Noncircular Cavity Expansion in Undrained Soil: Semi-Analytical Solution

Abstract

The cavity expansion approach has been a popular tool to interpret a wide range of geotechnical problems over the last several decades. Most previous research focused on the expansion of cylindrical and/or spherical cavities, whereas nonstandard cavities have received much less attention. To address this shortcoming, this paper presents a general theoretical framework for two-dimensional (2D) displacement-controlled undrained noncircular cavity expansion (N-CCE) in undrained soil. The new approach combines strain path method (SPM) concepts and conformal mapping to determine the soil velocity and strain rate fields analytically. The soil displacement and strain subsequently are determined by integrating the soil velocities and strain rates along the strain path using a series of transformed ordinary differential equations. In this study, the modified Cam Clay (MCC) effective stress constitutive model was used to determine the soil stress–strain relationship, and consolidation effects were captured using finite-difference calculations. The proposed methodology was validated by comparing the reduced solution for a circular cavity with traditional circular cavity expansion theory. A parametric analysis subsequently was undertaken to explore the influence of three noncircular cavity shapes on expansion-induced soil deformation mechanisms, shear strains, effective stresses, and pore-water pressure development and consolidation. The proposed solution can be implemented with any critical state–based soil model and can be applied to arbitrary noncircular cavity problems.