岩体工程有限元分析中弱面的力学模型——弱面单元分析

本文较系统地讨论了模拟岩体弱面的等厚度四节点弱面单元,着重分析了岩体转动对弱面单元的影响。并指出:即使弱面厚度很小,但只要弱面产状处在不太有利位置,或绕弱面单元端点转动,都会给单元剪应力从正或负的方面带来很大影响,甚至改变单元由滑动所产生的剪应力的符号。文中详细的推导了考虑转动影响的弱面单元的几何矩阵B]~e、单元应力矩阵S]~e、单元刚矩度阵K]~e以及单元初始应力所引起的等效结点荷载等计算公式。文中还证明了古德曼节理单元是等厚度弱面单元的一种特殊情况--即δ/l趋于零的情况.

The Mechanical Model for the Weak Plane with Finite Element Analysis in Rock Mass Engineering——-Element Analysis of the Weak Plane

This paper discusses the simulation of weak plane by means of four-node weak plane element with uniform thickness, laying emphasis on the influence of turning rock mass to the weak plane element. No matter how small the thickness of the weak plane is, the great influence to shear stress is produced due to rock mass turning if the element of the weak plane is turned round the end of the element, even the positive and negative symbols of the shear stress of element are changed due to rock mass slipping. A set of mathematical formulas are well established in the paper, including the geometric matrix B]e, stress matrix S]e and stiffness matrix K]e of the elements referring to turning influence as well as the equivalent nodel load equation due to initial stress. It is proved that Goodman's joint element is a special case of four-node weak plane element with uniform thickness whenδ/1= 0.