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Purpose is the development of a mathematical model to study and describe thermal processes within the borehole wall in terms of plasma-based rock breaking.Methods. The following has been applied: theoretical analysis in the framework of a theory of brittle thermoelasticity breaking, methods of mathematical modeling, and computational experiment.Findings. Brief information on the results of the development of advanced plasma-based technology for borehole reaming for hard mineral mining has been represented. The results of industrial tests of plasma plant of 150-200 kW·s power with plasma-generating gas in the air for hard rock breaking have been represented. The plant and plasma-based technology of borehole reaming were tested in underground conditions of Kryvbas mines while reaming a perimeter hole to drive a ventilation rise in silicate-magnetite quartzites. A mathematical model has been proposed to analyze heat and mechanical fields in the rock during the plasma-based action on the borehole walls. Numerical studies of the temperature dynamics and thermal stresses within the borehole-surrounding rock layer have been carried out. It has been demonstrated that if low-temperature plasma is used (Т = 3500-4000°С), thermal compressing stresses are induced within the thin rock layer; the stresses may exceed the boundary admissible ones. It has been identified that plasma-based effect on the borehole wall makes it possible to create the conditions for intense rock fracturing and breaking.Originality. Solution of a new problem of thermoelastic state of a borehole wall in terms of plasma action has been obtained. The proposed mathematical model has been formulated in a cylindrical coordinate system and considers convective and radiation heat exchange between a plasma jet and a borehole wall.Practical implications. The obtained results make it possible to assess the rock state depending on the plasma jet parameters. The proposed methods of calculations will help carry out research to evaluate breaking parameters (the required heating time, thickness of the heated layer, and approximate spall dimensions) and develop different methods for the breaking process control.

Mathematical modelling of thermal stresses within the borehole walls in terms of plasma action