Universal linear viscoelastic approximation property of fractional viscoelastic models with application to asphalt concrete

The paper presents a comprehensive linear viscoelastic characterization of asphalt concrete using fractional viscoelastic models. For this purpose, it is shown that fractional viscoelastic models are universal approximators of relaxation and retardation spectra. This essentially means that any spectrum can be mathematically represented by fractional viscoelastic models. Characterization of asphalt concrete is performed by constructing the dynamic modulus master curve and determining the parameters of the generalized fractional Maxwell model (GFMM). This procedure is similar to the widely used one of determining the master curve of asphalt concrete using a statistical function such as the sigmoidal model. However, from the GFMM, the relaxation modulus, creep compliance, continuous relaxation spectrum, and Prony series parameters can be determined analytically. A further advantage of the GFMM is that unlike the sigmoidal model, which only gives a representation of either the dynamic modulus or the storage modulus, the GFMM gives a representation of both the storage modulus and loss modulus (and therefore also the dynamic modulus and phase angle). The procedure was successfully applied to ten different mixes used in the State of Virginia.