A simplified procedure for the interaction between fully-grouted bolts and rock mass for circular tunnels

This paper provides a simplified procedure for analysing the interaction between fully-grouted bolts and rock mass for circular tunnels under a hydrostatic stress field. In this procedure, the relative movement between the rock mass and the bolt is accounted for by considering the shearing stiffness at interface. Further, the elastic elongation of the bolt is considered. Two cases of elastic-brittle-plastic and elastic-perfectly-plastic rock mass behaviours are considered. The rock-bolt interaction is modelled at the initial and final states. At the initial state, immediately after the bolt is installed, a finite difference solution to obtain stresses and strains in the rock mass is proposed. At the final state, after the tunnel excavation advances and the fictitious support pressure becomes zero, another finite difference solution for computing stresses along the bolt and rock mass displacements is presented. To obtain the final converged results, an iterative process is performed by repeating the above solution at the final stage. The simplified procedure is validated by comparison with the commercial finite difference software, FLAC3D. A series of parametric studies is conducted to assess the sensitivity of the bolt and rock behaviours to variations in interface shear stiffness, the stiffness of the end plate and the assumed post-peak behaviour of the rock mass. The results indicate that the post-peak behaviour of the rock mass has an important effect on the bolt performance and, in turn, it should be a key design consideration. It is also shown that, under squeezing conditions, the failure mode of the bolt is influenced by the stiffness of the end plate.