Approximation of the Continuous Spectrum by the Discrete Spectrum for Tridimensional Linear Viscoelastic Models of Bituminous Materials

Within the small strain domain, the behavior of bituminous materials including bitumen, asphalt mastics, asphalt mixtures are considered as linear viscoelastic and can be simulated by analogical models. The spectrum of the linear viscoelastic models can be either continuous or discrete. Continuous spectrum models are often used to simulate experimental results due to the simple fitting between experiments and modelling. Meanwhile, discrete models are more convenient in computational programs that require explicit behavior equations. This paper focuses on the approximation of two linear viscoelastic parameters of bituminous materials including complex modulus and complex Poisson’s ratio by both continuous and discrete spectrum models. The continuous and discrete spectrum models used in this study are 2S2P1D and generalized Kelvin–Voigt model respectively. The 3D behavior formulas of these models are presented in the paper. The parameters of 2S2P1D continuous spectrum model were obtained by fitting the experimental results. In this paper, a method has been developed to determine the parameters of generalized Kelvin–Voigt discrete model by approximating the complex modulus and complex Poisson’s ratio from continuous model 2S2P1D. The obtained results show that the approximation method gives very good results for both complex modulus and complex Poisson’s ratio (i.e., the tridimensional behavior of the material). The method works efficiently even when the number of discrete elements is limited to 20 elements.