有限土层轴对称Biot固结的一个新的解析解

A New Analytical Solution for Axisymmetric Biot's Consolidation of a Finite Soil Layer

提出一个新的解析方法来研究有限土层的轴对称Biot固结.从轴对称Biot固结的控制方程出发,结合Laplace变换的微分性质,建立了Laplace和Hankel变换域内有限土层地基表面(z=0)和任意深度z处基本变量之间的关系.然后结合有限土层的边界条件,推导出Laplace和Hankel变换域内任意一点的解析解.通过进行Laplace逆变换和Hankel逆变换得到了物理域内的解.编制了计算程序,并对有限土层轴对称固结进行了数值分析.

A new analytical method is presented to study the axis-symmetric Biot＇s consolidation of a finite soil layer. Starting from the governing equations of axis-symmetric Biot＇ s consolidation, and based on the property of the Laplace transform, the relationship of basic variables for a point of a finite soil layer was established between the ground surface （ z = 0） and the depth z in the Laplace and Hankel transform domain. Combined with the boundary conditions of the finite soil layer, the analytical solution of any point in the transform domain can be obtained. The actual solution in the physical domain can be acquired by inverting the Laplace and the Hankel transforms. The numerical analysis for the axis-symmetric consolidation of a finite soil layer was carried out by program.