On the information content of coarse data with respect to the particle size distribution of complex granular media: rationale approach and testing

Authors: GARCIA-GUTIERREZ, CARLOS - Polytechnic University Of Madrid; Pachepsky, Yakov

Submitted to: Entropy Journal
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 7/17/2019
Publication Date: 7/17/2019
Citation: Garcia-Gutierrez, C., Pachepsky, Y.A. 2019. On the information content of coarse data with respect to the particle size distribution of complex granular media: rationale approach and testing. Entropy Journal. 21(6):601. https://doi.org/10.3390/e21060601.
DOI: https://doi.org/10.3390/e21060601

Interpretive Summary: Particles of different sizes play different role in soil functioning and use. Knowing the statistical distribution of particle sizes in soil is of utmost importance. Measuring the entire distribution in details is cost- and labor intensive. Only small number of particle size ranges is usually measured. A method has been developed to convert data on three particle size ranges into detailed particle size distribution. However, this method does not provide recommendations on the particle size ranges to use. This work emt two objectives. First the method of particle size distribution reconstruction was theoretically supported using the thermodynamic notion of entropy. Second, the dependence of the distribution reconstruction accuracy om the sizes of three particle size ranges was derived for a large database on detailed particle size distribution collected in Spain. The best particle size distribution reconstruction was found when the particle range of the fine particles included clay, silt, and fine sand, the medium range was composed of medium and coarse sand, and the large range comprised very coarse sand and gravel. Results of this work can be used in geotechnics, agronomy, surface hydrology, contaminant transport, and other application fields in which the detailed soil particle size distributions are of importance.

Technical Abstract: The particle size distribution (PSD) of complex granular media is seen as a mathematical measure supported in the interval of grain sizes. A physical property characterizing granular products used in the Andreasen and Andersen model of 1930 is re-interpreted in Information Entropy terms leading to a differential information equation as a conceptual approach for the PSD. Under this approach, measured data which give a coarse description of the distribution may be seen as initial conditions for the proposed equation. A solution of the equation agrees with a selfsimilar measure directly postulated as a PSD model by Martin and Taguas almost 80 years later, thus both models appear to be linked. A variant of this last model, together with detailed soil PSD data of 70 soils are used to study the information content of limited experimental data formed by triplets and its ability in the PSD reconstruction. Results indicate that the information contained in certain soil triplets is sffcient to rebuild the whole PSD: for each soil sample tested there is always at least a triplet that contains enough information to simulate the whole distribution.