Two-dimensional face stability analysis in rock masses governed by the Hoek-Brown strength criterion with a new multi-horn mechanism

Abstract

The face stability problem is a major concern for tunnels excavated in rock masses governed by the Hoek-Brown strength criterion. To provide an accurate prediction for the theoretical solution of the critical face pressure, this study adopts the piecewise linear method (PLM) to account for the nonlinearity of the strength envelope and proposes a new multi-horn rotational mechanism based on the Hoek-Brown strength criterion and the associative flow rule. The analytical solution of critical support pressure is derived from the energy-work balance equation in the framework of the plastic limit theorem; it is formulated as a multivariable nonlinear optimization problem relying on 2m dependent variables (m is the number of segments). Meanwhile, two classic linearized measures, the generalized tangential technique (GTT) and equivalent Mohr-Coulomb parameters method (EMM), are incorporated into the analysis for comparison. Surprisingly, the parametric study indicates a significant improvement in support pressure by up to 13% compared with the GTT, and as expected, the stability of the tunnel face is greatly influenced by the rock strength parameters. The stress distribution on the rupture surface is calculated to gain an intuitive understanding of the failure at the limit state. Although the limit analysis is incapable of calculating the true stress distribution in rock masses, a rough approximation of the stress vector on the rupture surface is permitted. In the end, sets of normalized face pressure are provided in the form of charts for a quick assessment of face stability in rock masses.