Interconversion between viscoelastic functions using the Tikhonov regularisation method and its comparison with approximate techniques

Abstract

Asphalt concrete behaves as a viscoelastic material under normal traffic loading and field conditions. The stress–strain behaviour depends on the rate of loading as well as the actual pavement temperature. In order to model the viscoelastic behaviour of the asphalt materials, viscoelastic functions need to be determined. In this study, a uniaxial static creep test was carried out for AC 20 and AC 14 asphalt mixtures. Several asphalt specimens were tested at different temperatures subjected to various deviator stresses in order to verify the proposed approach. Prony series for the creep compliance were determined for raw and smoothed data. Various optimisation techniques were utilised to ensure a monotonic increase in the Prony coefficient. A number of approximate interconversion techniques were evaluated in determining relaxation modulus resulted from the creep compliance interconversion. It was clear that Prony series constants affect the interconverted relaxation modulus. It was also obvious that using the discretisation of the slope of n value (slope of log creep compliance with log t) over the time domain instead of using one single constant value of the slope provides a better solution of the interconverted relaxation modulus. Finally, the exact interconversion method was applied to check the accuracy of approximate techniques. Tikhonov regularisation with the L-curve method was considered to solve the convolution integral. The exact solution was recommended as a result of investigating the extracted data. The approximate solution showed around 7.0% error comparing different approaches.