Undrained solution of cylindrical cavity expansion for unsaturated soils with modified Cam-clay model

Abstract

This paper develops a new semi-analytical approach for undrained cylindrical cavity expansions in unsaturated soils. The unsaturated soil behavior is described within a simple, yet effective, critical state-based elastoplastic framework with suction being treated as a hardening parameter. Different from its saturated counterpart, the cavity expansion problem in unsaturated soils involves five basic variables, namely, the three stress components, specific volume, and suction. A constitutive equation for the water phase, in addition to the soil elastoplastic constitutive relationship plus the radial equilibrium condition, is therefore required to construct a set of coupled, self-contained differential equations for the solution of the cavity boundary value problem. With the introduction of an auxiliary variable, all these governing equations can be expressed in terms of the Lagrangian formulation and then simultaneously solved through the standard numerical procedure. The numerical example results show that the suction has significant hardening effects on the overall cavity expansion responses and, in particular, the stress trajectories calculated for a representative soil element at the cavity surface. It is also interesting to observe that the shear dilation phenomenon, developed during the course of cavity expansion, usually occurs in relatively dense unsaturated soils with high unsaturated suction.