Fractional Derivative Viscoelastic Response Model for Asphalt Binders

The main goal of this paper is to establish an appropriate fractional derivative model with fewer parameters that can model all the viscoelastic characteristics of asphalt binders. Based on this, the fractional derivative model elements and combination types were selected by analyzing the dynamic viscoelastic data. The model consists of two Abel dashpots in series with a Maxwell element (the model is a fractional derivative model composed of four elements in series, called the FDM-4 model). It was validated by describing both the dynamic and static viscoelastic properties of asphalt binders and by comparison with classical viscoelastic models. The advantages and disadvantages of the models were analyzed. Finally, the fractional derivative model was applied to describe the viscoelastic characteristics of asphalt mastics, and it was proved that the model could well describe the viscoelastic characteristics of asphalt mastics. The results indicate that the elements (an elastic spring and Abel dashpot) connected in series with a linear dashpot are better than those connected in parallel from the perspective of model fitting precision. Increasing the number of Abel dashpots in series in the FDM-4 model has little effect on the fitting results. The FDM-4 model can accurately describe the dynamic viscoelastic behavior, static creep, and relaxation characteristics of asphalt binders and asphalt mastics.