An entropy-like parameter of particle size distributions as packing density index in complex granular media

Abstract

Information entropy dimension (ED) has been used earlier in the characterization of the particle size distribution (PSD) in complex multi-particle granular media. In this work the ED is first proposed as an indicator of the packing density on the basis of the theoretical based interpretation of the ED in the granular media PSD context. A one-parametric exact self-similar PSD model, where the information ED is known, together with a 2-D computational random packing algorithm, are used to test the ability of the ED as an indicator of packing density. It is found that the packing density increases when the ED does. Moreover, results show a strong linear dependence between packing density and the ED. Empirical results from a large soil data base also reinforce the computational results. As ED may be estimated from field or laboratory data, the above mentioned results suggest its use as an indicator of packing density in complex granular media and material science in order to predict their properties.