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TECHNICAL PAPERS

The Generalized Lamé Problem—Part II: Applications in Poromechanics

[+] Author and Article Information
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

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

J. Appl. Mech 71(2), 180-189 (May 05, 2004) (10 pages) doi:10.1115/1.1683800 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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Cooling,  L. F., and Smith,  D. B., 1936, “The Shearing Resistance of Soils,” J. of the Institution of the Civil Engineers, 3, pp. 333–343.
Ewy,  R. T., and Cook,  N. G. W., 1990, “Deformation and Fracture Around Cylindrical Openings in Rock—I. Observations and Analysis of Deformations,” Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 27(5), pp. 387–407.
Sherwood,  J. D., and Bailey,  L., 1994, “Swelling of Shale Around a Cylindrical Wellbore,” Proc. R. Soc. London, Ser. A, 444, pp. 161–184.
van den Hoek, P. J., Smit, D.-J., Kooijman, A. P., de Bree, Ph., Kenter, C. J., and Khodaverdian, M., 1994, “Size Dependency of Hollow-Cylinder Stability,” Proceedings SPE/ISRM Rock Mechanics in Petroleum Engineering Conference, SPE# 28051, Delft, The Netherlands, Aug. 29–31, pp. 191–198.
Papamichos, E., and van den Hoek, P. J., 1995, “Size Dependency of Castlegate and Berea Sandstone Hollow-Cylinder Strength on the Basis of Bifurcation Theory,” Proc. of the 35th US Symp. on Rock Mech., Daemen and Schultz, eds., Reno, NV, June 5–7, pp. 301–306.
Talesnick,  M. L., Haimson,  B. C., and Lee,  M. Y., 1997, “Development of Radial Strains in Hollow Cylinders of Rock Subjected to Radial Compression,” Int. J. Rock Mech. Min. Sci., 34(8), pp. 1229–1236.
Lee,  D.-H., Juang,  C. H., Chen,  J.-W., Lin,  H.-M., and Shieh,  W.-H., 1999, “Stress Paths and Mechanical Behavior of a Sandstone in Hollow Cylinder Tests,” Int. J. Rock Mech. Min. Sci., 36, pp. 857–870.
Papamichos, E., Skjærstein, A., and Tronvoll, J., 2000, “A Volumetric Sand Production Experiment,” 4th North Amer. Rock Mech. Symp., Seattle, WA, July 31–Aug. 3, pp. 303–310.
Sugiyama,  T., Bremner,  T. W., and Holm,  T. A., 1996, “Effect of Stress on Gas Permeability in Concrete,” ACI Mater. J., 93(5), Sept.–Oct., pp. 443–450.
Subramaniam,  K. V., Popovics,  J. S., and Shah,  S. P., 1998, “Testing Concrete in Torsion: Instability Analysis and Experiments,” J. Eng. Mech., 124(11), pp. 1258–1268.
Taber, L. A., Yang, M., Keller, B. B., and Clark E. B., 1991, “Poroelastic Model for the Trabecular Embryonic Heart,” Proc. Winter Annual Meeting of the ASME, Bioengineering Division, Dec. 1–6, Atlanta, GA, ASME, New York, pp. 623–626.
Lim,  T.-H., and Hong,  J. H., 2000, “Poroelastic Properties of Bovine Vertebral Trabecular Bone,” J. Orthop. Res., 18(4), pp. 671–677.
Kanj,  M. Y., and Abousleiman,  Y., 2003, “The Generalized Lamé Problem: Part I—Coupled Poromechanical Solutions,” ASME J. Appl. Mech., 71, pp. 168–179.
Lamé, G., 1852, “Leçons sur la Théorie Mathématique de l’Élasticité des Corps Solides,” Gautheir-Villars, Paris.
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.
Kanj,  M., Abousleiman,  Y., and Ghanem,  R., 2003, “Anisotropic Poromechanics Solutions for the Hollow-Cylinder,” J. Eng. Mech., 129(11), pp. 1277–1287.
Kanj, M., and Abousleiman, Y., 2003. “Porothermoelastic Analyses of Anisotropic Hollow Cylinders,” Proceedings of the 39th U.S. Rock Mechanics Symposium (Soil Rock America 2003), Cambridge, MA, June 23–25, pp. 1211–1218.
Abousleiman, Y., and Kanj, M., 2002, “Generalized Lamé Solutions in Poromechanics,” Proceedings, Second Biot Conference in Poromechanics, Grenoble, France, Aug. 26–28, A.A. Balkema, Rotterdam, pp. 79–84.

Figures

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Axisymmetric problem setup validation. The hollow core sample is subjected to step loading in the axial direction only: mode 14.
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Pore pressure response trends versus the radial aspect ratio parameter. The plots are made at different simulation times.
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Pore pressure response isochrones given in terms of the testing simulation time and the radial distance from the center of the cylinder
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Axial stress response curves for a hollow cylinder subject to the uniaxial loading setup
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Time-dependent flux responses in the subject cylinder
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Radial displacement histograms at the inner and outer boundaries of the unaxially loaded hollow cylinder
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Radial stress response trends plotted versus the radial aspect ratio parameter in the uniaxially loaded hollow cylinder. The plots are processed at different simulation times.
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Shear stress response trends plotted versus the radial aspect ratio parameter in the cylinder at different simulation times
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Deviatoric setup validation mode 10. The hollow cylinder is subject to only pure deviatoric stress effects on the outer boundary. Axially, the sample is subject to zero loading at all times.
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Pore pressure response trends (θ=0,π) for a hollow cylinder subjected to pure deviatoric effects at its outer boundary
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Tangential stress response trends made close to the boundaries of the deviatorically loaded sample
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Radial displacement trends at the inner wall of the deviatorically loaded hollow cylinder
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Radial displacement trends at the outer boundary of a cylinder subjected to the stress deviator effects of mode 10
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A hollow cylinder subject to the uniaxial loading condition: mode 14. The layer of interest is defined at a radial distance of 0.035 m from the center.
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Pore pressure response curves at r=0.035 m. The markings on the curves indicate the inner hole size of the test cylinder.
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Tangential stress responses at the layer r=0.035 m for uniaxially loaded hollow cylinders. The outer diameter is the same for all cylinders (Ro=0.0508 m).
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Tangential stress responses at the layer r=0.045 m for hollow cylinders subjected to uniaxial loading. All samples are assumed to have the same outer dimension (Ro=0.0508 m). The markings on the curves indicate the hole’s radial dimension.
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A hollow cylinder subjected to the inner drawdown pressure condition of mode 5
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Isochrones of the pore pressure trends (non dimensionalized as p/po) versus time (nondimensionalized as t/tc) for different cylinder’s outer radial dimensions. The response is observed at the layer, r=0.15 m.
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Isochrones of the tangential stress trends (non dimensionalized as σθθ/ηpo) versus time (nondimensionalized as t/tc) for different cylinder’s outer radial dimensions. The response is observed at the layer, r=0.15 m.

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