs. Basic Safety Estimate. In one procedural step, a predictive model is used to estimate the expected crash frequency of a site. A predictive model combines the SPF with CMFs and a calibration factor. The expected crash frequency can be estimated as a total for all crash types and severities, or separately by crash type and severity, if desired. Enhanced Safety Estimate. An optional procedural step can be used to incorporate reported crash data into the evaluation of an existing site. This procedure uses the empirical Bayes (EB) approach to combine the expected crash frequency from the predictive model with the reported crash data to obtain a more-reliable estimate of the site’s expected crash frequency.

58 Figure 36. HSM predictive method.

59 Scalable Evaluation. The predictive method is scalable such that it can be used to evaluate an individual site or a facility. If the analyst desires to evaluate a facility, then the road is divided into individual sites and each site is separately evaluated using a single application of the method. The results for each site are then added to obtain an estimate of the expected crash frequency for the facility. Multiple-Year Evaluation. If it is desired to evaluate a site (or facility) for multiple years (e.g., for a facility’s design life), then the analysis period is divided into one-year increments and each year is separately evaluated using a single application of the method. The results for each year are then added to obtain an estimate of the expected crash frequency for the analysis period. Freeway and Interchange Methodology The methodology for freeway and interchange evaluation will consist of two separate predictive methods. One method will describe the evaluation of freeway sections and one method will describe the evaluation of interchanges. Collectively, the two methods can be used to evaluate a freeway facility. Each method will include predictive models that can be used to estimate the expected crash frequency for a segment or ramp terminal. An overview of each method is provided in the following subsections. Freeway Predictive Method The freeway predictive method will include predictive models for evaluating the following freeway components. ● freeway segment, and ● freeway speed-change lane. These predictive models will be developed to support freeway safety evaluation, as may be influenced by road geometry, roadside features, traffic volume, and lane-change-related traffic maneuvers. The models will be calibrated using site-based observations that include the AADT volume and crash counts for one or more years. The segment-based observations will represent both travel directions combined. Interchange Predictive Method The interchange predictive method will include predictive models for the following interchange components on a site-by-site basis. ● interchange ramp, and ● crossroad ramp terminal. These predictive models will be developed to support interchange safety evaluation, as may be influenced by ramp configuration, ramp terminal configuration, and ramp-crossroad interaction. Ramp configuration influences are likely to be sensitive to ramp cross section and

60 alignment. Ramp terminal configuration influences are likely to be sensitive to intersection control mode, number of legs, and turn movement accommodation. The influence of ramp- crossroad interaction is likely to be reflected in the travel path orientation through the interchange and the spacing between ramps (as measured along the crossroad). All predictive models will be calibrated using AADT volume and crash counts for one or more years. The ramp model will be calibrated using ramp segments or entire ramps, the choice depending on their representation in the state DOT database. The ramp model will be described in the predictive method in a manner that will allow it to be used to evaluate specific ramp segments if desired. It is envisioned that some CMFs in the HSM will be applicable to crossroad ramp terminals. Specifically, some CMFs applicable to conventional intersections should also be applicable to ramp terminals. Role of SPFs and CMFs The SPFs are intended to quantify the relationship between exposure and crash frequency, where exposure is represented by traffic count, segment length, and possibly other events that combine to form a chance set up for a crash (i.e., the necessary conditions). The crash frequency estimate from the SPF is intended to represent typical design and operating conditions. The CMFs are intended to quantify the relative association between one or more design or operational elements and crash frequency. They are typically described as functions. However, the simplest CMFs can be represented using a constant. CMFs are used in a multiplicative manner with the SPFs to adjust the estimate from the SPF to account for elements whose dimensions, conditions, or presence at the subject site are not consistent with those sites represented by the SPF. PRIORITIZED LIST OF SPFS AND CMFS This part of the chapter summarizes the candidate SPFs and CMFs for the freeway and interchange methodology. It also describes of their estimated relative priority, as related to the objectives and scope of this research. The first section describes the procedure used to prioritize the SPFs and CMFs. The second section provides the prioritized list for each freeway facility component. Prioritization Process Several SPFs and CMFs are needed for the freeway and interchange methodology. These SPFs and CMFs were identified using the ranked list of safety information needs obtained from the practitioner interviews (as summarized in Appendix A). A separate set of SPFs and CMFs are planned for each of the following freeway and interchange components: ● freeway segment, ● interchange ramp, ● crossroad ramp terminal, and

61 ● freeway speed-change lane. The SPF and CMF identification process was intentionally broad to ensure that a wide range of safety influences were fairly considered. The prioritization process was undertaken because of the large number of candidate SPFs and CMFs that were identified and the realization that sufficient project resources would not be available to adequately address each potential influence through statistical analysis. The prioritization process focused on consideration of four criteria. One criterion used represents the “importance” of the SPF or CMF. This determination was based on input provided during a survey of practitioners. It reflects consideration of (1) the frequency that a topic is considered by practitioners in the design or operation of a facility, and (2) the perceived influence that a topic has on safety. A ranking of “high,” “medium,” or “low” was used to indicate the importance of each SPF or CMF. A second criterion used is the level of effort required to obtain the raw data needed to define the key (or only) input variables for a given SPF or CMF. The effort was considered to have a low resource cost if the data were directly available from a state DOT database. The effort was considered to have a medium cost if the data had to be obtained by making a measurement from on an aerial photograph. It was considered to have a high cost if the data required multiple measurements from an aerial photograph, consultation of a video log, or submission of a special data request to a DOT. A third criterion addresses the case where an SPF or CMF is associated with multiple input variables. The data collection effort was considered to be significant when multiple variables were needed for an SPF or CMF and each variable required multiple measurements. For example, the horizontal curvature CMF requires curve length and radius input variables, each of which are based on multiple measurements from an aerial photograph. Thus, this CMF will require more resources to calibrate. A fourth criterion used is the relative need of the SPFs or CMFs for each of the freeway or interchange components. The goal of this criterion was to equalize the priorities among the components such that the relative need for each SPF or CMF was comparable among components. The relative need was determined to be higher for SPFs associated with the more commonly found facility types. In contrast, SPFs and CMFs for less common facility types (e.g., HOV facilities) were judged to have lower relative need. Of particular note in this regard was the finding that there are several variations of HOV facility that are each sufficiently unique as to require the development of a separate set of predictive models, yet no one HOV facility type exists with sufficient frequency as to be used on more than 2 percent of the freeway mileage in the U.S. A priority index was computed for each SPF and CMF. It represents the weighed sum of the four criteria. This process yields larger index values for higher priority SPFs and CMFs. The weight for each criterion and the value for each criterion level are identified in the following list.

62 ● Importance: weight = 3 ○ high = 3, medium = 2, and low = 1. ● Level of effort: weight = 2 ○ high = 1, medium = 2, and low = 3. ● Number of attributes: weight = -1 ○ value equal to the number of attributes associated with a variable. ● Relative need: weight = 1 ○ value varies (see discussion below). The value for the “relative need” criterion is 1 for many SPFs and CMFs; however, higher or lower values are used in some instances, based partly on guidance from the project panel. The specific values used as a basis for the prioritization are documented in the tables described in the next section. Based on the aforementioned weights and values, the priority index was calculated for each SPF and CMF. For example, the index for a basic freeway segment is based on its high importance (= 3), a low level of effort (= 3), a relative-need value of 1, and a number-of- attributes value of 0.8 (this value is less than 1.0 because this SPF’s variables are shared with other SPFs). The index is computed as 15.2 (= 3 x 3 + 3 x 2 + 0.8 x [-1] + 1 x 1). As a last step, the collective set of indices was used to determine the priority group for each SPF or CMF. Those SPFs and CMFs with an index value that ranks in the top one-third of all values are assigned “high” priority. Those in the bottom one-third are assigned a “low” priority. Those in the middle one-third are assigned a “medium” priority. Prioritized Lists This section provides the prioritized list of SPFs and CMFs for each freeway or interchange component. Separate subsections are provided for each component. Freeway Segment This subsection describes the prioritized list of SPFs and CMFs for the evaluation of basic freeway segment safety. The freeway segment predictive model is envisioned to be capable of evaluating the following scenarios: ● interchange or ramp spacing, ● changes in lane continuity (e.g., outside lane drop and inside lane add), and ● changes in cross section to add capacity. Table 7 identifies the prioritized list of SPFs and CMFs for freeway segments. The table has two sections. The first section identifies the different types of freeway segment analysis units that were identified. Each unique combination of segment type and basic descriptor is considered to represent a separate SPF.

63 TABLE 7. Prioritized list of SPFs and CMFs for freeway segments Category Topic 1 Importa nce Level of Effort Number Attrib. Relative Need Priority Different Analysis Units Segment types Basic segment High Low 0.8 1 High Basic segment with HOV lane present Medium Medium 2.8 0 Medium Basic segment with ramp meter operation Low Medium 1.8 1 Low Basic segment with truck lane restriction Low High 1.8 4 Medium Basic segment with shoulder use by time of day Low High 1.8 1 Low Basic descriptors Area type (urban, rural) High Low 1 1 High Number of lanes High Low 1 1 High Design or Operation Elements Operation elements Effect of lane changing downstream of entrance ramp (after speed-change lane) High High 3.3 3 High Effect of lane changing upstream of exit ramp (before speed-change lane) High High 3.3 3 High Effect of recurring congestion (percent hours per day that are congested) High High 1 1 High Roadway elements Combined effect of lane and shoulder width Medium Medium 3 1 Medium Effect of lane drop (with and without horizontal curvature) Medium Medium 1.5 1 Medium Effect of lane add Low Medium 1 1 Low Roadside elements and barrier Combined effect of median width and barrier (incl. barrier length and offset) High High 4 4 High Combined effect of clear zone width and barrier (incl. barrier length and offset) High High 4 4 High Effect of side slope (traversable or not) Medium High 1 4 High Effect of crash cushion presence at roadside features Medium High 2 1 Low Effect of median crossover Low Medium 1 1 Low Alignment elements Effect of horizontal curvature (including tangent length before curve) High High 3.5 1 Medium Effect of superelevation rate of horizontal curve Low High 1 1 Low Effect of grade (including length of grade) Low High 2 1 Low Other elements Effect of continuous shoulder rumble strips Low High 1 1 Low Effect of highway illumination between interchanges Medium High 1 1 Medium Note: 1 - High and medium priority topics are identified by bold font. The second section of Table 7 lists the various design or operation elements that were identified during the literature search or interview process. Each element listed is considered to represent a CMF.

64 The “clear zone width” listed in Table 7 is specific to vertical objects in the clear zone, and does not include non-traversable slopes. This limitation reflects the type of information that can be discerned from aerial photographs (which was the primary source of supplemental data for this project, as described in Chapter 4). The clear zone width is measured from the edge of traveled way to the nearest continuous line of vertical objects that are roughly parallel to the road centerline. This line is typically indicated as a tree line, fence line, or utility poles. The third through sixth columns of Table 7 indicate the importance, level of effort, number of attributes, and relative need, respectively, for each analysis unit or element. These descriptors were described in the previous section and used to estimate the priority for each unit and element. The number of attributes associated with a given topic is sometimes represented as a decimal value. In these instances, one or more of the attributes needed to calibrate the associated topic is shared with other topics such that the “cost” of acquiring the attribute is spread among topics. It is important to note that the use of the “relative need” criterion is intended to yield priorities that can be compared among the subsequent tables of freeway and interchange components. The proposed priority associated with each SPF or CMF topic is shown in the last column of Table 7. This priority is an indication of which topics should be considered first during the development of safety predictive models. Every effort will be made to ensure that the SPF or CMF associated with a high-priority topic is calibrated. Remaining resources will be used to calibrate medium priority topics. The low priority topics will be considered after the higher priority topics have been addressed. HOV facilities have a unique influence on freeway operation—to the extent that the presence of an HOV lane on a freeway segment requires treatment of the segment as a separate facility type. The literature review indicated that HOV facilities constitute only about 3 percent of the freeway mileage in the U.S. For this reason, safety predictive models for HOV facilities are not believed to be highly important in achieving the project objectives. Moreover, there are many different types of HOV facilities, as distinguished by flow direction (contra-flow, or concurrent flow) and lane separation (i.e., barrier, buffer, and continuous access). For this reason, a comprehensive set of safety predictive models for HOV facility analysis would likely require a large amount of effort to develop. Interchange Ramp This subsection describes the prioritized list of SPFs and CMFs for the evaluation of interchange ramp safety. The ramp predictive model is envisioned to be capable of evaluating both individual ramp segments and entire ramp configurations. Table 8 identifies the prioritized list of SPFs and CMFs for interchange ramps. The proposed priority associated with each SPF or CMF topic is shown in the last column. This priority is an indication of which topics deserve first consideration during the development of safety predictive models.

65 TABLE 8. Prioritized list of SPFs and CMFs for interchange ramp Category Topic 1 Importa nce Level of Effort Number Attrib. Relative Need Priority Different Analysis Units Segment types Basic segment High Low 2.3 1 High Basic segment with ramp meter operation Low Medium 1.8 1 Low Basic seg. with ramp meter and HOV bypass lane Low Medium 2.8 0 Low Basic descriptors Area type (urban, rural) High Low 1 1 High Ramp type (exit, entrance) Low Low 1 2 High Number of lanes Medium Low 1 1 High Design or Operation Elements Operation elements Effect of combined merge, diverge, and lane changing in coll.-distributor weaving section Low High 7 8 Medium Roadway elements Effect of lane width Low Medium 1 1 Low Effect of inside and outside shoulder width Medium Medium 2 1 Medium Roadside elements and barrier Effect of roadside barrier (barrier length and offset) High High 4 1 Medium Effect of side slope (traversable or not) Medium High 1 1 Medium Effect of crash cushion presence at roadside features High High 2 1 Medium Alignment elements Effect of horiz. curvature (including distance to freeway ramp terminal and crossroad ramp terminal as surrogates for curve operating speed) High High 5 1 Medium Effect of superelevation rate of horizontal curve Medium High 1 1 Low Effect of compound curve or spiral transition Medium High 1 1 Medium Other elements Effect of ramp illumination Low Medium 1 1 Low Effect of ramp-to-ramp merge point presence Medium Medium 1 1 Medium Effect of ramp-to-ramp diverge point presence Medium Medium 1 1 Medium Note: 1 - High and medium priority topics are identified by bold font. A segment-based predictive model for ramps should be developed, as opposed to an entire-ramp-based model that is characterized by its configuration (e.g., diamond, free-flow parclo, etc.). As documented in Chapter 2, previous attempts at developing the latter type of SPF have not demonstrated a consistent trend among configurations. It is likely that differences in cross section and alignment at the segment level are causing this inconsistency. Crossroad Ramp Terminal This subsection describes the prioritized list of SPFs and CMFs for the evaluation of crossroad ramp terminal safety. The ramp terminal predictive model is envisioned to be capable of evaluating alternative interchange type comparisons and ramp terminal spacing.

66 Table 9 identifies the prioritized list of SPFs and CMFs for crossroad ramp terminals. The proposed priority associated with each SPF or CMF topic is shown in the last column. This priority is an indication of which topics deserve first consideration during the development of safety predictive models. TABLE 9. Prioritized list of SPFs and CMFs for crossroad ramp terminals Category Topic 1 Importa nce Level of Effort Number Attrib. Relative Need Priority Different Analysis Units Terminal types Basic ramp terminal High Low 2 1 High Ramp terminal with frontage road movements Low Medium 2 0 Low Roundabout ramp terminal Low High 1 0 Low Basic descriptors Area type (urban, rural) High Low 1 1 High Terminal configuration (number of legs and movements) High Medium 1 1 High Control mode (signalized, two-way stop) High Medium 1 1 High Design or Operation Elements Roadway elements Effect of left-turn bay provision on crossroad High Medium 1 1 High Effect of right-turn bay provision on crossroad Low Medium 1 1 Low Effect of channelized (free) right-turn lane on crossroad Medium Medium 1 1 Medium Effect of channelized (free) right-turn lane on ramp Medium Medium 1 1 Medium Effect of lane width Low Medium 1 1 Low Effect of outside shoulder width Low Medium 1 1 Low Effect of median presence and width Medium Medium 3 1 Low Effect of number of lanes on crossroad High Low 1 1 High Effect of number of lanes on ramp approach High Low 2 1 High Alignment elements Effect of intersection skew angle Medium Medium 1 1 Medium Effect of approach grade Low High 2 1 Low Other elements Effect of distance between ramps Medium Medium 1 1 Medium Effect of sight distance restrictions (due to crossroad crest curve) Medium High 1 1 Medium Effect of driveway presence on the approach Low Medium 1 1 Low Effect of illumination at terminal Low Medium 1 1 Low Effect of innovative signing and marking to prevent wrong-way ramp entry Low High 1 1 Low Effect of protected left-turn phasing (if signal) Medium High 1 4 High Effect of right-turn on red (if signal) Low High 1 1 Low Note: 1 - High and medium priority topics are identified by bold font.

67 The findings from the review of the literature and several state DOT databases indicated that only about 1 percent of all interchanges have the SPUI form. Thus, the challenge to developing an SPF for the SPUI is to find a sufficient number of these interchanges to quantify statistically valid relationships. Freeway Speed-Change Lanes This subsection describes the prioritized list of SPFs and CMFs for the evaluation of freeway speed-change lane safety. The speed-change lane predictive model is envisioned to be capable of evaluating ramp entrance length, ramp exit length, ramp entrance/exit side (i.e., left or right-hand side of freeway), and weaving section length and type. Table 10 identifies the prioritized list of SPFs and CMFs for freeway speed-change lanes. The proposed priority associated with each SPF or CMF topic is shown in the last column. This priority is an indication of which topics deserve first consideration during the development of safety predictive models. TABLE 10. Prioritized list of SPFs and CMFs for freeway speed-change lanes Category Topic 1 Importa nce Level of Effort Number Attrib. Relative Need Priority Different Analysis Units Terminal types Basic speed-change lane High Low 2 1 High Basic descriptors Area type (urban, rural) High Low 1 1 High Ramp type (exit, entrance) High Low 1 1 High Lane design (parallel, tapered) Medium Medium 1 1 High Design or Operation Elements Operation elements Effect of combined merge, diverge, and lane changing in weaving section High High 4.3 4 High Roadway elements Effect of number of lanes on ramp Medium Medium 1 1 Medium Alignment elements Effect of ramp entrance (or exit) length High Medium 1 1 High Effect of horizontal curvature on ramp entrance (or exit) Low High 1 1 Low Other elements Effect of illumination at terminal Low Medium 1 1 Low Effect of entrance/exit side (left or right side) Medium Medium 2 1 Medium Effect of lane drop at exit ramp High Medium 1 1 High Note: 1 - High and medium priority topics are identified by bold font. Desirably, separate predictive models would be developed for the speed-change lane and for the basic freeway segment. This approach is used successfully in the HSM to describe

68 predictive methods for intersections and segments. However, unlike intersection-related crashes, speed-change-related crashes are difficult to accurately identify using the attributes provided in highway crash databases. For this reason, the SPFs and CMFs described in this subsection are envisioned to be based on the combined speed-change lane and freeway segment adjacent to the speed-change lane. In this manner, the SPFs and CMFs for speed-change lanes may be functionally similar to those for freeway segments.

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Prior to this research project, state highway agencies did not have tools for reflecting safety in their decisions concerning freeway and interchange projects.

The TRB National Cooperative Highway Research Program's NCHRP Web-Only Document 306: Safety Prediction Methodology and Analysis Tool for Freeways and Interchanges documents a safety prediction method for freeways that is suitable for incorporation in the Highway Safety Manual. Within the document are Appendices A through F: Practitioner Interviews, Database Enhancement, Proposed HSM Freeways Chapter, Proposed HSM Ramps Chapter, Proposed HSM Appendix B for Part C, and Algorithm Description.

Supplemental to the document are an Enhanced Safety Analysis Tool, a User Manual for the Tool, a Workshop Agenda, an Instructor Guide, and a PowerPoint Presentation.

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