Shape analysis of sand particles based on Fourier descriptors

Particle shape greatly influences the mechanical behavior of geotechnical materials. For a specific material, for example, a sand particle, it remains an open question how to provide a comprehensive quantitative information about the particle shape. While Fourier descriptors, as a sequence of good shape descriptors, are well addressed in the literature, approaches mainly aim at pattern recognition in the field of computer vision. In this paper, Fourier descriptors are used to analyze the particle shape of geotechnical material. A total of 600 sand particles were collected from the Hutuo River, the main water resource of Shijiazhuang County, Hebei Province. Several shape descriptors, elongation, circularity, convexity, and roughness, are identified and further analyzed statistically. The Andrews plot of Fourier descriptors can be used to discriminate the sand samples. And it is convenient to use Fourier descriptors to reconstruct sand particles. A functional relationship between Fourier descriptors D(k) and k, the frequency of the kth components is proved to exist. Moreover, the relationship between shape descriptors and Fourier descriptors is investigated in a correlation analysis. The elongation has a moderate correlation with Fourier descriptors of D(1).