Correlations for shear-induced percolation segregation in granular shear flows

Characterization of particle size segregation and heterogeneity along the slopes of a waste rock pile using image analysis

Large amounts of waste rock are produced during mining operations and often disposed of in large piles. Particle size segregation usually occurs during waste rock disposal, which can lead to high variations of particle size distribution (PSD) along the pile slope, increasing the risk for hydrogeotechnical instabilities. Determining segregation in situ is, therefore, critical to implement control measures and optimize deposition plans. However, characterizing PSD at field scale remains challenging because of the large dimensions of the pile, the instability of the blocks and the steep slopes. In this study, images, covering a 1400 m wide and 10 m high section of a waste rock pile, were taken and analyzed using image analysis to characterize segregation along the slope of the pile. PSD curves in different sections along the slope were determined and the segregation degree and characteristic diameters (e.g., D10, D50, D80, D95) were quantitatively compared. Results allowed to quantify segregation along the vertical direction of the pile, showing that segregation degree increased from - 0.77 ± 0.39 in the top (finer zone) to + 0.4 ± 0.14 in the bottom (coarser zone). Significant lateral heterogeneity was also observed with maximum diameters varying between 80 and 180 cm in the bottom section. Such segregation and lateral heterogeneity could induce significant variations of waste rock properties, with, for example, hydraulic conductivities varying by more than 2 orders of magnitude within the pile.

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.

Local Percolation of a Binary Particle Mixture in a Rectangular Hopper with Inclined Bottom during Discharging

To reveal the local percolation characteristics of a binary particle mixture in a rectangular hopper with inclined bottom, the discrete element method (DEM) is used to simulate the discharging process. A local percolation evaluation method is proposed, and the percolation strength grid maps are drawn. The effects of geometric parameters, particle properties, and interaction parameters on percolation are investigated. Apart from the free surface, percolation is mainly concentrated near the wall and at the bottom. With the increase in the orifice width, the average local percolation strength index (ALPSI) of the near-wall region increases and that of the bottom region decreases. The effect of the angle on percolation in the near-wall region can be ignored. The effect of friction on local percolation is significant. Increasing the fine particle mass fraction and reducing the difference in particle size can effectively avoid percolation.

Granular segregation induced by a moving subsurface blade

Size-driven particle segregation can occur when an object such as a blade moves through an otherwise static bed of granular material. Here we use discrete element method (DEM) simulations to study segregation resulting from a subsurface blade moving through a bed of size-bidisperse spherical particles. Segregation increases with each pass of the blade until a surface layer of mostly large particles forms above a small-particle layer adjacent to the bottom wall. The rate of segregation decreases with each pass so that the degree of segregation asymptotically approaches its maximum value, and the number of passes to reach a steady segregation state increases as the bed depth is increased or the blade height decreased. In shallow beds, the characteristic number of passes for segregation, τ, scales with the inverse of the granular inertial number, I. In deep beds with small blade heights, the effect of the blade is more localized to its immediate vicinity, resulting in many more passes of the blade to reach a steady segregation state, and a corresponding deviation from the shallow bed scaling of τ with I^{-1}.

Modeling Segregation in Granular Flows

Accurate continuum models of flow and segregation of dense granular flows are now possible. This is the result of extensive comparisons, over the last several years, of computer simulations of increasing accuracy and scale, experiments, and continuum models, in a variety of flows and for a variety of mixtures. Computer simulations-discrete element methods (DEM)-yield remarkably detailed views of granular flow and segregation. Conti-nuum models, however, offer the best possibility for parametric studies of outcomes in what could be a prohibitively large space resulting from the competition between three distinct driving mechanisms: advection, diffusion, and segregation. We present a continuum transport equation-based framework, informed by phenomenological constitutive equations, that accurately predicts segregation in many settings, both industrial and natural. Three-way comparisons among experiments, DEM, and theory are offered wherever possible to validate the approach. In addition to the flows and mixtures described here, many straightforward extensions of the framework appear possible.

Effect of pressure on segregation in granular shear flows

The effect of confining pressure (overburden) on segregation of granular material is studied in discrete element method (DEM) simulations of horizontal planar shear flow. To mitigate changes to the shear rate due to the changing overburden, a linear with depth variation in the streamwise velocity component is imposed using a simple feedback scheme. Under these conditions, both the rate of segregation and the ultimate degree of segregation in size bidisperse and density bidisperse granular flows decrease with increasing overburden pressure and scale with the overburden pressure normalized by the lithostatic pressure of the particle bed. At overburdens greater than approximately 20 times the lithostatic pressure at the bottom of the bed, the density segregation rate is zero while the size segregation rate is small but nonzero, suggesting that different physical mechanisms drive the two types of segregation. The segregation rate scales close to linearly with the inertial number for both size bidisperse and density bidisperse mixtures under various flow conditions, leading to a proposed pressure dependence term for existing segregation velocity correlations. Surprisingly, particle stiffness has only a minor effect on segregation, although it significantly affects the packing density.

Transport analogy for segregation and granular rheology

Here, we show a direct connection between density-based segregation and granular rheology that can lead to insight into both problems. Our results exhibit a transition in the rate of segregation during simple shear that occurs at I∼0.5 and mimics a coincident regime change in flow rheology. We propose scaling arguments that support a packing fraction criterion for this transition that can both explain our segregation results as well as unify existing literature studies of granular rheology. By recasting a segregation model in terms of rheological parameters, we establish an approach that not only collapses results for a wide range of conditions, but also yields a direct relationship between the coordination number z and the segregation velocity. Moreover, our approach predicts the precise location of the observed regime change or saturation. This suggests that it is possible to rationally design process operating conditions that lead to significantly lower segregation extents. These observations can have a profound impact on both the study of granular flow or mixing as well as industrial practice.