Closed-Form Solution for Undrained Cavity Expansion in Anisotropic Soil Mass Based on Spatially Mobilized Plane Failure Criterion

Abstract

A closed-form solution for the undrained cavity expansion problem in an anisotropic soil mass is investigated based on the spatially mobilized plane (SMP) model in this study. Stress and strain around the cavity are subdivided into elastic and plastic regions. The small-strain theory in the elastic region and the large-strain theory in the plastic region are assumed in the closed-form solution, respectively. The closed-form solution is derived by introducing the stress anisotropy factor into the traditional solution in the undrained cavity expansion condition. Stress and strain in the elastic and plastic regions, plastic radius, effective stress, and limited expanding pressure are obtained considering the stress anisotropy and undrained condition. The validity of the presented solution is verified by comparing the prediction with the previous cases. Finally, parametric analysis is performed to investigate the effect of stress anisotropy on the plastic radius, effective stress, and strain in the plastic region.