Elasto‐plastic analytical model for the design of grouted bolts in a Hoek–Brown medium

Abstract

AbstractThis paper presents an elasto‐plastic analytical solution of an axi‐symmetrical problem for a circular tunnel reinforced by grouted bolts. Considered as the improved model of Indraratna and Kaiser (Int. J. Rock. Mech. Min. Sci. Geomech. Abstr. 1990; 27:269–281; Int. J. Numer. Anal. Meth. Geomech. 1990; 14:227–251), in proposed solution the rock mass obeys the non‐linear Hoek–Brown yield criterion (version 2002) in terms of its peak and residual strength parameters (the most spread strength criterion for the rock masses). The proposed approach considers a⩾0.5 for the rock mass and is based on the assumption that after the peak strength of the rock is reached, the material loses its strength, as dictated by a strength loss parameter. The strength loss parameter makes it possible to model either elastic–perfectly plastic or elastic–brittle–plastic behaviour. Because of the mathematical complexity, numerical treatments have been used to assist the solution in order to evaluate the equilibrium and compatibility equations. The concept of equivalent material for Hoek–Brown strength parameters is introduced to describe the rock mass improvement due to bolting effect. The results of the numerical analyses reveal a linear relation between the improved Hoek–Brown strength parameters and residual ones, taking into consideration the bolt density parameter (β). The proposed solution is able to analyse the stress and displacement state in the presence of a bolting intervention with the objective of improving the degree of stability of the rock around the tunnel. Descriptive applications of the derived elasto‐plastic solutions are also presented to explain the effectiveness of the grouted bolts in convergence reduction. Evidences obtained by numerical analysis verify the analytical solution. Copyright © 2009 John Wiley & Sons, Ltd.