Poromechanics solutions to plane strain and axisymmetric mandel-type problems in dual-porosity and dual-permeability medium

Journal of Applied Mechanics, Transactions ASME

Volumn 77, Issue 1, 2010, Pages 1-18

  Nguyen, Vinh X ^a   Abousleiman, Younane N ^a  

^a UNIVERSITY OF OKLAHOMA   (United States)

Author keywords

Analytical solution; Cylinder; Dual permeability; Dual porosity; Fracture; Poroelastic; Unconfined compression

Indexed keywords

ANALYTICAL SOLUTIONS; DUAL-PERMEABILITY; DUAL-POROSITY; POROELASTIC; UNCONFINED COMPRESSION;

CEMENTS; CYLINDERS (SHAPES); FRACTURE; MECHANICAL PERMEABILITY; POROUS MATERIALS;

POROSITY;

EID: 77955286827     PISSN: 00218936     EISSN: 15289036     Source Type: Journal    
DOI: 10.1115/1.3172146     Document Type: Article

References (33)

1. Dickey, J. W., Ladd, C. C., and Ringer, J. J., 1968, "A Plane Strain Device for Testing Clays," Civil Engineering Research Report No. R68-3.
2. Abousleiman, Y., and Cui, L., 1998, "Poroelastic Solutions in Transversely Isotropic Media for Wellbore and Cylinder," Int. J. Solids Struct., 35(34-35), 4905-4929.
3. Wang, H., 2000, Theory of Poroelasticity With Applications to Geomechanics and Hydrology, Princeton University Press, Princeton, NJ, Chap. 7 and 8.
4. Woo, S. L.-Y., Simon, B. R., Kuei, S. C., and Akeson, W. S., 1980, "Quasi-Linear Viscoelastic Properties of Normal Articular Cartilage," ASME J. Biomech. Eng., 102(2), 85-90.
5. Buschmann, M. D., Soulhat, J., Shirazi-Ald, A., Jurvelin, J. S., and Hunziker, E. B., 1998, "Confined Compression of Articular Cartilage: Linearity in Ramp and Sinusoidal Tests and the Importance of Interdigitation and Incomplete Confinement," J. Biomech., 31(2), 171-178.
6. Mandel, J., 1953, "Consolidation des sols (étude mathématique)," Geotechnique, 3(7), 287-299.
7. Biot, M. A., 1941, "General Theory of Three-Dimensional Consolidation," J. Appl. Phys., 12(2), 155-164.
8. Kenyon, D. E., 1979, " Consolidation in Transversely Isotropic Solids," ASME J. Appl. Mech., 46(1), 65-70.
9. Terzaghi, K., 1943, Theoretical Soil Mechanics, Wiley, New York.
10. Abousleiman, Y., Cheng, A. H.-D., Cui, L., Detournay, E., and Roegiers, J.-C., 1996, "Mandel's Problem Revisited," Geotechnique, 46(2), 187-195.
11. Hoang, S. K., and Abousleiman, Y., 2009, "Poroviscoelastic Two-Dimensional Anisotropic Solution With Application to Articular Cartilage Testing," J. Eng. Mech., 135(5), 367-374.
12. Christian, J. T., and Boehmer, J. W., 1970, "Plane Strain Consolidation by Finite Elements," J. Soil Mech. Found. Div., 96(4), 1435-1457.
13. Cui, L., Abousleiman, Y., Cheng, A. H.-D., and Kaliakin, V., 1996, "Finite Element Analyses of Anisotropic Poroelasticity: A Generalized Mandel's Problem and an Inclined Borehole Problem," Int. J. Numer. Analyt. Meth. Geomech., 20(6), 381-401.
14. Yin, S., Rothenburg, L., and Dusseault, M. B., 2006, "3D Coupled Displacement Discontinuity and Finite Element Analysis of Reservoir Behavior During Production in Semi-Infinite Domain," Transp. Porous Media, 65(3), 425-441.
15. Phillips, P. J., and Wheeler, M. F., 2007, "A Coupling of Mixed and Continuous Galerkin Finite Element Methods For Poroelasticity I: The Continuous Time Case," Comput. Geosci., 11(2), 131-144.
16. Odgaard, A., and Linde, F., 1991, "The Underestimation of Young's Modulus in Compressive Testing of Cancellous Bone Specimens," J. Biomech., 24(8), 691-698.
17. Wang, C., Chahine, N., Hung, C., and Ateshian, G., 2003, "Optical Determination of Anisotropic Material Properties of Bovine Articular Cartilage in Compression," J. Biomech., 36, 339-353.
18. Saada, A., 1974, Elasticity: Theory and Applications, Pergamon Press, New York.
19. Armstrong, C. G., Lai, W. M., and Mow, V. C., 1984, "An Analysis of the Unconfined Compression of Articular Cartilage," ASME J. Biomech. Eng., 106(5), 165-173.
20. Cui, L., and Abousleiman, Y., 2001, "Time-Dependent Poromechanical Responses of Saturated Cylinders," J. Eng. Mech., 127(4), 391-398.
21. Cowin, S. C., and Mehrabadi, M. M., 2007, "Compressible and Incompressible Constituents in Anisotropic Poroelasticity: The Problem of Unconfined Compression of a Disk," J. Mech. Phys. Solids, 55, 161-193.
22. Cowin, S. C., 1999, "Bone Poroelasticity," J. Biomech., 32, 217-238.
23. Barenblatt, G. I., Zheltov, I. P., and Kochina, I. N., 1960, "Basic Concept in the Theory of Seepage of Homogeneous Liquid in Fissured Rocks," J. Appl. Math. Mech., 24(5), 1286-1303.
24. Warren, J. E., and Root, P. J., 1963, "The Behavior of Naturally Fractured Reservoirs," SPEJ, 228, 245-255.
25. Wilson, R. K., and Aifantis, E. C., 1982, "On the Theory of Consolidation With Double Porosity," Int. J. Eng. Sci., 20, 1009-1035.
26. Berryman, J. G., 2002, "Extension of Poroelastic Analysis to Double-Porosity Materials: New Technique in Microgeomechanics," J. Eng. Mech., 128(8), 840-847.
27. Stehfest, H., 1970, "Numerical Inversion of Laplace Transforms," Commun. ACM, 13, 47-49.
28. Cheng, A. H.-D., Sidauruk, P., and Abousleiman, Y., 1994, "Approximate Inversion of Laplace Transform," Math. J., 4(2), 76-82.
29. Aguilera, D., 1995, Naturally Fractured Reservoirs, 2nd ed., PennWell Books, Tulsa, OK, Chap. 1.
30. Bear, J., 1972, Dynamics of Fluids in Porous Media, 3rd ed., American Elsevier, New York, Chap. 1.
31. Berryman, J. G., and Pride, S. R., 2002, "Models for Computing Geomechanical Constants of Double-Porosity Materials from the Constituents' Properties," J. Geophys. Res., 107(B3), ECV2-1-ECV2-14.
32. Churchill, R. V., 1972, Operational Mathematics, McGraw-Hill, New York.
33. Polyanin, A. D., and Manzhirov, A. V., 1998, Handbook of Integral Equations, 1st ed., CRC, Florida, Chap. 2.