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

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 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 ρ, 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 ρ, 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 .