Statistical interdependence of multi-scale 3D morphological descriptors of sand grains

Particle morphology at different length scales is important in understanding the mechanical behaviour of granular materials. In this sense, it is crucial to accurately describe and measure the size and shape of the grains using suitable definitions of morphological descriptors. Most of the research up until this point has analyzed particle shape in a two-dimensional framework, and sieving has typically been used to determine size. This paper describes the use of x-ray micro-computed tomography (µCT) which enables the visualization and quantification of three-dimensional particle morphology. Spherical harmonic analysis was used to reconstruct the three-dimensional (3D) realistic surface of the granular particles. 3D morphological descriptors were then introduced and computed to obtain the overall form, local features, and surface textures of the particle morphology based on the spherical harmonic reconstructed surface. To describe the fractal nature of the surfaces of natural sand particle morphology, the 3D fractal dimension was quantified using spherical harmonic-based fractal analysis. Complete volume-based distributions of particle morphological descriptors were presented and compared for four different sand samples with different grain size and shape characteristics. According to the statistical analysis, there is a clear correlation between the shape parameters at various characteristic scales, indicating that they are not independent measures. The correlation between any two parameters was observed to rely on the distance between the characteristic scales of the morphological parameters.