3D fractal analysis of multi-scale morphology of sand particles with μCT and interferometer

Abstract

The particle morphology of granular materials comprises different characteristic scales, including particle shape and surface texture. Different methods have been proposed to characterise the morphology using three-dimensional parameters, among which is the fractal method. These methods, however, are applied either at the scale of particle shape or surface texture. A framework unifying the multi-scale morphology obtained from different measuring instruments could advance the current understanding to this topic, but is still lacking. This paper proposes a novel methodology to characterise the morphology of sand particles across different scales based on results from two previously adopted instruments with different measuring capabilities – an X-ray micro-computed tomography (μCT) and a high-resolution optical microscope equipped with an interferometer. The methodology is applied to sand-sized particles of a crushed granitic rock and a natural quarzitic sand (Fujian sand). By using spectrum analysis on data from both μCT and interferometer measurements, a single fractal dimension is found linking the spectrum of the two measurements for the crushed granitic rock. For Fujian sand, two self-affine patterns are observed, which serves as a separation between particle shape and surface texture, and also indicates that the fractal dimension obtained at larger scale may not be simply extended to small scales. The translation of surface measurements into numerically reconstructed particle morphology at particle shape and surface texture scale is demonstrated by using spherical harmonic expansion and power spectral density functions.