Analytical and numerical study of the mechanics of rockbolt reinforcement around tunnels in rock masses

This paper addresses the problem of quantifying the mechanical contribution of rockbolts installed systematically around tunnels excavated in rock masses. The mechanical contribution referred to here is that of increased stress confinement and decreased tunnel convergences as compared with corresponding stresses and displacements obtained for non-reinforced tunnels. The problem is treated analytically first by presenting a closed-form solution for stress and displacement distributions around a circular tunnel excavated in elastic material and reinforced by grouted or anchored rockbolts. The analytical solution assumes that rockbolts are regularly spaced around the tunnel and that axi-symmetry conditions of geometry and loading apply. The results obtained with the closed-form solution are shown to be equivalent to the results of the same problem solved with traditional numerical methods. Based on the analytical and numerical results and by introducing dimensionless ratios that allow to quantify the increase of radial stresses and the decrease of radial displacements in the reinforced region of the tunnel, the paper shows that reinforcement can have a significant mechanical effect (i.e., increasing the confinement and decreasing the convergences) in tunnels excavated in rock masses of poor to very poor quality. The paper analyzes then the mechanical contribution of rockbolt reinforcement when the rock mass is assumed to behave elasto-plastically. For this case, it is shown that rockbolt reinforcement can also have a critical effect in controlling the extent of the plastic failure zone and the convergences of the tunnel.