Rheology of dense granular mixtures: particle-size distributions, boundary conditions, and collisional time scales

Universal behavior in fragmenting brittle, isotropic solids across material properties

A bonded particle model is used to explore how variations in the material properties of brittle, isotropic solids affect critical behavior in fragmentation. To control material properties, a model is proposed which includes breakable two- and three-body particle interactions to calibrate elastic moduli and mode I and mode II fracture toughnesses. In the quasistatic limit, fragmentation leads to a power-law distribution of grain sizes which is truncated at a maximum grain mass that grows as a nontrivial power of system size. In the high-rate limit, truncation occurs at a mass that decreases as a power of increasing rate. A scaling description is used to characterize this behavior by collapsing the mean-square grain mass across rates and system sizes. Consistent scaling persists across all material properties studied, although there are differences in the evolution of grain size distributions with strain as the initial number of grains at fracture and their subsequent rate of production depend on Poisson's ratio. This evolving granular structure is found to induce a unique rheology where the ratio of the shear stress to pressure, an internal friction coefficient, decays approximately as the logarithm of increasing strain rate. The stress ratio also decreases at all rates with increasing strain as fragmentation progresses and depends on elastic properties of the solid.

Influence of fine particle content in debris flows on alluvial fan morphology

Alluvial fans are large-scale depositional structures commonly found at the base of mountain ranges. They are relatively soil-rich compared to the rocky terrains, or catchment areas, from which their material originates. When frequented by debris flows (massive, muddy, rocky flows) they contribute significantly to local hazards as they carry focused, collisional, fast-moving materials across alluvial fans, unpredictable in size, speed, and direction. We research how fine particle content in debris flows correlates with directional changes, i.e., debris flow avulsions. Toward this, we analyzed field data from two neighboring alluvial fans in the White Mountains (California, USA) that exhibit dramatically different topographies despite their proximity and associated similar long-term climates. Informed by these measurements, we performed long-term and incremental alluvial fan experiments built by debris flows with systematically-varied fine particle content. We found that (1) decreasing fine particle content increases the variability of fan slopes and associated channelization dynamics, and (2) for all mixtures longer-term continuous alluvial fan experiments form more complex surface channelizations than repeated flows for the same total time, indicating the importance of both particle sizes and timescales on alluvial fan surface morphology.

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.

Internal Stability Evaluation of Soils

Suffusion constitutes a major threat to the foundation of a dam, and the likelihood of suffusion is always determined by the internal stability of soils. It has been verified that internal stability is closely related to the grain size distribution (GSD) of soils. In this study, a numerical model is developed to simulate the suffusion process. The model takes the combined effects of GSD and porosity (n) into account, as well as Wilcock and Crowe’s theory, which is also adopted to quantify the inception and transport of soils. This proposed model is validated with the experimental data and shows satisfactory performance in simulating the process of suffusion. By analyzing the simulation results of the model, the mechanism is disclosed on how soils with specific GSD behaving internally unstable. Moreover, the internal stability of soils can be evaluated through the model. Results show that it is able to distinguish the internal stability of 30 runs out of 36, indicating a 83.33% of accuracy, which is higher than the traditional GSD-based approaches.

Binary mixtures of disks and elongated particles: Texture and mechanical properties

We analyze the shear strength and microstructure of binary granular mixtures consisting of disks and elongated particles by varying systematically both the mixture ratio and degree of homogeneity (from homogeneous to fully segregated). The contact dynamics method is used for numerical simulations with rigid particles interacting by frictional contacts. A counterintuitive finding of this work is that the shear strength, packing fraction, and, at the microscopic scale, the fabric, force, and friction anisotropies of the contact network are all nearly independent of the degree of homogeneity. In other words, homogeneous mixtures have the same strength properties as segregated packings of the two particle shapes. In contrast, the shear strength increases with the proportion of elongated particles correlatively with the increase of the corresponding force and fabric anisotropies. By a detailed analysis of the contact network topology, we show that various contact types contribute differently to force transmission and friction mobilization.

Stress partition and microstructure in size-segregating granular flows

When a granular mixture involving grains of different sizes is shaken, sheared, mixed, or left to flow, grains tend to separate by sizes in a process known as size segregation. In this study, we explore the size segregation mechanism in granular chute flows in terms of the pressure distribution and granular microstructure. Therefore, two-dimensional discrete numerical simulations of bidisperse granular chute flows are systematically analyzed. Based on the theoretical models of J. M. N. T. Gray and A. R. Thornton [Proc. R. Soc. A 461, 1447] and K. M. Hill and D. S. Tan [J. Fluid Mech. 756, 54 (2014)], we explore the stress partition in the phases of small and large grains, discriminating between contact stresses and kinetic stresses. Our results support both gravity-induced and shear-gradient-induced segregation mechanisms. However, we show that the contact stress partition is extremely sensitive to the definition of the partial stress tensors and, more specifically, to the way mixed contacts (i.e., involving a small grain and a large grain) are handled, making conclusions on gravity-induced segregation uncertain. By contrast, the computation of the partial kinetic stress tensors is robust. The kinetic pressure partition exhibits a deviation from continuum mixture theory of a significantly higher amplitude than the contact pressure and displays a clear dependence on the flow dynamics. Finally, using a simple approximation for the contact partial stress tensors, we investigate how the contact stress partition relates to the flow microstructure and suggest that the latter may provide an interesting proxy for studying gravity-induced segregation.

Phase transitions in shear-induced segregation of granular materials

We computationally study shear-induced segregation of different-sized particles in vertical chute flow. We find that, for low solid fractions, large particles segregate toward regions of low shear rates where the granular temperature (velocity variance) is low. As the solid fraction increases, this trend reverses, and large particles segregate toward regions of high shear rates and temperatures. We find that this is a global phenomenon: local segregation trends reverse at high system solid fractions even where local solid fractions are small. The reversal corresponds to the growth of a single enduring cluster of 30%-60% of the particles that we propose changes the segregation dynamics.

Rheology of dense granular mixtures: boundary pressures

Models for dense sheared granular materials indicate that their rheological properties depend on particle size, but the representative size for mixtures is not obvious. Here, we computationally study pressure on a boundary due to sheared granular mixtures to determine its dependence on particle size distribution. We find that the pressure does not depend monotonically on average particle size. Instead it has an additional dependence on a measure of the effective free volume per particle we adapt from an expression for packing of monosized particles near the jammed state.