Direct expressions for linearization of shear strength envelopes given by the Generalized Hoek–Brown criterion using genetic programming

The non-linear Generalized Hoek–Brown (GHB) criterion is one of the most broadly adopted failure criteria used to estimate the strength of a rock mass. However, when limit equilibrium and shear strength reduction methods are used to analyze rock slope stability, the strength of the rock mass is generally expressed by the linear Mohr–Coulomb (MC) criterion. If the GHB criterion is used in conjunction with existing methods for analyzing the rock slope, methods are required to determine the equivalent MC shear strength from the GHB criterion. Deriving precise analytical solutions for the equivalent MC shear strength from the GHB criterion has not proven to be straightforward due to the complexities associated with mathematical derivation. In this paper, an approximate analytical solution for estimating the rock mass shear strength from the GHB criterion is proposed. The proposed approach is based on a symbolic regression (SR) analysis performed by genetic programming (GP). The reliability of the proposed GP solution is tested against numerical solutions. The results show that shear stress estimated from the proposed solution exhibits only 0.97% average discrepancy from numerical solutions using 2451 random sets of data. The proposed solution offers great flexibility for the application of the GHB criterion with existing methods based on the MC criterion for rock slope stability analysis.