Discrete element modelling of scaled railway ballast under triaxial conditions

The aim of this study is to demonstrate the use of tetrahedral clumps to model scaled railway ballast using the discrete element method (DEM). In experimental triaxial tests, the peak friction angles for scaled ballast are less sensitive to the confining pressure when compared to full-sized ballast. This is presumed to be due to the size effect on particle strength, whereby smaller particles are statistically stronger and exhibit less abrasion. To investigate this in DEM, the ballast is modelled using clumps with breakable asperities to produce the correct volumetric deformation. The effects of the quantity and properties of these asperities are investigated, and it is shown that the strength affects the macroscopic shear strength at both high and low confining pressures, while the effects of the number of asperities diminishes with increasing confining pressure due to asperity breakage. It is also shown that changing the number of asperities only affects the peak friction angle but not the ultimate friction angle by comparing the angles of repose of samples with different numbers of asperities.     

Discrete element modelling of railway ballast

The discrete element method has been used to simulate the behaviour of railway ballast under different test conditions. Single particle crushing tests have been simulated using agglomerates of bonded balls, and the distribution of strengths correctly follows the Weibull distribution, and the size effect on average strength is also consistent with that measured in the laboratory. Realistic fast fracture can be obtained if non-viscous damping is reduced. Oedometer tests on aggregates of crushable ballast particles have also been simulated and compared with the results from laboratory tests. Finally, box tests which simulate traffic loading have been simulated using both spherical balls and 8-ball clumps. It is found that the 8-ball clumps give much more realistic behaviour due to particle interlocking.     

Discrete element analysis for shear band modes of granular materials in triaxial tests

The discrete element method (DEM) is adopted to simulate the triaxial tests of granular materials in this study. In the DEM simulations, two different membrane-forming methods are used to generate triaxial samples. One method is to pack the internal particles first, then to generate the enclosed membrane; the other is to generate the internal particles and the enclosed membrane together. A definition of the effective strain, which combines microscopic numerical results with macroscopic expression in three-dimensional space, is presented to describe the macroscopic deformation process of granular materials. With these two membrane generation methods, the effective strain distributions in longitudinal section and transverse section of the triaxial sample are described to investigate the progressive failure and the evolution of the shear bands in granular materials. Two typical shear band failure modes in triaxial tests are observed in the DEM simulations with different membrane-forming methods. One is a single shear band like a scraper bowl, and the other is an axial symmetric shear band like two hoppers stacking as the shape of rotational “X” in triaxial sample. The characteristics of the shear bands during the failure processes are discussed in detail based on the DEM simulations.     

Cyclic loading of railway ballast under triaxial conditions and in a railway test facility

A recently developed large-scale triaxial test apparatus for railway ballast testing comprises a double-cell arrangement for measuring volume change by differential pressure. Monotonic and cyclic tests were performed on limestone ballast samples. Axial and volumetric strains and breakage were determined from both types of test. Resilient modulus and Poisson’s ratio were obtained only from the cyclic tests. The permanent axial strain and breakage results from the cyclic tests are compared with the simulated traffic loading in the railway test facility (RTF) which comprises three sleepers embedded in ballast over a subgrade. The traffic loading in the RTF was applied by hydraulic actuators with built-in displacement transducers. A column of painted ballast was placed under a rail seat of the middle sleeper to ease sample collection for sieve analysis at the end of the test. The stress condition in the RTF is predicted by a simple calculation based on findings of previous literature. It was found that the results from the cyclic triaxial test with conditions similar to the predicted conditions in the RTF were comparable to those results from the RTF tests.     

Discrete element modelling of uniaxial constant strain rate tests on asphalt mixtures

Constant strain rate tests for a graded asphalt mixture under three constant strain rates have been undertaken in the laboratory. The Discrete Element Model has been used to simulate the laboratory tests with a numerical sample preparation procedure being developed to represent the physical specimen. The Burger’s model has been used to represent the time dependent behavior of the asphalt mixture. The Burger’s model was implemented to give bending and torsional resistance as well as in direct tension and compression. The stress-strain response for the laboratory tests and the simulations under three loading speeds were recorded. The results show reasonable agreement when the bond strengths in the model are made to be a function of strain rate. Both normal and Weibull distributions have been used for the bond strengths between the aggregate particles. The effects on the stress-strain response of bond strength variability and particle position are proved to be negligible. Bond breakage was recorded during the simulations to explain the internal damage within the sample. The modified Burger’s model has proved to be a useful tool in modeling the bending and torsional resistance at particle contacts in an asphalt mixture, in order to correctly predict observed behavior.     

Discrete element modelling of grain flow in a planar silo: influence of simulation parameters

There is extensive engineering literature concerning the prediction of pressure and flow in a silo. The great majority of them are based on continuum theories. The friction between the stored material and the silo wall as well as the inclination of the hopper at its base are considered to be the most influential parameters for the flow pattern within the silo. In this paper, the filling and discharge of a planar silo with a hopper at its base has been modelled using DEM. The aim is to investigate the influence of DEM model parameters on the predicted flow pattern in the silo. The parametric investigation particularly focused on the hopper angle of inclination and the contact friction between particles and walls. The shape of the particles was also considered by comparing spherical and non-spherical particles, thus providing an insight into how particle interlocking might influence solids flow behaviour in silos. The DEM computations were analysed to evaluate the velocity profiles at different levels as well as the wall pressure distribution at different stages during filling and discharge. A detailed comparison reveals several key observations including the importance of particle interlocking to predict a flow pattern that is similar to the ones observed in real silos.     

Discrete element simulation of ballast and gravel under special consideration of grain-shape,grain-size and relative density

A particle based numerical simulation procedure is presented, which allows the reproduction of the stress-strain characteristics of stiff granular material (ballast or gravel) under quite different loading conditions. If grain-shape, grain-size and relative density is considered in a proper manner, a relatively simple constitutive law with only three constants (friction coefficient, shear and normal stiffness) is sufficient for the reproduction of the observed stress-deformation behaviour. The paper describes the procedures, how to get information about grain-shape and size and how to generate samples with realistic grain-shape, size and relative density under the pre-requisite to optimize the computational effort. The procedure was successfully tested using five different lab test: soil-dump test, soil-pouring test, oedometer test, triaxial test and multi-stage shear test, also under consideration of different initial densities.     

基于激光扫描法的铁路道砟级配对道床动力特性影响的离散元研究

铁路碎石道床的道砟级配对道床的力学性能具有显著的影响,采用三维激光扫描技术对道砟颗粒的形状特征进行了获取及分析,并提出了基于道砟外形重建结果的离散元颗粒数值模型构造方法;在此基础上建立了循环荷载道砟箱数值模型。以此研究在高速及重载线路条件下,道砟级配对散体道床动力沉降特性的影响规律,并从细观角度分析了道床的沉降机理。研究结果表明:不同运营条件下铁路碎石道床的沉降机理有所不同。道砟颗粒间的相互错动是引发重载铁路道床沉降主要原因。而对于高速铁路,道床沉降还会受到高频荷载作用下颗粒自身转动的影响。因此,建议在规范中针对不同的线路条件提出不同的道砟级配曲线要求。     

Discrete element modelling and simulation of sand mould manufacture for the lost foam process

This paper presents a numerical model of mould manufacture for the lost foam casting process. The process of mould filling with sand and sand compaction by vibration are modelled using spherical (in 3D) or cylindrical (in 2D) discrete elements. The motion of discrete elements is described by means of equations of rigid body dynamics. Rigid particles interact among one another with contact forces, both in normal and tangential directions. Numerical simulation predicts defects of the mould due to insufficient sand compaction around the pattern. Combining the discrete element model of sand with the finite element model of the pattern allows us to detect possible distortion of the pattern during mould filling and compaction. Results of numerical simulation are validated by comparison with experimental data. Copyright © 2004 John Wiley & Sons, Ltd.     

The importance of modelling ballast particle shape in the discrete element method

The discrete element method has been used to model railway ballast. Particles have been modelled using both spheres and clumps of spheres. A simple procedure has been developed to generate clumps which resemble real ballast particles much more so than spheres. The influence of clump shape on the heterogeneous stresses within an aggregate has been investigated, and it has been found that more angular clumps lead to a greater degree of homogeneity. A box test consisting of one cycle of sleeper load after compaction has been performed on an aggregate of spheres and also on an alternative aggregate of clumps. The interlocking provided by the clumps provides a much more realistic load- deformation response than the spheres and the clumps will be the basis for future work on ballast degradation under cyclic loading.     

Discrete element modelling of cyclic loading of crushable aggreates

This paper examines the discrete element modelling of cyclic loading of an aggregate of crushable sand grains. Each grain of sand is modelled as an agglomerate of balls bonded together. The aggregate is subjected to compaction followed by isotropic normal (plastic) compression, and then unloaded to half the maximum applied stress. The aggregate is then subjected to cyclic loading to a maximum stress ratio of 0.8. The aim of the paper is to examine the reduction of the rate of axial strain with number of cycles, and to determine the relative influences of volumetric strain and shear strain rates on the axial strain rate. In particular, the paper aims to show whether particle breakage is mainly related to the accumulation of volumetric strain. This is found to be the case, which is consistent with proposals by other authors that plastic hardening under monotonic loading is due to particle fracture.     

Discrete element modelling of one-dimensional compression of cemented sand

It has recently been shown that the one-dimensional normal compression of sand can be modelled effectively in three-dimensions using the discrete element method, and that the slope of the compression curve (in log voids ratio–log stress space) is controlled by the size effect on average particle strength. This paper incorporates soil structure by simulating cemented sand, and the effects of inter-particle bonding (including bond strength and strength distributions) on the one-dimensional compression behaviour and evolving particle size distributions are investigated. The results show that bonding reduces particle crushing, and it is both the magnitude and distribution of bond strengths that influence the compression curve of the structured material.     

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.     

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.     

Discrete element modelling of a bucket elevator head pulley transition zone

This paper presents the results of discrete element simulations applied to a bucket elevator model with particular reference to the head pulley transition zone. This is the first stage in a larger study to better understand the mechanics of bucket elevator operation with reference to the discharge of particles at the head end. At the head end two issues arise; mechanically, the buckets are bolted to the conveying media (typically a fabric reinforced belt) and at the point of belt to headpulley tangency, the tip of the bucket undergoes a theoretical step change in velocity. This theoretical step change results in a classical under-damped response in the buckets tip velocity. In undergoing this motion, there are stresses that are passed to the carcass of the conveying media; understanding the magnitude of these stresses is one longer term goal of this research allowing a quantitative basis for the existing qualitative design guidelines such as (Handbook for conveyor and elevator belting, Apex Belting Pty Ltd). The discharge of the bulk material from the bucket has been addressed Beverly et al. (Bulk Solids Handling, 1983) but this analysis is dependent on simple, but common, bucket geometry and ignores the initial transition to the headpulley. Ignoring the transition with a low speed discharge elevator is not likely to impact on the predicted discharge pattern, however with high speed discharge elevators, the destabilising effect of the transition is expected to promote premature discharge of bulk material from the bucket. Depending on the design of the elevator casing this early discharge may or may not impact on the overall conveying efficiency.     

Two-dimensional discrete element modelling of bender element tests on an idealised granular material

The small-strain (elastic) shear stiffness of soil is an important parameter in geotechnics. It is required as an input parameter to predict deformations and to carry out site response analysis to predict levels of shaking during earthquakes. Bender element testing is often used in experimental soil mechanics to determine the shear (S-) wave velocity in a given soil and hence the shear stiffness. In a bender element test a small perturbation is input at a point source and the propagation of the perturbation through the system is measured at a single measurement point. The mechanics and dynamics of the system response are non-trivial, complicating interpretation of the measured signal. This paper presents the results of a series of discrete element method (DEM) simulations of bender element tests on a simple, idealised granular material. DEM simulations provide the opportunity to study the mechanics of this testing approach in detail. The DEM model is shown to be capable of capturing features of the system response that had previously been identified in continuum-type analyses of the system. The propagation of the wave through the sample can be monitored at the particle-scale in the DEM simulation. In particular, the particle velocity data indicated the migration of a central S-wave accompanied by P-waves moving along the sides of the sample. The elastic stiffness of the system was compared with the stiffness calculated using different approaches to interpreting bender element test data. An approach based upon direct decomposition of the signal using a fast-Fourier transform yielded the most accurate results.     

Comparison of two different types of railway ballast in compression and direct shear tests: experimental results and DEM model validation

Railway ballast is an angular and coarse material, which demands careful DEM modelling and validation. Particle shape is often modelled in high accuracy, thus leading to computational expensive DEM models. Whether this effort will increase the DEM model’s overall prediction quality will also vitally depend on the used contact law and the validation process. In general, a DEM model validated using different types of principal experiments can be considered more trustworthy in simulating other load cases. Here, two types of railway ballast are compared and DEM model validation is conducted. Calcite and Kieselkalk are investigated under compression and direct shear test. All experimental data will be made openly accessible to promote further research on this topic. In the experiments, the behaviour of Calcite and Kieselkalk is surprisingly similar in the direct shear test, while clear differences can be seen in the stiffnesses in the compression test. In DEM modelling, simple particle shapes are combined with the Conical Damage Model contact law. For each type of ballast, one set of parameters is found, such that simulation and experimental results are in good accordance. A comparison with the simplified Hertz-Mindlin contact law shows several drawbacks of this model. First, the model cannot be calibrated to meet both compression and shear test results. Second, the similar behaviour in shear testing but differences in compression cannot be reproduced using the Hertz-Mindlin model. For these reasons, the CDM model is considered the better choice for the simulation of railway ballast, if simple particle shapes are used.