二维圆形截面浅埋硐室双层围岩塌落形态上限变分分析  

Upper bound variation analysis of two-layer rock collapse overlying a two dimensional circular shallow buried chamber

作　　者：曾中林 左学贤 王志斌[2] 赵志刚 ZENG Zhonglin;ZUO Xuexian;WANG Zhibin;ZHAO Zhigang(School of Civil Engineering,Central South University,Changsha 410075,China;School of Civil Engineering,Hunan University of Science and Technology,Xiangtan 411201,China;China Railway Seven Engineering Group Co.,Ltd,Zhengzhou 450016,China)

机构地区：[1]中南大学土木工程学院,湖南长沙410075 [2]湖南科技大学土木工程学院,湖南湘潭411201 [3]中铁七局集团有限公司,河南郑州450016

出　　处：《自然灾害学报》2019年第5期96-104,共9页Journal of Natural Disasters

基　　金：国家自然科学基金项目(51478477)~~

摘　　要：考虑岩土体材料的非均质性,本文分析了圆形浅埋硐室顶部双层围岩塌落稳定性。在极限分析上限定理的基础上,构建圆形截面浅埋硐室双层围岩机动许可的速度场,根据Hoek-Brown非线性破坏准则及相关流动法则,推导了塌落极限状态下内能耗散功率以及外力做功功率计算式。根据虚功原理构造泛函,利用变分法求解泛函的极值,进而根据边界条件求得待定系数,并得到了塌落破坏曲面形状。参数分析表明,材料参数A和B以及容重γ的变化对破坏形状有显著影响,而单轴抗拉强度对破坏形状的影响较小。对比了极限分析有限元软件Optum G2的上限结果,两者破坏面吻合较好,由此可说明本文方法的有效性,可为浅埋隧道设计提供理论参考。Considering the heterogeneity of geotechnical materials,the collapse stability of the overlying two layers rock in dimensional circular shallow buried chamber was analyzed in this paper.On the basis of the upper bound theorem of limit analysis,the kinematical admissible velocity field of the two layers rock with a circular chamber was established.According to the Hoek-Brown failure criterion and the associated flow rule,the rate of internal energy dissipation and that of external forces under limit state were calculated.The function was obtained by the virtual work principle,and the extreme value was determined by adopting the variational method.Further,the unknown coefficients were solved according to the boundary conditions,and the shape of collapse surface was obtained.The parametric analysis shows that the material parameters A and B and the bulk densityγhave a great influence on the failure shape,and the uniaxial tensile strength has little effect on that.Compared with the upper bound results of limit analysis finite element software Optum G2,and the failure surfaces of the two methods were in good agreement,which could illustrate the effectiveness of this method and provide theoretical reference for the design of shallow tunnels.

关 键 词：圆形浅埋硐室 塌落稳定性 双层围岩 上限变分分析 Hoek-Brown破坏准则 

分 类 号：U458.3[建筑科学—桥梁与隧道工程] X9[交通运输工程—道路与铁道工程]