Laser diffraction and multifractal analysis for the characterization of dry soil volume-size distributions

Abstract

Fractal scalings of the type N( x> X)≈ X − D f and M( x< X)≈ X d have been studied in previous works for the cumulative number and mass distributions of soil aggregates and particles of size x greater or less, respectively, than a characteristic size X. The exponents D f (fragmentation fractal dimension) and d represent rough estimates of the scale dependence that takes place in the number or mass accumulated, with respect to length scale. A closer look at the mass of soils (aggregates and primary particles) accumulated across the different regions of the interval of sizes would lead, in general, to detect denser or rarer regions across different length scales. These heterogeneity features are present in most real distributions in nature, displaying a behavior named multifractal. The laser scattering method and the multifractal analysis offer the possibility of studying the volume distribution of soils in scales that are not often explored. The goal of this paper is the application of laser diffraction and multifractal analysis to the characterization of dry volume-size distributions in soils. For each of the 20 soil samples considered for the study, an adequate measure is constructed with data corresponding to laser diffraction analysis of those samples. Multifractal analysis techniques are applied to such measures. Volume-size distribution of soils showed, in general, suitable scaling properties that make multifractal analysis a useful mathematical tool for its characterization by means of the singularity spectrum f( α( q)). Samples showed great variability in their multifractal behavior. An adequate range of the parameter q is selected for the characterization of each sample, in such a way that the R 2 values of the corresponding scaling fits are greater than 0.95. In that range, different features of the singularity spectrum f( α( q)) have been analyzed. The singularity spectrum f( α( q)) reveals to be useful for the characterization of soil volume-size distributions.