Undrained Cylindrical Cavity Expansion Analysis in Mohr-Coulomb Soil Based on Graphical Method

This paper develops a rigorous solution for the undrained cylindrical cavity expansion problem in non-associated Mohr-Coulomb soil under non-hydrostatic initial stress field, that is, with moderate K₀ values of the earth pressure coefficient. The proposed novel, graphical analysis-based theoretical framework contains two essential components: the geometrical analysis to track the stress path trajectory/evolution in the deviatoric plane and a full Lagrangian formulation of both the constitutive relationship and radial equilibrium equation to analytically determine the representative soil particle responses at the cavity surface. The salient advantage/feature of the present graphical approach lies in that it can deduce the cavity expansion responses in full closed form, nevertheless being free of the limitation of the intermediacy assumption for the vertical stress and of the difficulty existing in the traditional zoning method that involves cumbersome, sequential determination of distinct Mohr-Coulomb plastic regions. The analytical solution/model is used to predict the cavity expansion responses and to investigate how the undrained cavity expansion curve and the ultimate cavity pressure are influenced by the key soil plasticity parameters and the earth pressure coefficient at rest.