Abstract
In this paper the field equations governing the dynamic response of a fluid-saturated elastic porous medium are analyzed and built up for the study of quasi-static and dynamical problems like the consolidation problem and wave propagation. The two constituents are assumed to be incompressible. A numerical solution is derived by means of the standard Galerkin procedure and the finite element method.
Similar content being viewed by others
References
Bathe, K. J.: 1990, Finite-Element-Methoden, Springer-Verlag, Berlin.
Biot, M. A.: 1955, Theory of elasticity and consolidation for a porous anisotropic solid, J. Appl. Phys. 26, 182.
Biot, M. A.: 1956, Theory of propagation of elastic waves in fluid-saturated porous soil: I. Low-frequency range, J. Acoust. Soc. Am. 28, 168.
Bluhm, J.: 1997, A consistent model for empty and saturated porous media, Habilitation Thesis, University of Essen, Essen.
Bluhm, J. and de Boer, R.: 1997, The volume fraction concept in the porous media theory, Zeitschr. Angew. Math. Mech. (ZAMM) 77(8), 563.
de Boer, R.: 1982, Vektor-und Tensorrechnung füur Ingenieure, Springer-Verlag, Berlin.
de Boer, R.: 1996, Highlights in the historical development of the porous media theory: toward a consistent macroscopic theory, Appl. Mech. Rev. 49, 201.
de Boer, R., Ehlers, W. and Liu, Z.: 1993, One-dimensional transient wave propagation in fluid-saturated incompressible porous media, Arch. Appl. Mech. 63, 59.
Bowen, R. M.: 1980, Incompressible porous media models by use of the theory of mixtures, Int. J. Engng. Sci. 18, 1129.
Breuer, S.: 1997, Dynamic response of a fluid-saturated elastic porous solid, Arch. Mech. 49(4), 771.
Diebels, S. and Ehlers, W.: 1996, Dynamic analysis of a fully saturated porous medium accounting for geometrical and material non-linearities, Int. J. Numerical Methods Engng. 39, 81-97.
Ehlers, W.: 1989, Poröse Medien-ein kontinuumsmechanisches Modell auf der Basis der Mischungstheorie, Forschungsbericht aus dem Fachbereich Bauwesen 47, Essen.
Ehlers, W. and Diebels, S.: 1994, Dynamic deformations in the theory of fluid-saturated porous solid materials, Proc. IUTAMSymp. Anisotropy, Inhomogeneity and Nonlinearity in Solid Mechanics, Nottingham, U.K.
Fillunger, P.: 1936, Erdbaumechanik?, Selbstverlag des Verfassers, Wien.
Lewis, R. W. and Schrefler, B. A.: 1987, The finite element method in the deformation and consolidation of a porous media, Wiley.
Prévost, J. H.: 1981, Consolidation of an elastic porous media, J. Eng. Mech. Div. ASCE 107 (EM 1), 169-186.
Rayleigh, L.: 1885, On waves propagating along the plane surface of an elastic solid, Proc. Lond. Math. Soc. 17, 4.
Richart, F. E., Hall, J. R. and Woods, R. D.: 1970, Vibrations of Soils and Foundations, Prentice-Hall, Englewood Cliffs, N.J.
Zienkiewicz, O. C.: 1984, Methode der Finiten Elemente, Carl Hanser Verlag, München.
Zienkiewicz, O. C. and Shiomi, T.: 1984, Dynamical behaviour of saturated porous media; the generalized Biot formulation and its numerical solution, Int. J. Num. Anal. Methods Geomech. 8, 71.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Breuer, S. Quasi-Static and Dynamic Behavior of Saturated Porous Media with Incompressible Constituents. Transport in Porous Media 34, 285–303 (1999). https://doi.org/10.1023/A:1006586130476
Issue Date:
DOI: https://doi.org/10.1023/A:1006586130476