Undrained cylindrical cavity expansion in anisotropic critical state soils

Abstract

This paper develops a rigorous semi-analytical approach for the undrained cylindrical cavity expansion problem using an anisotropic critical state clay plasticity model. The model, originally proposed by Y. F. Dafalias in 1987, is capable of capturing the inherent anisotropy of the soil due to its initial K0 consolidation history, as well as the subsequent stress-induced anisotropy, through the proper incorporation of the rotation and/or distortion of the ellipsoidal yield surface. It is found that the cavity expansion boundary value problem can be eventually reduced to solving a system of six first-order ordinary differential equations in the plastic zone, with the radial, tangential and vertical stresses in association with the three anisotropic variables controlling the yield surface evolution being the basic unknowns. The pore water pressure can be subsequently deduced from the radial equilibrium equation. Extensive parametric studies have been made of the effects of K0 consolidation anisotropy (including also the subsequent stress-induced anisotropy) and past consolidation history (overconsolidation ratio) on the calculated distributions of stress components and excess pore pressure, the progressive development of the stress-induced anisotropy, and on the effective stress trajectory for a soil particle at the cavity surface due to the cavity expansion. The present solution on account of the natural and induced anisotropy is expected to be able to provide more realistic analyses for a variety of geotechnical problems such as the pile installation prediction and interpretation of pressuremeter tests. It can also serve as a benchmark for the finite-element numerical modelling of the cavity expansion problem involving the advanced anisotropic critical state plasticity models.