Exact undrained elasto-plastic solution for cylindrical cavity expansion in modified Cam Clay soil

This paper presents an exact semi-analytical analysis for cylindrical cavity expansion in modified Cam Clay critical state soil under the undrained condition. By assuming small-strain deformation in the elastic region and large-strain deformation in the plastic region, the formulation of the problem is reduced to solving a system of first-order ordinary differential equations for the radial, tangential and vertical effective stresses in the plastic zone. The pore pressure distribution can subsequently be determined from the radial equilibrium equation in terms of the total stresses. The semi-analytical solution derived in this paper follows the rigorous definitions for the two effective stress invariants instead of approximate ones, as usually assumed in the existing literature, and applies to the more general case where the out-of-plane (vertical) in situ stress may be different from the in-plane (horizontal) one. The results show clearly that the stress history (overconsolidation ratio) has a significant influence on the stress and pore pressure distributions around the cavity. The present solution provides an exact and realistic theoretical framework for predicting the soil behaviour around the cylindrical cavity, with applications to the interpretation of pressuremeter tests and to pile installation problems. It also serves as a valuable benchmark for verifying various cavity expansion numerical methods involving the critical state plasticity model.