A two–dimensional depth–integrated theory is derived for the gravity–driven free surface flow of cohesionless granular avalanches over complex shallow basal topography. This an important extension one–dimensional Savage–Hutter theory. simple curvilinear coordinate system adopted, which fitted to ‘mean’ downslope chute defines a quasi–two–dimensional reference on top three–dimensional topography superposed. The governing equations are expressed in and mass– momentum–balance integrated through...

Data from large‐scale debris‐flow experiments are combined with modeling of particle‐size segregation to explain the formation lateral levees enriched in coarse grains. The experimental flows consisted 10 m 3 water‐saturated sand and gravel, which traveled ∼80 down a steeply inclined flume before forming an elongated leveed deposit long on nearly horizontal runout surface. We measured surface velocity field observed sequence deposition by seeding tracers onto flow tracking them video...

Granular materials composed of particles with differing grain sizes, densities, shapes, or surface properties may experience unexpected segregation during flow. This review focuses on kinetic sieving and squeeze expulsion, whose combined effect produces the dominant gravity-driven mechanism in dense sheared flows. Shallow granular avalanches that form at more complex industrial flows such as heaps, silos, rotating drums provide ideal conditions for to separate, large rising small percolating...

Shock waves, dead zones and particle-free regions form when a thin surface avalanche of granular material flows around an obstacle or over change in the bed topography. Understanding modelling these is considerable practical interest for industrial processes, as well design defences to protect buildings, structures people from snow avalanches, debris rockfalls. These flow phenomena also yield useful constitutive information that can be used improve existing models. In this paper simple...

Abstract Granular materials composed of a mixture grain sizes are notoriously prone to segregation during shaking or transport. In this paper, binary theory is used formulate model for kinetic sieving large and small particles in thin, rapidly flowing avalanches, which occur many industrial geophysical free-surface flows. The based on simple percolation idea, the preferentially fall into underlying void space lever upwards. Exact steady-state solutions have been constructed general steady...

Segregation and mixing of dissimilar grains is a problem in many industrial pharmaceutical processes, as well hazardous geophysical flows, where the size-distribution can have major impact on local rheology overall run-out. In this paper, simple binary mixture theory used to formulate model for particle-size segregation diffusive remixing large small particles shallow gravity-driven free-surface flows. This builds recent process kinetic sieving, which dominant mechanism granular avalanches...

Abstract The $\mu (I)$ -rheology is a nonlinear viscous law, with strain-rate invariant and pressure-dependent viscosity, that has proved to be effective at modelling dry granular flows in the intermediate range of inertial number, $I$ . This paper shows how incorporate rheology into depth-averaged avalanche models. To leading order, generates an basal friction, which equivalent rough bed friction law. A viscous-like term can derived by integrating in-plane deviatoric stress through depth,...

In light of the successes Navier–Stokes equations in study fluid flows, similar continuum treatment granular materials is a long-standing ambition. This due to their wide-ranging applications pharmaceutical and engineering industries as well geophysical phenomena such avalanches landslides. Historically this has been attempted through modification dissipation terms momentum balance equations, effectively introducing pressure strain-rate dependence into viscosity. Originally, popular model...

Stratification patterns are formed when a bidisperse mixture of large rough grains and smaller more mobile particles is poured between parallel plates to form heap. At low flow rates discrete avalanches down the free surface brought rest by propagation shock waves. Experiments performed in this paper show that larger segregated top avalanche, where velocity greatest, transported front. Here overrun but may rise again size segregation create recirculating coarse-grained Once front established...

We experimentally investigated how a binary granular mixture made up of spherical glass beads (size ratio 2) behaved when flowing down chute. Initially, the was normally graded, with all small particles on top coarse grains. Segregation led to grading inversion, in which smallest percolated bottom flow, while largest rose toward top. Because diffusive remixing, there no sharp separation between small-particle and large-particle layers, but continuous transition. Processing images taken at...

A general continuum theory for particle-size segregation and diffusive remixing in polydisperse granular avalanches is formulated using mixture theory. Comparisons are drawn to existing theories bi-disperse mixtures the case of a ternary large, medium small particles investigated. In this case, reduces system two coupled parabolic segregation–remixing equations, which have single diffusion coefficient three parameters control rates between each pair constituents. Considerable insight into...

We experimentally study particle scale dynamics during segregation of a bidisperse mixture under oscillatory shear. Large and small particles show an underlying asymmetry that is dependent on the local concentration, with segregating faster in regions many large slower particles. quantify bulk scales, capture it theoretically. This gives new physical insight into reveals similarity sedimentation, traffic flow, diffusion.

Machine-to-machine (M2M) communication is a key enabling technology for the future industrial Internet of Things applications. It plays an important role in connectivity and integration computerized machines, such as sensors, actuators, controllers, robots. The requirements flexibility, efficiency, cross-platform compatibility intermodule between connected machines raise challenges M2M messaging mechanism toward ubiquitous data access events notification. This investigation determines facing...

Abstract Debris flows can spontaneously develop regular large-amplitude surge waves that are interspersed by periods in which the channel fill is completely stationary. These important because each individual much more destructive than a steady uniform flow with same mass flux. In this paper small-scale experiments exhibit similar behaviour described. The consists of carborundum particles down rough inclined chute covered static erodible layer grains. For inflow conditions close to minimum...

Abstract

In this paper a fully coupled particle-size segregation model for granular flows (Barker et al. , J. Fluid Mech. vol. 909, 2021, p. A22) is used to simulate the development of patterns in triangular rotating drum. The results are compared with experimental formed bidisperse and tridisperse mixtures, varying compositions fill heights. all cases agreement between simulations experiments remarkably good. generated narrow gap transparent front back sidewalls. These prevent three-dimensional...

In many industrial processes granular materials are mixed together in partially filled slowly rotating drums. this paper a general theoretical framework is developed for the quasi-two-dimensional motion of material drum. The key assumption that body can be divided into fluid-like and solid-like region, separated by non-material singular surface at which discontinuities occur. Experiments show close to free there thin rapidly moving avalanche flows downslope, beneath it large region material....

A series of laboratory experiments and numerical simulations have been performed to investigate the rapid fluid-like flow a finite mass granular material down chute with partial lateral confinement. The consists section inclined at 40° horizontal, which is connected plane run-out zone by smooth transition. confined on shallow parabolic cross-slope profile. Photogrammetric techniques used determine position evolving boundary during flow, free-surface height stationary deposit in zone. results...

Particle size segregation can have a significant feedback on the motion of many hazardous geophysical mass flows such as debris flows, dense pyroclastic and snow avalanches. This paper develops new depth-averaged theory for that easily be incorporated into existing structure typical models flows. The is derived by depth-averaging segregation-remixing equation bi-disperse mixture large small particles assuming (i) avalanche always inversely graded (ii) there linear downslope velocity profile...

Catastrophic dense granular flows, such as occur in rock avalanches, debris flows and pyroclastic move fully shearing mixtures that have approximately 60 vol.% solids tend to segregate form coarse-grained fronts leveed channels. Levees restrict spreading of unconfined coarse particles become concentrated the top flow are transported front then advect sides head. Channels from which most material has drained away down slope commonly lined with fine-grained deposit, widely thought remain tail...

Abstract Snow avalanches and other hazardous geophysical granular flows, such as debris lahars pyroclastic often impact on obstacles they flow down a slope, generating rapid changes in the height velocity their vicinity. It is important to understand how material flows around improve design of deflecting catching dams, correctly interpret field observations. In this paper small-scale experiments numerical simulations are used investigate supercritical gravity-driven free-surface avalanche...

In recent years considerable progress has been made in the continuum modelling of granular flows, particular $\unicode[STIX]{x1D707}(I)$ -rheology, which links local viscosity a flow to strain rate and pressure through non-dimensional inertial number $I$ . This formulation greatly benefits from its similarity incompressible Navier–Stokes equations as it allows many existing numerical methods be used. Unfortunately, this system is ill posed when too high or low. The consequence posedness that...

Steady uniform granular chute flows are common in industry and provide an important test case for new theoretical models. This paper introduces depth-integrated viscous terms into the momentum-balance equations by extending recent depth-averaged ${\it\mu}(I)$ -rheology dense to two spatial dimensions, using principle of material frame indifference or objectivity. Scaling cross-slope coordinate on width channel velocity one-dimensional steady solution, we show that two-dimensional downslope...

Continuum modelling of granular flow has been plagued with the issue ill-posed dynamic equations for a long time. Equations incompressible, two-dimensional based on Coulomb friction law are regardless deformation, whereas rate-dependent μ(I)-rheology is when non-dimensional inertial number I too high or low. Here, incorporating ideas from critical-state soil mechanics, we derive conditions well-posedness partial differential that combine compressibility I-dependent rheology. When...