Finite difference modelling of wave propagation in fractured media with imperfect contact interface conditions

An effective preconditioning method for in situ leaching utilises blasting to enhance orebody permeability, enabling the extraction of minerals from geologically complex formations. However, the limited understanding of the complex interaction between blast-induced stress waves and natural and induced fractures highlights the need for robust and accurate numerical simulations to optimise the process. This work presents a novel finite-difference treatment of the linear slip model, in which traction remains continuous and displacement discontinuous. The fracture interface is represented by splitting the velocity nodes into coincident pairs coupled through a single interface traction, such that the displacement jump is resolved directly as a discontinuity. The interface condition enters as a flux on the fracture face of the control volume, so that the traction-displacement relation is imposed exactly at the discrete level. Fractures are thereby accommodated on a uniform grid through duplication of nodes along the fracture plane alone. Since only two interface nodes are updated differently, the treatment integrates naturally into existing velocity-stress staggered-grid implementations. The scheme is shown to conserve the total discrete energy, including the energy stored within the fracture interface. Furthermore, second-order convergence is demonstrated for the displacement jump arising in elastic media exhibiting widely varying fracture behaviour.