VGeST - Virtual Geoscience Simulation Tools

Ellipsoid and sand grain packing

This research was undertaken by Dr. Xavier Garcia during his PhD studies while at Imperial College under the supervision of Dr. J-P Latham.

The development of a fast clustered overlapping sphere algorithm to represent real particles in discrete element modelling (Garcia et al. 2009a) provided the means to study the influence of shape on 3D grain packing, using DEM. Both ellipsoids and natural rounded grain shapes selected from the VGeST shape library were studied. Care was taken to introduce realistic dynamics into the grain accumulation process, shown in the figure below while porosity was determined using a point sampling method that achieves accuracies in porosity values greater than 0.25%.

In this construction of the granular packs, a small number of randomly oriented grains are dropped in batches (light colours), one batch at a time, to simulate a low settling rate. Three stages during the construction are shown after settling 1000, 2000 and 3000 grains.

As a consequence new research using dynamic ballistic deposition simulations of the packing of prolate ellipsoids, including spheres, a great many contradictory results for pack porosities reported in the literature covering experimental and numerical simulation can now be explained, as shown in the graph below. The conditions favouring packs of lower porosity than 36.7%, the widely reported value for dense random sphere packs, are well described in the plot that shows how friction effects compete with aspect ratio or sphericity. For low friction (μ) our results show that the porosity of slightly elongated particles is smaller than in sphere packs. Numerical algorithms of a geometrical nature have also been devised that will rearrange different particles into packs denser than for spheres, however without mechanical realism in the simulation there has always remained some doubt whether grain packs in nature can find these algorithmically created space-filling configurations with any natural sedimenting or packing processes. For high friction the spheres pack more densely than the rest of the particles considered, in agreement with simulations employing algorithms that constrain the dynamics or non-dynamic methods that invoke “frozen” status for all previously settled grains in a continuous packing process.

The porosity of ellipsoid packs are shown as a function of aspect ratio and sphericity for various friction coefficients determined by DEM simulations and compared with non-dynamic simulations.

The porosity minimum is better developed here for low friction coefficients, whereas in the 2D FEMDEM simulations of ellipse packing, the better developed porosity minimum occurred when the friction coefficient was 0.5 compared to the zero friction case. These 3D DEM and 2D FEMDEM methods are very different and neither are creating perfect ellipses or ellipsoids. There therefore remain some contradictory trends that need further investigation.

Cluster representations of aspherical grains that were used in DEM simulations of realistic rounded sand grains are shown above, the left is an elongated grain with aspect ratio α = 2.09, and sphericity Ψ= 0.90, the right has low aspect ratio grain α = 1.30, Ψ = 0.92.

Non-symmetrical rounded natural grain shapes selected from the shape library were also investigated (using the above representations) to see if packs denser than for spheres could be obtained with particles with reduced rotational freedom compared with ellipsoids, but with the same packing conditions.

Above are two examples of packs of non-symmetrical grains identically constructed by DEM with friction coefficient μ = 0.2. Both these non-symmetrical particles packed at lower porosity than that achieved for sphere packs constructed under the same conditions with μ = 0.2. Left: Porosity = 35.4%, Elongated grain α = 2.09, Ψ= 0.9, Right: Porosity = 34.9%, low aspect ratio grain α = 1.3, Ψ = 0.92.

These simulations demonstrate the ability to isolate particle Form as distinct from roundness and angularity in a manner rare if not impossible for experiments on natural sediments. Discussion as to whether porosity can be captured by just one function of Form, such as sphericity or aspect ratio, and a measure of friction is included in Garcia’s (2009) PhD thesis.The details of the DEM packing simulation and clustering algorithm are given in the paper entitled numerical study of the effects of particle shape and polydispersity on permeability, (Garcia et al. 2009b) where the purpose of the simulations is to create a grain pack skeleton for fluid flow and permeability modelling.

References

Garcia, X., Latham, J.-P., Xiang, J., Harrison., J. 2009a. A clustered overlapping sphere algorithm to represent real particles in discrete element modelling, Geotechnique, 59, No. 9, 779-784 doi:10.1680/geot.8.T.037

Garcia, X., Lateef, A., Blunt, M., Matthai, S., Latham J.-P., 2009b. Numerical study of the effects of particle shape and polydispersity on permeability, Physics Review E, Vol 80, doi/10.1103/PhysRevE.80.021304