3-D shape descriptors for geomaterial aggregates using multiple projective representations

The dependence of liquefaction susceptibility and shear behavior of sands and gravels on particle shape and angularity has been well documented in the literature. However, quantification of particle morphology and its direct influence on liquefaction susceptibility and shear behavior has been hindered by the absence of quantitative models for particle shape, as well as the difficulty in modeling angular particle assemblies. In this paper, a method for quantitative identification of particle morphology is described using three-dimensional numerical shape descriptors. Representative particles from six different types of sands and glass beads are scanned using a digital image analyzer. The sands vary in angularity, from subrounded to highly angular, and consist of both natural and industrial sands as well as glass beads. This paper describes the design and development of automated image processing algorithms that can estimate 3-D shape-descriptors for particle aggregates using a statistical combination of 2-D shape-descriptors from multiple 2-D projections. In particular, Fourier descriptors and invariant moments are employed for representing the shapes of the 2-D projections. The consistency, separability and uniqueness of the newly developed 3-D shape-descriptor algorithm are demonstrated by exercising the method on the different particle mixes. This method will eventually be used in a Discrete Element Method (DEM) program to simulate the shear behavior and liquefaction performance of angular soils.