General fractional models for linear viscoelastic characterization of asphalt cements

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Rheological models based on fractional order derivatives have been applied to characterize the linear viscoelasticity of asphalt cements for a long time. Such models provide continuous spectra which are fundamentally related to the molecular characteristics and facilitate analytical investigations as compared to discrete representations. With the increasing complexity in asphalt composition to satisfy various purposes, however, the inadequacy of existing fractional models has been noted. This paper proposed a generalized fractional Maxwell-dashpot (GFMD) model as a general framework for describing the modulus behaviors of asphalt cements. The generalized fractional Voigt (GFV) model was considered the counterpart for the compliances. The material functions given by each model are primarily the superposition of its constituent fractional Maxwell-dashpot or fractional Voigt (FV) elements. Geometric features of these elements were investigated such that a proper initial guess of model parameters can be obtained graphically with relative ease. For computational efficiency, the continuous spectra were discretized to provide the Prony representations of the material functions. To demonstrate the model capability, the dynamic mechanical data of a neat asphalt showing the typical behavior and a heavily polymer-modified asphalt exhibiting strong cross-linking were utilized. For the typical behavior, the GFMD and GFV models containing two fractional elements yielded excellent descriptions. A third fractional unit was necessitated in both models to account for the cross-linking mechanism for the modified asphalt. A relaxation/retardation mode density of two points equidistantly per decade produced material functions with negligible waviness and almost the same accuracy as compared to the use of the continuous spectra.