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

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.