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 'non-standard' cavities have received much less attention. To address this shortcoming, this paper presents a general theoretical framework for two-dimensional (2D) displacementcontrolled undrained non-circular 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 are subsequently 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 is used to determine the soil stress-strain relationship while consolidation effects are captured using finite difference calculations. The proposed methodology is validated by comparing the reduced solution for a circular cavity with traditional circular cavity expansion theory. A parametric analysis is subsequently undertaken to explore the influence of three non-circular 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 non-circular cavity problems.

Large‐strain analysis for cylindrical cavity contraction in strain‐softening geomaterials

“…Since then, a large number of scholars have continuously enriched and developed this theory and applied it to solve practical problems. In the field of geotechnical engineering, the research directions of cavity expansion theory include: theoretical research [1][2][3][4][5][6][7][8][9][11][12][13]15 ; numerical simulation and soil test [16][17][18][19] ; engineering application [20][21][22][23] ; and others.…”