层状饱和半空间轴对称Biot固结问题

本文针对饱和多孔介质空间轴对称Biot固结问题，引入状态变量，构造了一组状态变量方程。并利用Laplace-Hankel变换和矩阵理论，提出了单层饱和多孔介质空间轴对称Biot固结问题的传递矩阵。得出饱和半空间表面排水和表面不排水两种情况下场变量积分形式的解。由层间完全接触的条件，给出了N层饱和半空间轴对称Biot固结问题的一般解析表达式和数值算例。Laplace逆变换的计算采用Crump、Durbin、Stehfest和Schapery 4种方法。数值结果表明本文方法有较好的计算效率和较高的计算精度。

Axisymmetric Biot's consolidation problems for multi-layered saturated half space

In this paper axisymmetric Biot's consolidation problems for multi-layered saturated soil are studied. By means of state vectors, state space equation are formulated. Using the Laplace-Hankel transforms and matrix theory, the transfer matrix of axisymmetric Biot's consolidation problems for single layer saturated clay is deduced. The cases of surface permeable and impermeable for the saturated half space are considered. According to the continuity conditions of traction and displacements at layer interfaces, the solutions of axisymmetric Biot's consolidation problems for N Layers saturated half space are presented in the integral form. The numerical example is given. The time domain solutions are obtained by applying the numerical scheme proposed by Crump, Durbin, Stehfest and Schapery for Laplace inversion. Numerical example shows that the proposed method has the advantage of high calculation efficiency and accuracy.