This Letter introduces unexpected diffusion properties in dense granular flows and shows that they result from the development of partially jammed clusters of grains, or granular vortices. Transverse diffusion coefficients D and average vortex sizes ℓ are systematically measured in simulated plane shear flows at differing inertial numbers I revealing (i) a strong deviation from the expected scaling D∝d^{2}γ[over ˙] involving the grain size d and shear rate γ[over ˙] and (ii) an increase in average vortex size ℓ at low I, following ℓ∝dI^{-1/2} but limited by the system size. A general scaling D∝ℓdγ[over ˙] is introduced that captures all the measurements and highlights the key role of vortex size. This leads to establishing a scaling for the diffusivity in dense granular flow as D∝d^{2}sqrt[γ[over ˙]/t_{i}] involving the geometric average of shear time 1/γ[over ˙] and inertial time t_{i} as the relevant time scale. Analysis of grain trajectories is further evidence that this diffusion process arises from a vortex-driven random walk.

We investigate the properties of self-diffusion in heterogeneous dense granular flows involving a gradient of stress and inertial number. The study is based on simulated plane shear with gravity and Poiseuille flows, in which non-local effects induce some creep flow in zones where stresses are below the yield. Results show that shear-induced diffusion is qualitatively different in zones above and below the yield. Below the yield, diffusivity is no longer governed by velocity fluctuations, and we evidenced a direct scaling between diffusivity and local shear rate. This is interpreted by analysing the grain trajectories, which exhibit a caging dynamics developing in zones below the yield. We finally introduce an explicit scaling for the profile of local inertial number in these zones, which leads to a straightforward expression of the diffusivity as a function of the stress and position in non-local flows.Introduction. -Shearing dense granular flows induces diffusion of grains. This mechanism of shearinduced diffusion underpins the rate of mixing [1], heat transfer [2] and segregation [3] in a variety of natural and industrial granular flows. It is usually modelled by a coefficient of self-diffusion, also called diffusivity D [m 2 /s].In homogeneous shear flows, in which there is no gradient of shear rate, three relationships have been established from which diffusivity can be predicted:

This letter investigates the uplift capacity of plate anchors in granular soils. Simulations based on a discrete-element method are used to measure the uplift capacity of anchors of differing widths to embedment B/H and width to grain-size B/d ratios. Results confirm that the uplift capacity of anchors with a large B/d ratio is well described by existing models developed from continuum mechanics, with no grain-size effect. In contrast, results reveal a strong deviation from these models for anchors with relatively small B/d ratios. A semi-empirical model is introduced that captures this strong grain-size effect. This model is further supported by a micro-mechanical analysis, indicating that anchor uplift capacities are not only governed by a frustum mechanism predicted by continuum mechanics but also involve the mobilisation of grains surrounding this frustum. These results and model are particularly important to rationalise uplift capacities measured in small-scale experiments, typically involving small B/d ratios, and to safely upscale them to larger anchor size relevant to field applications.

Abstract. Dense granular flows exhibit fascinating kinematic patterns characterised by strong fluctuations in grain velocities. In this paper, we analyse these fluctuations and discuss their possible role on macroscopic properties such as effective viscosity, non-locality and shear-induced diffusion. The analysis is based on 2D experimental granular flows performed with the stadium shear device and DEM simulations. We first show that, when subjected to shear, grains self-organised into clusters rotating like rigid bodies. The average size of these so-called granular vortices is found to increase and diverge for lower inertial numbers, when flows decelerate and stop. We then discuss how such a microstructural entity and its associated internal length scale, possibly much larger than a grain, may be used to explain two important properties of dense granular flows: (i) the existence of shear-induced diffusion of grains characterised by a shear-rate independent diffusivity and (ii) the development of boundary layers near walls, where the viscosity is seemingly lower than the viscosity far from walls.

Abstract. Dense granular flows can exhibit non-local flow behaviours that cannot be predicted by local constitutive laws alone. Such behaviour is accompanied by the existence of diverging cooperativity length. Here we show that this length can be attributed to the development of transient clusters of jammed particles within the flow. By performing DEM simulation of dense granular flows, we directly measure the size of such clusters which scales with the inertial number with a power law. We then derive a general non-local relation based on kinematic compatibility for the existence of clusters in an arbitrary non-homogenous flow. The kinematic nature of this derivation suggests that non-locality should be expected in any material regardless of their local constitutive law, as long as transient clusters exist within the flow.