Three-dimensional sphericity, roundness and fractal dimension of sand particles

Particle morphological features at different scale levels hold the key to understanding the geological origin and mechanical behaviour of natural sands. In this context, it is necessary to characterise and quantify these morphological features by defining a series of reasonable descriptors. In this study, based on X-ray micro-computed tomographic (mu CT) images collected from a series of image-processing techniques, the authors first introduced spherical harmonic analysis to reconstruct a three-dimensional (3D) realistic surface of the sand particles. Then 3D sphericity, roundness and fractal dimension were introduced to define the global form, local features and surface textures of the particle morphology. Based on the spherical harmonic-reconstructed surface, a novel framework was established to measure the descriptors of 3D sphericity, roundness and fractal dimension of sand particles. The 3D fractal dimension was an original descriptor used to characterise the fractal nature of the surface textures of real sand particle morphology. By using the proposed methods, these morphological descriptors were measured for two types of natural sand particle. The statistical results show clear correlations between different descriptors at different characteristic scales. The correlation relies heavily upon the distance between the characteristic scales of the morphological descriptors.