莫尔圆极点法的数学理论探源和工程应用探讨

Discussion on Mathematical Theory and Engineering Application of Mohr's Circle Pole Method

莫尔圆在应力路径、地基承载力、挡土压力等方面得到了广泛应用,也常用于解释试验数据和预测岩土变形。莫尔应变圆上有一个特殊的点,这个点被称为极点。这个极点跟单元体的应变状态有关,而且其特点在于可以通过它来达到任何平面的应变状态。首先,分析了莫尔圆极点法的数学原理,介绍极点和极线;其次,探讨了莫尔圆极点法的内在特性;最后,分析了其在工程应用中的优势。

Mohr's circle has been widely used in stress paths,foundation bearing capacity,retaining pressure,and other aspects,and is also commonly used to interpret test data and predict rock and soil deformation.There is a spe-cial point on the Mohr strain circle,which is called a pole.The pole is related to the strain state of the element,and its characteristic is that the strain state of any plane can be reached through it.This article first analyzes the math-ematical principles of the Mohr's circle pole method and introduce poles and polar lines,then explores the inherent characteristics of the Mohr's circle pole method,and finally analyzes its advantages in engineering applications.