Non-smooth contact dynamic approach for railway engineering: investigation of ballast behaviour under stabilisation process

Railway maintenance procedures include the stabilisation of ballasted tracks. The procedure of dynamic stabilisation which consists in vibrating laterally the rail while applying a vertical load is analysed using a discrete element code based on non-smooth contact dynamics. The ballast stones are modelled realistically using polyhedrons based on real ballast stones scans. The evolution of the compaction level and contact number between particles is analysed during the dynamic stabilisation process. A model is proposed to predict settlement. The results of simulation show the effectiveness of this maintenance procedure. It also points out the relevance of the model to predict settlement

Surface composition and properties of Ganymede: Updates from ground-based observations with the near-infrared imaging spectrometer SINFONI/VLT/ESO

Ganymede's surface exhibits great geological diversity, with old dark terrains, expressed through the surface composition, which is known to be dominated by two constituents: H2O-ice and an unidentified darkening agent. In this paper, new investigations of the composition of Ganymede's surface at global scale are presented. The analyses are derived from the linear spectral modeling of a high spectral resolution dataset, acquired with the near-infrared (1.40–2.50 μm) ground-based integral field spectrometer SINFONI (SINgle Faint Object Near-IR Investigation) of the Very Large Telescope (VLT hereafter) located in Chile. We show that, unlike the neighboring moon Europa, photometric corrections cannot be performed using a simple Lambertian model. However, we find that the Oren-Nayar (1994) model, generalizing the Lambert's law for rough surfaces, produces excellent results. Spectral modeling confirms that Ganymede's surface composition is dominated by H2O-ice, which is predominantly crystalline, as well as a darkening agent, but it also clearly highlights the necessity of secondary species to better fit the measurements: sulfuric acid hydrate and salts, likely sulfates and chlorinated. A latitudinal gradient and a hemispherical dichotomy are the strongest spatial patterns observed for the darkening agent, the H2O-ice, and the sulfuric acid: the darkening agent is by far the major compound at the equator and mid-latitudes (≤ ± 35°N), especially on the trailing hemisphere, while the H2O-ice and the sulfuric acid are mostly located at high latitudes and on the leading hemisphere. This anti-correlation is likely a consequence of the bombardment of the constituents in the Jovian magnetosphere which are much more intense at latitudes higher than ±35°N. Furthermore, the modeling confirms that polar caps are enriched in small, fresh, H2O-ice grains (i.e. ≤50 μm) while equatorial regions are mostly composed of larger grains (i.e. ≥200 μm, up to 1 mm). Finally, the spatial distribution of the salts is neither related to the Jovian magnetospheric bombardment nor the craters. These species are mostly detected on bright grooved terrains surrounding darker areas. Endogenous processes, such as freezing of upwelling fluids going through the ice shell, may explain this distribution. In addition, a small spectral residue that might be related to brines and/or hydrated silica-bearing minerals are located in the same areas

Comparison between a μFE model and DEM for an assembly of spheres under triaxial compression

This paper presents a simple case of a Face Centred Cubic (FCC) array of 2,000 spheres under triaxial compression to compare the results obtained using the Discrete Element Method (DEM) and a micro finite element model (μFE). This μFE approach was developed so that the internal structure of the soil can be obtained using x-ray computed tomography and converted into a numerical fabric. The individual grains are represented as continuum deformable bodies and the inter-granular interaction based on the defined contact laws. In order to demonstrate the simple contact constitutive behaviour used in this μFE model, the response for two contacting elastic spheres is compared with theoretical equations. The strength at failure of the packing of 2,000 spheres is seen to yield similar values for DEM, μFE and the analytical solution. When comparing the evolving void ratio, a good agreement between the two numerical models was observed for very small strains but as the strain increases, the values start to diverge, which is believed to be related with the rigidity of the grains used in DEM

True triaxial testing of geogrid for high speed railways

This work describes a series of novel experimental tests to determine the potential of geogrids to confine granular layers within ballasted railway lines operating at speeds close to critical velocity. This is important because at low train speeds, vertical stresses are dominant, but when approaching critical velocity conditions, dynamic horizontal stress levels are magnified. Therefore the majority of previous geogrid investigations have been performed assuming constant horizontal stress levels, thus making them more relevant for lower speed lines. To investigate settlement under high relative train speeds, ballasted railway track samples were subject to combined vertical-horizontal cyclic loading. Three areas were explored: (1) the performance benefit from placing geogrid at the ballast-subballast interface, (2) the performance benefit from placing geogrid at the subballast-subgrade interface, (3) the effect of subgrade stiffness on geogrid performance at the subballast-subgrade interface. Testing was performed using a unique large-scale true triaxial apparatus which had the ability to vary stress levels in three Cartesian directions. Compared to the control conditions, the geogrid offered a settlement improvement of approximately 35% when placed at the ballast-subballast interface, and 10–15% when placed at the subballast-subgrade interface. Regarding subgrade CBR, it was found that the geogrid offered the greatest performance benefits when the subgrade was soft. Therefore it was concluded that for the ballasted rail structures under test, when subject to elevated levels of horizontal stress, geogrids reduced settlements compared to non-geogrid solutions

Discreet element modeling 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

Validation of a stochastic digital packing algorithm for porosity prediction in fluvial gravel deposits

Porosity as one of the key properties of sediment mixtures is poorly understood. Most of the existing porosity predictors based upon grain size characteristics have been unable to produce satisfying results for fluvial sediment porosity, due to the lack of consideration of other porosity-controlling factors like grain shape and depositional condition. Considering this, a stochastic digital packing algorithm was applied in this work, which provides an innovative way to pack particles of arbitrary shapes and sizes based on digitization of both particles and packing space. The purpose was to test the applicability of this packing algorithm in predicting fluvial sediment porosity by comparing its predictions with outcomes obtained from laboratory measurements. Laboratory samples examined were two natural fluvial sediments from the Rhine River and Kall River (Germany), and commercial glass beads (spheres). All samples were artificially combined into seven grain size distributions: four unimodal distributions and three bimodal distributions. Our study demonstrates that apart from grain size, grain shape also has a clear impact on porosity. The stochastic digital packing algorithm successfully reproduced the measured variations in porosity for the three different particle sources. However, the packing algorithm systematically overpredicted the porosity measured in random dense packing conditions, mainly because the random motion of particles during settling introduced unwanted kinematic sorting and shape effects. The results suggest that the packing algorithm produces loose packing structures, and is useful for trend analysis of packing porosity

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

An extended Greenwood-Williamson modelbased normal interaction law for discrete element modelling of spherical particles with surface roughness

The current work aims to develop an improved random normal interaction law based on an extended Greenwood‐Williamson (GW) model for spherical particles with surface roughness in the discrete element modelling of particle systems. The extended GW model overcomes some theoretical defects of the classic GW model when incorporated into the discrete element framework. Based on 2 nondimensional forms in which only 2 surface roughness parameters are involved, an empirical formula of the improved interaction law is derived by the curve‐fitting technique. The resulting interaction law is incorporated into discrete element modelling to investigate the mechanical response of particle systems with different surface roughness. Numerical simulations are performed to model 1‐dimensional and 3‐dimensional compression tests to explore the macro and micro characteristics of granular particles with surface roughness. The results show that surface roughness makes the initial packing of a particle assembly looser and has a greater influence on looser packed samples as expected, but an assembly with moderate roughness may exhibit a higher strength. The limitations of the current development are also highlighted

Towards stochastic discrete element modelling of spherical particles with surface roughness: A normal interaction law

The current work is the first attempt towards establishing a stochastic discrete element modelling framework by developing a normal contact interaction law based on the classic Greenwood and Williamson (GW) model for spheres with rough surfaces. Two non-dimensional forms of the model that have a substantial impact on the computational efficiency are discussed and the theoretical relationship between the GW model and the Hertzian model for smooth spheres is formally established. Due to the inter-dependence between the contact pressure and deformation distributions in the model, a Newton-Raphson based iterative solution procedure is proposed to effectively and accurately obtain the contact force in terms of the overlap and two surface roughness parameters. The related key components of the procedure are addressed in detail. The numerical results obtained are first validated and then curve-fitted to derive an empirical formula as a new normal interaction law for spheres with surface roughness. The explicit nature of the new interaction law makes it readily be incorporated into the current discrete element modelling framework. A simple example is presented to illustrate the effect of surface roughness on the packing behaviour of a particle assembly