关键词: 流变固结, 分数阶导数, Kelvin模型, Laplace变换, 孔隙水压力, 固结度

Abstract: The Kelvin model is modified by the spring-pot element based on the Caputo fractional derivative to describe the one-dimensional rheological constitutive relation of saturated clay. The rheological consolidation equation is derived with the assumptions proposed in Terzaghi's one-dimensional consolidation theory of saturated soil. The numerical analysis is performed by using the Laplace transform and its numerical inversion based on Fourier series expansions. To verify this method, the numerical solutions by the present method for the cases of the integer order derivative are compared with their analytical solutions. The applicability of the modified Kelvin model is verified by the simulation results of one-dimensional rheological consolidation test in the literature. The influences of the fractional order and the coefficient of viscosity of spring-pot component on the rheological consolidation process of soil are investigated. The calculated results show that the dissipation rate of pore water pressure is greater than that based on Terzaghi's one-dimensional consolidation theory in a long period of consolidation and then less than the latter in the final stage of consolidation. Furthermore, the settlement rate of ground is always less than that based on Terzaghi's theory in the process. Overall, the settlement of ground lags the dissipation of pore water pressure. This phenomenon is obvious and it takes more time to achieve the final settlement with the decrease of the fractional order or the increase of the coefficient viscosity.

Key words: rheological consolidation, fractional order derivative, Kelvin model, Laplace transform, pore water pressure, degree of consolidation