Plasticity solutions for soil behaviour around contracting cavities and tunnels

The action of tunnel excavation reduces the in-situ stresses along the exca vated circumference and can therefore be simulated by unloading of cavities from the in-situ stress state. Increasing evidence suggests that soil beha vior in the plane perpendicular to the tunnel axis can be modelled reasonab ly by a contracting cylindrical cavity, while movements ahead of an advanci ng tunnel heading can be better predicted by spherical cavity contraction t heory. In the past, solutions for unloading of cavities from in-situ stress es in cohesive-frictional soils have mainly concentrated on the small strai n, cylindrical cavity model. Large strain spherical cavity contraction solu tions with a non-associated Mohr-Coulomb model do not seem to be widely ava ilable for tunnel applications. Also, cavity unloading solutions in undrain ed clays have been developed only in terms of total stresses with a linear elastic-perfectly plastic soil model. The total stress analyses do not acco unt for the effects of strain hardening/softening, variable soil stiffness, and soil stress history (OCR), The effect of these simplifying assumptions on the predicted soil behavior around tunnels is not known. In this paper, analytical and semi-analytical solutions are presented for u nloading of both cylindrical and spherical cavities from in-situ state of s tresses under both drained and undrained conditions. The nonassociated Mohr -Coulomb model and various critical state theories are used respectively to describe the drained and undrained stress-strain behaviors of the soils. T he analytical solutions presented in this paper are developed in terms of l arge strain formulations. These solutions can be used to serve two main pur poses: (1) to provide models for predicting soil behavior around tunnels; ( 2) to provide valuable benchmark solutions for verifying various numerical methods involving both Mohr-Coulomb and critical state plasticity models. C opyright (C) 1999 John Wiely & Sons, Ltd.