Sphericity measures of sand grains

The sphericity of a grain should measure the similitude of its shape with that of a sphere. Sphericity is a shape descriptor of long-standing interest for sedimentology. Now it has gained also interest to facilitate discrete element modelling of granular materials. True sphericity was initially defined by a surface ratio that requires three-dimensional (3D) grain surface measurement. That kind of measurement has been practically impossible until recently and, as a consequence, a number of alternative 3D measures and 2D proxies were proposed. In this work we present results from a study of grain shape based on x-ray tomography of two different sand specimens, containing more than 110.000 particles altogether. Sphericity measures were systematically obtained for all grains. 2D proxy measures were also obtained in samples of oriented and not-oriented grains. It is shown that the 2D proxy best correlated with true sphericity is perimeter sphericity, whereas the traditional Krumbein-Sloss chart proxy is poorly correlated. 2D measures acquired through minor axis projection are more closely related to 3D measures than those acquired using random projections.