Dimensional Discrete Element Method Research Articles

A particle-scale insight into the face stability of shallow EPB shield tunnels in dry cobble-rich soil

The aim of this paper is to provide a particle-scale insight into the face stability of shallow (C/D = 1.0; C = tunnel buried depth and D = tunnel diameter) earth pressure balanced (EPB) shield tunnels in cobble-rich soil, considering both the dynamic excavation process and particle size gradation. The work was performed by three dimensional discrete element method (DEM). Results show that particle size greatly influences the movement of cobble particles. The coarse particles serve as the skeleton of the ground and provide the stability. The erosion of fine particles has little influence on tunnel face stability, while the erosion of middle particles weakens tunnel face stability. The limit support pressure pf increases with increasing cutterhead rotating speed, and the normalized limit support pressure pf/γD (γ = soil unit weight, D = tunnel diameter) obtained in this paper is larger than existing researches. The abrupt increase of middle particles in the muck composition can be recognized as the forewarning information against face failure.

Soil disturbance induced by EPB shield tunnelling in multilayered ground with soft sand lying on hard rock: A model test and DEM study

A large scale model test and numerical simulation using three dimensional discrete element method (3D DEM) were carried out in parallel to study the soil disturbance induced by earth pressure balanced (EPB) shield tunnelling in multilayered ground with soft sand lying on hard rock. The model test used a miniature EPB shield machine which could fully reproduce the real tunnel construction of excavation and support. The DEM model simulating the model test was developed to capture the microscopic mechanisms of ground deformation. The surface and subsurface settlement were closely recorded in model test and compared with those of homogeneous ground to clarify the influence of underlying rock on the movement of overlying sand. The volume ratio of rock to sand in excavated muck was closely recorded in DEM simulation to quantitatively analyse the over excavation of soft sand. Results show that both the surface and subsurface settlement trough in multilayered ground are narrower than those in homogeneous ground, while the subsurface settlement in multilayered ground is larger than that in homogeneous ground. The width parameter of settlement trough decreases nonlinearly along the gravitational direction. The over excavation of overlying soft sand is influenced by the ratio of hard rock to tunnel cross section and the rotating speed of shield cutterhead.

DEM simulation of particle crushing in a triaxial test considering the influence of particle morphology and coordination number

This paper aims to simulate the particle crushing events occurring in the triaxial test considering the irregularity of particles and the coordination number using the three dimensional discrete element method (DEM). Firstly, based on the published micro computed tomography data, the irregular particle shapes were reproduced using the spherical harmonic analysis. The flexible membrane in the triaxial test was modelled using the structural shell elements in FLAC3D. Secondly, a particle crushing criterion based on the maximum interparticle contact force was adopted to predict any particle crushing event. Next, the fragments were generated based on a specific fragmentation pattern once the maximum contact force of a particle satisfies the crushing criterion. This fragmentation pattern depends on the coordination number of the crushed particle and is used to determine the fragment number and volumes. Finally, the particle crushing events were successfully modelled by replacing the crushed particle with the generated fragments with a consideration of the mass conservation. Given the absence of any approach for reproducing the realistic fragmentation pattern of sand particles while maintaining the mass conservation in the existing DEM studies, this paper makes a salient contribution to the DEM modelling of real particle crushing behavior of sands.

Face stability of EPB shield tunnels in multilayered ground with soft sand lying on hard rock considering dynamic excavation process: A DEM study

This paper aims at studying the face stability of earth pressure balanced (EPB) shield tunnels in multilayered ground with soft sand lying on hard rock considering dynamic excavation process. The analysis was performed using three dimensional discrete element method (DEM). The present work has two advantages: (1) it reveals the influence of soil disturbance induced by dynamic cutting process on tunnel stability in multilayered ground; (2) it reveals the influence of soil retaining provided by cutterhead panel on tunnel face stability in multilayered ground. Results show that tunnel face collapse undergoes two stages. The underlying hard rock restricts the movement of overlying soft soil, and face failure happens more abruptly with decreasing η (η = a/D. a = height of soft sand within tunnel cross section; D = tunnel diameter). The normalized limit support pressure pf/γD (pf = limit support pressure; γ = soil unit weight) obtained from this paper is larger than that of existing research, i.e. existing research underestimate the limit support pressure. The weakening effect of cutterhead dynamic cutting process on face stability is larger than the strengthening effect of cutterhead panel retaining on face stability. The difference generally increases with increasing C/D (C = tunnel cover depth) and η. Partial collapse occurs in multilayered ground with soft sand lying on hard rock. C/D mainly influences the shape of the failure zone, and η mainly determines the size of the failure zone.

Discrete Element Simulation Study on Particle Segregation Effect of a Hemispherical Shell Swing-Oscillating Trough Under Combination Swing-Oscillating

In order to enhance the segregation effect of material particles in a hemispherical shell swing-oscillating trough under combination swing-oscillating, by means of three dimensional discrete element method, and by use of the two-dimensional dry granules of plastic ball and steel ball, the discrete element simulation study of particle segregation process is carried out in turn in three cases, which is composed of a single swing-oscillating in smooth trough, a combination swing-oscillating in smooth trough, and a combination swing-oscillating in adding bulge trough. The particle segregation effect was evaluated by particle volume concentration and combined with segregation cloud picture simulated. The result indicates that segregation effect of combination swing-oscillating is better than that in single swing-oscillating; layering effect of the trough added bulge is better than that in the smooth trough. And compared to single swing-oscillating in smooth trough, the degree of segregation of particles in added bulge trough can be increased by 10–15% when being combination swing-oscillating.

Discrete element simulation of the resistance of a ship in unconsolidated ridges

Resistance on a ship penetrating a sea ice ridge is a key design parameter of ice breaking ships. The resistance of a ship in an unconsolidated ridge has been studied by using a three dimensional discrete element method. Ridges of equal depth but different widths were used and it was observed that the ridge width has a major effect on the ridge resistance: the ridge resistance increases with increasing ridge width, until the ridge width is of the same order as the ship length. The ridge resistance was decomposed into a frictional force and a deformation force. The deformation force is due to the ridge deformation by the ship bow and it was shown that the deformation force is related with the mass of ice blocks accelerated by and moving with the ship.

DEM modelling of screw pile penetration in loose granular assemblies considering the effect of drilling velocity ratio

Screw piles have been widely used as foundations for various types of structures. Drilling velocity ratio, the ratio of rotational velocity to driven velocity, is a critical parameter that affects the driven behaviors of screw piles. Three dimensional discrete element method, with a particle refinement method to enhance computation efficiency, is used to study the driven behaviors of screw piles to compare with the laboratory mini screw pile test results achieved by Shi et al. (Rock Soil Mech 39(6):1981–1990, 2018). The driven behaviors of a mini screw pile (900 mm long and 40 mm shaft diameter) with a variable diameter auger into loose granular assemblies under 0.5, 1 and 1.5 critical drilling velocity ratios are studied. The variation of stress distribution in the assemblies, particle movement around the piles, and evolution of void ratio in the assemblies are investigated. The results indicate that particles around the piles behave differently under different drilling velocity ratios. The reduction of driven force with the increase of drilling velocity ratio can be explained using the direction of particle movement around the piles and the vertical force acting on the screw blades. It was found that under high drilling velocity ratio, higher downward vertical force can be provided by the blades.

Effect of Gradation Segregation on Mechanical Properties of an Asphalt Mixture

Gradation segregation strongly affects the service performance of asphalt pavement. However, rare studies focus on the influences of segregation on asphalt mixture as it is difficult to simulate segregation in a laboratory. This paper presents a research aiming to evaluate the effects of gradation segregation using the two dimensional (2D) discrete element method (DEM). To achieve this objective, the gradation segregation levels are defined according to the differences between control and segregated gradations. Based on this, asphalt mixtures with three gradations at three segregation levels were selected. The corresponding 2D DEM models were then built using Particle Flow Code 2D (PFC 2D). The aggregate skeletons in the asphalt mixture were determined separately by means of the contact point and contact force. Based on this, the variations on the aggregate skeleton, aggregate distribution, and mechanical properties of the asphalt mixture under vertical load were studied at three different segregation levels. This study indicates that the aggregate skeleton in asphalt mixture can be affected by the gradation segregation. The correlation between gradation segregation and mechanical property is also determined in this study.

Three dimensional discrete element method simulations of interface shear

Granular-continuum interfaces are widely present in geotechnical applications, including deep foundations, retaining structures, and anchoring applications. Interface mechanical properties are a function of the characteristics of the contacting soil and the opposing interface. Therefore, a robust understanding of granular-continuum interface behavior is essential to geotechnical practice. In this work, we did the following: (1) summarized the recent research on the effects of interface roughness, soil density, particle shape, and friction coefficient on interface behavior and strength; (2) simulated granular-continuum interface shear using the three-dimensional discrete element method (DEM); (3) compared the trends in DEM results to previously published physical experiments; and (4) investigated the microscale responses of the interface simulations. The DEM simulations were generally in good agreement with previously reported experimental results for similar interface roughness. DEM simulations give a bilinear strength-displacement trend consistent with that previously reported from physical experiments. The microscale investigations showed that, in the case of rougher interfaces, contact reorientation was the interface failure mechanism, and in the case of smoother interfaces, it was contact sliding. The mobilization of rougher interfaces tends to alter the force distribution in the surrounding soil.

On the Micromechanics of True Triaxial Test, Insights from 3D DEM Study

In this paper, three dimensional discrete element method simulations of true triaxial test are presented. During simulations, the major, the intermediate and the minor principal strains are monitored to maintain the b-value constant. The effect of intermediate principal stress on the frictional parameters of granular materials is studied. Furthermore, the micromechanics of samples using the Stress–Force–Fabric (SFF) relationship is investigated. The SFF relationship is comprised of anisotropy tensors of fabric, contact normal and tangential forces. Results show that, the mobilized friction angles in simulations with different b-values have very good agreements with results of the so-called general stress tensors, which are made of force and position vectors at contact points. It is observed that the evolution of anisotropy in the sample is at the origin of different responses of granular materials in macro scale. The frictional properties of granular materials is observed sensitive to the intermediate principal stress both at macro and grain scale. Our observations highlight the important role of intermediate principal stress, and are consistent with experimental studies of true triaxial tests on granular materials.

Numerical modeling of compaction and flow of coke/pitch mixtures using discrete element method

A variety of composite materials are composed of a viscoelastic matrix and elastic fillers. These materials range from polymer matrix composites to asphalt concretes. Discrete element method (DEM) has the capability of explicitly modeling the mechanical and physical properties of both matrix and aggregates. In the present work, DEM is applied to simulate the compaction and deformation of mixtures of coal tar pitch and calcined coke at 135, 140, 145 and 150 °C. Rheological properties of pitch and those of the binder matrix (mixture of pitch and fine coke particles) were experimentally measured by means of a dynamic shear rheometer. Obtained data was then used to estimate the four parameters of Burger’s viscoelastic model for pitch and binder matrix. The dynamic shear rheometer test was simulated by a three dimensional DEM model to verify the proposed viscoelastic model. Results showed that there is a very good agreement between the measured values and model predictions for complex, storage and loss moduli of pitch and binder matrix in a wide range of frequencies at all studied temperatures. The verified models were then used to study the compaction and densification of coke/pitch mixtures. Results showed that temperature has a positive effect on densification of coke/pitch mixtures and lower value of porosity is expected for the material pressed or vibrated at higher temperatures.

Particle shape effects on fabric of granular random packing

A numerical investigation of particle shape effects on fabric of granular packing is carried out using the three dimensional discrete element method with a superellipsoid model. A broad range of particle shapes controlled by two shape parameters (i.e., aspect ratio and blockiness) are taken into account. A series of random packing of non-cohesive, frictional monodisperse superellipsoids is conducted under gravitational forces in simulations. Fabric of a granular packing is quantified in terms of packing density, coordination number, distribution of particle orientations, anisotropy of three types of fabric vectors (i.e., particle orientation, contact normal and branch vector), and distribution of normalized contact forces. It is shown that the effects of particle shape on packing density and mean coordination number are in agreement with the reported in the literature. Moreover, ellipsoids show the lowest packing density in the family of superellipsoids. The distribution of particle orientations is much more sensitive to blockiness than aspect ratio. It is also found out that anisotropy of both particle orientations and contact normals shows a similar M-type relationship with aspect ratio, two times larger than that of branch vectors. Interestingly, particle shape has an insignificant effect on the probability distribution of normalized contact forces which shows a clear exponential distribution. Those findings would be useful for a better understanding of the initial fabric of granular packing, especially in granular mechanics and geomechanics.

Micromechanics of non-active clays in saturated state and DEM modelling

The paper presents a conceptual micromechanical model for 1-D compression behaviour of non-active clays in saturated state. An experimental investigation was carried out on kaolin clay samples saturated with fluids of different pH and dielectric permittivity. The effect of pore fluid characteristics on one-dimensional compressibility behaviour of kaolin was investigated. A three dimensional Discrete Element Method (DEM) was implemented in order to simulate the response of saturated kaolin observed during the experiments. A complex contact model was introduced, considering both the mechanical and physico-chemical microscopic interactions between clay particles. A simple analysis with spherical particles only was performed as a preliminary step in the DEM study in the elastic regime.

Effect of friction on pebble flow pattern in pebble bed reactor

Friction affects pebble flow pattern in pebble-bed high temperature gas-cooled reactor (HTGR) significantly. Through a series of three dimensional DEM (discrete element method) simulations it is shown that reducing friction can be beneficial and create a uniform and consistent flow field required by nuclear engineering. Particle–wall friction poses a decisive impact on flow pattern, and particle–particle friction usually plays a secondary role; relation between particle–wall friction and flow pattern transition is also concluded. Moreover, new criteria are created to describe flow patterns quantitatively according to crucial issues in HTGR like stagnant zone, radial uniformity and flow sequence. Last but not least, it is proved that friction control of hopper part is more important than that of cylinder part in practical pebble beds, so reducing friction between pebbles and hopper surface is the engineering priority.

Effect of Interparticle Friction on the Micromechanical Strength Characteristics of Three Dimensional Granular Media

The role of interparticle friction on the micromechanical strength characteristics of granular assembly subjected to gradual shearing was analyzed. Three dimensional discrete element method (DEM) was applied in the simulation of quasi-static shearing of granular assemblies with varying interparticle frictional coefficients [µ= 0.10, 0.25, 0.50]. From the reported simulation results, analysis of the following was performed for varying interparticle frictional capacities.i. The normal and tangential stress contributions of weak and strong contacts to principal stress components.ii. Contribution of strong and weak contacts to principal and deviator stress.iii. Evolution of mechanical coordination number and fabric anisotropy of strong contact forces.From this analysis, it is safe to conclude that interparticle friction has a direct effect on the major and minor principal stress components in sheared granular assemblies. Consequently, increasing interparticle friction capacity enhances macroscopic shear strength in sheared granular assemblies. Likewise, at the peak shear strength of the sheared granular media, there exists a maximum fabric anisotropy of strong contact forces and this corresponds to a minimum value of mechanical coordination number (minimum possible number of load bearing contacts per particle).

Numerical investigation on angle of repose and force network from granular pile in variable gravitational environments

This paper presents a numerical investigation on the relationship between the angle of repose and gravity by a three dimensional discrete element method. Taking particle shape, particle size and surface roughness of particle into account, the forming of granular pile was simulated under four different gravitational conditions: the Moon gravity, Martian gravity, Earth gravity and super-gravity. The angle of repose at macro level and the contact forces between particles of the pile were analyzed. Results show that the contact forces are lognormal distributed with about 65% smaller than the mean, and the ratio of tangential to normal force is uniformly distributed except for a small peak where the friction force is fully mobilized. The probability distribution of contact forces normalized by particle's weight under all gravity conditions shows to be in mutual coincidence, and the distribution of the ratio of tangential to normal force is independent of gravity. Although the microstructure of pile varies randomly, the angle of repose will not be affected by the magnitude of gravity.

Discrete element modelling of unidirectional fibre-reinforced polymers under transverse tension

The mechanical behaviour of unidirectional fibre-reinforced polymer composites subjected to transverse tension was studied using a two dimensional discrete element method. The Representative Volume Element (RVE) of the composite was idealised as a polymer matrix reinforced with randomly distributed parallel fibres. The matrix and fibres were constructed using disc particles bonded together using parallel bonds, while the fibre/matrix interfaces were represented by a displacement-softening model. The prevailing damage mechanisms observed from the model were interfacial debonding and matrix plastic deformation. Numerical simulations have shown that the magnitude of stress is significantly higher at the interfaces, especially in the areas with high fibre densities. Interface fracture energy, stiffness and strength all played important roles in the overall mechanical performance of the composite. It was also observed that tension cracks normally began with interfacial debonding. The merge of the interfacial and matrix micro-cracks resulted in the final catastrophic fracture.

Simulation of shale–proppant interaction in hydraulic fracturing by the discrete element method

In this paper, a three dimensional discrete element method (3D DEM) was proposed and deployed to simulate shale–proppant interaction in hydraulic fracturing. Shale is represented by particles with cement bond, and proppant is represented by particles without a cement layer. The velocity Verlet method is implemented to substitute the traditional central time integration scheme. The proposed DEM is used to investigate the shale–proppant interactions and evaluate the fracture aperture under different proppant sizes, Young׳s moduli and pressure levels. The results reveal that, the more soft shale particle, the higher pressure and the larger proppant size imply smaller crack aperture and larger plastic zone for other given conditions.

Study on Sand Group Motion Characteristics of Vibration Moulding

Vibration moulding of expendable pattern casting (EPC) was simulated by three dimensional discrete element method, a special EPS tube for test was devised, and the law of vibration form on the motion of sand group was summed up. The results show that vibration form and filling motion of sand group in-tube has consistency in the direction, at the same time gravity and tube direction have a great influence on sand group motion, which leads to particularity of Z tube and Z vibration.

Study on Influence Factors of Underground Joint Rock Cavern Displacement

The safety response of joint rock underground tunnels is one of the many problems that draw the attention of geology specialists and scholars. Adopting two dimensional discrete element method, a numerical model of joint rock underground cavern is established to study its stability. The buried depth and the lateral pressure coefficient are considered respectively. The result shows: when the lateral pressure coefficient is identical, the depth is bigger the displacement is more bigger, and the displacement is strong influenced by the buried depth when the lateral pressure coefficient is big; In the same depth the tunnel is buried, the tunnel rocks displacement is slightly influenced by the lateral pressure coefficient when it is small, but the influence is seriously as the lateral pressure coefficient is big. The simulation in the context can be used to provide guide for joint rock tunnel excavation and supporting.