Three-dimensional Wadell roundness for particle angularity characterization of granular soils

The geologist Hakon Wadell proposed the roundness definition in the 1930s for quantifying the particle angularity of granular soils. Due to the difficulty in obtaining three-dimensional (3D) particle geometries in the 1930s, Wadell used two-dimensional (2D) projections of particles to develop his roundness definition, although it is limited for analyzing 3D particles. This study shows that Wadell’s 2D roundness could be extended to a 3D definition. The 3D roundness is defined as the ratio of the average radius of spheres fitting to corners and ridges of a 3D particle to the radius of the maximum inscribed sphere of the 3D particle. A computational geometry algorithm is proposed to automatically identify corners and ridges, fit appropriate spheres to corners and ridges, identify the maximum inscribed sphere of the 3D particle, and compute 3D roundness. The number of slices per diameter of the maximum inscribed sphere of the particle, NSD, is defined for controlling the sphere fitting process. The minimum required NSD = 300 is established to ensure the reliable use of the proposed 3D computational geometry algorithm. Finally, a total of 20,000 particles from five sand specimens with various angularities are scanned by X-ray computed tomography. The 2D and 3D roundnesses of these 20,000 particles are compared. The 2D roundnesses capture the general trend of the corresponding 3D roundnesses, but vary in a large range, resulting in significant uncertainties when using 2D images to infer 3D particle angularities.