Figure 9
A circular slice diagram shows radius R, horizontal r sub i comma j, vertical d sub i comma j, and coordinate axes X, Y, and Z.A circle is divided by a horizontal diameter. The upper half contains geometric annotations. A slanted line from the centre to the boundary is labelled R. A horizontal red line across the upper region is labelled r sub i comma j with double-headed arrows. A vertical double-headed arrow from the horizontal diameter to the red line is labelled d sub i comma j. An arrow on the right points to the boundary and is labelled Slice. In the lower-left corner, a three-axis indicator marks X, Y, and Z directions.

Vertical cross-section of a given spherical particle, where R is the particle’s radius (constant) and di,j is the distance between the particle’s centroid and slice height shi⁠, at which the planar void ratio, epi⁠, will be computed. The radius ri,j of the particles cut can be then computed for every particle within the specimen

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