This study describes the dynamic response of a two-dimensional hexagonal packing of uncompressed stainless steel spheres excited by localized impulsive loadings. The dynamics of the system are modeled using the Hertzian normal contact law. After the initial impact strikes the system, a characteristic wave structure emerges and continuously decays as it propagates through the lattice. Using an extension of the binary collision approximation for one-dimensional chains, we predict its decay rate, which compares well with numerical simulations and experimental data. While the hexagonal lattice does not support constant speed traveling waves, we provide scaling relations that characterize the directional power law decay of the wave velocity for various angles of impact. Lastly, we discuss the effects of weak disorder on the directional amplitude decay rates.

The prediction quality of discrete element method (DEM) models for railway ballast can be expected to depend on three points: the geometry representation of the single particles, the used contact models and the parametrisation using principal experiments. This works aims at a balanced approach, where none of the points is addressed with excessive depth. In a first step, a simple geometry representation is chosen and the simplified Hertz-Mindlin contact model is used. When experimental data of cyclic compression tests and monotonic direct shear tests are considered, the model can be parametrised to fit either one of the two tests, but not both with the same set of parameters. Similar problems can be found in literature for monotonic and cyclic triaxial tests of railway ballast. In this work, the comparison between experiment and simulation is conducted using the entire data of the test, e.g. shear force over shear path curve from the direct shear test. In addition to a visual comparison of the results also quantitative errors based on the sum of squares are defined. To improve the fit of the DEM model to both types of experiments, an extension on the Hertz-Mindlin contact law is used, which introduces additional physical effects (e.g. breakage of edges or yielding). This model introduces two extra material parameters and is successfully parametrised. Using only one set of parameters, the results of the DEM simulation are in good accordance with both experimental cyclic compression test and monotonic directs shear test.

The mechanical behaviour of fibre-reinforced sands is primarily governed by the three-dimensional fibre architecture within the sand matrix. In laboratory, the normal procedures for sample preparation of fibre-sand mixtures generally produce a distribution of fibre orientations with a preferential bedding orientation, generating strength anisotropy of the composite's response under loading. While demonstrating the potential application of X-ray tomography to the analysis of fibre-reinforced soils, this paper provides for the first time a direct experimental description of the three-dimensional architecture of the fibres induced by the laboratory sample fabrication method. Miniature fibre reinforced sand samples were produced using two widely used laboratory sample fabrication techniques: the moist tamping and the moist vibration. It is shown that both laboratory fabrication methods create anisotropic fibre orientation with preferential sub-horizontal directions. The fibre orientation distribution does not seem to be affected by the concentration of fibres, at least for the fibre concentrations considered in this study and, for both fabrication methods, the fibre orientation distribution appears to be axisymmetric with respect to the vertical axis of the sample. The X-ray analysis also demonstrates the presence of an increased porosity in the fibre vicinity, which confirms the assumption of the "stolen void ratio" effect adopted in previous constitutive modelling. A fibre orientation distribution function is tested and a combined experimental and analytical method for fibre orientation determination is further validated.

We study the response to simple shear start-up of an overdamped, athermal assembly of particles with tuneable attractive interactions. We focus on volume fractions close to the jamming point, where such systems can become disordered elastoplastic solids. By systematically varying the strength of the particle-particle attraction and the volume fraction, we demonstrate how cohesion and confinement individually contribute to the shear modulus and yield strain of the material. The results provide evidence for the influence of binding agents on the rheology of dense, athermal suspensions and describe a set of handles with which the macroscopic properties of such materials can be engineered.

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.

This paper presents the results of an experimental study of the particle scale mechanisms that underpin creep, on-going deformations under constant external load, in dry non-cemented sand under 1D oedometric compression loading at 2500 kPa. Traditional observations on the boundary of the sample are complemented with simultaneous measurements of the 3D kinematics of both the entire grain assembly and details of grain-scale mechanisms using synchrotron based X-ray tomography at two different spatial resolutions. Both the continuum response and the local grain scale response are captured using two spatial resolutions, i.e.  and respectively. The results, for the first time, illustrate that small displacements measured at the boundary can be the result of rather pronounced fracturing at the individual grain scale.

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.

We describe here experiments on the mechanics of hydrogel particle packings from the Behringer lab, performed between 2012 and 2015. These experiments quantify the evolution of all contact forces inside soft particle packings exposed to compression, shear, and the intrusion of a large intruder. The experimental set-ups and processes are presented and the data are concomitantly published in a repository (Barés et al. in Dryad, Dataset 10.5061/dryad.6djh9w0x8, 2019).

Ballasted tracks are the commonly used railway track systems with constant demands for reducing maintenance cost and improved performance. Elastic layers are increasingly used for improving ballasted tracks. In order to better understand the effects of elastic layers, physical understanding at the ballast particle level is crucial. Here, discrete element method (DEM) is used to investigate the effects of elastic layers - under sleeper pad ( ) at the sleeper/ballast interface and under ballast mat ( ) at the ballast/bottom interface - on micro-mechanical behavior of railway ballast. In the DEM model, the Conical Damage Model (CDM) is used for contact modelling. This model was calibrated in Suhr et al. (Granul Matter 20(4):70, 2018) for the simulation of two different types of ballast. The CDM model accounts for particle edge breakage, which is an important phenomenon especially at the early stage of a tamping cycle, and thus essential, when investigating the impact of elastic layers in the ballast bed. DEM results confirm that during cyclic loading, reduces the edge breakage at the sleeper/ballast interface. On the other hand, shows higher particle movement throughout the ballast bed. Both the edge breakage and particle movement in the ballast bed are found to influence the sleeper settlement. Micro-mechanical investigations show that the force chain in deeper regions of the ballast bed is less affected by for the two types of ballast. Conversely, dense lateral forces near to the box bottom were seen with . The findings are in good (qualitative) agreement with the experimental observations. Thus, DEM simulations can aid to better understand the micro-macro phenomena for railway ballast. This can help to improve the track components and track design based on simulation models taking into account the physical behavior of ballast.

The orientation of, and contacts between, grains of sand reflect the processes that deposit the sands. Grain orientation and contact geometry also influence mechanical properties. Quantifying and understanding sand microstructure thus provide an opportunity to understand depositional processes better and connect microstructure and macroscopic properties. Using x-ray computed microtomography, we compare the microstructure of naturally-deposited beach sands and laboratory sands created by air pluviation in which samples are formed by raining sand grains into a container. We find that naturally-deposited sands have a narrower distribution of coordination number (i.e., the number of grains in contact) and a broader distribution of grain orientations than pluviated sands. The naturally-deposited sand grains orient inclined to the horizontal, and the pluviated sand grains orient horizontally. We explain the microstructural differences between the two different depositional methods by flowing water at beaches that re-positions and reorients grains initially deposited in unstable grain configurations.

In any DEM simulation, the chosen particle shape will greatly influence the simulated material behaviour. For a specific material, e.g. railway ballast, it remains an open question how to model the particle shape, such that DEM simulations are computationally efficient and simulation results are in good accordance with measurements. While DEM shape modelling for railway ballast is well addressed in the literature, approaches mainly aim at approximating the stones' actual shape, resulting in rather complex and thus inefficient particle shapes. In contrast, very simple DEM shapes will be constructed, clumps of three spheres, which aim to approximate shape descriptors of the considered ballast material. In DEM simulations of the packing behaviour, a set of clump shapes is identified, which can pack at porosities observed at track sites, as well as in lab tests. The relation between particle shape (descriptors) and obtained packing (characteristic) is investigated in a correlation analysis. The simulated packing's porosity is strongly correlated to four shape descriptors, which are also strongly correlated among each other. Thus, to derive simple shape models of a given particle shape, matching one of these shape descriptors, might be a good first step to bring simulated porosities closer to measured ones. The conducted correlation analysis also shows that packing's coordination number and isotropic fabric are correlated to more shape descriptors, making it more difficult to estimate the effect of particle shape on these quantities.

Despite ongoing research, the parametrisation of a DEM model is a challenging task, as it depends strongly on the particle shape representation used, particle-particle contact law and the simulated applications: for railway ballast e.g. lab tests or track conditions. The authors previously modelled railway ballast with a DEM model using a simple particle shape. The DEM model was parametrised, by trial-and-error, to compression and direct shear test results. A good agreement between DEM model and experimental results was achieved only when the Conical Damage Model (CDM) was used as the contact law. Compared to the well-known linear-spring Cundall-Strack law or the Hertz-Mindlin law, this contact law takes into account additional physical effects (e.g. edge breakage) occurring in the experiment. Little is known on the influence of the CDM model parameters on the simulation results or on possible parameter ambiguities. This lack of knowledge hinders a reliable and efficient parametrisation of DEM models using different particle shapes. Both points are addressed in this work in detail by investigating a DEM model for railway ballast using one simple particle shape. Suggestions for a parametrisation strategy of reduced computational effort are formulated and tested using a second particle shape. In future works, the newly presented parametrisation strategy can help to calibrate different DEM models and to study the influence of particle shape.

The calculation of the impact pressure on obstacles in granular flows is a fundamental issue of practical relevance, e.g. for snow avalanches impacting obstacles. Previous research shows that the load on the obstacle builds up, due to the formation of force chains originating from the obstacle and extending into the granular material. This leads to the formation of a mobilized domain, wherein the flow is influenced by the presence of the obstacle. To identify the link between the physical mobilized domain properties and the pressure exerted on obstacles, we simulate subcritical cohesionless and cohesive avalanches of soft particles past obstacles with circular, rectangular or triangular cross-section using the Discrete Element Method. Our results show that the impact pressure decreases non-linearly with increasing obstacle width, regardless of the obstacle's cross-section. While the mobilized domain size is proportional to the obstacle width, the pressure decrease with increasing width originates from the jammed material inside the mobilized domain. We provide evidence that the compression inside the mobilized domain governs the pressure build-up for cohesionless subcritical granular flows. In the cohesive case, the stress transmission in the compressed mobilized domain is further enhanced, causing a pressure increase compared with the cohesionless case. Considering a kinetic and a gravitational contribution, we are able to calculate the impact pressure based on the properties of the mobilized domain. The equations used for the pressure calculation in this article may be useful in future predictive pressure calculations based on mobilized domain properties.

For complex shaped materials, computational efficiency and accuracy of DEM models are usually opposing requirements. In the literature, DEM models of railway ballast often use very complex and computationally demanding particle shapes in combination with very simple contact laws. In contrast, this study suggests efficient DEM models for railway ballast using simple particle shapes together with a contact law including more physical effects. In previous works of the authors, shape descriptors, calculated in a shape analysis of two types of ballast, were used to construct simple particle shapes (clumps of three spheres). Using such a shape in DEM simulations of compression and direct shear tests, accurate results were achieved only when the contact law included additional physical effects e.g. edge breakage. A parametrisation strategy was developed for this contact law comparing DEM simulations with the measurements. Now, all the constructed simple particle shapes are parametrised allowing to study their suitability and relating their shape descriptors to those of railway ballast. The most suitable particle shapes consist of non-overlapping spheres, thus have a high interlocking potential, and have lowest sphericity and highest convexity values. In a micromechanical analysis of the four best performing shapes, three shapes show similar behaviour on the bulk and the micro-scale, while one shape differs clearly on the micro-scale. This analysis shows, which shapes can be expected to produce similar results in DEM simulations of other tests/load cases. The presented approach is a step towards both efficient and accurate DEM modelling of railway ballast.

A snow slab avalanche releases after failure initiation and crack propagation in a highly porous weak snow layer buried below a cohesive slab. While our knowledge of crack propagation during avalanche formation has greatly improved over the last decades, it still remains unclear how snow mechanical properties affect the dynamics of crack propagation. This is partly due to a lack of non-invasive measurement methods to investigate the micro-mechanical aspects of the process. Using a DEM model, we therefore analyzed the influence of snow cover properties on the dynamics of crack propagation in weak snowpack layers. By focusing on the steady-state crack speed, our results showed two distinct fracture process regimes that depend on slope angle, leading to very different crack propagation speeds. For long experiments on level terrain, weak layer fracture is mainly driven by compressive stresses. Steady-state crack speed mainly depends on slab and weak layer elastic moduli as well as weak layer strength. We suggest a semi-empirical model to predict crack speed, which can be up to 0.6 times the slab shear wave speed. For long experiments on steep slopes, a supershear regime appeared, where the crack propagation speed reached approximately 1.6 times the slab shear wave speed. A detailed micro-mechanical analysis of stresses revealed a fracture principally driven by shear. Overall, our findings provide new insight into the micro-mechanics of dynamic crack propagation in snow, and how these are linked to snow cover properties.

Understanding grain fragmentation in fault gouge is essential for capturing the mechanical behavior and evolution of fault zones under shear. In this study, we present a 2D Discrete Element Method (2D-DEM) framework that simulates comminution using angular, breakable grains, overcoming limitations of traditional models based on spherical particles. Our approach incorporates realistic fracture mechanics and grain geometries to better represent microstructural evolution during shearing. A series of numerical experiments, including Brazilian, oedometric, and shear tests, were conducted to calibrate the model and examine the roles of grain strength, friction, and Young's modulus. The simulations reproduce key numerical observations such as strain localization, force chain evolution, and grain rounding through chipping mechanisms. Results show that the model captures the onset and progression of fragmentation, as well as its impact on fault strength and mechanical stability. A comparison with a dedicated laboratory experiment is provided. This work provides a robust numerical tool for studying fault gouge behavior and lays the foundation for future studies exploring the influence of initial grain size and material properties on fault mechanics.