The mathematical modeling of creep and long-term strength of rocks uses the non-associated flow rule. The authors propose a unified approach to the plasticity and creep processes. The theoretical calculations are compared with the testing data of different materials. In creep deformation in rocks, the applied problems on limit state of rock mass in plain strain are considered: pressure applied by a solid die block with flat bottom on rock mass limited by a horizontal plane and occupying the bottom part of a half-space; instability of pit wall or natural slope under different loads. These problems evaluate stresses in the limit state zones and the times-to-failure in rocks mass with regard to internal friction.
The problem on elastoplastic deformation and rock failure around boreholes under the action of internal pressure is considered. The stress state in the intact rock mass is assumed to be hydrostatic. The hydraulic fracturing pressure is conventionally determined by the maximum normal stress criterion. However, the experimental studies described in scientific articles show that this criterion is not consistent with the results obtained in the course of laboratory tests on failure of cylindrical and spherical cavities made in rock samples. It has been known that test results on complex loading for solid samples of various materials are not confirmed by the theory of maximum normal stress both in terms of ultimate load value and direction of failure surface propagation. In this case, for the complex stress state of rocks, it is proposed to determine the ultimate pressure by the experimentally substantiated fracture criteria which are in good agreement with the results of laboratory tests on hydraulic fracturing of boreholes.
The article describes the theoretical and experimental research into the strength of cylindrical specimens made of layered and anisotropic geomaterials exposed to axial compression and lateral pressure. The tests used INSTRON 8802 versatile servohydraulic fatigue testing system. The experimental results are the relationships between the ultimate strength and bedding angle in specimens of an artificial material, meta-siltstone and shale. The experimental data agree well with the theoretical calculations.
It is assumed that irreversible deformation is a result of shearing in certain planes. In perpendicular directions to these planes, normal strain undergoes change that is proportional to the associated shear. This approach allows accounting for growth of fractures and pores in the background of increasing creep strains without using Kachanov-Rabotnov's kinetic equation for development of damage. Material begins failing when maximum shear creep strain reaches critical value, which initiates drop in shear strength. Using the model based on the maximum shear stress and the exponential law, the authors solve problems on deformation and failure of an elastic-creeping body at the stages of unstable and stable creep.
The ideal plasticity model based on the Tresca-Saint-Venant criterion is used to solve one-dimensional problems of deformation and fracture of solids with circular boundaries. A thickwalled cylinder and a hollow sphere under pressure, cylindrical and hollow cavities in an unbounded body, and uniform extension at infinity of a plate with a free circular hole are considered. In simple elastoplastic problems, the proposed approach allows one to determine the value of the maximum external load at the fracture initiation and the motion of the fracture front for a given displacement of points of the contour on which this load acts.
A new solution for the shear angle is proposed which is a generalization of the solution Lee-Shaffer solution and allows the determination of the cutting force and the shearing-element size. Merchant’s experimental data are processed taking into account the resistance force at the cutting edge, and it is shown that accounting for this force leads to the need to increase the internal friction angle in the calculated dependences in order to match theory with experiment. It is shown that the obtained theoretical results agree well with experimental results.
We show that, as long as one deals with a plane stress state, the Coulomb-Mohr fracture criterion traditionally used in soil and rock mechanics is in a rather good agreement with the results of fracture experiments for metal materials under the conditions of creep caused by a long-term action of a constant load. We perform statistical analysis to compare the proposed theoretical limiting-stress-fracture-time dependencies with the experimental results given in [1–3] and the results of computations by other authors [1, 4, 5].
The paper describes an approach to finding the maximum and minimum destruction time of an open or underground structural element under creep in the case of the plane-strain state of a rock mass, by an inelastic creep model. Using the elastic creep model, the author is solving problems on deformation and failure of a cylindrical excavation and a spherical cavity under the action of hydrostatic rock pressure. The times of the failure origin and of the complete failure of structural elements under the long-term stress have been determined.
It is proposed to construct long-term strength and creep relations for metals on the basis of the Coulomb-Mohr criterion. The creep equations and the long-term strength criterion for plane stress are analyzed in detail. Results of long-term strength calculations are compared with data of experiments with metallic materials. It is established that theoretical and experimental results are in satisfactory agreement.
To describe the process of cutting of geomaterials by a two-sided wedge, a rigid-plastic model is considered taking into account the influence the wedge speed has on the cutting force, shear plane orientation, and sizes of sheared pieces.
A rigid-plastic model of shearing chip formation is proposed. The model is based on the Mohr-Coulomb yield criterion and allows one to determine the size of chipped elements in orthogonal cutting of plastic and brittle metals.
Systems of equations for plastic stresses and velocities based on the von Mises–Schleicher criterion are obtained for plane stresses. The regions of ellipticity and hyperbolicity of these systems are found, and the limiting stresses and fracture directions identified with the characteristics of the velocity field equations are determined. The results agree well with experimental data for plastic and brittle materials.
The analysis and comparison are performed for the directions of stress- and velocity-field characteristics in hyperbolic equations of nonassociated plastic models on the basis of the Coulomb - Mohr and Huber - Mises - Shleiher criteria for various stress states. In the particular cases, the classic results are obtained for soils and ductile metals, among them the slipping lines observed in experiments.
A method is proposed for calculating the rock strength criterion by the results of sample tests under uniaxial compression and tension, as well as hydrostatic compression. The method makes it possible to simplify considerably the procedure of determining the rock strength parameters and improves the existing State Standard.
Calculation results obtained on the basis of Coulomb-Mohr and Mises-Schleicher theories are compared with experimental data for rock samples.
Numerical calculations for the magnitudes of stresses at the instant of failure and angles at which it occurs are presented on the basis of stiff- and elastoplastic body models for plane and axially symmetric strain.
