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TECHNICAL PAPERS

The Generalized Lamé Problem—Part I: Coupled Poromechanical Solutions

[+] Author and Article Information
Mazen Y. Kanj

Saudi Aramco, Exploration and Petroleum Engineering Technology Department, P.O. Box 9892, Dhahran, Eastern Province 31311, KSAe-mail: mazen.kanj@aramco.com

Younane N. Abousleiman

PoroMechanics Institute, School of Petroleum and Geological Engineering, School of Civil Engineering and Environmental Science, The University of Oklahoma, SEC P119, 100 E. Boyd Street, Norman, OK 73019-1014e-mail: yabousle@ou.edu

J. Appl. Mech 71(2), 168-179 (May 05, 2004) (12 pages) doi:10.1115/1.1683751 History: Received August 08, 2002; Revised November 03, 2003; Online May 05, 2004
Copyright © 2004 by ASME
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References

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Abousleiman,  Y., and Kanj,  M., 2003, “The Generalized Lamé Problem:—Part II: Applications in Poromechanics,” ASME J. Appl. Mech., 71, pp. 180–189.
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Kanj, M. Y., and Abousleiman, Y., 2003, “Porothermomechanics of Anisotropic Hollow Cylinders in Oedometric-Like Setups,” CD-Proceedings of the 16th ASCE Engineering Mechanics Conference, Seattle, WA, July 16–18.
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Figures

Grahic Jump Location
Solutions to either the borehole or the full cylinder problems are special cases of the generalized hollow-cylinder one. The bore hole can be envisioned as a very long hollow cylinder with an infinite outer radius. On the other hand, the full cylinder is merely a hollow cylinder with zero inner radius.
Grahic Jump Location
The (as simulated) generalized hollow-cylinder problem. The subject case involves inner/outer confining and pore fluid pressures as well as inner/outer deviatoric stresses (Pi,Po,pi,po,Si, and So). In addition, the hollow core is assumed subject to either a load or a stroke control mode represented by Uz.
Grahic Jump Location
Due to the geometry involved, the cylindrical coordinate system is used to present the problem and its solution. The z-coordinate of the representative element is measured from the bottom of the sample. The radial distance, r, is marked from the center. The angle θ is measured counterclockwise from the direction of the x-axis coinciding with that of the compressive deviatoric effect as depicted.
Grahic Jump Location
Due to the assumed linear nature of this problem, the (as presented) case can be decomposed into an axisymmetric case, Case 1, and a deviatoric case, Case 2. In the deviatoric case, Vz can be switched ON or OFF to toggle between an all time zero axial displacement and an all-time zero axial loading. The switch status of Vz depends on the control mode depicted by Uz in the axisymmetric case.

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