We study the mobility of objects embedded in an immersed granular packing and subjected to cyclic loadings. In this aim, we conducted experiments using glass beads immersed in water and a horizontal plate subjected to a cyclic uplift force. Tests performed at different cyclic force frequencies and amplitudes evidence the development of three mobility regimes whereby the plate stays virtually immobile, moves up steadily or slowly creeps upwards. Results show that steady plate uplift can occur at lower force magnitudes when the frequency is increased. We propose an interpretation of this frequency-weakening behaviour based on force relaxation experiments and on the analysis of the mobility response of theoretical visco-elasto-plastic mechanical analogue. These results and analysis point out inherent differences in mobility response between steady and cyclic loadings in immersed granular materials.
We report the formation of a crater at the free surface of an immersed granular bed,locally crossed by an ascending gas flow. In two dimensions, the crater consists of two piles which develop around the location of the gas emission. We observe that the typical size of the crater increases logarithmically with time, independently of the gas emission dynamics. We describe the related granular flows and give an account of the influence of the experimental parameters, especially of the grain size and of the gas flow.
The friction of a sliding plate on a thin immersed granular layer obeys Amonton-Coulomb law. We bring to the fore a large set of experimental results which indicate that, over a few decades of values, the effective dynamical friction-coefficient depends neither on the viscosity of the interstitial fluid nor on the size of beads in the sheared layer, which bears out the analogy with the solid-solid friction in a wide range of experimental parameters. We accurately determine the granular-layer dilatancy, which dependance on the grain size and slider velocity can be qualitatively accounted by con…
We investigate the drag forces acting on large objects moving through a granular packing immersed in water. In this aim, we conducted uplift experiments involving pulling out horizontal plates at a prescribed velocity vertically. During these tests, we observed that the drag force reaches to peak at a low displacement and then decays. Results show that the peak drag force strongly increases with the velocity and depends on the plate size and grain diameter. We identify empirical scaling laws for these properties and introduce a Darcy-flow mechanism that can explain them. Furthermore, we conduc…
We study in this work the dynamics of a granular impurity immersed in a low-density granular gas of identical particles. For description of the kinetics of the granular gas and the impurity particles we use the rough hard sphere collisional model. We take into account the effects of non-conservation of energy upon particle collision. We find an (approximate) analytical solution of the pertinent kinetic equations for the single-particle velocity distribution functions that reproduces reasonably well the properties of translational/rotational energy non-equipartition. We assess the accuracy of t…
This paper investigates the lift force exerted on an elliptical obstacle immersed in a granular flow through analytical calculations and computer simulations. The results are shown as a function of the obstacle size, orientation with respect to the flow direction (tilt angle), the restitution coefficient and ellipse eccentricity. The theoretical argument, based on the force exerted on the obstacle due to inelastic, frictionless collisions of a very dilute flow, captures the qualitative features of the lift, but fails to reproduce the data quantitatively. The reason behind this disagreement is …
Large objects, immersed in a homogeneous granular system, migrate when subjected to vibrations. Under certain conditions large heavy objects rise and similar light ones sink to the bottom. This is called reverse buoyancy. We report an experimental study of this singular behavior, for a large sphere immersed in a deep granular bed. A simple mechanism is proposed to describe the motion of a sphere, inside a vertically vibrated granular system. When reverse buoyancy is observed, the measured vertical velocity of the immersed object, as a function of its density, shows a simple behavior. With a on…
In this letter, we investigate the transient rheological behavior of immersed granular flows using both experiments of submerged granular column collapses and corresponding numerical simulations. The simulations are performed with the lattice-Boltzmann method (LBM) coupled with the discrete element method (DEM) and provide a significant amount of data of the stress and deformation conditions at different positions and times during the granular collapse. We derive a new dimensionless number $\mathcal{G}$ that can unify the rheology of transient granular flows in different regimes for all the si…
We investigate the mechanical behavior of a confined granular packing of irregular polyhedral particles under repeated heating and cooling cycles by means of numerical simulations with the Non-Smooth Contact Dynamics method. Assuming a homogeneous temperature distribution as well as constant temperature rate, we study the effect of the container shape, and coefficients of thermal expansions on the pressure buildup at the confining walls and the density evolution. We observe that small changes in the opening angle of the confinement can lead to a drastic peak pressure reduction. Furthermore, th…
Heterogeneity is classified in five categories---topologic, geometric, kinematic, static, and constitutive---and the first four categories are investigated in a numerical DEM simulation of biaxial compression. The simulation experiments show that the topology and geometric fabric become more variable during loading. The measured fluctuations in inter-particle movements are large, they increase with loading, and they extend to distances of at least eight particle diameters. Deformation and rotation heterogeneity are large and are expressed in spatial patterning. Stress heterogeneity is moderate…
The loading of a granular material induces anisotropies of the particle arrangement (fabric) and of the material's strength, incremental stiffness, and permeability. Thirteen measures of fabric anisotropy are developed, which are arranged in four categories: as preferred orientations of the particle bodies, the particle surfaces, the contact normals, and the void space. Anisotropy of the voids is described through image analysis and with Minkowski tensors. The thirteen measures of anisotropy change during loading, as determined with three-dimensional discrete element simulations of biaxial pla…
The transport coefficients of a dilute gas of inelastic hard spheres immersed in a molecular gas are determined. We assume that the number density of the granular gas is much smaller than that of the surrounding molecular gas, so that the latter is not affected by the presence of solid particles. In this situation, the molecular gas may be treated as a thermostat (or bath) of elastic hard spheres at a fixed temperature. This system (granular gas thermostated by a bath of elastic hard spheres) can be considered as a reliable model for describing the dynamic properties of particle-laden suspensi…
Bulldozing an immersed granular material in a confined channel
University of Oxford（牛津大学）；The Australian National University（澳大利亚国立大学）；Max Planck Institute for Dynamics and Self-Organization（马克斯·普朗克动力学与自组织研究所）；University of Bristol（布里斯托大学）；University of Cambridge（剑桥大学）；Swansea University（斯旺西大学）
Discrete-element simulations are used to monitor several micro-scale characteristics within a granular material, demonstrating their convergence during loading toward the critical state, their stationarity at the critical state, and the evolution of their disorder toward the critical state. Convergence, stationarity and disorder are studied in the context of the Shannon entropy and two forms of Kullback-Leibler relative entropy. Probability distributions of 20 aspects of micro-scale configuration, force and movement are computed for three topological objects: particles, voids and contacts. The…
The irregularity of particle motions during quasi-static deformation is investigated using discrete element (DEM) simulations of sphere and sphere-cluster assemblies. A total of three types of interparticle movements are analyzed: relative motions of particle centers, relative motions of material points of two particles at their contact, and the traversal of contacts across the surfaces of particles. Motions are a complex combination of rolling, sliding, and elastic distortion at the contacts, and all motions are highly irregular and variant, qualities that increase with increasing strain. The…
We integrate a small and portable medical x-ray device with mechanical testing equipment to enable in-situ, non-invasive measurements of a granular material's response to mechanical loading. We employ an orthopedic C-arm as the x-ray source and detector to image samples mounted in the materials tester. We discuss the design of a custom rotation stage, which allows for sample rotation and tomographic reconstruction under applied compressive stress. We then discuss the calibration of the system for 3d computed tomography, as well as the subsequent image reconstruction process. Using this system …
The paper addresses a common assumption of elastoplastic modeling: that the recoverable, elastic strain increment is unaffected by alterations of the elastic moduli that accompany loading. This assumption is found to be false for a granular material, and discrete element (DEM) simulations demonstrate that granular materials are coupled materials at both micro- and macro-scales. Elasto-plastic coupling at the macro-scale is placed in the context of thermomechanics framework of Tomasz Hueckel and Hans Ziegler, in which the elastic moduli are altered by irreversible processes during loading. This…
We consider a dilute system of small hard beads or hard fibers immersed in a very soft gel able to withstand large elastic deformations. Because of its low to very low shear modulus, this system is very sensitive to small forces. We calculate the local deformation induced by a constant volume force, the inclusion weight. We explain how this deformation could be put in evidence by using techniques similar to the PIV method (particle image velocimetry) used to show complex velocity fields in transparent fluids.
We present a numerical implementation of an active inclusion in a granular material submitted to a biaxial test. We discuss the dependence of the response to this perturbation on two parameters: the intra-granular friction coefficient on one hand, the degree of the loading on the other hand. We compare the numerical results to theoretical predictions taking into account the change of volume of the inclusion as well as the anisotropy of the elastic matrix.
The paper addresses the underlying source of two forms of induced anisotropy in granular materials: contact orientation anisotropy and contact force anisotropy. A rational, mathematical structure is reviewed for the manner in which fabric anisotropy emerges and evolves during loading. Fabric is expressed as an orientation density, and transport phenomena such as convection, contact generation, and diffusion control the rate of fabric evolution during loading. The paper proposes specific measurable forms for all terms, based upon the micro-mechanics of particle interactions. Discrete element (D…
The complex incremental behavior of granular materials is explored with multi-directional loading probes. An advanced discrete element model (DEM) was used to examine the reversible and irreversible strains for small loading probes, which follow an initial monotonic axisymmetric triaxial loading. The model used non-convex non-spherical particles and an exact implementation of the Hertz-like Cattaneo-Mindlin model for the contact interactions. Rectilinear true-triaxial probes were used in the study (i.e., no direct shear strain or principal stress rotation), with small strains increments of $2\…
We present an experimental apparatus specifically designed to investigate the precursors of failure in granular materials. A sample of granular material is placed between a latex membrane and a glass plate. A confining effective pressure is applied by applying vacuum to the sample. Displacement-controlled compression is applied in the vertical direction, while the specimen deforms in plane strain. A Diffusing Wave Spectroscopy visualization setup gives access to the measurement of deformations near the glass plate. After describing the different parts of this experimental setup, we present a d…
Like in liquids, objects moving in granular materials experience a drag force. We investigate here whether and how the object acceleration affect this drag force. The study is based on simulations of a canonical drag test, which involves vertically uplifting a plate through a granular packing with a prescribed acceleration pattern. Depending on the plate size, plate depth and acceleration pattern, results evidence a rate-independent regime and an inertial regime where the object acceleration strongly enhances the drag force. We introduce an elasto-inertial drag force model that captures the me…
We show that granular media consisting of metallic microparticles immersed in a poorly conducting liquid in strong DC electric field self-assemble a rich variety of novel phases. These phases include static precipitate: honeycombs and Wigner crystals; and novel dynamic condensate: toroidal vortices and pulsating rings. The observed structures are explained by the interplay between charged granular gas and electrohydrodynamic convective flows in the liquid.
The series of equilibrium states reached by disordered packings of rigid, frictionless discs in two dimensions, under gradually varying stress, are studied by numerical simulations. Statistical properties of trajectories in configuration space are found to be independent of specific assumptions ruling granular dynamics, and determined by geometry only. A monotonic increase in some macroscopic loading parameter causes a discrete sequence of rearrangements. For a biaxial compression, we show that, due to the statistical importance of such events of large magnitudes, the dependence of the resulti…
We study the impact of a projectile onto a bed of 3 mm grains immersed in an index-matched fluid. Specifically, we vary the amount of prestrain on the sample, strengthening the force chains within the system. We find this affects only the prefactor of linear depth-dependent term in the stopping force. We therefore attribute this term to pressure within the material, and not the grain-intruder friction as is sometimes suggested. Using a laser sheet scanning technique to visualize internal grain motion, a high-speed camera, and particle tracking, we can measure the trajectory of each grain throu…
We measure the torque acting on a rod rotated perpendicular to its axis in a granular bed, through which an upflow of gas is utilized to tune the hydrostatic loading between grains. At low rotation rates the torque is independent of speed, but scales quadratically with rod-length and linearly with depth; the proportionality approaches zero linearly as the upflow of gas is increased towards a critical value above which the grains are fluidized. At high rotation rates the torque exhibits quadratic rate- dependence and scales as the rod's length to the 4th power. The torque has no dependence on e…
We measure the quasi-static friction force acting on intruders moving downwards into a granular medium. By utilizing different intruder geometries, we demonstrate that the force acts locally normal to the intruder surface. By altering the hydrostatic loading of grain contacts by a sub-fluidizing airflow through the bed, we demonstrate that the relevant frictional contacts are loaded by gravity rather than by the motion of the intruder itself. Lastly, by measuring the final penetration depth versus airspeed and using an earlier result for inertial drag, we demonstrate that the same quasi-static…
We present a minimalistic approach to simulations of force transmission through granular systems. We start from a configuration containing cohesive (tensile) contact forces and use an adaptive procedure to find the stable configuration with no tensile contact forces. The procedure works by sequentially removing and adding individual contacts between adjacent beads, while the bead positions are not modified. In a series of two-dimensional realizations, the resulting force networks are shown to satisfy a linear constraint among the three components of average stress, as anticipated by recent the…
We investigate the effective long-range interactions between intruder particles immersed in a randomly driven granular fluid. The effective Casimir-like force between two intruders, induced by the fluctuations of the hydrodynamic fields, can change its sign when varying the control parameters: the volume fraction, the distance between the intruders, and the restitution coefficient. More interestingly, by inserting more intruders, we verify that the fluctuation-induced interaction is not pairwise additive. The simulation results are qualitatively consistent with the theoretical predictions base…
Understanding the coupled thermo-mechanical behaviour of compacted granular beds can benefit various industrial applications, such as pebble bed design in fusion reactors. In this study, a thermo-mechanical discrete element method based on our previous work is improved and adapted to investigate the cyclic thermo-mechanical performance of gas-filled granular materials composed of elastoplastic grains. An interparticle contact model is developed considering the plastic deformation of grains. Through the simulation on a representative volume element of beryllium pebble beds, we provide grain-sca…
Both the shape of individual particles and their surface properties contribute to the strength of a granular material under shear. Here we show the degree to which these two aspects can be intertwined. In experiments on assemblies of 3D printed, convex lens-shaped particles, we measure the stress-strain response under repeated compressive loading and find that the aggregate's shear strength falls rapidly when compared to other particle shapes. We probe the granular material at mm-scales with X-ray computed tomography and $μ$m-scales with high-resolution surface metrology to look for the cause …
Matrix stiffness expressions are derived for the particle movements in an assembly of rigid granules having compliant contacts. The derivations include stiffness terms that arise from the particle shapes at their contacts. These geometric stiffness terms may become significant during granular failure. The geometric stiffness must be added to the mechanical stiffnesses of the contacts to produce the complete stiffness. With frictional contacts, this stiffness expression is incrementally nonlinear, having multiple loading branches. To aid the study of material behavior, a modified stiffness is d…
We present a visco-elastic coupling model between caked spheres, suitable for DEM simulations, which incorporates the different loading mechanisms (tension, shear, bending, torsion) in a combined manner and allows for a derivation of elastic and failure properties on a common basis. In pull, shear, and torsion failure tests with agglomerates of up to 10000 particles, we compare the failure criterion to different approximative variants of it, with respect to accuracy and computational cost. The failure of the agglomerates, which behave according to elastic parameters derived from the contact el…
Making use of the system of pulling a spherical intruder in static three-dimensional granular media, we numerically study the scaling law for the drag force $F_{\rm drag}$ acting on the moving intruder under the influence of the gravity. Suppose if the intruder of diameter $D$ immersed in a granular medium consisting of grains of average diameter $d$ is located at a depth $h$ and moves with a speed $V$, we find that $F_{\rm drag}$ can be scaled as $(D+d)^{ϕ_μ} h^{α_μ}$ with two exponents $ϕ_μ$ and $α_μ$, which depend on the friction coefficient $μ$ and satisfy an approximate sum rule $ϕ_μ+α_μ\…
We performed a series of numerical vertical compression tests on assemblies of 2D granular material using a Discrete Element code and studied the results with regard to the grain shape. The samples consist of 5,000 grains made from either 3 overlapping discs (clumps - grains with concavities) or six-edged polygons (convex grains). These two grain type have similar external envelopes, which is a function of a geometrical parameter $α$. In this paper, the numerical procedure applied is briefly presented followed by the description of the granular model used. Observations and mechanical analysis …
Upon mechanical loading, granular materials yield and undergo plastic deformation. The nature of plastic deformation is essential for the development of the macroscopic constitutive models and the understanding of shear band formation. However, we still do not fully understand the microscopic nature of plastic deformation in disordered granular materials. Here we used synchrotron X-ray tomography technique to track the structural evolutions of three-dimensional granular materials under shear. We establish that highly distorted coplanar tetrahedra are the structural defects responsible for micr…
We investigate the approach to catastrophic failure in a model porous granular material undergoing uniaxial compression. A discrete element computational model is used to simulate both the micro-structure of the material and the complex dynamics and feedbacks involved in local fracturing and the production of crackling noise. Under strain-controlled loading micro-cracks initially nucleate in an uncorrelated way all over the sample. As loading proceeds the damage localizes into a narrow damage band inclined at 30-45 degrees to the load direction. Inside the damage band the material is crushed i…
We experimentally and numerically examine stress-dependent electrical transport in granular materials to elucidate the origins of their universal dielectric response. The ac responses of granular systems under varied compressive loadings consistently exhibit a transition from a resistive plateau at low frequencies to a state of nearly constant loss at high frequencies. By using characteristic frequencies corresponding to the onset of conductance dispersion and measured direct-current resistance as scaling parameters to normalize the measured impedance, results of the spectra under different st…
A numerical study of multi-phase granular materials based upon micro-mechanical modelling is proposed. Discrete element simulations are used to investigate capillary induced effects on the friction properties of a granular assembly in the pendular regime. Capillary forces are described at the local scale through the Young-Laplace equation and are superimposed to the standard dry particle interaction usually well simulated through an elastic-plastic relationship. Both effects of the pressure difference between liquid and gas phases and of the surface tension at the interface are integrated into…
Discrete numerical simulations are performed to study the evolution of the micro-structure and the response of a granular packing during successive loading-unloading cycles, consisting of quasi-static rotations in the gravity field between opposite inclination angles. We show that internal variables, e.g., stress and fabric of the pile, exhibit hysteresis during these cycles due to the exploration of different metastable configurations. Interestingly, the hysteretic behaviour of the pile strongly depends on the maximal inclination of the cycles, giving evidence of the irreversible modification…
Shear banding and stick-slip instabilities have been long observed in sheared granular materials. Yet, their microscopic underpinnings, interdependencies and variability under different loading conditions have not been fully explored. Here, we use a non-equilibrium thermodynamics model, the Shear Transformation Zone theory, to investigate the dynamics of strain localization and its connection to stability of sliding in sheared, dry, granular materials. We consider frictional and frictionless grains as well as presence and absence of acoustic vibrations. Our results suggest that at low and inte…
The arrangements of particles and forces in granular materials have a complex organization on multiple spatial scales that ranges from local structures to mesoscale and system-wide ones. This multiscale organization can affect how a material responds or reconfigures when exposed to external perturbations or loading. The theoretical study of particle-level, force-chain, domain, and bulk properties requires the development and application of appropriate physical, mathematical, statistical, and computational frameworks. Traditionally, granular materials have been investigated using particulate or…
