Instabilities in slowly driven granular packing

Evolution of force networks during stick-slip motion of an intruder in a granular material: Topological measures extracted from experimental data

In quasi-two-dimensional experiments with photoelastic particles confined to an annular region, an intruder constrained to move in a circular path halfway between the annular walls experiences stick-slip dynamics. We discuss the response of the granular medium to the driven intruder, focusing on the evolution of the force network during sticking periods. Because the available experimental data do not include precise information about individual contact forces, we use an approach developed in our previous work [Basak et al., J. Eng. Mech. 147, 04021100 (2021)0733-939910.1061/(ASCE)EM.1943-7889.0002003] based on networks constructed from measurements of the integrated strain magnitude on each particle. These networks are analyzed using topological measures based on persistence diagrams, revealing that force networks evolve smoothly but in a nontrivial manner throughout each sticking period, even though the intruder and granular particles are stationary. Characteristic features of persistence diagrams show identifiable slip precursors. In particular, the number of generators describing the structure and complexity of force networks increases consistently before slips. Key features of the dynamics are similar for granular materials composed of disks or pentagons, but some details are consistently different. In particular, we find significantly larger fluctuations of the measures computed based on persistence diagrams and, therefore, of the underlying networks, for systems of pentagonal particles.

In-depth influence of the top surface fabrication of a bead packing

Packings of beads confined in slowly tilted containers with a top free surface are commonly used in laboratory experiments to model natural grain avalanches and better understand and predict critical events from optical measurements of the surface activity. To that aim, after reproducible packing preparations, the present paper focuses on the effects of the surface fabrication, which can be scraped or soft leveled, on both the avalanche stability angle and the dynamic of precursory events for glass beads of 2-mm diameter. A depth effect of a scraping operation is highlighted by considering different packing heights and inclination speeds.

Stochastic methods for slip prediction in a sheared granular system

We consider a sheared granular system experiencing intermittent dynamics of stick-slip type via discrete element simulations. The considered setup consists of a two-dimensional system of soft frictional particles sandwiched between solid walls, one of which is exposed to a shearing force. The slip events are detected using stochastic state space models applied to various measures describing the system. The amplitudes of the events spread over more than four decades and present two distinctive peaks, one for the microslips and the other for the slips. We show that the measures describing the forces between the particles provide earlier detection of an upcoming slip event than the measures based solely on the wall movement. By comparing the detection times obtained from the considered measures, we observe that a typical slip event starts with a local change in the force network. However, some local changes do not spread globally over the force network. For the changes that become global, we find that their size strongly influences the further behavior of the system. If the size of a global change is large enough, then it triggers a slip event; if it is not, then a much weaker microslip follows. Quantification of the changes in the force network is made possible by formulating clear and precise measures describing their static and dynamic properties.

On intermittency in sheared granular systems

We consider a system of granular particles, modeled by two dimensional frictional soft elastic disks, that is exposed to externally applied time-dependent shear stress in a planar Couette geometry. We concentrate on the external forcing that produces intermittent dynamics of stick-slip type. In this regime, the top wall remains almost at rest until the applied stress becomes sufficiently large, and then it slips. We focus on the evolution of the system as it approaches a slip event. Our main finding is that there are two distinct groups of measures describing system behavior before a slip event. The first group consists of global measures defined as system-wide averages at a fixed time. Typical examples of measures in this group are averages of the normal or tangent forces acting between the particles, system size and number of contacts between the particles. These measures do not seem to be sensitive to an approaching slip event. On average, they tend to increase linearly with the force pulling the spring. The second group consists of the time-dependent measures that quantify the evolution of the system on a micro (particle) or mesoscale. Measures in this group first quantify the temporal differences between two states and only then aggregate them to a single number. For example, Wasserstein distance quantitatively measures the changes of the force network as it evolves in time while the number of broken contacts quantifies the evolution of the contact network. The behavior of the measures in the second group changes dramatically before a slip event starts. They increase rapidly as a slip event approaches, indicating a significant increase in fluctuations of the system before a slip event is triggered.

Robust experimental study of avalanche precursory events based on reproducible cycles of grain packing destabilizations

Quasi-periodic collective displacements of grains at the free surface of a tilted grain packing constitute precursors of granular avalanches. Laboratory experiments are commonly performed by slowly tilting the packing from 0° to the maximal stability angle θA. In these conditions, the number of precursors is too small to assess reproducible and robust statistical analyses of the precursor activity. To go beyond this limitation, we have developed a specific experimental protocol consisting of tilting the packing with successive oscillation cycles. We use a high-resolution optical camera and process the images of the packing free surface to identify precursory events during many consecutive cycles of a single packing. We observe the same behavior for all half-cycles, forth and back: appearance of the first precursors after the same variation of inclination, exponential evolution of the weak surface activity for the first precursors and linear growth of stronger surface activity for the following ones. The experimental protocol provides both reproducible precursor measurements based on large sample statistical inferences and a quasi-stationary state after one full-cycle. This approach is very promising for highlighting the effects of external parameters, including humidity and packing geometry.

Dynamic behavior of humid granular avalanches: Optical measurements to characterize the precursor activity

Laboratory study of slope stability of granular media remains a challenge for modeling, understanding, and predicting natural hazards, such as avalanches and landslides, precursory signs of which are controlled by numerous physical parameters. The present work focuses on the impact of the humidity, in the range of 40-90%, on the stability of monodisperse dense packings of spherical beads. The beads are in a transparent box that is slowly and continuously tilted and allows simultaneous top and lateral optical measurements of global displacements of grains at the surface, defined as precursors. Humidity increases the cohesion between the grains. By performing successive avalanches that destabilize deeper granular layers, we assess the role of the exposure time to the high humidity rates in the diffusion process to reach the hygroscopic equilibrium inside the packing. We highlight an increase of the stability and first precursor angles, associated to a constant angle increment between two consecutive precursors, with a dependency with both the diameter (0.2,0.5, and 0.75 mm) and the material (glass and polystyrene) of the grains.

Breakdown of Scaling and Friction Weakening in Intermittent Granular Flow

Many materials are produced, processed and stored as grains, while granularity of matter can be crucial in triggering potentially catastrophic geological events like landslides, avalanches and earthquakes. The response of grain assemblies to shear stress is therefore of utmost relevance to both human and natural environment. At low shear rate a granular system flows intermittently by distinct avalanches. In such state the avalanche velocity in time is expected to follow a symmetrical and universal average behavior, whose dependence on the slip size reduces to a scale factor. Analyzing data from long lasting experiments, we observe a breakdown of this scaling: While in short slips velocity shows indeed a self-similar and symmetric profile, it does not in long slips. The investigation of frictional response in these different regimes evidences that this breakdown can be traced back to the onset of a friction weakening, which is of dynamical origin and can amplify instabilities exactly in this critical state, the most frequent state for natural hazards.

Avalanche precursors in a frictional model

We present a one-dimensional numerical model based on elastically coupled sliders on a frictional incline of variable tilt. This very simple approach makes it possible to study the precursors to the avalanche and to provide a rationalization of different features that have been observed in experiments. We provide a statistical description of the model leading to master equations describing the state of the system as a function of the angle of inclination. Our central results are the reproduction of large-scale regular events preceding the avalanche, on the one hand, and an analytical approach providing an internal threshold for the outbreak of rearrangements before the avalanche in the system, on the other hand.

Spatially resolved measurements of micro-deformations in granular materials using diffusing wave spectroscopy

This article is a tutorial on the practical implementation of a method of measurement of minute deformations based on multiple scattering. This technique has been recently developed and has proven to give new insights into the spatial repartition of strain in a granular material. We provide here the basics to understand the method by giving a synthetic review on diffusing wave spectroscopy and multiple scattering in granular materials. We detail a simple experiment using standard lab equipment to pedagogically demonstrate the implementation of the method. Finally we give a few examples of measurements that have been obtained in other works to discuss the potential of the method.

Polydirectional stability of granular matter

We investigate jammed granular matter in a slowly rotating drum partially filled with granular material and find a state of polydirectional stability. In this state, the material responds elastically to small stresses in a wide angular interval while it responds by plastic deformation when subjected to small stresses outside this interval of directions. We describe the evolution of the granulate by means of a rate equation and find quantitative agreement with the experiment. The state of polydirectional stability complements the fragile state, where the material responds elastically to small applied stresses only in a certain direction but even very small stresses in any other direction would lead to plastic deformations. Similar to fragile matter, polydirectionally stable matter is created in a dynamic process by self-organization.

Experimental investigation of plastic deformations before a granular avalanche

We present an experimental study of the deformation inside a granular material that is progressively tilted. We investigate the deformation before the avalanche with a spatially resolved diffusive wave spectroscopy setup. At the beginning of the inclination process, we first observe localized and isolated events in the bulk, with a density which decreases with the depth. As the angle of inclination increases, series of microfailures occur periodically in the bulk, and finally a granular avalanche takes place. The microfailures are observed only when the tilt angles are larger than a threshold angle much smaller than the granular avalanche angle. We have characterized the density of reorganizations and the localization of microfailures. We have also explored the effect of the nature of the grains, the relative humidity conditions, and the packing fraction of the sample. We discuss those observations in the framework of the plasticity of granular matter. Microfailures may then be viewed as the result of the accumulation of numerous plastic events.

Avalanche dynamics on a rough inclined plane

The avalanche behavior of gravitationally forced granular layers on a rough inclined plane is 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 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 nonspherical grains, avalanches are faster, bigger, and overturning in the sense that individual particles have down-slope speeds u p that exceed the front speed uf as compared with avalanches of spherical glass beads that are quantitatively slower and 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 tan theta r where theta r is the bulk angle of repose, or with increasing beta P, the slope of the depth averaged flow rule, where both theta r and beta 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.

Rearrangements in a two-dimensional packing of disks

Several aspects of the dynamics of a granular two-dimensional (2D) packing of disks slowly tilted until the system loses stability and an avalanche takes place are discussed. The evolution of the system, constructed with monodisperse disks placed on a thin cell, is studied by image analysis. As in the 3D case (packing of spheres), the system undergoes several rearrangements of different magnitude before the avalanche takes place. For thick systems, not only are small rearrangements detected but also displacements of large clusters of disks are observed in the bulk and on the free surface of the packing. In particular, characteristic angles and the avalanche mass were determined for samples of different heights. On thick systems, velocity fields of large rearrangements are presented and changes in the internal structure of the packing produced by these rearrangements are analyzed. It is found that the main effects of rearrangements is to increase the disorder of the system. Also, as the disorder of the system increases its stability threshold decreases.