A closed-form solution to spherical wave propagation in triaxial stress fields

Cost-effective exploration and exploitation activities hinge upon the production of optimum fracture networks via rock blasting. The concurrent increases in lithostatic pressure and temperature have posed significant challenges to mining at deeper formations within the Earth’s crust. To better understand the influences of in-situ stresses on rock blasting efficiency, a new closed-form elastodynamic solution to stress wave propagation from a spherical cavity in a general triaxial stress field is proposed. By transforming the solutions from the time domain to the space of stress invariants, novel insights into the intricate effects of in-situ stresses on dynamic rock behavior are obtained. This paper demonstrates that the different responses of radial and circumferential stresses to static and dynamic loadings draw the initial stress states closer to the yield envelope and thus divert the loading paths during ensuing dynamic impacts. The resulting changes in the patterns of stress trajectories hence cause various mechanisms of dynamic rock yielding in triaxial stress fields under different loading amplitudes. Based on spherical charges rather than the more typical cylindrical ones, our results show quantitatively that in-situ stresses can impair blast fragmentation by promoting dynamic compaction and delaying or even inhibiting tensile fracturing. While dynamic yielding becomes complex in anisotropic stress fields, the major principal stress (σ1) direction tends to be associated with better fragmentation efficiency for the same mode of yielding and radial cracks also propagate preferentially along σ1. Moreover, rational design of loading intensity can enhance rock fragmentation efficiency by promoting brittle yielding in certain in-situ stress conditions.