Simulation of the process of destruction of cylindrical rock samples

  • Leonid Vasilyev
  • Dmytro Vasilyev
  • Mykola Malich
  • Alexander Nazarov

Abstract

The shear strength of a material is a constant for any point on the crack line. In this case, on the trajectory of maximum effective tangential stresses with the appearance of the first crack, spontaneous destruction of the body would occur. In real conditions, this does not happen. Layered rocks in the presence of cracks carry a certain load. The fact is that contact friction is inevitably involved in the fracture process and slip lines are not linear. During the destruction of brittle rocks with internal and external friction, the final result of the calculation of stresses at the crack tip in rock samples, and in general, in the massif, is significantly distorted. In the presence of contact tangential stresses, for example, from contact friction, the Coulomb criterion of the limiting state is met only locally, at the crack top. In other areas of the slip lines, the material is in an elastic state.
Therefore, for layered rocks, this situation requires the development of a new approach to describing the process of local destruction, which must be taken into account.
The purpose of this article is to develop a mathematical model and reveal the mechanism of local rock destruction.
The work considers a cylindrical rock sample loaded with press plates with a distribution of contact stresses between the sample and the plate according to Prandtl.
A mathematical model is proposed and the mechanism of local fracture is revealed, which consists in the formation of ultimate shear strength of rocks at the crack tops - ultimate effective shear stresses and effective shear stress values ​​that do not reach the shear strength at the points where their trajectories reach the boundary surface.
A dependence is derived for calculating the tensile strength of cylindrical rock samples with a truncated pyramidal form of fracture using the tensile strength of the material, the angle of internal friction, and the coefficient of contact friction, which can be easily established experimentally in mining enterprises, where the calculation results can be quickly used.
A comparison of the calculated values of the ultimate strength under uniaxial compression of the samples with the experimental ones convincingly indicates the high efficiency of the proposed analytical method.

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Published
2020-05-04