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This paper develops a general and complete solution for the undrained cylindrical cavity expansion problem in nonassociated Mohr‐Coulomb soil under nonhydrostatic initial stress field (i.e., arbitrary K0${{K}_0}$ values of the earth pressure coefficient), by expanding a unique and efficient graphical solution procedure recently proposed by Chen and Wang in 2022 for the special in situ stress case with K0=1${K}_{0}=1$. 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 K0 being involved. When the cavity is sufficiently expanded, the stress path will eventually end, exclusively, in a major sextant with Lode angle θ in between 5π3$\frac{{5\pi }}{3}$ and 11π6$\frac{{11\pi }}{6}$ or on the specific line of θ=11π6$\theta = \frac{{11\pi }}{6}$. 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. Some typical results for the desired cavity expansion curves and the limit cavity pressure are presented, to investigate the impacts of soil plasticity parameters and the earth pressure coefficient on the cavity responses. The proposed graphical method/solution will be of great value for the interpretation of pressuremeter tests in cohesive‐frictional soils. [ABSTRACT FROM AUTHOR]

Stress and deformation analysis of a cavity in an infinite/finite medium is a fundamental applied mechanics problem of interest in multiple physics and engineering disciplines. This paper develops a complete semianalytical solution for the cylindrical cavity expansion in nonassociated Mohr–Coulomb materials, by using the graphical approach and Lagrangian formulation of the cavity boundary value problem (through tracing the responses of a single material point at the cavity wall). The novelty of the new solution framework lies not only in the relaxation of the stringent intermediacy assumption for the vertical stress as usually adopted in the previous analyses, but also in the comprehensive consideration of nonhydrostatic initial stress conditions via arbitrary values of K0 (the coefficient of earth pressure at rest defined as the ratio between the horizontal and vertical initial stresses). The essence of the so-called graphical method, i.e., the unique geometrical analysis and tracking of the deviatoric stress trajectory, is fulfilled by leveraging the deformation requirement that during cavity expansion the progressive development of the radial and tangential strains must maintain to be compressive and tensile, respectively. With the incorporation of the radial equilibrium condition, the problem is formulated to solve a single first-order differential equation for the internal cavity pressure with respect to a pivotal auxiliary variable, for all the distinct scenarios of K0 being covered. Some selected results are presented for the calculated cavity pressure-expansion curve and limit cavity pressure through an example analysis. The definitive semianalytical solution proposed will be not only substantially advancing the current state of knowledge on the fundamental cavity expansion theory, but also able to serve as a unique benchmark for truly verifying the correctness and capability of the classical cornered Mohr–Coulomb constitutive model built in commercial finite element programs. [ABSTRACT FROM AUTHOR]

This paper presents analytical solutions for the finite expansion problems of a spherical or cylindrical cavity, using a simple yet novel graphical approach recently proposed by Chen & Abousleiman in 2022, in both original Cam Clay (OCC) and modified Cam Clay (MCC) soils under undrained conditions. It is shown that, for a soil mass subjected to isotropic in situ stress conditions, the stress paths in the deviatoric plane for the spherical and cylindrical cavity expansions turn out to be two straight lines, which correspond to Lode angles equal to 11π6$\frac{{11\pi }}{6}$ and 5π3$\frac{{5\pi }}{3}$, respectively. The desired limiting cavity pressure therefore can be directly and accurately evaluated through simple numerical integration with respect to the mean effective stress, while the relationship between the internal cavity pressure and the cavity radius, the cavity expansion curve, may be equally conveniently determined. Numerical results obtained from the current graphical method, for a range of the values of over consolidation ratio considered, compare extremely well with those from the conventional semianalytical formulations of the undrained cavity problem that involve solving a system of coupled governing differential equations. It is interesting to note that the representative and approximate solution developed by Collins & Yu in 1996 indeed is a correct one for the spherical cavity expansion problem, and, with minor modifications, will be applicable for the accurate calculation of the responses of the cylindrical cavity as well. [ABSTRACT FROM AUTHOR]