基于改进迭代求解的双孔洞围岩应力场解析研究  

Study on stress field analysis for rock mass containing two cavities based on improved iterative solution

作　　者：蔡鑫[1] 陈立业 周子龙[1] 谭力海 阳俊 CAI Xin;CHEN Liye;ZHOU Ziong;TAN Lihai;YANG Jun(School of Resources and Safety Engineering,Central South University,Changsha 410083,China;School of Resource Environment and Safety Engineering,University of South China,Hengyang 421000,China;Department of Resources and Environment,Hunan Nonferrous Metals Vocational and Technical College,Zhuzhou 412000,China)

机构地区：[1]中南大学资源与安全工程学院,湖南长沙410083 [2]南华大学资源环境与安全工程学院,湖南衡阳421000 [3]湖南有色金属职业技术学院资源环境系,湖南株洲412000

出　　处：《中南大学学报（自然科学版）》2023年第11期4493-4503,共11页Journal of Central South University:Science and Technology

基　　金：国家重点研发计划项目(2022YFC2903901);国家自然科学基金资助项目(52104111,52274249);湖南省自然科学基金资助项目(2021JJ30819,2020JJ7059)。

摘　　要：针对含双孔洞岩体应力迭代求解计算过程中多余面力的求解难题,提出新的理论解析方法。通过引入最优化技术,直接进行不同坐标系和平面中孔洞边界坐标点的变换,无需在求解过程中引入逆映射函数,避免了逆映射函数求解造成的误差。随后,以双拱形孔洞为例,对不同布局下的孔周应力场进行求解与分析,并利用数值模拟对理论求解结果进行验证。研究结果表明:采用所提出的方法可以精确获得双孔洞周边应力分布,显著降低求解难度;在单轴压缩条件下,孔洞体系的初始萌生裂纹为孔洞顶底板拉应力集中区域形成的拉伸裂纹,但最终破坏表现为双孔洞间的贯通破坏;不同连接角的双孔洞体系峰值应力与压应力集中系数呈线性相关关系,说明双孔洞岩石的破坏取决于孔洞边界的压应力集中程度。To address the issue of calculating the residual surface stress during the process of stress iteration solution in the rock mass containing two cavities,a new analytic method was proposed.By introducing the optimization technique,the coordinate transformation of the cavity boundary points was directly realized without considering the of inverse mapping function,so that the error caused by solving inverse mapping function can be avoided,and then the stress solution for plate containing two arched cavities with various layouts were calculated,and corresponding numerical simulations were performed to verify the proposed method.The results show that the more precise stress solution around the arched cavities can be obtained by the proposed method,the computational difficulty is reduced.Under uniaxial compression,the tensile cracks occur near the central top and bottom of hole of the tensile stress concentrations.However,the ultimate failure is characterized by the coalescence in the area between the two holes.In addition,the strength of rock mass containing two arched cavities with different angles shows good linear relationship with the compressive stress concentration factor(SCF),which indicates that the ultimate failure of hole depends on the compressive stress concentration factor around the hole boundary.

关 键 词：复变函数方法 共形映射 应力解析解 双孔洞体系 数值模拟 

分 类 号：TU452[建筑科学—岩土工程]