Numerical simulation of bolt-supported tunnels by means of a multiphase model conceived as an improved homogenization procedure

This paper examines the possibility of applying a homogenization procedure to analyze the convergence of a tunnel reinforced by bolts, regarded as periodically distributed linear inclusions. Owing to the fact that a classical homogenization method fails to account for the interactions prevailing between the bolts and the surrounding ground and thus tends to significantly overestimate the reinforcement effect in terms of convergence reduction, a so-called multiphase model is presented and developed, aimed at improving the classical homogenization method. Indeed, according to this model, the bolt-reinforced ground is represented at the macroscopic scale as the superposition of two mutually interacting continuous phases, describing the ground and the reinforcement network, respectively. It is shown that such a multiphase approach can be interpreted as an extension of the homogenization procedure, thus making it possible to capture the ground-reinforcement interaction in a proper way, provided the constitutive parameters of the model and notably those relating to the interaction law can be identified from the reinforced ground characteristics. The numerical implementation of this model in a finite element method-based computer code is then carried out, and a first illustrative application is finally presented.