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

Abstract

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 R 2 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 ( D 1= D 2≅3), while clay texture soils were fractal only within the domain 0< δ 1≤0.2 mm according to the PSF model developed by Perrier et al. [Geoderma 88 (1999) 137]. Fractal dimensions of the first domain, D 1, correlated significantly well with clay content following a linear trend ( R 2=0.771, P<0.001), while those corresponding to the second domain, D 2, correlated negatively with sand for clay loam, loam, and sandy soils ( R 2=0.792, P<0.001), the constant c 1 correlated well with soil bulk density. In general, PSDs can present different behaviour depending on soil texture.