Proposed solution for the ground reaction of non-circular tunnels in an elastic-perfectly plastic rock mass

Abstract

The Convergence Confinement Method (CCM) is a solution typically employed for the preliminary evaluation of tunnel convergence and support suitability. The CCM represents stress relaxation on circular tunnel boundaries in hydrostatic stress field and isotropic conditions. However, the CCMs employ yield criteria which neglect the intermediate principal stress as well as are not tailored for non-circular tunnels. This paper evaluates the CCMs for elastic-perfectly plastic (EPP) ground response in circular tunnels governed by the Mohr-Coulomb and Hoek-Brown criteria. Thereafter, presents an analytical solution which considers non-circular tunnels and the intermediate principal stress. This is achieved by the integration of an equivalent radius function and the circumscribed Drucker Prager yield criterion expressed by the stress Lode parameter. Furthermore, a numerical simulation is conducted in FLAC3D to verify the presented solution with a native constitutive model for a chosen rock mass condition. The extent of the plastic zone and tunnel convergence predicted by the proposed solution are 10% and 4% more than the conventional solutions. Hence, the effect of the intermediate principal stress should be considered for accurate ground reaction estimation. The proposed solution can be used to predict tunnel convergence and design appropriate tunnel support structures.