LAUSR

The analysis of tunnel extrusion during full-face excavation necessitates a fully three-dimensional modeling which requires much effort to develop a numerical model and is thus very time-consuming, in particular, for complex cases to study the effect of face reinforcement by fiberglass bolts. It is, therefore, very useful to be able to dispose of a simplified tool permitting to make such evaluative analysis rapidly, in particular at the preliminary design stage. This paper presents a finite difference solution (FDM) for a spherical cavity reinforced by passive bolts in either brittle–plastic or strain-softening infinite medium subjected to a homogeneous initial stress field. Both linear Mohr–Coulomb (M–C) and nonlinear generalized Hoek–Brown (H–B) failure criterion is considered. The comparison of the solution against the published analytical results for the classic cases without bolts reinforcement is in good agreement for displacements as well as stresses. The solution is then applied to two real cases of face extrusion analysis of tunnel excavation in France and compared with both field measurements from the Tartaiguille tunnel and the extrusometer data as well as the three-dimensional (3D) calculation integrating face bolting reinforcement for the Toulon tunnel. The comparison of the results ensures full consistency of the solution in the predictive extrusion of the tunnel face and demonstrates, therefore, its efficacy and significant advantage in parametric analysis during the preliminary design stage.