Impact of Shoulder Width and Median Width on Safety (2009)

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A-1 Model Use This report presents the use of AMFs as a recommended approach for determining the relative safety of design ele- ment choices. An alternative method that will yield similar results is the use of the prediction models developed herein; this approach is illustrated in this appendix. This process can be applied to determine the safety implications of using dif- ferent values for a single or combination of design elements; it may be implemented using the models with or without calibration to local conditions or by simply using the AMFs to determine the anticipated percent change in crashes. Steps 1 through 5 of the process are also illustrated in Figure A-1: • Step 1: Apportion the roadway section in homogenous segments where geometry and traffic are constant. This requires dividing the roadway section into individual homo- geneous segments without intersections. Each segment is defined when a change in the value of the average daily traf- fic, lane, shoulder and median width occurs or a median is introduced. The roadway then comprises a number of segments of varying length. • Step 2: Determine the geometric design elements and val- ues to be considered. In this step, the choice of shoulder widths, median widths, median presence, and shoulder type are determined in order to identify the possible roadway geometric design elements to be evaluated. • Step 3: Estimate the number of crashes for each condition to be evaluated using the appropriate prediction model for each segment of concern. To do this, the user must decide whether to estimate single-vehicle, multi-vehicle, or all crashes and to address the severity of crashes. Once these choices are made, the appropriate models are selected from Equations 6 though 14 (see Chapter 3 for equations). • Step 4: Apply a calibration factor to adjust predictions to local jurisdiction. The calibration factor is a multiplier used to adjust the predictions to the local conditions. This process is described in the following section. • Step 5: Summarize the predictions of the safety implica- tions of the design choices. The total number of predicted crashes for the entire roadway section can be obtained by simply summing up all individual predictions from Step 4. Calibration Process Calibration to adjust the model estimates for the local con- ditions is recommended. A simple, four-step calibration pro- cedure is as follows: • Step 1: Randomly select a sample of the data set to be evaluated; a set of 75 to 100 segments is suitable. The seg- ments should satisfy the basic assumptions of the models (i.e., four-lane rural highways with 12-ft lanes and divided or undivided). • Step 2: Apply the model of concern for each selected seg- ment to determine the expected number of crashes for the segment. For example, if all crashes for divided high- ways are to be estimated, Equation 8 should be used. • Step 3: Compare the expected values obtained in Step 2 with those actually observed and determine the relative differences between observed and expected values. • Step 4: Calculate a ratio of the observed to the expected values by summing all crashes for the selected segments. This is the calibration factor that can be used as a multiply- ing factor for prediction obtained from the models as described above. This calibration process is required for each for the mod- els to be applied, and it may be difficult to implement since it is possible that for certain categories the necessary data will be inadequate or not available. An example of the use of the calibration process is presented in the next section. A P P E N D I X A Using Prediction Models to Determine Relative Safety of Design Element Choices

A-2 Examples Two examples are presented to demonstrate the use of the models and AMFs for estimating the safety implications from design choices. The first example demonstrates the use of the models without calibration; the second illustrates the appli- cation of calibration factors. Example 1: No Calibration An agency is evaluating the effects of shoulder widths for a roadway project with a length of 0.75 miles and an ADT of 10,000 vehicles/day. The roadway will be a principal arterial with these characteristics: (1) divided with a 30-ft median, (2) four 12-ft lanes, (3) no median barrier, (4) paved shoulders, and (5) no access points along the segment. Designs with 4-ft and 8-ft shoulders will be evaluated where the agency is con- cerned with the effect of the choice on all crashes. Equation 8 is used since all crashes for divided roads must be estimated. It is assumed that the geometric features of the roadway segment are homogeneous (i.e., there is no need to subdivide the segment): So, the choice of the wider shoulder will result in a reduction of 0.69 crashes per year per mile for this roadway segment. E N e AD [ ] = − − + + 4 4 235 12 0 835 10000 0 7810 75. . ln . ln . 0 0 172 1 0 228 1 0 118 4 1 84( ) ( ) ( ) ( )+ + − =. . . . cr yr E mi N e AD [ ] = − − + + 8 4 235 12 0 835 10000 0 7810 75. . ln . ln . 0 0 172 1 0 228 1 0 118 8 1 15( ) ( ) ( ) ( )+ + − =. . . . cr yr mi The California intercept value was used in this analysis. The use of either of the other two intercepts produces similar results, and the percent change between the two choices is the same. The Kentucky intercept produces an estimate of 1.47 and 0.91 crashes per year per mile for the 4-ft and 8-ft shoul- ders; the use of the Minnesota intercept gives estimates of 1.69 and 1.05 crashes per year per mile. All three estimates have a crash reduction of approximately 38% with the use of the 8-ft shoulder compared with the 4-ft shoulder. Example 2: Calibration An agency is designing a roadway project where an 8-ft shoulder is considered. The roadway project has a length of 1.0 miles and an ADT of 15,000 vehicles/day. The roadway will be a principal arterial, it will be undivided with four 12-ft lanes, the shoulders will be paved, and there are no access points along the segment. The agency wishes to estimate the safety effect of the choice of shoulder width on all crashes. To develop a calibration factor, a set of 100 segments is randomly chosen within the agency’s jurisdiction. All seg- ments are undivided four-lane rural highways with 12-ft lanes and paved shoulders. For each segment the total num- ber of crashes is estimated for the period of concern. Using Equation 11, the expected number of total crashes for undi- vided four-lane rural highways is calculated for each segment (see Table A-1). Summing over the 100 segments, the ratio of observed to expected crashes is 70/50 = 1.4, and this calibration factor is applied in Equation 11: Using the calibrated equation, the total number of expected crashes per year per mile for this segment with 8-ft shoulders will be 0.419. E N e AD[ ] = − − + − (1 0 5 105 12 0 960 15000 0 067 8. . ln . ln . )( ) =1 4 0 419. . cryr mi Figure A-1. Flow chart of model application. Crashes Segment Length ADT Shoulder Obs Exp 1 0.25 12,000 6 4 2.38 2 0.30 10,000 4 3 3.02 3 0.44 16,000 8 6 4.51 4 0.20 18,000 8 4 2.36 … … … … … … … … … … … … … … … … … … 100 0.42 17,000 6 6 6.09 Total 70 50 Table A-1. Sample data set calculations for calibration factor.