Effect of sediment form and form distribution on porosity: a simulation study based on the discrete element method

Abstract

Porosity is one of the key properties of dense particle packings like sediment deposits and is influenced by a multitude of grain characteristics such as their size distribution and shape. In the present work, we focus on the form, a specific aspect of the overall shape, of sedimentary grains in order to investigate and quantify its effect on porosity, ultimately deriving novel porosity-prediction models. To this end, we develop a robust and accurate simulation tool based on the discrete element method which we validate against laboratory experiments. Utilizing digital representations of actual sediment from the Rhine river, we first study packings that are composed of particles with a single form. There, porosity is found to be mainly determined by the inverse equancy, i.e., the ratio of the longest to the smallest form-defining axis. Only for small ratios, additional shape-related properties become relevant, as revealed by a direct comparison to packings of form-equivalent but smooth ellipsoids. Since sediment naturally features form mixtures, we extend our simulation tool to study sediment packings with normally-distributed forms. In agreement with our single form studies, porosity is found to depend primarily on the inverse of the mean equancy. By supplying additional information about a second form factor and the standard deviations, we derive an accurate model for porosity prediction. Due to its simplicity, it can be readily applied to sediment packings for which some measurements of flatness and elongation, the two most common form factors, are available. Graphical abstract

On the use of packing models for the prediction of fluvial sediment porosity

“…Here, this resulted in n 0,i = 0.338±0.002 for all size 235 classes i. This value is slightly less than the typically used value of 0.36 for random sphere packings, which can be attributed to the non-spherical sediment shape (Rettinger et al, 2022b).…”

“…Generally, if form information like the average elongation or flatness is available, the porosity predictions for dense uniform packings derived by Rettinger et al (2022b) could be used to determine n 0,i where the effect of form is explicitly taken into account. Since porosity also strongly depends on the packing conditions, available relations for minimal and maximal porosity of dense and loose packings, respectively, can be used to define a valid range of initial porosity values.…”

“…For this study, we made use of the numerical method, the simulation setup and the evaluation approach that had been validated extensively in a similar recent study by Rettinger et al (2022b) and were contained in the WALBERLA simulation framework (Bauer et al, 2021). Here, for brevity, we just summarize the key aspects and specifics of the simulation setup and refer to the original work for an in-depth discussion of all parts.…”

“…For each grain, the size was chosen from the complete interval of the sieve mesh size corresponding to the respective size class, assuming a uniform distribution within this interval. Following the previous findings (Rettinger et al, 2022b), we also assumed that the shape of all particles is similar and independent of the actual size, such that there are no shape-differences between size classes. Thus, each particle shape was randomly sampled from a set of meshes (Rettinger et al, 2022c), obtained by computer tomography (CT) scans of actual gravel-sized sediment from the Rhine River in Germany with an average flatness of 0.647 and average elongation of 0.682.…”

“…Additionally, size-dependent effects like cohesive interactions become relevant once small particles like fine sand and silt are involved which again influence the packing (Yu et al, 2003;Zou et al, 2011). Furthermore, the average grain shape varies from river to river (Oakey et al, 2005;Liang et al, 2015;Rettinger et al, 2022b), in contrast to the usually rather similar and often simpler shapes encountered in industrial applications. The shape is known to strongly influence the interaction among grains which must be accounted for in the model (Yu et al, 1996).…”