Analysis of undrained cylindrical cavity contraction in anisotropic soils under constant total vertical stress condition

Abstract

A semi-analytical solution to cylindrical cavity contraction in anisotropic soils under constant total vertical stress and undrained condition is presented in this paper. The elastoplastic constitutive relationship for the problem considered is obtained via Hooke’s law in the elastic stage and the anisotropic modified Cam-Clay model in the plastic stage. By employing an auxiliary parameter to transform the equilibrium equation from Eulerian scheme into Lagrangian scheme, the problem reduces to an initial value problem with the vertical strain and the effective radial, circumferential, vertical stresses as four basic unknowns. The governing equations of this problem in the plastic region are solved as an initial value problem with the mechanical states of soil at the elastic-plastic boundary as the initial values. Parametric analyses show that, owing to the large deformation in the vertical direction, the material particle at cavity surface reaches the critical state much more quickly under constant total vertical stress condition than that under plane strain condition. The distribution of stress components does not manifest a critical-state region as a traditional plane strain solution does. Also, the overconsolidation ratio has an obvious influence on contraction responses. The proposed solution is expected to provide a more accurate prediction of stress and displacement around a drilled wellbore and to other similar geotechnical problems.