A generalized three-dimensional failure criterion for rock masses

The smooth convex generalized failure function, which represents 1/6 part of envelope in the deviatoric plane, is proposed. The proposed function relies on four shape parameters (L_s, a, b and c), in which two parameters (a and b) are dependent on the others. The parameter L_s is called extension ratio. The proposed failure function could be incorporated with any two-dimensional (2D) failure criteria to make it a three-dimensional (3D) version. In this paper, a mathematical formulation for incorporation of Hoek-Brown failure criterion with the proposed function is presented. The Hoek-Brown failure criterion is the most suited 2D failure criterion for geomaterials. Two types of analyses for best-fitting solution of published true tri-axial test data were made by considering (1) constant extension ratio and (2) variable extension ratio. The shape and strength parameters for different types of rocks have been determined by best-fitting the published true tri-axial test data for both the analyses. It is observed from the best-fitting solution by considering uniform extension ratio (L_s) that shape constants have a correlation with Hoek-Brown strength parameters. Thus, only two parameters (σ_c and m) are needed for representing the 3D failure criterion for intact rock. The statistical expression between shape and Hoek-Brown strength parameters is given. In the second analysis, when considering varying extension ratio, another parameter f is introduced. The modified extension ratio is related to f and extension ratio. The results at minimum mean misfit for all the nine rocks indicate that the range of f varies from 0.7 to 1.0. It is found that mean misfit by considering varying extension ratio is lower than that in the first analysis. But it requires three parameters. A statistical expression between f and Hoek-Brown strength parameters has been established. Though coefficient of correlation is not reasonable, we may eliminate it as an extra parameter. At the end of the paper, a methodology has also been given for its application to isotropic jointed rock mass, so that it can be implemented in a numerical code for stability analysis of jointed rock mass structures.