Mass, surface, and fragmentation fractal dimensions of soil fragments produced by tillage

Structural units in freshly tilled soil are mainly fragments derived from tillage. Fractal geometry is potentially useful to model this structure. This research was designed to test the applicability of fractal models for mass- and number-size distributions, and surface roughness of soil fragments produced by tillage; and evaluate relationships among parameters of these fractal models. Fragments were sampled from the soil surface of three soil management experiments on a Normania clay loam: (1) moldboard, chisel, and disc as primary tillage tools, (2) three sequences of primary and secondary tillage, and (3) three crops followed by one tillage sequence. Air-dried samples were sieved to obtain eight fragment-size fractions with average diameters, x(m), ranging from 0.4 to 28.0 mm. The size fraction with x(m) = 0.4 mm had different patterns of fragmentation and mass distribution and was not used to estimate fractal parameters. Mass-size relations from size fractions and individual fragments did not show evidence of a fractal distribution of mass; but soil management influenced the estimated mass of fragments of unit diameter, k(m). Two-dimensional roughness of fragment surfaces measured on thin sections was fractal with dimensions, D(s), between 1.02 and 1.18. Disc tillage produced the highest D(s) among primary tillage tools. Fragment number-size distributions were fractal with the fragmentation fractal dimension. D(f) between 2.14 and 3.19, and sensitive to management effects. The number of fragments of unit diameter, k(f), was inversely related to k(m), but relationships of D(f)-k(f) and D(f)-D(s) were not consistent with present fragmentation fractal models. Parameters, D(f) and k(f) were valuable for characterizing freshly tilled soils. More research is needed to understand links between D(f), k(f), and the geometrical configuration of a tilled layer.