Analytical modelling of a tunnel accounting for elastoplastic unloading and reloading with reverse yielding and plastic flow

Abstract

Abstract Applying a high internal pressure inside an underground cavity can increase the extent or intensity of the Excavation Damaged Zone (EDZ). This issue arises in many situations: the geological disposal of radioactive waste where different swelling materials can be encountered (engineered barriers, …), in-situ pressuremeter tests, gas storage projects, etc. This paper presents an analytical approach of the elastoplastic behaviour of a tunnel subjected to a simplified 2-stage loading under the assumption of small strains. In stage-1 (unloading), its excavation is represented in a classical way by cancelling the fictitious internal pressure initially applied to the wall of the future tunnel. In stage-2 (reloading), the internal pressure is increased up to relatively high values. The mechanical behaviour considered is elastic-perfectly-plastic, obeying Tresca's yield criterion and its associated flow rule. In both stages, the elastic phase preceding yielding is considered. During stage-2, the reversed direction of the stress path compared to stage-1 induces reverse yielding, reversing the direction of plastic strain rates. A fully analytical solution is presented, where all field quantities can be assessed by entirely explicit equations. Notably, the critical values of the internal pressure for which yielding resumes, then further extends, are presented.