Session LM: Sheared Granular Matter and Granular Collapse

The response of dense dry granular material to the shear reversal

We have performed two dimensional granular experiments under pure shear using bidisperse photo-elastic disks. Starting from a stress free state, a square box filled with granular particles is subject to shear. The forward shears involved various number of steps, leading to maximum strains between 0.1 and 0.3. The area is kept constant during the shear. The network of force chains gradually built up as the strain increased, leading to increased pressure and shear stress. Reverse shear was then applied to the system. Depending on the initial packing fraction and the strain at which the shear is reversed, the force chain network built prior to the shear reversal may be destroyed completely or partially destroyed. Following the force chain weakening, when the reserve shear is continuously applied to the system, there is a force chain strengthening. Following each change of the system, contact forces of individual disks were measured by applying an inverse algorithm. We also kept track of the displacement and angle of rotation of every particle from frame to frame. We present the results for the structure failure and reconstruction during shear reversals. We also present data for stresses, contact force distributions and other statistical measures.   

Slow Shear of Non-Spherical Particles

We probe the microscopic properties of granular materials consisting of ellipsoidal particles. The aim of these studies is to understand the role played by particle shape. The experiments are carried out in 2D and consist of pure shear with maximum strains up to 0.3, followed by reverse shear. The particles are made of a photoelastic material, so that we can determine particle-scale forces as well as particle displacements, rotations and orientations. We present results for the stresses, strains, contact forces, etc.   

Boundary stresses due to sheared granular mixtures

Models for stress produced by a sheared granular layer indicate stress should scale with particle size (such as the classic model suggested by Bagnold in 1954 where stress scales as particle size squared [1]). However, it is not clear how this particle-size scaling should be modified for a mixture of different-sized particles, important for applications such as debris flows. We investigate external stresses generated by a dense sheared granular mixture flowing in a thin layer over a solid boundary. To do so, we use Distinct Element Method (DEM) simulations based on a soft sphere model and compare the results with large-scale experimental measurements. Based on results from a variety of mixtures of different-sized particles, we have found that the scaling of the stress at the boundary does not depend on a simple metric such as average particle size. Instead, the scaling of the stress appears to have a more complicated dependence on both the relative sizes of the particles in the mixture and the relative concentration of the different species. [1]R.A. Bagnold (1954) Proc. R. Soc. Lond., A 225 pp. 49-63.   

Green function measurements in the bulk of the 2D granular systems

We have performed experiments to measure the Green function responses to local perturbations in the bulk of the 2D granular systems using photo-elastic disks. The local perturbations were created in several different ways by applying pulling forces along a fixed direction, by applying forces pushing uniformly outwards, and by removing individual particles from force chains. Responses of systems were studied at different packing fractions for systems under isotropic compression and pure shear. We will present the results from the measurements of contact forces, particle displacement and rotation, and force chain networks.   

Stick-Slip and Granular Force Networks: A Statistical Description

We probe the nature of granular friction and stick-slip using a novel apparatus that combines photoelastic response at the grain scale, and quantitative measurements of pulling force and kinematics. In the experiments, a slider is pulled across the surface of a granular layer consisting of photoelastic particles. A pulling device moves at constant velocity, $V$, and acts on the slider through a spring of constant $k_s$. Non-periodic stick-slip motion results. During stick, the spring loads up, and the force network of the granular material evolves steadily. Slip is preceded by a creep regime involving small rearrangements of the force network. Slip is rapid and consists of one or more 'force chain' failures. Most properties, including energy losses at slip, forces at failure and immediately after slip, slipping times, etc. are characterized by broad distributions. For instance, the slip energy losses, in analogy to the Gutenberg-Richter law for earthquakes, has a probability distribution function that varies as a powerlaw in $\Delta E$ with and exponent of $\epsilon = 1.2 \pm 0.1$ The detailed motion of the slider during a slip event may be quite complex, as individual force chains fail, and new chains form to take their place. We present details of distributions and we relate our observations to expectations from a simple friction model and to an elastic failure model. We appreciate input from Paul Johnson (LANL) and Chris Marone (Penn State University).   

Non-linear and linear wave propagation in booming sand dunes

For centuries booming sand dunes have intrigued travelers and scientists alike. These dunes emit a persistent, low-frequency sound during a slumping event or natural avalanche on the leeward face of the dune. This sound can last for several minutes and be audible for miles. The acoustic emission is characterized by a dominant audible frequency (70 - 105 Hz) and several higher harmonics. In the work of Vriend et al. (2007), seismic refraction experiments show the existence of a multi-layer internal structure in the dune, which acts as a waveguide for the acoustic energy. The waveguide channel, within the subsurface structure of the dune, amplifies the sound and determines the booming frequency. The recorded booming frequency depends directly on the spatial dimension of the natural waveguide. The current study presents additional insight in the wave propagation characteristics. The source of the acoustic emission is burping sand - sand with a narrow particle size distribution that emits short broadband squeaks (50 - 100 Hz) upon direct shearing of the grains. The burping emission displays non-linear and dispersive effects in its wave propagation characteristics during field experiments. The emission cannot develop into the loud, sustained booming without the proper subsurface structure.   

Influence of volume fraction on the dynamics of granular impact

Variation of the volume fraction $\phi$ of non-cohesive granular media causes disproportionate changes in the forces exerted on impacting objects and, consequently, the impact kinematics. In our experiments, a computer controlled air fluidized granular bed is used to vary $\phi$ from 0.58 (low) to 0.62 (high) for 0.3~mm diameter glass spheres and \~1~mm poppy seeds. An accelerometer attached to a 4.0~cm diameter steel sphere measures collision forces for initial impact velocities ranging from 0.5 to 3.5~m/s. As an example of the dramatic changes produced by varying $\phi$, time series of the force during impact with poppy seeds at an impact velocity of 1~m/s change from monotonically increasing with slope 100~N/s at $\phi=0.59$ to monotonically decreasing with slope -100~N/s at $\phi=0.62$; glass beads show similar behavior. Increasing $\phi$ from low to high at fixed collision velocity causes the penetration depth to decrease monotonically by approximately 50\%. However, for the same parameters, the collision duration changes little, decreasing by $\approx 10$\% as $\phi$ is increased from 0.58 to $\approx 0.6$ and then increasing by about 3\% as $\phi$ is increased to 0.63. Our impact simulations exhibit the same collision dynamics vs.\ $\phi$ and reveal qualitative differences in grain velocity fields and local volume fraction changes between low and high $\phi$ states. Support by the Burroughs Wellcome Fund and the Army Research Lab MAST CTA.   

The effect of particle shape in the collapse of a granular column

Some previous experiments on the collapse of a granular column have reported that the shape of the grains has little influence in the collapse process and the shape of final deposit. In contrast, other studies indicate that the flow of long grains has a very different behavior than that of simple grains. To investigate this apparent discrepancy, we performed Discrete Element (DE) simulations of the collapse of 2D granular columns under the action of gravity. In contrast to similar previous investigations, we consider elongated grains formed by constraining several individual particles on a straight line. The main parameter used to describe the final state of the deposit is the aspect ratio, $a$, of initial height ($H_0$) to initial radius ($R_0$) of the column ($a=H_0/R_0$). We have performed simulations using 2000 elongated grains with length/width ratios up to 5, varying the value of the initial aspect ratio to characterize different flow regimes and the final deposit, and compare with the monodisperse case. Preliminary results indicate that the grain geometry has a significant influence on the collapse of the column.   

Axisymmetric Granular Collapse: a Transient 3D flow Test of Viscoplasticity

The collapse of a stationary cylinder of granular material onto a horizontal plan is a deceptively simple experiment rich in flow behaviour. Using 3-dimensional soft particle simulations, we reproduce the observed scaling laws for the maximum final runout and height of the deposit as a function of the initial aspect ratio. The flow simulations of this unsteady, largely axisymmetric flow are then used to confront a recently-introduced visco-plastic continuum theory (Jop, Forterre \& Pouliquen, {\em Nature}, {\bf 441},727,2006) which has seen some success modelling steady, unidirectional flows.   

Experimental measurements of the collapse of a 2D granular gas under gravity

We experimentally measure the decay of a quasi-2D granular gas under gravity. A granular gas is created by vibro- fluidization, after which the energy input is halted, and the time-dependent statistical properties of the decaying gas are measured with video particle tracking. There are two distinct cooling stages separated by a high temperature settling shock. In the final stage, the temperature of a fluid packet decreases as a power law $T \propto (t_c-t)^\alpha$ just before the system collapses to a static state. The measured value of $\alpha$ ranges from 3.3 to 6.1 depending on the height, significantly higher than the exponent of 2 found in theoretical work on this problem [Phys Rev. E 73, 61305 (2006)]. We also address the question of whether the collapse occurs simultaneously at different heights in the system.   

Three dimensional particle rearrangements during oscillatory flow in a split bottom geometry

We carry out three dimensional imaging of the positions and rearrangements of all particles during slow shear flow of granular matter in a split bottom shear cell geometry. The aim is to gain insights into dense granular flows at the level of individual particle displacements. To image particle motion in three dimensions plastic spheres are used that are immersed in index matching fluid that is fluorescently dyed. This allows for imaging of cross sections with a laser sheet and sensitive camera. Scanning the laser sheet generates a 3D image, from which we reconstruct the position of all particles in a 3D volume. We find that the interior of this fluid immersed material flows in a similar way as dry materials. Our focus is on reversible vs irreversible deformations in granular flows. Reversing the shear direction leads to a flow profile that does not exactly mirror the flow profile before reversal, indicating irreversible deformations in the shear zone. Following the motion of individual particles through at least 10 oscillations shows that the particles far from the shearband return to their original position, but particles in the shear band rearrange. Their mean squared displacement increases subdiffusively with the number of oscillations.