Densest arrangement of frictionless polydisperse sphere packings with a power-law grain size distribution
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ORIGINAL PAPER
Densest arrangement of frictionless polydisperse sphere packings with a power‑law grain size distribution William Fernando Oquendo‑Patiño1,2 · Nicolas Estrada3 Received: 20 December 2019 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this work we use DEM simulations to find the densest packing of frictionless spheres subject to mechanical compression by changing systematically the grain size distribution (GSD). This is done by modeling the GSD as a power law and varying the GSD describing parameters: the size span and the distribution shape, while relating these parameters to the density and other micro-structural parameters. For large size spans, the optimal GSD resembles the century old Fuller-Thomson distribution that is commonly used in the field of cements and pavements. This optimal power-law GSD produces not only the densest packing but also presents good connectivity, measured from a small proportion of floating particles, and reduces the packing internal spatial correlations, measured by the pair correlation function. Thus, tuning the GSD appropriately allows for designing mechanically stable packings that have the highest density, a small number of floating particles, and less local correlations. Keywords Granular materials · DEM · Packing · Density · Polydispersity · Grain size distribution
1 Introduction Granular media are materials composed of interacting bodies with many types of possible microscopic parameters that impact the global response of the system under given external conditions. In particular, polydispersity, which characterizes the differences in size for the constituent grains and can be described by the cumulative fractional volume or grain size distribution (GSD), has been shown to strongly influence the packing properties of the system. In this work, the GSD is modeled as a truncated power law that can be characterized by its shape (exponent, 𝜂 ) and
* William Fernando Oquendo‑Patiño [email protected]; [email protected] Nicolas Estrada [email protected] 1
Faculty of Engineering, Universidad de la Sabana, Chía, Colombia
2
Department of Physics, National University of Colombia, Bogotá, Colombia
3
Department of Civil and Environmental Engineering, Universidad de los Andes, Bogotá, Colombia
its size span (ratio of the largest to the smallest particle size, 𝜆 ), and is defined as
𝜌=
�
d − dmin dmax − dmin
�𝜂
𝜂
⎛ d − 1⎞ d ⎟ , = ⎜ min ⎜ 𝜆−1 ⎟ ⎝ ⎠
(1)
where dmin ( dmax ) is the minimum (maximum) diameter in the sample, and 𝜌 is the fraction of volume occupied by particles of diameter smaller than d. This distribution arises as a result of the previous works of Fuller, Thompson, and Talbot [1–3] (experimental) and those by Furnas [4, 5] (theoretical) between 1907 and 1931. Some theoretical and numerical examples of this distribution are shown in Fig. 1. One common and important question is if there is an optimal GSD that generates the best packing measured in terms of variables such as the pack
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