Semi-analytical solution for the undrained expansion of a cylindrical cavity in saturated soil

The existing solution for undrained cylindrical cavity expansion, based on the modified Cam clay model, is limited in its applicability to saturated, normally consolidated, and slightly over-consolidated clays, excluding heavily over-consolidated soils and granular materials. To address this limitation, a general solution is proposed for the expansion of a cylindrical cavity in saturated soil under undrained conditions. The solution utilizes a Unified State Parameter Model (CASM) incorporating Rowe's stress-dilatancy relation to derive the elastoplastic stress-strain relationship of saturated soil. By employing the large deformation theory and introducing an auxiliary variable, expressions for the effective stress and excess pore water pressure of the soil in the elastoplastic zone are derived using the Lagrangian analysis method. A semi-analytical solution for undrained cylindrical cavity expansion is obtained under the elastic-plastic boundary conditions. The results demonstrate that the present solution yields consistent calculations with the modified Cam clay model when appropriate spacing ratio and stress-state parameters are selected, and it provides more reasonable results for heavily over-consolidated soils. Furthermore, the proposed solution can be applied to calculate undrained cylindrical cavity expansion in various types of saturated soils by adjusting the parameter values.