一种模拟岩体裂纹扩展的三角单元网格开裂技术

基于三角网格的几何特征,提出一种利用有限元方法模拟岩体裂纹扩展的三角单元网格开裂技术。该方法选取三角网格进行单元离散,采用远场围线积分计算裂尖应力强度因子,由最大周向应力准则确定裂纹扩展方向,最后通过开裂单元的网格分裂或节点移动,实现裂纹扩展的数值模拟。以有限宽中心裂纹板、曲线翼型裂纹扩展和含孔洞多裂隙岩体的裂纹扩展为例进行模拟验证。结果表明:在该方法中,裂纹可以直接劈开一个单元,或沿单元边界扩展,因此裂纹能够不受初始网格的限制沿任意路径扩展;与现有的网格重构算法相比,该方法只须对裂尖局部单元进行网格开裂或节点移动,更加简便、高效,该方法还具有较好的适用性,能够准确模拟拉伸、压剪等复杂应力状态下的裂纹萌生和扩展。

A triangular mesh split method for simulating crack propagation in rock matrix

Based on the geometrical characteristics of triangular meshes, a triangular mesh split method was proposed to simulate the propagation of cracks in rock matrix. Firstly,the rock matrix with primary cracks was divided by triangular elements. Then the stress intensity factors were calculated using a far-field contour integral, and the orientation of the crack propagation can be determined via the maximum circumferential stress criterion. Finally,the numerical simulation of crack propagation was realized by the mesh splitting or node movement. The applicability of the triangular mesh split algorithm was verified in case studies, including the crack propagation in a centrally cracked panel with a finite width, along curved wings and in a multi-fractured rock matrix with holes. The results show that the crack can split a unit element or can be extended along the mesh boundary,therefore the crack can be extended along arbitrary path without the limitation of the original mesh. Compared with the existing mesh reconstruction algorithm,this method is more convenient and efficient for use, and it can be also used effectively to simulate the initiation and propagation of cracks under complex stresses including tension, compression and shearing.