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 × L/6, is introduced to translate the 3D particle morphology as a function of surface area, volume, and size. The A/V × 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 × 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 × 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.

这项研究为3D粒子几何学提供了新的解释，揭示了四个几何学参数（形态M，表面积A，体积V和尺寸L）的“相互关系”，为此，新公式M = A / V×引入L / 6以将3D粒子形态转换为表面积，体积和大小的函数。球的A / V×L始终为6，位于公式的分母中，因此M表示与球相比相对的形态不规则性。M的最小可能值显然为1，对于粗粒矿物颗粒，M的范围可能约为3。此外，提出的公式M = A / V×L / 6，可以在绘制几何参数分布时以图形方式保留四个参数的关系。