Closed-Form Solutions for Bimodal Axle Load Spectra and Relative Pavement Damage Estimation

Abstract

The mechanistic-empirical (ME) design procedures utilize axle load spectra to characterize the individual traffic loadings for a site. These loading characteristics are employed to calculate pavement response and for subsequent damage computations. Generally, these axle load distributions exhibit a bimodal shape and a combination of two continuous statistical distributions can be used to model them. In this paper, closed-form solutions are developed to estimate the parameters of the bimodal distribution from data. A combination of two normal distributions is shown to reasonably fit observed axle spectra. Since it is anticipated that the AASHTO equivalent single-axle load (ESAL) concept will continue to be used by pavement engineers even after the full adoption of ME design methods, a closed-form statistical relationship between ESALs and axle load spectra is proposed. Such a relationship will be useful in estimating a traffic level index from an axle distribution. In addition, the relationship can provide an estimate of the relative pavement damage caused by axle distributions, and be used to rank axle load spectra within a geographical region, or between regions in order to identify heavier traffic loading corridors.