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21 Chapter 1 â Crash Prediction Model Overview This chapter describes the crash prediction models (CPMs) developed in NCHRP Project 17-89 (Error! Reference source not found.). It also discusses their relationship to the freeway crash prediction models in the HSM Supplement (2), describes local calibration, and discusses how inclusion into a future edition of the HSM is envisioned. The CPMs are intended to be used to evaluate alternative freeway operational features or design elements, as may be developed during the preliminary design or final design stages of the project development process. The Federal Highway Administration (FHWA) recognizes three types of part-time shoulder use operation (3): ï· Bus-on-shoulder (BOS)âopen only to authorized buses and usually at the driver's discretion. ï· Static part-time shoulder use (S-PTSU)âopen to all vehicles during predetermined hours. ï· Dynamic part-time shoulder use (D-PTSU) âopen to all vehicles during time periods specified in real-time based on observed traffic conditions. This document discusses S-PTSU and D-PTSU operation. For simplicity, this operation is referred to herein as âPTSU operation.â Any reference in this document to âPTSUâ is referring to shoulder use by all vehicle types during a few hours of the day; it is not referring to BOS operation. PTSU is defined as a case where the shoulder is used by all vehicles and this use is permitted during some (but not all) hours of the day. 1.1 Key Attributes This section describes the CPMs for freeways with PTSU operation developed in NCHRP Project 17- 89. An overview of the process for applying the CPMs is presented in this section. Chapter 2 of this document describes this process in the form of proposed text for a future edition of the HSM. The CPMs are used to predict the average crash frequency associated with one direction of travel on a freeway. Each CPM includes a safety performance function (SPF); one or more adjustment factors (AFs), a calibration factor, a severity distribution, and a crash type distribution. Note that AFs are called crash modification factors (CMFs) in the HSM (4). The SPF, AFs, and calibration factor are multiplied together to form the predictive model equation. One predictive model is described herein for each of the following site types: ï· Freeway segment ï· Ramp entrance speed-change lane ï· Ramp exit speed-change lane The SPF is derived to estimate the crash frequency for a site with typical design and operating conditions. The AFs can be used to adjust the SPF estimate whenever one or more design or operational elements are atypical. Separate SPFs and AFs were developed for fatal-and-injury (FI) and property- damage-only (PDO) crashes. The CPMs include a crash type distribution and a crash severity distribution. These distributions are used with an associated CPM to estimate the average crash frequency for various combinations of crash type, severity, or both. A severity distribution function (SDF) is used to estimate the severity distribution. It is used to compute the proportion of K (fatal), A (incapacitating injury), B (non-incapacitating injury), and C (possible injury) severities within the frequency of FI crashes predicted by the CPM.
22 To facilitate interpretation and implementation of the CPMs developed for this project, the variable names and definitions used in these CPMs are consistent with those used in Chapter 18 of the HSM Supplement (2). 1.1.1 Segmentation 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 âsites.â Figure 1 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. There are three freeway segments, one ramp exit speed-change lane, and one ramp entrance speed-change lane. Note that the speed-change lane sites encompass all lanes (in one direction) on the freeway in addition to the speed-change lane associated with the ramp. Figure 1. Illustrative sites for one-directional freeway facility evaluation. As indicated in Chapter 18 of the HSM Supplement (2), freeway segment boundaries are typically defined by speed-change-lane presence or by a change in the cross section. This guidance is equally applicable to a one-directional freeway facility evaluation. Specifically, HSM-based freeway segment
23 boundaries are defined by the presence of a speed-change lane, a change in number of through lanes, or a relatively large change in the width of various cross section components. For the NCHRP Project 17-89 CPMs, segment boundaries are also defined by the start or end of a horizontal curve. Figure 1 only depicts site boundaries associated with the start and end of speed-change lanes. However, any of the sites shown in Figure 1 would be sub-divided into multiple sites if they contained the start or end of a horizontal curve or a change in cross section. Chapter 18 of the HSM Supplement (2) and Chapter 2 of this document provide additional information on specific cross-sectional dimension changes dictating segmentation. 1.1.2 Model Form The CPMs developed for this research project follow the model structure used in Part C of the HSM (4). The predictive model equation in each CPM was developed as a regression model having multiple independent variables that relate crash frequency to various site characteristics. The independent variables were also used to establish representative base conditions for the SPF (following the guidance provided in the appendix to HSM Part C). Additionally, the variables were also used to derive AFs for those specific site characteristics that were found to have a logical and statistically valid association with crash frequency. Separate CPMs were developed for FI and PDO crashes. Creation of separate CPMs for FI and PDO removes the effects of jurisdiction-to-jurisdiction differences in PDO crash reporting from the FI CPM and provides a more reliable means of modeling the influences of geometric and traffic features on FI and PDO crashes. The approach is also consistent with the current freeway CPMs in the HSM Supplement and other recent projects that have developed CPMs for inclusion in a future edition of the HSM (e.g., NCHRP Project 17-58, NCHRP Project 17-62, and NCHRP Project 17-70). The NCHRP Project 17-89 final report (1) provides additional information on this topic. 1.1.3 Model Framework The predictive model framework for freeway segments is presented in Equation 1. This equation consists of two terms, where Equation 2 and Equation 3 each correspond to one term. Equation 1 ð , , , ð , , , ð , , , Equation 2 ð , , , ð¶ , , ð , , , ð´ð¹ , , , â¦ ð´ð¹ , , , Equation 3 ð , , , ð¶ , , ð , , , ð´ð¹ , , , â¦ ð´ð¹ , , , 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,w,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 1 shows that freeway segment crash frequency is estimated as the sum of components: FI crash frequency and PDO crash frequency. Equation 2 is used to estimate the FI crash frequency and Equation 3 is used to estimate the PDO crash frequency. The CPMs for ramp entrance speed-change lanes and ramp exit speed-change lanes have a similar structure. The SPFs include the following variables:
24 ï· Freeway segments (FI and PDO SPFs): length of freeway segment, directional annual average daily traffic (AADT) volume of freeway segment. ï· Ramp entrance speed-change lane (FI and PDO SPFs): length of speed-change lane site, directional AADT volume of freeway, and AADT volume of entrance ramp. ï· Ramp exit speed-change lane (FI and PDO SPFs): length of speed-change lane site, directional AADT volume of freeway, and number of through lanes on the freeway adjacent to the speed-change lane. The AFs in each equation are used to quantify the association of geometric design and operational features with crash potential. They are specific to the FI and PDO severity categories because the strength of the association tends to vary by crash severity. 1.1.4 Adjustment Factor Summary This section presents and overview of AFs in the CPMs that were developed. The next section provides a greater level of detail on the AFs related to PTSU. Table 1 lists AFs in the CPMs that predict fatal-and- injury average crash frequency, and Table 2 lists the AFs in the CPMs that predict property-damage-only average crash frequency. Table 1. Adjustment factors in NCHRP Project 17-89 FI crash prediction models. Adjustment Factor Adjustment Factor in Crash Prediction Model? Freeway Segment Ramp Entrance Speed-Change Lane Ramp Exit Speed- Change Lane? Horizontal Curvature Yes Yes Yes Lane Width Yes Yes Yes Inside Shoulder Width Yes Yes Yes Inside Shoulder Rumble Strips Yes Yes Yes Median Width Yes Yes Yes Median Barrier Yes Yes Yes Part-time Shoulder Use Yes Yes Yes Lane Changes Yes No No Outside Shoulder Width Yes No No Outside Shoulder Rumble Strips Yes No No Outside Clearance Yes No No Outside Barrier Yes No No Turnouts Yes No No Speed-Change Lane Length No Yes Yes
25 Table 2. Adjustment factors in NCHRP Project 17-89 PDO crash prediction models. Adjustment Factor Adjustment Factor in Crash Prediction Model? Freeway Segment Ramp Entrance Speed-Change Lane Ramp Exit Speed- Change Lane? Horizontal Curvature Yes Yes Yes Lane Width Yes Yes Yes Inside Shoulder Width Yes Yes Yes Inside Shoulder Rumble Strips No No No Median Width Yes Yes Yes Median Barrier Yes Yes Yes Part-time Shoulder Use Yes Yes Yes Lane Changes No No No Outside Shoulder Width Yes No No Outside Shoulder Rumble Strips No No No Outside Clearance Yes No No Outside Barrier Yes No No Turnouts Yes No No Speed-Change Lane Length No Yes Yes The AFs in the CPMs are generally functions with one or more independent variables. The segmentation enabled some AFs to be developed for homogeneous conditions within a site. For example, AFs for lane width, shoulder width, median width, and horizontal curvature assume lane width, shoulder width, median width, and horizontal curvature, respectively, are the same throughout a site. Other geometric features tend to vary or start and stop more frequently along a freeway, and it is impractical to begin a new segment at every location where this occurs. These geometric elements include rumble strip presence on the inside shoulder, rumble strip presence on the outside shoulder, median barrier presence, outside barrier presence, and turnout presence. AFs for these geometric features have an equation form enabling non-homogeneous segments. For example, the AF for rumble strip presence on the inside shoulder contains a term for the proportion of the segment with rumble strips present on the inside shoulder. The AF value for a segment with rumble strips present on 50 percent of the inside shoulder will be differ from the AF value for a segment with rumble strips present on 75 percent of the inside shoulder. The formulation of most of the AFs in the aforementioned regression equations is based on the formulations of similar CMFs in Chapter 18 of the HSM Supplement (2). The base conditions established for the SPFs (i.e., conditions at which AFs equal 1.00) match those used in Chapter 18. These base conditions include the following: ï· Horizontal curve presence: not present ï· Lane width: 12 feet ï· Inside shoulder width (paved): 6 feet ï· Length of rumble strip on inside shoulder: 0.0 mile (i.e., not present) ï· Median width: 60 feet ï· Length of median barrier: 0.0 mile (i.e., not present) ï· Outside shoulder width: 10 feet ï· Length of rumble strip on outside shoulder: 0.0 mile (i.e., not present) ï· Clear zone width: 30 feet ï· Length of outside barrier: 0.0 mile (i.e., not present)
26 ï· PTSU operation: no PTSU operation during any hour of the day ï· PTSU lane width: 0 feet ï· Turnout length in segment: 0.0 mile (i.e., not present) ï· Ramp entrance speed-change lane length: 0.142 mile ï· Ramp exit speed-change lane length: 0.071 mile The variable names and definitions used in the AFs are consistent with those used in Chapter 18 of the HSM Supplement (2). 1.1.5 Part-time Shoulder Use-Related Adjustment Factors Two AFs unique to PTSU developed in NCHRP Project 17-89 are presented in this section â a PTSU operation AF and turnout presence AF. PTSU Operation AF. The estimated PTSU operation AF for the FI CPM is described by the following equations. The PTSU operation AF for the PDO CPM has the same form but the coefficient values are different. Equation 4 ð´ð¹ | , , 1.0 ð , exp ð , ð , exp ð , ð , , ð , with Equation 5 ð , 0.04106/ð min ð , , 12 ð¼ Equation 6 ð , 0.04106 min ð , , 13 12 ð¼ Equation 7 ð , 1.318 ð¼ Equation 8 ð , , 1.305 1 ð¼ ð , where Pt,ptsu = proportion of time during the average day that PTSU operates; n = number of through lanes within site (including managed lanes but not including auxiliary lanes or PTSU lanes); 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) (feet); IptsuLane = indicator variable (= 1.0 if PTSU lane [or tapered transition] is present, 0.0 otherwise); Ptransition,w = proportion of site length with PTSU transition zone present upstream, downstream, or both for site type w (w = fs: freeway segment, en: ramp entrance speed-change lane, ex: ramp exit speed-change lane) (see Equation 9); The variable Wptsu,s represents the average width of the shoulder that is allocated to vehicular traffic use (i.e., as an additional travel lane) during 1 or more hours of the typical day. 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. The proportion Pt,ptsu represents the proportion of time during the average day that PTSU operates in the vicinity of (or at) the subject site. All days of the year, including weekdays and weekend days, are considered when computing Pt,ptsu. It has a nonzero value if (a) the site has a full-width or tapering PTSU lane, or (b) the site does not have a PTSU lane but a portion of it is within 0.152 miles of a PTSU lane (i.e., just upstream or downstream). Case âaâ is referred herein to as a PTSU lane and case âbâ is referred to as a PTSU transition zone. Case âaâ is addressed by Equation 7. Case âbâ is addressed by Equation 8. The proportion Pt,ptsu is computed using Equation 22.
27 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 Wptsu is 16.8 feet or less. The base condition for this AF is âno PTSU operation during any hour of the dayâ (i.e., Pt,ptsu = 0.0) and PTSU lane width Wptsu equal to 0.0 feet. A 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 feet (0.152 miles) in length based on the researchersâ experience with PTSU operations and design. To accurately quantify the influence of PTSU transition zone presence on freeway safety, a variable was defined to quantify the portion of a siteâs length that included a transition zone. This variable is computed using the following equation. Equation 9 ð ð¿transition, /ð¿ where Ptransition = proportion of site length with PTSU transition zone present upstream, downstream, or both; L = site length (mile); and Ltransition,site = total length of PTSU transition zones within site (i.e., between site begin and end mileposts) (mile). The proportion computed using Equation 9 ranges between 0.0 (i.e., no transition zone present) and 1.0 (transition zone present for the length of the site). 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 2. a. Upstream transition zone. b. Downstream transition zone. c. Transition zones between PTSU lanes. Figure 2. Example calculation of the length of transition zone within a site.
28 In Figure 2a, the site is shown as a freeway segment located upstream of a PTSU lane. The segmentâs length is shown to exceed that of the transition zone (which always equals 0.152 miles). As a result, the proportion of the site length with PTSU transition zone Ptransition is computed to be less than 1.0. In Figure 2b, the site is shown as a freeway segment located downstream of a PTSU lane. Its length is shown to be less than that of the transition zone. As a result, the variable Ptransition is equal to 1.0. If the next downstream segment of freeway is also evaluated, it too will have a non-zero value for Ptransition because it includes the remaining portion of the transition zone. Figure 2a and Figure 2b depict PTSU lanes that start and end via taper, but PTSU lanes may also start and end in other manners, such as a transition to or from a general purpose lane or managed lane. In Figure 2c, 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. Because this sum is less than the segment length, Ptransition is computed as a value less than 1.0. Turnout Presence AF. Turnouts are paved areas immediately adjacent to PTSU lanes that are wide enough to serve as a refuge for disabled vehicles. The estimated turnout presence AF is described for FI crash frequency on freeway segments using the following equation. Equation 10 ð´ð¹ | , , 1.0 ð 1.0 ð exp 0.7873/ð with, Equation 11 ð ð¿ , /ð¿ The proportion Pturnout represents the proportion of the segment length that is adjacent to a turnout. It is computed by measuring the length of roadway adjacent to a turnout and dividing by the segment length. If the turnout extends beyond one or both of the segment boundaries, then only that portion of the turnout that lies within the segment is measured. This AF is applicable to values of Pturnout that range from 0.0 to 1.0. The number of through lanes range from 2 to 7. The base condition for this AF is âno turnout presentâ (i.e., Pturnout = 0.0). This AF is applicable to freeway segments with PTSU operation during some portion of the typical day. The manner in which it is used (i.e., as a divisor) in the AF suggests that turnout presence has less influence on crash frequency when there are more lanes. In other words, when there are many lanes, the turnout (like a shoulder) is laterally more distant from the center of the traveled way such that the crashes occurring in the middle lanes are less influenced by turnout presence. 1.2 Relationship to Current Highway Safety Manual NCHRP Project 17-89 produced CPMs capable of analyzing urban freeways with or without PTSU. These CPMs complement the CPMs in Chapter 18 of the HSM. For a given project, analysts will need to choose which set of CPMs to use when analyzing a freewayâs safety performance. Situations in which it would generally be more desirable to use the NCHRP Project 17-89 CPMs include the following: ï· A site where PTSU is provided or being considered for implementation. ï· A project that includes some sites or alternatives with PTSU. ï· A freeway where six or seven lanes in one direction are being analyzed. ï· The freeway of interest is located in a jurisdiction that has calibrated the NCHRP Project 17-89 CPMs but not the current HSM freeway CPMs. ï· The analysis results will be compared with prior analysis results from NCHRP Project 17-89 CPMs.
29 The NCHRP Project 17-89 CPMs were developed exclusively using data from urban sites, and their applicability to rural sites is unknown. Traffic volumes were relatively high as many sites were on or near PTSU facilities that were implemented to reduce congestion. Care was taken to keep variable definitions and the data requirements of AFs in the NCHRP Project 17- 89 CPMs similar to the current HSM when possible. The relative effects of AFs on crash frequency are generally similar. Analysts who are familiar with data needs for the current HSM freeway CPMs should find data collection necessary for application of the NCHRP Project 17-89 models similar, except for the collection of additional variables related to PTSU. 1.3 Local Calibration In general, the HSM recommends that CPMs be calibrated before they are used for predictive analysis in a given jurisdiction. The level of crash frequencies often varies, sometimes substantially, from jurisdiction to jurisdiction. Reasons for this variation include: climate, driver populations, animal populations, crash reporting thresholds, and crash reporting system procedures (4). Without calibration, CPMs may not provide meaningful and accurate results. Appendix B of the HSM Supplement provides a procedure for local calibration of CPMs that is applicable to the NCHRP Project 17-89 CPMs. The NCHRP Project 17-89 CPMs were developed using data from five states. The model development process included the use of indicator variables for states and state-to-state differences. The coefficients for these variables were generally found to be statistically significant. Use of indicator variables to account for state-to-state differences enabled the model to better capture the effect of varying geometric and traffic conditions among the sites analyzed. State indicator variables were removed from the final CPMs so the CPMs can be used for roadways outside the states from which NCHRP Project 17-89 data was collected. However, the magnitude and statistical significance of differences between states observed in NCHRP Project 17-89 reinforce the importance of local calibration by practitioners prior to using the CPMs. The NCHRP Project 17-89 CPMs were developed using data comprised of freeway sites with PTSU and freeway sites without PTSU. This database composition facilitated the development of an AF that quantified the difference in crash frequency relative to sites with and without PTSU. As a result, the CPMs can be calibrated using data from a jurisdiction that does not currently have PTSU provided that the sites included in the calibration data have sufficiently high volume as to reasonably be candidates for PTSU implementation. The SDFs should also be calibrated for local conditions, and the default crash type distributions can be replaced with local values. Appendix B of the HSM Supplement provides a procedure for calibrating SDFs. Uncalibrated SDFs and default crash type distributions may be used with calibrated or uncalibrated CPMs because they only provide a proportion of crash severities/types within a crash frequency predicted by the CPM. While it is desirable to calibrate CPMs and SDFs and obtain local crash type distributions, calibration of CPMs should be prioritized in the event of limited resources. 1.4 Future Highway Safety Manual Inclusion Chapter 2 of this document presents proposed text for a future edition of the HSM. The text has been prepared as a âstandaloneâ HSM chapter, rather than as an addition to the current freeway chapter (i.e., Chapter 18). The text was prepared in this manner to maximize clarity to readers and avoid have multiple CPMs (i.e., current HSM freeway models, NCHRP Project 17-89 freeway models, and, potentially, NCHRP Project 17-89A managed-lane CPMs) presented simultaneously in one chapter. This approach does result in some duplication with the current HSM freeway, notably in some areas such as introductory sections and sections with definitions and equations common to both sets of models. The manner in which NCHRP Project 17-89 models appear in the next edition of the HSM will ultimately be determined by
30 others in the future, but the proposed text presented in this document will serve in the interim as the definitive resource for those applying the model. 1.5 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). 2014. Highway Safety Manual Supplement. Washington D.C. 3. Jenior, P., B. Schroeder, R. Dowling, J. Geistefeldt, and D. Hale. 2019. Decision Support Framework and Parameters for Dynamic Part-Time Shoulder Use: Considerations for Opening Freeway Shoulders for Travel as a Traffic Management Strategy. Report No. FHWA-HOP-19-029. Federal Highway Administration, Washington D.C. 4. American Association of State Highway and Transportation Officials (AASHTO). 2010. Highway Safety Manual. Washington D.C.