Safety Impacts at Intersections on Curved Segments

Transcription

1 Safety Impacts at Intersections on Curved Segments Peter T. Savolainen Phone: Andrew P. Tarko Phone: Purdue University School of Civil Engineering 550 Stadium Mall Drive West Lafayette, IN Fax: Word Count: 4,473 words, 8 tables, 4 figures (7,473 words) Abstract: Indiana geometric design policy, consistent with national standards, allows for the design of intersections on superelevated curves if other solutions prove to be prohibitively expensive. Consequently, the Indiana Department of Transportation (INDOT) has built a number of such intersections. Following a series of fatal crashes at one of these intersections, INDOT made a decision to avoid designing intersections on segments with steep superelevation. This design restriction calls for expensive alternatives, such as realigning roads or adding grade separations. The purpose of this research is to determine whether or not superelevated intersections are truly more hazardous than similar intersections located on tangents, and, if so, to determine what combination of factors makes this true. The research focuses on two-way stop-controlled intersections where the mainline is a high-speed four-lane divided highway located on a superelevated curve. An attempt was made to analyze as many factors as possible using appropriate comparison techniques. Negative binomial models were developed to determine the statistical relationship between crash occurrence and intersection geometric characteristics, including curvature of the main road. Crash severity and the joint impacts of curvature with weather and lighting conditions were examined by using binomial comparisons of proportions. The findings of this study resulted in the development of a set of design recommendations for cases where an intersection is to be designed on a superelevated curve.

2 Savolainen and Tarko INTRODUCTION Designers have to deal with road intersections where one or both roads are located on superelevated curves. In such cases, the AASHTO Policy on Geometric Design of Highways and Streets () recommends, the alignment should be as straight and the gradient as flat as practical. This wording allows for designing intersections on curves if other solutions are deemed prohibitively expensive. The policy warns, however, This practice may have the disadvantage of adverse superelevation for turning vehicles and may need further study where curves have high superelevation rates and where the minor-road approach has adverse grades and a sight distance restriction due to grade line. In summary, locating intersections on curves is not forbidden but avoiding this where practical is recommended. Part V of the Indiana Design Manual () is consistent with the national standards and does not strictly forbid the design of intersections on curves. Consequently, the Indiana Department of Transportation (INDOT) has built a number of such intersections. Some of these intersections have raised safety concerns, most notably the intersection of US-3 and SR-4 in Rochester. Over a seven-year period beginning in 986, this intersection experienced, on average, over 4 crashes per year. Following a series of recurring fatal events, INDOT made the decision to close turning movements at this intersection. After the median treatment, the crash frequency has been reduced to fewer than two per year. Unfortunately, by restricting turning movements, many travelers are inconvenienced by having to alter their travel patterns. This design restriction calls for expensive alternatives, such as realigning roads or adding grade separations. In the Rochester case, a bridge to allow SR-4 trips to cross over the mainline is currently programmed for construction. Due to situations like the one in Rochester, INDOT currently avoids designing intersections on segments with a steep superelevation. The purpose of this research is to determine whether these superelevated intersections are truly more hazardous than similar intersections located on tangents, and, if so, to determine cost-effective methods of safety improvement. Past research has conclusively shown that horizontal curvature negatively impacts safety. Zeeger et al. found curvature to increase the crash rate by.5 to 4 times that of a similar tangent section (3). Shankar et al. (4) found increasing curvature to have a negative impact on safety in their study of rural freeway accidents. Hauer (5) found that for any given deflection angle, the design with the larger curve radius is always safer than a similar intersection with a smaller radius and the change in accidents is proportional to the change in radius length. High superelevation rates have also been shown to lead to increases in crash frequency according to Zegeer et al. (3). He concluded that improving the superelevation of curves below the AASTHO guidelines would yield an expected reduction of up to %. Further explanations of the relationship between curvature and safety are provided by McGee et al. (6) and Vogt and Bared (7). While the literature review provided several studies on the safety impact of curves, the effect of curvature in conjunction with other factors at intersections along four-lane divided highways has not been directly examined. This project examines two-way stop-controlled intersections where the mainline is a rural high-speed divided highway located on a superelevated curve. Intersections along two-lane state highways were also examined in an attempt to gain further insight on potential safety factors. An attempt was made to analyze as many factors as possible using appropriate comparison techniques. Negative binomial models were developed to determine the statistical relationship between crash occurrence and intersection geometric characteristics, including curvature of the main road. Crash severity and the joint impacts of curvature with environmental factors, such as weather and lighting, were examined by using binomial comparisons techniques DATA COLLECTION A sample of intersections located along four-lane divided high-speed rural highways throughout Indiana was selected using aerial photographs and state transportation maps. Through consultation with INDOT, it was established that all such intersections located on superelevated curves within the state were identified, as well as a group of comparable tangent intersections. This final sample consisted of 49 intersections. At each of these intersections, complete geometric data was measured in the field, with distances obtained using a measuring wheel and times measured with a stopwatch. While volumes for state roads were obtained from flow maps provided by

3 Savolainen and Tarko INDOT, traffic counts were completed for local and county roads where such figures were not readily available. Crash data was obtained for the years from the Indiana State Police crash database. SIGHT DISTANCE ANALYSIS A primary concern for the geometric design of intersections is to allow for adequate sight distance for vehicles attempting to enter or cross the major road. Extreme curvature and superelevation rates have been associated with reductions in sight distance. As such, the relationship between curvature and sight conditions was examined to determine possible effects on safety. Available sight distances were determined at each intersection in the sample by measuring the time- to-cross (TTC). The TTC is the travel time of a priority vehicle between the position it is seen first time by a driver on a minor approach and the collision point. Analyzing sign conditions in time domain is consistent with the current AASHTO standards (). The TTC values were then compared to the crossing time (CT) required. The crossing time measurement is similar to the time gap (t g ) in AASHTO (), which is the time required by a stopped vehicle to clear the major road. In this study, all intersections had a usable median. For that reason, the crossing time was defined to be the time required for a car to safely pass from the stop bar to the median. For modeling purposes, the marginal time to cross (MTTC) was defined as the time to cross minus the crossing time. Figures and illustrate the relationships between TTC, crossing time, and degree of curvature. All 49 intersections in the sample met this minimum sight distance requirement for traffic crossing to and from the median. As expected, the available gaps were shortest on the approach inside the curve and longest on the approach outside the curve with a few exceptions. Based on the results of these field measurements, reduced sight distances do not appear to be directly related to curvature. Furthermore, there was no clear pattern between sight distance and crash occurrence within the sample. This does not mean that sight distance is not an important safety factor; rather, it simply confirms that the sight distance provided in Indiana at intersections on a curve is sufficient. SPATIAL DISTRIBUTION OF CRASHES A summary of the number of crashes by type and subtype within the intersection sample is given in Table 8. The subtype denotes the approach upon which the involved vehicles were traveling. Among the crashes occurring at the intersections located on superelevated curves, one particular type of collision proved to be prevalent. The rightangle collision case for vehicles traveling from the median to the outside approach of the minor leg, as illustrated in Figure 4, had the highest number of crashes among the crash subtypes. Over 40% of the total crashes for the superelevated sample were of this subtype. It is not particularly clear what makes this type a greater crash risk than the others. One possible problem may be the intersection angle or skew of the intersection. Intersections skewed to the left (from the inside of the curve) tended to experience more crashes of this type. Although the results were not statistically significant, it should be noted that both the US-3/SR-4 intersection (the motivation for this study) and the SR-67/Centerton/Robb Hill Road (the location with the greatest number of crashes in the sample) are skewed significantly to the left. Further research on this issue may prove helpful in explaining why this type of crash is more prevalent. The zone with the second greatest number of crashes in the sample is also shown in Figure 4. Over 6% of the total crashes were right-angle crashes involving vehicles traveling from the outside approach of the minor leg to the median. It appears that vehicles traveling on the major approach on the outside of the curve are at the highest risk as they are involved in both of the two most frequent crash types. ANALYSIS OF GEOMETRIC FACTORS: NEGATIVE BINOMIAL REGRESSION Methodology In accident analysis, the consensus of contemporary empirical work is that Poisson and negative binomial regression count models are the most appropriate methodological techniques for frequency modeling. Selection of an appropriate model between the Poisson and the negative binomial is based upon the presence of overdispersion in

4 Savolainen and Tarko 3 the data. Overdispersion results when the variance of the predicted variable is greater than the mean, as is often the case in transportation safety analysis. If overdispersion exists, the negative binomial is the appropriate distribution. For modeling purposes, the negative binomial is preferred to the Poisson by the authors because exclusion of the overdispersion parameter, a as shown in Equations, 3 and 4, may lead to incorrectly specified parameters in the model. The variability otherwise explained by overdispersion will instead be incorrectly incorporated into other variables. Hauer et al. (8), Bonneson and McCoy (9), Bauer and Harwood (0), Poch and Mannering (), and Vogt and Bared (7) all used negative binomial models in their research on intersection safety. The negative binomial model is, ( ) P n = / ( / ) + n ) / ( / ) n! ( / ) + ( / ) + n, () where P(n ) is the probability of n accidents occurring at intersection i in time period j and is the expected value of n, E ( n ) = ( + ) = exp, () for an intersection i in time period j, is a vector of unknown regression coefficients that can be estimated by standard maximum likelihood methods (), is a vector of variables describing traffic volume and intersection geometry characteristics, and is a Gamma-distributed error term. The error term allows the variance to differ from the mean as, Var [ n ] E[ n ][ + E[ n ] = E[ n ] + E[ n ] =. (3) Model Development Traditionally, intersection crash frequency models express exposure in terms of the average annual daily traffic (AADT) for each of the intersecting roads as shown in Equation 4. C ( ) ( ) exp( ) AADT AADT =... N N where: C = expected number of crashes, AADT = average annual daily traffic on primary road, AADT = average annual daily traffic on secondary road,,, 0,,... n = constants,,,, N = explanatory variables. 0, (4) The model in Equation 4 was fit via negative binomial regression using LIMDEP 7.0 (3) with the collected data to establish that the only significant variables are volumes. Although the small number of intersections on curves present in the sample might be blamed for this result, an attempt was made to improve the model structure by improving the volume functions. Clearly, traffic volumes on each approach cannot be expected to have the same impact on all types of crashes. For example, the volume of traffic on the minor road is likely to have a significant influence on right-angle crashes, but not on single-vehicle crashes occurring on the major road. In order to improve the estimation of the effects of traffic volume, separate exposure functions were proposed for each of the six types of crashes. Table lists the types of crashes and the corresponding exposure functions. Each of the six crash frequency models has its own volume function, or exposure function E t, and a common exponential function that describes the impact of intersection characteristics on crash frequency. An improved model structure for a specific type of crash t is shown in Equation 5. 3

5 Savolainen and Tarko 4 C t ( ) = Et exp... N N t, (5) To be able to estimate all six models at once, the generalized model shown in Equation 6 has been calibrated. The sample size was six times larger than the original one due to the change in the dependent variable, which was no longer the total number of crashes but the number of crashes of type t. In the generalized model, binary variables b t takes value if the observation is for crash type t and 0 for other types of crashes. b t Ct = Et exp N N + tbt t t, (6) Each of the variables included in the modeling process is explained in Table 3. Summary statistics for each variable are given in Table 4. It should be noted that degree of curvature and superelevation variables have not been included together in the model due to the strong correlation between the two variables (r=0.64). The degree of curvature variable therefore represents the full curvature effect of both degree of curvature and superelevation. The total number of crashes at the intersection is estimated by adding the expected counts in each of the six crash categories. The model in Equation 5 and its equivalent version suitable for calibration in Equation 6 return crash frequency by crash type. Equation 7 calculates the frequency of all crashes by summing the frequencies of each individual crash type. To evaluate the type-specific model, comparisons were made between it and the traditional model of the form shown in Equation 4. The crash-type specific model was found to be superior over the traditional model, exhibiting both a higher r value and a substantially lower overdispersion parameter. The statistically significant overdispersion parameter indicates the appropriateness of the negative binomial over the Poisson model. Modeling results for the full model with all variables included (Equation 7) are shown in Table 5. The full model most accurately explains the effects of each individual variable in the model. As variables are removed, their effects are captured by other variables in the model. For this reason, the effects of curvature were determined from this model, rather than from a reduced model with the statistically insignificant variables removed. Using parameter estimates for the full model, the sensitivity of each variable was calculated to determine the practical significance of each variable. The sensitivity is the effect on crash frequency that occurs as a result of increasing a variable from its minimum to its maximum value with all other variables held constant at their average values as expressed in Equation 8. Two forms of the sensitivity equation are presented, the first for variable with a positive coefficient, the second for variable with a negative coefficient. As such, if the absolute value of the sensitivity term for a variable is equal to one, the variable has no effect in the model. The magnitude of the sensitivity value increases as the effect of the variable increases. Sensitivity values for all variables are shown in Table 6. For variables with positive coefficients: For variables with negative coefficients: where: C= expected number of crashes = parameter of interest, Y= set of all remaining parameters, b= explanatory variables. C =... t ( + + ) exp( t ) Et exp + N N, (7) C Sensitivity = C C Sensitivity = C ( max, Ymean ) max = ( min, Ymean ) min ( min, Ymean ) min = ( max, Ymean ) max (8) 4

6 Savolainen and Tarko 5 While the focus of the research was on investigating impacts and crash prediction, a reduced model was also developed and is presented for the sake of completeness as Equation 9. Model statistics are included in Table 7. This model can be used to predict the total number of crashes at unsignalized intersections located on four-lane rural segments with curves. By removing statistically insignificant variables, fewer variables are necessary as inputs. However, the explanatory power of this model is less than that of the full model AADT AADT AADT AADT AADT C = AADT exp( 0.4 D SR FLASHER +.45 MED LT +.09 SPDLIMIT CREST 0.59 RT 6.70) (9) The Effect of Curvature The modeling results show curvature to have both statistical and practical significance. As the degree of curvature (D) is increased from zero to the maximum value in the sample of 3., crashes were found to increase by over 300%. These results are comparable to the results of Zeeger s study of roadway sections. It appears that curvature may lead to similar increases in crash frequency for both road segments and intersections. The results of the sensitivity analysis were used to determine critical design values for curvature and superelevation in consultation with the Indiana Department of Transportation. The maximum recommended and allowable design values for degree of curvature are shown in Figure 3. The maximum recommended design value for degree of curvature is. degrees per 00 foot chord length (Radius, R, =5300 ft). Designing an intersection at this D value may lead to an increase in crashes of up to 50% in comparison to a tangent intersection. If designing to such a curvature proves to be prohibitively expensive, D may be increased to the minimum allowable design value of.6 (R=3500 ft), creating an increase in crash frequency of up to 90%. An alternative solution to the problem would be to restrict turning movements at the median, similar to the treatment done for the US-3/SR-4 intersection mentioned previously. To accommodate travelers, a superstreet design may be added, allowing for U-turns and minimizing the amount of lost time. The Effect of Other Variables As expected, traffic volume plays a significant role in crash occurrence. Crash frequency increases significantly as the volume is increased on each road and these increases vary by crash type as the exposure function coefficients show. While not all exposure terms were found to be significant, this is likely a function of the limited number of crashes of a particular type. The minor road AADT was shown to have a stronger effect on crash frequency than the major road AADT. However, this result has little impact on design as traffic levels cannot be controlled through the design process. While sight distance, in terms of the marginal time-to-cross, was not found to be significant, there appeared to be several sight-related problems. Sight restriction is a possible cause of the increase in crashes associated with left-turn lanes. The view of oncoming traffic from the median may be obstructed by vehicles in the auxiliary lane. Conversely, right-turn lanes tend to significantly decrease the number of crashes occurring at an intersection. When no right-turn lanes are present, several problems are possible. Stopped vehicles may not know whether oncoming traffic will turn or continue past the intersection. Additionally, traffic behind right-turning vehicles may be surprised by sudden deceleration prior to exiting the major road. Crest vertical curvature was also found to increase crash occurrence. Driver perception may again be an issue, particularly for vehicles attempting to cross from the minor roads. The model shows crashes to decrease, in general, as median width is increased. However, excessively wide medians (wider than 60 feet) show an increase in crash frequency within the sample. Only three intersections in the sample had medians of such widths, making it difficult to determine the true effects of this design element. 5

7 Savolainen and Tarko 6 ANALYSIS OF ENVIRONMENTAL FACTORS: BINOMIAL COMPARISON The relationship between curvature and a number of variables could not be determined directly from the crash frequency models. These variables include crash type, crash severity, lighting, and weather conditions at the time of each crash. By comparing two samples, one with intersections located on curves and another with intersections located on tangents, inferences can be made about the effects of curvature based on the difference in crash proportions between the two samples. Methodology A statistical test is performed using the binomial distribution. It uses an estimate of the true proportion of crashes occurring at intersections on curves: s C C + T where C = the total number of crashes at intersections located on curves T = the total number of crashes at intersections located on tangents. = (0) The value of s estimates the proportion of the total number of crashes in the sample that occur on curves. Let s k be the proportion of crashes of k category (night, right-angle, injuries, etc.) in the sample that occur on curves. Statistical evidence of s k > s indicates that this category of crashes is overrepresented on curves which may be interpreted as the joint effect of the curve and the condition represented by category k. The test assumes that and it calculates the binomial likelihood, P( ), given the number of trials, ( C + ) C k k T k s k = s, likelihood of success s, and the number of successes C k. If the likelihood is smaller than the level of significance f, then the category k is underrepresented, implying that the true likelihood of success s k is lower than s. Similarly, if the likelihood is larger than -f, then the category is overrepresented. A threshold f-value of 0.0 was used for this analysis. The Indiana crash database was used to obtain crash information for 507 intersections along four-lane divided highways. The,6 crashes occurring at these intersections were separated into two groups. The first group consisted of the 44 crashes occurring at the intersections located on curves. The second group consisted of the,378 crashes occurring at the tangent intersections along the same divided four-lane highways over the same time period. Among the information collected were crash severity, crash type, lighting conditions, and weather conditions at the time of each crash. Proportionally, 5.04% of the total crashes in the sample occurred within the sample located on curves (s=0.50). If a significantly larger proportion of the crashes occurred under certain conditions within the road sample, it can be claimed that the combination of that condition and curvature tends to make intersections more hazardous. Table 8 provides details of the binomial comparisons for crash type, crash severity, lighting conditions, and weather conditions. The table displays the total number of crashes within each sample, as well as the proportion of total crashes occurring on curves under various conditions. Likelihood values are also displayed, along with the conclusion of whether or not the crash category is overrepresented on curves, underrepresented, or neither. Crash Type Right-angle and single-vehicle crashes were shown to be overrepresented at the intersections located on curves. There are several possible explanations for the increase in right-angle crashes. Vehicles entering the divided highway from the minor road may have difficulty perceiving the speed of oncoming vehicles due to the presence of curvature. Similarly, drivers on the major road may have difficult viewing traffic entering from the minor road along curves. As for single-vehicle collisions, the increased difficulty of maneuvering on curves is a possible explanation for the increase in crashes. Additionally, drivers may not perceive these curved sections to be more hazardous and, consequently, this fact may compound the problem of decreased maneuverability. Crash Severity The severity of a crash is typically measured as the level of injury sustained by the most severely injured vehicle occupant. In Indiana, crash severity is classified as either property damage only (PDO), injury (I), or fatality (F). 6

8 Savolainen and Tarko 7 For analysis purposes, a severe crash was defined as any collision in which an injury or fatality occurred. The binomial comparison shows the intersections located on curves to experience a greater proportion of severe crashes than the intersections in the tangent sample. The right-angle and single-vehicle crash types are again shown to be overrepresented in terms of proportion of severe crashes. Night Conditions In the case of nighttime crashes, over % of the total crashes occurred within the sample of intersections located on curves. The combination of curvature and darkness appears to make intersections particularly susceptible to crashes. Of the four possible collision types, the right-angle crashes were the only individual type to be overrepresented. However, single-vehicle collisions missed the significance threshold by only In the case of right-angle collisions, it is possible that the intersection is not illuminated well enough for drivers to be able to spot each other. Consequently, vehicles may attempt crossing the major road without a sufficient gap between vehicles. In the single-vehicle case, drivers simply may not be able to properly read the curve as they are approaching the intersection. Lack of sufficient lighting is again a likely cause of this problem. Based on these findings, it was recommended that lighting installation be considered in cases where an intersection is located on a superelevated curve. Weather Effects The number of crashes occurring under adverse weather conditions was examined between the two samples to see if the combination of curvature and rain or snow had an effect on crash occurrences. The results of the binomial comparison showed the sample of intersections on curves to be underrepresented. The tangent sample experienced.% of its crashes during rain events and 4.6% during snow events. Conversely, the intersections on curves experienced only 3.3% and.% for the two cases, respectively. Proportionally, less than 5% of the total crashes during rain and snow events occurred within the curve sample, which was about one-third of the number expected. Intuitively, one would expect the opposite to be true. This result is possibly due to changes in driver behavior under adverse weather conditions. As weather conditions worsen, drivers may begin to drive more cautiously than under normal weather conditions. When traveling along curves, drivers may tend to drive more slowly if the roads are wet or icy. Such results do not translate into the intersection itself being safer. It is more likely indicating that drivers perceive the intersection as less safe and, consequently, they are driving more cautiously. SUMMARY OF FINDINGS In summary, the most important findings and recommendations for designers and safety managers from this study are as follows.. Crashes were found to increase in both frequency and severity at intersections where the four-lane major road was on a superelevated curve. Maximum curvature was found to increase crashes by over 300% compared to tangent intersections. Based on this finding, and in coordination with INDOT, maximum design values were determined for degree of curvature, curve radius, and superelevation. A minimum design value for a curve radius of 5300 feet (degree of curvature=.) is recommended when intersections are to be located on curves. In cases where such a design value is prohibitively expensive, a radius as small as 3500 feet (degree of curvature=.6) is allowable. A maximum design value of 3% was recommended for superelevation, except for cases where using such a design value is prohibitively expensive, then a maximum design value of 4% is allowable. These values were determined by running a regression between degree of curvature and superelevation for the data collected at the sample intersections.. Intersections on curves experience a higher percentage of right-angle and single-vehicle crashes. Possible causes for this are that drivers are having difficulty negotiating the curve or drivers entering the divided highway from the minor road are misperceiving the speed or location of oncoming vehicles. 3. In comparison to tangent intersections, the intersections on curves experienced a higher proportion of crashes during night conditions. It is recommended that lighting installation be considered in cases where an intersection is located on a curve, particularly where severe superelevation is present. 7

9 Savolainen and Tarko 8 4. Curvature was not a cause of sight distance problems for the intersections in the sample. Furthermore, there was no evidence of a pattern between sight distance and crash frequency. This serves as further evidence that the design sight distance criteria in the Indiana Design Manual is acceptable. ACKNOWLEDGEMENTS This work was supported by the Joint Transportation Research Program administered by the Indiana Department of Transportation and Purdue University. The contents of this paper reflect the views of the authors, who are responsible for the facts and the accuracy of the data presented herein, and do not necessarily reflect the official views or policies of the Federal Highway Administration and the Indiana Department of Transportation, nor do the contents constitute a standard, specification, or regulation. REFERENCES. American Association of State Highway and Transportation Officials, A Policy on Geometric Design of Highways and Intersections, Washington, D.C., 00.. Indiana Department of Transportation, Indiana Design Manual, Part V, Indianapolis, IN, Zegeer, C.V., J.R. Stewart, F.M. Council, D.W. Reinfurt, and E. Hamilton, Safety Effects of Geometric Improvements on Horizontal Curves, Transportation Research Record 356, Shankar, V., F. Mannering, and W. Barfield, Effect of Roadway Geometrics and Environmental Factors on Rural Freeway Accident Frequencies, Accident Analysis and Prevention 7 (3): , Hauer, E., Observational Before-After Studies in Road Safety, Permagon Press, Elsevier Science Ltd., Oxford, England, McGee, H.W., W.E. Hughes, and K. Daily, Effect of Highway Standards on Safety, National Cooperative Highway Research Program Report 374, Transportation Research Board, National Research Council, National Academy Press, Washington, D.C., Vogt, A. and J.G. Bared, Accident Models for Two-Lane Rural Roads: Segments and Intersections, Report No. FHWA-RD-98-33, Federal Highway Administration, McLean, Va., Hauer, E., J.C.N. Ng, and J. Lovell, Estimation of Safety at Signalized Intersections, Transportation Research Record 85: 48-6, Bonneson, J.A. and P.T. McCoy, Estimation of Safety at Two-Way Stop-Controlled Intersections on Rural Highways, Transportation Research Record 40: 83-89, Bauer, K.M. and D. Harwood, Statistical Models of At-Grade Intersection Accidents, Report No. FHWA-RD- 96-5, Federal Highway Administration, McLean, Va., Poch, M. and F. Mannering, Negative Binomial Analysis of Intersection-Accident Frequencies, Journal of Transportation Engineering (): 05-3, Greene, W.H., Econometric Analysis, 5 th Edition, Prentice Hall, New York, Greene, W.H., LIMDEP, Version 7.0, Econometric Software,

10 Savolainen and Tarko 9 List of Tables and Figures Table Crash Statistics by Type...0 Table Crash Type-Specific Exposure Terms... Table 3 Variable Descriptions... Table 4 Descriptive Statistics for Variables...3 Table 5 Crash Frequency Model (All Variables)...4 Table 6 Crash Frequency Model Sensitivity...5 Table 7 Crash Frequency Model (Statistically Significant Variables)...6 Table 8 Binomial Comparison of Proportions...7 Figure Time To Cross vs. Degree of Curvature for Inside Approach...8 Figure Most Frequent Crashes Types...9 Figure 3 Design Recommendations for Curvature...0 Figure 4 Time To Cross vs. Degree of Curvature for Outside Approach... 9

11 Savolainen and Tarko 0 Table Crash Statistics by Type Type Acronym Subtype # of Crashes By Subtype # of Crashes By Type Primary Outside-Secondary Outside 4 Right-Angle A Primary Outside-Secondary Inside 04 Primary Inside-Secondary Inside 88 Primary Inside-Secondary Outside 0 Single-Vehicle on Primary Outside 5 S Major Road Primary Inside 7 Single-Vehicle on Secondary Outside S Minor Road Secondary Inside 0 Rear-End on Primary Outside 8 R Major Road Primary Inside 4 Rear-End on Secondary Outside R Minor Road Secondary Inside 9 Median-Opposing M Secondary Outside-Secondary Inside 8 8 Total 58 0

12 Savolainen and Tarko Table Crash Type-Specific Exposure Terms Collision Type Type Indicator Exposure Term Right-Angle Rear-End on Major R Road Rear-End on Minor R Road Single-Vehicle on S Major Road Single-Vehicle on S Minor Road Median-Opposing between Minor Road Traffic A AADT A AADT A AADT R AADT R AADT S AADT S M ( ) AADT M

13 Savolainen and Tarko Variable Name ONE AADT Constant Term Table 3 Variable Descriptions Variable Definition Average Annual Daily Traffic on Major Road (vehicles per day) AADT Average Annual Daily Traffic on Minor Road (vehicles per day) SPDLIMIT Posted speed limit on major road ( 0 = 50 mph, = 55 mph ) SR Minor road is state route ( 0 = no, = yes ) CREST Intersection located on crest vertical curve ( 0 = no, = yes ) CHAN Channelization is present ( 0 = no, = yes ) PLW Lane width on major road (ft) ML Multi-lane approach on minor road ( 0 = no, = yes ) PSW Shoulder width on major road (ft) SSW Shoulder width on minor road (ft) RT Right-turn lane present ( 0 = no, = yes ) LT Left-turn lane present ( 0 = no, = yes ) D Degree of curvature (degrees per 00-ft chord length) LEG Three-legged intersection ( 0 = no, = yes) MED Median width greater than 40 ft ( 0 = no, = yes ) MED3 Median width greater than 60 ft ( 0 = no, = yes ) FLASHER Flashing beacon installed ( 0 = no, = yes ) SKEWLEFT Intersection angle to the left measured from inside minor approach (degrees) SKEWRIGHT Intersection angle to the right measured from inside minor approach (degrees) MTTCINV Inverse of marginal time to cross (/sec) b S Single-vehicle collision type on major road ( 0 = no, = yes ) b S Single-vehicle collision type on minor road ( 0 = no, = yes ) b R Rear-end collision type on major road ( 0 = no, = yes ) b R Rear-end collision type on minor road ( 0 = no, = yes ) b M Median-opposing collision type ( 0 = no, = yes ) ALPHA Overdispersion parameter

14 Savolainen and Tarko 3 Table 4 Descriptive Statistics for Variables Continuous Variables Variable Name (Units) Min Mean Max Std.Dev. AADT (veh/day) AADT (veh/day) PLW (ft) PSW (ft) SSW (ft) D ( o per 00-ft chord length) SKEWLEFT (degrees) SKEWRIGHT (degrees) MTACINV (sec - ) Binary Variables Variable Name Variable Definition = 0 = SPDLIMIT Posted speed limit on major road ( 0 = 50 mph, = 55 mph ) 47 SR Minor road is state route ( 0 = no, = yes ) 38 CREST Intersection located on crest vertical curve ( 0 = no, = yes ) 45 4 CHAN Channelization is present ( 0 = no, = yes ) 43 6 ML Multi-lane approach on minor road ( 0 = no, = yes ) 45 4 RT Right-turn lane present ( 0 = no, = yes ) 0 39 LT Left-turn lane present ( 0 = no, = yes ) 4 35 LEG Three-legged intersection ( 0 = no, = yes) 34 5 MED Median width greater than 40 ft ( 0 = no, = yes ) 34 5 MED3 Median width greater than 60 ft ( 0 = no, = yes ) 46 3 FLASHER Flashing beacon installed ( 0 = no, = yes )

15 Savolainen and Tarko 4 Table 5 Crash Frequency Model (All Variables) = 0.06 Parameter Parameter Estimate Standard Error P-value ONE A A S S R R M SPDLIMIT SR CREST CHAN PLW ML PSW SSW RT LT D LEG MED MED FLASHER SKEWLEFT SKEWRIGHT MTTCINV b S b S b R b R b M ALPHA

16 Savolainen and Tarko 5 Table 6 Crash Frequency Model Sensitivity Variable Coeff. Std.Err. P-value Min Mean Max Sensitivity MED D LT CREST SPDLIMIT FLASHER SR LEG SSW PLW CHAN SKEWLEFT MED ML SKEWRIGHT MTTCINV RT PSW

17 Savolainen and Tarko 6 Table 7 Crash Frequency Model (Statistically Significant Variables) = 0.03 Parameter Parameter Estimate Standard Error P-value ONE A A S R R M SPDLIMIT CHAN RT LT D MED FLASHER b R ALPHA

18 Savolainen and Tarko 7 Table 8 Binomial Comparison of Proportions Crashes by Type Number of Crashes Proportion Crash Type Tangent Curve on Curve Likelihood Conclusion Right-Angle %.000 Overrepresented Rear-End % Underrepresented Sideswipe % 0.00 Underrepresented Single-Vehicle % Overrepresented Total % Reference Value Injury Crashes Number of Crashes Proportion Crash Type Tangent Curve on Curve Likelihood Conclusion Right-Angle % Overrepresented Rear-End 8 7.9% Underrepresented Sideswipe % 0.88 Uncertain Single-Vehicle % Overrepresented Total % 0.94 Overrepresented Crashes Under Dark Conditions Number of Crashes Proportion Crash Type Tangent Curve on Curve Likelihood Conclusion Right-Angle %.000 Overrepresented Rear-End % Uncertain Sideswipe % 0.39 Uncertain Single-Vehicle % Uncertain Total % Overrepresented Crashes Under Rain Conditions Number of Crashes Proportion Crash Type Tangent Curve on Curve Likelihood Conclusion Right-Angle % Underrepresented Rear-End 55.79% 0.00 Underrepresented Sideswipe % 0.0 Uncertain Single-Vehicle % Underrepresented Total % Underrepresented Crashes Under Snow Conditions Number of Crashes Proportion Crash Type Tangent Curve on Curve Likelihood Conclusion Right-Angle % 0.08 Underrepresented Rear-End % Underrepresented Sideswipe % Uncertain Single-Vehicle % Uncertain Total % Underrepresented 7

19 Savolainen and Tarko 8 Time To Cross vs Degree of Curvature (From Inside Approach to Median) Time To Cross (sec) Range of Crossing Times Degree of Curvature (degrees per 00-ft chord length) Time To Cross vs Degree of Curvature (From Median to Inside Approach) Time To Cross (sec) Range of Crossing Times Degree of Curvature (degrees per 00-ft chord length) Figure Time To Cross vs. Degree of Curvature for Inside Approach 8

20 Savolainen and Tarko 9 Figure Most Frequent Crashes Types 9

21 Savolainen and Tarko Maximum Allowable Design Value.5 Maximum Recommended Design Value Crash Modification Factor Degree of Curvature (degrees per 00-ft chord length) Figure 3 Design Recommendations for Curvature 0

22 Savolainen and Tarko Time To Cross vs Degree of Curvature (From Outside Approach to Median) Time To Cross (sec) Range of Crossing Times Degree of Curvature (degrees per 00-ft chord length) Time To Cross vs Degree of Curvature (From Median to Outside Approach) Time To Cross (sec) Range of Crossing Times Degree of Curvature (degrees per 00-ft chord length) Figure 4 Time To Cross vs. Degree of Curvature for Outside Approach