Computational Geometric and Discrete Fourier Series Approaches for Particle Shape Analysis

Granular materials in nature possess a wide range of morphologies, varying from very round to highly irregular shapes. It has been reported that the morphological characteristics play a crucial role in the interlockings or arrangements of the particles, which affect the mechanical behaviour of granular material during compaction, consolidation and conventional monotonic, cyclic loadings, etc. Therefore, knowing the quantitative parameterisation of a particle’s morphological properties is very important for the macro- and micro-investigations of granular materials, especially for the discrete element methods (DEM). However, it is challenging to quantify the morphological properties for highly angular particles by traditional methods such as visual inspection, etc. This study adopted a numerical method to analyze the parameterisation of morphological properties by using computational geometric and discrete Fourier series (FS) approaches. Using a 2-dimensional SEM image with a high density of the boundary points, a complex particle shape was reconstructed. The re-produced points are used for corner detection and computationally measuring some particle shape descriptors. From the results, for complex particles, the FS degree is recommended should be higher than 15 for good results. Besides, the roles of some shape descriptors in geomechanics are discussed to provide some remarkable points for readers on the influences of particle properties on the behaviour of granular materials.