Critical plane analysis for interpreting experimental results on anisotropic rocks

This paper deals with a coherent analytical interpretation of the anisotropic strength of rocks as derived from standard laboratory experimental compression tests on rock samples under confinement. The critical plane approach is herein revisited by reformulating the Mohr-Coulomb failure criterion on a sliding plane when the operative strength parameters are direction dependent. Detailed attention is paid to the solution of the emerging equations that describe an optimization problem where the failure function is maximized with respect to orientation. This encompasses a tangency condition that has to be explicitly solved for as the stress state approaches failure from the inside of the plastic limit surface. However, this tangency condition cannot be graphically represented in the Mohr space as classically done in the isotropic case. A new graphical construction is herein proposed that offers insights to the problem by illustrating how anisotropy of strength juxtaposes with stress variations during a typical loading path to failure. More importantly, a perturbation analysis is conducted to obtain an approximated closed-form solution of the equations arising from the description of anisotropy. Within such a framework, salient features describing anisotropy of strength can be systematically related to inherent material symmetries so that laboratory experimental test data can be thus interpreted on a mathematically sound basis.