Discrete simulation of dense flows of polyhedral grains down a rough inclined plane

The effect of grain shape and material on the nonlocal rheology of dense granular flows

Nonlocal rheologies allow for the modeling of granular flows from the creeping to intermediate flow regimes, using a small number of parameters. In this paper, we report on experiments testing how particle properties affect the model parameters used in the Kamrin & Koval cooperative nonlocal model, using particles of three different shapes (circles, ellipses, and pentagons) and three different materials, including one which allows for the measurement of stresses via photoelasticity. Our experiments are performed on a quasi-2D annular shear cell with a rotating inner wall and a fixed outer wall. Each type of particle is found to exhibit flows which are well-fit by nonlocal rheology, with each particle having a distinct triad of the local, nonlocal, and frictional parameters. While the local parameter b is always approximately unity, the nonlocal parameter A depends sensitively on both the particle shape and material. The critical stress ratio μ_s, above which Coulomb failure occurs, varies for particles with the same material but different shape, indicating that geometric friction can dominate over material friction.

Discharge of elongated grains from silo with rotating bottom

We study the flow of elongated grains (wooden pegs of length L=20 mm with circular cross section of diameter d_{c}=6 and 8 mm) from a silo with a rotating bottom and a circular orifice of diameter D. In the small orifice range (D/d<5) clogs are mostly broken by the rotating base, and the flow is intermittent with avalanches and temporary clogs. Here d≡(3/2d_{c}^{2}L)^{1/3} is the effective grain diameter. Unlike for spherical grains, for rods the flow rate W clearly deviates from the power law dependence W∝(D-kd)^{2.5} at lower orifice sizes in the intermittent regime, where W is measured in between temporary clogs only. Instead, below about D/d<3 an exponential dependence W∝e^{κD} is detected. Here k and κ are constants of order unity. Even more importantly, rotating the silo base leads to a strong-more than 50%-decrease of the flow rate, which otherwise does not depend significantly on the value of ω in the continuous flow regime. In the intermittent regime, W(ω) appears to follow a nonmonotonic trend, although with considerable noise. A simple picture, in terms of the switching from funnel flow to mass flow and the alignment of the pegs due to rotation, is proposed to explain the observed difference between spherical and elongated grains. We also observe shear-induced orientational ordering of the pegs at the bottom such that their long axes in average are oriented at a small angle 〈θ〉≈15^{∘} to the motion of the bottom.

Inertial shear flow of assemblies of frictionless polygons: Rheology and microstructure

Motivated by the understanding of shape effects in granular materials, we numerically investigate the macroscopic and microstructural properties of anisotropic dense assemblies of frictionless polydisperse rigid pentagons in shear flow, and compare them with similar systems of disks. Once subjected to large cumulative shear strains their rheology and microstructure are investigated in uniform steady states, depending on inertial number I, which ranges from the quasistatic limit ([Formula: see text]) to 0.2. In the quasistatic limit both systems are devoid of Reynolds dilatancy, i.e., flow at their random close packing density. Both macroscopic friction angle [Formula: see text], an increasing function of I , and solid fraction [Formula: see text], a decreasing function of I, are larger with pentagons than with disks at small I, but the differences decline for larger I and, remarkably, nearly vanish for [Formula: see text]. Under growing I , the depletion of contact networks is considerably slower with pentagons, in which increasingly anisotropic, but still well-connected force-transmitting structures are maintained throughout the studied range. Whereas contact anisotropy and force anisotropy contribute nearly equally to the shear strength in disk assemblies, the latter effect dominates with pentagons at small I, while the former takes over for I of the order of 10^-2. The size of clusters of grains in side-to-side contact, typically comprising more than 10 pentagons in the quasistatic limit, very gradually decreases for growing I.

Geometrical properties of rigid frictionless granular packings as a function of particle size and shape

Three-dimensional discrete numerical simulation is used to investigate the properties of close-packed frictionless granular assemblies as a function of particle polydispersity and shape. Unlike some experimental results, simulations show that disordered packings of pinacoids (eight-face convex polyhedra) achieve higher solid fraction values than amorphous packings of spherical or rounded particles, thus fulfilling the analog of Ulam's conjecture stated by Jiao and co-workers for random packings [Y. Jiao and S. Torquato, Phys. Rev. E 84, 041309 (2011)PLEEE81539-375510.1103/PhysRevE.84.041309]. This seeming discrepancy between experimental and numerical results is believed to result from difficulties in overcoming inter particle friction through experimental densification processes. Moreover, solid fraction is shown to increase further with bidispersity and peak when the volume proportion of small particles reaches 30%. Contrarily, substituting up to 50% of flat pinacoids for isometric ones yields solid fraction decrease, especially when flat particles are also elongated. Nevertheless, particle shape seems to play a minor role in packing solid fraction compared to polydispersity. Additional investigations focused on the packing microstructure confirm that pinacoid packings fulfill the isostatic conjecture and that they are free of order except beyond 30% to 50% of flat or flat-elongated polyhedra in the packing. This order increase progressively takes the form of a nematic phase caused by the reorientation of flat or flat-elongated particles to minimize the packing potential energy. Simultaneously, this reorientation seems to increase the solid fraction value slightly above the maximum achieved by monodisperse isometric pinacoids, as well as the coordination number. Finally, partial substitution of elongated pinacoids for isometric ones has limited effect on packing solid fraction or order.

Numerical study of one-dimensional compression of granular materials. I. Stress-strain behavior, microstructure, and irreversibility

The behavior of a model granular material, made of slightly polydisperse beads with Hertz-Mindlin elastic-frictional contacts, in oedometric compression (i.e., compression along one axis, with no lateral strain) is studied by grain-level numerical simulations. We systematically investigate the influence of the (idealized) packing process on the microstructure and stresses in the initial, weakly confined equilibrium state, and prepare both isotropic and anisotropic configurations differing in solid fraction Φ and coordination number z. Φ (ranging from maximally dense to moderately loose), z (which might vary independently of Φ in dense systems), fabric and force anisotropy parameters, and the ratio K_{0} of lateral stresses σ_{2}=σ_{3} to stress σ_{1} in the compression direction are monitored in oedometric compression in which σ_{1} varies by more than three orders of magnitude. K_{0} reflects the anisotropy of the assembling process and may remain nearly constant in further loading if the material is already oedometrically compressed (as a granular gas) in the preparation stage. Otherwise, it tends to decrease steadily over the investigated stress range. It is related to force and fabric anisotropy parameters by a simple formula. Elastic moduli, separately computed with an appropriate matrix method, may express the response to very small stress increments about the transversely isotropic well-equilibrated states along the loading path, although oedometric compression proves an essentially anelastic process, mainly due to friction mobilization, with large irreversible effects apparent upon unloading. While the evolution of axial strain ε_{1} and solid fraction Φ (or of the void ratio e=-1+1/Φ) with axial stress σ_{1} is very nearly reversible, especially in dense samples, z is observed to decrease (as previously observed in isotropic compression) after a compression cycle if its initial value was high. K_{0} relates to the evolution of internal variables and may exceed 1 in unloading. The considerably greater irreversibility of oedometric compression reported in sands, compared to our model systems, should signal contact plasticity or damage.

Flow of wet granular materials: A numerical study

We simulate dense assemblies of frictional spherical grains in steady shear flow under controlled normal stress P in the presence of a small amount of an interstitial liquid, which gives rise to capillary menisci, assumed isolated (pendular regime), and attractive forces, which are hysteretic: Menisci form at contact, but do not break until grains are separated by a finite rupture distance. The system behavior depends on two dimensionless control parameters, inertial number I and reduced pressure P*=aP/(πΓ), comparing confining forces ∼a2P to meniscus tensile strength F0=πΓa, for grains of diameter a joined by menisci with surface tension Γ. We pay special attention to the quasistatic limit of slow flow and observe systematic, enduring strain localization in some of the cohesion-dominated (P*∼0.1) systems. Homogeneous steady flows are characterized by the dependence of internal friction coefficient μ* and solid fraction Φ on I and P*. We also record normal stress differences, fairly small but not negligible and increasing for decreasing P*. The system rheology is moderately sensitive to saturation within the pendular regime, but would be different in the absence of capillary hysteresis. Capillary forces have a significant effect on the macroscopic behavior of the system, up to P* values of several units, especially for longer force ranges associated with larger menisci. The concept of effective pressure may be used to predict an order of magnitude for the strong increase of μ* as P* decreases but such a crude approach is unable to account for the complex structural changes induced by capillary cohesion, with a significant decrease of Φ and different agglomeration states and anisotropic fabric. Likewise, the Mohr-Coulomb criterion for pressure-dependent critical states is, at best, an approximation valid within a restricted range of pressures, with P*≥1. At small enough P*, large clusters of interacting grains form in slow flows, in which liquid bonds survive shear strains of several units. This affects the anisotropies associated with different interactions and the shape of function μ*(I), which departs more slowly from its quasistatic limit than in cohesionless systems (possibly explaining the shear banding tendency).

Effects of shape and size polydispersity on strength properties of granular materials

By means of extensive contact dynamics simulations, we analyze the combined effects of polydispersity both in particle size and in particle shape, defined as the degree of shape irregularity, on the shear strength and microstructure of sheared granular materials composed of pentagonal particles. We find that the shear strength is independent of the size span, but unexpectedly, it declines with increasing shape polydispersity. At the same time, the solid fraction is an increasing function of both the size span and the shape polydispersity. Hence, the densest and loosest packings have the same shear strength. At the scale of the particles and their contacts, we analyze the connectivity of particles, force transmission, and friction mobilization as well as their anisotropies. We show that stronger forces are carried by larger particles and propped by an increasing number of small particles. The independence of shear strength with regard to size span is shown to be a consequence of contact network self-organization, with the falloff of contact anisotropy compensated by increasing force anisotropy.

Internal friction and absence of dilatancy of packings of frictionless polygons

By means of numerical simulations, we show that assemblies of frictionless rigid pentagons in slow shear flow possess an internal friction coefficient (equal to 0.183±0.008 with our choice of moderately polydisperse grains) but no macroscopic dilatancy. In other words, despite side-side contacts tending to hinder relative particle rotations, the solid fraction under quasistatic shear coincides with that of isotropic random close packings of pentagonal particles. Properties of polygonal grains are thus similar to those of disks in that respect. We argue that continuous reshuffling of the force-bearing network leads to frequent collapsing events at the microscale, thereby causing the macroscopic dilatancy to vanish. Despite such rearrangements, the shear flow favors an anisotropic structure that is at the origin of the ability of the system to sustain shear stress.

Internal structure of inertial granular flows

We analyze inertial granular flows and show that, for all values of the inertial number I, the effective friction coefficient μ arises from three different parameters pertaining to the contact network and force transmission: (1) contact anisotropy, (2) force chain anisotropy, and (3) friction mobilization. Our extensive 3D numerical simulations reveal that μ increases with I mainly due to an increasing contact anisotropy and partially by friction mobilization whereas the anisotropy of force chains declines as a result of the destabilizing effect of particle inertia. The contact network undergoes topological transitions, and beyond I≃0.1 the force chains break into clusters immersed in a background "soup" of floating particles. We show that this transition coincides with the divergence of the size of fluidized zones characterized from the local environments of floating particles and a slower increase of μ with I.

Packings of irregular polyhedral particles: strength, structure, and effects of angularity

We present a systematic numerical investigation of the shear strength and structure of granular packings composed of irregular polyhedral particles. The angularity of the particles is varied by increasing the number of faces from 8 (octahedronlike shape) to 596. We find that the shear strength increases with angularity up to a maximum value and saturates as the particles become more angular (below 46 faces). At the same time, the packing fraction increases to a peak value but declines for more angular particles. We analyze the connectivity and anisotropy of the microstructure by considering both the contacts and branch vectors joining particle centers. The increase of the shear strength with angularity is shown to be due to a net increase of the fabric and force anisotropies but at higher particle angularity a rapid falloff of the fabric anisotropy is compensated by an increase of force anisotropy, leading thus to the saturation of shear strength.

Rheology of three-dimensional packings of aggregates: microstructure and effects of nonconvexity

We use three-dimensional contact dynamics simulations to analyze the rheological properties of granular materials composed of rigid aggregates. The aggregates are made from four overlapping spheres and described by a nonconvexity parameter depending on the relative positions of the spheres. The macroscopic and microstructural properties of several sheared packings are analyzed as a function of the degree of nonconvexity of the aggregates. We find that the internal angle of friction increases with the nonconvexity. In contrast, the packing fraction first increases to a maximum value but declines as the nonconvexity increases further. At a high level of nonconvexity, the packings are looser but show a higher shear strength. At the microscopic scale, the fabric and force anisotropy, as well as the friction mobilization, are enhanced by multiple contacts between aggregates and interlocking, thus revealings the mechanical and geometrical origins of shear strength.

Influence of the feeding mechanism on deposits of square particles

In a previous paper [Hidalgo et al., Phys. Rev. Lett. 103, 118001 (2009)] it was shown that square particles deposited in a silo tend to align with a diagonal parallel to the gravity, giving rise to a deposit with very particular properties. Here we explore, both experimentally and numerically, the effect on these properties of the filling mechanism. In particular, we modify the volume fraction of the initial configuration from which the grains are deposited. Starting from a very dilute case, increasing the volume fraction results in an enhancement of the disorder in the final deposit characterized by a decrease of the final packing fraction and a reduction of the number of particles oriented with their diagonal in the direction of gravity. However, for very high initial volume fractions, the final packing fraction increases again. This result implies that two deposits with the same final packing fraction can be obtained from very different initial conditions. The structural properties of such deposits are analyzed, revealing that, although the final volume fraction is the same, their micromechanical properties notably differ.

Nonlinear effects of particle shape angularity in sheared granular media

We analyze the effects of particle shape angularity on the macroscopic shear behavior and texture of granular packings simulated by means of the contact dynamics method. The particles are regular polygons with an increasing number of sides ranging from 3 (triangles) to 60. The packings are analyzed in the steady shear state in terms of their shear strength, packing fraction, connectivity, and fabric and force anisotropies, as functions of the angularity. An interesting finding is that the shear strength increases with angularity up to a maximum value and saturates as the particles become more angular (below six sides). In contrast, the packing fraction declines towards a constant value, so that the packings of more angular particles are looser but have higher shear strength. We show that the increase of the shear strength at low angularity is due to an increase of both contact and force anisotropies and the saturation of the shear strength for higher angularities is a consequence of a rapid falloff of the contact and normal force anisotropies compensated for by an increase of the tangential force anisotropy. This transition reflects clearly the rather special geometrical properties of these highly angular shapes, implying that the stability of the packing relies strongly on the side-side contacts and the mobilization of friction forces.