Avalanche behavior of gravitationally-forced granular layers on a rough inclined plane are investigated experimentally for different materials and for a variety of grain shapes ranging from spherical beads to highly anisotropic particles with dendritic shape. We measure the front velocity, area and the height of many avalanches and correlate the motion with the area and height. We also measure the avalanche profiles for several example cases. As the shape irregularity of the grains is increased, there is a dramatic qualitative change in avalanche properties. For rough non-spherical grains, avalanches are faster, bigger and overturning in the sense that individual particles have down-slope speeds $u_p$ that exceed the front speed $u_f$ as compared with avalanches of spherical glass beads that are quantitatively slower, smaller and where particles always travel slower than the front speed. There is a linear increase of three quantities i) dimensionless avalanche height ii) ratio of particle to front speed and iii) the growth rate of avalanche speed with increasing avalanche size with increasing $\tanθ_r$ where $θ_r$ is the bulk angle of repose, or with increasing $β_P$, the slope of the depth averaged flow rule, where both $θ_r$ and $β_P$ reflect the grain shape irregularity. These relations provide a tool for predicting important dynamical properties of avalanches as a function of grain shape irregularity. A relatively simple depth-averaged theoretical description captures some important elements of the avalanche motion, notably the existence of two regimes of this motion.
We report experimental measurements of avalanche behavior of thin granular layers on an inclined plane for low volume flow rate. The dynamical properties of avalanches were quantitatively and qualitatively different for smooth glass beads compared to irregular granular materials such as sand. Two scenarios for granular avalanches on an incline are identified and a theoretical explanation for these different scenarios is developed based on a depth-averaged approach that takes into account the differing rheologies of the granular materials.
The problem of the spreading of a granular mass released at the top of a rough inclined plane was investigated. We experimentally measure the evolution of the avalanche from the initiation up to the deposit using a Moiré image processing technique. The results are quantitatively compared with the prediction of an hydrodynamic model based on depth averaged equations. In the model, the interaction between the flowing layer and the rough bottom is described by a non trivial friction force whose expression is derived from measurements on steady uniform flows. We show that the spreading of the mass…
A simple geometrical model is presented for the gravity-driven motion of a single particle on a rough inclined surface. Adopting a simple restitution law for the collisions between the particle and the surface, we arrive at a model in which the dynamics is described by a one-dimensional map. This map is studied in detail and it is shown to exhibit several dynamical regimes (steady state, chaotic behavior, and accelerated motion) as the model parameters vary. A phase diagram showing the corresponding domain of existence for these regimes is presented. The model is also found to be in good quali…
We perform a laboratory-scale experiment of submarine avalanches on a rough inclined plane. A sediment layer is prepared and thereafter tilted up to an angle lower than the spontaneous avalanche angle. The sediment is scrapped until an avalanche is triggered. Based on the stability diagram of the sediment layer, we investigate different structures for the avalanche front dynamics. First we see a straight front descending the slope, and then a transverse instability occurs. Eventually, a fingering instability shows up similar to rivulets appearing for a viscous fluid flowing down an incline. Th…
Combining X-ray tomography with simultaneous shear force measurement, we investigate shear-induced granular avalanches using spherical particles with different surface roughness. We find that systems consisting of particles with large surface roughness display quasi-periodic avalanches interrupted by crackling-like small ones. In contrast, systems consisting of particles with small roughness display no detectable avalanches. The stress drop of quasi-periodic avalanche shows a linear relation with the correlation length of particle non-affine displacement, suggesting that roughness enhances int…
We present a two-dimensional system which exhibits features of self-organized criticality. The avalanches which occur on the surface of a pile of rice are found to exhibit finite size scaling in their probability distribution. The critical exponents are $τ$ = 1.21(2) for the avalanche size distribution and $D$ = 1.99(2) for the cut-off size. Furthermore the geometry of the avalanches is studied leading to a fractal dimension of the active sites of $d_B$ = 1.58(2). Using a set of scaling relations, we can calculate the roughness exponent $α= D - d_B$ = 0.41(3) and the dynamic exponent $z = D(2 …
We study the flow of equal-volume binary granular mixtures of spheres and dumbbells with different aspect ratios down a rough inclined plane, using the discrete element method. We consider two types of mixtures -- in the first type the particles of the two species have equal volume but different aspect ratios (EV) and in the second type they have variable volumes and aspect ratios (VV). We also use mixtures of spheres of two different sizes (SS) with the same volume ratios as in the mixtures of the second type, as the base case. Based on the study of Guillard, Forterre and Pouliquen [\textit{J…
Recent studies have pointed out the importance of the basal friction on the dynamics of granular flows. We present experimental results on the influence of the roughness of the inclined plane on the dynamics of a monodisperse dry granular flow. We found experimentally that it exists a maximum of the friction for a given relative roughness. This maximum is shown to be independent of the angle of the slope. This behavior is observed for four planes with different bump sizes (given by the size of the beads glued on the plane) from 200 microns to 2 mm. The relative roughness corresponding to the m…
We performed computer simulations based on a two-dimensional Distinct Element Method to study granular systems of magnetized spherical particles. We measured the angle of repose and the surface roughness of particle piles, and we studied the effect of magnetization on avalanching. We report linear dependence of both angle of repose and surface roughness on the ratio $f$ of the magnetic dipole interaction and the gravitational force (\emph{interparticle force ratio}). There is a difference in avalanche formation at small and at large interparticle force ratios. The transition is at $f_c \approx…
The rheology of granular particles in an inclined plane geometry is studied using molecular dynamics simulations. The flow--no-flow boundary is determined for piles of varying heights over a range of inclination angles $θ$. Three angles determine the phase diagram: $θ_{r}$, the angle of repose, is the angle at which a flowing system comes to rest; $θ_{m}$, the maximum angle of stability, is the inclination required to induce flow in a static system; and $θ_{max}$ is the maximum angle for which stable, steady state flow is observed. In the stable flow region $θ_{r}<θ<θ_{max}$, three flow regime…
We present here experimental results on the effect of a forest of cylinder obstacles (nails) on the stability of a granular layer over a rough incline, in a so-called "fakir plane" configuration. The nail forest is found to increase the stability of the layer, the more for the densest array, and such an effect is recovered by a simple model taking into account the additional friction force exerted by the pillar forest onto the granular layer.
We report an experimental, numerical and theoretical study of the motion of a ball on a rough inclined surface. The control parameters are $D$, the diameter of the ball, $θ$, the inclination angle of the rough surface and $E_{ki}$, the initial kinetic energy. When the angle of inclination is larger than some critical value, $θ>θ_{T}$, the ball moves at a constant average velocity which is independent of the initial conditions. For an angle $θ< θ_{T}$, the balls are trapped after moving a certain distance. The dependence of the travelled distances on $E_{ki}$, $D$ and $θ$. is analysed. The exis…
We study the driven collective dynamics of a colloidal monolayer sedimentating down an inclined plane. The action of the gravity force parallel to the bottom wall creates a flow around each colloid, and the hydrodynamic interactions among the colloids accelerate the sedimentation as the local density increases. This leads to the creation of a universal "triangular" inhomogeneous density profile, with a traveling density shock at the leading front moving in the downhill direction. Unlike density shocks in a colloidal monolayer driven by applied torques rather than forces [Phys. Rev. Fluids, 2(9…
Flows of granular media down a rough inclined plane demonstrate a number of nonlocal phenomena. We apply the recently proposed nonlocal granular fluidity model to this geometry and find that the model captures many of these effects. Utilizing the model's dynamical form, we obtain a formula for the critical stopping height of a layer of grains on an inclined surface. Using an existing parameter calibration for glass beads, the theoretical result compares quantitatively to existing experimental data for glass beads. This provides a stringent test of the model, whose previous validations focused …
Elastic systems, such as magnetic domain walls, density waves, contact lines, and cracks, are all pinned by substrate disorder. When driven, they move via successive jumps called avalanches, with power law distributions of size, duration and velocity. Their exponents, and the shape of an avalanche, defined as its mean velocity as function of time, have recently been studied. They are known approximatively from experiments and simulations, and were predicted from mean-field models, such as the Brownian force model (BFM), where each point of the elastic interface sees a force field which itself …
The motion of a ruck in a rug is used as an analogy to explain the role of dislocations in the deformation of crystalline solids. We take the analogy literally and study the shape and motion of a bump, wrinkle or ruck in a thin sheet in partial contact with a rough substrate in a gravitational field. Using a combination of experiments, scaling analysis and numerical solutions of the governing equations, we first quantify the static shape of a ruck on a horizontal plane. When the plane is inclined, the ruck becomes asymmetric and moves by rolling only when the the inclination of the plane reach…
Experiments on dry granular matter flowing down an inclined plane are performed in order to study the dynamics of dense pyroclastic flows. The plane is rough, and always wider than the flow, focusing this study on the case of laterally unconfined (free boundary) flows.We found that several flow regimes exist depending on the input fluxand on the inclination of the plane. Each flow regime corresponds to a particular morphology of the associated deposit. In one of these regimes, the flow reaches a steady state, and the deposit exhibits a levee/channel morphology similar to those observed on smal…
