On the fractal scaling of soil data. Particle-size distributions

Fractal geometry concepts have been widely applied as a tool for describing complex natural phenomena, in particular, in mechanics and physics of rocks and soils. The introduction of scaling has allowed a fractal representation of particle-size distributions (PSDs) of geological materials. In many cases, both log-linear and nonlinear regressions on empirical data have showed a clear deviation from the traditional fractal behaviour in terms of R2 or standard error of estimates. The objectives of this work were (i) to partition PSDs collected from soils into two scaling domains using a piecewise fractal model, (ii) study the relationship between scaling exponents and soil texture (clay and/or sand content), and (iii) compare goodness-of-fit of traditional Weibull and normal distributions, and the proposed piecewise fractal function. A total of 140 PSDs were considered. They corresponded to five textural classes. The clay content ranged from 3% for sandy soils to 93% for very clay soils. Eighty-four PSDs (60%) showed two fractal scaling domains within the range 0–2.0 mm, and only five PSDs (3.6%) were fractal within this conventional domain. Very clayed texture soils were not fractal within the context of the present study (D1=D2≅3), while clay texture soils were fractal only within the domain 0<δ1≤0.2 mm according to the PSF model developed by Perrier et al. [Geoderma 88 (1999) 137]. Fractal dimensions of the first domain, D1, correlated significantly well with clay content following a linear trend (R2=0.771, P<0.001), while those corresponding to the second domain, D2, correlated negatively with sand for clay loam, loam, and sandy soils (R2=0.792, P<0.001), the constant c1 correlated well with soil bulk density. In general, PSDs can present different behaviour depending on soil texture.