Packing Densities of Mixtures of Spheres with Log-normal Size Distributions

Abstract

SEVERAL common granular materials have a spread of particle sizes which is well described by a log-normal distribution function, that is, the weights of the particle sizes present are distributed normally with respect to the logarithms of the respective particle diameters. This distribution has been justified theoretically by Griffith¹ in the case of a comminuted system in which all of the particles have an equal chance of being broken. Soils produced largely by glaciation in the higher latitudes on Earth provide excellent examples of granular systems which approximately obey the log-normal function. It has also been found that this distribution is applicable to the next higher level of organization in field soils, the aggregates of particles which are known as clods or crumbs, although the mechanism of formation is less well understood in this case².