A novel graphical analysis-based method is proposed for analysing the responses of a cylindrical cavity expanding under undrained conditions in modified Cam Clay soil. The essence of developing such an approach is to decompose and represent the strain increment/rate of a material point graphically into the elastic and plastic components in the deviatoric strain plane. It allows the effective stress path in the deviatoric plane to be readily determined by solving a first-order differential equation with the Lode angle being the single variable. The desired limiting cavity pressure and pore pressure can be equally conveniently evaluated, through basic numerical integrations with respect to the mean effective stress. Some ambiguity is clarified between the generalized (work conjugacy-based) shear strain increments and the corresponding deviatoric invariants of incremental strains. The present graph-based approach is also applicable for the determination of the stress and pore pressure distributions around the cavity. When used for predicting the ultimate cavity/pore pressures, it is computationally advantageous over the existing semi-analytical solutions that involve solving a system of coupled governing differential equations for the effective stress components. It thus may serve potentially as a useful and accurate interpretation of the results of in-situ pressuremeter tests on clay soils.

This paper develops a rigorous semi-analytical approach for the undrained cylindrical cavity expansion problem using an anisotropic critical state clay plasticity model. The model, originally proposed by Y. F. Dafalias in 1987, is capable of capturing the inherent anisotropy of the soil due to its initial K0 consolidation history, as well as the subsequent stress-induced anisotropy, through the proper incorporation of the rotation and/or distortion of the ellipsoidal yield surface. It is found that the cavity expansion boundary value problem can be eventually reduced to solving a system of six first-order ordinary differential equations in the plastic zone, with the radial, tangential and vertical stresses in association with the three anisotropic variables controlling the yield surface evolution being the basic unknowns. The pore water pressure can be subsequently deduced from the radial equilibrium equation. Extensive parametric studies have been made of the effects of K0 consolidation anisotropy (including also the subsequent stress-induced anisotropy) and past consolidation history (overconsolidation ratio) on the calculated distributions of stress components and excess pore pressure, the progressive development of the stress-induced anisotropy, and on the effective stress trajectory for a soil particle at the cavity surface due to the cavity expansion. The present solution on account of the natural and induced anisotropy is expected to be able to provide more realistic analyses for a variety of geotechnical problems such as the pile installation prediction and interpretation of pressuremeter tests. It can also serve as a benchmark for the finite-element numerical modelling of the cavity expansion problem involving the advanced anisotropic critical state plasticity models.

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Hydraulic fracturing is the primary method of stimulation in unconventional reservoirs, playing a significant role in oil and gas production enhancement. A key issue for the analysis of hydraulic fracture initiation is to accurately determine the stress distributions in the vicinity of the borehole caused by the injection of pressurized fluids. This paper develops an exact, three-dimensional, poroelastic coupled analytical solution for such stress analysis of an arbitrarily inclined borehole subjected concurrently to a finite-length fluid discharge and in situ stresses, using Fourier expansion theorem and the Laplace–Fourier integral transform technique. The complicated boundary conditions, which involve the mixed boundary values at the borehole surface and the coupling between the total radial stress and injection-induced pore pressure over the sectioned borehole interval, as well as the fully three-dimensional far field in situ stresses, are addressed in a novel way and deliberately/elegantly decomposed into five fundamental, easier to handle modes. The rigour and definitive nature of the proposed analytical methodology facilitates fundamental understanding of the mechanism underlying the stress responses of the borehole and porous medium. It can be and is used here as a benchmark for the numerical solutions obtained from the finite-element analysis commercial program (ABAQUS).

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