Shear flow of dense granular materials near smooth walls. I. Shear localization and constitutive laws in the boundary region

Fabric-based jamming phase diagram for frictional granular materials

A jamming phase diagram maps the phase states of granular materials to their intensive properties such as shear stress and density (or packing fraction). We investigate how different phases in a jamming phase diagram of granular materials are related to their fabric structure via three-dimensional discrete element method simulations. Constant-volume quasi-static simple shear tests ensuring uniform shear strain field are conducted on bi-disperse spherical frictional particles. Specimens with different initial solid fractions are sheared until reaching steady state at a large shear strain (200%). The jamming threshold in terms of stress, non-rattler fraction, and coordination numbers (Z's) of different contact networks is discussed. The evolution of fabric anisotropy (F) of each contact network during shearing is also examined. By plotting the fabric data in the F-Z space, a unique critical fabric surface (CFS) becomes apparent across all specimens, irrespective of their initial phase states. Through the correlation of this CFS with fabric signals corresponding to jamming transitions, we introduce a novel jamming phase diagram in the fabric F-Z space, offering a convenient approach to distinguish the various phases of granular materials solely through the direct observation of geometrical arrangements of particles. This jamming phase diagram underscores the importance of the microstructure underlying the conventional jamming phenomenon and introduces a novel standpoint for interpreting the phase transitions of granular materials that have been exposed to processes such as compaction, shearing, and other complex loading histories.

Tensor electromagnetism and emergent elasticity in jammed solids

The theory of mechanical response and stress transmission in disordered, jammed solids poses several open questions of how nonperiodic networks-apparently indistinguishable from a snapshot of a fluid-sustain shear. We present a stress-only theory of emergent elasticity for a nonthermal amorphous assembly of grains in a jammed solid, where each grain is subjected to mechanical constraints of force and torque balance. These grain-level constraints lead to the Gauss's law of an emergent U(1) tensor electromagnetism, which then accounts for the mechanical response of such solids. This formulation of amorphous elasticity has several immediate consequences. The mechanical response maps exactly to the static, dielectric response of this tensorial electromagnetism with the polarizability of the medium mapping to emergent elastic moduli. External forces act as vector electric charges, whereas the tensorial magnetic fields are sourced by momentum density. The dynamics in the electric and magnetic sectors naturally translate into the dynamics of the rigid jammed network and ballistic particle motion, respectively. The theoretical predictions for both stress-stress correlations and responses are borne out by the results of numerical simulations of frictionless granular packings in the static limit of the theory in both 2D and 3D.

Shear-induced mixing of granular materials featuring broad granule size distributions

Granular flows during a shear-induced mixing process are studied using discrete element methods. The aim is to understand the underlying elementary mechanisms of transition from unmixed to mixed phases for a granular material featuring a broad distribution of particles, which we investigate systematically by varying the strain rate and system size. Here the strain rate varies over four orders of magnitude and the system size varies from ten thousand to more than a million granules. A strain rate-dependent transition from quasistatic to purely inertial flow is observed. At the macroscopic scale, the contact stresses drop due to the formation of shear-induced instabilities that serves as an onset of granular flows and initiates mixing between the granules. The stress-drop displays a profound system size dependence. At the granular scale, mixing dynamics are correlated with the formation of shear bands, which result in significantly different timescales of mixing, especially for those regions that are close to the system walls and the bulk. Overall, our results reveal that although the transient dynamics display a generic behavior, these have a significant finite-size effect. In contrast, macroscopic behaviors at steady states have negligible system size dependence.

Strain localization in planar shear of granular media: the role of porosity and boundary conditions

Shear strain localization into shear bands is associated with velocity weakening instabilities and earthquakes. Here, we simulate steady-state plane-shear flow of numerical granular material (gouge), confined between parallel surfaces. Both constant shear stress and constant strain-rate boundary conditions are tested, and the two types of boundary conditions are found to yield distinct velocity profiles and friction laws. The inertial number, I, exerts the largest control on the layers' behavior, but additional dependencies of friction on normal stress and thickness of the layer are observed under constant stress boundary condition. We find that shear-band localization, which is present in the quasistatic regime ([Formula: see text]) in rate-controlled shear, is absent under stress-controlled loading. In the latter case, flow ceases when macroscopic friction coefficient approaches the quasistatic friction value. The inertial regime that occurs at higher inertial numbers ([Formula: see text]) is associated with distributed shear, and friction and porosity that increase with shear rate (rate-strengthening regime). The finding that shear under constant stress boundary condition produces the inertial, distributed shear but never quasistatic, localized deformation is rationalized based on low fluctuations of shear forces in granular contacts for stress-controlled loading. By examining porosity within and outside a shear band, we also provide a mechanical reason why the transition between quasistatic and inertial shear coincides with the transition between localized and distributed strain.

Unsteady granular flows down an inclined plane

The continuum description of granular flows is still a challenge despite their importance in many geophysical and industrial applications. We extend previous works, which have explored steady flow properties, by focusing on unsteady flows accelerating or decelerating down an inclined plane in the simple shear configuration. We solve the flow kinematics analytically, including predictions of evolving velocity and stress profiles and the duration of the transient stage. The solution shows why and how granular materials reach steady flow on slopes steeper than the angle of repose and how they decelerate on shallower slopes. The model might facilitate development of natural hazard assessment and may be modified in the future to explore unsteady granular flows in different configurations.

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).

Evolution of shear zones in granular materials

The evolution of wide shear zones or shear bands was investigated experimentally and numerically for quasistatic dry granular flows in split bottom shear cells. We compare the behavior of materials consisting of beads, irregular grains, such as sand, and elongated particles. Shearing an initially random sample, the zone width was found to significantly decrease in the first stage of the process. The characteristic shear strain associated with this decrease is about unity and it is systematically increasing with shape anisotropy, i.e., when the grain shape changes from spherical to irregular (e.g., sand) and becomes elongated (pegs). The strongly decreasing tendency of the zone width is followed by a slight increase which is more pronounced for rodlike particles than for grains with smaller shape anisotropy (beads or irregular particles). The evolution of the zone width is connected to shear-induced packing density change and for nonspherical particles it also involves grain reorientation effects. The final zone width is significantly smaller for irregular grains than for spherical beads.

Sliding friction on wet and dry sand

We show experimentally that the sliding friction on sand is greatly reduced by the addition of some-but not too much-water. The formation of capillary water bridges increases the shear modulus of the sand, which facilitates the sliding. Too much water, on the other hand, makes the capillary bridges coalesce, resulting in a decrease of the modulus; in this case, we observe that the friction coefficient increases again. Our results, therefore, show that the friction coefficient is directly related to the shear modulus; this has important repercussions for the transport of granular materials. In addition, the polydispersity of the sand is shown to also have a large effect on the friction coefficient.

Shear flow of dense granular materials near smooth walls. II. Block formation and suppression of slip by rolling friction

The role of rotational degrees of freedom and of microscopic contact properties at smooth walls in two dimensional planar shear has been investigated by contact dynamics simulations of round hard frictional particles. Our default system setup consists of smooth frictional walls, giving rise to slip. We show that there exists a critical microscopic friction coefficient at the walls, above which they are able to shear the granular medium. We observe distinctive features at this critical point, which to our knowledge have not been reported before. Activating rolling friction at smooth walls reduces slip, leading to similar shear behavior as for rough walls (with particles glued on their surface). Our simulations with rough walls are in agreement with previous results, provided the roughness is strong enough. In the limit of small roughness amplitude, however, the distinctive features of shearing with smooth walls are confirmed.