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This article in SSSAJ

  1. Vol. 57 No. 4, p. 891-895
     
    Received: Mar 4, 1992
    Published: July, 1993


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doi:10.2136/sssaj1993.03615995005700040002x

New Mass-Based Model for Estimating Fractal Dimensions of Soil Aggregates

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

Abstract

Abstract

Values of the fractal dimension, D, for soil aggregates may vary with the model used and the assumptions invoked in formulating the model. The objectives of this study were to: (i) develop a new mass-size-based model, not assuming that probability of failure, P, and bulk density, ρ, are scale-invariant for the estimation of D (defined DR), and (ii) compare the values of DR with those obtained using three other procedures. In the first procedure, manually counted aggregate numbers were used in the number-size relation model for the estimation of D (defined Dn). Aggregate numbers were computed, assuming scale-invariant ρ, in the second procedure and these numbers were used in the same number-size relation model for the estimation of D (defined Dm). In the third procedure, a mass-size-based model, which has an upper limit to D and assumes scale-invariant ρ, was used for the estimation of D (defined DT). Aggregate-size distributions and P for different sizes of aggregates arising from fragmentation during wet sieving in water were obtained for three soils under two cropping treatments (CT) using a modified form of the Yoder apparatus. The P of soil aggregates ranged, depending on soil type, CT, and aggregate size, from 0.30 to 0.91. Values of DR ranged from 2.02 to 3.19 and those for Dm and DT ranged from 2.32 to 3.28 and from 2.46 to 2.84, respectively. Significant 1:1 linear correlations existed only between DR and Dm and between Dm and Dn. Values of DR, Dm, and DT were strongly influenced by soil type, CT, and the estimation model used. The interaction between clay and organic matter contents and CT accounted for 74% of the variability in DR, compared with 54% for DT and 52% for Dm.

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