Random generation of natural sand assembly using micro X-ray tomography and spherical harmonics

Particle morphology is an essential characteristic in determining the mechanical properties of natural sands. Based on micro x-ray computed tomography data, this paper introduces a mathematical approach using spherical harmonics (SHs) to characterise and reconstruct particle morphology in three dimensions. The basic geometric properties of natural sand particles (volume and surface area) and two empirical engineering indices (sphericity and convexity) are the main focus of the investigation on validating the efficiency of SH analysis. This approach is shown to be a robust technique for reproducing particle morphology in terms of shape irregularity and surface texture when the maximum harmonic degree is greater than ten. By using principal component analysis for the obtained SH descriptors of the scanned particles, a virtual sand assembly, consisting of statistically reconstructed particles with random shapes but major morphological features, is successfully generated. This approach can be used in efficient discrete element modelling to further study the micromechanics of natural sands.