A Complete Graphical Solution for Undrained Cylindrical Cavity Expansion in K_0-Consolidated Mohr-Coulomb Soil

TL;DR

This paper presents a comprehensive graphical and analytical solution for undrained cylindrical cavity expansion in Mohr-Coulomb soils with arbitrary initial stress states, improving accuracy and simplicity over previous methods.

Contribution

It generalizes a recent graphical solution to include non-hydrostatic initial stresses, providing a full closed-form analytical framework for undrained cavity expansion in Mohr-Coulomb soils.

Findings

Deviatoric stress path is piecewise linear for all K_0 cases.

The solution is free of intermediate assumptions and complex zoning methods.

Provides a definitive analytical solution for pressuremeter test interpretation.

Abstract

This paper develops a general and complete solution for the undrained cylindrical cavity expansion problem in non-associated Mohr-Coulomb soil under non-hydrostatic initial stress field (i.e., arbitrary K_0 values of the earth pressure coefficient), by expanding a unique and efficient graphical solution procedure recently proposed by Chen & Wang in 2022 for the special in situ stress case with K_0 = 1. The new generalized, graph-based theoretical framework contains two essential components: the geometrical analysis to track the stress path trajectory/evolution in different sectors of 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. It is interesting to find that the cavity expansion deviatoric stress path is always composed of a series of piecewise straight lines, for all different case scenarios of K_0 being involved. The salient advantage/feature of the present general 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 closed-form solutions developed herein can be regarded as a definitive one for the undrained cavity expansion problem in classical Mohr-Coulomb materials without the approximations and simplifications in previous solutions, and will be of great value for the interpretation of pressuremeter tests in cohesive-frictional soils.