A Critical Plane Approach to Anisotropic Strength of Rocks

The paper is concerned with the derivation of failure criteria for anisotropic materials through a simple extension of the Mohr Coulomb failure criterion and embracing the critical plane concept. We revisit the classic problem of determining the macroscopic strength of a rock specimen with an initial structural anisotropy in relation to the directions of externally applied principal stresses. Macroscopic friction angle and cohesion, as two main elements of material strength, are essentially made to be direction dependent following a distribution that depends on only 3 additional parameters describing: (1) the ratio of the maximum to minimum strength, (2) a shape parameter for the transition rate from maximum to minimum values, and (3) the non-coaxiality between principal stress and strength directions. The search for the critical plane is interpreted graphically showing the existence of multiple solutions and the switching of resulting modes for the same externally applied stress. One of the essential benefits of the proposed model is the capture of material characteristics such as failure plane orientation and macroscopic strength over a large range of stress conditions using only a few parameters that have physical meaning and which can be easily determined experimentally. This is demonstrated through various examples involving experimental results. Finally, a micromechanical model and the developed critical plane model are juxtaposed to show the same trend in results. Second International Symposium on Computational Geomechanics (ComGeo II), 27/04/2011, Cavtat-Dubrovnik, HRV ha l-0 06 22 15 4, v er si on 1 12 S ep 2 01 1 Author manuscript, published in "Second International Symposium on Computational Geomechanics (ComGeo II), CavtatDubrovnik : France (2011)"