Tunnel Convergence in Squeezing Ground with Strain Localisation

Modelling strain-softening behaviour in rocks and hard clays presents significant challenges due to strain localisation, which may lead to non-unique and mesh-dependent numerical solutions. In engineering practice, computationally tractable alternatives are therefore often used, including softening models suppressing strain localisation (hereafter referred to as non-localised softening analyses) or perfectly plastic models based on residual strength (hereafter referred to as perfectly plastic residual-strength analyses). Their adequacy for predicting unsupported tunnel convergence under squeezing conditions is investigated through comparative numerical computations using a conventional, non-regularised strain-softening model. The study covers a wide range of softening parameters and problem layouts, including circular and horseshoe-shaped tunnels under isotropic and anisotropic stress fields, as well as spatial discretisations based on structured and unstructured meshes. The finest structured mesh had boundary elements as small as 12 mm and produced numerical shear bands with thicknesses of the same order as those seen experimentally; the corresponding results are used as pragmatic reference solutions. The results show that a distinction must be made between average and local maximum convergence. For the rotationally symmetric tunnel problem, the perfectly plastic residual-strength model may underestimate local maxima; in the structured-mesh study, the underestimation reached about 30%, while the unstructured analyses showed that point-wise maxima are sensitive to mesh topology and symmetry assumptions. For the non-rotationally symmetric layouts examined, however, the model was conservative with respect to local maxima. The model predicted average convergence closely, although moderate underestimation occurred in some cases. This is the main practical result: average or diametral convergence usually governs design, whereas local maxima matter for concentrated support loading or local clearance loss.