J. M. N. T. Gray

The University of Manchester · School of Mathematics

Geophysical granular flows, such as avalanches, debris flows, lahars and pyroclastic flows, are always strongly influenced by the basal topography that they flow over. In particular, localised bumps or obstacles can generate rapid changes in the flow thickness and velocity, or shock waves, which dissipate significant amounts of energy. Understandin...

Geophysical granular flows, such as landslides, pyroclastic flows and snow avalanches, consist of particles with varying surface roughnesses or shapes that have a tendency to segregate during flow due to size differences. Such segregation leads to the formation of regions with different frictional properties, which in turn can feed back on the bulk...

Debris and pyroclastic flows often have bouldery flow fronts, which act as a natural dam resisting further advance. Counter intuitively, these resistive fronts can lead to enhanced run-out, because they can be shouldered aside to form static levees that self-channelise the flow. At the heart of this behaviour is the inherent process of size segrega...

We experimentally study particle scale dynamics during segregation of a bidisperse mixture under oscillatory shear. Large and small particles display an underlying asymmetry that is dependent on the local relative volume fraction, with small particles segregating faster in regions of many large particles and large particles segregating slower in re...

Continuum modelling of granular flow has been plagued with the issue of ill-posed dynamic equations for a long time. Equations for incompressible, two-dimensional flow based on the Coulomb friction law are ill-posed regardless of the deformation, whereas the rate-dependent μ(I)-rheology is ill-posed when the non-dimensional inertial number I is too...

The dynamic behaviour of granular media can be observed widely in nature and in many industrial processes. Yet, the modelling of such media remains challenging as they may act with solid-like and fluid-like properties depending on the rate of the flow and can display a varying apparent friction, cohesion and compressibility. Over the last two decad...

Landslides comprised of a wide range of particle sizes (e.g. debris flows) exhibit flow structures arising from particle size segregation. Segregation influences the mobility of the flow, the development of debris fans, and the resulting impact forces to be expected when designing barriers and containment structures. In order to capture the flow dy...

Waves are omnipresent in avalanches on Earth and other planets. The dynamic nature of waves makes them dangerous in geological hazards such as debris flows, turbidity currents, lava flows, and snow avalanches. Extensive research on granular waves has been carried out by using theoretical and numerical approaches with idealized assumptions. However,...

Field observations of debris flows often show that a deep dry granular front is followed by a progressively thinner and increasingly watery tail. These features have been captured in recent laboratory flume experiments (Taylor-Noonan et al., J. Geophys. Res.: Earth Surf., vol. 127, 2022, e2022JF006622). In these experiments different initial releas...

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 the patterns in a triangular rotating drum. The results are compared with the experimental patterns formed with bidisperse and tridisperse granular mixtures, and with varying...

Debris flows are particle-fluid mixtures that pose a significant hazard to many communities throughout the world. Bouldery debris flows are often characterized by a deep dry granular flow front, which is followed by a progressively thinner and increasingly watery tail. The formation of highly destructive bouldery wave fronts is usually attributed t...

Geophysical mass flows such as debris flows, dense pyroclastic flows and snow avalanches can self-channelize on shallow slopes. The confinement afforded by formed levees helps to maintain the flow depth, and hence mobility, allowing self-channelized flows to run out significantly farther than unconfined, spreading flows. Levee formation and self-ch...

Classical theories for suspensions have been formulated by starting from the Navier-Stokes equations describing pure liquid flow and then introducing additional dependencies to account for the presence of suspended particles. These models are often accurate for low particle concentrations but have lacked a convincing description of the frictional i...

Debris flows are particle–fluid mixtures that pose a significant hazard to many communities throughout the world. Bouldery debris flows are often characterised by a deep dry granular flow front, which is followed by a progressively thinner and increasingly watery tail. The formation of highly destructive bouldery wave fronts is usually attributed t...

A blunt obstacle in the path of a rapid granular avalanche generates a bow shock (a jump in the avalanche thickness and velocity), a region of static grains upstream of the obstacle, and a grain-free region downstream. Here, it is shown that this interaction is qualitatively altered if the incline on which the avalanche is flowing is changed from s...

The net erosion-deposition rate of an avalanche is fundamental to its dynamics and in determining its growth or decay. Small-scale experiments are performed by releasing a given volume of yellow sand onto a stationary erodible red sand layer on a rough inclined plane. Depending on the erodible layer depth and the slope angle, the avalanche is found...

We studied the segregation of single large intruder particles in monodisperse granular materials. Experiments were carried out in a two-dimensional shear cell using different intruder and media diameters, whose quotient defined a size ratio R that ranged from 1.2 to 3.333. When sheared, the intruders segregated and rotated at different rates, which...

Particles of differing sizes are notoriously prone to segregation in shear driven flows under the action of gravity. This has important implications in many industrial processes, where particle-size segregation can lead to flow problems and reduced product quality, as well as longer product development and start-up times. Particle-size segregation...

When opening a box of mixed nuts, a common experience is to find the largest nuts at the top. This well-known effect is the result of size-segregation where differently sized ‘particles’ sort themselves into distinct layers when shaken, vibrated or sheared. Colloquially this is known as the ‘Brazil-nut effect’. While there have been many studies in...

During the last fifteen years there has been a paradigm shift in the continuum modelling of granular materials; most notably with the development of rheological models, such as the μ(I)-rheology (where μ is the friction and I is the inertial number), but also with significant advances in theories for particle segregation. This paper details theoret...

Grain-scale discrete element simulations of bidisperse mixtures during bedload transport are used to understand, and model, bedload transport and particle-size segregation in granular media. For an initial distribution of fine particles on top of a coarse granular bed, this paper investigates the gravity driven percolation/segregation of the fine p...

Dense granular flows can spontaneously self-channelise by forming a pair of parallel-sided static levees on either side of a central flowing channel. This process prevents lateral spreading and maintains the flow thickness, and hence mobility, enabling the grains to run out considerably further than a spreading flow on shallow slopes. Since levees...

A continuous exchange of particles between an erodible substrate and the granular flow above it occurs during almost all geophysical events involving granular material, such as snow avalanches, debris flows and pyroclastic flows. The balance between eroded and deposited material can drastically influence the runout distance and duration of the flow...

Shallow granular avalanches on slopes close to repose exhibit hysteretic behaviour. For instance, when a steady-uniform granular flow is brought to rest it leaves a deposit of thickness h_stop(ζ) on a rough slope inclined at an angle zeta to the horizontal. However, this layer will not spontaneously start to flow again until it is inclined to a hig...

Size segregation in bedload transport is studied numerically with a coupled fluid-discrete element model. Starting from an initial deposit of small spherical particles on top of a large particle bed, the segregation dynamics of the bed is studied as it is driven by the fluid flow. Focusing on the quasi-static part of the bed, the small particles ar...

Granular flows occur in a wide range of situations of practical interest to industry, in our natural environment and in our everyday lives. This paper focuses on granular flow in the so-called inertial regime, when the rheology is independent of the very large particle stiffness. Such flows have been modelled with the µ(I), Φ(I)-rheology, which pos...

When a layer of static grains on a sufficiently steep slope is disturbed, an upslope-propagating erosion wave, or retrogressive failure, may form that separates the initially static material from a downslope region of flowing grains. This paper shows that a relatively simple depth-averaged avalanche model with frictional hysteresis is sufficient to...

De par le vaste champ d’applications qu’elle offre, l’étude des écoulements granulaires a connu une expansion considérable au cours de ces vingt dernières années, autant du point de vue industriel que géophysique. Ces écoulements granulaires ont une grande influence dans le monde qui nous entoure. Or, différentes instabilités hydrodynamiques peuven...

Rapid shallow granular flows over inclined planes are often seen in nature in the form of avalanches, landslides and pyroclastic flows. In these situations the flow develops an inversely graded (large at the top) particle-size distribution perpendicular to the plane. As the surface velocity of such flows is larger than the mean velocity, the larger...

Small perturbations to a steady uniform granular chute flow can grow as the material moves downslope and develop into a series of surface waves that travel faster than the bulk flow. This roll wave instability has important implications for the mitigation of hazards due to geophysical mass flows, such as snow avalanches, debris flows and landslides...

Through experiments and discrete particle method (DPM) simulations we present evidence for the existence of a recirculating structure, that exists near the front of dense granular avalanches, and is known as a breaking size-segregation (BSS) wave. This is achieved through the study of three-dimensional bidisperse granular flows in a moving-bed chan...

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 segregation mechanism in dense sheared flows. Shallow granular avala...

In recent years considerable progress has been made in the continuum modelling of granular flows, in particular the μ(I)-rheology, which links the local viscosity in a flow to the strain rate and pressure through the non-dimensional inertial number I . This formulation greatly benefits from its similarity to the incompressible Navier–Stokes equatio...

Seven lunar crater sites of granular avalanches are studied utilizing high-resolution images (0.42-1.3 m/pixel) from the Lunar Reconnaissance Orbiter Camera; one, in Kepler crater, is examined in detail. All the sites are slopes of debris extensively aggraded by frictional freezing at their dynamic angle of repose, four in craters formed in basalti...

Snow avalanches are typically initiated on marginally stable slopes with a surface layer of fresh snow that may easily be incorporated into them. The erosion of snow at the front is fundamental to the dynamics and growth of snow avalanches and they may rapidly bulk up, making them much more destructive than the initial release. Snow may also deposi...

Continuum modelling of granular flow has been plagued with the issue of ill-posed equations for a long time. Equations for incompressible, two-dimensional flow based on the Coulomb friction law are ill-posed regardless of the deformation, whereas the rate-dependent $\mu(I)$-rheology is ill-posed when the non-dimensional strain-rate $I$ is too high...

Particle size-segregation can have an important feedback on the bulk flow of geophysical granular avalanches. As a polydisperse material travels downhill the larger particles rise to the surface, where they are preferentially sheared to the flow front. This coarse-rich region experiences a greater resistance to motion and the large particles are sh...

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 the recent depth-averaged ${\it\mu}(I)$ -rheology for dense granular flows to two spatial dimensions, using the principle of...

In light of the successes of the Navier–Stokes equations in the study of fluid flows, similar continuum treatment of granular materials is a long-standing ambition. This is due to their wide-ranging applications in the pharmaceutical and engineering industries as well as to geophysical phenomena such as avalanches and landslides. Historically this...

When a mixture of particles, which differ in both their size and their density, avalanches downslope, the grains can either segregate into layers or remain mixed, dependent on the balance between particle-size and particle-density segregation. In this paper, binary mixture theory is used to generalize models for particle-size segregation to include...

Particles of differing sizes are notoriously prone to segregate, which is a chronic problem in the manufacture of a wide variety of products that are used by billions of people worldwide every day. Segregation is the single most important factor in product non-uniformity, which can lead to significant handling problems as well as complete batches b...

Debris flows can spontaneously develop regular large-amplitude surge waves that are interspersed by periods in which the channel fill is completely stationary. These are important because each individual surge is much more destructive than a steady uniform flow with the same mass flux. In this paper small-scale experiments that exhibit similar beha...

We study a system in which granular matter, flowing down an inclined chute with periodic boundary conditions, organizes itself in a train of roll waves of varying size. Since large waves travel faster than small ones, the waves merge, and their number gradually diminishes. This coarsening process, however, does not generally proceed to the ultimat...

Particle-size segregation commonly occurs in both wet and dry granular free-surface flows through the combined processes of kinetic sieving and squeeze expulsion. As the granular material is sheared downslope, the particle matrix dilates slightly and small grains tend to percolate down through the gaps, because they are more likely than the large g...

The mu(I)-rheology is a nonlinear viscous law, with a strain-rate invariant and pressure-dependent viscosity, that has proved to be effective at modelling dry granular flows in the intermediate range of the inertial number, I. This paper shows how to incorporate the rheology into depth-averaged granular avalanche models. To leading order, the rheol...

Catastrophic dense granular flows, such as occur in rock avalanches, debris flows and pyroclastic flows, move as fully shearing mixtures that have approximately 60 vol.% solids and tend to segregate to form coarse-grained fronts and leveed channels. Levees restrict spreading of unconfined flows and form as coarse particles that become concentrated...

Particle size segregation in granular avalanches occurs due to inter-particle percolation and squeeze expulsion. The general theory for a polydisperse mixture yields a segregation equation for each grain size class. For a three constituent mixture of large, small and medium sized particles there are three segregation equations, one of which can be...

We have carried out laboratory experiments to determine the internal structure of segregating dense granular avalanches and test the recent theoretical predictions of the existence of breaking size-segregation waves [Thornton & Gray, 2008]. Measurements were performed on a quasi-stationary avalanche that flows down an inclined upward-moving conveyo...

Snow avalanches and other hazardous geophysical granular flows, such as debris flows, lahars and pyroclastic flows, often impact on obstacles as they flow down a slope, generating rapid changes in the flow height and velocity in their vicinity. It is important to understand how a granular material flows around such obstacles to improve the design o...

It is important to be able to predict the distance to which a hazardous natural granular flows (e.g. snow slab avalanches, debris-flows and pyroclastic flows) might travel, as this information is vital for accurate assessment of the risks posed by such events. In the high solids fraction regions of these flows the large particles commonly segregate...

Particle-size segregation can have a significant feedback on the bulk motion of granular avalanches when the larger grains experience greater resistance to motion than the fine grains. When such segregation-mobility feedback effects occur the flow may form digitate lobate fingers or spontaneously self-channelize to form lateral levees that enhance...

Data from large-scale debris-flow experiments are combined with modeling of particle-size segregation to explain the formation of lateral levees enriched in coarse grains. The experimental flows consisted of 10 m3 of water-saturated sand and gravel, which traveled ˜80 m down a steeply inclined flume before forming an elongated leveed deposit 10 m l...

We combine data from large-scale debris-flow experiments with modelling of particle-size segregation to explain the formation of lateral levees enriched in coarse grains. The experimental flows consisted of 10 cubic meters of water-saturated sand and gravel, which travelled ~80m down a steeply inclined flume before forming an elongated leveed depos...

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 segregation theories for bi-disperse mixtures and the case of a ternary mixture of large, medium and small particles is investigated. In this case, the general theo...