Comparing the generalized Hoek-Brown and Mohr-Coulomb failure criteria for stress analysis on the rocks failure plane

Abstract

Determination of mobilized shear strength parameters (that identify stresses on the failure plane) is required for analyzing the stability by limit equilibrium method. Generalized Hoek-Brown (GHB) and Mohr-Coulomb (MC) failure criteria are usually used for obtaining stresses on the plane of failure. In the present paper, the applicability of these criteria for determining the stresses on failure plane is investigated. The comparison is based on stresses on the real failure plane which are obtained from the Mohr stress circle. To do so, 18 sets of data (consist of principal stresses and angle of failure plane) presented in the literature are used. In addition, the values account for (VAF) and the root mean square error (RMSE) indices were calculated to check the determination performance of the obtained results. Values of VAF and RMSE for the normal stresses on the failure plane evaluated from MC are 49% and 31.5 where for GHB are 55% and 30.5, respectively. Also, for the shear stresses on failure plane, they are 74% and 36 for MC, 76% and 34.5 for GHB. Results show that the obtained stresses and angles of failure plane for each criterion differ from real ones, but GHB results are closer to the empirical results. Also, it is inferred that results are affected by the failure envelope not real failure plane. Therefore, obtained shear strength parameters are not mobilized. Finally, a multivariable regressed relation is presented for determining the stresses on the failure plane.