Approximating an Analytic Solution for the Optimal Design of Asphalt Pavement: Limited Example

Abstract

This paper considers how the expected service life of asphalt pavement can be modeled taking into consideration different climates, different amounts of traffic, and an opportunity for optimal design, namely, the choice of the bitumen’s softening point. A methodology was employed for the derivation that is standard in the economics literature but is not standard in the pavement design literature. The current work achieves a limited goal, which is to demonstrate the feasibility of the methodology and give four examples of the potential benefits that can result. The model includes only two damage mechanisms: thermal cracking and rutting. Even so, the standard steps followed in the economics literature are mathematically infeasible. Infeasibility is in the practical sense, as in many functions are invertible in theory but not in practice. Various approximation techniques were used to circumvent these difficulties so that, in the end, it was possible to present a closed-form expression for the expected service life in which the variables describing the climate, traffic, and quality requirement remain variables. This is a qualitatively different result than what arises from current design procedures. As a second step, it was possible to derive a design function that expresses the optimal choice of the asphalt’s softening point. Together, the two functions provided a third closed-form function for the optimal service life. The optimal service life function can be used to derive further results. Four examples of potential applications 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 empirical success of the example model in predicting differential rates of deterioration across environments despite its limitation to two damage processes.