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This article in SSSAJ

  1. Vol. 56 No. 5, p. 1407-1409
    Received: Nov 8, 1991

    * Corresponding author(s):


Fractal Dimensions of Soil Aggregate-size Distributions Calculated by Number and Mass

  1. E. Perfect ,
  2. V. Rasiah and
  3. B. D. Kay
  1. Department of Land Resource Science, Univ. of Guelph, Guelph, ON N1G 2W1, Canada



The fractal dimension, D, has been used to characterize soil aggregate-size distributions. However, D is based on the number-size relationship. In most soils applications, it is the mass-size relationship that is determined. A number-size distribution can be generated from the mass-size distribution, assuming scale-invariant shape and density. Variation in shape and density as a function of size may introduce errors in the calculation of D. We compared the fractal dimensions of soil aggregates estimated from mass-size distribution data (Dm), with those computed from actual number-size distribution data determined by counting (Dn). The fractal dimension ranged from 0.67 to 3.92 for Dn, and from 0.79 to 4.06 for Dm. A significant linear relation was found between Dm and Dn, with R2 = 0.935. The resulting intercept and slope were not significantly different from zero and one, respectively, indicating a 1:1 relationship. This implies that the assumption of scale-invariant shape and density was valid across the range of aggregate sizes studied (5.0 × 10−1 to 3.2 × 101 mm). Thus, the fractal dimension can be estimated from mass-distribution data within this range.

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