TECHNICAL PAPERS
Jan 1, 1998

Fractal Model for Flow through Saturated Soils

Publication: Journal of Geotechnical and Geoenvironmental Engineering
Volume 124, Issue 1

Abstract

A fractal model for hydraulic conductivity of soils is presented. Based on similarities between fluid flow and propagation of electromagnetic field through soils, a parallel set of expressions is developed for hydraulic conductivity and dielectric dispersion. The models are expressed in terms of the same fractal model parameters that describe the soil structure. Dielectric dispersion data are used to predict the internal structure of the soil. The predicted fractal parameters are used to determine the hydraulic conductivity of the soil. The predicted hydraulic conductivity compares well with experimental data for kaolinite and montmorillonite. The influence of the differences in internal microstructure of the soil on the hydraulic conductivity is discussed. Potential application of the fractal concept to study soil behavior and for site characterization purposes is presented.

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References

1.
Bengochea, G. I., Lovell, C. W., and Altschaeffl, A. G.(1979). “Pore size distribution and permeability of silty clays.”J. Geotech. Engrg., ASCE, 105(7), 839–856.
2.
Carman, P. C. (1956). Flow of gases through porous media. Academic Press, New York, N.Y.
3.
Chapman, D. L.(1913). “A contribution of the theory of electrocapillarity.”Philosophical Mag., 25(6), 475–481.
4.
Childs, E. C., and Collins-George, N.(1950). “The permeability of porous materials.”Proc. Royal Soc., Series A, London, U.K., 201, 392–405.
5.
Clapp, R. B., and Hornberger, G. M.(1978). “Empirical equations for some soil hydraulic properties.”Water Resour. Res., 14, 601–604.
6.
Fernandez, F., and Quigley, R. M.(1985). “Hydraulic conductivity of natural clays permeated with simple liquid hydrocarbons.”Can. Geotech. J., Ottawa, Canada, 22, 205–214.
7.
Fernandez, F., and Quigley, R. M.(1988). “Viscosity and dielectric constant controls on the hydraulic conductivity of clayey soils permeated with water-soluble organics.”Can. Geotech. J., Ottawa, Canada, 25, 582–589.
8.
Freeze, R. A., and Cherry, J. A. (1979). Groundwater. Prentice-Hall, Inc., Englewood Cliffs, N.J.
9.
Gouy, G.(1910). “Sur la constitution de la charge electrique a la surface d'un electrolyte.”Anniue Physique (Paris), 4(9), 457–468.
10.
Juang, C. H., and Holtz, R. D.(1987). “Fabric, pore size distribution, and permeability of sandy soils.”J. Geotech. Engrg., ASCE, 112(9), 855–868.
11.
Kozney, J. (1927). “Ueber kapillare leitung des wassers im boden.”Wien, Akad. Wiss., 136, Part 2a, 271.
12.
Mandelbrot, B. B.(1968). “How long is the coast of Britain—statistical and self-similarity and fractional dimension.”Science, 156, 636–638.
13.
Mandelbrot, B. B. (1982). The fractal geometry of nature. W. H. Freeman and Co., San Francisco, Calif.
14.
Marshall, T. J.(1958). “A relation between permeability and size distribution of pores.”J. Soil Sci., 9(1), 1–8.
15.
Meegoda, N. J., and Gunasekera, S. D.(1992). “A new method to measure the effective porosity of clays.”Geotech. Testing J., 15(4), 340–351.
16.
Mitchell, J. K. (1993). Fundamentals of soil behavior, 2nd Ed., John Wiley & Sons, Inc., New York, N.Y.
17.
Olsen, H. W. (1961). “Hydraulic flow through saturated clays,” DSc thesis, Massachusetts Institute of Technology, Cambridge, Mass.
18.
Olsen, H. W. (1962). “Hydraulic flow through saturated clay.”Proc., 9th Nat. Conf. on Clays and Clay Minerals, 131–161.
19.
Sachs, S. B., and Spiegler, K. S.(1964). “Radiofrequency measurements of porous conductive plugs—ion exchange resin-solution systems.”J. Physical Chemistry, 68, 1214.
20.
Shepard, J. S.(1993). “Using a fractal model to compute the hydraulic conductivity function.”Soil Sci. Soc. Am. J., 57, 300–306.
21.
Sridharan, A., Altschaeffl, A. G., and Diamond, S.(1971). “Pore size distribution studies.”J. Soil Mech. and Found. Div., ASCE, 97(5), 771–787.
22.
Thevanayagam, S.(1997a). “Dielectric dispersion of porous media as a fractal phenomenon.”J. Appl. Physics, Am. Inst. of Physics, 82(5), 2538–2547.
23.
Thevanayagam, S. (1997b). “Fractal nature of transport through porous media.”Res. Rep., Dept. of Civ. Engrg., State Univ. of New York at Buffalo, N.Y.
24.
Thevanayagam, S. (1998). “Closure to `Frequency-domain analysis of electrical dispersion of soils.”' J. Geotech. Engrg., ASCE.
25.
Thevanayagam, S., and Nesarajah, S. (1997). “A study of the fractal nature of soil microstructure.” (in review) Geotechnique.
26.
Tyler, S. W., and Wheatcraft, S. W.(1989). “Application of fractal mathematics to soil water retention estimation.”Soil Sci. Soc. Am. J., 53, 987–996.
27.
Washburn, E. W.(1921). “Note on a method of determining the distribution of pore sizes in a porous material.”Proc. Nat. Acad. Sci., 7, 115–116.
28.
West, B. J., and Goldberger, A. L.(1987). “Physiology in fractal dimensions.”Am. Sci., 75, 354–352.

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Go to Journal of Geotechnical and Geoenvironmental Engineering
Journal of Geotechnical and Geoenvironmental Engineering
Volume 124Issue 1January 1998
Pages: 53 - 66

History

Published online: Jan 1, 1998
Published in print: Jan 1998

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Authors

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S. Thevanayagam, Member, ASCE,
Asst. Prof., Dept. of Civ., Struct., and Envir. Engrg., State Univ. of New York at Buffalo, 212, Ketter Hall, Buffalo, NY 14260.
S. Nesarajah, Student Member, ASCE
Grad. Student, Dept. of Civ., Struct., and Envir. Engrg., State Univ. of New York at Buffalo, 212, Ketter Hall, Buffalo, NY.

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