Sequential sphere packing by trilateration equations

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.