General Viscoelastic Solutions for Multilayered Systems Subjected to Static and Moving Loads

Abstract

Since the linear elastic layer solution for the layered systems was developed in the 1940s, the linear elastic layer analysis has been systemized and widely used for the designs of roadway pavements as a tool for evaluating the structural soundness of pavements. The primary assumption made in the analysis is that the layered system consisting of materials that are linear elastic; and hence, an application of the elastic layer analysis to asphalt mixtures, which is a well-known viscoelastic material, has been limited. Therefore, the intention of the study was to derive a viscoelastic solution able to take into account the time- and rate-dependent nature of the viscoelastic materials in the multilayered system. In this paper, a linear viscoelastic solution for the multilayered system subjected to a cylindrical unit step (static) load was derived from the elastic solution by using the principle of elastic-viscoelastic correspondence and the numerical inversion of Laplace transforms. The solution was then extended to simulating pavement responses subjected to a moving load by employing the Boltzmann’s superposition principle. The soundness of output from the viscoelastic solution was confirmed by comparing them to those of the finite-element analysis (FEA). Compared to the time and effort required in FEA, the analysis based on the viscoelastic solution was much faster. Therefore, it is expected that the viscoelastic solutions derived in this study will be an effective tool for the design of flexible pavements.