Numerical Simulation of Viscoelastic Behavior of Asphalt Mixture Using Fractional Constitutive Model

An innovative procedure was proposed to simulate the viscoelastic mechanical behavior of asphalt mixture. The existing fractional viscoelastic models were quantitatively analyzed, and the fractional Zener model was adopted. The model parameters were obtained by fitting the storage modulus and loss modulus simultaneously. The relaxation modulus of the fractional Zener model in the time domain was deduced using the Mittag-Leffler function. The numerical algorithm of the fractional Zener model was proposed and implemented into finite-element (FE) software ABAQUS version 6.9. Simulations of the relaxation test were conducted to verify the effectiveness of the numerical algorithm and the FE implementation. Then dynamic modulus tests were simulated, and the master curve of the storage and loss modulus was calculated. The simulation results indicated that the fractional Zener model can be effectively applied to FE analysis and accurately predict the storage modulus and loss modulus master curve of asphalt mixture in a wide frequency or temperature range.