Revisiting undrained cavity expansion problem in critical state soils: A simple graph‐based approach

Abstract

This paper presents analytical solutions for the finite expansion problems of a spherical or cylindrical cavity, using a simple yet novel graphical approach recently proposed by Chen & Abousleiman in 2022, in both original Cam Clay (OCC) and modified Cam Clay (MCC) soils under undrained conditions. It is shown that, for a soil mass subjected to isotropic in situ stress conditions, the stress paths in the deviatoric plane for the spherical and cylindrical cavity expansions turn out to be two straight lines, which correspond to Lode angles equal to 11𝜋 6 and 5𝜋 3, respectively. The desired limiting cavity pressure therefore can be directly and accurately evaluated through simple numerical integration with respect to the mean effective stress, while the relationship between the internal cavity pressure and the cavity radius, the cavity expansion curve, may be equally conveniently determined. Numerical results obtained from the current graphical method, for a range of the values of over consolidation ratio considered, compare extremely well with those from the conventional semianalytical formulations of the undrained cavity problem that involve solving a system of coupled governing differential equations. It is interesting to note that the representative and approximate solution developed by Collins & Yu in 1996 indeed is a correct one for the spherical cavity expansion problem, and, with minor modifications, will be applicable for the accurate calculation of the responses of the cylindrical cavity as well.