Simulation of polyaxial tests using a failure condition for transversely isotropic rocks

Abstract

Considering that most sedimentary and metamorphic rocks display some degree of anisotropy in failure strength, the conventional isotropic failure criteria including the Mohr-Coulomb (M-C) and the Hoek-Brown have their limitations in characterizing the strength of these anisotropic rocks. An improved understanding of the orientation dependency of strength in anisotropic rocks can be achieved if a systematic way of establishing a condition at failure in anisotropic rock is provided. In this research, a general procedure to extend the M-C failure criterion to its anisotropic version is presented in which the friction angle and cohesion are not constant but defined as functions of the relative orientation of physical plane to the principal material triad. In the formulation of the anisotropic failure condition, the directional variation of the strength parameters is described by incorporating a traceless symmetric second-rank fabric tensor that defines the orientation bias in their spatial distribution. Subsequently, the critical plane approach is employed to implement the formulated transversely isotropic M-C failure function in the numerical polyaxial tests on the transversely isotropic rock samples, whereby the polyaxial stress at failure and the corresponding direction of the failure plane are specified by maximizing the failure function with respect to the orientation. A series of numerical polyaxial tests is conducted to investigate how the orientation of weak planes affects the failure behavior of transversely isotropic rocks. The simulation result strongly suggests that the microstructures embedded in the samples and their attitude with respect to the loading direction have much influence on the variation of the polyaxial strength and the orientation of the corresponding failure plane.