Elastic properties of sands, Part 1: Micro computed tomography image analysis of grain shapes and their relationship with microstructure

Elastic properties of an unconsolidated sand are largely dependent on the elastic properties of its constituent grain and the micro-structure that defines how the grains are arranged within themselves. Coordination number, that is the average number of contacts a grain has with its neighbours, and contact surface area are the two parameters closely related to the microstructure. Moreover, grain shapes and sorting also have substantial influence on these parameters. To calculate these parameters and find any potential relationships with the shape factors, we acquire high-resolution micro computed tomography images of four mechanically compacted unconsolidated dry sand samples that are of different shape factors and sorting indices. After a comprehensive voxel-based data processing, we calculate shape factors such as sphericity and roundness of each grain in all samples. Using own algorithm, we then calculate the coordination number and contact surface area. Results show that samples of well-sorted and higher spherical and rounded grains have higher coordination number and contact surface area than the samples of poorly sorted and lower spherical and rounded grains. Among the poorly sorted samples, coordination number is largely dependent on the fraction of larger grain sizes present in the sample. Inside any given sample, grains of lower sphericity tend to have higher coordination numbers. Moreover, more spherical and rounded grains have greater contact surface area with their neighbours.