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A-1 This appendix supplements Chapter 4, Safety, to provide details of literature reviews and findings on the safety performance of diverging diamond interchanges (DDIs). A.1 Literature Review The primary measure of safety performance is long-term annual average crash frequency. Crash modification factors (CMFs) based on significant samples of data from treatment and reference sites that remove bias found in most safety studies, especially regression-to-the-mean, have been developed in several studies. This section provides a summary of safety effects from early DDI implementations and surrogate measures collected at several DDIs in a recent FHWA study. A.1.1 Chilukuri et al. (2011) (1) A safety evaluation was conducted in 2011 on the first DDI opened at MO-13 and I-44 in Springfield, Missouri. Crash data obtained from the Missouri Department of Transportation and the City of Springfield were analyzed for a 5-year period before the improvements and 1 year after improvements. Roadway segment crash rates were compared to determine any changes in the pre-construction and post-construction periods. The safety conclusion included the following: ⢠Total crashes were down by 46% in the first year of operation. ⢠Left-turn type crashes were eliminated and left-turn right-angle type crashes were down 72% because of how left turns are handled within the DDI (free-flow movements or yield control). ⢠Rear-end type crashes were down slightly. This might also be due to how left turns are handled without traffic signal controls. ⢠DDI post-construction crash types are similar to those for any other signalized intersection; in the review, no definite crash pattern was noticed that could lead to determining that a certain type of crash increased within a DDI. A.1.2 Edara et al. (2015) (2) Data from six DDI sites in Missouri were used to conduct a before-after evaluation in 2015. The safety evaluation consisted of three types of observational before-after evaluation methods: Naïve, empirical Bayes (EB), and Comparison Group (CG). All three methods showed that there was decreased crash frequency for all severities in locations where a DDI replaced a conventional diamond intersection. A P P E N D I X Safety Details
A-2 Diverging Diamond Interchange Informational Guide The safety evaluation at the project-level accounts for the influence of the DDI treatment in the entire footprint of the interchange. The findings include: ⢠The highest crash reduction was observed for fatal and injury (FI) crashes: 63.2% (Naïve), 62.6% (EB), and 60.6% (CG). ⢠Property Damage Only (PDO) crashes were reduced by 33.9% (Naïve), 35.1% (EB), and 49.0% (CG). ⢠Total crash frequency also decreased by 41.7% (Naïve), 40.8% (EB), and 52.9% (CG). The site-specific approach focused on the influence at the ramp terminals only. Main findings include: ⢠The highest crash reduction was observed for FI crashes: 64.3% (Naïve), 67.8% (EB), and 67.7% (CG). ⢠PDO crashes were reduced by 35.6% (Naïve), 53.4% (EB), and 47.0% (CG). ⢠Total crash frequency also decreased by 43.2% (Naïve), 56.6% (EB), and 53.3% (CG). A collision type analysis revealed that the DDI, as compared to a diamond, traded high severity for lower severity crashes. While 34.3% of ramp terminal-related FI crashes in a diamond occurred due to the left-turn angle crashes with oncoming traffic, the DDI eliminated this crash type. A.1.3 Lloyd (2016) (3) Lloyd (2016) conducted a safety analysis at five locations in Utah that have been converted from traditional diamond interchanges to DDIs. The EB before-after method, using the Highway Safety Manual (HSM) and Interchange Safety Analysis Tool Safety Performance Functions (ISAT SPFs), was applied to the selected locations in order to provide a statistical analysis of the increase or decrease of crashes at the location since the DDI conversion. A.1.4 Claros et al. (2017) (4) Claros et al. (2017) generated CMFs for ramp terminals at DDIs in Missouri using EB evalu- ation. The authors obtained CMFs of 0.45 for FI crashes, 0.686 for PDO crashes, and 0.625 for total crashes. A.1.5 Nye (2018) (5) Nye (2018) examined the change in safety associated with the conversion of a conventional interchange to a DDI. For this examination, Nye compared crash records for multiyear time periods before and after the conversion at 15 interchanges. Nye analyzed the data using two before-after study methods. One method was called the Naïve Method by Nye. [However, it is more appropriately called the Volume-Corrected Method because it includes the use of annual average daily traffic (AADT) data to account for changes in traffic volume between the before and after periods.] The second method was called the Comparison-Group Method. It is used to account for changes in traffic volume, driver behavior, weather, vehicle fleet, traffic safety programs, and crash reporting threshold between the before and after periods. A.1.6 Nye et al. (2019) (6) Nye et al. built on the work of Nye (2018) and subsequently obtained data for 11 more inter- changes and re-evaluated the data for all 26 sites using the Comparison-Group Method. For both the original 15-site database and the 26-site database, CMFs were computed for each site and for the combined group of sites. CMFs were also computed for specific crash types
Safety Details A-3 (e.g., angle, rear-end, sideswipe, all types combined), crash severity categories (e.g., FI crashes, PDO crashes, and for all crash severities combined), and for light conditions (e.g., day, night, all conditions combined). The site-specific CMFs for FI crashes indicated that CMF values ranged from 0.193 to 1.208. Similar wide ranges were obtained for the site-specific CMFs for the other crash severity, crash types, and lighting condition categories. It is likely that some of this variation is attributable to the variation in geometric design elements and features among sites. Given that there are a large number of geometric elements and features at an interchange that influence safety, it is almost a certainty that some of the changes at one converted site will be different from those at other sites. The range in site-specific CMF values reported by Nye et al. (2019) is likely a reflection of the differences among sites (6). Information in the HSM indicates that road safety is affected by a change in number of lanes, lane width, shoulder width, median width, intersection skew angle, speed, traffic control type (i.e., stop, signal), and horizontal curvature. Each new interchange conversion represents unique combinations of change in most of these elements and features. The calculation of a CMF that summarizes the overall change in safety associated with a specific interchange conversion describes the combined safety effect of the changes in each element and feature at that site. This âoverallâ (or project-level) CMF can be a reliable descriptor of the change in safety at the converted site. However, it will not be a reliable descriptor of the change in safety associated with a proposed new site unless the changes in elements and features at the converted site are a match to those at the proposed site. If one or more changes at the proposed site do not match those at the converted site, then a different project-level CMF value will be obtained for the proposed site. A.2 Crash Modification Factor Development The objective of this section is to document the findings from a re-examination of the project-level CMFs produced by Nye et al. (2019) (6). The purpose of this re-examination is to determine whether the reported variation among CMF values can be explained by one or more geometric elements or features at the interchanges. A.2.1 Data Summary The database assembled by Nye et al. (2019) consists of data for 26 sites at which an existing interchange was converted to a DDI. One observation in the database represents one inter- change site (6). The location of each site is identified in Exhibit A-1. The AADT volume data listed in Exhibit A-1 are indicated by Nye (2018) to describe cross- road traffic conditions for most sites (both travel directions combined). For at least one site, the crossroad AADT was not available, and volume information for the ramps was substituted (5). The AADT data were evaluated further for this re-examination. Specifically, the AADT volume was combined with the crossroad lane count and a typical ratio of peak-hour volume to AADT volume (i.e., K factor) to compute a peak-hour lane volume. This lane volume was then compared to a typical peak-hour lane volume of 700 vehicles per hour (vph). Those sites with a lane volume greatly in excess of this amount were flagged as having an unusual AADT volume. One site was found to have a peak-hour volume of 2,600 vph/lane. Eight of the 26 sites had a peak-hour volume in excess of 800 vph/lane. As a spot check of the AADT values, the crossroad AADT volumes for the three sites in North Carolina were obtained from the North Carolina Department of Transportation (NCDOT) (7)
A-4 Diverging Diamond Interchange Informational Guide No. Road Names City State AADT (vpd), Before1 AADT (vpd), After1 Crossroad Through Lanes2, Before1 1 I-85/Jimmy Carter Blvd. Atlanta GA 53,465 58,350 4 4 2 I-85/Pleasant Hill Rd. Duluth GA 50,766 54,475 4 6 3 I-86/Yellowstone Ave. Pocatello ID 26,800 28,500 4 4 4 I-435/Roe Ave. Overland Park KS 42,925 37,500 4 4 5 KY 4/US-68 Lexington KY 36,550 33,095 4 6 6 I-494/34th Ave. S Bloomington MN 17,300 17,750 4 4 7 I-70/Stadium Blvd. Columbia MO 42,247 52,452 4 4 8 US-65/East Chestnut Expy. Springfield MO 22,900 24,000 2 4 9 US-60/S Kansas Expy. Springfield MO 24,900 26,782 3 4 10 US-67/Columbia St. Farmington MO 12,550 12,100 2 4 11 US-65/MO-248 Branson MO 31,800 33,150 2 3 12 I-44/Range Line Rd. Joplin MO 23,421 22,817 4 4 13 I-70/Mid Rivers Mall Dr. St. Peters MO 27,060 22,443 4 4 14 I-70/Woods Chapel Rd. Kansas City MO 17,412 17,676 4 4 15 I-29/Tiffany Springs Pkwy. Kansas City MO 19,090 20,637 3 4 16 I-77/Catawba Ave. Cornelius NC 25,969 27,938 4 4 17 I-85/NC-73 Concord NC 25,643 23,460 2 5 18 I-85/Poplar Tent Rd. Concord NC 18,655 24,536 2 4 19 I-590/S Winton Rd. Rochester NY 17,716 17,464 4 4 20 I-15/St. George Blvd. St. George UT 36,111 36,917 4 4 21 UT-201/UT-154 Salt Lake City UT 35,233 33,130 5 5 22 I-15/S 500 E St. American Fork UT 18,927 18,213 2 4 23 I-15/Timpanogos Hwy. American Fork UT 22,960 23,511 3 4 24 I-15/US-91 Brigham City UT 18,483 19,000 2 2 25 I-64/US-15 Gordonsville VA 6,700 7,000 4 4 26 I-25/College Dr. Cheyenne WY 13,374 11,253 4 2 Notes: 1. Before = conditions present before conversion to DDI. After = conditions present after conversion to DDI. 2. Number of lanes on the crossroad that serve vehicles traveling as a through movement. Total of both travel directions. Each lane can be traced as a continuous traffic lane through the interchange (including both crossroad ramp terminals). Crossroad Through Lanes2, After1 Exhibit A-1. Interchange site location, traffic volume [vehicles per day (vpd)], and lanes.
Safety Details A-5 and are shown in Exhibit A-2. They can be compared with those obtained from a spreadsheet prepared by Nye et al. (2019) (6). The volumes reported by Nye et al. are consistently higher than the crossroad AADTs obtained from the NCDOT website. It is possible that the AADTs attributed to Nye et al. may be inclusive of volumes on the ramps as well as the crossroad. Given the uncertainty, AADT was not considered in the development of a CMF function. If crossroad AADT volume could be confirmed for all sites in Exhibit A-1, then this variable should be evaluated to determine if CMF value is a function of crossroad AADT. Exhibit A-3 identifies several supplemental variables that were collected from Google Earth and added to the database. The site number in the first column of this table coincides with the site numbers in Exhibit A-1. The methods by which each variable was measured are listed in the table footnotes. The variables listed in Exhibit A-3 were selected because of their documented correlation with road safety. Although not shown, several additional variables were also collected: ramp-to-ramp distance, skew angle, median type, and number of curves along the crossroad. A.2.2 Analysis Results Nye (2018) used both the Volume-Corrected Method and the Comparison-Group Method to compute site-specific CMFs for a 15-site database (5). Subsequently, Nye et al. (2019) used only the Comparison-Group Method to compute the same CMFs for a 26-site database (6). For both applications of the Comparison-Group Method, they used âtotalâ crashes (i.e., all crash severities and types combined) to describe the change in safety at the comparison sites. The use of total crashes to compute the comparison site ratio is appropriate for the evaluation of total crash frequency at the interchange conversion sites. However, the use of total crashes to evaluate specific severity categories (e.g., FI), crash types (e.g., angle), or lighting conditions (e.g., day) may not produce the most reliable CMF values. For example, a change in the reporting threshold (between the before and after evaluation periods) is likely to have a significant effect on PDO crash frequency and a small effect on FI crash frequency. Arguably, it would be more appropriate to quantify the comparison ratio using FI crash frequency when estimating a CMF for FI crashes at the conversion sites (and a ratio based on PDO crash frequency when estimating a CMF for PDO crashes). In support of this claim, Hauer (1997, p. 131) advises that when selecting the comparison group, âthere should be reason to believe that the change in factors influencing safety is similar in the treatment and comparison groupsâ (11). Nye (2018) identified a comparison group for each of the interchange conversion sites. He computed the odds ratio and its variance for the comparison group (5). This variance was subsequently used in the calculation of the CMF value and its standard error. Roughly speaking, a reduction of 0.03 in this variance corresponds to about a 3% increase in the CMF value. 16 I-77/Catawba Ave. Cornelius NC 25,969 27,938 33,000 31,500 17 I-85/NC-73 Concord NC 25,643 23,460 52,000 47,000 18 I-85/Poplar Tent Rd. Concord NC 18,655 24,536 37,000 50,000 Notes: 1. Before = conditions present before conversion to DDI. After = conditions present after conversion to DDI. No. Road Names City State NCDOT AADT (vpd), Before1 NCDOT AADT (vpd), After1 Nye et al. AADT (vpd), Before1 Nye et al. AADT (vpd), After1 Exhibit A-2. North Carolina AADTs.
A-6 Diverging Diamond Interchange Informational Guide No. Before Control Type1, Terminal 1 Before Control Type1, Terminal 2 Crossroad Lane Drops2 Area Type Stop Line to Stop Line Distance3, ft Crossroad Speed Limit, mph Median Width4 Before, ft Median Width4 After , ft signal signal 2 Urban 600 40 1 17 signal signal 2 Urban 435 40 1 15 signal signal 0 Urban 600 35 4 81 signal signal 2 Urban 620 25 1 55 signal signal 0 Urban 710 45 16 30 signal signal 2 Suburban 600 35 40 64 signal signal 0 Suburban 640 40 1 22 signal signal 0 Suburban 375 40 16 15 signal signal 1 Suburban 670 45 6 24 stop stop 0 Rural 700 40 1 21 sig/sig signal 0 Suburban 810 40 1 30 full clover full clover 0 Suburban 750 40 8 40 signal signal 2 Urban 465 35 8 33 signal signal 1 Suburban 525 35 1 17 signal signal 2 Suburban 325 25 16 28 signal signal 1 Urban 645 30 4 36 stop signal 0 Suburban 860 45 4 50 stop stop 2 Rural 590 45 1 30 signal signal 0 Suburban 605 45 1 12 signal signal 1 Urban 760 30 4 34 signal signal 0 Suburban 815 50 10 27 signal stop 0 Urban 890 45 1 78 signal signal 1 Suburban 710 45 1 26 stop stop 1 Rural 740 30 1 23 signal signal 0 Rural 1,020 30 42 45 stop stop 0 Rural 613 40 1 35 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 Notes: 1. Traffic control type at the interchange crossroad ramp terminals before conversion to DDI (note: all DDI terminals are signalized). All interchanges have two crossroad ramp terminals. Stop = ramp approach is stop controlled; crossroad approach is uncontrolled. Full clover = no stop- or signal-controlled approaches at terminal; ramp approach may have yield control or no control. 2. At some DDIs, the outside lane of the crossroad is dropped at the entrance ramp (i.e., the outside crossroad lane becomes a turning roadway at the ramp and continues onto the ramp). The value in the table describes the number of lanes that are dropped at the DDI. Total of both travel directions. 3. Travel distance measured along the crossroad from the stop line at one crossroad ramp terminal to the stop line at the downstream terminal in a given travel direction. Distance is measured for both directions of travel, and the average value is shown in the table. 4. Median width is measured for the crossroad between the edge of traveled way for the two opposing roadbeds. It is measured between the two crossroad ramp terminals. If this width varies between the terminals, then it is measured at the widest point. Exhibit A-3. Interchange geometric elements and features.
Safety Details A-7 An examination of the computed variance of the odds ratio indicated that (1) it is likely biased to a value that is smaller than the true value, and (2) it includes a large random variation. These issues stem from the use of a small number of years of before data at most of the sites. The Chi-Square distribution can be used to describe the distribution of standard deviation values. In the extreme, when there are only two samples of a populationâs standard deviation, it can be shown using the Chi-Square distribution that (1) the true standard deviation is likely to exceed the computed value in 68 of 100 samples and (2) the 90% confidence interval for an estimate of standard deviation is about 15 times the size of the computed standard deviation. For example, consider a site that has 3 years of before data. These data can be used to compute two odds ratio estimates. The standard deviation of these two estimates is computed as 0.10. Using the Chi-Square distribution, the 90% confidence interval of the standard deviation is 0.05 to 1.55, which is quite large. In fact, the range of the interval is 1.5 (=1.55 â 0.05), which is equal to 15 Ã 0.10. Moreover, there is 68% chance that the true standard deviation is larger than 0.10 (and 32% chance that it is 0.10 or less). With an increase in the sample size, the true value of the standard deviation approaches a 50th percentile representation, and the confidence interval decreases. In general, there would need to be five or more before-years of data at each site to obtain a reasonably reliable estimate of the variance of the odds ratio. The issue noted in the previous two paragraphs (i.e., variance of the odds ratio) has less impact on the CMF results if the analysis of the site-specific CMFs indicates that they can be combined to produce one CMF for all sites. When the data for all sites are combined, the variance of the odds ratio becomes negligibly small such that concerns about its reliability are more likely to be inconsequential. Hauer (1997, Chapter 10) describes the issues associated with variation in CMF values among sites. He also describes a procedure for combining the estimates across sites if the CMF variation is considered to be negligibly small (11). However, the variation in site- specific CMF values reported by Nye et al. (2019) for the interchange conversions is quite large, so the reliability of the variance of the odds ratio is a valid concern when a CMF is computed at the site-specific level (6). Based on the discussion in the previous paragraphs, the Volume-Corrected Method was used for this re-examination to compute the CMF values for each site. The calculations asso- ciated with this method are described by Hauer (1997, Chapter 8) (11). CMFs were computed for FI, PDO, and all severities combined (i.e., total crashes). The computed CMFs and the asso- ciated standard errors are listed in Exhibit A-4. A Chi-Square test of homogeneity was conducted to determine if the CMF values in Exhibit A-4 are sufficiently similar that their combined value could reasonably describe the change in safety at a typical interchange site. The calculations associated with this test are described by Griffin and Flowers (1997) (10). The calculations are also summarized in a paper by Kittelson and Associates, Inc. (2015) (8). The findings indicate that the hypothesis that the CMFs are equal can be rejected (p = 0.001); that is, there is sufficient evidence that the variation in CMF values is larger than can be explained by random variation. It is likely that there are design elements or features that vary among the conversion sites and are causing some of the variation in the computed CMF values. A.2.3 Modeling Approach This section describes the development of a model for predicting the CMF value as a function of a siteâs geometric elements and features. Separate models were developed to predict CMFs for FI crashes, PDO crashes, and all severity categories combined (i.e., total crashes).
A-8 Diverging Diamond Interchange Informational Guide No. CMF (Std. Error) for All Severities Combined CMF (Std. Error) for Fatal and Injury CMF (Std. Error) for Property Damage Only 2.034 (0.229) 1.590 (0.254) 2.151 (0.249) 1.177 (0.117) 0.767 (0.114) 1.291 (0.132) 0.623 (0.133) 0.726 (0.226) 0.562 (0.145) 0.629 (0.110) 0.543 (0.164) 0.659 (0.128) 0.746 (0.077) 0.527 (0.101) 0.788 (0.084) 0.645 (0.126) 0.823 (0.249) 0.558 (0.133) 0.376 (0.087) 0.320 (0.111) 0.410 (0.117) 0.408 (0.070) 0.442 (0.126) 0.391 (0.076) 0.617 (0.110) 0.824 (0.225) 0.520 (0.112) 1.042 (0.177) 0.783 (0.255) 1.107 (0.205) 0.515 (0.094) 0.294 (0.095) 0.620 (0.128) 0.974 (0.168) 0.679 (0.295) 1.013 (0.183) 0.741 (0.100) 0.740 (0.176) 0.738 (0.104) 0.472 (0.084) 0.349 (0.127) 0.506 (0.098) 0.449 (0.117) 0.365 (0.186) 0.461 (0.132) 0.368 (0.083) 0.307 (0.134) 0.382 (0.095) 0.646 (0.124) 0.405 (0.141) 0.746 (0.158) 0.371 (0.085) 0.277 (0.123) 0.397 (0.101) 0.821 (0.125) 0.727 (0.141) 0.926 (0.185) 0.843 (0.139) 0.549 (0.159) 0.994 (0.184) 1.871 (0.243) 1.268 (0.252) 2.188 (0.321) 0.498 (0.091) 0.268 (0.085) 0.667 (0.142) 1.940 (0.262) 1.071 (0.229) 2.431 (0.375) 0.729 (0.182) 0.462 (0.248) 0.813 (0.221) 0.438 (0.120) 0.341 (0.167) 0.477 (0.150) 1.113 (0.193) 0.770 (0.277) 1.198 (0.224) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 Exhibit A-4. Computed CMF values. The development of the CMF model form focused on the site-specific FI CMF values. There are two reasons for this focus. The first reason relates to the variation in crash reporting threshold between and within jurisdictions. An evaluation of PDO CMFs in the database indicated a wider variation in their value relative to that for the FI CMFs. This wider variation is likely to be the result of differences in the legal reporting threshold between jurisdictions and differences in the level of adherence to this threshold within jurisdictions. The wider variation in PDO CMFs can cloud the search for association between database variables and crash frequency. In contrast, FI crashes are more consistently reported among jurisdictions, and thus the FI CMFs provide a more reliable basis for model structure development. A second reason for focusing model development on the FI CMFs (as opposed to total crashes) is that developing models using total crashes may increase the potential for creating suboptimal
Safety Details A-9 formulations for the CMF functions. A suboptimal formulation will bias the model predictions at some factor levels. Recent research indicates that the underlying causal mechanisms for FI crashes can be different from those for PDO crashes. These important differences may be missed by the analyst when a CMF model is developed using total crashes. In contrast, they are more likely to be detected (and accounted for) when separate models are developed for FI crashes and for PDO crashes. Elvik (2011) discusses the potential for biased estimates and misleading conclu- sions when the wrong model form is calibrated (9). For this analysis, the FI CMF model was developed first, followed by the PDO CMF model. The minimal influence of reporting threshold variation on the FI CMF values ensured that this approach would provide an effective means of identifying those factors that have a true effect on safety. Once the FI CMF model was developed, the same model form was used in the development of the PDO CMF model. The retention of a variable in either the FI or PDO model was based on consideration of its regression coefficients and overall model fit [i.e., p-value, direction of effect, practical significance, Akaike information criterion (AIC) value]. As a result of this approach, the âFI CMF modelâ and âPDO CMF modelâ have a similar struc- ture and common variables. As a final step, the FI CMF model form was used as a starting point for the development of a total crash CMF model. The total crash CMF model was developed to provide a general indication of the relative change in overall safety associated with interchange conversion. The FI CMF model and the PDO CMF model are recommended for use when quantifying the change in safety associated with a proposed conversion at a specific location. A.2.4 Statistical Analysis Methods The nonlinear regression procedure (NLMIXED) in the software package SAS was used to estimate the proposed model coefficients. This procedure was used because it supports the examination of nonlinear model forms, the specification of the distribution of the dependent variable, and the assessment of fixed versus random effects for selected model variables. A maximum likelihood criterion was used in NLMIXED to quantify the regression model coefficients and variance scale parameter. The dependent variable of the regression model is the CMF, which is asymptotic to the lognormal distribution when the CMF is based on a large number of crashes (Griffin and Flowers, 1997) (10). For this application, the log-likelihood function for the lognormal distribution is described by the following equations: 1 2 ln ln 0.5 ln ln 2 2 ln Equation A-1 2 LL CMF CMF v w v w v w CMFi i i i i i i ( )( ) ( ) ( )= â +  + ï£ï£¬   + p +         with Equation A-2 2 w CMF s i i i = ï£ï£¬   where LLi = log likelihood for observation i; v = predicted variance scale parameter;
A-10 Diverging Diamond Interchange Informational Guide wi = weight of CMF observation i (from Equation A-2); CMFi = value of CMF observation i; CMFi = predicted value of the CMF for observation i; si = standard error of CMF observation i; and p = 3.14159 . . . When the weight of each CMF observation is defined using Equation A-2, the variance term v in Equation A-1 represents a scale parameter. Values of this parameter equal 1.0 when the variance in the CMFs is explained by their standard error. Values of this parameter that exceed 1.0 indicate the presence of additional variability in the CMF observations (i.e., beyond that explained by their standard error). Each observation in the regression database represents the CMF, its standard error, and selected geometric elements and features for one interchange conversion site. A.2.5 Model Fit Statistics The calibrated regression model can be evaluated using a Chi-Square analysis of the observed and predicted CMF values. The Chi-Square treatment and Chi-Square homogeneity statistics in Exhibit A-5 can be used for this purpose. The Chi-Square treatment is used to determine if the treatment affects crash frequency. The Chi-Square homogeneity is used to determine if the observed treatment effect varies from the predicted effect by an amount that is more than can be explained by just random variation (i.e., that some unexplained systematic influence is likely present such that the predicted effect may not accurately describe the treatment effect associated with each observation). To assess the level of treatment influence or homogeneity, the computed Chi-Square statistic is compared with the Chi-Square distribution for the specified degrees of freedom. If the computed Chi-Square statistic for treatment has a probability less than 0.05, then the null hypothesis that the treatment has no effect is rejected (i.e., the treatment is likely to have some effect on crash frequency). If the computed Chi-Square statistic for homogeneity is less than 0.05, then the null hypothesis that the CMF observations are equal is rejected (i.e., there is likely some unexplained systematic variation present). A useful measure of model fit is one that relates the residual error of the predicted value to the residual error associated with the use of an overall mean value. For normally distributed data with constant variance, the coefficient of determination R2 is commonly used for this purpose. This coefficient has a similar interpretation when the log transform of the dependent variable is normally distributed with constant variance. Under these conditions, the following equations can be used to describe model fit. Source Chi-Square Statistic Degrees of Freedom Treatment (i.e., model) p + 1 Homogeneity N â p â 1 Total N Note: p = number of regression coefficients in model; N = number of CMF observations; â1â for predicted variance scale parameter. Exhibit A-5. Chi-Square analysis of regression model.
Safety Details A-11 1.0 ln ln ln Equation A-32 2 2R w CMF CMF w CMF L t i i i i i â â ( ) [ ] ( ) ( ) = â â  â with ln Equation A-4L W CMF w i i i â â ( ) = where L _ is the weighted average value of the natural log of the CMF; and all other variables are previously defined. A.2.6 Predictive Model Form The general form of the CMF model is shown in the following equation. It is shown as a regression model with a calibration coefficient for each of several variables that describe selected geometric elements and features. CMF b b N b S b N N b N b I b Idrop l lanes a lanes b s b exp 30 1 0.5 Equation A-5 0 1 2 3 , , 4 , 5 18 6 9[ ]( ) ( )( )= + + â + â + â + + where CMF = predicted CMF value; Ndrop = number of crossroad lanes dropped at the entrance ramp; applies to the DDI design (total for both travel directions; = 0, 1, 2), lanes; Sl = speed limit for the crossroad through the DDI, mph; Nlanes,a = number of crossroad through lanes at the DDI (total for both travel directions), lanes; Nlanes,b = number of crossroad through lanes at the interchange before the conversion (total for both travel directions), lanes; Ns,b = number of signalized crossroad ramp terminals at the interchange before the conver- sion (= 0, 1, 2); I18 = indicator variable for site 18 (= 1 if site 18; 0 for other sites); I9 = indicator variable for site 9 (= 1 if site 9; 0 for other sites); and bi = calibration coefficient i. This model was estimated using the site-specific CMFs listed in Exhibit A-4. Separate versions of the model were estimated for FI CMFs, PDO CMFs and total-crash CMFs. The variables found to be correlated with CMF value are listed as variables in the model. Other variables were considered for inclusion in the model but were not retained because they were not statistically significant or the effect implied by the regression coefficient was not logical. Variables consid- ered included skew angle, median type, median width, number of curves per direction, area type, and stop-line-to-stop-line distance. At some DDIs, the outside lane of the crossroad is dropped at the entrance ramp (i.e., the outside crossroad lane becomes a turning roadway at the ramp and continues onto the ramp). The number-of-crossroad-lanes-dropped variable Ndrop is used to describe this characteristic. None of the interchanges present before conversion to the DDI were noted to have a crossroad lane drop. Hence, this variable also describes the change in ânumber of lanes droppedâ associated with the interchange conversion. The speed-limit variable Sl was obtained from Google Earth Street View. The Street View images are fairly current and coincide with the time period in which the DDI is present. Informa- tion about the crossroad speed limit before the conversion was not available.
A-12 Diverging Diamond Interchange Informational Guide The number-of-crossroad-through-lanes variable Nlanes describes the number of lanes on the crossroad that serve vehicles traveling as a through movement. Each through lane can be traced as a continuous traffic lane through the interchange (including both crossroad ramp terminals). The number-of-signalized-crossroad-ramp-terminals-at-the-interchange-before-the- conversion variable Ns,b describes the traffic control type at the existing interchange. After con- version to the DDI, both terminals are signalized at the interchanges studied. A.2.7 Model Calibration The results of the model estimation process for FI CMFs are presented in Exhibit A-6. The p-value for the homogeneity Chi-Square statistic is 0.114. This value is larger than 0.05, so the null hypothesis is not rejected (i.e., it is unlikely that there is any systematic variation in the CMFs that is not explained by the model). The coefficient of correlation for the log-transformed data Rt 2 is 0.69. This value indicates that the model explains about 69% of the variation in the data. The model coefficients are provided in the bottom half of Exhibit A-6. The t-statistics listed in the last column indicate a test of the hypothesis that the coefficient value is equal to 0.0. Those t-statistics with an absolute value larger than 2.0 indicate that the hypothesis can be rejected with the probability of error in this conclusion being less than 0.05. For the one variable in which the absolute value of the t-statistic is smaller than 2.0, it was decided that the variable was important to the model, and its trend was found to be logical and consistent with previous research findings (even if the specific value was not known with a great deal of certainty as applied to this database). The findings from an examination of the coefficient values and the corresponding CMF predictions are documented in a subsequent subsection. Indicator variables for sites 9 and 18 were included in the regression model. The coefficient for site 18 variable is statistically significant. Its value indicates that the CMF value at site 18 is about 88% smaller than that at the other sites, all other factors being the same. This result cannot be explained by differences in area type, median width, skew angle, and other factors in the Statistics Value Degrees of Freedom p-value Number of observations 26 N/A N/A Model Chi-Square 93.4 7 0.001 Homogeneity Chi-Square 26.6 19 0.114 0.69 N/A N/A Estimated Effect of... Variable Coefficient Value Standard Error t- statistic Intercept b0 -1.1529 0.166 -6.96 Crossroad lane drops at DDI (crossroad to ramp) b1 0.3988 0.0715 5.58 DDI speed limit b2 0.0619 0.0108 5.72 Changing the number of crossroad through lanes b3 -0.2224 0.0539 -4.13 Changing the traffic control type b4 0.1820 0.206 0.88 Site 18: I-85 and Poplar Tent Rd. b5 -1.4955 0.512 -2.93 Site 9: US-60 and S Kansas Expy. b6 0.00 Variance scale parameter v 0.9954 0.275 3.62 Exhibit A-6. Model estimation results for fatal-and-injury crashes.
Safety Details A-13 database. It is likely due to factors at site 18 that are different from the other jurisdictions and not represented in the database (e.g., signing, pavement condition, weather, or curve radius). The results of the model estimation process for PDO CMFs are presented in Exhibit A-7. The p-value for the homogeneity Chi-Square statistic is 0.001. This value is not larger than 0.05, so the null hypothesis is rejected (i.e., it is likely that there is some systematic variation in the CMFs that is not explained by the model). The coefficient of correlation for the log-transformed data Rt 2 is 0.68. This value indicates that the model explains about 68% of the variation in the data. The model coefficients are provided in the bottom half of Exhibit A-7. The t-statistics listed in the last column indicate a test of the hypothesis that the coefficient value is equal to 0.0. Those t-statistics with an absolute value larger than 2.0 indicate that the hypothesis can be rejected with the probability of error in this conclusion being less than 0.05. For the one variable where the absolute value of the t-statistic is smaller than 2.0, it was decided that the variable was important to the model, and its trend was found to be logical and consistent with previous research findings (even if the specific value was not known with a great deal of certainty as applied to this database). The findings from an examination of the coefficient values and the corresponding CMF predictions are documented in a subsequent subsection. Indicator variables for sites 9 and 18 were included in the regression model. The coefficient for each variable is statistically significant. Its value indicates that the CMF value at site 18 is about 85% smaller than that at the other sites, all other factors being the same. Similarly, the CMF value at site 9 is about 63% smaller than that at the other sites. These results cannot be explained by differences in area type, median width, skew angle, and other factors in the database. It is likely due to factors at sites 9 and 18 that are different from the other jurisdictions and not represented in the database (e.g., signing, pavement condition, weather, or curve radius). The results of the model estimation process for crashes of all severities combined are presented in Exhibit A-8. The p-value for the homogeneity Chi-Square statistic is 0.001. This Statistics Value Degrees of Freedom p-value Number of observations 26 Treatment Chi-Square 153 8 0.001 Homogeneity Chi-Square 78.2 18 0.001 0.68 Estimated Effect of... Variable Coefficient Value Standard Error t- statistic Intercept b0 -1.0437 0.190 -5.49 Crossroad lane drops at DDI (crossroad to ramp) b1 0.4176 0.0852 4.90 DDI speed limit b2 0.0800 0.0126 6.37 Changing the number of crossroad through lanes b3 -0.1558 0.0590 -2.64 Changing the traffic control type b4 0.3591 0.197 1.82 Site 18: I-85 and Poplar Tent Rd. b5 -1.8691 0.512 -3.65 Site 9: US-60 and S Kansas Expy. b6 -1.0045 0.378 -2.65 Variance scale parameter v 2.9144 0.805 3.62 Exhibit A-7. Model estimation results for PDO crashes.
A-14 Diverging Diamond Interchange Informational Guide Statistics Value Degrees of Freedom p-value Number of observations 26 Treatment Chi-Square 180 8 0.001 Homogeneity Chi-Square 83.0 18 0.001 0.68 Estimated Effect of... Variable Coefficient Value Standard Error t-statistic Intercept b0 -1.0919 0.174 -6.25 Crossroad lane drops at DDI (crossroad to ramp) b1 0.4257 0.0808 5.27 DDI speed limit b2 0.0748 0.0116 6.43 Changing the number of crossroad through lanes b3 -0.1564 0.0558 -2.81 Changing the traffic control type b4 0.3538 0.185 1.91 Site 18: I-85 and Poplar Tent Rd. b5 -1.8330 0.480 -3.82 Site 9: US-60 and S Kansas Expy. b6 -0.7336 0.327 -2.24 Variance scale parameter v 3.1097 0.860 3.61 Exhibit A-8. Model estimation results for crashes of all severities combined. value is not larger than 0.05, so the null hypothesis is rejected (i.e., it is likely that there is some systematic variation in the CMFs that is not explained by the model). The coefficient of correlation for the log-transformed data Rt 2 is 0.68. This value indicates that the model explains about 68% of the variation in the data. The model coefficients are provided in the bottom half of Exhibit A-8. The t-statistics listed in the last column indicate a test of the hypothesis that the coefficient value is equal to 0.0. Those t-statistics with an absolute value larger than 2.0 indicate that the hypothesis can be rejected with the probability of error in this conclusion being less than 0.05. For the one variable in which the absolute value of the t-statistic is smaller than 2.0, it was decided that the variable was important to the model, and its trend was found to be logical and consistent with previous research findings (even if the specific value was not known with a great deal of certainty as applied to this database). The findings from an examination of the coefficient values and the corresponding CMF predictions are documented in a subsequent subsection. Indicator variables for sites 9 and 18 were included in the regression model. The coefficient for each variable is statistically significant. Its value indicates that the CMF value at site 18 is about 84% smaller than that at the other sites, all other factors being the same. Similarly, the CMF value at site 9 is about 52% smaller than that at the other sites. These results cannot be explained by differences in area type, median width, skew angle, and other factors in the database. It is likely due to factors at sites 9 and 18 that are different from the other jurisdic- tions and not represented in the database (e.g., signing, pavement condition, weather, or curve radius). The fit of each model to the CMF data is shown in Exhibit A-9. This figure compares the predicted and reported crash frequency in the calibration database. The thick trend line shown represents a ây = xâ line. A data point would lie on this line if its predicted and reported crash frequencies were equal. The shorter thin line corresponds to a best-fit linear regression model. The fact that this line is very near to the ây = xâ line confirms the good fit of the predictive model (i.e., Equation A-5).
Safety Details A-15 a. CMF comparison for FI CMFs. b. CMF comparison for PDO CMFs. c. CMF comparison for total-crash CMFs. Exhibit A-9. Predicted versus reported CMFs. A.2.8 Sensitivity Analysis The coefficient values in the three preceding tables were used in Equation A-5 to compute the predicted CMF values by varying each of the equationâs input variables in isolation. The results are shown in Exhibit A-10. Exhibit A-10 is divided into four sectionsâone section for each of four input variables. The first section in the table lists the predicted CMF values when the number of crossroad through lanes is changed during the conversion. The values shown indicate that the addition of one through lane to the DDI reduces the FI CMF by 20%, the PDO CMF by 14%, and the total- crash CMF by 14%. This trend likely reflects the reduced density of traffic (i.e., increased vehicle spacing) as a result of the additional lane. This safety benefit from an increase in through lanes would likely be realized regardless of the form of interchange to which the location is converted. In fact, crashes would likely be reduced at the existing interchange if it were reconstructed to include additional crossroad through lanes. The second section of Exhibit A-10 lists the predicted CMF values based on the number of crossroad lane drops at the DDI. The values shown indicate that dropping one through lane at the entrance ramp increases the FI CMF by 49%, the PDO CMF by 52%, and the total-crash CMF by 53%. This trend is likely a reflection of the increased lane-changing activity associ- ated with a lane drop (especially a lane drop that occurs just after a horizontal curve).
A-16 Diverging Diamond Interchange Informational Guide Traffic Control Type before Conversion Crossroad Speed Limit, mph Change in Crossroad Through Lanes1 Crossroad Lane Drops2 CMF, FI CMF, PDO CMF, Total Change in crossroad through lanes Signal 30 2 0 0.20 0.26 0.25 Signal 30 1 0 0.25 0.30 0.29 Signal 30 0 0 0.32 0.35 0.34 Number of crossroad lane drops at DDI Signal 30 0 0 0.32 0.35 0.34 Signal 30 0 1 0.47 0.53 0.51 Signal 30 0 2 0.70 0.81 0.79 Conversion from specific traffic control type to signalized DDI3 Unsignalized 30 0 0 0.38 0.50 0.48 Signal 30 0 0 0.32 0.35 0.34 Crossroad speed limit Signal 25 0 0 0.23 0.24 0.23 Signal 30 0 0 0.32 0.35 0.34 Signal 35 0 0 0.43 0.53 0.49 Signal 40 0 0 0.59 0.78 0.71 Signal 45 0 0 0.80 1.17 1.03 Notes: 1. Number of through lanes at the DDI minus the number of through lanes at the interchange before conversion (i.e., = , â , ). Total of both travel directions. 2. At some DDIs, the outside lane of the crossroad is dropped at the entrance ramp (i.e., the outside crossroad lane becomes a turning roadway at the ramp and continues onto the ramp). The value in the table describes the number of lanes that are dropped at the DDI. Total of both travel directions. 3. Traffic control type listed in column 1 corresponds to that in service at both crossroad ramp terminals before conversion to DDI. If one terminal is signalized and the other is unsignalized, then use Equation A-5 with Ns,b = 1. Exhibit A-10. Single-factor sensitivity analysis. The third section of Exhibit A-10 lists the predicted CMF values based on a change in traffic control type as part of the conversion. The values shown indicate that converting from an unsignalized interchange to a signalized DDI increases the FI CMF by 20%, the PDO CMF by 43%, and the total-crash CMF by 42%. This trend is likely a reflection of the increase in crash rate (especially the less severe rear-end crash rate) when an unsignalized intersection is converted to signal control. This degradation in safety associated with the change in control type would likely be realized regardless of the form of interchange to which the location is converted. In fact, crashes would likely be increased at the existing interchange if its crossroad ramp terminals were converted from unsignalized to signalized control. The last section of Exhibit A-10 lists the predicted CMF values for various crossroad speed limits. The CMF values shown indicate that interchanges with a 5 mph higher speed limit are associated with FI CMF values that are larger by 27%, PDO CMF values larger by 33%, and total- crash CMF values larger by 31%.
Safety Details A-17 The CMFs in the last section of Exhibit A-10 describe the best estimate of the influence of DDI design on safety. It is noted that the total-crash CMF associated with a speed limit of 45 mph is greater than 1.0, which suggests that the conversion to a DDI with a 45-mph cross- road is likely to increase crash frequencyâmost notably, it will increase the PDO crash frequency. Fortunately, the FI crash frequency is likely to decrease for this speed limit. A.2.9 Summary This re-examination of the site-specific CMFs reported by Nye et al. (2019) led to the devel- opment of a CMF function for each of three severity categories (i.e., FI, PDO, and all severi- ties combined) (6). Each function included variables that quantified the change in CMF value associated with a change in key geometric features. The analysis results indicate that the conversion to DDI is often associated with a reduction in crashes; however, crash frequency may be increased for combinations of higher crossroad speed limit, one or more crossroad lanes dropped at the DDI, and the existing interchange having unsignalized terminals. The use of CMF functions was found to explain more than one-half of the systematic variability in the CMF values. However, it is believed that there is still some unexplained systematic variable in the predicted CMF values. Data for additional sites will help in this investigation by increasing the sample size. Also, some investigation of the AADT data provided by Nye et al. (6) indicates that there may be some correlation between the CMF value and traffic volume level. However, the crossroad AADT data for the before period and after period at each site will need to be obtained before this investigation can be undertaken. The total crash CMF model is offered to provide a general indication of the relative change in overall safety associated with interchange conversion. However, the FI CMF model and the PDO CMF model are recommended for use when quantifying the change in safety associated with a proposed conversion at a specific location. A.3 References 1. Chilukuri, V., S. Siromaskul, M. Trueblood, and T. Ryan (2011). Diverging Diamond Interchange Performance Evaluation (I-44 & Route 13). Report OR11.012. Organizational Results Research Report, Missouri Department of Transportation, February 2011. 2. Edara, P., C. Sun, B. R. Claros, and H. Brown (2015). Safety Evaluation of Diverging Diamond Interchanges in Missouri. Report cmr 15-006. Missouri Department of Transportation, January 2015. 3. Lloyd, H. (2016). A Comprehensive Safety Analysis of Diverging Diamond Interchanges. MS thesis. Utah State University, Logan, UT, 2016. 4. Claros, B., P. Edara, and C. Sun (2017). When driving on the left side is safe: Safety of the diverging diamond interchange ramp terminals. Accident Analysis & Prevention, Vol. 100, March 2017, pp. 133â142. 5. Nye, T. (2018). A National Safety Evaluation for Converting a Conventional Diamond Interchange to a Diverging Diamond Interchange. MS thesis. North Carolina State University, Raleigh, NC, 2018. Retrieved from https:// repository.lib.ncsu.edu/handle/1840.20/35368. 6. Nye, T., C. Cunningham, and E. Byrom (2019). National-Level Safety Evaluation of Diverging Diamond Interchanges. Transportation Research Record: Journal of the Transportation Research Board, No. 2673, Issue 7, July 2019, pp. 696â708. https://doi.org/10.1177%2F0361198119849589. 7. North Carolina Department of Transportation (2018). Traffic Volume Maps website. https://connect.ncdot.gov/ resources/State-Mapping/Pages/Traffic-Volume-Maps.aspx. Accessed on 10/26/2018. 8. Kittelson & Associates, Inc. (2015). âAppendix C - Procedure for Combining Multiple CMFs for a Common Treatment.â Developed for NCHRP Project 17-63: Guidance for the Development and Application of Crash Modification Factors. Retrieved from https://sites.google.com/site/jbreportsandtools2/home/reports/cmfs. 9. Elvik, R. (2011). Assessing Causality in Multivariate Accident Models. Accident Analysis and Prevention, Vol. 43, Issue 1, January 2011, pp. 253â264. 10. Griffin, L. and R. Flowers. (1997). A Discussion of Six Procedures for Evaluating Highway Safety Projects. Report No. FHWA-RD-99-040. Texas Transportation Institute, College Station, Texas. 11. Hauer, E. (1997). Observational Before-After Studies in Road Safety. Elsevier Science Inc., Tarrytown, NY.
Abbreviations and acronyms used without definitions in TRB publications: A4A Airlines for America AAAE American Association of Airport Executives AASHO American Association of State Highway Officials AASHTO American Association of State Highway and Transportation Officials ACIâNA Airports Council InternationalâNorth America ACRP Airport Cooperative Research Program ADA Americans with Disabilities Act APTA American Public Transportation Association ASCE American Society of Civil Engineers ASME American Society of Mechanical Engineers ASTM American Society for Testing and Materials ATA American Trucking Associations CTAA Community Transportation Association of America CTBSSP Commercial Truck and Bus Safety Synthesis Program DHS Department of Homeland Security DOE Department of Energy EPA Environmental Protection Agency FAA Federal Aviation Administration FAST Fixing Americaâs Surface Transportation Act (2015) FHWA Federal Highway Administration FMCSA Federal Motor Carrier Safety Administration FRA Federal Railroad Administration FTA Federal Transit Administration HMCRP Hazardous Materials Cooperative Research Program IEEE Institute of Electrical and Electronics Engineers ISTEA Intermodal Surface Transportation Efficiency Act of 1991 ITE Institute of Transportation Engineers MAP-21 Moving Ahead for Progress in the 21st Century Act (2012) NASA National Aeronautics and Space Administration NASAO National Association of State Aviation Officials NCFRP National Cooperative Freight Research Program NCHRP National Cooperative Highway Research Program NHTSA National Highway Traffic Safety Administration NTSB National Transportation Safety Board PHMSA Pipeline and Hazardous Materials Safety Administration RITA Research and Innovative Technology Administration SAE Society of Automotive Engineers SAFETEA-LU Safe, Accountable, Flexible, Efficient Transportation Equity Act: A Legacy for Users (2005) TCRP Transit Cooperative Research Program TDC Transit Development Corporation TEA-21 Transportation Equity Act for the 21st Century (1998) TRB Transportation Research Board TSA Transportation Security Administration U.S. DOT United States Department of Transportation
N O N -P R O F IT O R G . U .S . P O S TA G E P A ID C O LU M B IA , M D P E R M IT N O . 88 Transportation Research Board 500 Fifth Street, N W W ashington, D C 20001 AD D RESS SERVIC E REQ U ESTED ISBN 978-0-309-67369-3 9 7 8 0 3 0 9 6 7 3 6 9 3 9 0 0 0 0
