Applying 2D shape analysis techniques to granular materials with 3D particle geometries

It is well established that particle geometry is a key parameter influencing the response of a granular material as well as its packing density. There are many challenges associated with obtaining data for full 3D quantification of the geometry (shape) of large numbers of particles. Consequently we typically assess particle shape by considering two dimensional images of the particles. This paper proposes a technique for developing a three dimensional description of particle geometry by combining sets of two dimensional images with multiple orientations. The paper establishes a relationship between the two-dimensional measure of particle geometry circularity (as defined by ISO standard 9276-6/2006) and the three-dimensional measure sphericity as defined by Wadell. An analytical comparison between these measures is achieved by considering a set of scalene ellipsoids (with three differing principal diameters). Each ellipsoid was systematically rotated to obtain a set of 2D projections and the circularity of each projection was quantified. ne results indicate that there is a close relationship between the mean circularity and Wadell's sphericity. The results of this analysis have implications for modern image analysis based technologies that can automatically assess the shape of large numbers of particles. Data for real coarse sand size particles obtained using the QicPic apparatus (Sympatec) are reviewed in light of the findings of the analytical parametric analysis.