Micromorphological characterization and random reconstruction of 3D particles based on spherical harmonic analysis

Abstract

The microscopic characteristics of skeletal particles in rock and soil media have important effects on macroscopic mechanical properties. A mathematical procedure called spherical harmonic function analysis was here developed to characterize micromorphology of particles and determine the meso effects in a discrete manner. This method has strong mathematical properties with respect to orthogonality and rotating invariance. It was used here to characterize and reconstruct particle micromorphology in three-dimensional space. The applicability and accuracy of the method were assessed through comparison of basic geometric properties such as volume and surface area. The results show that the micromorphological characteristics of reproduced particles become more and more readily distinguishable as the reproduced order number of spherical harmonic function increases, and the error can be brought below 5% when the order number reaches 10. This level of precision is sharp enough to distinguish the characteristics of real particles. Reconstructed particles of the same size but different reconstructed orders were used to form cylindrical samples, and the stress-strain curves of these samples filled with different-order particles which have their mutual morphological features were compared using PFC3D. Results show that the higher the spherical harmonic order of reconstructed particles, the lower the initial compression modulus and the larger the strain at peak intensity. However, peak strength shows only a random relationship to spherical harmonic order. Microstructure reconstruction was here shown to be an efficient means of numerically simulating of multi-scale rock and soil media and studying the mechanical properties of soil samples.