Stability assessment of slopes in rock governed by the Hoek-Brown strength criterion

Instabilities in rock slopes are often triggered along planar joints with weakened shear strength, inducing translational failures. In intact rocks, however, the kinematics of failure may exhibit rotation, which is a more common occurrence also in soil slopes. A slope instability in a geomaterial governed by the Hoek-Brown failure criterion is analyzed, and two measures of the slope safety are considered: the stability number and the factor of safety. A consistent method is developed to arrive at the factor of safety for geomaterials with nonlinear strength envelopes. An argument is presented to justify the application of plasticity theorems in rocks, and a collapse mechanism is developed consistent with the Hoek-Brown failure criterion and the normality flow rule. Not surprisingly, the kinematic approach of limit analysis indicates that the safety measures for slopes are greatly dependent on the Geological Strength Index of the rock. Although the limit analysis used in the paper does not allow calculation of the true stress distribution in the rock, the method allows approximately estimating the stress vector on the rupture surface. It appears that for gentle slopes the stress vector is predominantly in the compression regime, but with an increase in the slope inclination the range of the rupture surface with tensile stress increases. This may very well be the chief reason why steeper slopes are more prone to failures. Results of calculations presented in the paper indicate that the stability numbers based on the proposed method are generally higher compared to those from the limit equilibrium and finite element methods, and the factors of safety are lower. Considering that the method used yields a strict upper bound to the factor of safety and lower bound to the stability number, this observation imparts confidence in the method of analysis presented in the paper.