Interparticle Friction Coefficient Research Articles

Calibration of Contact Parameters of Biochar Based on Discrete Element Method

Highlights The rice husk and straw biochar particles were statistically analyzed, and two representative particles were obtained. A particle model was established using the discrete element method and the Johnson-Kendall-Roberts method. This study used a response surface design method to calibrate biochar particle parameters. Abstract. The discrete element method (DEM) is widely used in modelling particulate materials and related applications. DEM modelling requires the calibration of a large number of microparameters that are difficult to experimentally measure. This study aims to obtain the contact parameters of different types of biochar accurately and quickly and proposed a parameter calibration method for biochar particles to verify, which uses particle density, moisture content, inter-particle friction coefficient, particle and steel plates. A mathematical model was established for predicting parameter of friction coefficient, Johnson-Kendall-Roberts (JKR) surface energy, and contact behavior. The parameters were verified using the engineering design measurement method and a simulation analysis using a commercial software called Rocky. The results showed that: (a) the data obtained using the cylinder lifting method and the stacking and angle of repose tests of the drawing plate method were stable, the angle of repose of the biochar pellet pile was measured to be 36.55°; (b) the steepest climbing test results indicated that with the increased of Biochar-biochar rolling coefficient, Biochar-steel restitution coefficient, and JKR value, the angle of repose gradually increases; (c) a quadratic regression model was established through a Box-Behnken experiment, and it was found that the interaction term had an extremely significant effect on the angle of repose of biochar particles; (d) a preliminary design of a biochar return machine was created based on the calibration, simulation and actual test results. Keywords: Angle of repose, Biochar, Discrete element, Parameter calibration, Simulation parameters.

Scaling behavior of granular columns collapse on erodible-inclined surfaces

This paper explores the effects of slope angle, initial column aspect ratio, and interparticle friction coefficient on the mobility and erodibility of granular columns collapsing on an erodible-inclined layer before spreading and depositing on a nonerodable-horizontal surface using Discrete Element Method. The numerical results showed that the column collapse with higher aspect ratio or smaller friction coefficient induces larger normalized kinetic energy, leading to larger granular masses out the inclined region and longer runout distance. The slope angle, on the other hand, shows trivial impacts on the kinetic energy and apparent friction coefficient. Remarkably, these physical quantities are nontrivially behaved by a new dimensionless number that incorporates the initial column aspect ratio, inclination angle, and interparticle friction coefficient. These findings may significantly complement the better understanding of the behavior of natural disaster events such as landslides, rock and snow avalanches, or pyroclastic flows on complex surfaces.

Computer vision-aided DEM study on the compaction characteristics of graded subgrade filler considering realistic coarse particle shapes

The compaction quality of subgrade filler strongly affects subgrade settlement. The main objective of this research is to analyze the macro- and micro-mechanical compaction characteristics of subgrade filler based on the real shape of coarse particles. First, an improved Viola–Jones algorithm is employed to establish a digitalized 2D particle database for coarse particle shape evaluation and discrete modeling purposes of subgrade filler. Shape indexes of 2D subgrade filler are then computed and statistically analyzed. Finally, numerical simulations are performed to quantitatively investigate the effects of the aspect ratio (AR) and interparticle friction coefficient (μ) on the macro- and micro-mechanical compaction characteristics of subgrade filler based on the discrete element method (DEM). The results show that with the increasing AR, the coarse particles are narrower, leading to the increasing movement of fine particles during compaction, which indicates that it is difficult for slender coarse particles to inhibit the migration of fine particles. Moreover, the average displacement of particles is strongly influenced by the AR, indicating that their occlusion under power relies on particle shapes. The displacement and velocity of fine particles are much greater than those of the coarse particles, which shows that compaction is primarily a migration of fine particles. Under the cyclic load, the interparticle friction coefficient μ has little effect on the internal structure of the sample; under the quasi-static loads, however, the increase in μ will lead to a significant increase in the porosity of the sample. This study could not only provide a novel approach to investigate the compaction mechanism but also establish a new theoretical basis for the evaluation of intelligent subgrade compaction.

Impact of particle elongation on the behavior of round and angular granular media: Consequences of particle rotation and force chain development

We developed a 2D discrete element model to simulate shearing response of elongated round and angular particles. Model was calibrated and validated by comparing numerical results with corresponding biaxial shearing tests on circular (round) and hexagonal (angular) rods at microscopic and macroscopic scales. Then, the systematic effect of particles aspect ratio was investigated on quasi-static shearing response of round and angular granular materials. Macroscopically, we observed a nonlinear tendency wherein as the aspect ratio decreased from 1, the critical state stress ratio initially increased, reaching a maximum, followed by a decreasing trend. This effect was more prominent in round samples. Microscopically, decreasing the aspect ratio from 1 reduced particle rotations and increased the mean coordination number. Elongated particles exhibited significant contact anisotropy, forming irregular force chains, facilitating interparticle sliding, and reducing overall strength. Additionally, we explored the impact of the interparticle friction coefficient. A high value of interparticle friction coefficient led to a monotonically increasing strength with elongation, underscoring the importance of accurately calibrating microscopic friction coefficients.

PFC–FLAC coupling-based numerical simulation of triaxial test on soybean granular material

A discrete-continuous (PFC–FLAC) coupling method was used in this study to simulate laboratory triaxial tests with soybean granular material. The mesoscopic mechanical parameters of the soybean granular material were calibrated by comparing them with actual laboratory test results, and the validity of the modeling method was verified. Subsequently, the particle motion law and mechanical mechanism of the soybean granular materials were analyzed based on the particle displacement field, velocity field, and force chain network. The results showed that the coupled PFC–FLAC method could better describe the macroscopic stress–strain relationship, deformation damage characteristics, and shear strength mechanical indexes of soybean granular materials. With increasing confining pressure (50–200 kPa), the bulging deformation of the specimens changed from uniform to concentrated but uneven. The particle contact number and maximum particle contact stress increased by 19.3 and 48%, respectively. Additionally, variations of the macroscopic properties of the specimens with microscopic parameters were revealed. Under the same conditions, the change in the peak stress of the specimen was proportional to the interparticle friction coefficient. Moreover, the slope of the stress–strain curve increased gradually with an increase in the effective modulus.

Influence of the interparticle friction coefficient on the mechanical behaviour of breakable granular materials with realistic shape

Interparticle friction coefficient μ is an important factor affecting the mechanical properties of granular materials. In this study, the influence of μ on the mechanical behavior of granular materials is investigated by DEM. Through 3D scanning and Voronoi tessellations, the breakable particle model with realistic shape is constructed. A series of drained triaxial tests were performed at different μ values. Then, the particle breakage characteristics, including the degree of particle breakage and the breakage mode, were evaluated. In addition, microscopic characteristics, including coordination numbers and contact forces, were examined. Finally, the underlying mechanisms of φc evolution are explained from two perspectives of particle movement and fabric anisotropy. First, the rolling behavior of the particles increases with μ values, leading to a larger average displacement of particles. The influence of particle movement and friction coefficient balance each other, resulting in φc remaining constant when μ⩾0.4. Second, the initial increase of φc is due to the increase of the contact normal anisotropy ac, the normal contact force anisotropy an and the tangential contact force anisotropy at. Subsequently, the constant φc is the result of the decrease of ac and an being compensated by the increase of at.

Particle shape effects on dynamic properties of granular soils: A DEM study

Particle shape is an essential aspect of granular soils that affects their mechanical properties. It is challenging to isolate the effect of particle shape from other mechanical properties such as inter-particle friction coefficient and particle shear modulus in laboratory tests. The discrete element method (DEM) makes it feasible to investigate the effect of macroscopic and mesoscopic particle morphologies including sphericity and roundness. This study provides a systematical DEM investigation of the particle shape effect on the dynamic properties of granular soils by simulating cyclic undrained triaxial tests at various initial confining pressures and void ratios. The results indicate that specimen consisting of angular particles generally exhibit a higher secant shear modulus G than that of rounded particles. Additionally, particle shape has no significant effect on modulus ratio G/G0 but a noticeable impact on damping ratio D at relatively large strains due to dilatancy. A weighted coordination number CN' was proposed to reveal the microscopic effect of particle shape on G0. Contact sliding was found to be the main cause of modulus degradation and damping increase with increasing shear strain. The tangential shear modulus ratio Gtan/G0 is inversely correlated to the weighted contact sliding ratio fs'.

Uncertainty quantification for granular materials with a stochastic discrete element method

Significant uncertainty exists in granular materials, as demonstrated by experimental and simulation studies. Quantifying this uncertainty by integrating refined discrete element analysis with direct stochastic simulation is challenging due to computational cost constraints. To this end, the probability density evolution method (PDEM) is introduced to propose the methodology of stochastic discrete element analysis. The objective of this paper is to develop a formulation of the stochastic discrete element method (DEM) on uncertainty quantification for granular materials. First, the uncertainty characterization of inter-particle friction coefficients (μ) is performed via experimental data, resulting in the identification of an optimal probability distribution. Second, the 100 representative deterministic points of basic random variables are selected for subsequent DEM shearing simulation until the critical state. Third, the PDEM is developed to obtain the probability density function (PDF) surface representing the system’s performance, thus offering a comprehensive prediction of uncertainty for granular materials. The results show that the uncertainty of μ propagates to the behavior of granular materials. Utilizing the stochastic DEM methodology clarifies which behavior parameters exhibit significant randomness and which possess negligible randomness. Notable uncertainties are observed in large strain macro-scale behavior and the proportion of inactive particles. It can be inferred that conventional methods that neglect probability distributions might produce spurious results. Moreover, the influence of uncertainties on granular material behavior varies depending on the its shearing state and related soil parameters. In contrast, limited uncertainties are identified for the randomness of small strain stiffness, and the randomness on the particle scale stress transmission shape is also limited. This study marks the initial application of the PDEM in geotechnical engineering, suggesting that considering probability density evolution could enhance geotechnical engineering design. The current study highlights the necessity of using statistical methods to assess key geotechnical parameters.

Discrete element modelling of the effect of aspect ratio on compaction and shear behaviour of aggregates

Coarse aggregates are essential for constructing railways and highways, as they affect structural performance through their compacted state and shear strength. Particle geometry influences these properties, but little research has quantitatively investigated how shape indexes impact mechanical indicators. This study addresses this gap by exploring the effect of particle aspect ratio on coarse aggregate compaction and shear behavior using the discrete element method (DEM). The study's key contribution is the development of novel equations that describe the correlation between packing porosity, inter-particle contact state, and aspect ratio control thresholds in a practical format. To do so, first, a point cloud database is compiled from laser scans of 700 natural aggregate particles. Each particle is classified using three aspect-ratio parameters: elongation, flatness, and flatness-elongation index (FEI). They are then digitized as rigid block particle models and compared against actual point clouds. Next, nine aggregates of representative shapes are assessed for their macro and mesoscopic mechanical responses using DEM-based vibro-compaction and direct shear tests. The compaction simulations indicate an exponential relationship between porosity and inter-particle coefficient of friction and show that aggregates with FEI ≈ 0.5 are a good choice. The direct shear simulations consider the same initial porosity, and show that the relationship between peak shear strength and vertical stress follows a power function. Finally, the analysis of contact forces and fabric tensors implies that FEI ≈ 0.5 may also facilitate particle fragmentation control.

The Sensitivity of Micro—Macro Mechanical Behaviour of Sand to the Inter-Particle Properties

Sand is a particulate material but is treated as a continuum solid in some engineering analyses. This approach is proven to be acceptable when dealing with geotechnical structures, provided an adequate factor of safety is applied so that there is no risk of failure. However, the continuum approach does not account for the effect of interparticle forces on the micro–macro behaviour of sand. Sand could be modelled as a particulate material using the discrete element method (DEM), taking into account its discrete nature. This paper shows how the microscopic contact properties between the idealised sand particles influence the macro-mechanical behaviour, highlighting the development of the fabric as the soil approaches failure. Thirty DEM biaxial tests were performed to study the sensitivity of the macro–micro mechanical properties of sand to the inter-particle properties of an idealised sand particle. The conditions of these simulations were the same (e.g., particle size distribution, number of particles, porosity after radius enlargement, boundary conditions, and rate of loading). The sensitivity of the pre-peak, peak, and post-peak behaviour of these simulations to the inter-particle properties of an idealised sand particle was studied. Two extra DEM biaxial tests under different confining pressures were performed to verify the cohesionless nature of the synthetic material used for this study. Since a two-dimensional DEM is used for this study, a detailed approach to interpret the results assuming either a plane strain or a plane stress situation was discussed. This study highlighted the critical inter-particle properties and the range over which these influence macro-mechanical behaviour. The results show that Young’s modulus is mainly dependent on the normal contact stiffness, and peak stress and the angle of internal friction are greatly dependent on the inter-particle coefficient of friction, while Poisson’s ratio and volumetric behaviour of particulate sand are dictated mainly by shear contact stiffness. A set of relationships were established between inter-particle properties and macro-machinal parameters such as Young’s modulus, Poisson’s ratio, and angle of internal friction. The elastoplastic parameters obtained from these tests are qualitatively in agreement with the typical medium and dense sand behaviour.

Transport mechanism of temporary plugging agent in complex fractures of hot dry rock: A numerical study

Hydraulic fracturing with temporary plugging agents is one of the most promising technologies to improve the thermal efficiency of deep geothermal reservoirs. Understanding the migration and plugging mechanism of temporary plugging agents in artificial fractures is the key to successful fracturing operations. However, there is currently a lack of understanding of the high temperature effect on the migration of temporary plugging agents in fractures. Therefore, based on the Eulerian-Lagrangian description framework, this paper uses the computational fluid mechanics (CFD)-discrete element method (DEM) two-way coupling algorithm to establish a multiphase flow model for the migration of temporary plugging agents in complex fractures. We carried out relevant numerical simulation research and compared with the experimental results. Numerical simulation results show that the main factors affecting the migration of temporary plugging agent include formation temperature, fracture complexity, viscosity of carrier fluid, mass concentration of temporary plugging agent, flow regime of the carrier fluid, and inter-particle friction coefficient. Among these factors, the high temperature effect reduces the amount of temporary plugging agent entering complex branch fractures, thus weakening the plugging efficiency of temporary plugging agent for branch fractures. However, the adverse effect of high temperature on plugging can be overcome by increasing the injection rate of temporary plugging agent and increasing the width of the fracture to improve the plugging efficiency of branch fractures. The numerical results provide important theoretical and practical significance for the design scheme of temporary plugging and diverting fracturing in hot dry rock.

Predicting residual friction angle of lunar regolith based on Chang’e-5 lunar samples

With the rapid development of human lunar exploration projects, the lunar base establishment and resource utilization are on the way, and hence it is urgent and significant to reasonably predict engineering properties of the lunar regolith, which remains to be unclear due to limited lunar samples currently accessible for geotechnical tests. In this contribution, we aim to address this outstanding challenge from the perspective of granular material mechanics. To this end, the 3D multi-aspect geometrical characteristics and mechanical properties of Chang’e-5 lunar samples are for the first time evaluated with a series of non-destructive microscopic tests. Based on the measured particle surface roughness and Young’s modulus, the interparticle friction coefficients of lunar regolith particles are well predicted through an experimental fitting approach using previously published data on terrestrial geomaterials or engineering materials. Then the residual friction angle of the lunar regolith under low confining pressure is predicted as 53° to 56° according to the particle overall regularity and interparticle friction coefficients of Chang’e-5 lunar samples. The presented results provide a novel cross-scale method to predict engineering properties of the lunar regolith from particle scale information to serve for the future lunar surface engineering construction.

Tribological variable-friction coefficient models for the simulation of dense suspensions of rough polydisperse particles

The rheology of concentrated suspensions of particles is complex and typically exhibits a shear-thickening behavior in the case of repulsive interactions. Despite the recent interest arisen, the causes of the shear-thickening remain unclear. Frictional contacts have been able to explain the discontinuous shear thickening in simulations. However, the interparticle friction coefficient is considered to be constant in most simulations and theoretical works reported to date despite the fact that tribological experiments demonstrate that the friction coefficient can not only be constant (boundary regime) but also decrease (mixed regime) or even increase (full-film lubrication regime), depending on the normal force and the relative velocity between the particles and the interstitial liquid between them. Interestingly, the transition between the boundary regime and the full-lubrication regime is governed by the particle average roughness. Particle-level simulations of suspensions of hard spheres were carried out using short-range lubrication and roughness-dependent frictional forces describing the full Stribeck curve. Suspensions with different particle’s roughness were simulated to show that the particle roughness is a key factor in the shear-thickening behavior; for sufficiently rough particles, the suspension exhibits a remarkable shear-thickening, while for sufficiently smooth particles, the discontinuous shear-thickening disappears.

Calibration and Testing of Discrete Element Modeling Parameters for Fresh Goji Berries

This paper aims at the standard grading of fresh goji berries and develops a variable gap-type fresh goji berry grading machine. To establish a complete simulation model, the discrete element parameters of the model were calibrated by a combination of physical experiments and simulation experiments. The outline of the goji berry was extracted by the SFM-CMVS technique, and a goji berry model was obtained using the multi-spherical particle model filling method in the EDEM software. By designing the free-fall, suspension collision, slope slip, and slope rolling experiments, we obtained the discrete element simulation parameters: the inter-particle collision restitution coefficient was 0.158, the collision restitution coefficient of fresh goji berry–silicone rubber material was 0.195, the static friction coefficient of fresh goji berry–silicone rubber material was 0.377, and the rolling friction coefficient of fresh goji berry–silicone rubber material was 0.063. By designing the steepest ascent search and central composite design experiments with the angle of repose (AoR) value obtained from the physical experiment as the target value (31.27°), we determined the inter-particle static friction coefficient to be 0.454 and the inter-particle rolling friction coefficient to be 0.037. Validation tests were conducted on the calibrated discrete element modeling parameters, and the results showed that the established fresh goji berry model and the optimally calibrated parameter combination are effective for discrete element studies on fresh goji berries.

Modelling real particle shape in DEM: a comparison of two methods with application to railway ballast

Two different methods for the modelling of real particle shape in 3D DEM simulations are assessed in this paper. The first method uses overlapping spheres (clumps), while the second uses a block defined as a closed and convex polyhedron. The two methods are applied to the modelling of triaxial tests on a railway ballast. The macroscopic responses obtained with the two methods are compared, and it is observed that with clumps a higher shear strength, closer to the experimental response, can generally be achieved. A micromechanical analysis is also carried out to highlight how the modelled particle shape affects the mechanics, and consequently explain the difference in the macroscopic response. It is observed, in particular, that a key feature of real particle shape is concavity, that plays an important role in the mechanics of a granular assembly. Finally, the combined effect of particle shape and interparticle friction coefficient on the shear strength is assessed. This confirms that even for real (angular) shapes, peak strength increases with interparticle friction, while critical state strength first increases and then tends to saturate above a certain interparticle friction.

Three-dimensional discrete element modeling of the shear behavior of cemented hydrate-bearing sands

Understanding the shear behavior of hydrate-bearing sands is fundamental for the safe exploitation of natural gas hydrates. Calibration is necessary to accurately capture the shear behavior of hydrate-bearing sands when using the three-dimensional discrete element method (DEM). In this study, a new method is developed to quantify the hydrate saturation of hydrate-bearing sands by using a DEM model with Voronoi partitions. A series of DEM simulations with various hydrate saturations and confining pressures were performed to calibrate the DEM model, which was then compared with experimental results. The results demonstrate that the DEM can effectively capture the macroscopic properties, including the shear strength, secant modulus, cohesion, and friction angle of hydrate-bearing sands. The bond strength and inter-particle friction coefficient of hydrates mainly impact the shear strength of hydrate-bearing sands, whereas the bond stiffness of hydrates affects both the shear strength and secant modulus of hydrate-bearing sands. The number of broken hydrate-sand bonds is much larger than the number of hydrate-hydrate bonds, indicating that the contribution of the former bonds is more significant than the latter bonds during the shearing process. This calibration method helps improve the reliability and accuracy of the DEM simulations for hydrate-bearing sands under triaxial compression tests.

Some considerations on the rheology of dense frictional cylindrical particles

Discrete element method simulations of granular shear flows of frictional cylindrical particles are performed. From the simulations, solid-phase pressure, shear stress, and bulk friction coefficient μ can be measured, allowing the investigation of the effects of particle properties on the macroscopic flow behaviors. Thus, the inertial number I based rheological models, which were frequently used for the spherical particles in the previous work, are examined for the applicability to cylindrical particles in the present study. It is found that the particle aspect ratio, interparticle friction coefficient, and particle size polydispersity all affect the bulk friction coefficient-inertial number correlation and the solid volume fraction-inertial number correlation, and their effects vary in different flow regimes, which exhibit different mechanical behaviors.

Unified Elastic Modulus Characteristic Curve Equation for Variably Saturated Soils

A soil’s elastic modulus is a fundamental property defining the soil’s reversible stress-strain relation under mechanical and environmental loadings. It has been observed that a soil’s elastic modulus can increase up to several orders of magnitude from fully saturated to dry conditions due to two distinct soil water retention mechanisms: adsorption and capillarity. Adsorption affects interparticle stress through van der Waals and electrostatic attraction and interparticle friction coefficient through water film retained by soil sorptive potential. Capillarity governs interparticle stress through capillary pressure and surface tension. The onset and scaling laws of the two mechanisms depend on the soil properties of specific surface area, pore-size distribution, cation exchange capacity, and soil mineralogy. These mechanisms are unified by a proposed elastic modulus characteristic curve (EMCC) equation. It is demonstrated that the proposed EMCC equation can well describe the moisture-dependent elastic modulus of a wide array of soils. Further, an interrelation among the EMCC equation, suction stress and soil shrinkage curves is established, which can greatly facilitate predicting suction stress from soil shrinkage curves and vice versa, further validating the EMCC equation in capturing soil’s hydromechanical behavior. The practical importance of the EMCC equation is demonstrated through prediction of ground heave of various soils due to a hypothetical flooding event.

The Edwards volume ensemble in cyclically sheared granular experiments.

We experimentally investigate the Edwards volume ensemble in cyclically sheared bidisperse disks of two friction coefficients (μ ≈ 0.3 and μ → ∞) subjected to a range of shear amplitudes γm. Despite the local and global anisotropy, hysteresis, and the potential long-range correlation of the free volume, the Edwards volume ensemble surprisingly provides an excellent statistical description of disk packings in cyclically sheared systems. Our finding can be better understood from the comprehensive analysis of the geometric and statistical properties of Voronoi cells of individual particles. First, the average degrees of anisotropy of Voronoi cells are weak at both the microscopic and macroscopic scales within a range of shear amplitudes γm of up to γm = 12% regardless of the inter-particle friction coefficients μ even though the azimuthal distributions of the Voronoi cell depend on μ. Second, there is only negligible hysteresis of global compactivity and volume fluctuations. Finally, the spatial correlations of the free volume and the orientation are weakly anisotropic and short ranged for practical purposes. Both results are independent of μ. Interestingly, our free-volume statistical results are consistent with the simple physical picture that the free volume is directly proportional to the compactivity.

Shear Is Not Always Simple: Rate-Dependent Effects of Flow Type on Granular Rheology.

Despite there being an infinite variety of types of flow, most rheological studies focus on a single type such as simple shear. Using discrete element simulations, we explore bulk granular systems in a wide range of flow types at large strains and characterize invariants of the stress tensor for different inertial numbers and interparticle friction coefficients. We identify a strong dependence on the type of flow, which grows with increasing inertial number or friction. Standard models of yielding, repurposed to describe the dependence of the stress on flow type in steady-state flow and at finite rates, are compared with data.