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渗透各向异性可压缩地基固结的平面应变分析

Plane strain consolidation of a multi-layered soil with anisotrpic permeability and compressible constituents

  • 摘要: 对多层地基的平面应变固结问题进行了研究,并同时考虑了土体的渗透各向异性和孔隙流体的可压缩性. 从平面应变Biot固结的控制方程出发,对时间t, 坐标z和x进行Laplace和Fourier变换,建立了地基表面(z=0)和任意深度z处的基本量在Laplace-Fourier变换域内的传递矩阵关系. 利用传递矩阵法,结合土层连续条件和边界条件,并应用Laplace-Fourier逆变换技术,推导出渗透各向异性可压缩多层地基平面应变固结的理论解. 基于该解,编制了计算程序,并进行了数值计算. 讨论了土体的渗透各向异性、孔隙流体的可压缩性以及地基的分层特性对地基固结的影响,分析结果表明:土体的渗透各向异性、孔隙流体的可压缩性,以及地基的分层特性对地基的固结行为有着重要的影响.

     

    Abstract: This paper study the plane strain consolidation of a multi-layered soil, and the anisotropy of permeability and the compressibility of pore fluid are considered. Starting from the governing equations of plane strain Biot’s consolidation, taking the Laplace transform and the Fourier transform with respect to t, z and x, the transfer matrix relationship of basic variables in the transform domain between z = 0 and an arbitrary depth is obtained. The solutions of plane strain consolidation for the multi-layered soil with anisotropic permeability and compressible constituents can be acquired by using the transfer matrix method, continuity conditions and boundary conditions of the multi-layered soil and the inversion of the Laplace-Fourier transform. Numerical analysis is carried out by using corresponding program to investigate the influences of the anisotropy of permeability, the compressibility of pore fluid and the layered characteristic of soil on the consolidation behavior of soil.

     

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