Numerical solutions of elastoplastic problems with application to underground mining stability

"A limited area of plastically deformed rocks forms around underground workings due to a specific combination of the strength of the main rock mass, its structure, and burial depth. The size of this zone and the magnitude of displacements along the excavation boundary determine the stability of the excavation. Analytical solutions of elastic-plastic problems are typically limited to simplified models of the medium (solid, isotropic, homogeneous) and excavation shape (circular). Mathematical modeling of elastoplastic deformation in a structurally heterogeneous rock mass weakened by complex-shaped underground workings is performed solely using numerical methods, such as the finite element method (FEM). In this context, several challenges arise that necessitate a special approach and reasonable assumptions regarding the validation of the deformation model. Uniformly distributed external loads are applied at infinity along the X and Y axes, external, which may be either unequal (λ ≠ 1) or equal (λ = 1) (λ is the lateral thrust coefficient). The magnitude of these loads is sufficient to generate a plastic deformation zone completely enclosing the excavation boundary. Deformation and failure of the rock mass occur under prescribed deformation conditions from the elastically compressed part of the massif. The assumption of continuity of the medium is preserved in both elastic and plastic zones. Since rock mass movement along the longitudinal axis of the excavation is restricted, the case of plane deformation is considered. To solve the problem, it is necessary to determine stress, strain, and displacement components in both elastic and inelastic regions, as well as the size and shape of the boundary L that separates them."