Fractional viscoelastic constitutive modelling of real-time strain response for asphalt pavement composites subjected to simulating wheel loadings

This paper proposed a replacement of the Kelvin–Voigt model with fractional basic elements, and the model constructed with this method was used to describe the viscoelastic strain response of asphalt pavement materials under the simulated wheel loading. Similarities between Abel element and Kelvin–Voigt model were explored, and strain response analytical solutions of Burgers and 1S1A1D models under intermittent have sine loading were derived. Then, different intermittent loading tests of asphalt binder and mixture were carried out. The results showed that both the Abel element and the Kelvin–Voigt model could represent the delayed viscoelastic behaviours accurately, and the strain response represented by them could be fully recovered during the unloading stage. Furthermore, parameters of the Abel element and Kelvin–Voigt model showed a high degree of correlation, and the 1S1A1D model exhibited the best effects for asphalt binders, particularly during the unloading period, with correlation coefficients mostly above 0.999. Moreover, when expressing the strain response of asphalt mixture under simulated wheel loading, the 1S1A1D model outperformed the Burgers model in terms of peak strain value, residual strain and changing trends. This study demonstrated that the fractional constitutive model was advantageous in representing the strain response of asphalt pavement composites.