ACCIDENT MODIFICATION FACTORS FOR MEDIANS ON FREEWAYS AND MULTILANE RURAL HIGHWAYS IN TEXAS

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1 Fitzpatrick, Lord, Park ACCIDENT MODIFICATION FACTORS FOR MEDIANS ON FREEWAYS AND MULTILANE RURAL HIGHWAYS IN TEXAS Kay Fitzpatrick Senior Research Engineer Texas Transportation Institute, 335 TAMU College Station, TX phone: 979/ , fax: 979/ Dominique Lord Assistant Professor Texas A&M University, 336 TAMU College Station, TX phone: 979/ , fax: 979/ Byung-Jung Park Graduate Assistant Researcher Texas A&M University, 336 TAMU College Station, TX phone: 979/ , fax: 979/ July 27, Revised November 27 TOTAL WORDS: 725 [4 Words, 9 Tables, 4 Figures] ABSTRACT With the growing demand for safer streets and highways, state and national transportation agencies are investigating the relationships between roadway characteristics and crashes. The objective of this study was to develop accident modification factors (AMFs) for median characteristics on urban and rural freeways or rural, multilane highways. Data available for use in the evaluation included 458 miles of with barrier segments (primarily urban, with some rural sites), 359 miles of urban without-barrier segments, and 436 miles of rural without-barrier segments. A series of Negative Binomial regression models were used to determine the effects of independent variables on crashes. Variables considered in developing the base models included ADT, left shoulder width, barrier offset, median (with shoulder) width, and pole density. Crashes were examined in terms of median crashes for five years (997 to 2). An AMF represents the change in safety when a particular geometric design element changes in size from one value to another. In this project, the AMFs were estimated directly from the coefficients of the models. This approach for AMF development assumes that (a) each AMF is independent since the model parameters are assumed to be independent and (b) the change in crash frequency is exponential. AMF equations were developed for urban or rural medians with rigid barriers, urban medians without barrier, and rural median without barrier.

2 Fitzpatrick, Lord, Park 2 INTRODUCTION With the growing demand for safer streets and highways, state and national transportation agencies have developed safety programs. One example on a national level is the development of the Highway Safety Manual (HSM). The HSM is being developed under the direction of the Transportation Research Board Highway Safety Manual Task Force (). The manual s goal is to provide the best available safety knowledge in a condensed and widely usable form for designers and practitioners. The HSM is expected for public release in 28. Texas is also sponsoring research efforts to investigate the relationships between roadway characteristics and crashes. An Interim Roadway Safety Design Workbook (2) was developed for the Texas Department of Transportation (TxDOT) that contain methods for predicting crashes on freeway segments and on rural highway segments. The method includes accident modification factors (AMFs) for grade, lane width, outside shoulder width, inside shoulder width, median width, presence of shoulder rumble strips, and utility pole density and offset. Reviewers of the Workbook have expressed a preference for having an AMF for median barriers that is sensitive to the distance between the barrier and the edge of travel lane. They have also mentioned the desire to have information on the relationship between crashes and median characteristics for segments without rigid barriers. The overall objective for the research effort documented in this paper is to develop accident modification factors for median characteristics on freeways and rural, multilane highways. BACKGROUND Limited research has been conducted on crashes occurring within medians of high-speed highways. Within the past few years, however, greater attention has been focused on median crashes, in particular, cross-median crashes. These crashes, although not very frequent, tend to involve high speeds and result in multiple injuries and fatalities. The research into cross-median crashes typically provides advice on when to install a median barrier for a given ADT and median width. For example, a Texas study (3) developed improved guidelines for the use of median barriers on new and existing high-speed, multilane, divided highways. The guidelines were produced using Negative Binomial (NB) and ordered-logit regression models. As part of their research, they reviewed existing guidelines for the installation need of median barriers. Miaou et al. (3) noted that median barriers can reduce cross-median crashes by keeping errant vehicles from reaching the other side of the traffic lanes, however, they do not prevent crashes. Barriers are also obstacles on the roadside and there is a great likelihood that they will be struck because of their nearness to the moving vehicles. Miaou et al. (3) summarized the medianrelated crash rates from several studies as shown in Table. The crashes rates for the data used in this project are also listed in Table. Donnell and Mason (4) developed models to predict the frequency of median barrier crashes on Pennsylvania highways, including separate models for the Turnpike and all other Interstatedesignated highways. NB regression models were used to develop predictive crash frequency

3 Fitzpatrick, Lord, Park 3 tools. From the models developed, traffic volume, horizontal alignment, interchange entrance ramp presence, and median barrier offset distance from the travel lane all influenced median barrier crash frequency. General trends of crash frequency of interest to the TxDOT effort included the following: Increasing the median barrier offset from the left-edge of the travel way decreases median barrier crash frequency. A rural travel environment exhibits lower median barrier crash frequencies than an urban environment on the Turnpike road network. No median barrier or utility pole in median AMFs was specifically identified in the literature. Study Table. Median-Related Crash Rates. Crash rates (crashes/mvm) Subsets of Without With Without Barrier crashes Barrier Barrier Cross Median Other Median Related Previous Studies (as summarized by Miaou et al. 26) Miaou, data PA, data, Interstate PA, data, Freeways CA, data, Freeways Washington, Sites where barriers were added due to crash history Current Study (TX, data) With barriers, all crashes With barriers, KABC* crashes Without barrier, rural, all crashes Without barrier, rural, KABC crashes Without barrier, urban, all crashes Without barrier, urban, KABC crashes = crash rate not identified in the study * KABC crashes includes fatal (K), incapacitating injury (A), non incapacitating injury (B), and possible injury (C) DATA COLLECTION ACTIVITIES This section describes the data collection activities undertaken to assemble a database suitable for developing median-related accident modification factors. Selection Process Freeway and divided highways located in the following Texas districts were considered for inclusion in the databases:

4 Fitzpatrick, Lord, Park 4 Dallas, Ft. Worth, Austin, San Antonio, and Bryan. The TxDOT Reference Marker (TRM) database was used to identify potential highway segments. The roadway geometric characteristics for segments were included in the analysis when the following conditions were met: Mainlanes; Physical roadbed of right mainlane (to eliminate frontage road segments); Highway design type = Freeway or Expressway with no HOV or Railway crossings, and no Toll Median type = positive barrier or unprotected; Maximum speed limit of 55 mph or greater; and Number of lanes is four lanes or greater. Researchers located each segment within an aerial photograph. Preference was to use aerial photographs available from a city or metropolitan planning organization as these photographs were generally of higher quality or resolution. From the view available on the photograph, the following segment characteristics were identified: Barrier type (rigid (includes both concrete barrier and guardrail) or no barrier), Type of control (limited access freeway or divided highway), Pole type (lighting, power, no pole), Pole spacing (ft), and Widths of left shoulder, distance to face of barrier (when barrier is present), and median (ft). Table 2 and Table 3 summarize characteristics of the segments included in the evaluation. Urban was determined using the Urban-Rural code in the TRM database and represents segments in areas with populations of 5 and greater. Barrier offset was defined as being the distance between the edge of the left shoulder to the face of the barrier. Because of the limited number of rural with barrier segments, rural and urban segments were combined to a with barrier category. Crash Data Crash data for each segment were extracted from the Texas Department of Public Safety (DPS) electronic database. A total of five years of crash data (997 to 2) were used. Crashes for all severity levels were pulled. Analyses were performed using only fatal (K), incapacitating-injury (A), non-incapacitating injury (B), and minor injury (C). To be consistent with other AMFs in currently included in the Interim Workbook (2), property damage only (PDO) crashes were not used in the analysis.

5 Fitzpatrick, Lord, Park 5 Table 2. Distribution of With Barrier Variables by Number of Miles and Segments for Freeway and Rural, Multilane Highways Dataset. Range* Miles Segments Range* Miles Segments Segment Length (mi) ADT (in s) >6 TOTAL TOTAL Left Shoulder Width (ft) Barrier Offset (ft) TOTAL >2 TOTAL * Range of variables are listed as x-y with x being inclusive and y being exclusive The following subsets of crash type were identified: Mainlane crashes include all single or multi-vehicle crashes of which position prior to the accident was located on the main lanes of the highway Median-related crashes include mainlane crashes where the position of the impact occurred at inner shoulders of main lanes or median area between main lanes The numbers listed in Table 4 are based on crashes that occurred during the five-year period of 997 to 2. STATISTICAL MODELING Several statistical models were developed for estimating the safety of high-speed, divided highways. The coefficients from the models were used to generate AMFs. The probabilistic structure used for developing the models was the following: The number of crashes at the i-th segment, Y i, when conditional on its mean μ i, is assumed to be Poisson distributed and independent over all segments as: i =, 2,, I ()

6 Fitzpatrick, Lord, Park 6 Table 3. Distribution of Without Barrier Variables by Number of Miles and Segments for Freeway and Rural, Multilane Highways Dataset. Variable Without Barrier, Urban Without Barrier, Rural Range* Miles Segments Miles Segments Segment Length (mi) >6 TOTAL ADT (in s) Left Shoulder Width (ft) Median with Shoulders (ft) Pole Density (poles/mi) Total TOTAL < > Total >22 TOTAL * Range of variables are listed as x-y with x being inclusive and y being exclusive

7 Fitzpatrick, Lord, Park 7 Table 4. Crash Characteristics for the Segments in the Freeways and Multilane Rural Highways Dataset. Crash Characteristics All Severity Levels Crashes [KABC* Crashes] Variable Condition Without Without With Barrier, Barrier, Barrier Urban Rural Sum of Segment Length (mile) Number of Segments Average [.4] [3.5] Per Minimum segment [] [] Median Maximum [98] [29] Crashes in Five Years Sum [523] [82] (997 to Crash Count ) All (crashes/mile-yr) [2.28] [.66] segments Crash Rate (crashes/mvm)** [.59] [.362] Percent of Median Crashes.6% 2.5% to Mainlane Crashes [9.9]% [.7]% * Fatal (K), incapacitating-injury (A), non-incapacitating injury (B), and minor injury (C) crashes **Crash rate has units of yearly crashes per million vehicle miles (crashes/mvm) [3.4] [] 44 [32] 329 [73].6 [.33].682 [.239] 8.9% [7.8]% The mean of the Poisson is structured as: Y μ ~ Po( μ ) (2) i i i It is usually assumed that exp( e it ) is independent and Gamma distributed with a mean equal to and a variance / φ for all i (with φ > ). With this characteristic, it can be shown that Y i, conditional on f (.) and φ, is distributed as a Negative Binomial (or Poisson-gamma) random variable with a mean f (.) and a variance f (.)( + f (.)/ φ) respectively. The term φ is usually defined as the "inverse dispersion parameter" for the NB distribution. Usually the dispersion parameter ( α = φ ) or its inverse (φ ) is assumed to be fixed, but recent research in highway safety has shown that the inverse dispersion parameter could potentially be dependent on the covariates (5,6,7,8 9). Since this work focused on the coefficients and for

8 Fitzpatrick, Lord, Park 8 simplifying the model development, the models were estimated using a fixed dispersion parameter. An important characteristic associated with the development of statistical relationships is the choice of the functional form linking crashes to the covariates (see reference (7) about the justification for using this functional form). For this work, the selected functional form was the following: n x i βi Flow Length 365 i = μ i = β e (3),, Where, μ i = the estimated number of crashes per year for sitei ; Flow = vehicles per day (ADT) for segment i ; Length = length of segment i in miles; x = a series of covariates; and, i β, β i, K, β n = coefficients to be estimated. The coefficients of the predictive models were estimated with SAS (). The Generalized Modeling procedure (GENMOD) in SAS was used to automate the regression analysis. This procedure estimates model coefficients using the maximum-likelihood method. GENMOD is particularly well suited to the analysis of models with additive terms that are either continuous or categorical. The residual deviance statistics were used to assess the model goodness-of-fit. Additionally, the log-likelihood value and Akaike Information Criterion (AIC) value were used to assist in selecting the best model within each model category. At the beginning, all the variables were included in each model and the coefficients that were found to be non-significant (at the 95%-level) were eventually removed. Subsequent models were then estimated with the remaining coefficients. The coefficients were also evaluated for consistency to ensure the sign of each coefficient reflected previously observed crash characteristics. Models were developed for segments with and without median barriers. For each model category median-related KABC crashes were used as dependent variables in the models. These crashes include run-off-the-road accidents as well as vehicles hitting a fixed object or barrier located inside the median. MODELING RESULTS Several variables were tested along with different combinations of the variables. The research team started with all variables collected (or the set of logical variables for example shoulder width and total barrier offset would not both be used in the same model) and then removed variables if they were not significant. The model for a given model category included in this paper is, in the opinion of the researchers, the best model for the model category. This section

9 Fitzpatrick, Lord, Park 9 briefly describes the modeling results for estimating the safety performance of multilane rural highways and freeways. Table 5 summarizes the model output for median-related crashes. This table shows that total barrier offset is significant at the 5 percent level. As expected, a larger offset between the travel way and the barrier is associated with fewer crashes. Median barriers are hit less often as the offset increases. Table 5. Modeling Results for Median-Related Crashes for Segments with Median Barriers (Representing 9.9 Percent of Total Crashes). Model Variables Coefficient Value (Standard error) P-value Intercept (ln β ) (.62) <. Total Barrier Offset a ( β 2 ), ft -.58 (.44).4 Dispersion Parameter (α ).236 (.248) Summary Statistics Residual deviance = on 53 degrees of freedom 2 x log-likelihood = AIC = a Total Barrier Offset = Distance from traveled way to face of rigid barrier (Left Shoulder Width + Barrier Offset) Table 6 summarizes the modeling results for median-related crashes in urban areas. The table shows that all variables are significant at the 5 percent level. The table also illustrates that a wider median is associated with fewer median-related crashes and the increase in pole density is associated with an increase in median-related crashes. Table 6. Modeling Results for Median-Related Crashes in Urban Areas for Segments Without Median Barriers (Representing.7 Percent of Total Crashes). Model Variables Coefficient Value (Standard error) P-value Intercept (ln β ) (.228) <. Median Width a ( β ), ft -.53 (.8).25 Pole Density ( β 2 ), poles/mile.52 (.59).3 Dispersion Parameter (α ).4453 (.678) Summary Statistics Residual deviance = 39.2 on 338 degrees of freedom 2 x log-likelihood = AIC = a Median Width = Median width includes both left shoulders, all poles were assumed to be located at the middle of median.

10 Fitzpatrick, Lord, Park Table 7 summarizes the modeling results for median-related crashes in rural areas. Pole density was not considered since only.7 of 436 miles had poles. The table shows that the left shoulder width variable is significant at the 5 percent level. The table also illustrates that a wider leftshoulder width is associated with fewer median-related crashes. Table 7. Modeling Results For Median-Related Crashes In Rural Areas for Segments Without Median Barriers (Representing 7.8 Percent of Total Crashes). Model Variables Coefficient Value (Standard error) P-value Intercept (ln β ) (.258) <. Left Shoulder Width a ( β ), ft -.38 (.45).2 Dispersion Parameter (α ).3578 (.75) Summary Statistics Residual deviance = on 23 degrees of freedom 2 x log-likelihood = AIC = a Left Shoulder Width = Average of left shoulder widths in both travel direction Each model category included a different measure of the effect of the median. For sites with a barrier, the distance between the edge of the travel way and the barrier was significant. For urban without-barrier segments, the median width was the variable in the strongest model. For rural without-barrier segments, the width of the left shoulder rather than median width was the variable in the best model. Stated in another manner, the width of the left shoulder was more strongly associated with median crashes than the width of the median for rural without-barrier segments. ACCIDENT MODIFICATION FACTORS An AMF represents the change in safety when a particular geometric design element changes in size from one value to another. An AMF greater than. represents the situation where the design change is associated with more crashes while an AMF less than. indicates fewer crashes. In this project, the initial AMFs were estimated directly from the coefficients of the models, derived in the previous section. This approach for AMF development assumes that (a) each AMF is independent since the model parameters are assumed independent and (b) the change in crash frequency is exponential (as suggested by Equation 3). In practice, AMFs may not be completely independent, since changes in geometric design characteristics on highways are not done independently (e.g., lane and shoulder width may be changed simultaneously) and the combination of these changes can influence crash risk. Nonetheless, experience in deriving AMFs in this manner indicates that the assumptions are reasonable and, with thoughtful model development, the resulting AMFs can yield useful information about the first-order effect of a given variable on safety. Others who have used this approach for developing AMFs include Lord and Bonneson () and Washington et al. (2).

11 Fitzpatrick, Lord, Park Prior to deriving the AMFs, the base (or typical) condition for each design element was determined. Table 8 lists the base condition for each design variable used in this project. By definition, the base condition is associated with an AMF value of.. Table 8. Base Condition for Freeways and Multilane Rural Highways Design Elements Used in this Project. Design Elements Base Condition 4 ft (for four lanes) Left Shoulder Width ft (for six or more lanes) 6 ft (for four lanes) Total Barrier Offset* 2 ft (for six or more lanes) Median Width (includes Left Shoulder Widths) 76 ft rural for segments without barriers 48 ft urban Pole Density poles/mi * Measured as the distance between edge of travel lane and face of barrier, determined by adding the barrier offset (assumed to be 2 ft) and left shoulder width (assume to be 4 ft for fourlane highways and 6 ft for six or more lane highways) The TxDOT Roadway Design Manual (RDM) (3) was reviewed for guidance in determining appropriate base conditions. Within both the freeway and multilane rural highway chapters for new location or 4R reconstruction, left shoulder width is determined by the number of travel lanes. When four lanes are used, the minimum and desirable left shoulder width is 4 ft. When six or more lanes are designed, the inside left shoulder width is ft desirable and 4 ft minimum. For use with the AMFs, 4 ft was selected for four lanes and ft for six or more lanes. The minimum barrier offset, which would be measured from the edge of the shoulder to the face of the barrier, was assumed to be 2 ft. With the assumed 2 ft minimum barrier offset, the total barrier offset is 6 ft for four lane and 2 ft for six of more lanes. The guidance for depressed median width in the TxDOT Roadway Design Manual (RDM) (3) for multilane rural highways with either six or four lanes is 48 ft minimum and 76 ft desirable. Similar numeric values are provided in the freeway chapter (page 3-69 of the July 26 edition). The median widths included in the dataset were examined to determine if additional guidance on typical values could be identified. The average median width (weighted for length of segment) for the urban sites was 64.3 ft and 7.7 ft for rural sites. Because several segments had very wide medians, the weighted average may not appropriately reflect typical median widths. A review of the median widths included in the analysis revealed 5 th percentile values of 5 ft for urban and 58 ft for rural segments. About half of the urban segments had measured median widths between 47 and 5 ft, therefore, a 48-ft base condition appears reasonable. For rural segments, 25 percent of the segments had 74 ft or more for the measured width. Therefore, 76 ft is reasonable for the base condition for rural highways; however, the value is not needed since the best model (shown in Table 7) included the shoulder width variable and not the median width variable. Note that base conditions are not fixed and can be changed by the user of these AMFs. The AMFs can be re-adjusted to reflect the new base conditions.

12 Fitzpatrick, Lord, Park 2 The initial AMFs obtained from the models are applicable only to the specific crash type used to develop the regression model, that is, median-related crashes. They do not directly reflect the safety effect on total (or mainlane) crashes within a particular highway segment. They have to be adjusted in order to be applied to total crashes. The adjustment used the proportion of median-related to total crashes. These percentages were provided in Table 4. At this stage, it was assumed that the AMF of each design element for median-related crashes has a safety effect only on median-related crashes and has no effect on non median-related crashes. Based on this assumption, the adjusted AMF for total crashes was calculated by taking a weighted average between the AMF for median-related crashes and the AMF for nonmedian-related crashes (assumed to be.). The following equations were used: ( AMF( median) P( median) ) + ( AMF( non _ med) P( non _ )) AMF( total) = med (4) i i i AMF( total) i = ( AMF( median) i.) P( median) +. (5) Where, AMF(total) i = AMF of design element i for total crashes AMF(median) i = AMF of design element i for median-related crashes AMF(non_med) i = AMF of design element i for nonmedian-related crashes (=.) P(median) i = proportion of median-related crashes to total crashes P(non_med) i = proportion of nonmedian-related crashes to total crashes = -P(median) i In this manner the initial AMFs were adjusted to reflect total crashes. Median With-Rigid-Barrier Segments This section describes the development of AMFs for with-rigid-barrier segments using medianrelated crashes. The AMFs are developed based on barrier offset and number of lanes (to account for different minimum shoulder widths). Over 95 percent of the with-rigid-barrier segments are in an urban area; therefore, the dataset was not subdivided into urban and rural. The base condition for total barrier offset is the combination of base conditions for barrier offset and base condition for left shoulder width. The value of 2 ft was used for the base condition of barrier offset distance. For the left shoulder width, 4 ft for four lanes and ft for six or more lanes was used. Therefore, total barrier offset for four lanes is 6 ft and for six or more lanes it is 2 ft. Therefore, the AMFs for total barrier offset when predicting median-related crashes are:.58[ TBO 6] AMF ( M ) MwB,4 = e (6).58[ TBO 2] AMF ( M ) MwB,6 = e (7)

13 Fitzpatrick, Lord, Park 3 Where, AMF(M) MwB,4 = accident modification factor for median crashes for four-lane highways with rigid barrier in median AMF(M) MwB,6 = accident modification factor for median crashes for six or more lane highways with rigid barrier in median TBO = total barrier offset (barrier offset + left shoulder width), ft The graphical representation of AMF(M) MwB is shown in Figure (a). The relationship between total barrier offset and AMF values in this figure suggests that the median-related crash frequency is reduced by about.6 percent (i.e., - e -.58 ) for a -ft increase in total barrier offset. Although this relationship is true for both four lanes and six or more lanes, a wider total barrier offset is required for six or more lanes than four lanes in order to achieve the same value of AMF due to the different base conditions. The AMF(M) MwB needs to be adjusted to reflect the effects on total crashes. Median-related crashes were 9.9 percent of total crashes. Therefore, the AMFs for total barrier offset when predicting total crashes are:.58[ TBO 6] ( ( e ) ).99) AMF ( TM ) = (8) MwB, [ TBO 2] ( ( e ) ).99) AMF ( TM ) = (9) MwB, 6 + Where, AMF(TM) MwB,4 = accident modification factor for total crashes developed based on median-related crashes for four-lane highways with rigid barriers in median AMF(TM) MwB,6 = accident modification factor for total crashes developed based on median-related crashes for six or more lane highways with rigid barriers in median TBO = total barrier offset (barrier offset + left shoulder width), ft The graphical representation of AMF(TM) MwB is shown in Figure (b). Based on the range of total barrier offset in the database, the AMF(TM) MwB is applicable to total barrier offsets ranging from to 34 ft. Median Without-Barrier Segments, Urban Area For highways without rigid barriers, the assumed base condition for median width in an urban area is 48 ft. The recommended AMF using median width is:.53[ MW 48] AMF ( M ) UMW = e ()

14 Fitzpatrick, Lord, Park lanes 6 or more lanes AMF(M)MwB Total Barrier Offset, ft (a) AMF for With-Rigid-Barrier Segments, Median-Related Crashes lanes 6 or more lanes AMF(TM) MwB Total Barrier Offset, ft (b) AMF for With-Rigid-Barrier Segments, Total Crashes. Figure. AMFs for Medians With-Rigid-Barrier Segments Using Total Barrier Offset and Number of Lanes, Developed Based on Median-Related Crashes.

15 Fitzpatrick, Lord, Park 5 Where, AMF(M) UMW = accident modification factor using median width for median-related crashes for urban highways with no median barrier MW = median width (including left shoulder widths), ft The graphical representation of AMF(M) UMW is shown in Figure 2(a). The relationship shown in Figure 2(a) suggests that median-related crash frequency in without-barrier segments can be reduced by about.5 percent (i.e., -e -.53 ) for a -ft increase in median width. Based on the range of median width in the database, the AMF(M) UMW is applicable to median width ranging from 33 to 35 ft. Also shown in Figure 2(a) is the graph for AMF(TM) UMW after AMF(M) UMW has been adjusted to reflect total crashes. Like longitudinal barriers, the poles in the median are an obstruction for drivers. It was found that the pole density is associated with an increase in median-related crashes and hit-pole crashes. The base condition for pole density is no pole per mile. The recommended AMF for pole density for median-related crashes is:.52[ PD] AMF ( M ) UPD = e () Where, AMF(M) UPD = accident modification factor using pole density for median-related crashes for urban highways with no median barrier PD = pole density, poles/mi Figure 2(b) shows the graphical representation of AMF(M) UPD. The relationship suggests that median-related crash frequency in without-barrier segments can be increased by about.5 percent (i.e., e.52 -) for one additional pole per mile. Based on the range of pole density in the database, AMF(M) UPD is applicable to pole density ranging from to 25. poles/mi. Also shown in Figure 2(b) is graph for AMF(TM) UPD after AMF(M) UPD has been adjusted to reflect total crashes. The development of an AMF to reflect medians in an urban area would need to combine the AMF for median width with the AMF for pole density. The AMF equation would be:.53( MW 48).52PD ( ( e e ) ).7) AMF ( TM ) = (2) UMw / ob + Where, AMF(TM) UMw/oB = accident modification factor for urban medians without barriers developed using median-related crashes MW = median width (including left shoulder widths), ft PD = pole density, poles/mi

16 Fitzpatrick, Lord, Park 6 AMFs for Without-Barrier Segments, Median Crashes.25. AMFs for Without-Barrier Segments, Total Crashes.2. AMF (M)UMW Median Width, ft AMF(TM) UMW Median Width, ft (a) Based on Median Width AMF(M)UPD.3.2. AMF(TM) UPD Pole Density, poles/mi Pole Density, poles/mi (b) Based on Pole Density Figure 2. AMFs for Urban Without-Barrier Segments Using Median Width and Pole Density, Developed Based on Median Crashes. Figure 3 illustrates the plot of the AMF using increments of 5 poles/mi. The above equation can be used to determine the AMF when other values of pole density are present. Median Without-Barrier Segments, Rural Area This section describes the development of AMFs for without-barrier rural segments for medianrelated crashes. The AMF for rural areas was developed based on left shoulder width. The base condition for left shoulder width is: 4 ft for four lanes and ft for six or more lanes. Therefore, the recommended AMFs for median-related crashes on rural without-barrier segments are:.38[ LSW 4] AMF ( M ) RSW,4 = e (3).38[ LSW ] AMF ( M ) RSW,6 = e (4)

17 Fitzpatrick, Lord, Park 7 AMF(TM) UMw/oB poles/mi 5 poles/mi poles/mi 5 poles/mi 2 poles/mi 25 poles/mi Median Width, ft Figure 3. AMF for Urban Without-Barrier Segments Using Median Width and Pole Density, Developed Based on Median Crashes and Adjusted to Reflect Total Crashes. Where, AMF(M) RSW,4 = accident modification factor using shoulder width for median-related crashes for rural four-lane highways with no median barrier AMF(M) RSW,6 = accident modification factor using shoulder width for median-related crashes for rural six or more lane highways with no median barrier LSW = left shoulder width, ft The graphical representation of AMF(M) RSW for both four lanes and six or more lanes is shown in Figure 4(a). The relationship between left shoulder width and AMF values in this figure suggests that the median-related crash frequency is reduced by about 2 percent (i.e., -e -.38 ) for a -ft increase in left shoulder width. This relationship is true for both four lanes and six or more lanes, but a wider left shoulder width is required for six or more lanes than four lanes in order to get the same value of AMF due to the different base conditions. Based on the range of left shoulder width in the database, the AMF(M) RSW is applicable to left shoulder width ranging from 2 to ft. Shown in Figure 4(b) is the graph for AMF(TM) RSW after AMF(M) RSW has been adjusted to reflect total crashes.

18 Fitzpatrick, Lord, Park lanes 6+ lanes AMF(M) RSW Shoulder Width, ft (a) AMFs for Without-Barrier Segments, Median Crashes AMF(TM) RSW lanes 6+ lanes Shoulder Width, ft (b) AMFs for Without-Barrier Segments, Total Crashes Figure 4. AMFs for Rural Without-Barrier Segments Using Shoulder Width, Developed Based on Median Crashes. CONCLUSIONS The objective of this study was to develop AMFs for median characteristics on freeways or rural, multilane highways. Data available for use in the evaluation included 458 miles of with barrier segments, 359 miles of urban without-barrier segments, and 436 miles of rural without-barrier segments. A negative binomial regression model was used to determine the effects of

19 Fitzpatrick, Lord, Park 9 independent variables on crashes. Variables considered in developing the base models included ADT, left shoulder width, barrier offset, median (with shoulder) width, and pole density. Crashes are examined in terms of median crashes for five years (997 to 2). An AMF represents the change in safety when a particular geometric design element changes in size from one value to another. An AMF greater than. represents the situation where the design change is associated with more crashes while an AMF less than. indicates fewer crashes. In this project, the AMFs were estimated directly from the coefficients of the models. This approach for AMF development assumes that (a) each model variable is independent between the change in the variable value and (b) the change in crash frequency is exponential. AMF equations were developed for medians with rigid barriers, urban medians without barrier, and rural median without barrier. Table 9 lists the recommended AMFs. Table 9. Recommended AMFs for Medians on Freeways and Rural Multilane Highways. Median with Rigid Barrier.58[ TBO 6] AMF = e.99 AMF ( ( ) ) ) MwB, [ TBO 2] ( ( e ) ).99) MwB, 6 = + where, AMF MwB,4 = accident modification factor for four-lane highways with median rigid barrier AMF MwB,6 = accident modification factor for six or more lane highways with median rigid barrier TBO = total barrier offset (barrier offset + left shoulder width), ft Urban Median without Barrier.53( MW 48).52PD AMF = e e.7 ( ( ) ) ) UMw / ob + where, AMF UMw/oB = accident modification factor for urban medians without rigid barriers MW = median width (including left shoulder widths), ft PD = pole density, poles/mi Rural Median without Barrier AMF AMF.38( LSW 4) ( ( e ) ).78) RMw / ob,4 = +.38( LSW ) ( ( e ) ).78) RMw / ob,6 = + where, AMF RMw/oB,4 = accident modification factor for rural four-lane highways without median rigid barriers AMF RMw/oB,6 = accident modification factor for rural six or more lane highways without median rigid barriers LSW = left shoulder width, ft

20 Fitzpatrick, Lord, Park 2 REFERENCES Highway Safety Manual Website. available at accessed July 25, Bonneson, J., K. Zimmerman, and K. Fitzpatrick (26) Interim Roadway Safety Design Workbook. FHWA/TX-6/-473-P4. 3 Miaou, S.P., R.P. Bligh, and D. Lord (25) Developing Median Barrier Installation Guidelines: A Benefit/Cost Analysis using Texas Data. Transportation Research Record 94, pp Donnell, E. T. and J. M. Mason, Jr. (26) Predicting the Frequency of Median Barrier Crashes on Pennsylvania Interstate Highway Accident Analysis & Prevention. Vol. 38, pp Hauer, E. (2) Overdispersion in modelling accidents on road sections and in Empirical Bayes estimation. Accident Analysis & Prevention, Vol. 33, Number 6, pp Heydecker, B.G., J. Wu. (2) Identification of Sites for Road Accident Remedial Work by Bayesien Statistical Methods: An Example of Uncertain Inference. Advances in Engineering Software, Vol. 32, pp Lord, D., S.P. Washington, and J.N. Ivan (25) Poisson, Poisson-Gamma and Zero Inflated Regression Models of Motor Vehicle Crashes: Balancing Statistical Fit and Theory. Accident Analysis & Prevention. Vol. 37, Number, pp Miaou, S.-P., and D. Lord (23) Modeling Traffic-Flow Relationships at Signalized Intersections: Dispersion Parameter, Functional Form and Bayes vs Empirical Bayes. Transportation Research Record 84, pp Lord, D., A. Manar, and A. Vizioli (25b) Modeling Crash-Flow-Density and Crash- Flow-V/C Ratio for Rural and Urban Freeway Segments. Accident Analysis & Prevention. Vol. 37, Number, pp SAS Institute Inc. Version 9 of the SAS System for Windows. Cary, NC, 22. Lord, D., and J.A. Bonneson (27) Development of Accident Modification Factors for Rural Frontage Road Segments in Texas. Transportation Research Record, in press. 2 Washington, S.P., B.N. Persaud, C.Lyon, and J. Oh. (25) Validation of Accident Models for Intersections. Report No. FHWA-RD Federal Highway Administration, Washington, D.C. 3 Texas Department of Transportation (TxDOT) (26) Roadway Design Manual. Austin, TX, October 26. Access at: BookView. Accessed July 27.