A similarity solution for spherical cavity drained expansion in overconsolidated soils considering large deformation

Abstract

This paper presents a novel similarity solution for drained spherical cavity expansion in overconsolidated soils, which creatively incorporates the large strain into similarity solution. The salient feature of the present solution lies in that it properly represents the large deformation associated responses of the overconsolidated soil during cavity expansion. The logarithmic strain components are reasonably incorporated into the similarity solution, which is a general solution technique that has been widely used to solve cavity expansion problems, to creatively account for the large deformation of soils during cavity expansion in such a solution framework. The competent modified unified-hardening (UH) model is employed to properly represent the unique behavior of overconsolidated soils during expansion, where three-dimensional strength characteristics of the soil are taken into account as well. The partial differential governing equations under Eulerian description are transformed into a set of first order ordinary differential equations under Lagrangian description and further solved as an initial value problem by MATLAB. The present method is verified by comparing with the modified Cam-clay model based solutions and an extensive parameter analysis is subsequently conducted for soils with different overconsolidation ratio. The unique expansion behaviors in the overconsolidated soils including the peak strength behavior, strain-hardening/softening and shear dilatancy behaviors are discussed in a comprehensive and in-depth manner.