Abstract
Constitutive models for a general binary elastic-porous media are investigated by two complementary approaches. These models include both constituents treated as compressible/incompressible, a compressible solid phase with an incompressible fluid phase (hybrid model of first type), and an incompressible solid phase with a compressible fluid phase (hybrid model of second type). The macroscopic continuum mechanical approach uses evaluation of entropy inequality with the saturation condition always considered as a constraint. This constraint leads to an interface pressure acting in both constituents. Two constitutive equations for the interface pressure, one for each phase, are identified, thus closing the set of field equations. The micromechanical approach shows that the results of Didwania and de Boer can be easily extended to general binary porous media.
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References
Baer, M. R. and Nunziato, J. W.: 1986, A two-phase mixture theory for the defla-grationto-detonation transition (DDT) in reactive granular materials, Int. J. Multiphase Flow 12, 861-889.
Biot, M. A. and Willis, D. G.: 1957, The elastic coefficients of the theory of consolidation, J. Appl. Mech. 24, 594-601.
Biot, M. A.: 1972, Theory of finite deformations of porous solids, Indiana Uni. Math. J. 21, 597-620.
Bluhm, J.: 1997, A consistent model for saturated and empty porous media, Forschungsberichte aus dem Fachbereich Bauwesen 74, UniversitÄt-GH Essen.
Bluhm, J. and de Boer, R.: 1997, The volume fraction concept in the porous media theory, Zeitschrift für angewandte Mathematik und Mechanik ZAMM 77, 563-577.
Cieszko, M. and Kubik, J.: 1996, Constitutive relations and internal equilibrium condition for fluidsaturated porous solids, Arch. Mech. Stosow. 48(5), 893-923.
de Boer, R.: 1996, Highlights in the historical development of the porous media theory–toward a consistent macroscopic theory, Appl. Mech. Rev. 49, 201-262.
de Boer, R.: 1997, Compressible porous media: toward a general theory, Proceedings of the IUTAM Symposium on Mechanics of Granular and Porous Materials, N. A. Fleck and A. C. F. Cocks (eds), Kluwer Academic Publishers, Dordrecht, Boston, London.
de Boer, R. and Didwania, A. K.: 1997, The effect of uplift in liquid-saturated porous solids–Karl Terzaghi's contributions and recent findings. Géotechnique 47, 289-298.
de Boer, R.: 2000, Theory of Porous Media: Highlights in the historical development and current state, Springer-Verlag, Berlin, Heidelberg, New York.
Didwania, A. K. and de Boer, R.: 1999, Saturated compressible and incompressible porous solids: macro-and micromechanical approaches, Transport in Porous Media 34, 101-115.
Lade, P. V. and de Boer, R.: 1997, The concept of effective stress for soil, concrete and rock, Géotechnique 47, 61-78.
Nur, A. and Byerlee, J. D.: 1971, An exact effective stress law for elastic deformation of rock with fluid, J. Geophys. Res. 76, 6414-6419.
Rendulic, L.: 1936, Porenziffer und Porenwasserdruck in Tonen, Bauing 17, 559-564.
Suklje, L.: 1969, Rheological Aspects of Soil Mechanics, Wiley Interscience, New York.
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de Boer, R., Didwania, A.K. Saturated Elastic Porous Solids: Incompressible, Compressible and Hybrid Binary Models. Transport in Porous Media 45, 423–443 (2001). https://doi.org/10.1023/A:1012033106328
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DOI: https://doi.org/10.1023/A:1012033106328