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.
The discrete element method (DEM) has only rarely been used to simulate clay, due to difficulties in modelling clay particle shape and capturing the various particle interactions. This paper presents ...a new approach to simulate clay in three dimensions using DEM, featuring realistic particle shape and a new straightforward interaction law, which is able to reproduce all well-known characteristic platelet interactions. By varying the interactions between the platelets (including both the ‘edges’ and ‘faces’), it is possible to account for a range of environmental conditions. Simple sedimentation and one-dimensional compression tests are presented, which correctly reproduce the expected behaviour, confirming the validity of the model. Particle-scale analysis reveals the influence of the platelet interactions on the bulk behaviour, and it is also shown that platelet aggregation appears to lead to a fractal distribution of aggregated ‘stack’ sizes as a means of space filling.
In this paper we show DEM simulations of static and cyclic large triaxial tests on a sample of railway ballast. The sample is reconstructed from X-Ray tomography images of an untested laboratory ...sample, recovered by impregnation with an epoxy resin. Measurements of both shape and fabric are carried out; the sample shows a high anisotropy of particle orientations due to the preparation procedure and a high shape heterogeneity. A DEM model is then generated using clumps to model single particles, preserving the shape of each particle and the fabric of the sample. Results of static and cyclic simulations are shown and compared with previous simulations on numerically generated samples, showing the importance of an accurate representation of the whole range of particle shapes, as well as confirming the effect of particle anisotropy on the mechanical response.
Graphical Abstract
In DEM simulations of triaxial tests, modelling a flexible lateral membrane is crucial and challenging. It is essential for the correct application of a uniform lateral pressure and for an accurate ...measurement of sample volume. Here, we introduce a membrane made of triangular facets, and model it as a continuum; we then compare this approach with a well-established method that uses a layer of bonded spheres. With either method, it is also possible to assess the additional stress applied by the membrane as it deforms, i.e. the difference between the stress applied at the boundary and the actual stress within the sample. It is shown that this difference has two origins: the tension developed in the membrane, as it deforms; and the curvature of the membrane, since this causes a vertical component of the confining pressure which can be significant. These findings may be used to inform and improve the membrane correction commonly used in experiments, where similar effects occur.
Graphic abstract
This paper is a study of the dependence of the volume of voids in a granular material on the particle size distribution. It has previously been proposed that the volume of voids is proportional to ...the volume of the smallest particles. In a particle size distribution which is progressively becoming wider (e.g. as occurs due to crushing during the compression of sand), the smallest size of particle decreases, yet there are only ever a few of these particles out of many thousands or millions. This paper attempts to identify which particles govern the overall density of a granular material, and a new definition of the ‘smallest particles’ is proposed. These particles are shown to govern the void space in a range of simulations of spherical and non-spherical crushable particles. The theory also applies to idealised Apollonian sphere packings.
A simple and fast original method to create irregular particle shapes for the discrete element method using overlapping spheres is described. The effects of its parameters on the resolution of the ...particle shape are discussed. Overlapping spheres induce a non-uniform density inside the particle leading to incorrect moments of inertia and therefore rotational behaviour. A simple method to reduce the error in the principal moments of inertia which acts on the individual densities of the spheres is also described. The pertinence of the density correction is illustrated by the case of free falling ballast particles forming a heap on a flat surface. In addition to improve behaviour, the correction reduces also computational time. The model is then used to analyse the interaction between ballast and geogrid by simulating pull-out tests. The pulling force results show that the model apprehends better the ballast geogrid interlocking than models with simple representation of the shape of the particles. It points out the importance of modelling accurately the shape of particles in discrete element simulations.
The discrete element method (DEM) is a popular tool for simulating soils, however it has rarely been used for modelling clays. This is despite the behaviour of clays being much less well understood ...compared to sands. This paper aims to increase the use of DEM to investigate clays by highlighting some important issues concerning the implementation of particle interactions to any model. When using spheres as the elementary unit in DEM, it is shown how special attention is needed to ensure repeatable interactions between platelets, and also how the geometry of the platelets affect both the normal and tangential interactions.
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•Using Discrete Element Method, essential to model platelets with a high resolution.•Contact laws must be calibrated to ensure the expected model behaviour.•Random imperfections are required to ensure repeatable platelet interactions.•The specified model coefficient of friction does not correspond to measured value.
The fundamental fractal micro mechanics of normal compression of granular materials is studied using DEM. This paper examines the emergence of a finite fractal bounded by two particle sizes as stress ...increases, and the evolution of various definitions of the ‘smallest particles’. It is revealed that if particles are categorised according to their coordination number, then the volume of all particles with 4 contacts or fewer is directly proportional to the void space. These particles are called ‘critical particles’ and are shown, for the first time, to explain quantitatively the voids reduction with increasing vertical stress.
Stress path tests are used to investigate the yield surface of a crushable numerical soil. Triaxial samples with isotropic and anisotropic stress histories are examined to determine the nature of the ...yield surface and to establish what governs yield. Two separate yield surfaces are exposed: a shear yield surface at low p′ and high η which is governed by minor breakage of fine particles, and a compressive yield surface at high p′ and low η, governed by bulk breakage across all particle sizes. The shear yield surface is dependent on stress history, whilst the compressive yield surface is isotropic.
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