FRACTAL DIMENSION OF SOIL AGGREGATES

Researchers have used scale-invariant bulk density, ρ, to estimate values of fractal dimension, D, for soil aggregate fragmentation. Justification for this assumption has not been fully explored. The objectives of this study were to compare values of D obtained using (i) scale-invariant and scale-variant ρ and (ii) linear (defined D l ) and nonlinear (defined D nl ) fitting procedures, and also (iii) to evaluate the influence of oily waste sludge incorporation on D. Aggregate ρ and mass-size distribution for a Meota loamy sand treated with different rates of an oily waste sludge were determined in the laboratory. Bulk density of soil aggregates, average size ranging from 0.21 to 9.55 mm, ranged from 1.15 to 1.37 Mg m -3 (R 2 = 0.91). Fifty-four values of D were obtained using the scale-variant or scale-invariant ρ for D l or D nl . Values of D l ranged from 2.23 to 3.83, and those of D nl from 2.07 to 3.15. The values of D obtained using the scale-variant ρ were always smaller than those obtained using the scale-invariant ρ. A switch from linear to nonlinear fitting resulted in significantly smaller values of D (D l ≥ D nl ). Oily waste sludge incorporation resulted in marked reductions in D l (R 2 = 0.88) or D nl (R 2 = 0.88). The results show the values of D obtained using nonlinear fitting and scale-variant ρ are accurate and smaller than those obtained using nonlinear or linear fitting or scale-invariant ρ or a combination of the latter three.