Interparticle Friction Coefficient Research Articles

Discussion on “The inter-particle coefficient of friction at the contacts of Leighton Buzzard sand quartz mineralogy” by Kostas Senetakis, Matthew R. Coop, M. Cristina Todisco, Soils and Foundations 53 (5) (2013) 746–755

Discussion on “The inter-particle coefficient of friction at the contacts of Leighton Buzzard sand quartz mineralogy” by Kostas Senetakis, Matthew R. Coop, M. Cristina Todisco, Soils and Foundations 53 (5) (2013) 746–755

On the effect of stress dependent interparticle friction in direct shear tests

Contact friction is a key influence factor for the shearing behaviour of granular media. In the discrete element method (DEM) contact friction is usually modelled with Coulomb's law assuming a constant interparticle friction coefficient. From tribology it is known that friction is influenced by several factors, e.g., temperature, normal stress, surface condition, etc. None of these influences can be modelled with the constant interparticle friction coefficient from Coulomb's law. For a given granular material (particle shape distribution), the usage of constant interparticle friction in DEM models generally results in constant bulk friction coefficients in the simulation of direct shear tests. While this is frequently seen in experiments with equi-sized spherical particles, papers exist in literature which report a stress dependency of bulk friction for non-spherical particles of certain materials. In this work, a stress dependency of bulk friction is obtained by introducing a model for stress dependent interparticle friction in DEM simulations. For validation experimental results of direct shear tests conducted on single or paired glass beads are used. While the bulk friction of paired spheres clearly decreases with increasing normal stress, it is nearly constant for single spheres. DEM simulations with the stress dependent interparticle friction are in good accordance with the experimental results of both single and paired spheres. A comparison with simulations, using constant interparticle friction, clearly shows the advantage of the proposed model.

Partition of the contact force network obtained in discrete element simulations of element tests

The transmission of stress within a granular material composed of rigid spheres is explored using the discrete element method. The contribution of contacts to both deviatoric stress and structural anisotropy is investigated. The influences of five factors are considered: inter-particle friction coefficient, loading regime, packing density, contact model, and boundary conditions. The data generated indicate that using the above-average normal contact force criterion to decompose the contact force network into two subsets with distinct contributions to stress transmission and structural anisotropy is not robust. The characteristic normal contact forces marking the transition from negative to positive contribution to the overall deviatoric stress and structural anisotropy are not unique values but vary during shearing. Once the critical state is attained (i.e., once shearing continues at a constant deviator stress and solid fraction), the characteristic normal contact force remains approximately constant and this critical state characteristic normal force is observed to decrease with increasing inter-particle friction. The characteristic normal contact force considering the contribution to deviatoric stress has a power-law relationship with the mean effective stress at the critical state.

Discrete Element Simulations of Shallow Plate-Load Tests

AbstractShallow plate-load tests were simulated using a two-dimensional discrete element procedure together with parameters calibrated from a series of biaxial compression experiments on aluminum rods. The deformation and force transmission characteristics within ground materials were investigated first, and then attentions were focused on studying the influences of the interparticle friction coefficient, the roughness of the loading plate, and the size of loading plate on the testing results, including the ultimate bearing capacity, the deformation behavior, and the failure mode. The well-known scale effect in plate-load tests was also analyzed from the perspectives of both continuum mechanics and discrete element method simulations. It was proven that the nonlinear strength behavior of the materials beneath the foundation is a possible source of the scale effect; however, this effect may be counterbalanced by the boundary restriction effect in laboratory experiments.

The Micromechanical Behaviour of a Biogenic Carbonate Sand

An experimental investigation of the micromechanical behaviour of a biogenic carbonate sand from the Philippines was conducted. Mechanical parameters of sands at the micro-scale are required in order to simulate the particle interactions in numerical analyses carried out using the Discrete Element Method (DEM). The tests were performed on particles obtained from the sedimentation of coral fragments and they were carried out by means of a custom-made inter-particle loading apparatus that enabled the investigation of both the normal and tangential loading behaviour at the particle contacts. The normal loading tests showed a reversible behaviour after the first loading, while the tangential loading behaviour of this sand appears to be dependent on the vertical confinement and mainly reversible for small displacement cycles. Also, the inter-particle friction coefficients at larger displacements are substantially higher than those calculated for other sands using the same experimental procedures.

Micromechanical Modeling of Yield in Isotropic Non-Cohesive Particulate Materials

We perform a micromechanical analysis of general isotropic non-cohesive particulate materials idealized as three-dimensional random assemblies of uniform spheres with a simple linear elastic inter-particle contact force law and inter-particle Coulomb friction law. We obtain analytical relationships between the inter-particle friction coefficient $$\mu$$ (or inter-particle friction angle $$\phi _\mu = \tan ^{-1} \mu$$ ) on the microscale and the material friction angle $$\phi$$ on the macroscale. Our micromechanical analysis directly employs force and moment equilibrium (together with compatibility and the contact constitutive assumptions noted) rather than energy methods, and thus can account for the effects of particle rotation, and in particular the effects of mechanisms or zero-energy modes due to particle rotation. To explore the effects of particle rotation, we perform analyses with particle rotation either allowed or prohibited. To validate the analytical results obtained here, we compare the $$\phi$$ versus $$\phi _\mu$$ curves determined theoretically to those obtained by the discrete element method (DEM) for six randomly packed specimens of 3430–29, 660 uniform spherical elements with uniform inter-element Coulomb friction in Fleischmann et al. in Geotech Geol Eng 32(4):1081–1100, (2014). The $$\phi$$ versus $$\phi _\mu$$ curves derived here show remarkable agreement with those obtained via DEM simulations in Fleischmann et al. in Geotech Geol Eng 32(4):1081–1100, (2014), especially for the case in which particle rotation is not artificially restrained.

Discrete element modelling (DEM) input parameters: understanding their impact on model predictions using statistical analysis

Selection or calibration of particle property input parameters is one of the key problematic aspects for the implementation of the discrete element method (DEM). In the current study, a parametric multi-level sensitivity method is employed to understand the impact of the DEM input particle properties on the bulk responses for a given simple system: discharge of particles from a flat bottom cylindrical container onto a plate. In this case study, particle properties, such as Young’s modulus, friction parameters and coefficient of restitution were systematically changed in order to assess their effect on material repose angles and particle flow rate (FR). It was shown that inter-particle static friction plays a primary role in determining both final angle of repose and FR, followed by the role of inter-particle rolling friction coefficient. The particle restitution coefficient and Young’s modulus were found to have insignificant impacts and were strongly cross correlated. The proposed approach provides a systematic method that can be used to show the importance of specific DEM input parameters for a given system and then potentially facilitates their selection or calibration. It is concluded that shortening the process for input parameters selection and calibration can help in the implementation of DEM.

Numerical investigation of the at-rest earth pressure coefficient of granular materials

The at-rest earth pressure coefficient, $$\hbox {K}_{0}$$ , is one of the most fundamental values for evaluating in-situ soil stresses and designing foundation. Research has been expanded to investigate the correlation between $$\hbox {K}_{0}$$ and micro-scale characteristic of granular soils, beyond the macroscopic approach empirically correlated with internal friction angle. This study presents the evolution of $$\hbox {K}_{0}$$ values of irregularly shaped natural sand, spherical shaped smooth and rough surfaced glass beads along with the stress history, estimated by the discrete element method. The surface roughness and non-spherical particles were emulated by inter-particle friction coefficient and the clumped particles. Results exhibit that the $$\hbox {K}_{0}$$ during loading stage nonlinearly decreases with increasing values of friction coefficient and the assemblies with clumped particles present the lower values of $$\hbox {K}_{0}$$ than spherical particle assemblies of the same friction coefficient. The varying friction coefficient seems enough to capture the evolution of $$\hbox {K}_{0}$$ during loading, unloading and reloading cycles, while the natural sand inevitably requires the assembly with clumped particles to capture the experimentally observed $$\hbox {K}_{0}$$ evolutions.

The Development of a New Micro-Mechanical Inter-Particle Loading Apparatus

The inter-particle coefficient of friction comprises an essential input parameter in computer codes that utilize the discrete element method. This paper describes the main features of a custom-built apparatus of a new generation, capable of performing inter-particle shearing tests at very small displacements on the order of tens to hundreds of microns and measuring the frictional forces developed at the contacts of coarse-grained particles of sand to gravel size. Linear, micro-stepping motors are used for the inter-particle shearing tests of a displacement-controlled type and the application of the vertical confinement of a force-controlled type at the particle contacts. The apparatus is designed to work at very small confining forces, in general between 1 and 20 N, and utilizes a system of bearings of small friction, which can be calibrated following simple procedures. The experiments are controlled and monitored through a computer code developed for the apparatus. The signal conditioning and data-logging systems were optimized to give the minimum environmental and electrical noise in the experimental data. The particles tested must have a relatively convex shape and be fairly symmetrical about the axis of shearing to avoid significant lateral forces in the out-of-plane horizontal direction during sliding, and, in general, the size of particles is limited from about 0.50 to 5.0 mm. Tests on reference particles composed of chrome steel balls and quartz particles demonstrated high repeatability of the results and agreement with the literature data. The experimentally derived horizontal force–displacement data showed that the stiffness of the apparatus is sufficiently high to prevent significant stick-slip phenomena, allowing a stable sliding.

Determination of Yield Surfaces for Isotropic Non-Cohesive Particulate Materials by the Discrete Element Method

We perform numerical simulations using the discrete element method (DEM) to determine yield surfaces for large samples of randomly packed uniform spheres with constant normal and tangential contact stiffnesses (linear spring model) and uniform inter-particle friction coefficient μ, for a large range of values of the inter-particle friction coefficient μ. The beauty of DEM is that the micromechanical properties of the spheres, especially the inter-particle friction coefficient μ, are known exactly. Further, simulations can be performed with particle rotation either prohibited or unrestrained, which provides an effective means for evaluating analytical models that employ these assumptions. We compare the resulting yield surfaces to the Mohr–Coulomb, Matsuoka–Nakai, Lade–Duncan, and Drucker–Prager yield surfaces, and determine the relationship between the resulting material friction angle ϕ on the macroscale and the inter-particle friction coefficient μ (or the inter-particle friction angle ϕμ) on the microscale. We find the Lade–Duncan yield surface provides the best agreement, by far, with the simulations in all cases. We also monitor inter-particle friction work and particle rotation within each specimen during the DEM simulations, both globally and on a particle-by-particle basis, and we compare the results obtained from DEM simulations in which the spheres were allowed full three-dimensional translational and rotational freedom of motion and DEM simulations in which particle rotation was prohibited.

On micromechanical characteristics of the critical state of two-dimensional granular materials

In micromechanics of quasi-static deformation of granular materials, relationships are investigated between the macro-scale, continuum-mechanical characteristics, and the micro-scale characteristics at the particle and interparticle contact level. An important micromechanical quantity is the fabric tensor that reflects the distribution of contact orientations. It also contains information on the coordination number, i.e. the average number of contacts per particle. Here, the focus is on characteristics of the critical state in the two-dimensional case. Critical state soil mechanics is reviewed from the micromechanical viewpoint. Two-dimensional discrete element method (DEM) simulations have been performed with discs from a fairly narrow particle-size distribution. Various values for the interparticle friction coefficient and for the confining pressure have been considered to investigate the effect of these quantities on critical state characteristics (shear strength, packing fraction, coordination number and fabric anisotropy). Results from these DEM simulations show that a limiting fabric state exists at the critical state, which is geometrical in origin. The contact network tessellates the assembly into loops that are formed by contacts. For each loop, a symmetrical loop tensor is defined, based on its contact normals. This loop tensor reflects the shape of the loop. An orientation is associated with each loop, based on its loop tensor. At the critical state, the frequencies with which loops with different number of sides occur depend on the coordination number. At the critical state, these loops have, on average, the following universal characteristics, i.e. independent of the coordination number: (1) loops with the same number of sides and orientation have identical anisotropy of the loop tensor, (2) the anisotropy of the loop tensor depends linearly on the number of sides of the loop, (3) the distribution of loop orientations is identical, (4) Lewis’s law for the loop areas, which is a linear relation between the number of sides of loops and their area, is satisfied (not exclusively at the critical state) and (5) the areas of the loops do not depend on their orientation.

Exploring the influence of interparticle friction on critical state behaviour using DEM

SUMMARYUnderstanding the extent to which discrete element method (DEM) simulations can capture the critical state characteristics of granular materials is important to legitimize the use of DEM in geomechanics. This paper documents a DEM study that considered the sensitivity of the critical state response characteristics to the coefficient of interparticle friction (μ) using samples with gradings that are representative of a real soil. Most of the features that are typically associated with sand behaviour at the critical state were seen to emerge from the DEM simulation data. An important deviation occurs when high μ values (μ ≥ 0.5) are used, as has been the case in a number of prior DEM studies. While there is a systematic variation in the critical state behaviour with μ for μ < 0.5, when μ ≥ 0.5, the behaviour at the critical state seems to be insensitive to further increases in μ. In contrast to observations of conventional soil response, when μ ≥ 0.5, the void ratio at the critical state initially increases with increasing mean effective stress (p′). Analysis of the DEM data and use of simple models of isolated force chains enabled some key observations. When ‘floating’ particles that do not transmit stress are eliminated from the void ratio calculation, the void ratio at the critical state decreases consistently with increasing p′. There is a transition from sliding to rolling behaviour at the contact points as μ increases. Beyond a limiting value of μ, further increases in μ do not increase the buckling resistance of individual strong force chains. Copyright © 2014 John Wiley & Sons, Ltd.

Phonon dispersion and elastic moduli of two-dimensional disordered colloidal packings of soft particles with frictional interactions

Particle tracking and displacement covariance matrix techniques are employed to investigate the phonon dispersion relations of two-dimensional colloidal glasses composed of soft, thermoresponsive microgel particles whose temperature-sensitive size permits in situ variation of particle packing fraction. Bulk, B, and shear, G, moduli of the colloidal glasses are extracted from the dispersion relations as a function of packing fraction, and variation of the ratio G/B with packing fraction is found to agree quantitatively with predictions for jammed packings of frictional soft particles. In addition, G and B individually agree with numerical predictions for frictional particles. This remarkable level of agreement enabled us to extract an energy scale for the interparticle interaction from the individual elastic constants and to derive an approximate estimate for the interparticle friction coefficient.

The inter-particle coefficient of friction at the contacts of Leighton Buzzard sand quartz minerals

A series of micro-mechanical tests was carried out in order to investigate the inter-particle coefficient of friction at the contacts of quartz minerals of Leighton Buzzard sand. For this purpose, a custom-built inter-particle loading apparatus was designed and constructed, the main features of which are described briefly in this paper. This apparatus is capable of performing shearing tests at the contacts of soil minerals of a particle–particle type in the range of very small displacements, from less than 1μm to about 300μm, and very small normal loads, between about less than 1N and 15N. The laboratory data showed that the effects of the normal force and the sliding velocity on the coefficient of dynamic friction are not significant, while dry and saturated surfaces had similar frictional characteristics. The steady state sliding was mobilized within a range of 0.5–3.0μm of horizontal displacement, and the coefficient of static friction was very similar to the corresponding coefficient during constant shearing. Repeating the inter-particle shearing tests on the same particles and following the same shearing track indicated a small reduction in the inter-particle coefficient of friction after the first shearing, which is possibly related to plastic deformation and damage to the asperities.

Granular Flow in Silo Discharge: Discrete Element Method Simulations and Model Assessment

Discharge dynamics of granular particles from a flat-bottomed silo is studied using both continuum modeling and three-dimensional (3D) discrete element method (DEM) simulations. Using DEM, the influence of microscopic parameters (interparticle friction coefficient, particle–wall friction coefficient and particle coefficient of restitution) and system parameters (orifice width) on the discharge rate is quantified. The spatial extent of different regimes (quasi-static, intermediate and inertial) of granular rheology are quantified using a regime map previously established from DEM data of homogeneously sheared granular flow. It is shown that all three regimes of granular rheology coexist during silo discharge, and the intermediate regime plays a significant role in discharge dynamics. A quantitative comparison between results of continuum and DEM simulations is performed by computing discharge rates, solid velocities, and solid stresses for a three-dimensional (3D) flat-bottomed silo. It is found that the t...

Effect of particle friction and polydispersity on the macroscopic stress–strain relations of granular materials

The macroscopic mechanical behavior of granular materials inherently depends on the properties of particles that compose them. Using the discrete element method, the effect of particle contact friction and polydispersity on the macroscopic stress response of 3D sphere packings is studied. The analytical expressions for the pressure, coordination number and fraction of rattlers proposed for isotropically deformed frictionless systems also hold when the interparticle coefficient of friction is finite; however, the numerical values of the parameters such as the jamming volume fraction change with varying microscopic contact and particle properties. The macroscopic response under deviatoric loading is studied with triaxial test simulations. Concerning the shear strength, our results agree with previous studies showing that the deviatoric stress ratio increases with particle coefficient of friction μ starting from a nonzero value for μ = 0 and saturating for large μ. On the other hand, the volumetric strain does not have a monotonic dependence on the particle contact friction. Most notably, maximum compaction is reached at an intermediate value of the coefficient of friction μ ≈ 0.3. The effect of polydispersity on the macroscopic stress–strain relationship cannot be studied independent of initial packing conditions. The shear strength increases with polydispersity when the initial volume fraction is fixed, but the effect of polydispersity is much less pronounced when the initial pressure of the packings is fixed. Finally, a simple hypoplastic constitutive model is calibrated with numerical test results following an established procedure to ascertain the relation between particle properties and material coefficients of the macroscopic model. The calibrated model is in good qualitative agreement with simulation results.

Mechanistic modelling of tests of unbound granular materials

Various tests are used to characterise the strength and resilience of granular materials used in the subbase of a pavement system, but there is a limited understanding of how particle properties relate to the bulk material response under various test conditions. Here, we use discrete element method (DEM) simulations with a mechanistically based contact model to explore influences of the material properties of the particle on the results of two such tests: the dynamic cone penetrometer (DCP) and the resilient modulus tests. We find that the measured resilient modulus increases linearly with the particle elastic modulus, whereas the DCP test results are relatively insensitive to particle elastic modulus. The DCP test results are also relatively insensitive to inter-particle friction coefficient but strongly dependent on the particle shape. We discuss strengths and weaknesses of our modelling approach and include suggestions for future improvements.

Equilibrating Temperaturelike Variables in Jammed Granular Subsystems

Although jammed granular systems are athermal, several thermodynamiclike descriptions have been proposed which make quantitative predictions about the distribution of volume and stress within a system and provide a corresponding temperaturelike variable. We perform experiments with an apparatus designed to generate a large number of independent, jammed, two-dimensional configurations. Each configuration consists of a single layer of photoelastic disks supported by a gentle layer of air. New configurations are generated by cyclically dilating, mixing, and then recompacting the system through a series of boundary displacements. Within each configuration, a bath of particles surrounds a smaller subsystem of particles with a different interparticle friction coefficient than the bath. The use of photoelastic particles permits us to find all particle positions as well as the vector forces at each interparticle contact. By comparing the temperaturelike quantities in both systems, we find compactivity (conjugate to the volume) does not equilibrate between the systems, while the angoricity (conjugate to the stress) does. Both independent components of the angoricity are linearly dependent on the hydrostatic pressure, in agreement with predictions of the stress ensemble.

The influence of inter-particle friction and the intermediate stress ratio on soil response under generalised stress conditions

Previous research studies have used either physical experiments or discrete element method (DEM) simulations to explore, independently, the influence of the coefficient of inter-particle friction (μ) and the intermediate stress ratio (b) on the behaviour of granular materials. DEM simulations and experiments using photoelasticity have shown that when an anisotropic stress condition is applied to a granular material, strong force chains or columns of contacting particles transmitting relatively large forces, form parallel to the major principal stress orientation. The combined effects of friction and the intermediate stress ratio upon the resistance of these strong force chains to collapse (buckling failure) are considered here using data from an extensive set of DEM simulations including triaxial and true triaxial compression tests. For all tests both μ and b affected the macro- and micro-scale response, however the mechanisms whereby the force chain stability was improved differ. While friction clearly enhances the inherent stability of the strong force chains, the intermediate stress ratio affects the contact density and distribution of orthogonal contacts that provide lateral support to the force chains.

Length Scale for Transmission of Rotations in Dense Granular Materials

Deformation of granular materials is often characterized by strain localization in the form of shear bands, which exhibit a characteristic width of about 10–20 particle diameters. Much of the relative motion of particles within a shear band is accompanied by rolling, as opposed to sliding, since the latter requires more dissipative work. However, in a densely packed assembly, rolling cannot be accomplished without some sliding. This dissipative constraint implies a characteristic rotation transmission distance, i.e., the distance to which the information about rotation of a particle propagates. Here, we use the discrete element method to investigate this length and its directional dependence as function of the force chain network. We found that the rotation transmission distance correlates with the shear band width observed in experiments and previous numerical simulations. It is strongly dependent on the particle size distribution and the coefficient of interparticle friction, and weakly dependent on pressure. Moreover, the transmission of rotations is strongly directionally dependent following the pattern of force chains. To describe this dependence, we define a nonlocal tensorial description of force chain directionality.