Numerical simulation of the line of least resistanceduring the explosion of charges

Abstract

Purpose. To establish the analytical regularity of the calculation of the maximum value of the line of least resistance (LLR) of the explosive (E), taking into account the physical and mechanical properties of the rock mass and the detonation characteristics of the explosive. The methodology of research. Numerical modeling by the finite element method (FEM) to change the stress-strain state of the model established the value of the LLR at different diameters of the charge cavity, the pressure of explosion products and the tensile strength of rocks. Regression analysis obtained an empirical pattern of changes in the LLR depending on the physical and mechanical properties of the rock mass and the detonation characteristics of explosives. Mathematical modeling establishes analytical regularities of LLR calculation for zones of crack formation and intensive fragmentation. Findings. According to the change in the stress state of the model material around the charging cavity, the empirical regularity of changing the maximum value of the LLR depending on the diameter of the charging cavity and the diameter of the explosive charge, the density and rate of detonation of explosives, the compressive and shear strength. According to the developed calculation scheme, analytical regularities of LLR calculation for zones of crack formation and intensive fragmentation are obtained. By comparing the results of LLR calculation according to the obtained regularities, the most correct formula for LLR calculation was chosen, which turned out to be the analytical regularity of LLR calculation for the zone of intensive fragmentation. The originality. The power law is established for determining the LLR of an E, which comprehensively takes into account the radius of the crush zone, the diameter of the charging cavity and charge, the density and detonation velocity of E, the compressive strength of rocks, their fracturing and compaction under the action of rock pressure, which makes it possible to calculate the parameters of drilling and blasting (D&B) for breaking massif along the zone of intensive fragmentation. Practical implications. According to the results of the research, an analytical regularity of the calculation of the LLR of the explosive charge in the zone of intensive fragmentation was obtained, the use of which will allow to rationalize the D&B parameters in ore mining with the help of industrial explosives.