Sandstone Modeling under Axial Compression and Axisymmetric Lateral Pressure

The problems of the mechanical state of rocks and other brittle materials are studied from different sides in a large number of publications, the flow of which does not weaken with time, which is explained by the relevance and complexity of these problems. Quantitative values of strength and other characteristics of such materials can be obtained experimentally or using numerical and analytical models. This work is aimed at developing an analytical model for analyzing the state of brittle material on the example of sandstone under axial compression and axisymmetric proportional lateral pressure. The research uses methods of modeling mechanical systems based on the basic ideas of fracture mechanics. For axial compression with proportional lateral pressure, the equation of the load-strain curve is obtained, and the functions of residual life and damage are justified; effective stresses and effective modulus of elasticity are determined; a calculation algorithm and examples of its application are given. The results of the simulation are consistent with the experimental data known from the literature. The results obtained to a certain extent clarify the understanding of the mechanism of rock damage and destruction under axial compression with lateral pressure.