Fractional viscoelastic modeling of asphalt concrete: parameter evolution and application to cyclic creep-recovery behavior

This study presents the development of a fractional derivative viscoelastic creep model, specifically the fractional Burgers model with tandem dashpot (FBM-D), to characterize the creep-recovery behavior of asphalt mixtures under cyclic loading and unloading. Creep-recovery experiments were performed on multiple asphalt mixtures at various temperatures and stress levels. An enhanced particle swarm optimization algorithm, integrated with an inverse Laplace transform method, was employed to identify viscoelastic parameters efficiently and accurately. The FBM-D model demonstrated superior computational stability, parameter identifiability, and fitting accuracy compared to alternative fractional models. Analysis of parameter evolution revealed temperature and stress significantly influence the instantaneous modulus, viscosity coefficients, and fractional order, explaining the increased rutting susceptibility under hot and heavily loaded conditions. The viscosity coefficient η₁ of the series-connected dashpot follows an increase-stabilize-decrease trend with cyclic loading. The fractional operator α₁ was found to approach unity with loading time, indicating a transition from nonlinear fractional to classical integer-order viscoelastic behavior.