基于网格自适应加密策略的隧道稳定性三维极限分析下限有限元法研究  

Three-dimensional lower bound finite element limit analysis method for tunnel stability based on adaptive mesh refinement strategy

作　　者：孙锐 阳军生[2] 张庆贺 杨峰[2] SUN Rui;YANG Jun-sheng;ZHANG Qing-he;YANG Feng(School of Civil Engineering and Architecture,Anhui University of Science and Technology,Huainan,Anhui 232001,China;School of Civil Engineering,Central South University,Changsha,Hunan 410075,China)

机构地区：[1]安徽理工大学土木建筑学院,安徽淮南232001 [2]中南大学土木工程学院,湖南长沙410075

出　　处：《岩土力学》2024年第4期1256-1264,共9页Rock and Soil Mechanics

基　　金：安徽高校自然科学研究重点项目(No.2022AH050840);安徽理工大学高层次引进人才科研启动基金(No.2022yjrc31)。

摘　　要：网格分布形式对三维极限分析下限有限元法的计算精度影响较大,为获取精确下限解,通常需对破坏区域进行密集网格划分,从而极易导致计算规模过大,求解效率低下。针对上述问题,提出一种基于单元应力的三维极限分析下限有限元“后验”网格自适应加密策略。首先,构建基于Mohr-Coulomb(M-C)准则和半定规划技术的三维极限分析下限有限元模型,避免了屈服准则的近似处理。其次,引入基于M-C准则的网格自适应加密策略,通过判断各个单元应力接近屈服的程度,确定加密点的坐标。然后,将加密点与原先节点组合构成新的点集,并重新划分网格,建立新的下限有限元计算模型。最后,利用所提方法研究隧道稳定性问题,表明利用所提网格自适应加密策略能够以较少单元精确模拟破坏区域应力分布,从而获取高精度下限解。The distribution of the mesh significantly impacts the accuracy of calculation in the three-dimensional lower bound finite element limit analysis method(3D LB-FELA).Achieving precise lower bound solutions requires a dense mesh to be pre-divided in the failure area,which can easily lead to excessive calculation scale and reduce solving efficiency.To address these challenges,this paper proposes a"posterior"adaptive mesh refinement strategy.Firstly,the paper proposes a 3D LB-FELA based on M-C criterion and semi-definite programming technique,which eliminates the need for approximating the yield criterion.Subsequently,it introduces an adaptive mesh refinement strategy based on the M-C criterion,determining the coordinates of the refinement points by evaluating the degree to which each element's stress approaches yield.This approach involves combining the refinement points with the original nodes to form a new point set,followed by re-meshing the mesh.Finally,the proposed method is used to study the tunnel stability,and the research results demonstrate that the proposed mesh adaptive refinement strategy can accurately simulate the stress distribution in the failure area with smaller scale elements,thereby obtaining high-precision lower bound solutions.

关 键 词：隧道稳定性 三维极限分析 下限有限元法 MOHR-COULOMB准则 网格自适应加密 

分 类 号：TU457[建筑科学—岩土工程]