A Three-Dimensional Microcrack Inclination–Dependent Anisotropic Compressive Failure Criterion in Brittle Rocks

Numerous microcracks with different angles of inclination are found in brittle rocks. The crack angles lead to anisotropic properties of the compression failure of the rock, which greatly affects the evaluation of the stability of the surrounding rock in deep underground engineering. However, there are a few studies on the macroscopic mechanical relationship applicable to true triaxial stress between the three-dimensional inclination angle of a microcrack and the anisotropic compression failure in brittle rock. This paper aims to propose a microscopic anisotropic failure criterion applicable to various stress states including true triaxial compression to solve the problem of compression yield, strength, and damage of brittle rock. Introduce the three-dimensional angle of the initial crack into the expression for the stress intensity factor KI at the tip of the compression wing crack. When the newly obtained KI reaches the fracture toughness KIC, the rock yields. Then considering the exchange of the principal stress order and the property that the wing crack always cracks along the direction of the maximum principal compressive stress, the complete anisotropic yield surface form is obtained. The stress–crack extension length curve is plotted by f(σ1, σ2, σ3, l) = 0. The stress corresponding to l = 0 is regarded as the yield stress, the peak of the stress as the strength, and the stress at l = llim as the residual stress at damage. The work hardening and softening after yield are realized, so that the yield criterion can be extended to the strength criterion and the damage criterion, and the successive yield surfaces under arbitrary crack lengths can be derived. The reasonableness of the failure criterion is verified by comparison with mechanical experiments on different types of rocks under different stress conditions. The three-dimensional yield surface is projected onto the π-plane to analyze the influence law of parameters on typical stress points. And the three-dimensional yield surface is projected onto the tensile and compressive meridian planes to analyze the influence law of hydrostatic pressure on the yield stress of rock.