Modified fractional-Zener model—Numerical application in modeling the behavior of asphalt mixtures

Abstract

To seek a constitutive model that can both describe the viscoelastic response of asphalt mixtures well and be applied to finite-element simulation, a modified fractional-order Zener model (MFZM) was adopted from the mathematical expressions describing viscoelastic materials based on fractional calculus theory in this study. The MFZM was verified by the generalized fractional-Zener model, and the corresponding model configuration was provided. In this model, the dynamic response and relaxation-modulus function were derived. Based on the relaxation-modulus function, a numerical algorithm for the MFZM that can be implemented in a finite-element environment was proposed. The ability of the fractional-Zener model (FZM) and MFZM to characterize the dynamic response of asphalt mixtures was compared using dynamic modulus test. The dynamic modulus and semicircular bending (SCB) tests of the asphalt mixture were simulated using the proposed numerical algorithm in the software ABAQUS. The results demonstrate that, unlike FZM, MFZM can characterize the asymmetric characteristics of viscoelastic response of the asphalt mixture in the frequency domain. The simulation result of the dynamic modulus test agreed with the analytical solution of the MFZM in the frequency domain, which illustrated the availability of the proposed numerical method for the response of the asphalt mixture in the frequency domain. Moreover, the consistency between the actual experimental and virtual results of SCB proved the accuracy of the model and applicability of the proposed numerical method, allowing the model to be used in a finite-element environment.