Sphericity measures of sand grains

Abstract

The sphericity of a grain should measure the similitude of its shape with that of a sphere. Sphericity as shape descriptor is of traditional interest for sedimentology. Now it has gained also interest to facilitate discrete element modelling of granular materials. True sphericity was initially defined by a surface ratio that requires three-dimensional (3D) grain surface measurement. That kind of measurement has been practically impossible until recently and, as a consequence, a number of alternative 3D measures and 2D proxies were proposed. In this work we present results from a study of grain shape based on x-ray tomography of two different sand specimens, containing more than 110.000 particles altogether. Sphericity measures were systematically obtained for all grains. 2D proxy measures were also obtained in samples of oriented and not-oriented grains. It is shown that the 2D proxy best correlated with true sphericity is perimeter sphericity, whereas the traditional Krumbein-Sloss chart proxy is poorly correlated. 2D measures acquired through minor axis projection are more closely related to 3D measures than those acquired using random projections.

Circulating fluidized bed reactors – part 01: analyzing the effect of particle modelling parameters in computational particle fluid dynamic (CPFD) simulation with experimental validation

“…The Richardson-Davidson-Harrison drag model is not a function of both parameters at high Reynolds number where the particle volume fraction is excluded in the full range of Re, which can be the reason for the large deviation. The particle sphericity was taken as 0.9 for models with sphericity as a parameter (Rorato et al 2019); Nonspherical-Ganser and Nonspherical-Haider-Levenspiel. Both of the models are a function of Re in the full range of Re, which is not the case for Wen-Yu model as the drag turns into a constant at high Re.…”

Comparison of 2D Optical Imaging and 3D Microtomography Shape Measurements of a Coastal Bioclastic Calcareous Sand

“…This would explain how Cx 2D and S 2D can be correlated ( Figure 8 c), but Cx 2D does not show the same variation in size that S 2D does ( Figure 5 b,c). The Correlation of sphericity with convexity in 2D DIA methods have also been shown by [ 22 ] and [ 24 ] for both siliceous and calcareous sands.…”

“…The complex shape of the grains in these calcareous sands contributes to their poor geotechnical behavior [ 16 , 17 , 18 , 19 , 20 ], such as pile running [ 21 ]. Although a few studies have examined the impact of 2D and 3D imaging techniques on the measurements of sand grains [ 22 , 23 , 24 ], there have been no direct comparisons of 2D DIA methods to 3D μCT of bulk samples. This paper investigates the impact of 2D DIA and 3D μCT imaging methods on the measured shape parameters, aspect ratio, convexity, and sphericity, of calcareous beach sand.…”

Proceedings of the 18th UK Travelling Workshop: GeoMechanics: from Micro to Macro (GM3), Dundee, 2021

“…For this reason, particle geometry is herein characterized using a 2D proxy measure of sphericity, the perimeter sphericity 𝑆 𝑝 ; defined as the ratio between the perimeter of the circle with area equivalent to the projected by the particle within the image, assuming the grain image is taken on the plane of maximum particle stability. Following (Rorato et al, 2019), these two descriptors are characterized by a linear relationship (1) , which appears to be constant for different sands. 𝜓 = 1.075(𝑆 𝑝 ) − 0.067…”