A numerical approach for design of bolt-supported tunnels regarded as homogenized structures

This paper is devoted to the theoretical modeling and numerical simulation by homogenization approach of the behaviour of a tunnel reinforced by fully grouted bolts, regarded as periodically distributed linear inclusions. Owing to the fact that a direct numerical simulation would require the ground and the reinforcing bolts be separately discretized, leading thus to a highly complex and oversized problem, a homogenization procedure is developed, aimed at circumventing the difficulties connected with the implementation of a direct simulation. The situations of reinforcement by radial bolts and horizontal anchors installed ahead the excavation face are both investigated. Considering a Drucker–Prager rock material, elastoplastic constitutive equations are formulated for the bolted rock mass regarded as a homogenized anisotropic medium at the macroscopic scale. Special attention is paid to the description of the algorithm of plastic integration involved in the finite element implementation. At this respect, closed-form expressions are derived for the stress projection onto the macroscopic yield surface. The finite element procedure is thus carried out for simulating the advancement of a bolt-supported tunnel and computing the displacements of the tunnel walls and the facing as the excavation proceeds. A parametric study, varying some relevant parameters defining the bolt reinforcement scheme, is undertaken by means of the finite element tool. The combination of rock bolting with a classical lining support system such as a shotcrete layer is also examined, thus providing some guidelines for the optimal design of the reinforcement pattern.