Evaluation of Pavement Safety Performance

APPENDIX A-INVESTIGATION OF THE DEVELOPMENT OF CMFUNCTIONS

OBJECTIVES

A thorough disaggregate analysis of the before-after evaluation data was undertaken in which regression analysis was used to investigate the effects on the CMFs of a number of variables, including AADT, precipitation, expected crash frequency before treatment, and environment (urban/rural). The primary objective was to investigate whether CMFunctions could be developed to capture the effects of these factors and more precisely estimate CMFs for prospective treatments.

If successful, such CMFunctions would allow a user to apply a more accurate CMF that better reflects the specific site characteristics than an average value.

METHODOLOGY

The methodology investigated was a relatively new and innovative approach that models the values of the CMF using weighted linear regression.⁽⁵⁰⁾ Because of the preponderance of sites with zero crashes and short segment lengths, each individual segment could not be used as an observation. Rather, all segments were grouped together by ranges of the variables being modeled and then used to estimate a CMF and its variance for that group. Segments were not aggregated across States because applications may vary across States in unknown ways. Also, consistency in results across States would be indicative of the accuracy of the results.

For example, if the model were only to consider an urban versus rural environment, then all urban sites would be used to estimate a CMF and its variance, and the same would be done for rural sites. This would be done separately for each State. Then the weighted linear regression model would be estimated using these estimates of the CMF as the dependent variable and a categorical variable to represent urban versus rural settings as the independent variable. The regression weights are assigned as the inverse of the variance of the CMF estimate.

The variable definitions for those independent variables considered are described below. For those variables that are continuous in nature (i.e., AADT and precipitation), the weighted mean for each category was used as the independent variable. The weights applied are the mile-years of after period data for each segment. The cutoff points for defining categories for the continuous variables were determined in an iterative manner and considering the goodness-of-fit of the estimated models and the number of observations in each category. Following are the variable specifications so obtained.

RURURB

if URBAN then rururb = 1.
if RURAL then rururb = 0.

PTYPE

if concrete pavement then ptype = 1.
if asphalt pavement then ptype = 0.

AADT Categories for Freeways (after period AADT)

if AADT >= 0 and AADT < 20,000 then volcat *= 1.
if AADT >= 20,000 and AADT < 40,000 then volcat = 2.
if AADT >= 40,000 and AADT < 60,000 then volcat = 3.
if AADT >= 60,000 and AADT < 80,000 then volcat = 4.
if AADT >=80,000 and AADT < 100,000 then volcat = 5.
if AADT >= 100,000 then volcat = 6.

*Weighted mean AADT for each category is used as the independent variable.

AADT Categories for Multilane Roads

if AADT >= 0 and AADT < 10,000 then volcat *= 1.
if AADT >= 10,000 and AADT < 20,000 then volcat = 2.
if AADT >=20,000 and AADT < 30,000 then volcat = 3.
if AADT >= 30,000 and AADT < 40,000 then volcat = 4.
if AADT >= 40,000 and AADT <50,000 then volcat = 5.
if AADT >= 50000 then volcat = 6.

*Weighted mean AADT for each category is used as the independent variable

AADT Categories for Two-Lane Roads

if AADT >= 0 and AADT < 5,000 then volcat* = 1.
if AADT >= 5,000 and AADT < 10,000 then volcat = 2.
if AADT >= 10,000 and AADT < 15,000 then volcat = 3.
if AADT >= 15,000 then volcat=4.

*Weighted mean AADT for each category is used as the independent variable

Precipitation Categories (the 5-year average precipitation in after period)

if precip <= 30 then prec = 1.
if precip > 30 and  yr_precip <= 40 then prec* = 2.
if precip > 40 and  yr_precip <= 45 then prec = 3.
if precip > 45 and  yr_precip <= 50 then prec = 4.
if precip > 50 then prec = 5.

*Weighted mean precipitation for each category is used as the independent variable.

ACCRATE

accrate= sum of expected crashes after without treatment/sum of mile-years of after-period data.

RESULTS

Models were attempted separately for all crash types and all road types (freeway, multilane, and two-lane) with varying success. Given the data demands for even estimating a single average CMF, it is perhaps not surprising that estimating several CMFs for categorized subsets of the same data proved challenging.

Nevertheless, in general, the results did suggest that there is a relationship between CMFs and AADT and sometimes precipitation, urban versus rural setting, and expected crash frequency. However, the direction of the effect is not always consistent, varying by crash type, site type, and treatment. Future research will need to reconcile (i.e. explain) these apparent inconsistencies.

Some of the more promising results are provided below to illustrate the potential for developing CMFunctions for pavement treatments. It is not, however, recommended to use these models for estimating CMFs. Rather the aggregate CMFs in chapter 6 are recommended at the current time.

Thin HMA-Freeway-Total Crashes

For thin HMA treatments on freeways, the model in figure 36 was estimated for total crashes, and table 41 presents the results.

Figure 36. Equation. Model estimated for total crashes on thin HMA treatments on freeways.

Table 41 . Results for model for total crashes on thin HMA treatments on freeways.

The results indicate that the CMF value increases with increasing AADT, meaning that the treatment is more effective at locations with lower AADTs.

OGFC-Two-Lane-Total Crashes

For OGFC treatments on two-lane roads, the model in figure 37 was estimated for total crashes and table 42 presents the results.

Figure 37. Equation. Model estimated for total crashes on OGFC treatments on two-lane roads.

Table 42 . Results for model for total crashes on OGFC treatments on two-lane roads.

The results indicate that the CMF value decreases with increasing AADT, meaning that the treatment is more effective at locations with higher AADTs. The model also indicates that the CMF decreases at higher levels of precipitation, indicating that the treatment is more effective in areas with higher precipitation. The parameter estimates for the model, however, are of low statistical significance.

Diamond Grinding-Freeway-Total Crashes

For diamond grinding treatments on freeways, the model in figure 38 was estimated for total crashes, and table 43 presents the results.

Figure 38. Equation. Model estimated for total crashes on diamond grinding treatments on freeways.

Table 43 . Results for model for total crashes on diamond grinding treatments on freeways.

The results indicate that the CMF value decreases with increasing AADT, meaning that the treatment is more effective at locations with higher AADTs. The model also indicates that the CMF decreases at higher levels of precipitation, indicating that the treatment is more effective in areas with higher precipitation. The parameter estimates for the precipitation variable is of low statistical significance however.