Water transport in soils as in fractal media

Water transport in soils as in fractal media Fractal scaling laws of water transport were found for soils. A water transport model is needed to describe this type of transport in soils. We have developed a water transport equation using the physical model of percolation clusters, employing the mass conservation law, and assuming that hydraulic conductivity is a product of a local component dependent on water content and a scaling component depending on the distance traveled. The model predicts scaling of water contents with a variable x t 1 (2+β) where β deviates from the zero value characteristic for the Richards equation. A change in the apparent water diffusivity with the distance is predicted if the apparent diffusivity is calculated using the Richards equation. An equation for the time and space invariant soil water diffusivity is obtained. Published data sets of five authors were used to test the scaling properties predicted by the model. The value of β was significantly greater than zero in almost all data sets and typically was in the range from 0.05 to 0.5. This exponent was found from regression equations that had correlation coefficients from 0.97 to 0.995. In some cases a dependence of β on water content was found indicating changes in scaling as the water transport progressed. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Hydrology Elsevier

Water transport in soils as in fractal media

Journal of Hydrology, Volume 204 (1) – Jan 30, 1998

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Publisher
Elsevier
Copyright
Copyright © 1998 Elsevier Ltd
ISSN
0022-1694
eISSN
1879-2707
D.O.I.
10.1016/S0022-1694(97)00110-8
Publisher site
See Article on Publisher Site

Abstract

Fractal scaling laws of water transport were found for soils. A water transport model is needed to describe this type of transport in soils. We have developed a water transport equation using the physical model of percolation clusters, employing the mass conservation law, and assuming that hydraulic conductivity is a product of a local component dependent on water content and a scaling component depending on the distance traveled. The model predicts scaling of water contents with a variable x t 1 (2+β) where β deviates from the zero value characteristic for the Richards equation. A change in the apparent water diffusivity with the distance is predicted if the apparent diffusivity is calculated using the Richards equation. An equation for the time and space invariant soil water diffusivity is obtained. Published data sets of five authors were used to test the scaling properties predicted by the model. The value of β was significantly greater than zero in almost all data sets and typically was in the range from 0.05 to 0.5. This exponent was found from regression equations that had correlation coefficients from 0.97 to 0.995. In some cases a dependence of β on water content was found indicating changes in scaling as the water transport progressed.

Journal

Journal of HydrologyElsevier

Published: Jan 30, 1998

References

  • Application of fractal geometry to the study of networks of fractures and their pressure transient
    Acuna, J.A.; Yortsos, Y.C.
  • The relationship between structure and the hydraulic conductivity of soil
    Crawford, J.W.
  • Fractals
    Feder, J.
  • Channeling and Fickian dispersion in fractal simulated porous media
    Grinrod, P.; Impey, M.D.
  • Fractal Geometry of Nature
    Mandelbrot, B.B.
  • On advective transport in fractal permeability and velocity fields
    Neuman, S.P.
  • Application of fractals in soil and tillage research: a review
    Perfect, E.; Kay, B.D.

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