非线性问题的有限单元法在工程地质中的应用

使用有限单元法对岩石基础、边坡和巷道等问题进行稳定分析在国内外做了大量的工作。本文结合我们自己的工作,以平面问题的位移法为例,介绍物理上非线性物体的有限单元分析的基本原理,并对某些具有非线性应力应变关系的岩体介质以及诸如节理、断层等间断面提出一些简单的力学模型。此外,还介绍几个和这些力学模型有关的通用程序以及使用它们得到的某些工程的计算成果。

THE APPLICATIONS OF NON-LINEAR FINITE ELEMENTS METHOD IN ENGINEERING GEOLOGY

The present study deals with the following aspects. The non-linear finite elements method, using initial stress approach, is introduced in detail. The elasto-plastic matrix with non-associated flow rule is extended to the case in which the surface of failure criterion involves singular points. The general theory is applied to establish the elasto-plastic matrices of the jointed rocks, viz. laminar and non-tension mediums, being semi-positive definite. Two simple examples show that the processes used in references 3] and 8] may lead to negative strain energy in some of the elements. By reducing the thickness of a rectangular element to zero, the matrix B] for joint elements in 9] is recovered, and the stress-strain relations for them are also given, thus we have derived stiffness matrix of joint elements. Finally, the brief comments are given for some programs written on the basis of the present mechanical model together with some examples worked out by the authors in applying the method to the stability analysis of the rock foundations, slopes and underground structures.