Contact Force Chains Research Articles

DEM simulation of the pullout behavior of geogrid-stabilized ballast with the optimization of the coordination between aperture size and particle diameter

Based on the well-established constitutive models and particular configurations used in the discrete element method (DEM) simulation of the geogrid-stabilized ballast system, this paper presents the pull-out behavior of a triangular geogrid embedded in ballast under special consideration of the particle size. A representative particle size that equals to the diameter of the inscribed circle of the triangular aperture was selected to visualize the axial force distribution and the interface responses regarding the contact force. Meanwhile, fabric anisotropy on the normal component of contact force was introduced to explain the development of macroscopic strength. Results show that the first transverse rib makes the most contribution to the pull-out force. The V-shaped strong contact force chains were mainly grown in the geogrid-ballast substantial interaction region R1, and this interaction mode is not affected by particle size. Moreover, the maximum number of particles trapped in an aperture, Nmax, is used as the quantized indicator for numerical pull-out tests on 6 controlled conditions, and results unveil that the optimal reinforcement can be achieved when Nmax = 2, by evaluating the pull-out resistance, the interlocking effect, the energy dissipation, and the volumetric response.

Migration mechanism of fine particles in aquifer during water injection

Water injection in aquifers to stabilize water level is a novel method to prevent shaft failure. However, with the progression of water injection, the flow rate of water injection decreases gradually. Through analysis, it is considered that the fine particles in sand migrate to form a dense structure, which hinders the increase of water flow. In order to investigate the migration mechanism of fine particles in the aquifer during water injection, experimental tests and numerical simulations were conducted in the present study. First, the physical experiment was designed, and it was shown that the water pressure difference between the two pressure gauges gradually decreased, while the water flow rate per hour slowly decreased. Furthermore, the permeability coefficient of sand near the outlet became smaller and smaller with the migration of fine particles, which indicated that the fine particles among sand grains migrated gradually from the water injection inlet to the outlet. Additionally, the water flow channels formed slowly. Then, the microscopic mechanism of fine particle migration was studied using particle flow code numerical simulation. During water injection, water pressure and porosity of sand decreased from the water injection inlet to the outlet, while the coordination number of particles increased on the whole. Contact force chain gradually strengthened near the outlet side during water injection. The trends of force chain distribution, the coordination number distributions and the evolution of porosity were consistent, which highlighted the process of fine particles migrating from the injection inlet to the outlet in the aquifer.

Analysis of Wear-Resistant Surface with Pangolin Scale Morphology by DEM Simulation

Based on the Discrete Element Method (DEM), an abrasive wear system composed of pangolin scale models and abrasive sand was established. The wear morphology of pangolin scale models under different velocities were simulated by PFC2D®. Their wear behaviors were discussed with regard to the contact bond fields, the contact force chains, the velocity fields and the displacement fields of the abrasive wear system. Moreover, the resistance of the pangolin scale models under different velocities were analyzed. In the DEM simulation, the fracture and debris locomotion on the scale model were observed at a meso-microscopic scale. The results show that the geometrical shape of the pangolin scale is helpful for decreasing the boundary stress, with the wear rate decreasing when the velocity is higher than 0.62 m·s−1. The wear rate is no more than 0.006 g/m under the abrasive sand, with a radius of 0.11–0.20 mm. The wear rates of the pangolin scale model agree with the experimental results, and the DEM provides a new way to study the abrasive wear behavior of this non-smooth biological surface.

Quantitative Study on the Contact Force and Force Chain Characteristics of Ore Particle Systems during Ore Drawing from a Single Drawpoint under the Influence of a Flexible Barrier

It is of great significance to carry out quantitative research on the contact force chain characteristics of ore particle systems during ore drawing to reveal the microscopic and mesoscopic characteristics of ore particle systems during implementation of the synchronous filling shrinkage stoping method. Based on the particle discrete element method, combined with the relevant knowledge of contact mechanics and statistical mechanics, microscopic properties of the ore particle system were studied quantitatively. (1) The probability distributions of the normal and tangential contact forces during ore drawing from a single drawpoint under a flexible barrier are similar, and both show exponential decay. (2) In the regions on both sides of the model, the ore particles will not be released because they are far from the drawpoint; there, the coordination number is stable, and the density of contact network is large. In the upper part of the drawpoint, ore particles flow, the coordination number fluctuates violently, and the density of contact network is small. (3) In the initial stage, the stress distribution of the ore particle system is uniform, and the strong force chain does not show obvious directivity. After that, the directions of the strong force chains in the ore particle system are inclined to the vertical direction, and the strong force chains mainly bear the load in the vertical direction. (4) In the initial stage of drawing, the normal contact force is mainly concentrated in the vertical direction. With the progression of drawing, the normal contact force at an angle of 30° to the horizontal direction increases gradually, and the number of the main direction of the average contact force distribution changes from one to three (the vertical direction and the direction with a ±30° angle to the horizontal direction).

Analysis on the contact force behaviors among strands of CICC conductor cross section

International Thermonuclear Experimental Reactor (ITER) hopes to achieve controllable thermonuclear fusion by constraining the motion of high temperature plasma by a strong magnetic field which is generated by superconducting magnets wound by the cable-in-conduit conductors (CICCs). The CICC structure is complex, usually with thousands of NbTi/Cu or Nb3Sn/Cu twisted in four or five stages. It operates in a complex environment of extremely low temperature, high current and strong magnetic field. The electromagnetic force generated by the superconducting material will cause deformation, reduce its characteristic parameters and bring hidden trouble to the safety of the device. Traditional studies on the contact force of the cross-section strand of CICC mostly adopt non-actual object photoelastic model in the experiment, and numerically adopt discrete element method (DEM) without particle deformation. However, it is difficult to give the contact force of the cross-section strand closer to the real working condition. In this experiment, the deformation characteristics were calculated between strands of the prototype of CICC by spraying speckle on the cross-section and using digital image correlation (DIC). Theoretically, taking the strand deformation obtained by DIC as the input parameter of granular element method (GEM), the distribution characteristics of the contact force of the CICC conductor under the action of transverse pressure are calculated, and the size and direction of the contact force chain are statistically analyzed.

Experimental Study on Mechanical Properties of Prefabricated Single‐Cracked Red Sandstone under Uniaxial Compression

This paper aims at the phenomenon of the fractured rock column in underground engineering which is prone to collapse when subjected to ground pressure. Uniaxial compression test and particle flow code (PFC2D) are used to analyze the influence of crack dip angle on the mechanical properties, crack propagation, and the failure mode of red sandstone. From the results, it is observed that the stress–strain curve of the precracked red sandstone can be divided into five stages, and there is a critical stress value in the stage of accelerated crack propagation and unstable fracture of the rock sample. Further, the peak strength, maximum strain, and the elastic modulus of the precracked red sandstone increase with the increase of crack dip angle, and the ultimate failure mode of rock sample changes from the “ladder” type failure to slope uneven failure. Furthermore, from PFC2D simulation, it is found that the tensile microcracks contribute more towards the failure of rock samples than the shear cracks. The contact force chain is very weak at the places where the precracks and macroshear planes are formed. This indicates that the original contact force is weakened due to particle fracture. Therefore, the bearing capacity of the precracked rock samples decreases with the increase in load. From the simulation results, it is found that the displacement at the shear plane of the rock sample is large, and the shear dilatation occurs. With the increase in load, the specimen falls off and is ejected. This is due to the weakening of the contact force between the internal particles. Thereafter, it fractures to produce microcracks, which gradually converge, thus providing a prerequisite for the transformation of elastic strain energy into kinetic energy.

Quantitative Detection of Contact Force Chains in a Model Particle Assembly Using Digital RGB Photoelastic Measurements

This paper explains a newly developed technique for identifying particles belonging to the contact force chains in a model particle assembly. This was accomplished through digital image analysis of the color images obtained from photoelastic measurements. Descriptive statistics for RGB color intensities of pixels in a central square region inside the particle were digitally measured to determine the particle force, as opposed to the traditional method of counting fringe orders. The relationships between the descriptive statistics of the RGB color intensities and the applied forces were analyzed. The developed image analysis technique was applied to digital photoelastic images of an assembly of stacked particles. This technique could embed the numeric data of the particle forces in the digital photoelastic images which provide comprehensive information for a quantitative analysis of the progressive evolution of the soil arching phenomena in a particulate media.

2D DEM analysis of the interactions between bio-inspired geo-probe and soil during inflation–deflation cycles

The cone penetration test and the standard penetration test are perhaps the most versatile techniques for investigating soil properties in-situ. Advancing the probe through the soil requires substantial downforce due to friction between the probe and the soil. Inspired by the ability of worms to conform their body to the most mechanically advantageous shape while tunneling, an innovative self-excavating geo-probe has been developed and deployed in a laboratory environment. Analogous to a worm’s ability to expand its body, a soft balloon mounted behind a rigid cone is inflated or deflated by applying pressure or vacuum periodically to alter the cone penetration resistance. Laboratory experiments have shown promising results that the new geo-probe can penetrate the soil more efficiently. However, the interactions at balloon–soil–cone interfaces are complex and not fully understood. This numerical study focuses on the behavior of the geo-probe during balloon inflation and deflation. A two-dimensional discrete element model is developed to provide particle-level insight into the micromechanics of the interactions between the geo-probe and the soil. A baseline simulation is first conducted to study the failure mechanisms of the bulk soil during inflation and deflation. Additionally, the contact forces at balloon–soil and soil–cone interfaces are analyzed to show the variation of penetration resistance. The displacement field, shear strain field, and contact force chains are numerically investigated to gain a fundamental understanding of the tool–soil interaction. Then, the effect of balloon locations and overburden stresses on the behavior of the probe are studied by performing sensitivity analyses. This study provides a numerical technique to study the tool–soil interactions that was inaccessible in laboratory test. Implementation of the simulation results enables extrapolation of bench-scale testing to a wider range of stresses and boundary conditions.

Effect of Initial Granular Structure on the Evolution of Contact Force Chains

The effect of initial granular structural conditions on load transmission patterns was experimentally investigated. Two types of granular structures were prepared by laminating cylindrical model particles of different diameters, to which photoelastic sheets were attached. Two-dimensional, reflective photoelasticity tests were performed under two granular conditions: (1) a uniform structure without initial defects and (2) with initial local imperfections at the bottom of the granular assembly. Two granular assemblies were tested for uniaxial compressive loading and shallow foundation loading conditions. For macroscopic analyses of the load–displacement relationship, the photoelastic response of individual particles was measured to microscopically observe the distribution of the main contact force chains within each granular assembly. Furthermore, the effect of initial local defects on the bearing capacity of granular assemblies was examined by confirming particle movement and the expansion of initial local defects in the granular assembly via particle image velocimetry (PIV). As a result, a completely different form of internal contact force chain was developed from the beginning of loading to the final failure stage, depending upon whether or not initial local instability existed in the granular assembly. In particular, a significant effect on the bearing capacity was found under shallow foundation loading conditions.

Macroscopic and microscopic simulation of silo granular flow based on improved multi-element model

In the PFC simulation of silo granular discharge, spherical particles were used in the traditional model, which could not accurately reflect macroscopic and mesoscopic mechanism during discharge of wheat, rice and other particles with non-spherical shapes. This research provides an improved multi-element model consisting of clump elements and ball elements. The model uses clump elements to simulate non-spherical grain particles and ball elements to simulate dust particles. The numerical simulation was carried out with the improved multi-element model, and the results are compared with the traditional simulation which uses the spherical ball elements and the experiment of grain discharge. It demonstrates that: (1) In terms of the normal wall pressure, the dynamic pressure fluctuation in flow with improved multi-element model is more gradual, and the discharge process lasts longer, the normal pressure simulation results are more accurate than the traditional model. (2) In terms of the meso-structure of the granular material, compared with traditional spherical ball model, the material packing porosity of the improved multi-element model decreases and the coordination number increases, which is denser and in consistent with the actual situation. (3) Particle shape would affect the meso-mechanical behavior of particles. The simulation results demonstrate that, compared with the traditional spherical ball model, the contact forces in the improved multi-element model increases, and the distribution of contact force chains is more uniform and denser; several arching force chains could be clearly seen in the improved multi-element model, which clearly reflects the dynamic change law of the instantaneous arch. The improved multi-element model established in this paper further improves the accuracy of simulation and reflects the dynamic changes of the normal pressure on the silo wall, granular material structure and meso-mechanical parameters during grain discharge.

Continuous-discrete coupling-based stability study of surrounding rock of limestone roadway in acid environment

To investigate the influence of acid environment on the stability of parallel limestone roadway, we carry out limestone mechanical characteristic degradation test, obtain the degradation rule of limestone, and utilize the FLAC and PFC2D softwares to construct the parallel roadway macroscopic–microscopic coupling computational model based on the continuous element and discrete element theory, thus analyzing the rock mass stress in the middle pillar, floor, and arch foot of the roadway, as well as the variation and failure pattern in the plastic zone under the long-term action of the acid environment from the macroscopic and microscopic points of view. Our results indicated that, relative to the neural water environment, the strength characteristic of limestone would basically show a linear degradation trend after the action of acid environment at pH 5 and 3 and that the influence on cohesion was greater than that on the internal frictional angle. Besides, under the acid environment, the middle pillar was subject to the greatest influence, which was likely to induce cutthrough of the plastic zone in the rock pillar, thus resulting in instability of the roadway. Additionally, the particle disruption distribution, displacement vector, and contact force chain in the discrete domain also revealed the deformation development rule of the plastic zone in the surrounding rock. This study has verified the feasibility of the coupling analysis method in studying the roadway macroscopic–microscopic deformation mechanism which is of reference significance to research on the parallel roadway stability under acid environment.

DEM analysis of the sand plug behavior during the installation process of open-ended pile

A DEM simulation of the installation process of open-ended pile is conducted by means of the particle flow code PFC 2D. Focus is placed on the investigation of the soil plug behavior, from both macroscopic and microscopic perspectives. A soil assembly with natural initial stress state is first generated and the validity of the numerical installation process is further checked. Afterwards, a macroscopic analysis is performed based on the porosity and stress state. Numerical results indicate that a dense zone, with the length about half the pile diameter, has formed at the pile tip. A dramatic load transfer is observed at the bottom of the soil plug, where the lateral pressure coefficient peaks at around 2.4. From a microscopic perspective, two modes of soil layer deflection exist for soil mass inside and under the pile, respectively. Different particle displacement patterns indicate that with increasing penetration depth and resistance accumulation, soil mass flows into the pile with a lower rate. Further analysis based on the distribution of contact force chain and principal stress rotation show that soil particles, when subjected to external disturbance, tend to rearrange to the most stable structure, which is in the arch shape. Finally, an improved arch model based on the numerical results is proposed to facilitate the understanding of the plug behavior.

Numerical Study of Damage Evolution Law of Coal Mine Roadway by Particle Flow Code (PFC) Model

Deformation and destruction of roadway surrounding rock is one of the main causes of coal mine accidents. In this paper, the horseshoe-shaped roadway model was established by particle flow code firstly and then analyzed the roadway damage process through the contact force chain, deformation displacement and distribution of micro-cracks. The research result show that the parallel bond model can well simulate the damage process of the coal mine roadway. The surrounding rock can be divided into four zones from the roadway side to the deep rock mass. The micro-contact force chain is the force transmission path and the principal stress is the macroscopic reflection of the micro-contact force chain.

Temperature effects and heat transfer in granular soils by discrete element modeling of CPT

This work performed the study of the mechanism of cone penetration test (CPT) in dry soil disks considering disk expansion subjected to the influence of heat transfer. The research was carried out with the application of discrete element method simulations in 2D. The coupling of heat transfer mechanism together with disk expansion mechanism was applied all through the sample heating preparation. The preparation of the numerical samples was done subjected to the particular temperature. Thereafter, CPT was penetrated in the numerical specimens under varied temperature conditions. With the increase in the specimen temperature, the soil disks exhibited expansion, resulting in a noticeable increase in the cone tip resistance. Moreover, the sleeve friction increased but much smaller than the cone tip resistance. The influences of the disk expansion coefficients were also examined in the study. As revealed by the microscale study, the larger velocity field, the larger displacement field, and the larger contact force chain of soil disks were close to the cone penetrometer independent of temperature variations. In the meantime, the magnitude of the velocity field, the displacement field, as well as the contact force chains of soil disks at low temperature amounted to be much smaller than soil disks at high temperature.

DEM-aided direct shear testing of granular sands incorporating realistic particle shape

Discrete element method (DEM) of granular sands incorporating the effect of the realistic particle shape has been an important issue for many years. In this context, this study proposed a novel framework for the generation of realistic-shaped particles of natural sands in 3D DEM simulations. The generation framework mainly included micro-CT (μCT) scanning of sand particles, image processing of μCT images, spherical harmonic reconstruction of the particle surface, and clump generation by the overlapping multisphere clump method (OMCM) in DEM simulations. To validate the accuracy of OMCM, the volume and inertia moment of the clump were carefully investigated, and a set of optimized generation parameters was then determined to ensure the accuracy of the clump and the limit number of the filling spheres. Based on the generation framework, a clump sample with realistic particle shapes and a corresponding sphere sample were generated to conduct a series of direct shear testing. The simulation results demonstrated that the realistic particle shape highly increases the particle interlocking rather than the anisotropic intensity of strong contact force chains, and in turn enhances the shear resistance and the shear-induced dilation of the sands. It was also found that the inter-particle contacts of the clump sample have higher friction mobilization than that of the sphere sample, which identified the micromechanism of the shape effect on the particle interlocking.

Dynamic Fragmentation of Jointed Rock Blocks During Rockslide‐Avalanches: Insights From Discrete Element Analyses

AbstractThe dynamic fragmentation of jointed rock blocks during rockslide avalanches has been investigated by discrete element method simulations for a multiple arrangement of a rock block sliding over a simple slope geometry. The rock blocks are released along an inclined sliding plane and subsequently collide onto a flat horizontal plane at a sharp kink point. The contact force chains generated by the impact appear initially at the bottom frontal corner of the rock block and then propagate radially upward to the top rear part of the block. The jointed rock blocks exhibit evident contact force concentration and discontinuity of force wave propagation near the joint, associating with high energy dissipation of granular dynamics. The corresponding force wave propagation velocity can be less than 200 m/s, which is much smaller than that of an intact rock (1,316 m/s). The concentration of contact forces at the bottom leads to high rock fragmentation intensity and momentum boosts, facilitating the spreading of many fine fragments to the distal ends. However, the upper rock block exhibits very low rock fragmentation intensity but high energy dissipation due to intensive friction and damping, resulting in the deposition of large fragments near the slope toe. The size and shape of large fragments are closely related to the orientation and distribution of the block joints. The cumulative fragment size distribution can be well fitted by the Weibull's distribution function, with very gentle and steep curvatures at the fine and coarse size ranges, respectively. The numerical results of fragment size distribution can match well some experimental and field observations.

Discrete element modelling of under sleeper pads using a box test

It has recently been reported that under sleeper pads (USPs) could improve ballasted rail track by decreasing the sleeper settlement and reducing particle breakage. In order to find out what happens at the particle–pad interface, discrete element modelling (DEM) is used to provide micro mechanical insight. The same positive effects of USP are found in the DEM simulations. The evidence provided by DEM shows that application of a USP allows more particles to be in contact with the pad, and causes these particles to transfer a larger lateral load to the adjacent ballast but a smaller vertical load beneath the sleeper. This could be used to explain why the USP helps to reduce the track settlement. In terms of particle breakage, it is found that most breakage occurs at the particle–sleeper interface and along the main contact force chains between particles under the sleeper. The use of USPs could effectively reduce particle abrasion that occurs in both of these regions.

DEM Investigation of Particle-Scale Mechanical Properties of Frozen Soil Based on the Nonlinear Microcontact Model Incorporating Rolling Resistance

Although frozen soil is in nature the discrete material, it is generally treated as the continuum material. The mechanical properties of frozen soil are so complex to describe adequately by conventional continuum mechanics method. In this study, the nonlinear microcontact model incorporating rolling resistance is proposed to investigate the particle-scale mechanical properties of frozen soil. The failure mechanism of frozen soil is explicated based on the evolution of contact force chains and propagation of microcracks. In addition, the effects of contact stiffness ratio and friction coefficient on stress-strain curve and energy evolution are evaluated. The results show that the nonlinear microcontact model incorporating rolling resistance can better describe the experimental data. At a higher axial strain, the contact force chains near shear band which can give rise to the soil arch effect rotate away from the shear band inclination but not so much as to become perpendicular to it. The propagation of microcracks can be divided into two phases. The stress-strain curve is strongly influenced by contact stiffness ratio. In addition, friction coefficient does not significantly affect the initial tangential modulus. Compared with frictional coefficient, the effect of contact stiffness ratio on stress-strain curve and energy evolution is greater.

Numerical simulation study on macroscopic mechanical behaviors and micro-motion characteristics of gangues under triaxial compression

This paper describes the numerical research that studied the macroscopic mechanical behavior and the microscopic particle movement of gangue with different gradation under different confining condition and loading rate. Two types of compression tests, confined compression tests and triaxial compression tests were simulated using the commercial numerical modeling software PFC3D. Most of the gangues are irregular convex polyhedron in shape. When under compression, huge contact force can be generated between particles result in interlocking effect. In order to reproduce the interaction between gangues, this research used Clump Template tool in PFC3D to generate clusters of particles to represent tailing particles. Following observations were made based on numerical modeling result: 1) reasonable particle gradation can significantly improve the anti-deformation capacity and decrease lateral stress coefficient of gangue. 2) In triaxial compression tests, the load bearing capacity of gangue increases with the increase of confining pressure. 3) Distribution of particles axial displacement showed ‘horizontal layering’ feature in confined compression tests, and showed ‘concave layering’ feature in triaxial compression tests. In triaxial compression tests, particles close to the mid-height and the sides of the sample have most significant lateral displacement, forming a triangular zone of significant lateral displacement. It is also found that smaller particles move more actively while the large particles have their own “movement inertia”. 4) With the increase of confining pressure, the number of the contact force chains and the maximum contact force between particles within the sample increases gradually, also the interpenetration degree of the contact force chains gradually increased. Meanwhile, the number of contact force chains and the maximum contact force are comparatively higher by using confined compression condition than the confining pressure at the same stress state. 5) Large size gangue particles play the main role in anti-deformation and transfer of axial stress; the surface contact force of large particles is significantly greater than that of the small particles. 6) Faster loading rate may increase the measured load bearing capacity of the gangue sample under the same confining condition.

DEM investigation of mechanical behavior and strain localization of methane hydrate bearing sediments with different temperatures and water pressures

This paper investigates the mechanical behavior and strain localization of methane hydrate bearing sediments (MHBS) at different temperatures and water pressures via the distinct element method (DEM). A thermo-hydro-mechanical contact model of MHBS has been employed in the DEM to simulate biaxial tests and mechanical behavior of MHBS is studied with different temperatures and water pressures. Three MHBS specimens are simulated at different temperature-pressure conditions to provide an insight on the evolution of macro and micro variables during strain localization of MHBS, as well as the geometric characteristics of shear band. The results show that MHBS appears to be strain-softening with dilatancy and the existence of MH will increase the cohesion but decrease the friction angle of MHBS. As temperature increases or water pressure decreases, the cohesion and friction angle of MHBS decrease with increasing dilatancy. The strain localization is closely related to bond breakage as well as localization of other micro and macro variables such as contact force chains, principal stress fields, particle velocity fields and average pure rotation rate distributions. As temperature and water pressure change, three different types of shear band can form. The thickness and inclination angle of these shear bands increase as the temperature increases or water pressure decreases.