Approximating an analytic solution for the optimal design of asphalt pavement

Abstract

This article considers how the expected service life of asphalt pavement can be modelled taking into consideration different climates, different amounts of traffic and an opportunity for optimal design. A methodology is proposed that follows the steps used by economists to describe how an optimizing producer would determine optimal inputs to use in a generic production process. Because realistic mechanistic models of thermal cracking and rutting are employed, the standard steps followed by economists are mathematically infeasible. Various approximation techniques are used to circumvent these difficulties so that, in the end, it is possible to present a completely analytic expression for the expected service life where the variables describing the climate, traffic and quality requirement remain variables. Further, it is also possible to derive a design function to determine the optimal choice of the asphalt’s softening point. These are the economist’s factor demand functions. Together the two functions provide a third function for the optimal service life, which is the equivalent of a profit function. Four examples of applications of the optimal service life function are given: for benchmarking, for estimating expected renewal cost, for calculating cost shares for heavy vehicles and for empirically testing mechanistic models of asphalt behavior on in-situ condition state data. A demonstration of the latter confirms the optimal service life function’s ability to predict in-situ service lives using data from Switzerland.