A Method of Calculating Critical Depth of Burial of Explosive Charges to Generate Bulging and Cratering in Rock

For underground explosions, a thin to medium thickness layer near the cavity of an explosion can be considered a theoretical shell structure. Detonation products transmit the effective energy of explosives to this shell which can expand thus leading to irreversible deformation of the surrounding medium. Based on mass conservation, incompressible conditions, and boundary conditions, the possible kinematic velocity fields in the plastic zone are established. Based on limit equilibrium theory, this work built equations of material resistance corresponding to different possible kinematic velocity fields. Combined with initial conditions and boundary conditions, equations of motion and material resistance are solved, respectively. It is found that critical depth of burial is positively related to a dimensionless impact factor, which reflects the characteristics of the explosives and the surrounding medium. Finally, an example is given, which suggests that this method is capable of calculating the critical depth of burial and the calculated results are consistent with empirical results.