SAFETY EFFECTIVENESS OF VARIOUS TYPES OF SHOULDERS ON RURAL TWO-LANE ROADS IN WINTER AND NON-WINTER PERIODS

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1 SAFETY EFFECTIVENESS OF VARIOUS TYPES OF SHOULDERS ON RURAL TWO-LANE ROADS IN WINTER AND NON-WINTER PERIODS By Huanghui Zeng (Corresponding Author) Graduate Research Assistant University of Virginia CEE Department McCormick Road Charlottesville, Virginia 0- Phone: () - Fax: () - hzxm@virginia.edu Steven D. Schrock, Ph.D., P.E. Associate Professor University of Kansas CEAE Department 0 W. th Street Lawrence, Kansas 0-0 Phone: () - Fax: () - schrock@ku.edu Paper prepared for Transportation Research Board st Annual Meeting Transportation Research Board Washington, D.C. January, 0 Word Count Abstract: Body:, Tables: 0 =,000 Figures: 0 = 00 Total:, Submitted for Presentation and Subsequent Publication: August, 0 Resubmitted for Presentation and Subsequent Publication with Reviewer Comments Addressed: November, 0 TRB 0 Annual Meeting

2 Zeng and Schrock ABSTRACT There has been growing recognition of the quantitative effects of various roadway designs and traffic control strategies on safety. Meanwhile, there is increasing interest in measuring the variances of safety effectiveness in different periods of the year for similar roadway designs or similar traffic control strategies. This study tried to address the variances of safety effectiveness between the winter and nonwinter periods for the ten most common shoulder designs in Kansas. Traffic and geometric data were collected on,0 miles (0, km) of rural two-lane highways in Kansas. A cross-sectional approach was applied to develop winter period safety performance functions (SPFs), non-winter period SPFs and SPFs aggregated at an annual level in which shoulder designs were treated as independent variables. A variance test was conducted based on these SPFs to investigate the variances of safety effectiveness between the two different periods. It was found that wider and upgraded shoulders offer significant less safety benefit in reducing total crash number during winter periods than during non-winter periods. The indexes of safety effectiveness for the winter period are larger than those for the non-winter period by between to percent. However, winter weather appears not to significantly diminish wider and/or upgraded shoulders safety benefit in reducing crash severity and the number of shoulder related crashes. The results demonstrate that treating the winter and non-winter data equally is likely to bias a shoulder s estimated safety effectiveness in total crashes. TRB 0 Annual Meeting

3 Zeng and Schrock INTRODUCTION There has been growing recognition of the effects of various roadway designs and traffic control strategies on safety. Considerable research work over the last few decades have led to the publication of the Highway Safety Manual in 00, whose primary goal was to provide a science-based technical approach to quantitative safety analysis. Safety performance functions (SPF) and crash modification factor (CMF) are two important concepts to indicate safety effectiveness in the HSM. SPFs are statistical models used to predict crash frequency based on traffic and roadway condition data. They are developed from history crash, traffic and roadway condition data. A CMF is a multiplicative factor used to compute the expected number of crashes after implementing a given highway safety countermeasure at a specific location (). The development of CMFs is also based on history crash and traffic data, and SPFs are critical tools in the approach. It s speculated that both SPFs and CMFs will differ from each other among individual highway safety countermeasures and various jurisdictions. A better understanding of the variances in safety effectiveness in different periods of the year for same roadway designs or similar traffic control strategies is need. For example, an identical design of shoulders might not have identical safety impacts between winter and non-winter periods of the year because of very different weather conditions. According to American Association of State Highway and Transportation Officials (AASHTO) A Policy on Geometric Design of Highways and Streets, shoulders located adjacent to travel lanes accomplish several functions including emergency stop and pull off, a recovery area for driver error, and pavement edge support (). However, in winter shoulders may not function or not function fully for their designed purposes. For example, turf shoulders turn to dirt in winter; friction reduction is more prevalent in winter with snow; driver behavior is likely to be different due to the changes of visibility, vehicle performance, and other changes caused by winter weather. As a result, the reported data in the winter period may be in a different pattern than in the non-winter period. These differences are not shown directly in most crash, traffic and roadway condition databases, which are the primary data sources for highway safety study. For decades, researchers have been working to address the safety effectiveness for various types and widths of shoulders. Many SPFs and CMFs were developed at the national level and local level. Some of them were based on the annual crash and geometric data, while some of them were based on data in some periods of the year. Researchers need to consider carefully the seasonal variances in safety effectiveness when developing SPFs and CMFs, as SPFs and CMFs based on the annual data may be significantly different with those based on seasonal data if the variances are significant. A better understanding of the variances would also help to know whether it can result in robust CMFs if data were not available along the whole year but only available in some periods of the year. However, limited research is able to investigate the variances of safety effectiveness between the winter and non-winter periods. This study tried to investigate the variances of safety effectiveness of the ten most common shoulder designs between winter and non-winter periods. With the investigation, the authors also seek to address the impacts of using aggregated data versus using data from only the winter period or the nonwinter period. For this, traffic and geometric data were collected on,0 miles (0, km) of rural twolane roads consistent with winter weather periods in Kansas. Based on history climate data, winter period was defined from the th of October to the th of April in the next year in this study. LITERATURE REVIEW Shoulder safety effectiveness research and the safety impact of winter-weather have been studied for decades. However, limited research was able to investigate shoulder and winter-weather s interactive impacts on highway safety. This section will give a general introduction on research for safety impact of winter weather, followed by discussions about shoulder safety studies. According to the Federal Highway Administration (FHWA) report, U.S. Highway Crashes in Adverse Road Weather Conditions, crashes during winter weather occur more frequently in the Midwest than they do nationwide. Nationally, percent of weather-related crashes happen in winter, while it is TRB 0 Annual Meeting

4 Zeng and Schrock percent in the Midwest (). Previous studies usually focused on the impact of winter events (such as snow, ice, etc.) on crash risk. Several key findings were listed as below: Winter-weather affects traffic safety by increasing crash frequency but decreasing severity (-); This can be explained by the fact that the average speed under adverse weather is lower than during normal weather conditions, which typically decreases crash severity (, ); Crash risk is higher at the start of a winter season than it is at the end (). Although none of these studies focused directly on shoulders safety effectiveness in the winter period, their findings lead to an important question: whether shoulders with an identical design have the same safety effectiveness in winter and non-winter periods? A better understanding of this will aid researchers conducting future CMF-related research. The safety benefits gained from widening shoulders have been studied for more than 0 years. Some of these studies were reviewed by an expert panel for the Interactive Highway Safety Design Model (IHSDM) and have since been adopted by the Highway Safety Manual (HSM) (). Zegeer, et al. identified run-off-road and opposite-direction crashes as crashes that could be reduced from shoulder width improvement projects (). Information concerning geometry, crashes, and traffic volume was obtained for more than,000 miles (,0 km) of roads. Summary tables were created to compare the safety effects of shoulder width. It was found that a percent reduction in related crashes would be expected on roadways with ft (. m) wide shoulders when compared with roadways with no shoulder. This study also found a diminishing safety benefit for each additional increment of paved shoulder width when shoulders are wider than three ft (0. m). A later study by Zegeer, et al. determined that crash types such as run-off-road, head-on, and sideswipe (same direction and opposite direction) crashes were considered related crashes in that they could be mitigated through shoulder widening improvements (). The research data were collected on,0 miles (, km) of two-lane roadway in seven states, including detailed traffic, crash, roadway, and roadside data. This study applied statistical testing along with a crash prediction model to determine the expected crash reductions related to geometric improvements. It also conducted a before and after study on control sites for comparison. The effects of shoulder widening on related crashes was determined for paved and unpaved shoulders. Compared with the first study, the second study obtained a higher reduction rate in related crashes (up to 0 percent). These two studies were included in the expert panel evaluation in the IHSDM and have since been adopted for use in the HSM. Not all studies were in favor of wider shoulders. Hauer conducted a literature review regarding CMFs and SPFs on shoulder width in 000 (0). He also reanalyzed some data sets. Within this study, Hauer found that while a wider shoulder allows for the safe recovery of stray vehicles. However, he also identified some detrimental tendencies. These negative safety effects may include inviting some voluntary shoulder stops, faster travel, the possibility of steeper roadside slopes, and shoulder use for travel. Another study by Gross and Jovanis used case control and cohort methods to estimate the safety benefits of shoulder widening (). Data were obtained for about,000 two-lane rural undivided highway segments in Pennsylvania from to 00. Both methods indicated that crashes decreased as shoulder width increased. For example, in the case control approach it was found that widening shoulders from ft (0. m) to ft (. m) provided a CMF of 0., while the cohort approach provided a CMF of 0. for the same improvement. This study included confidence intervals to illustrate the certainty of the estimates. Gross, Jovanis, et al. evaluated the safety effectiveness of various lane-shoulder width configurations for fixed total paved widths as a countermeasure for roadway departure crashes in 00 (). This study applied a matched case-control analysis to geometric, traffic, and crash data in Pennsylvania and Washington. Crash reductions were found for wider paved widths, lanes, and shoulders. Specifically, a ft (. m) lane provides the optimal safety benefit for to ft (. to. m) total paved widths, while a ft (. m) lane is safest for a ft (0. m) total paved width. Both of them provide the optimal safety benefit for a ft (0. m) total paved width. In the first edition of the HSM, CMFs for paved, gravel, composite and turf shoulders from one foot to 0 ft (. m) were developed based on previous studies (). Two tables and several equations TRB 0 Annual Meeting

5 Zeng and Schrock were created to calculate CMFs with the information of AADT, shoulder type, and shoulder width. However, those composite shoulder CMFs only considered a situation in which half of the shoulder width was paved and the remainder was turf. In addition, the values of CMFs were determined simply by averaging those CMFs for paved shoulders and turf shoulders. In order to provide a viable alternative when a before-after study is impractical due to data restrictions, Gross and Donnell studied case-control and cross-sectional methods for estimating CMFs for fixed roadway lighting and the allocation of lane and shoulder widths (). Crash data over a five-year period were obtained from Pennsylvania to conduct this shoulder study. In this study, both shoulder width and additional shoulder width, which was the difference between the total shoulder width and paved shoulder width, were stated as test variables. It was found that providing at least four ft (. m) of unpaved shoulder beyond that which was paved produced a beneficial safety effect. Hallmark et al. applied a generalized linear model using a Poission distribution to investigate the relationship between crash reduction and paved shoulder implementation (). They analyzed 0 non-interstate roadway sections in Iowa from to 00. The results indicated that higher number of crashes occurred in the winter and fall than in the spring and summer. It also found that the presence of rumble strips, paved shoulder width, unpaved shoulder width, and the presence of a divided median correlated with a decrease in crashes. However, this study did not try to address the seasonal variances of shoulders safety benefits. Zeng and Schrock studied the safety effectiveness of composite shoulders on rural two-lane highways in Kansas using a combined Empirical Bayes (EB) method (). The studied composite shoulders were shoulders consist of three ft (0. m) of pavement with the remainder turf. Kansas-specific Safety Performance Functions and composite shoulder CMFs were develop based on crash, geometric and traffic data collected from. miles (. km) of rural two-lane highways. It was estimated that upgrading narrow unpaved shoulders to composite shoulders could reduce shoulder related crashes by up to percent and fatal and injury crashes by percent. METHODOLOGY Although observational before-after studies such as the EB method are recommended in quantitative safety analysis (, ), before-after data are not always available. In this case, a cross-sectional approach can be a useful alternative method as it does not require before-after data (, ). Cross-sectional approaches are often accomplished through multiple variable regression models. Many model forms have been recorded by Miaou (), Vogt and Bared () and the negative binomial specification has become the forerunner in crash count regression modeling. For this specific research, negative binomial regression models were applied to develop SPFs and index of safety effectiveness (ISE). An ISE indicates the expected safety effectiveness from a safety countermeasure. While the variance in the number of crashes at a site is equal to the mean in the Poisson distribution, it is greater than the mean under the negative binomial distribution. This phenomenon is known as overdispersion. The negative binomial model takes the form (): ( yi ) K K i y i K P( yi ) ( ) ( ) Equation K i K y i i! ( ) K Where: P(yi)= the probability of y i crashes observed at site number i; µ i =the mean number of crashes to be expected at site number i; and K= the overdispersion parameter. In order to represent overdispersion, a quadratic term is added to the variance as shown in Equation (). If K equals 0, the negative binomial reduces to the Poisson model. The greater the value of K, the more variability there is in the data over and above that associated with the mean. TRB 0 Annual Meeting

6 Zeng and Schrock Var i K( i ) Equation The vector of coefficients β and K are estimated by maximizing the log-likelihood function for the negative binomial distribution as shown in Equation (). yi L(, K) [( log( Kj)) log( Ky i j i ) yi log i ( yi )log( K i ) log( yi!)] 0 K Equation In practice, negative binomial regression models are estimated by statistical software such as SPSS, SAS, and STATA using information about traffic volume, crash record, and roadway features. A common model form for a roadway segment is indicated as follows: L AADT I x i jx j n ( SegmentLength) ( AADT ) e e Equation Where: n = expected crashes for a site; x i = crash risk factors that are treated as continuous variables; x j = crash risk factors that are treated as categorical variables; β L, β AADT, β i, β j = coefficients. Using the estimated coefficients from the model, index of safety effectiveness (ISE) can be inferred. ISEs represent the changes in expected crash frequency when the value of a variable is changed. For example, an ISE of 0.0 indicates that the safety countermeasure is able to reduce the crash frequency by 0 percent. For continuous variables, ISE function can be developed by the exponential function below. ISE exp( i xi ) Equation Where: x i = the changed value of the variable. For categorical variables, one variable that is most likely to be treated is set to be the reference group, and its coefficient is defaulted as 0. ISEs for other variables can be calculated based on their coefficients. Those ISEs are equal to values of exp(β j ). Coefficient test can be applied to identify the variance of safety effectiveness between two crash risk factors. The null and alternative hypothesis was stated as follows: H 0 : = β m β n = 0, or there are no difference between β m and β n. H A :, or there are differences between β m and β n. Where: β m, β n = coefficients for crash risk factor m and n. DATA COLLECTION Data were extracted by the Geometric and Accident Data Unit of Kansas Department of Transportation (KDOT). Two separated databases were used to obtain roadway characteristics and crash history information. The CANSYS database is the primary repository of roadway feature data at KDOT. In this database rural two-lane highways were broken into approximately,0 segments. Each segment contained information such as county name, route name and number, district, beginning and ending county milepost, segment length, AADT, shoulder type/width, lane width, and record year. Vehicle crash database included every reported individual crash record. For this study, all crash records on rural two-lane highways for the years were gathered. Individual crash records contain information such as crash date/time, number of fatalities/injuries, crash county milepost, intersection/non-intersection crash, crash type, etc. With the information from the vehicle crash database, crash history for every segment in the CANSYS database can be summarized. Specifically, the number of total crashes, the number of fatal and injury (FI) crashes, and the number of shoulder related crashes were summarized in every six months period (winter period and non-winter period) and annually from 00 to 00. TRB 0 Annual Meeting

7 Zeng and Schrock In order to develop a robust cross sectional analysis, several activities were taken to adjust the dataset. First, only segments with the ten most common shoulder designs were chosen to ensure that every studied shoulder design had an adequate sample size. Second, very short segments (less than 0.0 mile (0. km)) were excluded to avoid too many zero-crash segments in the dataset which may result in a zero-inflation problem. Very long segments (exceeding 0 miles (.0 km)) were also excluded with the consideration that they may bring many unexplained factors that cannot be captured by the model. Third, only segment crashes were included into the final dataset, meaning that intersection/interchange related crashes, parking lot crashes and other non-segment crashes were removed. Fourth, segments were excluded if they experienced major construction activities or alignment changes during the studied period. 0 Table summarizes the collected data information based on shoulder designs. TABLE Data Information Summary Shoulder Turf Shoulder Composite Shoulder A CS B Paved C Paved D Type Shoulder ft ft ft ft ft ft 0 ft 0 ft 0 ft 0 ft Sum Width Code E Average AADT,,,,,,, Average Length Miles, 0, 0 0,0 T-w F,,0,0,,,0, T-nw F, 0,0,, 0, FI-w F 0 0, FI-nw F 0 0 0, Re-w F,0 Re-nw F, A Composite shoulder type, first three ft (0. m) bituminous with remainder turf; B Composite shoulder type, first three ft (0. m) bituminous with remainder aggregate; C Paved shoulder type, bituminous base; D Paved shoulder type, Portland cement concrete shoulder; E Each code represents the specific shoulder design if it appears in Figure, Tables, and ; F T-w = total crashes in the winter period, T-nw = total crashes in the non-winter period, FI = fatal and injury crash, Re = related crash. 0 As shown in Table, the collected data covered,0 miles (0, km), approximately percent of the rural two-lane highways in Kansas. The three most common shoulder designs were -ft (0. m) turf shoulders, 0-ft (.00 m) type composite shoulders, and 0-ft (.00 m) bituminous based paved shoulders, and each of them were present on more than,000 miles (,0 km) of rural two-lane highways. It can also be found that segments with paved shoulders had the highest average AADT, while segments with turf shoulders had the least, and the average AADTs were increased with shoulder width among the same shoulder type. From 00 to 00 there were, crashes in winter period on the studied segments, account for. percent of all crashes. Approximately percent of fatal and injury crashes, and percent of shoulder related crashes occurred in the winter period. 0 CRASH COUNT REGRESSION MODELS For the purpose of this study, two special SPF models were built for each of the three crash types: total crashes, FI crashes, and related crashes. One was developed based on every half-year period (winter period and non-winter period) crash data, while the other was an aggregated model, based on annual crash TRB 0 Annual Meeting

8 Zeng and Schrock 0 data between 00 and 00. The half year SPF model resulted in two sets of ISE: one for the winter period, and one for the non-winter period. The aggregated model resulted in only one set of ISEs as it did not divided the data into winter data and non-winter data. Readers can have an in-depth understanding of the variance of ISEs between winter and non-winter periods via comparing these three sets of ISEs. Six variables, listed as below, were applied to create the crash count regression models. Lane width information were not included since very few segments had lane width other than -ft (. m). LogAADT: a continuous variable which is the natural logarithm of AADT. LogLength: a continuous variable which is the natural logarithm of segment length. District: a categorical variable which is the geographic division to which a segment belonged. It helped to capture the spatial variance throughout the state. Highway systems were divided into six geographic districts in Kansas (Figure ). Year: a categorical variable which indicated the record year of data. It helped to capture the time variance in the study period. Win: a dummy variable which indicated the data period. Its value was set to if the data were for winter period, and 0 if for non-winter period. ShouDes: Shoulder design, a categorical variable which indicated the shoulder information of a segment. It included the ten most common shoulder designs, with -ft turf shoulder as the reference group. 0 0 FIGURE Geographic districts in Kansas. The following equation indicates the half year model form. log( n ) Win log Length log AADT hy b b L District idistrict i Year jyear j AADT ab( ShouDes a * Winb ) Equation Where n hy is the predicted half year crash number in either the winter or non-winter period, α and β are coefficients for relevant variables. It is important to note that an interaction term between ShouDes and Win were included to address the safety effectiveness of various shoulder designs in different periods. Table displays the results of the half year crash count models, as well as their goodness of fit information. The three models have the expected positive coefficients for both LogAADT and LogLength. Coefficients for District are significant at the 0.0 level in all three models, which means that spatial variances did exist on rural two-lane highways in Kansas and should not be ignored. Statistically significant yearly differences were found in total crash model and related crash model, while they did not exist in FI crash model. Generally, yearly differences should be considered in the crash count models. The safety effectiveness of the ten shoulder designs can be indicated by coefficients of the interaction form. For each shoulder design a smaller coefficient represents greater safety effectiveness compared with the reference group. Compared with -ft turf shoulders, -ft turf shoulders, composite shoulders, and paved shoulders were found to be able to significantly reduce the total number of crashes, TRB 0 Annual Meeting

9 Zeng and Schrock the number of FI crashes, and the number of related crashes in the non-winter period at the 0.0 level. In the winter period, wider and/or upgraded shoulders were expected to significantly reduce the number of FI crashes and related crashes. However, most shoulder designs except paved shoulder and a -ft composite shoulder were not found to significantly reduce total crash numbers in the winter period. For paved shoulders, the safety benefits in reducing total crashes were less in the winter period. TRB 0 Annual Meeting

10 Zeng and Schrock TABLE Results for the Half-Year Crash Count Regression Models Total Crashes FI Crashes Related Crashes Variable Coefficient (Std. Error) Wald Chi-Square F Coefficient (Std. Error) Wald Chi-Square Coefficient (Std. Error) Wald Chi-Square Win= -. (0.).*** A -. (0.).*** -. (0.).*** Win=0 -. (0.).*** -. (0.).*** -. (0.).0*** LogAADT 0.0 (0.0).*** 0. (0.0).*** 0. (0.0) 0.*** LogLength 0. (0.0) 0.0***.0 (0.0).0*** 0. (0.0).*** District= -0. (0.0) 0.0*** -0. (0.0).*** -0. (0.0).0*** District= -0.0 (0.0) 0.*** -0. (0.0).0*** -0. (0.0).*** District= -0.0 (0.0). -0. (0.0).0** -0.0 (0.0). District= -0. (0.0) 0.*** -0. (0.0).*** -0. (0.0).*** District= -0.0 (0.0).*** -0. (0.0).*** -0. (0.0).*** District= 0 B B B Year= (0.0).*** 0.0 (0.0) (0.0) 0.0 Year= (0.0).** -0. (0.0).0* -0. (0.0).*** Year= (0.0) (0.0) (0.0).*** Year= (0.0) (0.0) (0.0).*** Year=00 0 B B B [0]*W G -0. (0.0).*** -0. (0.).0*** -0. (0.).*** [0]*W -0. (0.0).*** -0. (0.0).*** -0. (0.).*** [0]*W 0.0 (0.0). -0. (0.0).*** -0.0 (0.).*** [0]* W 0.0 (0.0) (0.0).*** -0. (0.).*** []*W (0.0) (0.) 0.*** -0.0 (0.).*** []*W -0. (0.0).*** -0. (0.).*** -0. (0.).** [0]*W -0.0 (0.0) (0.).*** -0. (0.).*** [0]*W 0.00 (0.0) (0.).*** -0. (0.).** [0]*W -0.0 (0.0) (0.0) (0.).0** [0]*W 0 B B B [0]*NW -0. (0.0).*** -0. (0.).*** -0.0 (0.).*** [0]*NW -0. (0.0).0*** -0. (0.0).0*** -0. (0.).*** [0]*NW -0. (0.0).*** -0.0 (0.0).*** -0. (0.).*** [0]* NW -0. (0.0).*** -0. (0.0).*** -0. (0.).*** []*NW -0. (0.0).** -0. (0.).*** -0. (0.).*** []*NW -0. (0.0). -0. (0.).*** -0. (0.).0*** [0]*NW -0. (0.0).0** -0. (0.).** -0. (0.).0** [0]*NW -0.0 (0.0).0-0. (0.).** -0. (0.).* [0]*NW -0.0(0.0) (0.0) (0.) 0. [0]*NW 0 B B B k 0. (0.0) 0. (0.) Log-likelihood ratio Chi-Square C,***,0***,*** AIC D,,,0 Pseudo R Square E A * indicates statistically significant at the 0. level; ** indicates statistically significant at the 0.0 level; and *** indicates statistically significant at the 0.0 level; B The coefficient was defaulted as 0 if the variable were treated as the reference group; C Given by SPSS, it compares the fitted model against the intercept-only model; D Akaike s Information Criterion (AIC), a small-is-better criterion () (0); E Pseudo R = -k/k max, where k max is the estimated overdispersion parameter in the intercept-only model () (); F Wald Chi-Square is the default test statistic for coefficients in negative binominal regression models in SPSS; G Shoulder design 0 (refer to Table for shoulder codes) in the winter period; NW, in the non-winter period. TRB 0 Annual Meeting

11 Zeng and Schrock 0 The aggregated models had a different form by removing Win variable. log( n) log Length log AADT L AADT District i District i Year jyear j ShouDes a a Equation Where n is the predicted annual crash number, α and β are coefficients for relevant variables. Table displays the results for the aggregated models and their goodness of fit information. It was found that the aggregated models shared similar coefficients and standard errors for all other variables except the ShouDes variable with the half year models. The coefficients for the ShouDes variable indicated the safety effectiveness of the studied shoulder designs at an annual crash period. TABLE Results for the Aggregated Crash Count Regression Models Total Crashes FI Crashes Related Crashes Variable Coefficient (Std. Error) Wald Chi-Square Coefficient (Std. Error) Wald Chi-Square Coefficient (Std. Error) Wald Chi-Square Intercept -. (0.).*** -. (0.).*** -. (0.).*** Log AADT 0. (0.0).*** 0. (0.0).*** 0. (0.0) 00.*** Log Length 0. (0.0).***.0 (0.0).*** 0. (0.0).*** District= -0. (0.0).*** -0. (0.0).0*** -0. (0.0).*** District= -0.0 (0.0).*** -0. (0.0).*** -0. (0.0).*** District= -0.0 (0.0). -0. (0.0).** -0.0 (0.0). District= -0. (0.0).*** -0. (0.0).*** -0. (0.0).*** District= -0.0 (0.0).** -0. (0.0).*** -0. (0.0).0*** District= Year= (0.0).0*** 0.0 (0.0). 0.0 (0.0) 0. Year= (0.0).0* -0. (0.0).* -0. (0.0).0*** Year= (0.0) (0.0) (0.0).*** Year= (0.0). -0.0(0.0) (0.0).*** Year= [0] -0. (0.0).*** -0. (0.).00*** -0. (0.).*** [0] -0. (0.0).0*** -0. (0.0).*** -0. (0.0).*** [0] -0.0 (0.0) (0.0).*** -0. (0.0).*** [0] -0.0 (0.0). -0. (0.0).*** -0. (0.0).*** [] -0.0 (0.0) (0.).*** -0. (0.).*** [] -0. (0.0).00*** -0. (0.).*** -0. (0.).*** [0] -0. (0.0).** -0. (0.).*** -0. (0.).*** [0] -0.0 (0.0) (0.0).0*** -0. (0.0).0*** [0] -0.0(0.0) (0.) (0.0).** [0] k 0. (0.0) 0. (0.0) 0. (0.0) Log-likelihood ratio Chi-Square,0***,***,0*** AIC,, 0,0 Pseudo R Square INDEX OF SAFETY EFFECTIVENESS AND VARIANCE TEST With the resulted coefficients, ISEs based on -ft turf shoulders were determined, which are displayed in Table. TRB 0 Annual Meeting

12 Zeng and Schrock TABLE ISEs and Their Confident Intervals (%) 0 0 A Bold values were significant at the 0.0 level. Unlike FI crash ISEs and related crash ISEs, a majority of total crash ISEs were not significant at the 0.0 level in the winter period. Although both types of paved shoulders (0 and 0) had significant total crash ISEs in the winter periods, the ISEs were higher than those in the non-winter period by percent and percent, respectively. Based on these results, it is reasonable to conclude that upgraded shoulders offer less safety benefits in reducing the total number of crashes in the winter period than they do in the non-winter period. In general, all significant ISEs are less than one, indicating that widening or upgrading -ft turf shoulders is expected to reduce the total number, FI crash number, and related crash number. Also, related crash ISEs are usually the smallest while total crash ISEs are the largest, showing that widening or upgrading shoulders has most reduction impacts in the number of related crashes, followed by the number of FI crashes. It was found that the values of aggregated ISEs were always between the values of winter period ISEs and non-winter period ISEs. As a result, the aggregated model may overestimate or underestimate the safety effectiveness in different period. Another important point is to test whether the variances of safety effectiveness are significant between the winter and non-winter periods. The structure of the half-year models provided an opportunity to conduct such tests. For each shoulder design, a new coefficient Ɵ was generated to conduct the test, and it indicated the difference between the coefficients of the shoulder design in winter period (β w ) and non-winter period (β nw ). The null and alternative hypothesis was stated as follows: H 0 : = β w β nw = 0, or there are no difference between β w and β nw. H A :, or there are differences between β w and β nw. SPSS was applied to estimate the value of Ɵ, as well as its significant statistics. Figure was created to give readers a visual impression about the variances of various shoulder designs safety effectiveness. Besides the estimated Ɵs and their significant statistics, Figure also shows both winter period and non-winter period ISEs, which were determined by coefficients in the half-year models. TRB 0 Annual Meeting

13 Zeng and Schrock ISE ISE ISE FIGURE ISEs and variance test results. TRB 0 Annual Meeting

14 Zeng and Schrock It was found that the studied shoulder designs variances of safety effectiveness between the winter and non-winter periods varied across crash types. Regarding the number of total crashes, most composite shoulders and paved shoulders provided significant less effectiveness at the 0.0 level in the winter period than in the non-winter period. However, regarding the number of FI crashes and related crashes, no statistically significant variances were found between the winter and non-winter periods throughout all studied shoulder designs. The results indicated that treating the winter and non-winter data equally is likely to bias the estimated effectiveness in total crash frequency while it may not have significant negative impacts on the estimated effectiveness in FI crash and related crash. CONCLUSIONS This study seek to address the variances of safety effectiveness between the winter and non-winter periods for the ten most common shoulder designs on rural two-lane highways in Kansas. Based on,0 miles (0, km) of Kansas highways, a cross-sectional analysis was applied to develop three types of index of safety effectiveness (ISE) for every shoulder design. The three types of ISEs included winter period ISEs, non-winter period ISEs, and ISEs aggregated at the annual level. It was found that widening or upgrading -ft (0. m) turf shoulders is expected to reduce the total number of crashes, the number of FI crashes, and the number of related crashes in most cases. In addition, the reduction effect is most significant in related crashes, followed by FI crashes. It illustrated that shoulder designs impacted related crashes and FI crashes more than non-related crashes and non-fi crashes. The results of this research demonstrate that researchers need to carefully treat the variance between different periods in a year when studying shoulder designs safety effectiveness. Based on the results, wider and upgraded shoulders do not offer as much safety benefit in reducing the total number of crashes during winter periods as they do during non-winter periods. The differences were significant, and the indexes of safety effectiveness for the winter period are larger than those for the non-winter period by between to percent. This may due to the changes of pavement and shoulder surface condition, driver behaviors, and other driving environment because of winter weather, which would result in impacts on crash risk. As a result, ignoring the variance by treating the winter period data and non-winter period data equally may cause overestimate or underestimate shoulder designs safety effectiveness in total crashes. However, different scenarios were found regarding with FI crashes and related crashes. Regarding FI crashes and related crashes, no statistically significant safety effectiveness variances were found between the winter and non-winter periods throughout all studied shoulder designs. This indicated that winter weather appears not to diminish wider and/or upgraded shoulder s safety benefits in reducing crash severity and the number of related crashes. Thus, treating the winter period data and non-winter period data equally may not have significant negative impacts on the estimated effectiveness in FI crash and related crash. This research helps to understand the variances between the winter and non-winter periods in the research of safety effectiveness estimation for geometric designs. A better understanding of the seasonal differences in safety performance of geometric designs aids researchers in addressing the impacts of applying seasonal data versus annual data when conducting future safety effectiveness-related research. ACKNOWLEDGEMENTS The authors thank Jonathan Marburger, Ruby Bradley, Matthew Soper, and Kyle Gonterwitz of KDOT for providing crash and roadway data for this study. TRB 0 Annual Meeting

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