Unified elasto-plastic analysis of rock mass supported with fully grouted bolts for deep tunnels

This paper presents a unified elasto-plastic analysis of rock mass supported with fully ground bolts for deep tunnels. In the analysis, depending on whether the relative movement at the grout-bolt interface is considered, two finite-difference algorithms are discussed. For each algorithm, two conditions, one when the rock bolt is inserted into the elastic area and one when it is included within the plastic area, are comprehensively investigated. In the algorithms, the initial and final states for the rock-bolt interaction are presented, and for each state, the surrounding rock mass consisting of the bolt or the plastic area is divided into a finite number of annuli through a constant radius increment. Based on this, the stress and displacement for the rock mass and the rock bolt are obtained step by step. The results of the two algorithms are verified by the analytical method and the field test data, respectively. Parametric studies were conducted to compare bolt force, rock displacement and stress components that are solved by the algorithms with and without considering relative movement. The proposed algorithms can be written into the software for guiding the rock bolt design in practical engineering.