李群变换求解一维非线性有限变形固结问题(英文)

An analytical approach to one-dimensional finite strain non-linear consolidation by Lie group transformation

在对渗透系数与孔隙比以及有效应力与孔隙比的关系作出假设的基础上 ,讨论了不同初值和边值条件下的饱和粘土一维非线性有限变形固结方程 ,同时对不同边界条件的性质进行了评价。研究表明 ,对于一些相对简单的边界条件 ,通过李群变换的方法可以得到非线性固结方程的完整解析解。最后 ,将所得到的解答与Tan&Scott的有关解答进行了分析比较 。

Based on some assumptions for the relationship between permeability and void ratio and between effective stress and void ratio of the clay, the non linear equation governing the progress of one dimensional consolidation of the saturated clay, namely Gibson's Equation, is discussed under different initial and boundary conditions. The properties of different kinds of transformed boundaries are evaluated. It is shown that for some relatively simple conditions, exact analytical solutions of the non linear consolidation equation can be obtained by using the approach of the transformation of Lie group. Finally, the solution obtained in this paper is compared with Tan & Scott's solutions, and some problems that appeared in solutions are analyzed.