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Using a discrete element method, we investigate the phenomenon of geometric cohesion in granular systems composed of star-shaped particles with 3 to 13 arms. This was done by analyzing the stability of columns built with these particles and by studying the microstructure of these columns in terms of density and connectivity. We find that systems composed of star-shaped particles can exhibit geometric cohesion (i.e., a solidlike behavior, in the absence of adhesive forces between the grains), depending on the shape of the particles and the friction between them. This phenomenon is observed up to a given critical size of the system, from which a transition to a metastable behavior takes place. We also have evidence that geometric cohesion is closely linked to the systems' connectivity and especially to the capability of forming interlocked interactions (i.e., multicontact interactions that hinder the relative rotation of the grains). Our results contribute to the understanding of the interesting and potentially useful phenomenon of geometric cohesion. In addition, our work supplements an important set of experimental observations and sheds light on the complex behavior of real, three-dimensional, granular systems.

Granular materials are used in several fields and in a wide variety of processes. An important feature of these materials is the diversity of grain sizes, commonly referred to as polydispersity. When granular materials are sheared, they exhibit a predominant small elastic range. Then, the material yields, with or without a peak shear strength depending on the initial density. Finally, the material reaches a stationary state, in which it deforms at a constant shear stress, which can be linked to the residual friction angle ϕ_{r}. However, the role of polydispersity on the shear strength of granular materials is still a matter of debate. In particular, a series of investigations have proved, using numerical simulations, that ϕ_{r} is independent of polydispersity. This counterintuitive observation remains elusive to experimentalists, and especially for some technical communities that use ϕ_{r} as a design parameter (e.g., the soil mechanics community). In this Letter, we studied experimentally the effects of polydispersity on ϕ_{r}. In order to do so, we built samples of ceramic beads and then sheared these samples in a triaxial apparatus. We varied polydispersity, building monodisperse, bidisperse, and polydisperse granular samples; this allowed us to study the effects of grain size, size span, and grain size distribution on ϕ_{r}. We find that ϕ_{r} is indeed independent of polydispersity, confirming the previous findings achieved through numerical simulations. Our work fairly closes the gap of knowledge between experiments and simulations.

By means of discrete-element methods, we investigate the joint effects of the grain size distribution (GSD) and contact friction on the structure of three-dimensional samples composed of spherical grains. Specifically, we compress these systems isotropically until jamming and then analyze their structure in terms of density, connectivity, coefficients of uniformity and curvature, and parameters of grading entropy. Our study focuses on power-law GSDs and particularly on the Fuller and Thompson distribution, proposed over a century ago. First, we show that, among the set of GSDs investigated, this particular distribution produces the densest and best-connected systems, falsifying a conjecture recently posed in the literature. Second, we find that the jamming packing fraction can be accurately predicted as a function of simple descriptors of the GSD, but among these descriptors the granular entropy concept proves to be the most useful. This allows for an alternative interpretation of both jamming and grading entropy concepts. Finally, we compare the Fuller and Thompson distribution with two well-known GSDs: that of the Apollonian sphere packing and that towards which granular systems evolve after intensive grain fracturing. Surprisingly, we find that these three GSDs are practically coincident in the limit of large size spans, despite having been introduced or discovered in different scientific contexts (i.e., engineering, mathematics, and earth sciences, respectively).

We present a systematic numerical investigation concerning the combined effects of sliding friction and particle shape (i.e., angularity) parameters on the shear strength and microstructure of granular packings. Sliding friction at contacts varied from 0 (frictionless particles) to 0.7, and the particles were irregular polygons with an increasing number of sides, ranging from triangles to disks. We find that the effect of local friction on shear strength follows the same trend for all shapes. Strength first increases with local friction and then saturates at a shape-dependent value. In contrast, the effect of angularity varies, depending on the level of sliding friction. For low friction values (i.e., under 0.3), the strength first increases with angularity and then declines for the most angular shapes. For high friction values, strength systematically increases with angularity. At the microscale, we focus on the connectivity and texture of the contact and force networks. In general terms, increasing local friction causes these networks to be less connected and more anisotropic. In contrast, increasing particle angularity may change the network topology in different directions, directly affecting the macroscopic shear strength. These analyses and data constitute a first step toward understanding the joint effect of local variables such as friction and grain shape on the macroscopic rheology of granular systems.

The column collapse experiment is a simplified version of the complex granular flows observed in both natural and industrial contexts. Due to its simple setup and rich behavior, the column collapse has been studied experimentally and numerically by several authors. The purpose of the analyses presented in this paper is to verify whether some of the results presented in these publications are affected by grain-size effects. In order to do so, we simulate two-dimensional granular columns by means of a discrete-element method, i.e., contact dynamics. Specifically, we study the influence of the grain size, as compared to the system size, on the resultant deposit geometry and collapse duration. We show that (i) some of the previously published results may be affected by grain-size effects, (ii) in order to avoid these effects, the system-size to grain-size ratio must be larger than 75 for short columns and larger than 50 for tall columns, and (iii) the quantities that are the most affected by grain-size effects are the column mobility and the collapse duration. Our findings serve as a tool for comparing results obtained by different researchers and draw guidelines on the number of grains that must be used in order to avoid grain-size effects.

This article presents a numerical study of the effects of grain size distribution (GSD) on the microstructure of two-dimensional packings of frictionless disks. The GSD is described by a power law with two parameters controlling the size span and the shape of the distribution. First, several samples are built for each combination of these parameters. Then, by means of contact dynamics simulations, the samples are densified in oedometric conditions and sheared in a simple shear configuration. The microstructure is analyzed in terms of packing fraction, local ordering, connectivity, and force transmission properties. It is shown that the microstructure is notoriously affected by both the size span and the shape of the GSD. These findings confirm recent observations regarding the size span of the GSD and extend previous works by describing the effects of the GSD shape. Specifically, we find that if the GSD shape is varied by increasing the proportion of small grains by a certain amount, it is possible to increase the packing fraction, increase coordination, and decrease the proportion of floating particles. Thus, by carefully controlling the GSD shape, it is possible to obtain systems that are denser and better connected, probably increasing the system's robustness and optimizing important strength properties such as stiffness, cohesion, and fragmentation susceptibility.

By means of extensive contact dynamics simulations, we analyzed the effect of particle size distribution (PSD) on the strength and microstructure of sheared granular materials composed of frictional disks. The PSDs are built by means of a normalized β function, which allows the systematic investigation of the effects of both, the size span (from almost monodisperse to highly polydisperse) and the shape of the PSD (from linear to pronouncedly curved). We show that the shear strength is independent of the size span, which substantiates previous results obtained for uniform distributions by packing fraction. Notably, the shear strength is also independent of the shape of the PSD, as shown previously for systems composed of frictionless disks. In contrast, the packing fraction increases with the size span, but decreases with more pronounced PSD curvature. At the microscale, we analyzed the connectivity and anisotropies of the contacts and forces networks. We show that the invariance of the shear strength with the PSD is due to a compensation mechanism which involves both geometrical sources of anisotropy. In particular, contact orientation anisotropy decreases with the size span and increases with PSD curvature, while the branch length anisotropy behaves inversely.

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.