The discrete element method (DEM) has been confirmed as an effective numerical method for modelling railway ballast, and successfully used to analyse a wide range of ballast-related applications (e.g. geomaterials). However, there still exists some aspects under development. Among them, the model calibration can be the most significant one (morphology, degradation and contact model). Because reliable and accurate results can be obtained only when the parameters are carefully selected. Therefore, diverse DEM applications and developments in railway ballast are critically reviewed. Furthermore, the model calibration methods are discussed. This is able to help future researchers improve the existing calibration methods, further, build more accurate, standardised and validated DEM models for ballast-related studies. Additionally, this paper can assist researchers to choose an appropriate model for specific applications.@en

This paper presents a multi-layer railway ballast track and substructure model, where a coupled discrete and continuous method is used for macro-meso dynamic behaviour analysis under moving wheel loads. In this coupled model, the discrete element method (DEM) is utilised to build the superstructure of the ballast track (i.e. rail, fastener, sleeper and ballast layer), which considers the complex ballast shape and particle size distribution from mesoscopic level. The finite difference method (FDM) is used to simulate the substructure (i.e. subgrade and foundation) with a consideration of computing cost. And then, the coupled model is achieved by satisfying displacement, velocity and contact force compatibility between the FLAC and the PFC. Finally, the dynamic analysis is carried out by applying the wheel-rail forces obtained from a vehicle-track dynamics model into the coupled model. The DEM parameters of ballast particles are calibrated based on the results of the ballast direct shear tests, and the dynamic behaviour of railway ballast track and subgrade system is validated with the field measurement. Through the numerical analysis, it is confirmed that the coupled DEM/FDM model can reliably reflect macro-meso dynamic behaviour and accurately reveal the contact characteristics between the ballast layer and subgrade.@en

Railway ballasted track stiffness is an important indicator to identify supporting condition that ensures that the facility is well designed and functioned. Although many studies have been performed on track stiffness based on experimental tests and finite-element methods, the factors influencing the track stiffness have not been completely confirmed yet, especially the influences from ballast and subgrade layers at the mesoscopic level. To address this research gap, a combination of the discrete element method and the finite difference method model was utilized to study the factors influencing the track stiffness from the particle level. Factors (related to ballast layer properties) are bulk density, thickness, and stiffness, and another factor (related to subgrade properties) is elastic modulus. Additionally, the relationship between the track stiffness and the mechanical behavior of ballast was analyzed. This study quantified the influences of track components on the track stiffness and accordingly proposed how to improve it from the ballast and subgrade layers at the mesoscopic level, which can provide guidance for railway ballasted track design and maintenance. @en

Crumb rubber (CR) has been proposed to apply in the ballast or sub-ballast layer for ballast degradation mitigation and vibration (noise) reduction. The CR can change the ballast layer stiffness, which can affect the train-track-subgrade dynamic performance and cause travel comfort and safety issues. Towards this, this study aims at confirming 1) how much the CR application can affect the dynamic performance of train and ballast layer; 2) to what extent the CR-ballast layer can distribute the train loadings to reduce subgrade surface stress. To achieve this aim, a whole train-track-subgrade system model was built by coupling multibody dynamics (MD), discrete element method (DEM) and finite difference method (FDM). The MD was used to build the train, including one vehicle body, two bogies and four wheelsets. The DEM was used to build the ballasted track, including rail, sleepers and ballast layer. The FDM was used to build the subgrade. Using the coupled model, the dynamic performance of train and track were studied, including the vehicle body acceleration, wheel-rail force, rail dynamical bending moment, sleeper acceleration, sleeper displacement and ballast acceleration. In addition, the energy dissipation of the ballast bed was also presented. For the subgrade, the subgrade surface acceleration and surface stress were measured and analysed. In the model, different CR size and percentage were considered. Results show that using the CR in ballast layer can increase the accelerations of sleeper, rail and train. But it can decrease the ballast degradation, subgrade surface acceleration and subgrade surface stress. CR helps consume train loading energy, reducing the energy that has to be consumed by ballast friction. Small size CR (8–22.4 mm) has greater influence on dynamic performance of the whole train-track-subgrade system than big size CR (9.5–63 mm). In summary, 10% percentage of CR-ballast mixture is recommended, and for CR size it is difficult to give a recommendation. Small size CR increase ballast acceleration more than big size CR, but small size CR are better at improving sleeper displacement, subgrade stress and ballast bed stress.@en

To probe into the mechanical behaviour of railway transition zone from the macro-meso aspects, a numerical model of transition zone is built that hybrids the Discrete Element Method (DEM) and Finite Difference Method (FDM). The DEM is utilised to simulate the ballast bed and sleeper, because it can consider the realistic ballast shapes and complex contacts between them. The FDM based on the continuum theory is utilised to simulate the track substructure according to a real structural form. Afterwards, the coupling algorithm is used to achieve the hybrid DEM-FDM simulation. The engineering practicality of this model is validated using the dynamic responses of the transition zone from a field measurement, and the macro-meso mechanical behaviour of the transition zone is analysed with or without the wedge-shape backfill. The numerical results indicate that applying the wedge-shape backfill can considerably reduce the sudden changes of track vibration and substructure surface stresses at the vicinity of the connection between the structure and embankment. Moreover, the mesoscopic results show that the acceleration vector of the soil near the rigid structure fluctuates towards the embankment and the velocity responses of track components and substructure increase gradually when the train travels from the rigid structure to the soft embankment.@en

To simulate ballast performance accurately and efficiently, the input in discrete element models should be carefully selected, including the contact model and applied particle shape. To study the effects of the contact model and applied particle shape on the ballast performance (shear strength and deformation), the direct shear test (DST) model and the large-scale process simulation test (LPST) model were developed on the basis of two types of contact models, namely the rolling resistance linear (RRL) model and the linear contact (LC) model. Particle shapes are differentiated by clumps. A clump is a sphere assembly for one ballast particle. The results show that compared with the typical LC model, the RRL method is more efficient and realistic to predict shear strength results of ballast assemblies in DSTs. In addition, the RRL contact model can also provide accurate vertical and lateral ballast deformation under the cyclic loading in LPSTs.@en