Micromorphology characterization and reconstruction of sand particles using micro X-ray tomography and spherical harmonics

The particle micromorphology created by geological processes is an essential characteristic in determining the mechanical properties of natural sands. Based on micro X-ray computed tomography (μCT) data, we introduce a mathematical procedure using spherical harmonics to characterize and reconstruct the particle micromorphology in three dimensions. The basic geometric properties of natural sand particles, volume and surface area, and two empirical engineering indices, sphericity and angularity, are the main focus of the investigation using spherical harmonic analysis. By validating the spherical harmonic analysis against the tomography data, it is shown to be a robust technique for reproducing particle micromorphology in terms of the shape irregularity and surface texture. The precision of the method depends on the resolution of the μCT and the maximum harmonic degree used. Finally, by using principal component analysis for spherical harmonic descriptors of the scanned particles, two different kinds of sand assemblies consisting of statistically reconstructed particles with random shapes but major morphological features are successfully generated. This approach will be useful for the efficient discrete element modeling of real sands in the future.