二维渗透各向异性多层地基Biot固结分析

Two-dimensional Biot Consolidation of Multi-layered Soils with Anisotropic Permeability

从二维渗透各向异性Biot固结问题的基本控制方程出发,对时间t进行Laplace变换,对坐标x进行Fourier变换,构造出Laplace-Fourier变换域内的常微分方程,利用Cayley-Hamilton定理推导出单层地基的传递矩阵。根据传递矩阵的性质,并结合层间连续条件和边界条件,求得了二维渗透各向异性多层地基Biot固结问题在Laplace-Fourier变换域内的解,通过Laplace-Fourier逆变换可求得该问题物理域内的真实解。编制了相应的计算程序,并对数值计算结果进行了比较和分析。计算结果表明:土的渗透各向异性对固结过程中的地表位移有比较显著的影响。

Starting with the governing equations of two - dimensional Biot consolidation with anisotropic permeability, a set of ordinary differential equations in the Laplace - Fourier transforms domain are obtained by taking Laplace transform with respect to the time t and Fourier transform with respect to coordinate x, the transfer matrix of single soil layer is obtained by employing the Cayley - Hamilton theorem. According to the properties of transfer matrix, and combined with the continuity conditions between layers and boundary conditions, the solutions for two - d/mensional Biot consolidation of multi - layered soils with anisotropic permeability in the Laplace - Fourier transforms domain can be obtained, the actual solutions in the physical domain can be acquired by inverting the Laplace - Fourier transforms. A numerical analysis is carried out by using the corresponding program based on the theory given in this paper. The result shows that the anisotropic permeability of soils has a remarkable effect on the surface displacement in the process of consolidation.