Fractional Viscoelastic Models for Asphalt Concrete: From Parameter Identification to Pavement Mechanics Analysis

The fractional viscoelastic model has been applied to characterize the viscoelasticity of asphalt concrete (AC), but it rarely is adopted in pavement structure analysis due to the complicated calculating process. Therefore, simple methods of applying the fractional viscoelastic models in the pavement mechanic analysis are proposed. First, based on the derived complex modulus expressions of the typical fractional viscoelastic model of AC, combined with the particle swarm optimization and interior-point algorithm, a novel global optimization algorithm for the parameter identification of fractional viscoelastic models is proposed. Then, based on the dynamic modulus and phase angle data obtained in laboratory experiments, the viscoelastic parameters of AC were identified, and the performance of different viscoelastic models was evaluated. Subsequently, based on the Grunwald-Letnikov definition of the fractional operator and the Newton-Raphson integration scheme, the numerical implementation algorithm of some typical fractional viscoelastic models of AC in finite element analysis is proposed, followed by compiled user material subroutines (UMATs). Finally, the thermoviscoelastic analysis of an asphalt pavement structure under impact load was conducted, and the mechanical response laws revealed by different viscoelastic models were investigated. The results showed that the fractional viscoelastic model could yield a more accurate prediction of the viscoelasticity of AC in a wider frequency domain compared with the integer-order viscoelastic model. Moreover, due to the ability to simulate the mechanic behavior of the pavement structure in all temperature ranges with fewer parameters, the modified fractional Zener model is recommended for pavement mechanics analysis.