Traditional soil particle sphericity, roundness and surface roughness by computational geometry

Definitions of soil particle sphericity, roundness and roughness have existed since at least the 1930s. In the 1950s, charts of typical sphericity and roundness values were developed to alleviate tedious manual determination. They allowed users to classify particles by visual comparison to typical particles possessing ranges of sphericity and roundness. The original definitions and somewhat subjective chart methods are still widely used today. This paper describes robust numerical methods based on computational geometry to determine precisely the traditional values from two-dimensional images of particles. Statistical methods including locally weighted regression and K-fold cross-validation were used to discretise a mean particle surface and thereby quantify and remove roughness. The paper details the algorithms for identifying particle corners and fitting circles to them for computation of roundness. Conclusions are also drawn regarding the most appropriate definition for particle sphericity from among five that are commonly cited. Finally, recommendations are made for the minimum image resolutions and particle perimeter discretisation necessary to obtain accurate results.