A New Interpretation of Three-Dimensional Particle Geometry: M-A-V-L

TL;DR

This paper introduces a new formula linking 3D particle morphology parameters, enabling a comprehensive graphical analysis of their interrelations and implications for understanding granular material behavior.

Contribution

It proposes a novel formula M = A/V×L/6 that unifies surface area, volume, size, and morphology, facilitating 4D analysis of particle geometry.

Findings

The formula M = A/V×L/6 effectively relates the four parameters.

Graphical plots demonstrate the interrelation of parameters.

The approach enhances understanding of particle shape influence on material mechanics.

Abstract

This study provides a new interpretation of 3D particle geometry that unravels the 'interrelation' of the four geometry parameters, i.e., morphology M, surface area A, volume V, and size L, for which a new formula, M = A/V$\times$L/6, is introduced to translate the 3D particle morphology as a function of surface area, volume, and size. The A/V$\times$L of a sphere is invariably 6, which is placed in the denominator of the formula, and therefore M indicates a relative morphological irregularity compared to the sphere. The minimum possible value of M is clearly one, and M may range approximately to three for coarse-grained mineral particles. Furthermore, the proposed formula, M = A/V$\times$L/6, enables to graphically preserve the four parameters' relations when plotting the geometry parameter distributions. This study demonstrates the approach with two plot spaces that represent (i) L vs. M and (ii) A/V vs. V, where A/V works as the messenger between these two spaces as A/V = M/L$\times$6. Therefore, this approach helps comprehensively address the four-dimensional aspects of the 3D particle geometry and better understand the parameters' combined influence on the mechanical behavior of granular materials. Keywords: 3D particle geometry; Morphology; Surface area; Volume; Size;