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This article in SSSAJ

  1. Vol. 57 No. 4, p. 896-900
    Received: June 5, 1992

    * Corresponding author(s):
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Multifractal Model for Soil Aggregate Fragmentation

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



Dry aggregate size and strength distributions are important soil structural characteristics. We present a theoretical model based on multifractals for predicting one characteristic from the other. For a specified stress, σ, the strength of dry aggregates of normalized equivalent cubic length x* was expressed as a probability of failure, {P(x*)}σ. A method was developed for calculating {P(x*)}σ from tensile strength data. At intermediate levels of stress (0.3 ≤ σ ≤ 0.9 MPa), {P(x*)}σ decreased with decreasing x*. A Pareto distribution was used to model this scale dependency. The distribution's parameters, q and r, determine the probability of failure of the largest aggregate and the rate of change in scale dependency, respectively. The r increased and the q decreased logarithmically with increasing σ. The fractal dimension, D, was used to characterize the number-size distribution of dry aggregates after fragmentation. For mass-conserving cubic fragmentation, D is related to {P(x*)}σ by the multifractal spectrum, D ≅ log {8(2′ − qx*−r)}/log {2}. Previously published dry-sieving data were reanalyzed. The number-size distribution determined by visual counting gave a spectrum of fractal dimensions as predicted by the theory. Values of D ranged from 2.53 at x* = 4.7 × 10−2 to 3.46 at x* = 7.5 × 10−1. The multifractal spectrum was used to estimate q and r inversely. Further research is required to determine the level of stress associated with these values.

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