Particle-size distribution in soils: A critical study of the fractal model validation

Particle size distributions (PSDs) have been analyzed in the past with power-law functions relating cumulative number of particles to diameter and mass of particles to diameter, and the exponents interpreted as fragmentation fractal dimensions (D). More recently, a mass–time scaling model was proposed assuming a fractal mass–size distribution for particles settling in a liquid. The objective of this study was to test the mass–time and the mass–size relations in soil particle distributions settling in water, and to estimate the range of particle diameters where power-law scaling was applicable. Five soil samples from Argentina, with clay contents ranging from 8% to 32%, were used in the experiments. Particle size analysis was done with the Bouyoucos hydrometer method. Results for D ranged from 2.434 to 2.712 with R2 ranging from 0.922 to 0.998. The power-law scaling was applicable in the range of particle diameters from 1 to 50 μm, to four of the soils, and from 1 to 35 μm to the fifth one. Besides, a previous set of soil PSD from Argentina, with particle diameters ranging from 1 to 40 μm was also studied. The obtained D values were from 2.427 (8% clay) to 2.928 (75% clay), with R2 from 0.983 to 0.997. Power laws relating mass to size or mass to time of soil particles settling in a liquid were good models to describe particle size distributions in the silt particle range sizes.