Filgueira, Roberto  
Pachepsky, Yakov  
Fournier, Lidia 
Submitted to: European Journal of Soil Science
Publication Type: Peer Reviewed Journal Publication Acceptance Date: 5/5/2003 Publication Date: 11/4/2003 Citation: FILGUEIRA, R.R., PACHEPSKY, Y.A., FOURNIER, L.L. TIMEMASS SCALING IN SOIL TEXTURE ANALYSIS. EUROPEAN JOURNAL OF SOIL SCIENCE. 2003. Interpretive Summary: Data on soil texture are used in the majority of inferences about soil functioning and use. There is a need to find a minimum set of parameters to represent soil particle size distributions in such inferences. The sedimentation of dispersed soil is the routine procedure to find the particle size distributions. The hydrometer is employed that measures the mass of particles present in water column during sedimentation. It was shown recently that the distribution of particle radii within sand, silt and clay fraction often follows the fractal fragmentation model that predicts an inverse power law dependence of the mass of particles to their radius. We show that in this case the hydrometer data should demonstrate a linear dependence between the logarithm of mass of particles remaining in the solution and logarithm of the observation time. The slope of this straight line depends of the exponent in the dependence of the mass of particles to their radius. The rarer are large particles as compared to small ones that larger the slope is. This theoretical relationship was tested with samples of Typic Argiudoll and gave good approximation of hydrometer data on the sedimentation of silt fraction. Monitoring soil mass remaining in the solution presents a simple way to test applicability of fractal fragmentation model to the particle size distribution and to estimate the exponent in the dependence of the mass of particles to their radius. This compresses information about particle size distribution to a small number of parameters that can be then used to relate other soil properties to soil texture. Technical Abstract: Data on texture are used in the majority of inferences about soil functioning and use. The model of fractal fragmentation has attracted attention as a possible source of minimum set of parameters to describe observed particle size distributions. Popular techniques of textural analysis employ the relationship among time, the travel distance, and the radius of a particle subject to sedimentation in a viscous liquid. Assuming a fractal masssize distribution, one should expect the aforementioned relationship to reflect parameters of fractal scaling. The purpose of this note is to present and test an explicit relationship between time, the soil suspension density and the fragmentation fractal dimension in the course of the hydrometer analysis procedure applied to particles with the fractal masssize distribution. We have shown that the relationship between the logarithm of mass of particles remaining in the solution and logarithm of the observation time is linear with the slope equal to (3D)/2 where D is the fragmentation fractal dimension. This relationship was tested with samples of Typic Argiudoll and gave good approximation of hydrometer data on the sedimentation of silt fraction. Monitoring soil mass remaining in the solution presents a way to test applicability of fractal fragmentation model to the particle size distribution and to estimate the fragmentation fractal dimension.
