Analytical method for calculating the strength limit of rock specimens of wedge form of destruction at linear distributing of contact normal tensions

Abstract

Abstract. An analytical method for calculating the parameters of the “stress – deformation” diagrams of prismatic samples with their wedge-shaped destruction is presented based on the distribution of the L. Prandtl contact stresses with using experimental values of four indicators of rock properties: shear resistance limit, internal and external friction coefficients, elastic modulus, which can be determined experimentally by simple methods in mining enterprises, where the calculation results can be promptly used. The method is based on the theory of local destruction of rocks along sliding lines developed by the authors. The theory makes it possible to determine the current values of the normal stresses at the crack tip during its development. As a strength criterion, the Coulomb strength criterion was adopted, supplemented by the authors by taking into account contact friction. The regularities of the distribution of normal stresses from contact friction were previously established by E.P. Unksov and L. Prandtl. The regularity of E.P. Unksov was used by the authors earlier to develop a method for calculating the strength limit of rock samples of the mentioned form of destruction. In this paper, the method is based on the method of L. Prandtl. To determine the strength limit, it was necessary to develop a method for calculating the parameters of “normal stress – longitudinal deformation” diagrams. The fact is confirmed that the stress at which the crack is formed is not the limit strength. The limit strength in the case of wedge-shaped destruction of the samples is the maximum value of the normal stress on the out-of-limit branch of the “stress- deformation” diagram. Some exorbitant curves have stress discharge, which are confirmed by experimental observations. At the moment of discharge, areas appear in the form of a so-called yield tooth, the formation of which we explain by the stresses discharge on the convex part of the slip line. In the middle part, the out-of-limit curves have stress jumps, which indicate the strengthening of the samples, which have not yet received any theoretical justification. We explain this phenomenon by the transition of the destruction process from the convex part of the slip line to the concave one. Comparison of the calculated strength limit of prismatic samples obtained according to the laws of distribution of contact normal stresses, exponential – by E.P. Unksov and linear – by L. Prandtl testifies to their practical identity. Keywords:rock, strength limit, destruction, crack, “stress – deformation” diagram.