title: Effects of grain size distribution on the packing fraction and shear strength of frictionless disk packings.
abstract: Using discrete element methods, the effects of the grain size distribution on the density and the shear strength of frictionless disk packings are analyzed. Specifically, two recent findings on the relationship between the system's grain size distribution and its rheology are revisited, and their validity is tested across a broader range of distributions than what has been used in previous studies. First, the effects of the distribution on the solid fraction are explored. It is found that the distribution that produces the densest packing is not the uniform distribution by volume fractions as suggested in a recent publication. In fact, the maximal packing fraction is obtained when the grading curve follows a power law with an exponent close to 0.5 as suggested by Fuller and Thompson in 1907 and 1919 [Trans Am. Soc. Civ. Eng. 59, 1 (1907) and A Treatise on Concrete, Plain and Reinforced (1919), respectively] while studying mixtures of cement and stone aggregates. Second, the effects of the distribution on the shear strength are analyzed. It is confirmed that these systems exhibit a small shear strength, even if composed of frictionless particles as has been shown recently in several works. It is also found that this shear strength is independent of the grain size distribution. This counterintuitive result has previously been shown for the uniform distribution by volume fractions. In this paper, it is shown that this observation keeps true for different shapes of the grain size distribution.
authors.affiliation: Departamento de Ingeniería Civil y Ambiental, Universidad de los Andes, Bogotá 111711, Colombia.
authors.forename: Nicolas
authors.initials: N
authors.lastname: Estrada