Fig. 1

Schematic illustration of the 3-D model and the fault friction properties. a Geometry of the 3-D model simulating mining-induced faulting. b 3-D image illustrating the Mohr–Coulomb failure criterion for the friction cone on the fault plane. The shear stress state on the fault plane is represented by two orthogonal shear stresses, τ₁ and τ₂. The relationship between the normal stress σ_n and the shear stress τ indicates that particles adhering within the red circle slide undergo sliding once they intersect with this circle. c Slip-weakening diagram where the average shear stress is assumed to increase from an initial to peak stress with no slip and then linearly decrease to a dynamic resistance level over D_c