Behavior of tunnels reinforced by fully grouted bolts, radially disposed, is investigated in this paper. Perfect bonding and ideal diffusion of bolt tension are assumed, so that the bolt tension can be simulated by an equivalent uniaxial stress tensor. An analytical model, of convergence-confinement type, is proposed, which accounts for the delayed action of bolts due to ground decompression prior to bolt installation. This factor leads to non-simultaneous yielding, and more generally a different stress history for each constituent, requiring special treatments in the incremental elastoplasticity calculations. Nonetheless, the resulting model remains sufficiently simple and an analytical solution is still accessible. Comparisons with 3D numerical calculations show that the model gives precise results if the correct convergence at the moment of bolt installation Up is used as an "external" input parameter. An approximate methodology based on previous works is proposed to determine this parameter to render the proposed model "self-sufficient". Its predictions are again compared to 3D numerical computations. The results are found to be sufficiently accurate for practical applications.


Since the advent of the New Austrian Tunneling method (NATM) due to Rabcewicz and Golser (1973), use of bolting as a lining support has become more and more popular in tunneling projects, encouraged by the real efficiency observed on site. However, it turns out to be rather difficult to account for this efficiency in design calculations (Peila, 1996). Finite element analyses, simulating bolts as linear 1D "bar elements" is not only cumbersome (mesh generation difficult) but also turns out to underestimate the contribution of bolts. In a previous paper (Wong and Larue, 1998), an analytical model was proposed on radial bolting reinforcement of tunnels, presenting improvements over previously published solutions by Stille et al. (1989) and Greuell (1993 and 1994).

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