Rough Incline Research Articles

Cohesion and aggregates in unsaturated wet granular flows down a rough incline

Multi-phase flows, encountered in nature or in industry, exhibit non-trivial rheological properties, which we attempt to better understand thanks to model materials and appropriate rheometers. Unsaturated wet granular flows down a rough inclined plane turn out to be steady and uniform for a wide range of parameters, despite the cohesion and the grain aggregates. The cohesive Mohr–Coulomb yield criterion extended to inertial granular flows, with a cohesion stress dependent on the liquid content and an internal friction coefficient dependent on the inertial number, allows for predictions in good agreement with our experimental measurements, when one introduces a grain aggregate size, which defines the appropriate length and relaxation time scales in the inertial number. We found that the grain aggregate size depends not monotonically on the liquid content and does not scale with the cohesion length induced by the cohesion stress, due to the non-trivial distribution of the liquid within the granular material.

Characterizing the Effects of Friction Angles on Earth Pressures in the Flow of Granular Mass along Down-slope and Cross-slope in a Rough Incline

The tendency of the sliding mass to deform or deposit during the flow is dictated by the earth pressure coefficient (K) in the dynamics of a finite mass of cohesionless granular material discharged from rest on a rough inclined plane. When the flow’s velocities along the x and y-axes are decreasing, K=K_(y pas)^(x pas), the flow becomes convergent, and depositional behavior appears. On the other hand, if the flow velocity is increasing along x-axis but decreasing along y-axis, 〖K=K〗_(y pas)^(x act) and the flow is divergent and hence mass spreads. For K=K_(y act)^(x pas) and K=K_(y pas)^(x pas), the flow is neither convergent nor divergent, it remains constant throughout the domain. The mathematical relationship provided here and the associated 2D and 3D representation demonstrate how the internal angle (ϕ) and basal angle (δ) of frictions have a significant impact on the earth pressure coefficient in the dynamics of dry granular mass along a rough plane. The mathematical correlations for the soil mechanics are discussed along with these coefficients.

Subcritical and supercritical granular flow around an obstacle on a rough inclined plane

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 smooth to rough. On a rough incline, the friction between the grains and the incline depends on the flow thickness and speed, which allows both rapid (supercritical) and slow (subcritical) steady uniform avalanches. For supercritical experimental flows, the material is diverted around a blunt obstacle by the formation of a bow shock and a static dead zone upstream of the obstacle. Downslope, a grain-free vacuum region forms, but, in contrast to flows on smooth beds, static levees form at the boundary between the vacuum region and the flow. In slower, subcritical, flows the flow is diverted smoothly around the dead zone and the obstacle without forming a bow shock. After the avalanche stops, signatures of the dead zone, levees and (in subcritical flows) a deeper region upslope of the obstacle are frozen into the deposit. To capture this behaviour, numerical simulations are performed with a depth-averaged avalanche model that includes frictional hysteresis and depth-averaged viscous terms, which are needed to accurately model the flowing and deposited regions. These results may be directly relevant to geophysical mass flows and snow avalanches, which flow over rough terrain and may impact barriers or other infrastructure.

Adaptive tensegrity locomotion: Controlling a compliant icosahedron with symmetry-reduced reinforcement learning

Tensegrity robots, which are prototypical examples of hybrid soft–rigid robots, exhibit dynamical properties that provide ruggedness and adaptability. They also bring about, however, major challenges for locomotion control. Owing to high dimensionality and the complex evolution of contact states, data-driven approaches are appropriate for producing viable feedback policies for tensegrities. Guided policy search (GPS), a sample-efficient hybrid framework for optimization and reinforcement learning, has previously been applied to generate periodic, axis-constrained locomotion by an icosahedral tensegrity on flat ground. Varying environments and tasks, however, create a need for more adaptive and general locomotion control that actively utilizes an expanded space of robot states. This implies significantly higher needs in terms of sample data and setup effort. This work mitigates such requirements by proposing a new GPS -based reinforcement learning pipeline, which exploits the vehicle’s high degree of symmetry and appropriately learns contextual behaviors that are sustainable without periodicity. Newly achieved capabilities include axially unconstrained rolling, rough terrain traversal, and rough incline ascent. These tasks are evaluated for a small variety of key model parameters in simulation and tested on the NASA hardware prototype, SUPERball. Results confirm the utility of symmetry exploitation and the adaptability of the vehicle. They also shed light on numerous strengths and limitations of the GPS framework for policy design and transfer to real hybrid soft–rigid robots.

Evidence of reverse and intermediate size segregation in dry granular flows down a rough incline.

In a dry granular flow, size segregation had been shown to behave differently for a mixture containing a few large particles with a size ratio above 5 [N. Thomas, Phys. Rev. E 62, 961 (2000)1063-651X10.1103/PhysRevE.62.961]. For moderately large size ratios, large particles migrate to an intermediate depth in the bed: this is called "intermediate segregation." For the largest size ratios, large particles migrate down to the bottom of the flow: this is called "reverse segregation," in contrast with surface segregation. As the reversal and intermediate depth values depend on the fraction of particles, this numerical study mainly uses one single large tracer. Small fractions of large beads are also computed showing the link between single tracer behavior and collective segregation process. For each device (half-filled rotating tumbler and rough plane), two (2D) and three (3D) dimensional cases are distinguished. In the tumbler, the trajectories of a large tracer show that it reaches a constant depth during the flowing phase. For large size ratios, this depth is intermediate. A progressive sinking of the depth is obtained when the size ratio is increased. The largest size ratios correspond to tracers being at the bottom of the flowing layer. All 3D simulation results are in quantitative agreement with the experimental surface, intermediate, and reverse-segregation results. In the flow down a rough incline, a large tracer reaches an equilibrium depth during flow. For large size ratios, the depth is inside the bed, at an intermediate position, and for the largest size ratios, this depth is reverse, located near the bottom. Results are slightly different for a thin or a thick flow. For 3D thick flows, the reversal between surface and bottom positions occurs within a short range of size ratios: no tracer stabilizes near half-height and two reachable intermediate depth layers exist, below the surface and above the bottom reverse layer. For 3D thin flows, all intermediate depths are reachable by a tracer, depending on the size ratio. The numerical study of larger fractions of tracers (5% or 10%) shows the three segregation patterns (surface, intermediate, reverse) corresponding to the three types of equilibrium depth. The reversal is smoother than for a single tracer, and happens around the size ratio 4.5, in good agreement with experiments.

Granular front for flow down a rough incline: about the value of the shape factor in depths averaged models

The thin layer (or Boundary Layer scaling) approximation of the Navier Stokes equation with μ (I ) rheology for dry granular flows over an inclined plate is presented. It is called “Granular RNS/P” (Reduced Navier Stokes/ Prandtl). Integrated over the depth, it gives the classical depth averaged equations (Shallow Water type equations, popularized by Savage Hutter). But the process of depth averaging needs hypothesis on the velocity shape profile trough a “shape factor coefficient”. In the case of the displacement of the front of an avalanche down a rough incline, we present comparisons of “Granular RNS/P” simulations versus depth averaged model (which compares well with experimental data). One conclusion is that the shape factor goes from 5/4, the Bagnold value, to a unit value, corresponding to a flat velocity profile, in a region very close to the front of the avalanche.

Stopping dynamics of a steady uniform granular flow over a rough incline

Granular material flowing on complex topographies are ubiquitous in industrial and geophysical situations. Even model granular flows are difficult to understand and predict. Recently, the frictional rheology μ (I ) -describing the ratio of the shear stress to the normal stress as a function of the inertial number I , that compares inertial and confinement effects- allows unifying different configurations of granular flows. However it does not succeed in describing some phenomenologies, such as creep flow, deposit height, … Is it attributable to the rheology, to non-local effects, ...? Here, we consider a thin layer of grains flowing steadily and uniformly on a rough incline, when the input mass flow rate is suddenly stopped. We focus on the arrest dynamics by using both experimental and numerical approaches. We measure the height and surface velocities of the granular layer during the long-time stopping dynamics and we compare our experimental results with computations of depthaveraged equations for a fluid of rheology μ (I ).

Asymptotic analysis for the propagation and arresting process of a finite dry granular mass down a rough incline

This work presents an asymptotic analysis for the propagation and arresting process of a two-dimensional finite granular mass down a rough incline in a shallow configuration. Bulk shear stress and arresting mechanism are formulated according to the coherence length model that considers momentum transport at a length scale over which grains are spatially correlated. A Bagnold-like streamwise velocity and a non-zero transverse velocity are solved and integrated into a surface kinematic condition to give an advection–diffusion equation for the bulk surface profile, $h(x,t)$, that is solved using the matched asymptotic method. These flow solutions are further employed to determine composite solutions for a flow-front trajectory and a local coherence length, $l(x,t)$, which reveals smooth growth of $h(x,t)$ and $l(x,t)$ from zero at the propagating front with $l(x,t)\ll h(x,t)$. At the rear, $h(x,t)$ vanishes but $l(x,t)$ asymptotes to a constant that depends on inclination angle. According to the arresting mechanism, the location where $l(x,t)\sim h(x,t)$ is solved to the leading order to locate the deposition front so that its propagation dynamics can be derived. A finite flow arrest time, $T_{d}$, and the corresponding finite run-out distance, $L_{d}$, are evaluated when all the flowing mass has passed the deposition front and are employed to construct a modified front trajectory with the deposition effect. The predicted run-out distance and front trajectory profile compare reasonably well with experimental data in the literature on inclinations at angles higher than the material repose angle.

On the front shape of an inertial granular flow down a rough incline

Granular material flowing on complex topographies are ubiquitous in industrial and geophysical situations. In this paper, we study the small-scale experiment of a granular layer flowing on a rough incline. The shape of the granular front is solved analytically by using depth-averaged mass and momentum equations with a fractional expression for the frictional rheology μ(I), which is a generalization of Gray and Ancey [“Segregation, recirculation and deposition of coarse particles near two-dimensional avalanche fronts,” J. Fluid Mech. 629, 387 (2009)]. Unlike previous studies where a “plug flow dynamics” is assumed, a free shape factor α describing the vertical velocity profile is taken into account. The effect of inertia and shear rate on the front profile is evidenced through the introduction of the Froude number and the shape factor α. The analytical predictions are compared to experimental results published by Pouliquen [“On the shape of granular fronts down rough inclined planes,” Phys. Fluids 11, 1956 (1999)] and with our new experimental data obtained at higher Froude numbers. A good agreement between theory and experiments is found for α = 5/4, corresponding to a Bagnold-like velocity profile. However, we observe a systematic deviation near the head of the front where the height vanishes: the theory predicts a continuous precursor layer, while a grain-free region is observed experimentally. This suggests that the vertical velocity profile is not uniform inside the front, but the shape factor α tends to 1 near the head of the front. This raises questions about the vertical velocity profile in granular flows and about the expression of the rheological function μ(I) and its calibration from experimental data.

Stability of a granular layer on an inclined “fakir plane”

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.

Velocity fields of granular flows down a rough incline: a DEM investigation

This paper describes a statistical method to explore the velocity profiles of granular flows down rough inclines. Using 3D Discrete Element Method (DEM), granular material is released from a box onto a slope and allowed to flow indefinitely. Fluctuating velocity fields are observed, as particle motions become more dynamic and agitated. Linear regression is used to decompose the fluctuating velocity field into a best-fit velocity profile and a fluctuating component. Analysis shows that the slope inclination has a considerable influence on the rheology, in terms of both the fluctuating velocity and the shear rate of the flow.

Flow rule of dense granular flows down a rough incline

We present experimental findings on the flow rule for granular flows on a rough inclined plane using various materials, including sand and glass beads of various sizes and four types of copper particles with different shapes. We characterize the materials by measuring hs (the thickness at which the flow subsides) as a function of the plane inclination theta on various surfaces. Measuring the surface velocity u of the flow as a function of flow thickness h, we find that for sand and glass beads the Pouliquen flow rule u/sqrt[gh] approximately betahhs provides reasonable but not perfect collapse of the u(h) curves measured for various theta and mean particle diameter d. Improved collapse is obtained for sand and glass beads by using a recently proposed scaling of the form u/sqrt[gh]=betahtan2theta/hstan2theta1 where theta1 is the angle at which the hs(theta) curves diverge. Measuring the slope beta for ten different sizes of sand and glass beads, we find a systematic, strong increase of beta with the divergence angle theta1 of hs. Copper materials with different shapes are not well described by either flow rule with u approximately h3/2.

Rapid granular flows on a rough incline: Phase diagram, gas transition, and effects of air drag

We report experiments on the overall phase diagram of granular flows on an incline with emphasis on high inclination angles where the mean layer velocity approaches the terminal velocity of a single particle free falling in air. The granular flow was characterized by measurements of the surface velocity, the average layer height, and the mean density of the layer as functions of the hopper opening, the plane inclination angle, and the downstream distance x of the flow. At high inclination angles the flow does not reach an x -invariant steady state over the length of the inclined plane. For low volume flow rates, a transition was detected between dense and very dilute (gas) flow regimes. We show using a vacuum flow channel that air did not qualitatively change the phase diagram and did not quantitatively modify mean flow velocities of the granular layer except for small changes in the very dilute gaslike phase.

Segregation kinetics in the rapid gravity flow of granular materials

An experimental analytical method for determining the kinetic segregation coefficient in the rapid gravity flow of a granular material down a rough incline is proposed. It is found that it is possible to predict the velocity of transverse displacement of individual large and small particles in the rapid gravity flow using a single kinetic segregation coefficient for different particle sizes and structural and kinematic characteristics of the flow. A previously proposed equation of segregation kinetics is refined, and its predictive power is analyzed.

Rapid Gravity Flow of a Granular Medium

An experimental study is performed to analyze the equation of state of a granular medium, which relates its dilatancy, shear rate, and pressure by an analogy between a granular medium under rapid shear and a dense gas. A method is developed for the contactless determination of the solid-phase concentration distribution in the two-dimensional flow of a granular medium using x-ray analysis. The method is used to explore the concentration profiles in rapid gravity flows of ceramic particles down a rough incline. The adequacy of the equation of state of a granular medium under rapid shear and for unordinary properties of the gravity flow down a rough incline is directly confirmed.

Sliding susceptibility of a rough cylinder on a rough inclined perturbed surface

A susceptibility function χ( L) is introduced to quantify some aspects of the intermittent stick-slip dynamics of a rough metallic cylinder of length L on a rough metallic incline submitted to small controlled perturbations and maintained below the angle of repose. This problem is studied from the experimental point of view and the observed power-law behavior of χ( L) is justified through the use of a general class of scaling hypotheses.

How transversal fluctuations affect the friction of a particle on a rough incline

We present molecular-dynamics simulations of a sphere moving down an inclined plane consisting of similar spheres of smaller size. For a certain range of inclinations, the sphere moves down the plane with a mean velocity ${\overline{v}}_{x}\ensuremath{\ne}0.$ We investigate the properties of the motion in this steady state and the limits for its existence for a certain set of parameters. It is found that the steady-state velocity of the particle is independent of material properties and depends only on the geometry of the system. This means that the particle experiences an effective velocity-dependent friction force, with an effective ``viscosity'' determined only by the geometry. The fluctuations of the motion, however, can depend on the coefficient of restitution ${e}_{n}.$ For example, the diffusion coefficient ${D}_{x}$ is influenced by ${e}_{n},$ but hardly depends on the roughness of the plane, while for ${D}_{y}$ the reverse is true. The range of the inclination angle and the roughness for which a steady state exists also depends on ${e}_{n}.$ We discuss how these results can be understood by considering the details of the motion.

The motion of a finite mass of granular material down a rough incline

Rock, snow and ice masses are often dislodged on steep slopes of mountainous regions. The masses, which typically are in the form of innumerable discrete blocks or granules, initially accelerate down the slope until the angle of inclination of the bed approaches the horizontal and bed friction eventually brings them to rest. The present paper describes an initial investigation which considers the idealized problem of a finite mass of material released from rest on a rough inclined plane. The granular mass is treated as a frictional Coulomb-like continuum with a Coulomb-like basal friction law. Depth-averaged equations of motion are derived; they bear a superficial resemblance to the nonlinear shallow-water wave equations. Two similarity solutions are found for the motion. They both are of surprisingly simple analytical form and show a rather unanticipated behaviour. One has the form of a pile of granular material in the shape of a parabolic cap and the other has the form of anM-wave with vertical faces at the leading and trailing edges. The linear stability of the similarity solutions is studied. A restricted stability analysis, in which the spread is left unperturbed shows them to be stable, suggesting that mathematically both are possible asymptotic wave forms. Two numerical finite-difference schemes, one of Lagrangian, the other of Eulerian type, are presented. While the Eulerian technique is able to reproduce theM-wave similarity solution, it appears to give spurious results for more general initial conditions and the Lagrangian technique is best suited for the present problem. The numerical predictions are compared with laboratory experiments of Huber (1980) involving the motion of gravel released from rest on a rough inclined plane. Although in these experiments the continuum approximation breaks down at large times when the gravel layer is only a few particle diameters thick, the general features of the development of the gravel mass are well predicted by the numerical solutions.