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

Department of Land Resource Science, Univ. of Guelph, Guelph, ON, Canada N1G 2W1

*Corresponding author.

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, , are scale-invariant for the estimation of D (defined D_R), and (ii) compare the values of D_R 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 D_n). Aggregate numbers were computed, assuming scale-invariant , in the second procedure and these numbers were used in the same number-size relation model for the estimation of D (defined D_m). In the third procedure, a mass-size-based model, which has an upper limit to D and assumes scale-invariant , was used for the estimation of D (defined D_T). 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 D_R ranged from 2.02 to 3.19 and those for D_m and D_T ranged from 2.32 to 3.28 and from 2.46 to 2.84, respectively. Significant 1:1 linear correlations existed only between D_R and D_m and between D_m and D_n. Values of D_R, D_m, and D_T 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 D_R, compared with 54% for D_T and 52% for D_m.

Received for publication March 4, 1992.

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