Shear strength properties of wet granular materials

Experimental study of particle impact on cohesive granular packing

We investigate experimentally the impact process of sand particles onto a cohesive granular packing made of similar particles. We use a sand-oil mixture with varying liquid content to tune the cohesive strength of the packing. The outcome of the impact is analyzed in terms of the production of ejected particles from the packing. We quantify this production as a function of the impact velocity of the particles for increasing cohesion strength. We identified three different regimes depending on the cohesion number Co, defined as the ratio of the interparticle cohesive force to the particle weight. For small cohesion (i.e., Co⪅1), the ejection process is not modified by the cohesion. For intermediate cohesion (i.e., 1⪅Co⪅20), the ejection process becomes less efficient: the number of ejected particles per impact for a given impact velocity is decreased but the critical impact velocity to trigger the ejection process remains unchanged. Finally, for strong cohesion (i.e., Co⪆20), we observed a progressive increase of the critical impact velocity. These experimental results confirm spectacularly the outcomes of recent numerical simulations on the collision process of a particle onto a cohesive packing and open avenues to model the aeolian transport of moist sand.

Micromechanics of contact-bound cohesive granular materials in confined compression

The mechanical behavior of granular materials results from interparticle interactions, which are predominantly frictional. With the presence of even very small amounts of cohesion this frictional interparticle behavior significantly changes. In this study, we introduce trace amounts of cohesive binder between the intergranular contacts in a sample of quartz particles and apply one-dimensional (1D) compression loading. X-ray computed tomography is performed in situ during 1D compression. We make observations at three different length scales. At the macroscopic or ensemble scale, we track the evolution of the porosity, particle size and the stress-strain response during this compression. At the microstructure or interparticle scale, we compute the directional distribution of contacts and the particles. We also track the evolution of the fabric chains with continued compression. We also evaluate particle rotations, displacements, contact twist, rotation, and sliding. We show through our experiments that even a small amount of cohesion (as low as 1% by weight) significantly changes the response at multiple length scales. This interparticle cohesion suppresses the fragmentation of grains, alters force transmission and changes the structure of the ensemble.

External Stefan and Internal Marangoni Thermo-Fluid Dynamics for Evaporating Capillary Bridges

We probe the evaporation mechanisms of wettability-moderated, confined capillary bridges and bulges. For the first time, we explore the internal Marangoni hydrodynamics and external Stefan advection dynamics in the surrounding gaseous domain due to evaporative effects. A transient simulation approach based on the level set (LS) method and the Arbitrary Lagrangian-Eulerian (ALE) framework was adopted to computationally model the capillary bridge profiles and evaporation phenomenon with generic contact line dynamics (both CCR and CCA modes). The governing equations corresponding to the transport processes in both the liquid and gaseous domains are simulated in a fully coupled manner with appropriate boundary conditions to precisely trace the liquid-vapor interface and the three-phase contact point during evaporation. The effect of the bridge confinement phenomenon, i.e., the extent of confined ambient surrounding the liquid-vapor interface between the solid surfaces, is explored. Also, the role of wetting state and contact line dynamics during CCR and CCA modes of evaporation were probed, and good agreement with experimental observations was noted. Results show that the evaporation rate is primarily dictated by the confinement phenomenon, and wettability effects play a marginal role. A higher confinement curtails the evaporation rate due to an increased local vapor concentration around the liquid bridges. However, the wetting state substantially affects the internal Marangoni effect dynamics and the Stefan advection dynamics due to its explicit influence on the nonuniform evaporative flux along the liquid-vapor interface. Between superhydrophobic confinements, the contact lines are confined in the wedge-shaped region, thereby locally augmenting the vapor concentration. As a result, the large evaporative flux near the bulge region develops a higher temperature gradient, thereby inducing upscaled thermal Marangoni flow compared to hydrophilic confinements. These findings may have significant implications for the efficient designing and development of thermofluidic systems involving thermal transport, mixing, and deposition of dissolved particles in liquid bridges.

Micro computed tomography images of capillary actions in rough and irregular granular materials

The present work investigates the effect of both surface roughness and particle morphology on the retention behaviour of granular materials via X-ray micro-computed tomography (µCT) observations. X-ray µCT images were taken on two types of spherical glass beads (i.e. smooth and rough) and two different sands (i.e. natural and roughened). Each sample was subjected to drainage and soaking paths consisting in a multiphase 'static' flow of potassium iodine (KI) brine (wetting phase) and dry air (non-wetting phase). Tomograms were obtained at different saturation states ranging from fully brine saturated to air dry conditions with 6.2 μm voxel size resolution. The data acquisition and pre-processing are here described while all data, a total of 48 tomograms, are made publicly available. The combined dataset offers new opportunities to study the influence of surface roughness and particle morphology on capillary actions as well as supporting validation of pore-scale models of multiphase flow in granular materials.

Collapse dynamics and deposition morphology of low-viscocohesive granular columns on a rough horizontal surface

Using the three-dimensional discrete element method, we numerically investigate the collapse dynamics and deposition morphology of low-viscocohesive granular columns on a rough-horizontal plane by systematically varying a broad range of values of the initial column aspect ratio, cohesive stress, and liquid viscosity. The results show that the kinetic energy, half runout time, and runout distance increase with increasing the initial column aspect ratio but decrease with increasing the cohesive and viscous effects of the binding liquid, while the toe angle and deposit height decrease with increasing the aspect ratio and increase with increasing cohesive stress and liquid viscosity. Remarkably, by defining a dimensionless scaling number that incorporates the Bond number and initial column aspect ratio, this allows us to nicely describe the kinetic energy, half runout time, deposition height, runout distance, and toe angle. These unified descriptions may provide insights into the physical properties of the collapse dynamics and deposition morphology of low-viscocohesive granular columns, leading to good explanations of the complex properties of natural disaster events.

Two-dimensional spreading of frictionless adhesive oil droplets

When sand flows out of a funnel onto a surface, a three dimensional pile that is stabilized by friction grows taller as it spreads. Here we investigate an idealized two dimensional analogue: spreading of a pile of monodisperse oil droplets at a boundary. In our system the droplets are buoyant, adhesive, and in contrast to sand, friction is negligible. The buoyant droplets are added to the pile one-at-a-time. As the aggregate grows, it reaches a critical height and the 2D pile spreads out across the barrier. We find that, while granularity is important, the growth process is reminiscent of a continuum liquid. A "granular capillary length", analogous to the capillary length in liquids, sets the critical height of the aggregate through a balance of buoyancy and adhesion. At a coarse-grained level, the granular capillary length is capable of describing both steady-state characteristics and dynamic properties of the system, while at a granular level repeated collapsing events play a critical role in the formation of the pile.

Unified penetration depth of low-velocity intruders into granular packings

Penetration of intruders into granular packings is well described by separately considering the dry or wet case of granular environments in previous experiments and simulations; however, the unified description of such penetration depth in these two granular media remains elusive due to lacking clear explanations about its origins. Based on three-dimensional discrete element method simulations, we introduce a power-law fitting form of the final penetration depth of a spherical intruder with low velocity vertically penetrating into dry and wet granular packings, excellently expressed on a master curve as a power-law function of a dimensionless impact number that is defined as the square root of the ratio between the inertial stress of the intruder and the linear combination of the mean gravitational stress and the cohesive stress exerted on each grain in the packings, as a remarkable extension of the inertial number in dry granular flows. This scaling robustly provides physical insights inherent in the unified description of the material properties of granular packings and the impactor penetration conditions on the final penetration depth in the impact tests, providing evidence of impact properties in different disciplines and applications in science and engineering.

Particle impact on a cohesive granular media

We investigate numerically the impact process of a particle of diameter d and velocity V_{i} onto a cohesive granular packing made of similar particles via two-dimensional discrete element method simulations. The cohesion is ensured by liquid bridges between neighboring particles and described by short range attraction force based on capillary modeling. The outcome of the impact is analyzed through the production of ejected particles from the packing, referred to as the splash process. We quantify this production as a function of the impact velocity for various capillary strength Γ and liquid content Ω. The numerical data indicate that the splash process is modified when the dimensionless cohesion number Co=6Γ/ρ_{p}gd^{2} (where ρ_{p} is the particle density, d its diameter, and g the gravitational acceleration) exceeds a critical value of the order of the unity. Above this value, we highlight that the ejection process is triggered above a threshold impact Froude number, Fr=V_{i}/sqrt[gd], which depends both on Γ and Ω and scales as Γ^{β}Ω^{δ}, where the values of the exponents are found close to 1/2 and 1/6, respectively, and can be derived from rational physical arguments. Importantly, we show that, above the threshold, the number of splashed particles follows a linear law with the impact Froude number as in the cohesionless case.

Sheared granular matter and the empirical relations of seismicity

The frictional instability associated with earthquake initiation and earthquake dynamics is believed to be mainly controlled by the dynamics of fragmented rocks within the fault gauge. Principal features of the emerging seismicity (e.g., intermittent dynamics and broad time and/or energy scales) have been replicated by simple experimental setups, which involve a slowly driven slider on top of granular matter, for example. Yet these setups are often physically limited and might not allow one to determine the underlying nature of specific features and, hence, the universality and generality of the experimental observations. Here, we address this challenge by a numerical study of a spring-slider experiment based on two-dimensional discrete element method simulations, which allows us to control the properties of the granular matter and of the surface of the slider, for example. Upon quasistatic loading, stick-slip-type behavior emerges which is contrasted by a stable sliding regime at finite driving rates, in agreement with experimental observations. Across large parameter ranges for damping, interparticle friction, particle polydispersity, etc., the earthquake-like dynamics associated with the former regime results in several robust scale-free statistical features also observed in experiments. At first sight, these closely resemble the main empirical relations of tectonic seismicity at geological scales. This includes the Gutenberg-Richter distribution of event sizes, the Omori-Utsu-type decay of aftershock rates, as well as the aftershock productivity relation and broad recurrence time distributions. Yet, we show that the correlations associated with tectonic aftershocks are absent such that the origin of the Omori-Utsu relation, the aftershock productivity relation, and Båth's relation in the simulations is fundamentally different from the case of tectonic seismicity. This, we believe, is mainly due to a lack of macroscale relaxation processes that are closely tied to the generation of real aftershocks. We argue that the same is true for previous laboratory experiments.

Three-dimensional compaction of soft granular packings

This paper analyzes the compaction behavior of assemblies composed of soft (elastic) spherical particles beyond the jammed state, using three-dimensional non-smooth contact dynamic simulations. The assemblies of particles are characterized using the evolution of the packing fraction, the coordination number, and the von Misses stress distribution within the particles as the confining stress increases. The packing fraction increases and tends toward a maximum value close to 1, and the mean coordination number increases as a square root of the packing fraction. As the confining stress increases, a transition is observed from a granular-like material with exponential tails of the shear stress distributions to a continuous-like material characterized by Gaussian-like distributions of the shear stresses. We develop an equation that describes the evolution of the packing fraction as a function of the applied pressure. This equation, based on the micromechanical expression of the granular stress tensor, the limit of the Hertz contact law for small deformation, and the power-law relation between the packing fraction and the coordination of the particles, provides good predictions from the jamming point up to very high densities without the need for tuning any parameters.

How cohesion controls the roughness of a granular deposit

Cohesive granular materials often form clusters of grains, which alter their flowing properties. How these clusters form and evolve is difficult to visualize in the bulk of the material, and thus to model. Here, we use a proxy to investigate the formation of such clusters, which is the rough surface of a cohesive granular deposit. We characterize this roughness and show how it is related to the cohesion between beads. Specifically, the size of this roughness increases with the inter-particle cohesion, and the profile exhibits a self-affine behaviour, as observed for crack paths in the domain of fractography. In addition to providing a simple method to measure the inter-particle cohesion from macroscopic parameters, these results give better comprehension of the formation of clusters in cohesive granular materials.

Unearthing real-time 3D ant tunneling mechanics

Granular excavation is the removal of solid, discrete particles from a structure composed of these objects. Efficiently predicting the stability of an excavation during particle removal is an unsolved and highly nonlinear problem, as the movement of each grain is coupled to its neighbors. Despite this, insects such as ants have evolved to be astonishingly proficient excavators, successfully removing grains such that their tunnels are stable. Currently, it is unclear how ants use their limited information about the environment to construct lasting tunnels. We attempt to unearth the ants' tunneling algorithm by taking three-dimensional (3D) X-ray computed tomographic imaging (XRCT), in real time, of Pogonomyrmex ant tunnel construction. By capturing the location and shape of each grain in the domain, we characterize the relationship between particle properties and ant decision-making within an accurate, virtual recreation of the experiment. We discover that intergranular forces decrease significantly around ant tunnels due to arches forming within the soil. Due to this force relaxation, any grain the ants pick from the tunnel surface will likely be under low stress. Thus, ants avoid removing grains compressed under high forces without needing to be aware of the force network in the surrounding material. Even more, such arches shield tunnels from high forces, providing tunnel robustness. Finally, we observe that ants tend to dig piecewise linearly downward. These results are a step toward understanding granular tunnel stability in heterogeneous 3D systems. We expect that such findings may be leveraged for robotic excavation.

Scaling behavior of the tensile strength of viscocohesive granular aggregates

We numerically analyze the tensile strength of a single wet agglomerate modeled as a viscocohesive aggregate impacting a flat surface by using the discrete-element simulations. The viscocohesive agglomerate composed of primary spherical particles with the inclusion of the interstitial liquid in the form of the capillary bridges characterized by the cohesive and viscous forces between particles is extracted from a cuboidal sample of granular materials by applying a spherical probe. The tensile strength is measured from the impact test of a wet agglomerate by systematically varying different values of the surface tension of the interstitial liquid, the liquid viscosity, and the impact speed. We show that the tensile stress increases immediately when the collision occurs between the agglomerate and the flat surface. The peak of the tensile stress obtained after the collision, then decreases smoothly with increasing the particle movement. The maximum tensile stress is defined to be the tensile strength of such agglomerate. It is remarkable that the normalized tensile strength of such agglomerate can be well described as a function of a dimensionless impact number that incorporates the capillary number and Stokes number (calculated from the surface tension and the viscosity of the liquid and the impact rate of the agglomerate), thus providing the confirmation for the unified representation of the liquid properties and the impact rate of wet granular media.

Multi-scale cohesion force measurements for cemented granular materials

We experimentally investigated cohesion of artificially bonded granular materials made of spherical glass beads cemented by solid paraffin bonds. By means of laboratory tests designed and carried out for investigation at different scales, we measured the tensile yield strength for solid bonds both at the inter-particle micro-scale and cemented samples at the meso-scale. A parametric study has been performed by varying some of the granular material properties (bead diameter, paraffin content as well as the dimension of the sample for the meso-scale tensile tests. We finally propose a discusion on: (i) the relationship between the microscopic and macroscopic cohesion forces relying on classical homogenisation laws ; (ii) the potential impact of size effects based on a simple phenomenological model.

Flows of cohesive granular media

Cohesive granular media have broad applications in industries. However, our understanding of their flow behavior is still limited compared to dry granular media, although rich knowledge about their static and plastic properties has been gained. In this paper, we provide some insights into the flow behavior of cohesive granular media from our recent numerical studies using an inclined plane and a plane shear cell. We evidence that the cohesive nature of flows is significantly affected by material properties of the particles like stiffness and inelasticity in addition to the inter-particle adhesion and introduce the concept of “effective” adhesion, which incorporates the effects of these three variables. We propose constitutive relations involving dimensionless inertial number and “effective” cohesion number, based on the “effective” adhesion to describe the rheology. We also show that increasing adhesion increases the hysteresis in granular media, evidencing the existence of a prominent shear weakening branch in the friction coefficient versus inertial number rheological curve. Moreover, we reveal that this increasing hysteresis gives rise to the increasing occurrence of shear banding instability, pointing to the increasing possibility of jamming in cohesive granular media. Finally, we present a promising experimental approach to investigate the flow behavior of cohesive granular materials, based on a simple method of preparing a long time stable medium with a controlled adhesion between particles.

Capturing the failure of a cohesive granular step

A Contact Dynamics algorithm is applied to simulate the failure of 2-dimensional granular steps. Focussing on one single value for both the adhesive force threshold and the contact friction, we track the signature of the failure in the cumulative displacement of the grains. The introduction of a displacement threshold allows for the identification of the onset of a rapid failure and the formation of the corresponding shear band. The latter gives access to an estimation of the failure orientation.

The robustness of the measure thus performed for one single run is assessed by carrying out a series of 10 additional simulations, showing a fairly reproducible behaviour.

The role of inter-particle friction on rheology and texture of wet granular flows

In order to get insight into the rheology and texture of rough unsaturated granular flows, we study the effects of the inter-particle friction coefficient on the macroscopic attributes and the texture variables of steady-state shearing flow of wet granular materials by relying on three-dimensional (3D) particle dynamics simulations. The macroscopic attributes are characterized by the macroscopic friction coefficient, macroscopic cohesion, and the packing fraction. The microstructural variables are characterized by the fabric and force anisotropies, the coordination number, and the stress transmission ratio. We show that the macroscopic observables behave as a function of the inertial number as a dry case for different values of the inter-particle friction coefficient. In particular, the macroscopic friction coefficient increases and the packing fraction decreases rapidly for small values of the friction coefficient, then they almost reach plateaus for higher values of the friction coefficient. Interestingly, all the macroscopic observables nicely behave as a function of the small values of the friction coefficient. Similarly, we also observe these characteristics for the fabric and force anisotropies and the coordination number as well as the stress transmission ratio which reflects the intermediate relationship between the microstructure and the mechanical behavior of such flows.

Cohesion-controlled granular material

We present a simple method to prepare a granular material with a controlled cohesion between particles. The granular material is made of spherical glass beads coated with a polyborosiloxane polymer. This material is proved to be stable in time and nonsensitive to temperature and humidity. The interparticle force is measured and related to the size of the grain and the polymer coating thickness. Classical measurements (packing fraction, repose angle, macroscopic cohesion) are performed with this cohesion-controlled granular material. This model material opens many perspectives to study in a controlled manner the flow of cohesive grains.

Insights into the rheology of cohesive granular media

An uninterrupted flow of powders is the key to smooth production operations of many industries. However, powders have more difficulty flowing than coarse, granular media like sand because of the interparticle cohesive interactions. What precisely controls the “flowability” of powders remains unclear. Here, we address this issue by performing numerical simulations of the flow of cohesive grains. We show that the cohesiveness during flow is not only controlled by the interparticle adhesion, but also by the stiffness and inelasticity of the grains. For the same adhesion, stiffer and less dissipative grains yield a less cohesive flow, i.e., higher “flowability.” This combined effect can be embedded in a single dimensionless number—a result that enriches our understanding of powder rheology.

Characterization and prediction of the “flowability” of powders are of paramount importance in many industries. However, our understanding of the flow of powders like cement or flour is sparse compared to the flow of coarse, granular media like sand. The main difficulty arises because of the presence of adhesive forces between the grains, preventing smooth and continuous flows. Several tests are used in industrial contexts to probe and quantify the “flowability” of powders. However, they remain empirical and would benefit from a detailed study of the physics controlling flow dynamics. Here, we attempt to fill the gap by performing intensive discrete numerical simulations of cohesive grains flowing down an inclined plane. We show that, contrary to what is commonly perceived, the cohesive nature of the flow is not entirely controlled by the interparticle adhesion, but that stiffness and inelasticity of the grains also play a significant role. For the same adhesion, stiffer and less dissipative grains yield a less cohesive flow. This observation is rationalized by introducing the concept of a dynamic, “effective” adhesive force, a single parameter, which combines the effects of adhesion, elasticity, and dissipation. Based on this concept, a rheological description of the flow is proposed for the cohesive grains. Our results elucidate the physics controlling the flow of cohesive granular materials, which may help in designing new approaches to characterize the “flowability” of powders.

Additive rheology of complex granular flows

Granular flows are omnipresent in nature and industrial processes, but their rheological properties such as apparent friction and packing fraction are still elusive when inertial, cohesive and viscous interactions occur between particles in addition to frictional and elastic forces. Here we report on extensive particle dynamics simulations of such complex flows for a model granular system composed of perfectly rigid particles. We show that, when the apparent friction and packing fraction are normalized by their cohesion-dependent quasistatic values, they are governed by a single dimensionless number that, by virtue of stress additivity, accounts for all interactions. We also find that this dimensionless parameter, as a generalized inertial number, describes the texture variables such as the bond network connectivity and anisotropy. Encompassing various stress sources, this unified framework considerably simplifies and extends the modeling scope for granular dynamics, with potential applications to powder technology and natural flows.

Granular materials are abundant in nature, but we haven’t fully understood their rheological properties as complex interactions between particles are involved. Here, Vo et al. show that granular flows can be described by a generalized dimensionless number based on stress additivity.

Evolution of wet agglomerates inside inertial shear flow of dry granular materials

We use particle dynamics simulations to investigate the evolution of a wet agglomerate inside homogeneous shear flows of dry particles. The agglomerate is modeled by introducing approximate analytical expressions of capillary and viscous forces between particles in addition to frictional contacts. During shear flow, the agglomerate may elongate, break, or be eroded by loss of its capillary bonds and primary particles. By systematically varying the shear rate and surface tension of the binding liquid, we characterize the rates of these dispersion modes. All the rates increase with increasing inertial number of the flow and decreasing cohesion index of the agglomerate. We show that the data points for each mode collapse on a master curve for a dimensionless scaling parameter that combines the inertial number and the cohesion index. The erosion rate vanishes below a cutoff value of the scaling parameter. This leads to a power-law borderline between the vanishing erosion states and erosion states in the phase space defined by the inertial number and the cohesion index.

The Effect of Grain Size and Shape on Sliding Friction of Wet Granular Media

The wet granular material creates networks in which interstitial liquid provides capillary bridges needed to hold grains together. There is an optimal fraction of the interstitial liquid in which the bridges are formed and the friction coefficient is minimal. We found that the size of the grains affects the friction of wet granular media. Our observations demonstrates that the optimum volume fraction, in which the friction coefficient is minimized, increases with grain size, but for sand immersed in water, this minimum friction coefficient itself increases with size and for glass beads immersed in silicone oil it decreases, indicating that the shape of the grains also has an effect on this friction. It is also shown that there is a crossover point for grain size at which the network effect created by capillary bridges is dominated by wet granular media. This crossover point is found.

Agglomeration of wet particles in dense granular flows

In order to get insight into the wet agglomeration process, we numerically investigate the growth of a single granule inside a dense flow of an initially homogeneous distribution of wet and dry particles. The simulations are performed by means of the discrete element method and the binding liquid is assumed to be transported by the wet particles, which interact via capillary and viscous force laws. The granule size is found to be an exponential function of time, reflecting the conservation of the amount of liquid and the decrease of the number of available wet particles inside the flow during agglomeration. We analyze this behavior in terms of the accretion and erosion rates of wet particles for a range of different values of material parameters such as mean particle size, size polydispersity, friction coefficient and liquid viscosity. In particular, we propose a phase diagram of the granule growth as a function of the mean primary particle diameter and particle size span, which separates the parametric domain in which the granule grows from the domain in which the granule does not survive.

Capillary Stress and Structural Relaxation in Moist Granular Materials

A numerical and theoretical framework to address the poromechanical effect of capillary stress in complex mesoporous materials is proposed and exemplified for water sorption in cement. We first predict the capillary condensation/evaporation isotherm using lattice-gas simulations in a realistic nanogranular cement model. A phase-field model to calculate moisture-induced capillary stress is then introduced and applied to cement at different water contents. We show that capillary stress is an effective mechanism for eigenstress relaxation in granular heterogeneous porous media, which contributes to the durability of cement.

Effects of Polarization on Particle-Laden Flows

Simulations of particle-laden flow with dielectric particles are carried out with varying levels of electrical charging and particle polarization. Simulation results reveal three distinct flow regions. For low particle charge and polarizability, flow is nearly symmetric and nonmeandering. For strong charging and polarization, particles form a continuous and tightly clustered sheet close to one of the walls. Between these extremes, particles form localized particle-rich regions, around which the gas executes a meandering flow. These results indicate that polarization can lead to qualitative changes in the characteristics of particle-laden flows subject to tribocharging.

Shear strength of wet granular materials: Macroscopic cohesion and effective stress : Discrete numerical simulations, confronted to experimental measurements

Rheometric measurements on assemblies of wet polystyrene beads, in steady uniform quasistatic shear flow, for varying liquid content within the small saturation (pendular) range of isolated liquid bridges, are supplemented with a systematic study by discrete numerical simulations. The numerical results agree quantitatively with the experimental ones provided that the intergranular friction coefficient is set to the value [Formula: see text], identified from the behaviour of the dry material. Shear resistance and solid fraction [Formula: see text] are recorded as functions of the reduced pressure [Formula: see text], which, defined as [Formula: see text], compares stress [Formula: see text], applied in the velocity gradient direction, to the tensile strength [Formula: see text] of the capillary bridges between grains of diameter a, and characterizes cohesion effects. The simplest Mohr-Coulomb relation with [Formula: see text]-independent cohesion c applies as a good approximation for large enough [Formula: see text] (typically [Formula: see text]. Numerical simulations extend to different values of μ and, compared to experiments, to a wider range of [Formula: see text]. The assumption that capillary stresses act similarly to externally applied ones onto the dry granular contact network (effective stresses) leads to very good (although not exact) predictions of the shear strength, throughout the numerically investigated range [Formula: see text] and [Formula: see text]. Thus, the internal friction coefficient [Formula: see text] of the dry material still relates the contact force contribution to stresses, [Formula: see text], while the capillary force contribution to stresses, [Formula: see text], defines a generalized Mohr-Coulomb cohesion c, depending on [Formula: see text] in general. c relates to [Formula: see text] , coordination numbers and capillary force network anisotropy. c increases with liquid content through the pendular regime interval, to a larger extent, the smaller the friction coefficient. The simple approximation ignoring capillary shear stress [Formula: see text] (referred to as the Rumpf formula) leads to correct approximations for the larger saturation range within the pendular regime, but fails to capture the decrease of cohesion for smaller liquid contents.

Rheology of granular materials composed of crushable particles

We investigate sheared granular materials composed of crushable particles by means of contact dynamics simulations and the bonded-cell model for particle breakage. Each particle is paved by irregular cells interacting via cohesive forces. In each simulation, the ratio of the internal cohesion of particles to the confining pressure, the relative cohesion, is kept constant and the packing is subjected to biaxial shearing. The particles can break into two or more fragments when the internal cohesive forces are overcome by the action of compressive force chains between particles. The particle size distribution evolves during shear as the particles continue to break. We find that the breakage process is highly inhomogeneous both in the fragment sizes and their locations inside the packing. In particular, a number of large particles never break whereas a large number of particles are fully shattered. As a result, the packing keeps the memory of its initial particle size distribution, whereas a power-law distribution is observed for particles of intermediate size due to consecutive fragmentation events whereby the memory of the initial state is lost. Due to growing polydispersity, dense shear bands are formed inside the packings and the usual dilatant behavior is reduced or cancelled. Hence, the stress-strain curve no longer passes through a peak stress, and a progressive monotonic evolution towards a pseudo-steady state is observed instead. We find that the crushing rate is controlled by the confining pressure. We also show that the shear strength of the packing is well expressed in terms of contact anisotropies and force anisotropies. The force anisotropy increases while the contact orientation anisotropy declines for increasing internal cohesion of the particles. These two effects compensate each other so that the shear strength is nearly independent of the internal cohesion of particles.

Reply to "Comment on 'Flow of wet granular materials: A numerical study' "

In his Comment on our paper [Phys. Rev. E 92, 022201 (2015)10.1103/PhysRevE.92.022201], Chareyre criticizes, as inaccurate, the simple approach we adopted to explain the strong enhancement of the quasistatic shear strength of the material caused by capillary cohesion. He also observes that a similar form of the "effective stress" approach, accounting for the capillary shear stress, which we neglected, results in a quantitatively correct prediction of this yield stress. We agree with these remarks, which we deem quite relevant and valuable. We nevertheless point out that the initial approximation, despite ∼25% errors on shear strength in the worst cases, provides a convenient estimate of the Mohr-Coulomb cohesion of the material, which is directly related to the coordination number. We argue that the effective stress assumption, despite its surprising success in the range of states explored in Khamseh et al. [Phys. Rev. E 92, 022201 (2015)10.1103/PhysRevE.92.022201], is bound to fail in strongly cohesion-dominated material states.

Shear strength and microstructure of polydisperse packings: The effect of size span and shape of particle size distribution

By means of extensive contact dynamics simulations, we analyzed the effect of particle size distribution (PSD) on the strength and microstructure of sheared granular materials composed of frictional disks. The PSDs are built by means of a normalized β function, which allows the systematic investigation of the effects of both, the size span (from almost monodisperse to highly polydisperse) and the shape of the PSD (from linear to pronouncedly curved). We show that the shear strength is independent of the size span, which substantiates previous results obtained for uniform distributions by packing fraction. Notably, the shear strength is also independent of the shape of the PSD, as shown previously for systems composed of frictionless disks. In contrast, the packing fraction increases with the size span, but decreases with more pronounced PSD curvature. At the microscale, we analyzed the connectivity and anisotropies of the contacts and forces networks. We show that the invariance of the shear strength with the PSD is due to a compensation mechanism which involves both geometrical sources of anisotropy. In particular, contact orientation anisotropy decreases with the size span and increases with PSD curvature, while the branch length anisotropy behaves inversely.

Force Transmission Modes of Non-Cohesive and Cohesive Materials at the Critical State

This paper investigates the force transmission modes, mainly described by probability density distributions, in non-cohesive dry and cohesive wet granular materials by discrete element modeling. The critical state force transmission patterns are focused on with the contact model effect being analyzed. By shearing relatively dense and loose dry specimens to the critical state in the conventional triaxial loading path, it is observed that there is a unique critical state force transmission mode. There is a universe critical state force distribution pattern for both the normal contact forces and tangential contact forces. Furthermore, it is found that using either the linear Hooke or the non-linear Hertz model does not affect the universe force transmission mode, and it is only related to the grain size distribution. Wet granular materials are also simulated by incorporating a water bridge model. Dense and loose wet granular materials are tested, and the critical state behavior for the wet material is also observed. The critical state strength and void ratio of wet granular materials are higher than those of a non-cohesive material. The critical state inter-particle distribution is altered from that of a non-cohesive material with higher probability in relatively weak forces. Grains in non-cohesive materials are under compressive stresses, and their principal directions are mainly in the axial loading direction. However, for cohesive wet granular materials, some particles are in tension, and the tensile stresses are in the horizontal direction on which the confinement is applied. The additional confinement by the tensile stress explains the macro strength and dilatancy increase in wet samples.

Self assembly, mobilization, and flotation of crude oil contaminated sand particles as granular shells on gas bubbles in water

Contaminant fate and transport studies and models include transport mechanisms for colloidal particles and dissolved ions which can be easily moved with water currents. However, mobilization of much larger contaminated granular particles (i.e., sand) in sediments have not been considered as a possible mechanism due to the relatively larger size of sand particles and their high bulk density. We conducted experiments to demonstrate that oil contaminated granular particles (which exhibit hydrophobic characteristics) can attach on gas bubbles to form granular shells and transfer from the sediment phase to the water column. The interactions and conditions necessary for the oil contaminated granular particles to self assemble as tightly packed granular shells on the gas bubbles which transfer from sediment phase to the water column were evaluated both experimentally and theoretically for South Louisiana crude oil and quartz sand particles. Analyses showed that buoyancy forces can be adequate to move the granular shell forming around the air bubbles if the bubble radius is above 0.001mm for the sand particles with 0.28mm diameter. Relatively high magnitude of the Hamaker constant for the oil film between sand and air (5.81×10^-20J for air-oil-sand) indicates that air bubbles have high affinity to attach on the oil film that is on the sand particles in comparison to attaching to the sand particles without the oil film in water (1.60×10^-20J for air-water-sand). The mobilization mechanism of the contaminated granular particles with gas bubbles can occur in natural environments resulting in transfer of granular particles from sediments to the water column.

Direct numerical simulation of gas-solid-liquid flows with capillary effects: An application to liquid bridge forces between spherical particles

In this study, a numerical method is developed to perform the direct numerical simulation (DNS) of gas-solid-liquid flows involving capillary effects. The volume-of-fluid method employed to track the free surface and the immersed boundary method is adopted for the fluid-particle coupling in three-phase flows. This numerical method is able to fully resolve the hydrodynamic force and capillary force as well as the particle motions arising from complicated gas-solid-liquid interactions. We present its application to liquid bridges among spherical particles in this paper. By using the DNS method, we obtain the static bridge force as a function of the liquid volume, contact angle, and separation distance. The results from the DNS are compared with theoretical equations and other solutions to examine its validity and suitability for modeling capillary bridges. Particularly, the nontrivial liquid bridges formed in triangular and tetrahedral particle clusters are calculated and some preliminary results are reported. We also perform dynamic simulations of liquid bridge ruptures subject to axial stretching and particle motions driven by liquid bridge action, for which accurate predictions are obtained with respect to the critical rupture distance and the equilibrium particle position, respectively. As shown through the simulations, the strength of the present method is the ability to predict the liquid bridge problem under general conditions, from which models of liquid bridge actions may be constructed without limitations. Therefore, it is believed that this DNS method can be a useful tool to improve the understanding and modeling of liquid bridges formed in complex gas-solid-liquid flows.

Liquid morphologies and capillary forces between three spherical beads

Equilibrium shapes of coalesced pendular bridges in a static assembly of spherical beads are computed by numerical minimization of the interfacial energy. Our present study focuses on generic bead configurations involving three beads, one of which is in contact to the two others while there is a gap of variable size between the latter. In agreement with previous experimental studies, we find interfacial "trimer" morphologies consisting of three coalesced pendular bridges, and "dimers" of two coalesced bridges. In a certain range of the gap opening we observe a bistability between the dimer and trimer morphology during changes of the liquid volume. The magnitude of the corresponding capillary forces in presence of a trimer or dimer depends, besides the gap opening, only on the volume or Laplace pressure of the liquid. For a given Laplace pressure, and for the same gap opening, the capillary forces induced by a trimer are only slightly larger than the corresponding forces in the presence of three pendular bridges. This observation is consistent with a plateau of capillary cohesion in terms of the saturation of a wetting liquid in the funicular regime, as reported in the experimental work [Scheel et al., Nat. Mater. 7, 189 (2008)1476-112210.1038/nmat2117].

Flow of wet granular materials: A numerical study

We simulate dense assemblies of frictional spherical grains in steady shear flow under controlled normal stress P in the presence of a small amount of an interstitial liquid, which gives rise to capillary menisci, assumed isolated (pendular regime), and attractive forces, which are hysteretic: Menisci form at contact, but do not break until grains are separated by a finite rupture distance. The system behavior depends on two dimensionless control parameters, inertial number I and reduced pressure P*=aP/(πΓ), comparing confining forces ∼a2P to meniscus tensile strength F0=πΓa, for grains of diameter a joined by menisci with surface tension Γ. We pay special attention to the quasistatic limit of slow flow and observe systematic, enduring strain localization in some of the cohesion-dominated (P*∼0.1) systems. Homogeneous steady flows are characterized by the dependence of internal friction coefficient μ* and solid fraction Φ on I and P*. We also record normal stress differences, fairly small but not negligible and increasing for decreasing P*. The system rheology is moderately sensitive to saturation within the pendular regime, but would be different in the absence of capillary hysteresis. Capillary forces have a significant effect on the macroscopic behavior of the system, up to P* values of several units, especially for longer force ranges associated with larger menisci. The concept of effective pressure may be used to predict an order of magnitude for the strong increase of μ* as P* decreases but such a crude approach is unable to account for the complex structural changes induced by capillary cohesion, with a significant decrease of Φ and different agglomeration states and anisotropic fabric. Likewise, the Mohr-Coulomb criterion for pressure-dependent critical states is, at best, an approximation valid within a restricted range of pressures, with P*≥1. At small enough P*, large clusters of interacting grains form in slow flows, in which liquid bonds survive shear strains of several units. This affects the anisotropies associated with different interactions and the shape of function μ*(I), which departs more slowly from its quasistatic limit than in cohesionless systems (possibly explaining the shear banding tendency).

Grain-scale modeling of arbitrary fluid saturation in random packings

We propose a model for increasing liquid saturation in a granular packing, which can account for liquid redistribution at saturation levels beyond the well-studied capillary bridge regime. The model is capable of resolving and combining capillary bridges, menisci, and fully saturated pores to form local liquid clusters of any shape. They can exchange volume due to the local Laplace pressure gradient via a liquid film on the surfaces of grains. Local instabilities such as Haines jumps trigger the discontinuous evolution of the liquid front. The applicability of the model is demonstrated and compared to benchmark experiments on the level of individual liquid structures as well as on larger systems.

Bonded-cell model for particle fracture

Particle degradation and fracture play an important role in natural granular flows and in many applications of granular materials. We analyze the fracture properties of two-dimensional disklike particles modeled as aggregates of rigid cells bonded along their sides by a cohesive Mohr-Coulomb law and simulated by the contact dynamics method. We show that the compressive strength scales with tensile strength between cells but depends also on the friction coefficient and a parameter describing cell shape distribution. The statistical scatter of compressive strength is well described by the Weibull distribution function with a shape parameter varying from 6 to 10 depending on cell shape distribution. We show that this distribution may be understood in terms of percolating critical intercellular contacts. We propose a random-walk model of critical contacts that leads to particle size dependence of the compressive strength in good agreement with our simulation data.