A Graphical Solution Framework for Elastoplastic Cylindrical Cavity Problem in Mohr–Coulomb Material
Publication: Journal of Engineering Mechanics
Volume 150, Issue 5
Abstract
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 (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 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.
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Data Availability Statement
This work essentially develops a semianalytical solution through graphical analysis for the cavity expansion problem. The final results reported in Figs. 4–12 can be readily obtained by solving simple, single first-order differential equations, which has been realized by using the Wolfram Mathematica software through its built-in command “NDSolve.” All the computational results are reproducible, and the relevant data are available from the corresponding author upon reasonable request.
Acknowledgments
This research is funded by the Industrial Ties Research Subprogram of the Louisiana Board of Regents [Grant No. LEQSF(2019-22)-RD-B-01] and the ACS Petroleum Research Fund, American Chemical Society (PRF# 66583-ND9).
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Received: Jun 19, 2023
Accepted: Dec 2, 2023
Published online: Feb 22, 2024
Published in print: May 1, 2024
Discussion open until: Jul 22, 2024
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