Mathematical simulation of rock mass destruction zones by explosion

Purpose. Improving the parameters of the rock mass destruction zones by a blasting, depending on the pressure of the explosion products in the charging cavity and the physical and mechanical properties of rocks by combining analytical and numerical mathematical simulation. The methodology of research. Using the theory of elasticity and the main provisions of the quasi-static wave hypothesis of the mechanism of destruction of a solid medium under the action of an explosion, an analytical simulation of the parameters of the formation of crush zones and grinding of a rock mass around the charging cavity under its explosive load was carried out. After the change in the stress-strain state of the massif under the action of the explosion, numerical simulation of the crushing zones, intensive grinding and cracking by the finite element method was carried out. To establish the suitability of the obtained analytical models for calculating the radii of the indicated zones, the results of analytical and numerical simulation were compared. Findings. Analytical models have been developed for the radii of the zones of crushing, intense grinding and cracking, which are formed around the charging cavity in the rock mass under its explosive load, taking into account the pressure of the explosion products, the tensile-compressive strength of the rocks, their structural structure, and fracturing. Numerical simulation of the destruction of rocks around the charging cavity established the power-law dependences of the change in the radii of the crushing zones and the grinding of the massif depending on the diameter of the charging cavity, the pressure of the explosion products, and the compressive strength of the rocks. By comparing the results of analytical and numerical simulation for rigid boundary conditions of a homogeneous non-fractured massif, the discrepancy between the radii of the indicated zones is found to be 4, 8 and 6%, respectively. The originality. The radii of the zones of crushing, intense grinding and cracking, established by mathematicalsimulation, formed during the explosive destruction of the rock mass, change according to a power law dependence on the diameter of the explosive charge, the pressure of the explosion products in the charging cavity, the strength of the rocks in tension-compression, the coefficients of the rock structure, structural weakening and compaction, determine the increase in the accuracy of estimating the parameters of the destruction of the rock mass up to 50%. Practical implications. Based on mathematical models of the radii of the zones of crushing, intense grinding and cracking, which are formed in the rock mass around the charging cavity under the action of an explosion, improved parameters of drilling and blasting operations are determined for mine workings, special-purpose cavities and breaking of the massif.