SUMMARY The ground response to tunnel excavation is usually described in terms of the characteristic line of the ground (also called ‘ground response curve’, GRC), which relates the support pressure to the displacement of the tunnel wall. Under heavily squeezing conditions, very large convergences may take place, sometimes exceeding 10–20% of the excavated tunnel radius, whereas most of the existing formulations for the GRC are based on the infinitesimal deformation theory. This paper presents an exact closed‐form analytical solution for the ground response around cylindrical and spherical openings unloaded from isotropic and uniform stress states, incorporating finite deformations and linearly elastic‐perfectly plastic rock behaviour obeying the Mohr–Coulomb failure criterion with a non‐associated flow rule. Additionally, the influence of out‐of‐plane stress in the case of cylindrical cavities under plane‐strain conditions is examined. The solution is presented in the form of dimensionless design charts covering the practically relevant parameter range. Finally, an application example is included with reference to a section of the Gotthard Base tunnel crossing heavily squeezing ground. The expressions derived can be used for preliminary convergence assessments and as valuable benchmarks for finite strain numerical analyses. Copyright © 2014 John Wiley & Sons, Ltd.

This paper provides an overview of some significant aspects concerning the design of concrete tunnel linings subjected to severe fire exposure. The distinguishing feature of tunnel fires is the possible rapid rise of the air temperature within few minutes. The factors that contribute to this phenomenon in combination with the fire duration and the fire spread along the longitudinal direction are cited. Additionally, the widely used fire curves are presented, showing their influence on the predicted temperature profile of a concrete cross-section through uncoupled heat transfer transient numerical analyses. Then, the effect of fire on the concrete behaviour is briefly described with examples from real fire accidents. The focus is on the explosive spalling of concrete, provided that, in general, tunnels are at greater risk than other structures, principally due to the high heating rate and the high initial moisture content. The main features and mechanisms of spalling are presented in conjunction with the available modelling techniques and the design approaches against spalling. Finally, the effectiveness of several passive protection measures is discussed, based on the recent experiences.

This paper presents a generalized, rigorous and simple large strain solution for the undrained expansion of a vertical cylindrical cavity in critical state soils using a rate-based plasticity formulation: the initial stress field is taken as anisotropic, that is with horizontal stresses that differ from the vertical stress, and the soil is assumed to satisfy any two-invariant constitutive model from the critical state (Cam-clay) family; no simplifying assumption is made during the mathematical derivation; calculating the effective stresses around the cavity requires the solution of a nonlinear equation by means of the Newton-Raphson method in combination with quadrature. Cavity expansion curves and stress distributions in the soil are then presented for different critical state models (including the modified Cam-clay model). The solution derived can be useful for estimating the instantaneous response of saturated low-permeability soils around piles and self-boring pressuremeters and can serve as trustworthy benchmark for numerical analysis codes.

This paper presents a novel, very simple, accurate, theoretically well-founded and widely applicable relationship expressing the tunnel convergences obtained from large strain elasto-plastic analyses as a hyperbolic function solely of the corresponding small strain convergences. It can thus be used for 'selfcorrecting' small strain solutions, removing the need for large strain elasto-plastic analyses at least at the preliminary design stage and quantifying a hitherto unknown error caused by disregarding the geometric non-linearity. The proposed relationship can be proved rigorously for the plane strain rotationally symmetric ground response problem with a general elasto-plastic constitutive law with or without dilatancy and hardening. Numerical analyses of characteristic two-and three-dimensional excavation problems show that this relationship is generally applicable, irrespective of the in situ stress state and the tunnel geometry. It is therefore very useful from an engineering point of view for the design of tunnels crossing heavily squeezing ground, where the convergences may be so large (sometimes well in excess of 10% of the tunnel radius) that the usual small strain elasto-plastic analyses are deficient.

This paper presents a novel, very simple, accurate, theoretically well-founded and widely applicable relationship expressing the tunnel convergences obtained from large strain elasto-plastic analyses as a hyperbolic function solely of the corresponding small strain convergences. It can thus be used for 'selfcorrecting' small strain solutions, removing the need for large strain elasto-plastic analyses at least at the preliminary design stage and quantifying a hitherto unknown error caused by disregarding the geometric non-linearity. The proposed relationship can be proved rigorously for the plane strain rotationally symmetric ground response problem with a general elasto-plastic constitutive law with or without dilatancy and hardening. Numerical analyses of characteristic two-and three-dimensional excavation problems show that this relationship is generally applicable, irrespective of the in situ stress state and the tunnel geometry. It is therefore very useful from an engineering point of view for the design of tunnels crossing heavily squeezing ground, where the convergences may be so large (sometimes well in excess of 10% of the tunnel radius) that the usual small strain elasto-plastic analyses are deficient.