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This article in SSSAJ

  1. Vol. 55 No. 5, p. 1231-1238
    Received: Feb 12, 1990

    * Corresponding author(s):
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Fractal Fragmentation, Soil Porosity, and Soil Water Properties: I. Theory

  1. Michel Rieu  and
  2. Garrison Sposito
  1. Centre ORSTOM Bondy, 70-74 Route d'Aulnay, 93143 Bondy Cédex, France
    Dep. of Soil Science, Univ. of California, Berkeley, CA 94720



Recent efforts to characterize soil water properties in terms of porosity and particle-size distribution have turned to the possibility that a fractal representation of soil structure may be especially apt. In this paper, we develop a fully self-consistent fractal model of aggregate and pore-space properties for structured soils. The concept underlying the model is the representation of a soil as a fragmented fractal porous medium. This concept involves four essential components: the mathematical partitioning of a bulk soil volume into self-similar pore- and aggregate-size classes, each of which is identified with a successive fragmentation step; the definition of a uniform probability for incomplete fragmentation in each size class; the definition of fractal dimensions for both completely and incompletely fragmented porous media; and the definition of a domain of length scales across which fractal behavior occurs. Model results include a number of equations that can be tested experimentally: (i) a fractal dimension ≤3; (ii) a decrease in aggregate bulk density (or an increase in porosity) with increasing aggregate size; (iii) a power-law aggregate-size-distribution function; (iv) a water potential that scales as an integer power of a similarity ratio; (v) a power-law expression for the water-retention curve; and (vi) an expression for hydraulic conductivity in terms of the conductivities of single-size arrangements of fractures embedded in a regular fractal network. Future research should provide experimental data with which to evaluate these predictions in detail.

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