Evolution Of Force Chains Research Articles

2D and 3D discrete numerical modelling of soil arching

In this study, 2D and 3D soil arching phenomena associated with piled embankments were evaluated by performing a series of discrete numerical analyses using the particle flow code (PFC3D) software. After validating the micro-parameters with experimental results, we compared the stress-displacement distribution, force chain evolution, maximum vertical displacement of particles, and deformation characteristics induced by 2D and 3D arching effects. Additional analyses were carried out to understand the influence of the fill height, pile clear spacing, friction coefficient, and porosity on soil arching with respect to the stress concentration ratio (SCR) and settlement along the elevation at various sections. The numerical results indicated that a plane soil arch in a 2D embankment overestimates the degree of load transfer and underestimates the settlement at the crest and within the embankment along the elevation in a 3D embankment. A lower equal settlement plane can be found in a 2D embankment. Furthermore, an increase of fill height and friction angle, and a decrease of pile clear spacing and porosity can help to improve the degree of reduction in load transfer and settlement in both 2D and 3D embankments. However, for partially mobilized soil arching in the 3D condition, the increase of fill height reduces the settlement of soils mainly in the portion above the square subsoil area, but has less influence over the portion above the rectangular subsoil area.

3D Experimental Measurements of Evolution of Force Chains in Natural Silica Sand

AbstractThe mechanisms of force transmission in granular materials is a classic physics problem that has been addressed since the 19th century, when Heinrich Rudolf Hertz investigated the interacti...

Numerical Modeling of the Strata Deformation During Tunnel Excavation Based on Discrete Element Method

The construction of transportation infrastructure is transferring from ground to underground, which could evacuate the urban traffic and is also the future trend of the expansion of our cities. The cobble stratum brings about many technical problems in the underground engineering. Based on the calibration test and macroscopic mechanical characteristic curve, the microscopic calculation parameters of particle flow code simulation used for cobble strata in Urumchi were determined. According to establishing the numerical model of pebble tunnels using double-side-drift method, both the ground deformation and force chain evolution were analyzed for the tunnels using subsurface excavation method. This manuscript presented the differentiation of influence on ground deformation in cobble stratum under different excavation stages, the influence extent was ranked as follows, upper bench > double-side-drift > lower bench; the result of numerical simulation test was compared with the field monitoring data, proving that it is reasonable to adopt the particle flow code to simulate the excavation of pebble tunnels, and the research result could be provided for reference for the similar engineering.

Rattler wedging and force chain buckling: metastable attractor dynamics of local grain rearrangements underlie globally bistable shear banding regime

Grain rearrangements govern the mechanical response of granular materials under load. A comprehensive time series analysis of macroscopic stress, previously undertaken for the persistent shear banding regime, uncovered a bistable dynamical system with two interconnected attractor basins—one tied to jamming, the other to unjamming. Here we examine the state space of local fabric of a 3D granular material to uncover the underlying grain rearrangements which induce the system to switch basins and manifest macroscopic quasistationary dynamics. The fabric state space comprises metastable attractors organized according to structural determinacy: hypostatic, isostatic and hyperstatic. Although trajectories overwhelmingly favor identity transitions which preserve local fabric, rare nonidentity transitions hold the key to basin switching. Jamming basin dynamics is governed by force chain transitions in the hyperstatic region: here redundant constraints enable force reconfigurations with little to no change in the local fabric. But as force chains become overloaded, they buckle. Buckling and attendant dilatancy push grains to the isostatic region. This in turn triggers unjamming and ensuant transitions to the hypostatic region where rattlers, though few, dominate dynamics. Rattlers provide wedge-like supports to unstable misaligned particle columns, promoting force chain formation and return to the hyperstatic region. The lateral reinforcement of an isostatically constrained grain in a trimer by the addition of a contact and/or a 3-cycle is the most probable nonidentity transition during nascent force chain evolution.

Three-Dimensional Discrete Element Analysis on Tunnel Face Instability in Cobbles Using Ellipsoidal Particles.

Soil disturbance has always been the major concern in shield tunneling activity. This paper presents the investigation on the micro-scale responses of the soils during shield tunnel excavation in sandy-cobble stratum. The code paraEllip3d is employed in discrete element method (DEM) analysis in which the soils are mimicked as an assembly of ellipsoids. Triaxial tests on the micro-scale responses of cobbles are carried out using the materials sampled from the tunnel face during construction period, and corresponding DEM simulations are performed to calibrate the micro parameters for the ellipsoids. On this basis, the face instability process during the shield tunneling in cobbles is studied using 1 g model test as well as corresponding DEM simulation. The micro-scale responses of cobbles are investigated by triaxial test as well as corresponding DEM simulations. Multiple material responses are discussed in the DEM simulations, including the stress–strain relationship, the contact distribution, and the force chain evolution in the elementary and model test. Finally, the mechanism of tunnel face instability in cobbles are discussed on the basis of aforementioned investigations.

Simulation of Microscale Features Effect on Mechanical Properties of PTFE-Al Composites

The compression behavior of polytetrafluoroethylene (PTFE)–aluminum (Al) is studied by the means of the two-dimensional finite element analysis of mesoscale model containing a random dispersion of particles. The results show that for composite materials with a single particle size the strength of the material increases first and then decreases with the increase of the content of metal particles. When the particle content is high the strength of the material can be improved by a reasonable particle gradation. The influence of particle content and size on the strength of particle composites is obtained and theoretical analysis is carried out from the perspective of the formation and evolution of force chains.

Quantitative Investigation into the Relation between Force Chains and Stress Transmission During High-Velocity Compaction of Powder

High-velocity compaction (HVC), an innovative approach to obtain green compacts with high and uniform density, is widely used in the powder metallurgy industry. In this study, meso force chains, macro stress transmission, and their relation were investigated using the discrete element method. The simulation details of HVC and the quantitative characterization of force chains and stress transmission were shown. Then, the relation between force chains and stress was investigated. The evolution of force chains showed the same change tendency as the stress distribution. They evolved from top to bottom and then reflected backwards in HVC while they did not show this trend in conventional compaction. The strength of the force chains maintained good consistency with the stress magnitude. Meanwhile, the length of the force chains presented a negative correlation with the stress magnitude, and high stress may cause new force chains to shorten. The average collimation coefficient was affected by the transmission of stress, and the short force chains had better straightness. Furthermore, force chains parallel to the direction of gravity were observed in the region with no stress concentration. The directional coefficient of force chains also had the same fluctuation trend as the variation in the principal stress angle.

Particle mechanics modeling of the effect of aggregate shape on creep of durable rockfills

The role of aggregate shapes in creep of durable rockfills is investigated using particle mechanics method. Both one-dimensional compressional creep and direct shear creep tests are performed on numerical rockfills consisting of rounded or irregular aggregates. Under one-dimensional compression, the creep displacements of irregular samples were greater than rounded samples. Under direct shear, the creep displacements of rounded samples could be the same magnitudes of or even larger than irregular samples. A concept of key aggregates is proposed to explain the evolution of force chains in rockfills. The different creep behavior of wet rounded and irregular aggregates is briefly discussed.

Force Chain Characteristics and Effects of a Dense Granular Flow System in a Third Body Interface During the Shear Dilatancy Process

In order to investigate the characteristics of force chains in a granular flow system, a parallel plate shear cell is constructed to simulate the shear movement of an infinite parallel plate and observe variations in relevant parameters. The shear dilatancy process is divided into three stages, namely, plastic strain, macroscopic failure, and granular recombination. The stickslip phenomenon is highly connected with the evolution of force chains during the shear dilatancy process. The load–distribution rate curves and patterns of the force chains are utilized to describe the load-carrying behaviors and morphologic changes of force chains separately. Force chains, namely, “diagonal gridding,” “tadpole-shaped,” and “pinnate” are defined according to the form of the force chains in the corresponding three stages.

3D finite element modelling of force transmission and particle fracture of sand

Global compressive loading of granular media causes rearrangements of particles into a denser configuration. Under 1D compression, researchers observed that particles initially translate and rotate which lead to more contacts between particles and the development of force chains to resist applied loads. Particles within force chains resist most of the applied loads while neighbor particles provide lateral support to prevent particles within force chains from buckling. Several experimental and numerical models have been proposed in the literature to characterize force chains within granular materials. This paper presents a 3D finite element (FE) model that simulates 1D compression experiment on F-75 Ottawa sand. The FE mesh of particles closely matched 3D physical shape of sand particles that were acquired using 3D synchrotron micro-computed tomography (SMT) technique. The paper presents a quantitative assessment of the model, in which evolution of force chains, fracture modes, and stress-strain relationships showed an excellent agreement with experimental measurements reported by Cil et al. Alshibli (2017).

The impact of fluid flow on force chains in granular media

Fluid flow through granular media is an important process found in nature and various engineering applications. The effect of fluid flow on the evolution of force chains in the granular media is explored using the photoelasticity theory. A transparent cell is designed to contain several photoelastic disks of different sizes and to allow fluid flow through the particle packing. Water is injected into the cell while the particle packing is under confining stress. Several images are taken for the conditions of different confining stresses and fluid injection rates. An algorithm of an image processing technique is developed to detect the orientation and magnitude of contact forces. The results show that forces in parallel and transverse to the flow direction increase with increasing water velocity, while parallel force shows a higher increasing rate.

The drag on a vibrated intruder moving in the confined granular media

In this paper, we investigate the drag on an intruder moving in confined granular media based on a discrete element method when its self-induced vibration perpendicular to its moving direction occurs. The influence of vibrating parameters on its dynamical properties is mainly considered. With the enhancing intruder's vibration, we find that the dependence of drag force on its moving velocity exhibits different regimes and then a dimensionless acceleration is proposed as a more intrinsic vibrating parameter determining the drag-velocity relationship, which gradually changes from quadratic to linear with the increase of dimensionless acceleration. The criticality of this parameter is also discussed based on a proposed phase diagram. Finally, our simulating results suggest that, once the dimensionless acceleration exceeds its critical value from below, the evolution of force chains near the intruder exhibits a similar feature, which may account for a stable linear dependence of the drag force on its velocity.

Numerical Study on the Evolution of Force Chain inside Railway Ballast under Tamping Operation

The tamping maintenance of railway ballast is employed to restore the geometry of railway track distorted by train traffics. In this paper, based on the analysis of tamping principle, the three dimensional analysis model of railway ballast is created using the discrete element method, numerical simulations are performed to study the micro mechanical behavior of railway ballast under tamping operation. This paper presents the evolution of force chains inside railway ballast under tamping operation. The obtained results are showed that the contact force inside railway ballast is enhanced by tamping, so as to improve the carrying capacity and stability of railway track.

The Force Chains and Dynamic States of Granular Flow Lubrication

The distribution probability of contact force, force chain evolution law, dynamic states, and the force chain distribution characteristics for granular flow lubrication are researched. In order to study the above contents, a granular flow lubrication model of parallel sliding friction pairs basing on the discrete element method is built. The results show that the normal contact force, tangential contact force, and total contact force are all consistent with the power law, and the granular flow is mainly influenced by the normal contact force. When the lower friction pair speed increases from 1.5, 4.5, to 15 m/s, the dynamic behavior of granules can transform into four flow states: a jamming state, quasistatic flow, slow flow, and rapid flow. Under the four flow states, the magnitude of the total force chains is higher in the jamming, quasistatic flow, and slow flow state but lower in the rapid flow state. In the process of the granule dynamic flow state changing from a rapid flow state, to a slow flow state, to a quasistatic flow state, the number of weak force chains decrease notably, whereas the number of strong force chains and super strong force chains increases; in addition, the flow speed of the granular lubrication medium and the deconstruction and reconstruction speed of the force chains will obviously slow down.

Internal Deformation Measurement and Force Chain Characterization of Mason Sand under Confined Compression using Incremental Digital Volume Correlation

The mechanical behavior of granular materials such as sand is not well understood due to its complex solid/fluid-like behavior. In this paper, Mason sand was investigated to determine the grain-level Young’s modulus and hardness by nanoindentation, and the mesoscale behavior through X-ray tomography of a sample in compression. Mason sand specimen was confined in a polycarbonate tube and compressed in the axial direction at ten axial compressive strains up to -21.8 % while its microstructures were observed. The mesoscale deformations were determined by incremental digital volume correlation of reconstructed volumetric images. A procedure for characterization of internal force chains is developed. The minor principal strains and their principal directions were obtained and used to determine the formation and evolution of force chains.

Stick-slip and force chain evolution in a granular bed in response to a grain intruder

The mechanical response of granular beds under applied stresses is often characterized by repeated cycles of stick-slip. Using the discrete element method, we examine stick-slip from a concentrated force loading-imposed by a single grain that is drawn through a densely packed, periodic granular bed via a stiff virtual spring. Force chains continually form and collapse ahead of the intruder grain. A comprehensive characterization of the birth-death evolution of these load-bearing structures, along with their surrounding contact cycles, reveals a well-defined shear zone of around eight particle diameters from the intruder, encapsulating: (i) long force chains that form buttresses with the fixed bottom wall for support, (ii) a region where the collapse of the most stable, persistent three-cycles preferentially occur to the point where they are essentially depleted by the end of the first cycle of stick-slip, and (iii) an inner core where force chain buckling events concentrate. Dilatancy is greatest in this inner core, and in the region next to the free surface. During slip, secondary force chains briefly form behind the intruder: these transient force chains, most of which comprise only 3 particles, form in the direction that is roughly perpendicular to the intruder motion.

Stress–dilatancy and force chain evolution

AbstractThe evolution of internal structure plays a pivotal role in the macroscopic response of granular materials to applied loads. A case in point is the so‐called ‘stress–dilatancy relation’, a cornerstone of Soil Mechanics. Numerous attempts have been made to unravel the connection between stress–dilatancy and the evolution of fabric and contact forces in a deforming granular medium. We re‐examine this connection in light of the recent findings on force chain evolution, in particular, that of collective force chain failure by buckling. This study is focussed on two‐dimensional deformation of dense granular assemblies. Analysis of individual and collective force chain bucklings is undertaken using data from a discrete element simulation. It is shown that the kinematics of force chain buckling lead to significant levels of local dilatation being developed in the buckling force chain particles and their confining first‐ring neighbors. Findings from the simulation are used to guide the development of a lattice model of collective, localized force chain buckling. Consideration of the statics and kinematics of this process yields a new stress–dilatancy relation. The physics of buckling, even at its simplest form, introduces a richness into the stress–dilatancy formulation in a way that preserves the essential aspects of fabric evolution, specifically the buckling mode. Copyright © 2010 John Wiley & Sons, Ltd.

UNDERSTANDING FORCE CHAINS IN DENSE GRANULAR MATERIALS

When a load is applied to a dense granular material, the stress is largely transmitted by relatively rigid, heavily stressed chains of particles forming a sparse network of larger contact forces. Force chains act as the key determinant of mechanical properties such as stability, elasticity and flowability. To understand the structure and evolution of force chains, related physical processes and three corresponding characteristic time scales are analyzed in this study. We also propose three dimensionless numbers for the measurement of the relative importance of force chains. To solely study the effect of particle surface friction on force chains, uniaxial compression tests of 11,000 equal-sized particles in 2D were numerically simulated using the discrete element method. By proposing three conditions to define a force chain, the chain length distribution is found in the form of a power law. The exponent of 1.744 is independent of the surface friction. Although these results were obtained from partially crystallized jammed packings, they provide new insight into the physical processes and the structure of force chains, and thus will be helpful in the interpretation of force chains in other dense granular systems.

Evolution of force chains in shear bands in sands

Precise knowledge of the post-peak constitutive response occurring within shear bands in sands is of keen interest in geomechanics, particularly for accurate modelling of progressive failure phenomena. There is mounting evidence that the displacement field within shear bands in sands is non-uniform and distinguished by distinct meso-scale features: namely, particle force chains. Experimental validation of such features will help elucidate the precise nature of the deformation field within shear bands. This paper presents experimental evidence of the kinematic signatures of force chain activity within shear bands in sands. The meso-scale kinematics are quantified from digital-image-correlation-based, grain-scale displacement analyses performed on digital images of specimens undergoing plane strain compression. As in previous work, the data reveal distinct, systematic patterns in the kinematics along the length of the shear band, which serve as indirect evidence of force chain build-up and collapse. Herein, local volume changes are shown to integrate into this pattern. Temporal changes in these patterns with the progress of deformation are also tracked. It is argued that the changes observed in the kinematics from softening to critical state provide a physical, meso-scale explanation for the progress of global stress–strain response through the post-peak regime.

Force cycles and force chains

We examine the coevolution of N cycles and force chains as part of a broader study which is designed to quantitatively characterize the role of the laterally supporting contact network to the evolution of force chains. Here, we elucidate the rheological function of these coexisting structures, especially in the lead up to failure. In analogy to force chains, we introduce the concept of force cycles: N cycles whose contacts each bear above average force. We examine their evolution around force chains in a discrete element simulation of a dense granular material under quasistatic biaxial loading. Three-force cycles are shown to be stabilizing structures that inhibit relative particle rotations and provide strong lateral support to force chains. These exhibit distinct behavior from other cycles. Their population decreases rapidly during the initial stages of the strain-hardening regime-a trend that is suddenly interrupted and reversed upon commencement of force chain buckling prior to peak shear stress. Results suggest that the three-force cycles are called upon for reinforcements to ward off failure via shear banding. Ultimately though, the resistance to buckling proves futile; buckling wins under the combined effects of dilatation and increasing compressive load. The sudden increase in three-force cycles may thus be viewed as an indicator of imminent failure via shear bands.