Analytical and numerical modeling of rock blasting operations using a two-dimensional elasto-dynamic Green's function

Rock media may be exposed to dynamic forces and time-dependent stresses. Dynamic phenomena in rock such as blasting and earthquakes need to propagate waves and dynamic stresses through the body. Therefore, stresses, strains, and displacements in rocks should be defined as time-dependent due to the dynamic phenomena. In this study, a general Greeds function solution of an elastic wave propagation due to rock blasting has been analytically derived. The Navier's equations of motion have been assumed as governing equations and a general two-dimensional elastodynamic Greeds function has been obtained in terms of displacement. The strain and stress fields related to the displacement Greeds function have also been obtained using the theory of elasticity. Then, a generic two-dimensional problem containing an explosion in a blast hole has been solved using the resulting analytical solution. Moreover, a similar numerical modeling has been conducted using Finite Difference Method (FDM). Eventually, results from the analytical scheme have been compared with the finite difference numerical modeling and the valuable results from a previous experimental and numerical study.