Grain Shape Quantifications and Their Relationship to Dilatancy

Grain shape is a key factor affecting the mechanical properties of granular materials. However, grain shape quantification techniques to distinguish one granular material from another have not reached a stage of development for inclusion in modeling the behavior of granular materials. Part of the problem is the equipment of choice for grain shape measurement is the scanning electron microscope. This is a relatively expensive and complex device. In this paper, a practical approach using light microscopy to quantify grain shape and to identify the key shape parameters that can distinguish grains was investigated. A light microscope was found to produce grain images with sufficient quality for the purpose of observing the grain shape profile. Several grain shape parameters were determined for eight different sands — four sands chosen for this study and four sands from an outside source. Six of these - circularity, roundness, sphericity, aspect ratio, compactness and modratio — are shown to be the key shape parameters that differentiate these sand grains. Relationships between the six key grain shape parameters and dilatancy were developed to enable a better understanding of the mechanics of granular materials and for potential use in practice. Data to build the relationships were obtained using a light microscope, digital image processing software (ImageJ), and direct shear tests on four uniform sands composed of grains with shape profiles — ranging from very rounded grains in one granular conglomerate to very angular shaped grains in another.