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.