Multi-scale morphological descriptors from the fractal analysis of particle contour

The increasing understanding of the connection between particle morphology and mechanical behaviour of granular materials has generated significant research on the quantitative characterisation of particle shape. This work proposes a simple and effective method, based on the fractal analysis of their contour, to characterise the morphology of soil particles over the range of experimentally accessible scales. In this paper, three new non-dimensional quantitative morphological descriptors are introduced to describe (1) overall particle shape at the macro-scale, (2) particle regularity at the meso-scale, and (3) particle texture at the micro-scale. The characteristic size separating structural features and textural features emerges directly from the results of the fractal analysis of the contour of the particle, and is a decreasing fraction of particle dimension. To explore the meaning of the descriptors, the method is applied first to a variety of Euclidean smooth and artificially roughened regular shapes and then to four natural and artificial sands with different levels of irregularity. Relationships are established between the new morphological descriptors and other quantities commonly adopted in the technical literature.