Three-dimensional numerical simulation of rock deformation in bolt-supported tunnels: A homogenization approach

Despite fully grouted bolts are nowadays widely used for tunnel support, bolting design is still based in many cases on empirical or semi-empirical considerations. This paper describes a three-dimensional theoretical and numerical model for the behavior of tunnels reinforced by bolts. From a theoretical viewpoint, the elastoplastic constitutive equations for the reinforced rock are derived in the framework of homogenization method. Emphasis is given to the formulation of the homogenized strength criterion with account for the bolt/rock interface properties. The anisotropic constitutive equations are then implemented in a 3D finite element computer code in which the processes of excavation, installation of bolts and lining placement are simulated by means of the “activation/deactivation” technique. Due to the multi-potential nature of the plastic flow, a specific iterative algorithm for plastic integration is proposed. The finite element model is applied to the analysis of the Kielder experimental tunnel for which in situ measured data are available. The accuracy of the numerical predictions based on homogenization method is also assessed by comparison with the results derived from implementation of the so-called embedded model.

► The elastoplastic behavior of bolted rock is formulated by means of homogenization.
► The theoretical formulation includes the bolt/rock interface properties.
► Iterative algorithm for plastic integration is proposed for non-smooth yield surface.
► 3D finite element analysis of the Kielder experimental tunnel is carried out.
► It is found that the homogenized approach and embedded model provide similar results.