关键词: 半透水边界, 分数阶导数, 黏弹性, 饱和土, 一维固结, 半解析解

Abstract: The fractional Kelvin-Voigt viscoelastic model is introduced to describe the rheological characteristics of saturated soils. One-dimensional consolidation characteristics of saturated soils with fractional viscoelastic model under symmetric semi-permeable boundaries is studied. By applying these two models, the analytical solution to the one-dimensional consolidation is obtained in the Laplace transform domain. Crump’s method is adopted to perform the inverse Laplace transform to obtain semi-analytical solutions in the time domain. By reducing the proposed solution to one dimensional consolidation equation of saturated soils under symmetric semi-permeable boundaries using these two models, it is shown that the present solution is reliable and in a good agreement with the existing solutions from literatures. Finally, several numerical examples are provided to investigate the consolidation behavior of saturated soils with the fractional viscoelastic model under symmetric semi-permeable boundaries. It can be found that the one-dimensional consolidation process is affected by the semi-permeable boundary parameters, fractional order and viscosity coefficient, and the modulus of compressibility has a significant effect on the final settlement of saturated soil.

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