轴对称多层可压缩渗透各向异性岩基固结分析

从轴对称固结基本方程出发，通过对时间t、坐标r的Laplace-Hankel变换，再对坐标z的Laplace变换，得到三元一次方程组，解此方程组，并进行Laplace逆变换，得到了单层可压缩渗透各向异性岩基轴对称固结问题的传递矩阵，然后利用传递矩阵法，结合层间连续性条件和边界条件，得到了多层可压缩渗透各向异性岩基轴对称固结问题在积分变换域内的解。最后应用Laplace-Hankel逆变换技术得到轴对称固结问题在物理域内的理论解。编制了相应的计算程序，并进行了数值计算与分析，讨论了可压缩性和渗透各向异性对岩基固结的影响，结果表明：可压缩性越大，岩基瞬时沉降越大；渗透各向异性对固结过程影响明显，但对初始和最终沉降的影响很小。

Axisymmetric consolidation of a multilayer rock with anisotropic permeability and compressible constituents

Starting from the governing equations of axisymmetric consolidation, together with the technique of Laplace-Hankel transform with respect to time t, coordinate r, and Laplace transform to coordinate z, respectively, a set of linear equations in the transform domain is obtained. After solving these linear equations, the transfer matrix for a single layer rock with anisotropic permeability and compressible constituents is acquired. Based on the continuity and the boundary conditions, the transfer matrix method is utilized to derive the solution of the multilayer rock with anisotropic permeability and compressible constituents in the transform domain. By the inversion of the Laplace-Hankel transform, the solution of consolidation problems for the multilayer rock with anisotropic permeability and compressible constituents in the physical domain is obtained. Numerical calculation and analysis are carried out by the computer program; and the effects of the compressibility of pore fluid and anisotropic permeability on the process of consolidation is discussed. The results show that growing compressible constituents will cause larger immediate settlement of the rock; and the influence of anisotropic permeability on consolidation process is obvious, but minute on initial and immediate settlement.