Angle of repose revisited: When is a heap a cone?

The angle of repose is a frequently reported value in bulk solids characterisation and its popularity is based on the simple measurement setup. It can be useful to estimate the flowability of a bulk material or to estimate the inner friction coeffcient for cohesionless solids. The latter relies on Coulomb material theory, which yields that a bulk solid heap resembles a perfect cone. The aim of this study was to investigate if the cone assumption is valid for three distinct bulk materials. In order to address this question, the angle of repose was measured for each sample and the resulting ideal cone model compared with a respective 3D-scanned surface model of the physical heap. Differences were mapped onto a two-dimensional representation of the ideal cone's lateral surface. The heaps of two of the three investigated bulk solids showed considerable differences with regard to the cone assumption. Discrepancies can be divided into local and global shape deviations. The results show that measuring and reporting the angle of repose should be undertaken with care. Many publications list angle of repose values without reporting the measurement setup or the shape of the heap. However, the latter can vary significantly from Coulomb theory.