扩展有限元法在岩石断裂力学中的应用

APPLICATION OF EXTEND FINITE ELEMENT METHOD TO ROCK FRACTURE MECHANICS

岩石裂纹的扩展是一个经典的不连续问题,常规有限元方法难以实现裂纹扩展过程的仿真模拟。扩展有限元法(XFEM)实现了计算网格与不连续面相互独立,因此模拟移动的不连续面时无需对网格进行重新剖分。本文介绍了XFEM基本原理和岩石断裂力学常用判据,尝试对岩石类材料单缝Ⅰ型三点弯曲、单缝剪切和双缝平板实验进行模拟。分析结果表明:扩展有限元模拟岩石类材料断裂问题不受网格划分限制,裂纹以实际应力场分布随机扩展;直观地给出岩样的微裂纹产生、演化,直至完全破坏的全过程,并与实验结果吻合。该方法能够应用到岩石断裂力学方面的研究,模拟岩石类材料的宏细观破坏过程,为解决复杂问题提供了方便的途径。

Rock crack propagation cannot be simulated with conventional finite element method because it is a classic discontinuity problem. Extended finite element method( XFEM) can implement the mutual independence of computational grid and discontinuity. So there is no need to re-mesh the grid model for moving discontinuity simulation. This paper introduces the basic principles of XFEM and universal criterion for rock fracture mechanics.It utilizes XFEM to simulate I mode and II mode fracture in three-point bending test as well as the double-crack shear fracture test. All the obtained results indicate that using XFEM to simulate rock fracture cannot be restrained by mesh generation and the cracks propagate randomly according to the actual stress distribution. The whole process of micro crack generation and evolution until the final total destruction of rock can be directly observed,which havegreat agreement with laboratory test results. This method has demonstrated its ability to investigate rock fracture mechanics and to simulate rock macroscopic and microscopic fracture process. It provides a convenient way for complex issues solution.