Internal rolling method for particle shape evaluation and reconstruction

A concise and robust method for 2D particle shape evaluation and reconstruction is proposed using the concept of the internal rolling of covering discs within the outline of a particle. By downscaling the covering disc size for capturing multiscale features, the calculation of the Euclidean distance can effectively yield three indices for sphericity, roundness and roughness. The geometric-based evaluations of particle morphology are dimensionless and precisely distinguishable between shapes after calibration and validation against constructed particles and natural sands. A sphericity-roundness diagram is provided to visualize the particle shape characterization, and a probabilistic density surface in the sphericity-roundness diagram is then proposed to statistically represent the distributions of the particle shapes. The concept of internal rolling is also utilized for particle shape reconstruction using a limited number of balls to replicate the indices of sphericity, roundness and roundness characteristic curve. The probabilistic density surface is duplicated for statistical particle shape reconstruction, which provides an effective approach for numerical investigations of the relationships between particle shapes and mechanical behavior. The effect of image quality on 2D shape evaluation is also examined by using a minimum area per particle, and the proposed method is intuitively extendable to 3D measurements using rolling covering spheres.