Numerical simulation of the convergence of a bolt‐supported tunnel through a homogenization method

Abstract

Abstract The present paper describes the numerical implementation of constitutive relationships previously developed for modelling the elastoplastic behaviour of bolted rockmass regarded as a homogenized anisotropic medium on the macroscopic scale. Attention is more particulary focused on the iterative algorithm involved in such a numerical method, which makes use of projection formulas onto the yield surface. Those formulas are made explicit in the case of a purely cohesive rock material obeying a von Mises yield condition with associated flow rule. Combined with a finite element code, the proposed numerical procedure is then carried out for simulating the advancement of a bolt‐supported tunnel and calculating its convergence as the excavation proceeds. The results of this numerical simulation prove to agree perfectly well with those derived from an analytical model, thus validating the proposed numerical scheme. A quantitative study, varying some relevant parameters of the problem (bolt density, length of bolts, delay of placement behind the tunnel facing), is finally undertaken. It points to the versatility of the numerical approach, whose range of applicability can be further extended to various kinds of geotechnical structures reinforced by regularly distributed inclusions.