The method for determining the parameters of the diagrams of a truncated-wedge destruction of cylindrical samples of rocks

Abstract

Purpose. Development of an analytical method for calculating the parameters of complete diagrams longitudinal tension deformation for the truncated-wedge shape of destruction of cylindrical rock samples to control the stress-strain state of the rock mass and effective destruction of these materials during disintegration. Methodology. Analytically, by developing a mathematical model of the fracture process of cylindrical rock samples with their truncated-wedge form of crack development, an algorithm is created for calculating the full deformation diagram from the acting tension using the experimental values of four indicators of material properties the shear resistance limit, internal and external friction coefficients and elastic modulus. The method is based on the improved Coulomb strength criterion, supplemented by the parameters of contact friction and allowing one, using the theory of slip lines, to calculate the limiting state of the material at the tip of cracks developing from the edges of the sample of the correct geometry, taking into account the release of part of the material from the load and compliance with Hookes law deformation of the sample bearing area and the specific force on it. Findings. The method of mathematical modeling makes it possible to determine the ultimate strength and residual strength of cylindrical rock samples using four property indicators that can be experimentally established by simple methods. Originality. For the first time, analytical modeling of the process of destruction of cylindrical rock samples with their truncated-wedge form of destruction was carried out, taking into account the internal contact friction depending on the properties of the rock material and external contact friction. Practical value. The proposed method of mathematical modeling and the calculation algorithm make it possible to determine the limit and residual strength of rock samples using four property indicators, which can be established experimentally by simple methods under laboratory conditions of enterprises of the mining and metallurgical complex. The calculation results can be quickly used to control the state of the rock mass and effective destruction upon disintegration.