基于二阶锥规划的三维边坡极限分析下限法研究  

Lower Bound Limit Analysis of Three-Dimensional Slopes Using Second-Order Cone Programming

作　　者：孙聪 熊威 李春光[3] SUN Cong;XIONG Wei;LI Chunguang(Wuhan Ecological Environment Design and Research Institute Co.,Ltd,Wuhan 430050,China;Changjiang Survey,Planning and Design Research Co.,Ltd,Wuhan 430010,China;Institute of Rock and Soil Mechanics,Chinese Academy of Sciences,Wuhan 430071,China)

机构地区：[1]武汉生态环境设计研究院有限公司,湖北武汉430050 [2]长江勘测规划设计研究有限责任公司,湖北武汉430010 [3]中国科学院武汉岩土力学研究所,湖北武汉430071

出　　处：《武汉工程大学学报》2023年第4期468-472,共5页Journal of Wuhan Institute of Technology

基　　金：中国科学院国防科技创新基金(CXJJ-16M272)。

摘　　要：由于屈服面梯度不连续,导致基于摩尔库伦屈服准则的三维边坡极限分析问题无法直接使用线性规划求解,从而计算效率低。采用等面积德鲁克-普拉格屈服准则来代替摩尔库伦屈服准则,并在考虑应力平衡、应力连续性条件和应力边界条件的基础上,用非线性规划的二阶锥规划成功构建了三维问题的极限分析下限法计算模型,可以方便地通过凸规划软件直接求解出三维边坡的应力场和安全系数,从真实解的下方收敛,两个算例证明了其可行性。Due to the discontinuous gradient of the yield surface,the limit analysis of three-dimensional slope based on Mohr-Coulomb yield criterion can not be solved directly by linear programming,which causes an inefficient calculation.In this paper,the equal-area Drucker-Pluger yield criterion was used to replace the Mohr-Coulomb yield criterion.Considering the stress balance,stress continuity conditions and stress boundary conditions,we successfully constructed the limit analysis lower bound method calculation model of three-dimensional problems by using the second-order cone programming of nonlinear programming.The stress field and safety factor of three-dimensional slope can be directly solved by convex programming software,from the lower convergence of the real solution.Two examples are given to prove its feasibility.

关 键 词：下限分析 德鲁克-普拉格准则 二阶锥规划 凸规划 边坡稳定性 

分 类 号：TD712[矿业工程—矿井通风与安全]