A Novel Multi-Scale Particle Morphology Descriptor with the Application of SPHERICAL Harmonics

Particle morphology is of great significance to the grain- and macro-scale behaviors of granular soils. Most existing traditional morphology descriptors have three perennial limitations, i.e., dissensus of definition, inter-scale effect, and surface roughness heterogeneity, which limit the accurate representation of particle morphology. The inter-scale effect refers to the inaccurate representation of the morphological features at the target relative length scale (RLS, i.e., length scale with respective to particle size) caused by the inclusion of additional morphological details existing at other RLS. To effectively eliminate the inter-scale effect and reflect surface roughness heterogeneity, a novel spherical harmonic-based multi-scale morphology descriptor R(inc) is proposed to depict the incremental morphology variation (IMV) at different RLS. The following conclusions were drawn: (1) the IMV at each RLS decreases with decreasing RLS while the corresponding particle surface is, in general, getting rougher; (2) artificial neural network (ANN)-based mean impact values (MIVs) of R(inc) at different RLS are calculated and the results prove the effective elimination of inter-scale effects by using R(inc); (3) R(inc) shows a positive correlation with the rate of increase of surface area R(SA) at all RLS; (4) R(inc) can be utilized to quantify the irregularity and roughness; (5) the surface morphology of a given particle shows different morphology variation in different sections, as well as different variation trends at different RLS. With the capability of eliminating the existing limitations of traditional morphology descriptors, the novel multi-scale descriptor proposed in this paper is very suitable for acting as a morphological gene to represent the multi-scale feature of particle morphology.