The mechanics of cohesive or cemented granular materials is complex, combining the heterogeneous responses of granular media, like force chains, with clearly defined material properties. Here, we use a discrete element model (DEM) simulation, consisting of an assemblage of elastic particles connected by softer but breakable elastic bonds, to explore how this class of material deforms and fails under uniaxial compression. We are particularly interested in the connection between the microscopic interactions among the grains or particles and the macroscopic material response. To this end, the properties of the particles and the stiffness of the bonds are matched to experimental measurements of a cohesive granular media with tunable elasticity. The criterion for breaking a bond is also based on an explicit Griffith energy balance, with realistic surface energies. By varying the initial volume fraction of the particle assembles we show that this simple model reproduces a wide range of experimental behaviors, both in the elastic limit and beyond it. These include quantitative details of the distinct failure modes of shear-banding, ductile failure and compaction banding or anti-cracks, as well as the transitions between these modes. The present work, therefore, provides a unified framework for understanding the failure of porous materials such as sandstone, marble, powder aggregates, snow and foam.
We study the transition of a granular packing from liquid to solid bonding in the course of drying. The particles are initially wetted by a liquid brine and the cohesion of the packing is ensured by capillary forces, but the crystallization of the solute transforms the liquid bonds into partially cemented bonds. This transition is evidenced experimentally by measuring the compressive strength of the samples at regular intervals of times. Our experimental data reveal three regimes: 1) Up to a critical degree of saturation, no solid bonds are formed and the cohesion remains practically constant;…
We investigate the gravity driven rapid failure of a granular step composed of non-cohesive steel beads. The step is initially held together with electromagnets, and released when the current is switched off. We visualize the surface and the motion of the grains during the entire relaxation. The initial failure occurs at the surface and the subsequent flow is also confined to the surface as the step relaxes to its final state. The final shape of the surface is almost linear, depends on the initial angle of the step, and is not sensitive to the size of the grains. The average final slope of the…
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…
Granular materials can fail through spontaneous events like earthquakes or brittle fracture. However, measurements and analytic models which forecast failure in this class of materials, while of both fundamental and practical interest, remain elusive. Materials including numerical packings of spheres, colloidal glasses, and granular materials have been known to develop an excess of low-frequency vibrational modes as the confining pressure is reduced. Here, we report experiments on sheared granular materials in which we monitor the evolving density of excited modes via passive monitoring of aco…
The failure of 2D numerical cohesive granular steps collapsing under gravity are simulated for a large range of cohesion. Focussing on the cumulative displacement of the grains, and defining a displacement threshold, we establish a sensible criterion for capturing the failure characteristics. We are able to locate the failure in time and to identify the different stages of the destabilisation. We find that the onset of the failure is delayed by increasing cohesion, but its duration becomes shorter. Defining a narrow displacement interval, a well-defined shear band revealing the failure comes o…
We investigate computationally the pullout of a spherical intruder initially buried at the bottom of a granular column. The intruder starts to move out of the granular bed once the pulling force reaches a critical value, leading to material failure. The failure point is found to depend on the diameter of the granular column, pointing out the importance of particle-wall interaction in determining the material response. Discrete element simulations show that prior to failure, the contact network is essentially static, with only minor rearrangements of the particles. However, the force network, w…
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 micro-failures occur periodically in the bulk, and finally a granular avalanche takes place. The micro-failures are observed only when the tilt angles are larger than a threshol…
By means of contact dynamics simulations, we analyze the stress state in a granular bed slowly tilted towards its angle of repose. An increasingly large number of grains are overloaded in the sense that they are found to carry a stress ratio above the Coulomb yield threshold of the whole packing. Using this property, we introduce a coarse-graining length scale at which all stress ratios are below the packing yield threshold. We show that this length increases with the slope angle and jumps to a length comparable to the depth of the granular bed at an angle below the angle of repose. This trans…
Contacts at the Coulomb threshold are unstable to tangential perturbations and thus contribute to failure at the microscopic level. How is such a local property related to global failure, beyond the effective picture given by a Mohr-Coulomb type failure criterion? Here, we use a simulated bed of frictional disks slowly tilted under the action of gravity to investigate the link between the avalanche process and a global generalized isostaticity criterion. The avalanche starts when the packing as a whole is still stable according to this criterion, underlining the role of large heterogeneities i…
We employ a novel fluid-particle model to study the shearing behavior of granular soils under different saturation levels, ranging from the dry material via the capillary bridge regime to higher saturation levels with percolating clusters. The full complexity of possible liquid morphologies is taken into account, implying the formation of isolated arbitrary-sized liquid clusters with individual Laplace pressures that evolve by liquid exchange via films on the grain surface. Liquid clusters can grow in size, shrink, merge and split, depending on local conditions, changes of accessible liquid an…
An X-ray imaging technique is used to probe the stability of 3-dimensional granular packs in a slowly rotating drum. Well before the surface reaches the avalanche angle, we observe intermittent plastic events associated with collective rearrangements of the grains located in the vicinity of the free surface. The energy released by these discrete events grows as the system approaches the avalanche threshold. By testing various preparation methods, we show that the pre-avalanche dynamics is not solely controlled by the difference between the free surface inclination and the avalanche angle. As a…
The variation of metallic particle size and sample porosity significantly alters the dynamic mechanical properties of high density granular composites processed using a cold isostatically pressed mixture of polytetrafluoroethylene (PTFE), aluminum (Al) and tungsten (W) powders. Quasi-static and dynamic experiments are performed with identical constituent mass fractions with variations in the size of the W particles and pressing conditions. The relatively weak polymer matrix allows the strength and fracture modes of this material to be governed by the granular type behavior of agglomerated meta…
A heterogeneous quasi-brittle granular material can withstand certain levels of internal damage before global failure. This robustness depends not just on the bond strengths but also on the topology and redundancy of the bonded contact network, through which forces and damage propagate. Despite extensive studies on quasi-brittle failure, there still lacks a unified framework that can quantify the interdependent evolution of robustness, damage and force transmission. Here we develop a framework to do so. It is data-driven, multiscale and relies solely on the contact strengths and topology of th…
In this paper, we consider the effect of cohesion on the stability of a granular heap. We first briefly review literature results on the cohesion force between two rough granular beads and specifically consider the dependence of the adhesion force on the normal load. We then compute the dependence of the maximum angle of stability of the heap as a function of the cohesion. We point out that the dependence of the cohesive forces on the external normal load between grains is a key point in determining the localization of the failure plane. While for a constant cohesive force, slip occurs deep in…
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 paper develops the stiffness relationship between the movements and forces among a system of discrete interacting grains. The approach is similar to that used in structural analysis, but the stiffness matrix of granular material is inherently non-symmetric because of the geometrics of particle interactions and of the frictional behavior of the contacts. Internal geometric constraints are imposed by the particles' shapes, in particular, by the surface curvatures of the particles at their points of contact. Moreover, the stiffness relationship is incrementally non-linear, and even small asse…
Magic Sand, a hydrophobic toy granular material, is widely used in popular science instructions because of its non-intuitive mechanical properties. A detailed study of the failure of an underwater column of magic sand shows that these properties can be traced to a single phenomenon: the system self-generates a cohesive skin that encapsulates the material inside. The skin, consists of pinned air-water-grain interfaces, shows multi-scale mechanical properties: they range from contact-line dynamics in the intra-grain roughness scale, plastic flow at the grain scale, all the way to the sample-scal…
Theoretical treatments of frictional granular matter often assume that it is legitimate to invoke classical elastic theory to describe its coarse-grained mechanical properties. Here we show, based on experiments and numerical simulations, that this is generically not the case since stress auto-correlation functions decay more slowly than the elastic Green's function. It was shown theoretically that standard elastic decay demands pressure and torque density fluctuations to be normal, with possibly one of them being hyperuniform. Generic compressed frictional assemblies exhibit however abnormal …
Injection-rate effects on failure in a fluid-saturated granular fault gouge
Institute of Earth Sciences, Hebrew University of Jerusalem（耶路撒冷希伯来大学地球科学学院）；Faculty of Science, Jan Evangelista Purkyně University in Ústí nad Labem（乌斯季纳拉贝姆扬埃万杰利斯塔普尔金耶大学理学院）；Faculty of Science, Charles University（布拉格查理大学理学院）；Université de Strasbourg（斯特拉斯堡大学）；Institut Terre et Environnement de Strasbourg（斯特拉斯堡地球与环境研究所）；PoreLab, The Njord Centre, Departments of Physics and Geosciences, University of Oslo（奥斯陆大学物理与地球科学系尼约德中心孔隙实验室）
On the interaction of dilatancy and friction in the behavior of fluid-saturated sheared granular materials: a coupled Computational Fluid Dynamics--Discrete Element Method study
Department of Civil and Environmental Engineering, University of Houston（休斯顿大学土木与环境工程系）
Frictional granular matter is shown to be fundamentally different in its plastic responses to external strains from generic glasses and amorphous solids without friction. While regular glasses exhibit plastic instabilities due to a vanishing of a real eigenvalue of the Hessian matrix, frictional granular materials can exhibit a previously unnoticed additional mechanism for instabilities, i.e. the appearance of a pair of complex eigenvalues leading to oscillatory exponential growth of perturbations which are tamed by dynamical nonlinearities. This fundamental difference appears crucial for the …
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…
Recent experiments (Le Bouil et al., Phys. Rev. Lett., 2014, 112, 246001) have analyzed the statistics of local deformation in a granular solid undergoing plastic deformation. Experiments report strongly anisotropic correlation between events, with a characteristic angle that was interpreted using elasticity theory and the concept of Eshelby transformations with dilation; interestingly, the shear bands that characterize macroscopic failure occur at an angle that is different from the one observed in microscopic correlations. Here, we interpret this behavior using a mesoscale elastoplastic mode…
There have been many attempts to derive continuum models for dense granular flow, but a general theory is still lacking. Here, we start with Mohr-Coulomb plasticity for quasi-2D granular materials to calculate (average) stresses and slip planes, but we propose a "stochastic flow rule" (SFR) to replace the principle of coaxiality in classical plasticity. The SFR takes into account two crucial features of granular materials - discreteness and randomness - via diffusing "spots" of local fluidization, which act as carriers of plasticity. We postulate that spots perform random walks biased along sl…
We study experimentally the fracture mechanisms of a model cohesive granular medium consisting of glass beads held together by solidified polymer bridges. The elastic response of this material can be controlled by changing the cross-linking of the polymer phase, for example. Here we show that its fracture toughness can be tuned over an order of magnitude by adjusting the stiffness and size of the polymer bridges. We extract a well-defined fracture energy from fracture testing under a range of material preparations. This energy is found to scale linearly with the cross-sectional area of the bri…
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…
By mixing glass beads with a curable polymer we create a well-defined cohesive granular medium, held together by solidified, and hence elastic, capillary bridges. This material has a geometry similar to a wet packing of beads, but with an additional control over the elasticity of the bonds holding the particles together. We show that its mechanical response can be varied over several orders of magnitude by adjusting the size and stiffness of the bridges, and the size of the particles. We also investigate its mechanism of failure under unconfined uniaxial compression in combination with in situ…
According to the acoustic fluidization hypothesis, elastic waves at a characteristic frequency form inside seismic faults even in the absence of an external perturbation. These waves are able to generate a normal stress which contrasts the confining pressure and promotes failure. Here, we study the mechanisms responsible for this wave activation via numerical simulations of a granular fault model. We observe the particles belonging to the percolating backbone, which sustains the stress, to perform synchronized oscillations over ellipticlike trajectories in the fault plane. These oscillations o…
The dynamics of a tracer particle in a stationary driven granular gas is investigated. We show how to transform the linear Boltzmann equation describing the dynamics of the tracer into a master equation for a continuous Markov process. The transition rates depend upon the stationary velocity distribution of the gas. When the gas has a Gaussian velocity probability distribution function (pdf), the stationary velocity pdf of the tracer is Gaussian with a lower temperature and satisfies detailed balance for any value of the restitution coefficient $α$. As soon as the velocity pdf of the gas depar…
This work summarizes a series of studies on two-dimensional granular impact, where an intruding object strikes a granular material at high speed. Many previous studies on granular impact have used a macroscopic force law, which is dominated by an inertial drag term proportional to the intruder velocity squared. The primary focus here is on the microscopic force response of the granular material, and how the grain-scale effects give rise to this inertial drag term. We show that the inertial drag arises from intermittent collisions with force-chain-like structures. We construct a simple collisio…
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 investigate a model system for the rotational dynamics of inertial many-particle clustering, in which sub-millimeter objects are acoustically levitated in air. Driven by scattered sound, levitated grains self-assemble into a monolayer of particles, forming mesoscopic granular rafts with both an acoustic binding energy and a bending rigidity. Detuning the acoustic trap can give rise to stochastic forces and torques that impart angular momentum to levitated objects. As the angular momentum of a quasi-two-dimensional granular raft is increased, the raft deforms from a disk to an ellipse, event…
The mechanical properties of a disordered heterogeneous medium depend, in general, on a complex interplay between multiple length scales. Connecting local interactions to macroscopic observables, such as stiffness or fracture, is thus challenging in this type of material. Here, we study the properties of a cohesive granular material composed of glass beads held together by soft polymer bridges. We characterise the mechanical response of single bridges under traction and shear, using a setup based on the deflection of flexible micropipettes. These measurements, along with information from X-ray…
Nonlocal rheologies allow for the modeling of granular flows from the creeping to intermediate flow regimes, using a small number of parameters. In this paper, we report on experiments testing how particle properties affect model parameters, using particles of three different shapes (circles, ellipses, and pentagons) and three different materials, including one which allows for measurements of stresses via photoelasticity. Our experiments are performed on a quasi-2D annular shear cell with a rotating inner wall and a fixed outer wall. Each type of particle is found to exhibit flows which are w…
The structure and stresses of static granular packs in cylindrical containers are studied using large-scale discrete element molecular dynamics simulations in three dimensions. We generate packings by both pouring and sedimentation and examine how the final state depends on the method of construction. The vertical stress becomes depth-independent for deep piles and we compare these stress depth-profiles to the classical Janssen theory. The majority of the tangential forces for particle-wall contacts are found to be close to the Coulomb failure criterion, in agreement with the theory of Janssen…
Quasi-static tensile experiments were performed for a model disordered solid consisting of a two-dimensional raft of polydisperse floating granular particles with capillary attractions. The ductility is tuned by controlling the capillary interaction range, which varies with the particle size. During the tensile tests, after an initial period of elastic deformation, strain localization occurs and leads to the formation of a shear band at which the pillar later fails. In this process, small particles with long-ranged interactions can endure large plastic deformations without forming significant …
One long-lasting puzzle in amorphous solids is shear localization, where local plastic deformation involves cooperative particle rearrangements in small regions of a few inter-particle distances, self-organizing into shear bands and eventually leading to the material failure. Understanding the connection between the structure and dynamics of amorphous solids is essential in physics, material sciences, geotechnical and civil engineering, and geophysics. Here we show a deep connection between shear localization and the intrinsic structures of internal stresses in an isotropically jammed granular…
Granular materials react to shear stresses differently than do ordinary fluids. Rather than deforming uniformly, materials such as dry sand or cohesionless powders develop shear bands: narrow zones containing large relative particle motion leaving adjacent regions essentially rigid[1,2,3,4,5]. Since shear bands mark areas of flow, material failure and energy dissipation, they play a crucial role for many industrial, civil engineering and geophysical processes[6]. They also appear in related contexts, such as in lubricating fluids confined to ultra-thin molecular layers[7]. Detailed information…
The elastic coupling between plastic events is generally invoked to interpret plastic properties and failure of amorphous soft glassy materials. We report an experiment where the emergence of a self-organized plastic flow is observed well before the failure. For this we impose an homogeneous stress on a granular material, and measure local deformations for very small strain increments using a light scattering setup. We observe a non-homogeneous strain that appears as transient bands of mesoscopic size and well defined orientation, different from the angle of the macroscopic frictional shear ba…
Granular clogging across gravities: a unified scaling
Universität Duisburg-Essen（杜伊斯堡-埃森大学）；University of Amsterdam（阿姆斯特丹大学）；Institut Supérieur de l’Aéronautique et de l’Espace (ISAE-SUPAERO), Université de Toulouse（法国高等航空航天学院（ISAE-SUPAERO），图卢兹大学）；German Aerospace Center (DLR)（德国航空航天中心）；University of Cologne（科隆大学）
Compressing a porous, fluid-filled material will drive the interstitial fluid out of the pore space, as when squeezing water out of a kitchen sponge. Inversely, injecting fluid into a porous material can deform the solid structure, as when fracturing a shale for natural gas recovery. These poromechanical interactions play an important role in geological and biological systems across a wide range of scales, from the propagation of magma through the Earth's mantle to the transport of fluid through living cells and tissues. The theory of poroelasticity has been largely successful in modeling poro…
Hysteresis is a major feature of the solid-liquid transition in granular materials. This property, by allowing metastable states, can potentially yield catastrophic phenomena such as earthquakes or aerial landslides. The origin of hysteresis in granular flows is still debated. However, most mechanisms put forward so far rely on the presence of inertia at the particle level. In this paper, we study the avalanche dynamics of non-Brownian suspensions in slowly rotating drums and reveal large hysteresis of the avalanche angle even in the absence of inertia. By using micro-silica particles whose in…
Using numerical simulations, we consider an amorphous particle mixture which exhibits shear banding, and find that the addition of even a small fraction of chains strongly enhances the material strength, creating pronounced overshoot features in the stress-strain curves. The strengthening occurs in the case where the chains are initially perpendicular to the shear direction, leading to a suppression of the shear band. For large strain, the chains migrate to the region where a shear band forms, resulting in a stress drop. The alignment of the chains by the shear bands results in a Bauschinger-l…
