ORTHOTROPIC LAME FORMULATION OF THE CONSTITUTIVE-EQUATIONS FOR BRITTLE ROCK

Analyzing the results of standard uniaxial compressive tests on rock, the two terms of the isotropic Lame equation are viewed as the description of two models. By letting the cohesion model become orthotropic through continuous fracturing, as described by Dougill, and the bulk model become orthotropic through overcoming Coulomb friction, as described by Vreede, constituent equations for brittle materials are formulated. Assuming only tensile fracturing, the fit with the test data is excellent. The equation for brittle failure is derived from the incremental form of the orthotropic equations and is a function of tangential stiffnesses and boundary conditions. Cleavage failure depends strongly on tensile strain. The effect of confining pressure and the orientation of the plane of shear failure depend on the friction angle, but also on cohesion. The application of the theory to a number of geomechanical topics is discussed shortly. Rock with high friction, such as granite, exhibits Class II post-failure behaviour as described by Wawersik. The theory explains all the features of brittle behaviour. Formulae for Young's moduli E(i) and Poisson's ratios nu(ij) are given. The equations are therefore quite suitable for engineering applications.