Finite element implementation of Huet-Sayegh and 2S2P1D models for analysis of asphalt pavement structures in time domain

The Huet-Sayegh (HS) and 2S2P1D rheological models represent very well the linear viscoelastic behaviour of asphalt concrete and binder while using less parameters than other models. However, the finite element implementation in time domain of these two models encounters a great difficulty. In this paper, the author aims at developing a numerical implementation in time domain of the HS and 2S2P1D models. Firstly, the relaxation modulus is analytically approximated using Schapery and Park’s method or exactly calculated using the numerical algorithm proposed by Heck. Secondly, the relaxation modulus is once again approximated by the sum of exponential functions for deriving a recursive formula of stress–strain relationship. Since the relaxation modulus is approximated twice, a special technique is used to estimate the appropriate decay rates and coefficients of the sum of exponential functions to ensure high accuracy of the obtained results. It is shown that the calculations based on the proposed formulation achieve a very good level of accuracy.