zbMATH — the first resource for mathematics

An expression for the permeability of anisotropic granular media. (English) Zbl 0692.73071
Summary: There are many expressions proposed for the permeability of isotropic media based on flow channel and pore size distribution concepts, but there are no such expressions for anisotropic media. In this paper an expression for the permeability of an anisotropic medium is proposed, which has been verified in the laboratory. The mechanism behind fluid flow through soil was investigated using microscopic computer simulations to propose an expression for macroscopic permeability. The soil was assumed to be a spatially periodic porous medium, and the Navier-Stokes equation was solved using the FEM with appropriate boundary conditions for several different arrangements of the porous medium. The basic variables influencing flow through soil at the microscopic level were identified as specific surface area, void ratio, particle shape, material heterogeneity and the arrangement of particles in a porous medium. A sensitivity analysis was carried out to obtain an expression for the permeability in terms of the above variables.
The corresponding macroscopic variables for the above microscopic variables are average specific surface area, average void ratio, anisotropy, tortuosity due to material heterogeneity, and the arrangement of particles respectively. An expression for the directional permeability is proposed in terms of these variables for the most common occurrence of particles in a porous medium. For the verification of the proposed equation, the permeability values of a fine-grained sand were measured at different void ratios and were compared with those predicted by the proposed equation. The results show that the predicted permeability values from the proposed equation are very close to the measured values.

74L10 Soil and rock mechanics
74S05 Finite element methods applied to problems in solid mechanics
76S05 Flows in porous media; filtration; seepage
74E10 Anisotropy in solid mechanics
Full Text: DOI
[1] Hydrodynamics, 6th edn, Cambridge University Press, London, 1932.
[2] Les Fontaines Publiques de la Ville de Dijon, Dalmont, Paris, 1856.
[3] Kozeny, Wien Akad, Wiss. 136 (1927)
[4] Flow of Gases Through Porous Media, Academic Press, New York, 1956. · Zbl 0073.43304
[5] Childs, Proceedings of the Royal Society, A 201 pp 392– (1950)
[6] and , ’A finite element solution for two-dimensional density stratified flow’, Final report prepared for the U. S. Department of the Interior, Office of Water Resources Research by Water Resources Engineers, Inc., Walnut Creek, CA, 1973.
[7] Eidsath, Chemical Engineering Science 35 pp 1803– (1983)
[8] Irons, Int. j. numer. methods eng. 2 pp 5– (1970)
[9] Hood, Int. j. numer. methods eng. 10 pp 379– (1976)
[10] ’Functional dependence of permeability tensor’ private communication; see Reference 16.
[11] Whitaker, Transport in Porous Media 1 pp 3– (1986)
[12] Dafalias, Archives of Mechanics 31 pp 723– (1979)
[13] Fricke, Phys. Rev. 57 pp 934– (1953)
[14] Witt, ASCE, Geotechnical Engineering 108 pp 1181– (1983)
[15] ’Prediction of in situ stress state using the electrical method for fine grained soils’, Thesis, submitted in partial satisfaction of the requirement of Master of Science in Engineering, University of California, Davis, 1983.
[16] ’Fundamental characterization of soils for the development of an expression for permeability for application in in-situ testing’, Thesis, submitted in partial satisfaction of the requirement of Doctor of Philosophy in Engineering, University of California, Davis, 1985.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.