A geometric separation method for non-uniform disk packing with prescribed filling ratio and size distribution


This paper proposes an approach to obtain a set of particles with a prescribed filling ratio and size distribution, using only geometric procedures. An essential step in the analysis of discontinuous media using the discrete element method is to obtain an initial set of particles that represents the granular model. Various particle packing approaches are currently employed to achieve a numerical model similar to a real discrete medium. In this context, this paper proposes an alternative particle packing method using the geometric separation procedure. This strategy aims to generate granular models that present particles with desired sizes, without overlapping and that fill a prescribed area of the domain. The method consists of five macro-steps: (a) definition of the initial set of particles; (b) geometric separation; (c) particle reallocation; (d) particle removing, and (e) particle inserting. This work focus on the bi-dimensional approach, where disks represent the particles. An initial set of particles is generated using input data related to the size distribution and filling rate, obtaining random positions for them. The other steps are used to eliminate overlaps between the particles. The packing algorithm provides good performance and approximation to the input parameters filling ration and grain size distribution. Granular models generated from real soil data are presented for validation of the proposed strategy, and practical examples from the literature are reproduced to illustrate its applicability.

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The authors thank FAPEAL for their support and funding in research, and PETROBRAS for the development of projects that have resulted in this work.


This study was funded by Fundacão de Amparo a Pesquisa do Estado de Alagoas (FAPEAL).

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Correspondence to Lucas G. O. Lopes.

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Lopes, L.G.O., Cintra, D.T. & Lira, W.W.M. A geometric separation method for non-uniform disk packing with prescribed filling ratio and size distribution. Comp. Part. Mech. 8, 169–182 (2021). https://doi.org/10.1007/s40571-020-00320-x

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  • Particle packing
  • Granular modeling
  • Soil modeling
  • Discrete element method
  • Geometric packing methods