解析法求解成层渗透各向异性地基Biot固结轴对称问题

Solutions for Axisymmetric Biot Consolidation Problems of Layered and Anisotropic Permeability Soil by Analytics

采用解析法研究成层渗透各向异性地基 ,该法从渗透各向异性 Biot固结轴对称问题的基本方程 (静力平衡方程 ,物理方程及渗透连续方程 )出发 ,利用 L aplace～Hankel变换及有关矩阵理论等 ,得到 Biot固结基本量不同深度之间的传递矩阵。利用传递矩阵 ,边界条件以及 Laplace～Hankel逆变换技术可求解多层渗透各向异性地基体系。采用更为有效的 F.Durbin的方法实现 L aplace逆变换。编制了计算程序 ,可更方便地计算成层渗透各向异性地基 ,且精度高 ,速度快 ,假定少。

In this paper, layered and anisotropic permeability soil is studied by analytics. This method is based upon basic equations of static equilibrium, permeability continuum and physics of axisymmetric Biot consolidation, and by making use of Laplace Hankel transforms and related matrix theories, transfer matrix of Biot consolidation basic parameters between different depth is obtained. By associating the transfer matrix, boundary conditions and inverse Laplace Hankel transforms, multi layered soil can be calculated. More effective method of F. Durbin is applied to realize inverse Laplace transform. Program is written, and layered and anisotropic permeability soil can thus be caluclated more easily with advantages of high precision, fast execution and fewer hypotheses. An example is finally given.