A geometrically and locally adaptive remeshing method for finite difference modeling of mining-induced surface subsidence

Surface subsidence induced by underground mining is a typical serious geohazard. Numerical approaches such as the discrete element method (DEM) and finite difference method (FDM) have been widely used to model and analyze mining-induced surface subsidence. However, the DEM is typically computationally expensive, and is not capable of analyzing large-scale problems, while the mesh distortion may occur in the FDM modeling of largely deformed surface subsidence. To address the above problems, this paper presents a geometrically and locally adaptive remeshing method for the FDM modeling of largely deformed surface subsidence induced by underground mining. The essential ideas behind the proposed method are as follows: (i) Geometrical features of elements (i.e. the mesh quality), rather than the calculation errors, are employed as the indicator for determining whether to conduct the remeshing; and (ii) Distorted meshes with multiple attributes, rather than those with only a single attribute, are locally regenerated. In the proposed method, the distorted meshes are first adaptively determined based on the mesh quality, and then removed from the original mesh model. The tetrahedral mesh in the distorted area is first regenerated, and then the physical field variables of old mesh are transferred to the new mesh. The numerical calculation process recovers when finishing the regeneration and transformation. To verify the effectiveness of the proposed method, the surface deformation of the Yanqianshan iron mine, Liaoning Province, China, is numerically investigated by utilizing the proposed method, and compared with the numerical results of the DEM modeling. Moreover, the proposed method is applied to predicting the surface subsidence in Anjialing No. 1 Underground Mine, Shanxi Province, China.