Despite advancements in computational resources, the discrete element method (DEM) still requires considerable computational time to solve detailed problems, especially when it comes to the large-scale models. In addition to the geometry scale of the problem, the particle shape has a dramatic effect on the computational cost of DEM. Therefore, many studies have been performed with simplified spherical particles or clumps. Particle scaling is an approach to increase the particle size to reduce the number of particles in the DEM. Although several particle scaling methods have been introduced, there are still some disagreements regarding their applicability to certain aspects of problems. In this study, the effect of particle scalping on the shear behavior of granular material is explored. Real granular particles were scanned and imported as polygonal particles in the direct shear test. The effect of particle size distribution, particle angularity, and the amount of scalping were investigated. The results show that particle scalping can simulate the correct shear behavior of the model with significant improvement in computational time. Also, the accuracy of the scalping method depends on the particle angularity and particle size range.

Denna studie undersöker en metod för effektiv DEM-simulering av långa ballasterade järnvägsspår med hjälp av periodiska randvillkor. Små, jämviktade segment av banvallen, så kallade “bricks”, genererades separat för ballast- och underballastlager och replikerades därefter för att skapa en längre spårmodell. Metoden utvärderades genom jämförelser med en referensmodell utan brick-teknik, där kontaktkrafter, huvudspänningar och maximal skjuvspänning analyserades under passage av ett höghastighetståg. Resultaten visar god överensstämmelse mellan modellerna, särskilt avseende kvalitativ spännings- och kraftfördelning i lagren. Ballastlagret uppvisade högre dynamiska belastningar än underballasten, medan simuleringstiden reducerades kraftigt, upp till omkring 90 % för mindre brickstorlekar. Studien visar att tekniken möjliggör simulering av längre järnvägsmodeller med mer detaljerad partikelform inom rimlig beräkningstid.

This study investigates an efficient approach for DEM simulation of long ballasted railway tracks using periodic boundaries. Small equilibrium segments of the embankment, referred to as “bricks”, were generated separately for the ballast and sub-ballast layers and then replicated to form a longer track model. The method was evaluated by comparison with a reference model without the brick technique, where contact forces, principal stresses, and maximum shear stress were analyzed during the passage of a high-speed train. The results show good agreement between the models, particularly regarding the qualitative distribution of stresses and contact forces within the layers. The ballast layer exhibited higher dynamic loads than the sub-ballast, while the simulation time was substantially reduced, by up to approximately 90% for smaller brick sizes. The study demonstrates that the proposed technique enables longer railway models with more detailed particle shapes to be simulated within a reasonable computational time.

Modelling railway projects has a main challenge in the discrete element method (DEM). The granular material of the embankment consists of millions of fine angular particles which are difficult to model due to the long computational time. The long computational time also prevents the modeling of the higher number of loading cycles. As a result, researchers prefer to simulate the project in 2D to accelerate the simulation. While 2D simulations present a seemingly simple option for modeling railways, they tend to oversimplify the intricacies of particle interactions and the distribution of stress. Nonetheless, the extent to which these simplifications affect the authenticity of the simulations has remained ambiguous. In this study, the periodic cell replication method is used to build extensive long railway tracks significantly faster than conventional methods. Then, this DEM model is calibrated against the measurement results of a physical full-scale ballasted track. The model is then used to simulate several railway projects with different initial particle arrangements and model dimensions in both 2D and 3D. The results show that the 2D models are more dependant on the initial particle arrangement which shows different behavior for the same model. In addition, 2D simulations are incapable of reproducing the principal stress rotation in granular layers due to the moving load of the train wheel. As a result, 3D DEM simulations using the periodic cell replication method is suggested for studying the railway tracks.

Modellering av järnvägsprojekt med den diskreta elementmetoden (DEM) är utmanande eftersom järnvägsbanken består av miljontals små och kantiga partiklar, vilket leder till långa beräkningstider och begränsar antalet möjliga belastningscykler. För att minska beräkningstiden används ofta 2D-simuleringar, men dessa kan överförenkla partikelinteraktioner och spänningsfördelning. I denna studie används metoden med replikering av periodiska celler för att effektivt skapa långa järnvägsspår i DEM. Modellen kalibreras mot mätdata från ett fysiskt fullskaligt ballasterat spår och används därefter för att analysera järnvägsmodeller med olika initiala partikelarrangemang och dimensioner i både 2D och 3D. Resultaten visar att 2D-modeller är mer beroende av det initiala partikelarrangemanget och kan ge varierande resultat för samma modell. De kan dessutom inte återge huvudspänningsrotation orsakad av rörlig tåglast. Därför rekommenderas 3D DEM-simuleringar med periodisk cellreplikering för studier av järnvägsspår.

A numerical methodology for simulating the mechanisms during the initial phase of differential settlement in a railway transition zone using an integrated discrete–continuum approach is presented. The methodology involves the coupling of the Discrete Element Method (DEM), the Finite Difference Method (FDM), and the Finite Element Method (FEM) to model the vertical dynamic interaction between vehicle and transition zone. Specifically, the extensive three-dimensional (3D) DEM model captures the discrete granular behaviour of the ballast and sub-ballast layers, while the continuum-based FDM model is employed to represent the rail structure and the subgrade layer. Based on a time-domain representation of vertical dynamic vehicle–track interaction, the nonlinear two-dimensional (2D) FEM model of the track, together with a multi-body system (MBS) model of the vehicle, is used to calculate the contact forces between wheels and rails. These forces are subsequently used as input to the DEM–FDM simulation for evaluating the non-uniform permanent displacements that will evolve within the granular layers. The support stiffness for each sleeper that is used as input in the FEM model is precomputed during the DEM–FDM coupling stage by applying a static load to each sleeper and calculating the resulting displacement. The developed methodology effectively simulates the progressive formation of voids beneath the sleepers, the redistribution of sleeper-ballast contact force between adjacent sleepers, and the evolving irregularity in vertical track alignment due to the accumulated traffic loading. The approach is demonstrated for a transition zone involving a stiffness gradient between a softer track on ballast and a stiffer track form, and accumulated settlements are calculated for a total of 500 axle passages. The proposed hybrid DEM–FDM–FEM framework provides critical insights into track degradation mechanisms, emphasising the importance of designing a gradual variation in track stiffness to mitigate dynamic loading leading to long-term differential track settlement, thereby reducing maintenance requirements in railway transition zones. 

The transition zones between bridges and adjacent tracks in high-speed railway systems arecritical areas where dynamic interactions between the train and track infrastructure can lead to significantmaintenance and structural challenges. These zones are particularly susceptible to issues due to the abruptchange in stiffness between the bridge structure and the adjacent track, resulting in complex stress patterns anddifferential settlement. This study investigates the impact of train travel direction on the dynamic behavior andstress distribution within bridge-transition zones. Advanced numerical modeling techniques, including finitedifference method (FDM) for modeling the rail structure, and the discrete element method (DEM) forsimulating the behavior of sleepers, ballast, and sub-ballast layers, were utilized to provide a comprehensivesimulation of the effects of trains approaching or departing from bridges. The findings reveal that train traveldirection affects structural behavior, track deformation, and differential settlement within these zones. Dynamic loading conditions, which vary depending on whether the train is moving onto or off the bridge, leadto uneven stress distributions. These stress variations contribute to differential settlement, where the track andunderlying materials settle at different rates, exacerbating track wear and increasing maintenance needs. Thisstudy provides key insights into enhancing the design and upkeep of bridge-transition zones by analyzing theimpact of train travel direction. The findings enable engineers and designers to develop strategies to mitigatethe adverse effects of differential settlement and stress concentration, thereby enhancing track longevity,reducing maintenance costs, and improving the overall safety and reliability of high-speed railway systems.

Övergångszoner mellan broar och angränsande spår i ballasterade höghastighetsjärnvägar är kritiska områden där dynamiska interaktioner mellan tåg och spårinfrastruktur kan orsaka betydande underhålls- och konstruktionsutmaningar. Den abrupta styvhetsförändringen mellan bro och bank leder ofta till komplexa spänningsmönster och differentiella sättningar. Denna studie undersöker hur tågets färdriktning påverkar det dynamiska beteendet och spänningsfördelningen i dessa zoner. Finita differensmetoden (FDM) används för att modellera rälsstrukturen, medan den diskreta elementmetoden (DEM) används för att simulera sliprar, ballast och underballast. Resultaten visar att färdriktningen påverkar deformationer, spänningsfördelning och sättningsutveckling, särskilt beroende på om tåget kör upp på eller av bron. Studien ger viktiga insikter för förbättrad utformning och underhåll av övergångszoner, med målet att minska spänningskoncentrationer, begränsa differentiella sättningar och öka spårets livslängd.