Specific volume of the most probable disordered sphere packings

Civil Engineering Department, National University of Saint Agustine of Arequipa, Peru

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Published online: 1 December 2025

Abstract

Most granular materials are made of randomly distributed grains. Theoretical and experimental studies, carried on by several authors, have shown that minimum and maximum specific densities of random packings vary primarily according to the type of strain, such as vertical compression and horizontal shear. In this regard, there are two approaches; the statistical geometry of packings, and the statistical mechanics. The fundamental objective of these theories is to settle down the limiting values, called RLP and RCP. […]However, in the mechanics of granular materials, intermediate values are also important. For this reason, in this paper, a model for packings is proposed, based on elementary probability. The angles of a parallelepiped formed by eight spheres of equal size are taken as random variables, and the probability density function is assumed to be uniform. Specific volume of three-dimensional packings subject to two or three dimensional strain are calculated using conditional and joint probabilities, respectively.