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Sequential sphere packing by trilateration equations

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Abstract

Specimen generation by packing of particles is the initial step in most numerical simulations for discrete media. In many cases, especially for virtual soil compaction, filtration, or penetration tests, this preparation work is essential for the success of the tests because the discrete particles are not able to be redistributed during the simulation. This paper presents a novel sphere sequential packing method for specimen generation using the trilateration method and its relevant equations. The method is developed on an assumption that spherical particles must be in contact with at least three neighbour particles to be kept in balance. This semi-analytical method has three advantages: quick generation speed, adjustable porosity, and good control over the spatial distribution of particles at local scale. This paper is a study on two typical spatial distributions: (1) layer-wise, where particles with similar sizes have priority of being positioned next to each other; and (2) discrete, where small particles are located preferentially in between large particles.

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Acknowledgments

The first author was granted a scholarship from the Vietnamese Ministry of Education and Training (MOET). The support from Australian Research Council (ARC) through the Discovery Grant (DP120102188) Hydraulic erosion of granular structures: experiments and computational simulations is gratefully acknowledged. The simulations were based on Mechsys, an open source library and carried out using the Macondo Cluster from the School of Civil Engineering at The University of Queensland.

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Authors and Affiliations

  1. College of Science and Engineering, James Cook University, Townsville, QLD4811, Australia

    Huu Duc To

  2. Research Group on Complex Processes in Geo-Systems, Geotechnical Engineering Centre, School of Civil Engineering, The University of Queensland, Brisbane, Australia

    Sergio Andres Galindo-Torres & Alexander Scheuermann

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  1. Huu Duc To
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  2. Sergio Andres Galindo-Torres
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  3. Alexander Scheuermann
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Correspondence to Huu Duc To.

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To, H.D., Galindo-Torres, S.A. & Scheuermann, A. Sequential sphere packing by trilateration equations. Granular Matter 18, 70 (2016). https://doi.org/10.1007/s10035-016-0666-5

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