Nonlocal continuum modeling of dense granular flow in a split-bottom cell with a vane-shaped intruder

How vertical oscillatory motion above a saturated sand bed leads to heap formation

We show how oscillations in fluid flow over a fluid-saturated and porous sediment bed leads to the development of a bedform. To understand the role of pressure fluctuations on the bed associated with flow oscillations, we analyze how the flow penetrates into and through the bed. We then calculate the corresponding vertical pressure gradients within the bed that tend to expand the bed along the vertical direction. When these pressure gradients are large enough, they facilitate small irreversible rearrangements of the grains within the bed, and so cause granular creep. We conjecture that this granular creep alternates with jamming to produce a granular ratchet that slowly lifts the surface of the bed locally where pressure gradients dominate, and depresses the surface where shear stresses dominate. We observe that the shape of the resulting heap exhibits a constant characteristic width. The height of this heap evolves approximately as the square root of time, in agreement with dimensional arguments predicated on a coarse-grained viscous deformation of the bed. The surface of the heap contracts initially with the square root of time, consistent with an incompressible analysis of the flow of grains within the heap. Near its peak the heap grows due to a dilatation of the bed, to inward radial flux, or to a combination of the two.

Interplay between hysteresis and nonlocality during onset and arrest of flow in granular materials

The jamming transition in granular materials is well-known for exhibiting hysteresis, wherein the level of shear stress required to trigger flow is larger than that below which flow stops. Although such behavior is typically modeled as a simple non-monotonic flow rule, the rheology of granular materials is also nonlocal due to cooperativity at the grain scale, leading for instance to increased strengthening of the flow threshold as system size is reduced. We investigate how these two effects - hysteresis and nonlocality - couple with each other by incorporating non-monotonicity of the flow rule into the nonlocal granular fluidity (NGF) model, a nonlocal constitutive model for granular flows. By artificially tuning the strength of nonlocal diffusion, we demonstrate that both ingredients are key to explaining certain features of the hysteretic transition between flow and arrest. Finally, we assess the ability of the NGF model to quantitatively predict material behavior both around the transition and in the flowing regime, through stress-driven discrete element method (DEM) simulations of flow onset and arrest in various geometries. Along the way, we develop a new methodology to compare deterministic model predictions with the stochastic behavior exhibited by the DEM simulations around the jamming transition.

Evolution of shear zones in granular packings under pressure

Stress transmission in realistic granular media often occurs under external load and in the presence of boundary slip. We investigate shear localization in a split-bottom Couette cell with smooth walls subject to a confining pressure experimentally and by means of numerical simulations. We demonstrate how the characteristics of the shear zone, such as its center position and width, evolve as the confining pressure and wall slip modify the local effective friction coefficient of the material. For increasing applied pressure, the shear zone evolves toward the center of the cylinder and grows wider and the angular velocity reduces compared to the driving rate of the bottom disk. Moreover, the presence of slip promotes the transition from open shear zones at the top surface to closed shear zones inside the bulk. We also systematically vary the ratio of the effective friction near the bottom plate and in the bulk in simulations and observe the resulting impact on the surface flow profile. Besides the boundary conditions and external load, material properties such as grain size are also known to influence the effective friction coefficient. However, our numerical results reveal that the center position and width of the shear zone are insignificantly affected by the choice of the grain size as far as it remains small compared to the radius of the rotating bottom disk.