People of a race appear different but share a 'phenotypic trait' due to a
common genetic origin. Mineral particles are like humans: they appear different
despite having a same geological origin. Then, do the particles have some sort
of 'phenotypic trait' in the geometries as we do? How can we characterize the
phenotypic trait of particle geometries? This paper discusses a new perspective
on how the phenotypic trait can be discovered in the particle geometries and
how the 'variation' and 'average' of the geometry can be quantified. The key
idea is using the power-law between particle surface-area-to-volume ratio
($A/V$) and the particle volume ($V$) that uncovers the phenotypic trait in
terms of ${\alpha}$ and ${\beta}^*$: From the log-transformed relation of $V =
(A/V)^{\alpha} {\times} {\beta}^*$, the power value ${\alpha}$ represents the
relation between shape and size, while the term ${\beta}^*$ (evaluated by
fixing ${\alpha}$ = -3) informs the angularity of the average shape in the
granular material. In other words, ${\alpha}$ represents the 'variation' of the
geometry while ${\beta}^*$ is concerned with the 'average' geometry of a
granular material. Furthermore, this study finds that $A/V$ and $V$ can be also
used to characterize individual particle shape in terms of Wadell's true
Sphericity ($S$). This paper also revisits the $M = A/V {\times} L/6$ concept
originally introduced by Su et al. (2020) and finds the shape index $M$ is an
extended form of $S$ providing additional information about the particle
elongation. Therefore, the proposed method using $A/V$ and $V$ provides a
unified approach that can characterize the particle geometry at multiple scales
from granular material to a single particle.
Ref.: Su, Y.F., Bhattacharya, S., Lee, S.J., Lee, C.H., Shin, M.: A new
interpretation of three-dimensional particle geometry: M-A-V-L. Transp.
Geotech. 23, 100328 (2020).
