关键词: 分数阶导数, 黏弹性, 饱和土体, 一维固结, 半解析解

Abstract: Theory of fractional calculus is introduced to Kelvin-Voigt constitutive model to describe the mechanical behavior of viscoelastic saturated soil. Applying Laplace transforms upon the one-dimensional consolidation equation of saturated soil and the fractional order derivative Kelvin-Voigt constitutive equation, we derived analytical solutions of the effective stress and the settlement in transformed domains. Then the semi-analytical solution of one-dimensional consolidation problem in physical space was obtained after implementing Laplace numerical inversion by using Crump method. As for two classical cases of elasticity and viscoelasticity, the simplified semi-analytical solutions in this study are the same as those of the two classical cases. It indicates that the analytical solutions of two classical cases can be considered as the special cases of the solutions presented in this paper. Last, parameter studies were conducted to analyze the effects of the various parameters on the consolidation settlement. The results show that, in the case of instantaneous loading, the final settlement is independent on the viscosity coefficient and the fractional order, while the consolidation time is influenced greatly by the viscosity coefficient and the fractional order. The present study contributes to further understand the mechanical behavior of the consolidation of viscoelastic saturated soil.

Key words: fractional order derivative, viscoelasticity, saturated soil, one-dimensional consolidation, semi-analytical solution