Kittelson & Associates, Inc.

Kittelson & Associates, Inc.
NCHRP Project Development of Roundabout Crash Prediction Models and Methods Kittelson & Associates, Inc. In association with: Persaud and Lyon, Inc. Write Rhetoric

Project Objectives Develop Crash Prediction Models (CPMs) for U.S. roundabouts for planning and design decisions Specific questions addressed: How do geometric features – and combinations of features – influence the number and severity of crashes at the roundabout? How do operational features – and combinations of features – influence the number and severity of crashes at the roundabout? How do driver learning curves influence the number and severity of crashes at any age roundabout? CPMs to be included in next edition of the HSM, SafetyAnalyst and IHSDM This project focused on developing crash prediction models for roundabouts, using data from the U.S. with the intent of identifying, in different contexts (urban/suburban, rural), the features that influence crash frequency and severity. The goal of the research was to produce models that transportation professionals could use to inform their decisions at a planning-level (e.g., as it relates to selecting roundabouts as an intersection-control type for an intersection) as well as specific design decisions for roundabouts. The results of this research are documented so they can be incorporated into (1) a future edition of the HSM, (2) the AASHTO SafetyAnalyst software, and (3) the Interactive Highway Safety Design Model software.

Presentation Organization
Data collected Model development approach CPMs developed Driver learning curve findings Conclusions The focus of presentation is on the results. Will briefly discuss the data collected and approach to developing the models.

Data Collected Crash, traffic and geometric data collected
CA, FL, KS, MI, MN, NC, NY, ON, PA, WA, WI Intersection-level CPMs – 327 sites Leg-level CPMs – 150 sites, 534 individual legs Driver learning curve – 109 sites (FL, MI, NY, WA, WI)

Model Development Approach
Consistent with HSM chapter C predictive chapters Crashes predicted with a combination of SPFs and CMFs Cross-sectional negative binomial regression models developed Annual crash frequency modeled as a function of traffic volumes and geometric variables

CPMs for Planning-Level Analysis
Apply to entire intersection Developed using only AADT variables and basic geometric variables that would be known at the planning stage Models are applicable for average conditions of other geometric characteristics CPMs used early in the project development process Network screening Intersection control evaluations Predict crashes per year for crashes within circulating roadway and on legs and considered related to roundabout geometry or operation Pedestrian and bicycle crashes not included The planning-level models are relatively easy to apply (fewer data needs) and are intended to be used early in the project development process in activities such as network screening or intersection control evaluations where the potential safety performance of one type of control is being compared to another (e.g., potential safety performance of a signal vs. roundabout at a specific intersection. All crashes occurring within or related to the roundabout are included. Crashes involving pedestrians or bicycles are not included however due to their very low frequency.

Rural Roundabouts N = expaMAJAADTbMINAADTcexpd × NUMBERLEGS+e × CIRCLANES N = predicted average crash frequency, crashes/yr MAJAADT = Total entering AADT on major road MINAADT = Total entering AADT on minor road NUMBERLEGS = 1 if a 3-leg roundabout; 0 if 4-legs CIRCLANES = 1 if a single lane roundabout; 0 if more than 1 circulating lanes As an example of the planning-level CPMs the CPM for rural roundabouts is shown. Here, the number of crashes per year is predicted by the major and minor road AADT, the number of legs and the number off circulating lanes. If 2 circulating lanes exists anywhere within the roundabout it is classified as a 2 lane roundabout. Roundabouts with more than 2 circulating lanes were not included in the data so the CPM would not apply.

Rural Roundabouts N = expaMAJAADTbMINAADTcexpd × NUMBERLEGS+e × CIRCLANES Severity a b c d e k TOT 0.3356 0.5142 0.6292 FI 0.7756 0.4239 0.4424 PDO 0.2980 0.5463 0.7284 This slide shows the parameter estimates for the rural planning-level CPM. k is the overdispersion parameter of the SPF. As expected, the models indicate crashes increase as traffic volumes on the major and minor roads increase. For the same traffic volumes, fewer crashes are expected at 3-leg and single-lane roundabouts.

Urban Single-Lane Roundabouts N = expaMAJAADTbMINAADTcexpd × NUMBERLEGS Severity a b c d k TOT 0.3274 0.3960 0.5030 FI 0.5271 0.3505 0.3290 PDO 0.2653 0.4294 0.6064 This slide shows the parameter estimates for the urban single-lane planning-level CPM. Again, the models logically indicate that crashes increase as traffic volumes on the major and minor roads increase. For the same traffic volumes, fewer crashes are expected at 3-leg roundabouts.

Urban Two-Lane Roundabouts N = expaMAJAADTbMINAADTcexpd × NUMBERLEGS Severity a b c d k TOT 0.5210 0.2905 0.9263 FI 0.9134 0.1937 0.5611 PDO 0.4954 0.3098 1.0642 This slide shows the parameter estimates for the urban two-lane planning-level CPM. Consistently, the models indicate crashes increase as traffic volumes on the major and minor roads increase. For the same traffic volumes, fewer crashes are expected at 3-leg roundabouts.

CPMs for Intersection-Level Design Decisions
CPMs used during design or retrofit work Predict crashes per year for crashes within circulating roadway and on legs and considered related to roundabout geometry or operation Pedestrian and bicycle crashes not included CPMs developed for four site types 3 legs 1 circulating lane 3 legs 2 circulating lanes 4 legs 1 circulating lane 4 legs 2 circulating lanes The intersection-level design CPMs were developed to inform design decisions at a similar level of detail as the intersection crash prediction models for signals and two-way stop controlled intersections in the Highway Safety Manual, 1st Edition.

Model form: N = NSPF × CMF1 ... ×CMF2 NSPF = expa+c x Irural (ENTAADT/1000)b NSPF = predicted average crash frequency for base conditions on all legs, crashes/yr EntAADT = entering AADT for roundabout, veh/d Irural = area type indicator variable (= 1 if rural, 0 if urban) CMFs developed including various geometric variables SPFs developed for fatal+injury (FI) crashes and PDO crashes Consistent with Part C of the HSM, the number of crashes is predicted by a base SPF multiplied by CMFs. The base SPF is a function of the entering AADT and whether the environment is rural or urban.

N = expa+c x Irural (ENTAADT/1000)b Site/Severity Type a b c k FI 3 leg 1 circulating lane -4.404 1.084 0.206 0.31 3 leg 2 circulating lanes -3.887 1.306 0.250 0.36 4 leg 1 circulating lane -3.503 0.915 0.33 4 leg 2 circulating lanes -3.535 1.276 0.45 PDO -1.720 0.486 0.168 0.54 -1.565 1.055 0.496 1.06 -1.475 0.702 0.80 -1.536 1.131 0.79 This slide shows the base SPFs developed. The SPFs show crashes increasing with entering AADTs and more crashes in rural areas compared to urban.

Crash type distributions provided by site and severity type Head-on Right-angle Rear-end SSSD Other – single-vehicle Animal Fixed-Object Other-Object Parked vehicle Other – multiple-vehicle The proportion of specific crash types can be applied to CPM estimate for total crashes to estimate expected frequency of these crash types. Proportions are specific to each SPF by site type and severity. At present, crash types on crash reports still follow standard classifications in most states.

Pedestrian and bicycle crashes too few to model so are not included In data, 1% were vehicle-bicycle and 0.4% vehicle-pedestrian

Optional application of Severity Distribution Functions Break down estimates of FI into individual K, A, B, C estimates Considers speed limits on approaches (between 10 to 60 mph) Factor is leg specific An optional step is to break down the fatal+injury predictions into estimates of K, A, B or C severities on the KABCO scale. To do so severity distribution functions were developed that apply to individual approaches and consider the approach speed limit.

STEP 1 fj,sl = exp[ x {(SLj/100)2 – (35/100)2}] fj,sl = severity adjustment factor for leg j SLj = speed limit on leg j in mph Severity adjustment factors are first calculated for each leg.

STEP 2 Sk = exp[Fk] x [p1 x f1,sl + p2 x f2,sl +p3 x f3,sl +p4 x f4,sl ] SA = exp[FA] x [p1 x f1,sl + p2 x f2,sl +p3 x f3,sl +p4 x f4,sl ] SB = exp[FB] x [p1 x f1,sl + p2 x f2,sl +p3 x f3,sl +p4 x f4,sl ] Pi = AADTi/(AADT1+AADT2+AADT3+AADT4) P1to4 = proportion of total roundabout volume on leg FK, FA and FB estimated for each combination of number of legs and circulating lanes Severity adjustment factors are then aggregated to an intersection level factor, weighted by the proportion of total AADT on each leg.

STEP 3 PK = SK/(1+SK+SA+SB) PA = SA/(1+SK+SA+SB) PB = SB/(1+SK+SA+SB) PC = 1-(PK+PA+PB) The proportions of severity K, A, B and C are determined and can be applied to the CPM estimate of Fatal+Injury

CMFs for Intersection-Level Design Decisions
Two Types of CMFs Developed Those that apply to entire roundabout Those that apply to specific legs Leg-level CMFs are combined into a entire roundabout CMF prior to applying to SPF CMFs do not necessarily apply to all combinations of number of legs, circulating lanes and crash severities Where CMFs are not provided the evidence was insufficient

CMFICD – Inscribed Circle Diameter Applies to: urban roundabouts with a single circulating lane, ICD from 90 to 160 ft. Severity: FI CMFICD = exp( x (ICD – 125)] The CMF for inscribed circle diameter applies to the entire roundabout. As the ICD increases fatal+injury crashes decrease at urban single-lane roundabouts.

CMFoutbd – Outbound-Only Leg Applies to: urban/suburban/rural that are a interchange ramp terminal with crossroad with only one outbound only leg Severity: FI 1 Circulating Lane Circulating Lanes 0.455 The CMF for outbound leg applies to the entire roundabout. When an outbound leg is present fatal+injury crashes decrease.

CMFbypass – Right-Turn Bypass Lane Applies to – Individual leg in any area type Severity – FI CMF – 0.355 The CMF for right-turn bypass lane applies to an individual leg. When a bypass lane is present fatal+injury crashes decrease.

CMFap – Access Point Frequency Applies to – Individual leg in any area type Severity – FI, PDO CMFap, FI = exp( x nap] CMFap, PDO = exp( x nap] nap, = number of driveways or unsignalized access points on leg within 250 ft of yield line The CMF for access point frequency applies to an individual leg. Where more access points within 250 ft. are present more crashes are expected.

CMFew – Entry Width Applies to – Individual leg in any area type with 2 circulating lanes Severity – FI, PDO CMFew, FI = exp( x 29] CMFew, PDO = exp( x 29] The CMF for entry width applies to an individual leg. For legs approaching two circulating lanes, as entry width increases fewer crashes are expected.

CMFcl – Circulating Lanes Applies to – Individual leg in any area type (not outbound only legs) Severity – FI, PDO CMFcl, FI = exp( x (ncl x nel -4)] CMFcl, PDO = exp( x (ncl x nel-4)] ncl = number of circulating lanes nel = number of entering lanes The CMF for circulating lanes applies to an individual leg that is not an outbound only leg. Fewer crashes are expected when there is one circulating lane than two.

Aggregating Leg-Level CMFs to apply to roundabout Step 1 CMFleg = CMFbypass x CMFap x CMFew x CMFcl Step 2 CMFRnbt =(p1 x CMF1)+(p2 x CMF2)+(p3 x CMF3)+(p4 x CMF4) Pi = AADTi/(AADT1+AADT2+AADT3+AADT4) P1to4 = proportion of total roundabout volume on leg CMF1to4 = Combined CMFleg for each leg The leg-specific CMFs of interest need to have their effect aggregated to the overall intersection level to be consistent with the SPFs which are also applicable to the overall intersection. These include the CMFs for bypass lane, access point frequency, entry width and circulating lanes. A CMF for each leg is first estimated using each individual CMF that applies. The leg CMFs are then weighted by the proportion of total AADT on the legs to estimate a roundabout level CMF.

CPMs for Leg-Level Design Decisions
CPMs used during design or retrofit process Predict crashes per year for crashes associated with a specific roundabout leg Pedestrian and bicycle crashes not included Crash Types Modeled Entering-circulating (all severities and FI) Exiting-circulating (all severities) Rear-end (all severities) Single-vehicle approach (all severities) Single-vehicle approach + circulating (all severities) Circulating-circulating (all severities) Total (all severities) The leg-level crash prediction models were developed to inform design decisions at the leg-level.

Entering-Circulating Crashes N = crashes per year related to leg ENTAADT – entering AADT EXTAADT – exiting AADT CIRCAADT – circulating AADT APPRAADT – approach AADT N = expa(ENTAADT/1000)b(CIRCAADT)c Exiting-Circulating Crashes N = expa(EXTAADT/1000)b(CIRCAADT)c Rear-End Approach Crashes N = expa(APPRAADT/1000)b(CIRCAADT)c SV Approach and SV Approach +SV Circulating Crashes This slide shows the model forms for each of the leg-level CPMs. N = expa(APPRAADT/1000)b Circulating-Circulating Crashes N = expa(CIRCAADT/1000)b Total Crashes N = expa(APPRAADT/1000)b(CIRCAADT)c

Entering-Circulating Crashes N = expa(ENTAADT/1000)b(CIRCAADT)c Severity Entering Lanes Circulating Lanes a Coefficient k b c KABCO 1 -2.584 0.6091 0.3020 0.7470 2 -0.314 0.9636 0.3917 0.6232 -5.784 0.3608 0.6711 1.0734 -3.006 0.8054 0.7398 0.7759 As an example of the leg-level SPFs, this slide shows the coefficient estimates for entering circulating crashes of all severities. As would be expected, crashes are expected to increase with higher entering and circulating AADTs.

CMFs for Leg-Level Design Decisions
CMFs developed for: ICD – inscribed circle diameter Angle – angle to next leg Circwidth – circulating width NumberAccess – number of access points within 250ft. Luminaires – Number of luminaires within 250 ft. PostedSpeed – Posted speed limit on approach CMFs were developed for several variables. CMFs do not apply to all crash type models.

Entering-Circulating Crashes – All Severities Variable Circulating Lanes Entering Lanes Variable Levels CMF/unit change Base Value minimum maximum Circulating Width 1 2 30 ft. 15 ft. 42 ft. 1.0324 25 ft. 45 ft. 0.9860 24 ft. 0.8715 ICD 150 ft. 65 ft. 236 ft. 0.9932 110 ft. 314 ft. 0.9918 135 ft. 426 ft. 0.9853 Angle 90° 53° 182° 0.9769 69° 0.9867 Bypass Lane None 0.3685 This table shows the leg-level CMFs for entering-circulating crashes. For each CMF the base value and the CMF value per unit increase is shown. Also shown is the range of values in the data used to estimate the CMFs. While CMF values may appear small, it must be remembered they are for a unit change, e.g. feet. A larger circulating width is associated with more crashes for 1 circulating lane and fewer crashes for 2 circulating lanes. A larger ICD is associated with fewer crashes. An angle to next leg greater than 90 degress is associated with fewer crashes and less than 90 degrees with more crashes. A bypass lane is associated with fewer crashes.

Entering-Circulating Crashes – KABC Severities Variable Circulating Lanes Entering Lanes Variable Levels CMF/unit increase Base Value minimum maximum ICD 1 or 2 150 ft. 65 426 0.9951 Angle 90° 37° 186° 0.9825 This table shows the leg-level CMFs for entering-circulating crashes of K, A, B or C severity. A larger ICD is associated with fewer crashes. An angle to next leg greater than 90 degress is associated with fewer crashes and less than 90 degrees with more crashes.

Exiting-Circulating Crashes – All Severities Variable Circulating Lanes Entering Lanes Variable Levels CMF/unit increase Base Value minimum maximum Circulating Width 1 2 30 ft 15 ft. 42 ft. 1.198 25 ft. 45 ft. 0.772 ICD 150 ft 110 ft. 426 ft. 0.985 This table shows the leg-level CMFs for exiting-circulating crashes. A larger circulating width is associated with more crashes for 1 circulating lane and fewer crashes for 2 circulating lanes. A larger ICD is associated with fewer crashes.

Rear-End Crashes – All Severities Variable Circulating Lanes Entering Lanes Variable Levels CMF/unit increase Base Value minimum maximum NumberAccess 1 or 2 1 8 1.094 Luminaires 2 0.937 This table shows the leg-level CMFs for rear-end crashes. As the number of access points within 250 ft. increases more crashes are expected.. As the number of luminaires within 250 ft. increases fewer crashes are expected.

Single-Vehicle Approach Crashes – All Severities Variable Circulating Lanes Entering Lanes Variable Levels CMF/unit increase Base Value minimum maximum Posted Speed 1 or 2 40 mph 10 mph 60 mph 1.0451 This table shows the leg-level CMFs for single-vehicle approach crashes. As the speed limit increases more crashes are expected.

Circulating-Circulating Crashes – All Severities Variable Circulating Lanes Entering Lanes Variable Levels CMF/unit increase Base Value minimum maximum Circulating Width 1 or 2 30 ft. 24 ft. 45 ft. 0.917 This table shows the leg-level CMFs for circulating-circulating crashes. As circulating width increases fewer crashes are expected.

Single-Vehicle Approach + Single-Vehicle Circulating Crashes – All Severities Variable Circulating Lanes Entering Lanes Variable Levels CMF/unit increase Base Value minimum maximum PostedSpeed 1 or 2 40 mph 10 mph 60 mph 1.0356 CircWidth 30 ft. 14 ft. 45 ft. 0.9771 This table shows the leg-level CMFs for single-vehicle approach plus single-vehicle circulating crashes. As the posted speed increases more crashes are expected. A circulating width increases fewer crashes are expected.

Effect of a Driver Learning Curve
Testing thesis that driver behavior and safety may improve with familiarity Developed intersection-level SPFs including a variable for years post construction 109 sites where opening data was known were used Any trends are weak and vary from state to state Based on findings there is no satisfactory evidence of a driver learning curve Possible that DLC is for a shorter time period, e.g. over first few months of year 1, if one exists While not the focus of the project, the research looked into the possibility of a driver learning curve exhibited by a higher crash frequency in the year(s) immediately following construction.

Conclusions CPMs developed for both intersection-level and leg-level design analyses for U.S. roundabouts Estimate how geometric and operational features influence the number and severity of crashes SPFs also developed for planning-level analyses or network screening CPMs to be included in next edition of the HSM, SafetyAnalyst and IHSDM

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