Strong Force Network Research Articles

DEM investigation on flow instability of particulate assemblies under coupling between volumetric and axial strains

AbstractThe discrete element method (DEM) is employed to investigate the impact of coupling between volumetric and axial strains on the flow liquefaction vulnerability of 3D cubic particulate specimens. The virtual testing program conducted here encompasses a wide range of initial states and varying degrees of coupling between volumetric and axial strains. Utilizing data obtained from DEM simulations, the evolution of micro- and macroscale variables, including coordination number, contact fabric anisotropy, redundancy index, strong force networks, invariants of the effective stress tensor, and excess pore-water pressure, is examined. Results from DEM tests indicate that coupling expansive volumetric strain with axial strain leads to a gradual loosening of the load bearing microstructure, a decrease in coordination number, and a faster change in contact anisotropy. DEM simulations demonstrate that the triggering of flow liquefaction instability is followed by a sudden increase in contact fabric anisotropy and abrupt drops in coordination number and redundancy index. Moreover, a detailed analysis of the findings suggests that the stress ratio at the onset of post-peak softening decreases with increasing expansive volumetric strains.

Micro-mechanical perspective on the role of particle shape in shearing of sands

This study presents a micro-mechanical perspective on the role of realistic particle shapes in shearing of sands through calibration with physical experiments and parametric studies using discrete element method (DEM) to reveal the different mechanics between irregular particles and spherical particles incorporating rolling resistance (μr). To achieve this goal, particle shapes of Toyoura sand were captured by micro-computed tomography and reconstructed using a clump generation algorithm in DEM. The use of clumps in DEM led to closer match with experimental results of triaxial tests at various porosities and confining pressures, which could not be achieved by sphere models with μr. With realistic particle shapes, initial rotations of clumps were allowed until they became interlocked, while the load resistance built up gradually. High coordination numbers were observed, with force chains relatively evenly distributed. In contrast, the use of μr in sphere models promoted the formation of voids that were sustained during the loading process, because rotational motions of particles were hampered by μr and they did not easily collapse into the voids. This was accompanied by polarised strong force network around the voids, leading to more dilative and brittle macroscopic behaviour than observed in physical experiments. These findings illustrate that particle shapes cannot be sufficiently replaced by the use of sphere models and μr due to intrinsic differences in their micro-mechanics.

Direct shear behavior of gravel-rubber mixtures: Discrete element modeling and microscopic investigations

In this paper, a newly developed 3-dimentional discrete element model (DEM) for gravel-rubber mixtures (GRMs), namely DEM4GRM, that is capable of accurately describing the macro-scale shear response (from small to large deformation) of GRMs in a direct shear box apparatus is presented. Rigid gravel grains are modelled as simple multi-shape clumps, while soft rubber particles are modeled by using deformable 35-ball body-centered-cubic clusters. Mixtures are prepared with different volumetric rubber content (VRC) at 0, 10, 25, 40 and 100%, statically compressed under 30, 60 and 100 kPa vertical stress and then sheared, by closely simulating a reference laboratory test procedure. The variation of micro-scale factors such as fabric, normal and tangential force anisotropy is carefully examined throughout the shearing process and described by means of novel micro-mechanical relationships valid for GRMs. Moreover, strong-force chains are scrutinized to identify the transition from rigid to soft granular skeleton and gain insights on the load transfer and deformation mechanisms of GRMs. It is shown that the development of the fabric and force anisotropy during shearing is closely related to the macro-scale shear strength of GRMs, and strongly depends on the VRC. Besides, strong-force chains appear to be primarily formed by gravel-gravel contacts (resulting in a rigid-like mechanical behavior) up to VRC = 30%, and by rubber-rubber contacts (causing a soft-like mechanical response) beyond VRC = 60%. Alternatively, at 30% <VRC < 60%, gravel-rubber contacts are predominant in the strong-force network and an intermediate mechanical behavior is observed. This is consistent with the behavioral trends observed in the macro- and micro-mechanical responses.

A DEM study of the effect of the loss of fine particles on the mechanical behavior of gap-graded soils

Modeling of suffusion in granular soils by using a fully coupled fluid-DEM model is still challenging due to its very high cost of computation. The particle removal approach is an alternative to mimic the erosion of fine particles by the seepage flow. In this paper, we study different particle removal methods and their impact on the mechanical behavior of eroded samples. Gap-graded samples with different fine contents fc were simulated by using the DEM. Fine particles are removed from the original sample under constant stress state by using three different methods: random removal, the method of Scholtès et al. based on the particle internal moment mp, and a new method proposed here that is based on the concept of weak and strong force networks. A micro-mechanical investigation into numerical samples shows that the fine particles have small contribution in carrying stresses when fc≤30% but they offer a great bracing effect to the coarse fraction, which allows the latter to carry high stresses. As a result, a removal of fine particles destroys greatly this bracing system, leading to a great reduction in the bearing capability of the coarse fraction. A comparison between the three methods shows that a removal of fine particles belonging to the weak force network has a lower impact on the mechanical behavior of eroded samples than the random removal. In addition, the method of Scholtès et al. gives results quite similar to those given by the random removal in terms of the shear strength of eroded samples.

Finite‐Size Analysis of the Collapse of Dry Granular Columns

AbstractIn this letter, we focus on the size effect of granular column collapses, which are potentially connected to the dynamics of complex geophysical flows, even if the link between microscopic structures of granular assemblies and their macroscopic behaviors is still not well understood. Using the spheropolyhedral discrete element method (DEM), we show that the column radius/grain size ratio has a strong influence on the collapse behavior. A finite‐size analysis, which is inspired by a phase transition around an inflection point, is performed to obtain a general scaling equation with critical exponents for runout distances. We further link the size effect with the strong force network and formalize a correlation length scale that exponentially scales with the effective aspect ratio. Such a scaling solution shows similarities with the percolation problem of two‐dimensional random networks and can be extended to other similar natural and engineering systems.

The correlation of macro deformation and micro kinematics for dense granular material subjected to shearing

In the study, biaxial shearing tests were carried out through the numerical simulations based on the discrete element method to examine the correlation of macro deformation and micro kinematics characterization in contact scale. The contact motions were decomposed into three independent types, i.e., contact deformation, contact rolling and rigid-body motion. The simulated dense sample can qualitatively reproduce the experimental outcomes for the stress–strain and volumetric relationship. From the micro to macro scale, it is found that the particle nonaffine displacement and particle rotation have strong spatial correlations with development of the shear band and the different contact motions have different influences on the sample deformation. That is, the contact deformation dominates the whole sample deformation, while the contact rolling and the rigid-body rotation have relatively small contributions to the volume change during the whole shearing process. The external loading is mostly supported by the strong contact forces in the sample, but the dilation deformation is more obvious in the weak contact force network. In strong contact force network, the contact deformation mainly induces contraction for the sample; the rigid-body rotation and contact rolling also contribute to contraction slightly; hence, the overall deformation in the strong contact force network is contraction. In the weak contact force network, the contact deformation creates dilation; the contact rolling has a small contribution to contraction, and the rigid-body rotation has no contribution to the volume change; thus, the overall dilation for the sample in the weak contact force network is observed.

DEM Simulations of Energy Dissipation in Sand under Static and Cyclic Loading

Abstract In this study, numerical simulations by the discrete element method were carried out to examine the characteristics of energy dissipation in sand. In the simulations of static biaxial tests of loose and dense samples, it was found that the applied boundary work is either stored in the strain energy or dissipated through interparticle friction when viscous energy loss is not considered. At the critical state, the boundary work balances out the frictional loss and the strain energy ceases to increase. The release of frozen strain energy can be readily seen in the dense sample when the sample is sheared to dilation and under a strain softening response. In the simulations of cyclic simple shear tests at small strains from 6 × 10−6 to 1.5 × 10−4, both frictional and viscous energy losses were considered. The simulated damping ratio and associated shear modulus can be obtained from two methods: traced energy and the resulting hysteresis loop. These two methods render almost identical results. The simulation can reproduce similar responses like the experimental findings in both shear modulus and damping ratio at different confining pressures, strain levels, and strain rates. It is found that not only the lost energy but also the stored energy, which is related to the associated shear modulus, can significantly affect the response of the damping ratio. In addition, the frictional loss mainly takes place in the weak force network, but the viscous energy is quite evenly distributed in the strong and weak force networks.

Stress and force measurement uncertainties in 3D granular materials

We have developed and employed a 3D particle stress tensor and contact force inference technique that employs synchrotron X-ray tomography and diffraction with an optimization algorithm. We have used this technique to study stress and force heterogeneity, particle fracture mechanics, contact-level energy dissipation, and the origin of wave phenomena in 3D granular media for the past five years. Here, we review the technique, describe experimental and numerical sources of uncertainty, and use experimental data and discrete element method simulations to study the method’s accuracy. We find that inferred forces in the strong force network of a 3D granular material are accurately determined even in the presence of noisy stress measurements.

Experimental study of some properties of the strong and weak force networks in a jammed granular medium

We are experimentally investigating the force network of a monolayer of grains through the jamming transition. Once the packing has been compressed beyond the volume fraction of jamming $$\phi _J$$, we use particle tracking and photoelastic techniques to determine the network of forces in the grains. We experimentally quantify the pressure inside each grain and highlight the two networks of forces existing in jammed granular materials: the load bearing network (force chains strong network) and the dissipative network (weak network). For the strong network, we study the statistical properties of the stress state of the grains and in particular the exponential tails of the probability density function of pressure and shear stress. As the distance to jamming increases, the probability density function of local shear in the system evolves and tends to look like a normal distribution while the probability density function of pressure does not evolve. For the weak network, we study the contact cycles in the granular packing. By calculating their numbers, we determine some statistical properties of these cycles. The number of cycles of order $$n=3$$ which carries the dissipative network increases linearly with the number of contacts.

Influence of stress anisotropy on stress distributions in gap-graded soils

The behaviour of gap graded soils comprising non-plastic fines (sand or silt) mixed with a coarser sand or gravel fraction has received attention from researchers interested in internal instability under seepage loading (a form of internal erosion) as well as researchers interested in load:deformation responses. Skempton and Brogan [1] postulated that resistance to seepage induced instability depends upon the proportion of the overall applied stress that is transmitted by the finer fraction. Shire et al. [2] explored Skempton and Brogan’s hypothesis using DEM simulations to look at the proportion of the applied stress transmitted by the finer fractions (α) in ideal isotropic samples. They showed that at low fines contents (FC&lt; FC*) the average stress transmitted by the finer grains is less than the applied stress (α&lt;1), while for FC&gt;FC+ the fines play a key role in stress transmission (α&gt;1); for FC*&lt;FC&lt; FC+, α depends on the sample density. The current contribution describes a series of constant p’ DEM triaxial test simulations carried out to assess the evolution of stress heterogeneity with shearing. The simulation data generated indicate that a sample can transition from being fines dominated (with the fines transmitting a significant proportion of the applied stress and α ≥1) to coarse or sand- dominated (with α &lt;1) as the material dilates during shear deformation. While α reduces as the samples dilate, the relationship between the α and the sample void ratio is non-trivial. The anisotropy of the coarse-coarse contact network exceeds the overall contact force anisotropy; this indicates that the deviator stress is transmitted through a strong force network passing through the coarse-coarse contacts supported by the fine-coarse contacts.

Microscopic Origins of Shear Jamming for 2D Frictional Grains.

Shear jamming (SJ) occurs for frictional granular materials with packing fractions ϕ in ϕ_{S}<ϕ<ϕ_{J}^{0}, when the material is subject to shear strain γ starting from a force-free state. Here, ϕ_{J}^{μ} is the isotropic jamming point for particles with a friction coefficient μ. SJ states have mechanically stable anisotropic force networks, e.g., force chains. Here, we investigate the origins of SJ by considering small-scale structures-trimers and branches-whose response to shear leads to SJ. Trimers are any three grains where the two outer grains contact a center one. Branches occur where three or more quasilinear force chain segments intersect. Certain trimers respond to shear by compressing and bending; bending is a nonlinear symmetry-breaking process that can push particles in the dilation direction faster than the affine dilation. We identify these structures in physical experiments on systems of two-dimensional frictional discs, and verify their role in SJ. Trimer bending and branch creation both increase Z above Z_{iso}≃3 needed for jamming 2D frictional grains, and grow the strong force network, leading to SJ.

Characterization of force networks in a dense high-shear system

We detect strong force networks in a dense high-shear system and study their structure and stability in response to variations in the shearing rate. The presence of strong force networks, which usually have a heterogeneous structure, restricts particle movements and can impose non-local mechanisms of momentum transfer. We identify such networks in a dense high-shear system using a community detection algorithm. Moreover, we explain the association between the mechanisms of momentum transfer and the structure, population, strength, and stability of the force networks by tracking the spatial and temporal evolution of the detected networks. In addition, we show that the assumption of a monodisperse assembly of particles leads to an unrealistic enlargement of the force networks, underestimating both the rate of energy dissipation and the rate of mixing.

On weak and strong contact force networks in granular materials

In an influential study on the micromechanical origin of stress transmission in granular materials, Radjaï et al. (1998) have proposed a division of the network of interparticle contacts into ‘weak’ and ‘strong’ contacts. This division is based on a comparison of the force at contacts with the average (over all contacts) force. They observed, from the results of a two-dimensional computer simulation of the behaviour of a system of particles, that the shear stress of the granular material is mainly carried by the strong contacts and that the anisotropy in the orientational distribution of the weak contacts is in the direction perpendicular to that of the full contact network. These findings are analytically predicted here in a qualitative sense, within a statistical framework that is based on a simple, self-similar expression for the conditional probability function for the normal force at contacts with given contact orientation. An alternative definition of weak and strong contacts is proposed here, in which the division of the contacts is based on a comparison of the force at contacts with the average force corresponding to the contact orientation. Contrary to the finding based on the definition of weak and strong contacts by Radjaï et al. (1998), with this alternative definition the pressure and the shear stress are (almost) equally carried by the weak contact network.

Structural signature of a sheared granular flow

Various types of mesoscopic structures form in jammed granular materials due to the self-organization of their constituent particles. Internal structural degrees of freedom are introduced in addition to the translational degree of freedom, and both impact the intrinsic properties of granular materials from its constituent ordinary objects. In this study, we perform numerical simulations of plane shear granular flows confined with a constant pressure. Using the radical tessellation method, we investigate the temporal and spatial evolutions of granular structures. The simulation results show that the degree of local fivefold symmetry (LFFS) is a unique structural indicator due to its significant spatial heterogeneity and dramatic variance with shearing. In the steady state, regions with small LFFS possess large linear velocity gradients, large angular velocities, and consequently large fluctuations in kinetic energy and elastic energy. Thus, LFFS may link the internal structures and dynamic properties of granular materials. Inspired by this spatial distribution scenario consisting of LFFS and energy, we propose a structural unit composed of a strong force network (SFN) and a weak force network (WFN). The SFN has a high shear resistance that acts as the elastic backbone that supports the entire matrix of a granular assembly, whereas the WFN with high energy dissipation consists of embedded “inclusions” among the SFN. This structural analysis aids the understanding of the complex phenomena of granular materials and provides insight into the mechanisms.

A micromechanical analysis of the effect of fabric on low-strain stiffness of granular soils

The effect of fabric on low-strain shear stiffness properties of granular soils was assessed using Discrete Element simulations. These soils were idealized as a collection of non-spherical particles that interact according to Hertz׳s contact law. Different fabrics of the same soil were obtained by extracting particles from the weak or strong interparticle force networks. The associated stiffness properties were evaluated for various levels of isotropic triaxial confining stress conditions. The conducted analyses showed that a soil with a given void ratio and level of confining stress may have various fabrics associated with noticeably different low-strain shear moduli. The mechanical coordination number and particle shape were found to be the main factors that dictate the low-strain stiffness properties of a certain granular soil (with a specific contact law). For a defined level of confining stress, the shear stiffness of a particular soil is shown to be linked to the mechanical coordination number by a unique relation.

DEM analysis of “soil”-arching within geogrid-reinforced and unreinforced pile-supported embankments

Geogrid-reinforced and pile-supported (GRPS) embankments have been widely used in road engineering due to their economy and effectiveness. The soil arching effect is a key factor in the load transfer mechanism of GRPS technique. In this study, a series of numerical simulations are conducted with the particle flow code PFC2D to study the evolution of soil arching with increasing surcharge. First, an Improved Multi-layer Compaction Method (IMCM) is proposed and applied to establish the Discrete Element Method (DEM) models with more reasonable initial stress states. Validation is then conducted by comparing the DEM results with experimental data. Second, detailed macro-behaviour (e.g., efficacy) and micro-behaviour (e.g., contact forces and fabric anisotropy) analyses are performed. Finally, parametric study is performed to identify the effects of two key factors, i.e., the stiffness of subsoil and the grain composition of embankment fill. Simulation results indicate that the strong force network (SN) serves as a load-carrying force chain, which is the main component of soil arching; while the weak force network (WN) acts as a support system. When a pile-supported embankment is high enough, the soil arching will experience three stages as the surcharge increases. In the first stage, the soil arching develops and its effect is strengthened gradually. In the second stage, the soil arching is fully mobilized and experiences a “forming-failure-reforming” process as the surcharge increases. While in the third stage, the embankment is unable to form a new stable soil arching and the efficacy decreases gradually. However, for the GRPS embankment, due to the reinforcement of geogrid, the third stage will not occur throughout the entire surcharge range of interest in this study. On the basis of the macro- and micro-results, the conclusion can be drawn that the presence of geogrid does not alter the failure mode of soil arching under the surcharge, though it is able to evidently improve the efficacy of load transfer and enhance the stability of soil arching.

Collisional model for granular impact dynamics

When an intruder strikes a granular material from above, the grains exert a stopping force which decelerates and stops the intruder. Many previous studies have used a macroscopic force law, including a drag force which is quadratic in velocity, to characterize the decelerating force on the intruder. However, the microscopic origins of the force-law terms are still a subject of debate. Here, drawing from previous experiments with photoelastic particles, we present a model which describes the velocity-squared force in terms of repeated collisions with clusters of grains. From our high speed photoelastic data, we infer that "clusters" correspond to segments of the strong force network that are excited by the advancing intruder. The model predicts a scaling relation for the velocity-squared drag force that accounts for the intruder shape. Additionally, we show that the collisional model predicts an instability to rotations, which depends on the intruder shape. To test this model, we perform a comprehensive experimental study of the dynamics of two-dimensional granular impacts on beds of photoelastic disks, with different profiles for the leading edge of the intruder. We particularly focus on a simple and useful case for testing shape effects by using triangular-nosed intruders. We show that the collisional model effectively captures the dynamics of intruder deceleration and rotation; i.e., these two dynamical effects can be described as two different manifestations of the same grain-scale physical processes.

Strong force networks in granular mixtures

Using the results of 3D discrete element method simulations we study the force transmission through binary mixtures of sand and silt sized spheres under one-dimensional compression. Three types of contact are categorized depending on the size of the two spheres in contact. The contributions of each contact type to the deviator stress are dependent on the proportion of silt sized spheres. We demonstrate that the magnitude of the deviator stress is solely due to the normal and tangential forces at contacts transmitting normal forces greater than a characteristic normal force, which is generally slightly greater than the average normal force. The maximum packing efficiency was obtained with the mixture of 30 % silt sized spheres and this mixture corresponds to a transition point when there are enough silt sized particles to start to separate the sand sized particles from each other and establish contacts between silt sized spheres that contribute to the deviator stress.

Numerical Triaxial Apparatus and Application

A numerical triaxial apparatus based on discrete element method is developed on the platform of Yade using Python script. A DEM model with rolling resistance contact considered is proposed for dense granular materials, which is then applied in triaxial compression test of Chende sand. Stress-strain response and volume-axial strain response of the DEM model agree well with that of experiments, with a good prediction of dilatancy angle. Degradation of granular materials duo to particle erosion is also investigated using triaxial compression tests. It is indicated that peak friction angle decreases with the remove of particles if strong force network of granular materials is destroyed.

A DEM investigation of the effect of particle-size distribution on one-dimensional compression

The effect of particle-size distribution on the one-dimensional compressive behaviour of granular soil materials was investigated using the discrete-element method (DEM), and the results were compared with published experimental data with similar gradations. The particles used in this study were spherical, and their size range mimicked various power-law distributions. The contact formulation was calibrated such that the different compressibility and initial specific volume of non-uniform assemblies depended purely on the interaction of different particle sizes of the non-uniform gradations. The compressive behaviour of these assemblies can be classified as either big-particle-dominated or small-particle-dominated. The underlying micromechanical explanations for the effect of the particle-size distribution on the packing characteristics and on the compressibility are presented. Particles involved in the strong force transmission, which carried larger-than-average contact forces, were found to contribute to the stiffness of granular samples. When loose and dense samples with the same grading were compressed to a stage where their stiffnesses were identical, an identical size distribution was found for those particles involved in the strong force network. For some materials, there existed regions of particles that did not carry any strong force, and the non-affine movements of these small particles partially filling the void space between the bigger particles were especially significant. This behaviour was visualised in the DEM simulations. As these particles rearranged themselves, these regions contributed to a higher volumetric compression. It was also found that the coordination number of DEM particles significantly increased with better gradations. A change in the particle-size distribution of real sand through particle breakage would therefore lead to a higher coordination number of particles, and it would gradually reduce the probability of particle breakage during the later stages of the compression, as has been observed in other laboratory experiments.