An analytical solution for the undrained ground response to tunnelling considering the excavation-induced desaturation

When tunnelling through low-permeability saturated ground, the pore pressure decreases in the vicinity of the cavity. In certain instances of deep tunnels crossing weak rocks, the pore pressure may even become negative. All existing analytical solutions for the undrained ground response curve (GRC) in the literature assume that the ground fully retains its saturation, in which case the development of negative pore pressures has a stabilising effect – it results in increased effective stresses, and thus shearing resistance, which in turn leads to reduced deformations and plastification. In practice, however, negative pore pressures can induce partial or complete ground desaturation, which may even invalidate the premise of undrained conditions and lead to considerably increased deformations and plastification. In such cases, existing solutions are unsafe for design. The present paper aims to address this shortcoming, by presenting a novel analytical solution for the undrained GRC which incorporates the effect of the excavation-induced desaturation. The solution is derived under the assumption that the ground desaturates completely and immediately under negative pore pressures, which provides the upper bound of deformations and plastification for cases of partial desaturation. The rock is considered to be a linear elastic, brittle-plastic material, obeying a non-associated Mohr-Coulomb (MC) yield criterion. Nevertheless, the solution is also applicable to perfectly plastic rocks via a simple modification of the input parameters. Although the solution is in general semi-analytical, simple closed-form expressions are obtained in the special case of non-dilatant rocks. These expressions are also applicable to rocks exhibiting limited dilatancy, which is usually the case. An application example, based on the planned deep geological repository for radioactive waste in Switzerland, demonstrates the significant practical value and usefulness of the novel solution and underscores its necessity in cases where existing solutions that disregard desaturation are rendered thoroughly unsafe for design.