岩体多裂纹扩展演化过程数值流形方法研究  

STUDY ON NUMERICAL MANIFOLD METHOD FOR EVOLUTION PROCESS OF MULTI-CRACK PROPAGATION IN ROCK MASS

作　　者：韩智铭 刘庆宽 王雪[4] 谭超 高一帆 HAN Zhi-ming;LIU Qing-kuan;WANG Xue;TAN Chao;GAO Yi-fan(School of Civil Engineering,Shijiazhuang Tiedao University,Shijiazhuang 050043,China;State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures,Shijiazhuang Tiedao University,Shijiazhuang 050043,China;Wind Engineering Research Center,School of Civil Engineering,Shijiazhuang Tiedao University,Shijiazhuang 050043,China;School of Civil Engineering,Hebei College of Engineering,Shijiazhuang 050091,China)

机构地区：[1]石家庄铁道大学土木工程学院,石家庄050043 [2]石家庄铁道大学省部共建交通工程结构力学行为与系统安全国家重点实验室,石家庄050043 [3]河北省风工程和风能利用工程技术创新中心,石家庄050043 [4]河北工程技术学院土木工程学院,石家庄050091

出　　处：《工程力学》2021年第S01期7-13,共7页Engineering Mechanics

基　　金：河北省自然科学基金项目(E2019210182);石家庄铁道大学基本科研业务费科研项目(ZQK202007);国家自然科学基金项目(51778381);河北省自然科学基金项目(E2018210044)。

摘　　要：岩体中含有大量节理、裂隙、断层等各类结构面,结构面在应力作用下的扩展与贯通是导致岩体破坏的重要原因。数值流形方法(NMM)可以有效模拟连续和非连续问题,然而,其在多裂纹动态扩展的模拟方面仍处于探索阶段。该文以线弹性断裂力学原理为基础,提出了一种基于高阶数值流形方法的多裂纹扩展模拟算法。通过在基函数中增加关键项来考虑裂纹尖端位移场的奇异性;裂纹尖端的应力强度因子则采用了J积分来计算;Ⅰ型-Ⅱ型混合裂纹的开裂和扩展方向依据最大周向拉应力准则来判断;采用假设-修正的多裂纹扩展算法解决了多裂纹的扩展问题。根据强化后的基函数,对于不符合单纯形积分形式的被积函数,采用了泰勒级数展开式计算近似解。通过多个静态裂纹扩展的经典问题的数值模拟对计算方法的合理性和计算精度及进行了验证。Rock mass is a kind of geological material containing a large number of joints, cracks, faults and other structural planes. The expansion and penetration of the structural planes under stress is an important cause of rock mass failure. The numerical manifold method(NMM) can directly simulate continuous and discontinuous problems. However, in the simulation of multi-crack dynamic propagation, NMM is still in the exploratory stage.Based on the principle of linear elastic fracture mechanics, a multi-crack propagation simulation algorithm for higher-order numerical manifold method(NMM) is presented. The singularity of the crack tip displacement field was considered by adding key terms of the crack tip displacement field function to the basis function of the NMM. The stress intensity factor at the crack tip was calculated by J integral. The cracking and propagation directions of Ⅰ-Ⅱ mixed cracks were judged by the maximum circumferential tensile stress criterion. Hypothesismodified multi-crack propagation algorithm was used to solve the problem of multi-crack propagation. For those integral functions which do not conform to the simplex integral form, Taylor series expansion method was used to calculate the approximate solution. The accuracy of the calculation method were verified by numerical simulation of two classical static crack propagation problems.

关 键 词：多裂纹扩展 数值流形方法 断续节理 应力强度因子 J积分 

分 类 号：TU45[建筑科学—岩土工程]