Table 2 Definition and schematic diagram of particle aspect ratio and roundness.

From: Study on the geometry characteristics of soil primary mineral particles under cryogenic action

Particle geometry characteristics

Definition

Formula

Schematic diagram

Physical meaning

Aspect ratio

The ratio of the longest diameter passing through the interior of the particle to the shortest diameter perpendicular to the long diameter

\(\begin{array}{c}\theta =\frac{L}{B}\end{array}\) (1)

Fig. 2a

The aspect ratio can represent the elongation properties of the particles. The closer the value of the aspect ratio is to 1, the closer the particle is to a square or a circle. The larger the value of the aspect ratio, the more elongated the particle is

Roundness

The ratio of the perimeter of the equivalent area circle of the particle projection to the perimeter of the particle projected contour

\(\mathrm{\varnothing }=\frac{l}{P}\) (2)26

Fig. 2b

Generally, the smaller the value, the longer the projected particle contour and the more the particle shape deviates from the circle

  1. (θ: aspect ratio; \(L\): longest diameter inside the particle; B: shortest diameter perpendicular to the longest diameter; \(\varnothing\): roundness; A: projected area of particles (\(A=\pi {r}^{2}\) (3)); l: perimeter of the equivalent area circle of the particle projection (\(l=2\pi r\) (4)); r: equivalent circle radius of particles; P: perimeter of the particle projected contour; Substitute formula (3) and (4) into formula (2) to obtain the roundness formula: \(\mathrm{\varnothing }=\frac{2\sqrt{\pi A}}{P}\)).
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