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 Discrete Element Method (DEM) is a powerful computational approach for analyzing granular materials, such as those found in railway embankments. While DEM offers high-resolution insights into particle-scale interactions by solving force-displacement equations based on Newtonian mechanics, its computational intensity and limitations in representing continuous structural components remain challenges. This study addresses two core issues in the DEM modeling of granular materials for high-speed railway applications.

Firstly, the study investigates the impact of particle scaling techniques on the shear behavior and computational efficiency of granular materials with fine angular particles. By examining variations in particle size distribution and angularity, it is demonstrated that appropriate scaling can substantially reduce simulation time without compromising accuracy.

Secondly, to address DEM's limitations in modeling continuous components such as rails and subgrade, a novel hybrid modeling approach is developed. This integrates a 3D DEM model for ballast and sub-ballast layers with a continuum-based Finite Difference Method (FDM) for rail beams and subgrade layers, and a nonlinear 2D Finite Element Method (FEM) to model vehicle–track dynamic interaction. The hybrid DEM–FDM–FEM framework enables the simulation of both short-term dynamic responses and long-term differential settlements in railway transition zones. A specialized Periodic Cell Replication Method is used to create large-scale DEM models, enhancing realism and computational efficiency.

Validation against full-scale physical experiments and benchmark FEM models confirms the framework’s ability to capture critical mechanisms such as gap formation beneath sleepers, stiffness gradients, and vertical misalignment induced by repeated axle loads. Results reveal how abrupt stiffness transitions amplify dynamic loads, leading to progressive settlement and degradation of track geometry. The study highlights the importance of combining granular and continuum modeling techniques to more accurately predict and mitigate long-term degradation in ballasted railway transition zones.

The study shows that a stiffness gradient at railway transition zones amplifies dynamic wheel–rail forces, leading to voided sleepers and a peak in ballast settlement a few meters into the softer track, highlighting the need for a gradual stiffness change to limit long-term differential settlement. 

Den diskreta elementmetoden (DEM) är en kraftfull numerisk metod för att analysera granulära material, såsom de som förekommer i järnvägsbankar. Genom att lösa kraft-förskjutningsekvationer baserade på Newtonsk mekanik möjliggör DEM detaljerad analys på partikelskala. Dock kvarstår utmaningar relaterade till hög lång beräkningstid samt begränsningar i att modellera kontinuerliga strukturella komponenter. Denna studie behandlar två centrala frågeställningar i DEM-modelleringen av granulära material för höghastighetsjärnvägar.

Partikelskalning och dess inverkan på skjuvbeteende och beräkningseffektivitet. För det första undersöks hur olika tekniker för partikelskalning påverkar skjuvbeteendet och den numeriska effektiviteten hos granulära material bestående av finkorniga, kantiga partiklar. Genom att variera partikelstorleksfördelning och kantighet visar resultaten att en lämplig skalning av partiklarna kan reducera beräkningstiden avsevärt, utan att förlora noggrannhet i simuleringen.

Hybridmodellering av diskreta och kontinuerliga komponenter.För att övervinna DEM:s begränsningar vid modellering av kontinuerliga strukturer såsom räler och undergrund, utvecklas en ny hybridmodelleringsmetod. Denna metod kombinerar en tredimensionell DEM-modell för ballast- och underballastlager med en kontinuerlig Finita Differensmetod (FDM) för räler och undergrund. Dessutom inkluderas en icke-linjär tvådimensionell Finita Elementmetod (FEM) för att modellera den dynamiska interaktionen mellan fordon och spår. Detta integrerade DEM–FDM–FEM-ramverk möjliggör simulering av både kortsiktiga dynamiska responser och långsiktiga differentiella sättningar i övergångszoner för järnväg.

En särskild metod för periodisk cellreplikering används för att skapa storskaliga DEM-modeller, vilket förbättrar både realismen och den numeriska effektiviteten.

Modellen valideras mot storskaliga fysiska experiment samt etablerade FEM-referensmodeller. Resultaten bekräftar ramverkets förmåga att återge kritiska mekanismer såsom glappbildning under sliprar, styvhetsgradienter och vertikal avvikelse som uppstår till följd av upprepade axellaster. Studien visar att abrupta förändringar i styvhet förstärker de dynamiska belastningarna, vilket leder till progressiv sättning och degradering av spårgeometrin över tid.

Studien understryker vikten av att kombinera granulära och kontinuerliga modelleringsmetoder för att bättre förutsäga och motverka långsiktig degradering i ballasterade övergångszoner för järnväg.

Studien visar att en styvhetsgradient vid övergångszoner i järnväg förstärker dynamiska hjul–rälskrafter, vilket leder till urgröpta sliprar och en topp i ballastsättning några meter in i det mjukare spåret, vilket understryker behovet av en gradvis förändring i styvhet för att begränsa långsiktig differenssättning.

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.

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.

The Discrete element method (DEM) is a methodology to investigatethe interactions among granular materials. It analyzes the behavior of par-ticulate environments by solving force-displacement equations that adhereto Newton’s second law of motion. Despite its usefulness, the DEM is notwithout limitations, and researchers are still facing certain challenges thatrestrict them from performing detailed analyses of granular materials. Thisstudy addresses two issues in DEM modeling of granular materials in rail-way embankments. Firstly, the long computational time required by theDEM for modeling fine angular particles in granular materials is addressedby exploring the effects of particle scaling on the shear behavior of granularmaterial. This study investigates the impact of particle size distribution,particle angularity, and the amount of scaling on the accuracy and compu-tational efficiency of DEM. Secondly, the limitations of DEM in includingthe continuous rail beam structure in the track are addressed by verifyinga DEM model against physical measurements of a full-scale ballasted trackand investigating the influence of including the rail beam structure on high-speed railway ballasted tracks. The results show that the use of particlescaling in the first study significantly improves the computational efficiencyof the DEM while maintaining accuracy, and this method is used in thesecond study to investigate the influence of the rail beam structure on thebehavior of railway tracks.

Diskreta elementmetoden (DEM) är en effektiv metod för att undersö-ka interaktioner i granulära material. Metoden analyserar samverkan mellanpartiklar genom att lösa kraft-deformationsekvationer som följer Newtonsandra lag. Trots dess användbarhet har DEM vissa begränsningar och fors-kare stöter fortfarande på vissa utmaningar som hindrar dem från att ge-nomföra detaljerade analyser av granulära material. Denna studie tar upptvå frågeställningar vid DEM-modellering av granulära material i järnvägs-bankar. För det första behandlas den långa beräkningstiden som krävs föratt modellera granulära material genom att utforska effekterna av parti-kelskalning på skjuvbeteendet. Studien undersöker effekten av partikelstor-leksfördelning och spetsighet på noggrannheten och beräkningseffektivite-ten. För det andra behandlas begränsningarna hos DEM när det gäller attinkludera den kontinuerliga rälsstrukturen i spåret genom att verifiera enDEM-modell mot fysiska mätningar av ett ballasterat spår i full skala ochundersöka inverkan av att inkludera rälsstrukturen. Resultaten i den förstastudien visar att tillämpningen av partikelskalning avsevärt förbättrar be-räkningseffektiviteten samtidigt som noggrannheten bibehålls. Partikelskal-ning används i den andra studien för att undersöka inverkan av rälsstruk-turen på beteendet hos järnvägsspår.

Med påbörjad planering och projektering av nya stambanor för järnväg i Sverige, och med en ännu större utveckling och utbyggnad av ballastfria spår världen över, är det viktigt att undersöka möjliga riskområden som kan komma att påverka exempelvis drift och underhåll. Ett av dessa problemområden är övergången mellan järnvägsbank och järnvägsbro. I ett nyligen publicerat examensarbete, utfört på KTH tillsammans med Sweco, har detta problemområde under­sökts med hjälp av numeriska simuleringar med finita element­metoden.

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.

In the Netherlands, approximately 60% of drinking water is obtained from (generally anaerobic) groundwater. This requires aeration followed by rapid sand filtration (RSF) to remove iron, manganese, arsenic and ammonium. The mechanisms responsible for their removal or the clogging of RSFs and breakthrough of colloidal iron or manganese oxides have not been fully elucidated in previous studies. In this work, factors affecting iron precipitation have been studied in aerated, continuously stirred bench scale jar experiments to simulate the supernatant layer of submerged sand filters. Time series data of filtered iron concentration and precipitate size have been collected in experiments with synthetic groundwater with and without P, Si, HCO3 and Ca at neutral pH. We observed that precipitate growth is not influenced by different HCO3 concentrations but is reduced drastically when natural organic matter (NOM) is present in water and, to lesser extent, Si as well. The addition of P appears to hamper precipitate growth to some extent, but requires more research to fully understand the implications. We also observed that addition of Ca improved the growth of Fe precipitates in the presence of Si and especially NOM. These results have great significance for improving Fe removal efficiency of groundwater treatment plants in The Netherlands and abroad. 

Modelling railway embankments have two main challenges in the discrete ele-ment method (DEM). First, the granular material of the embankment consistof millions of fine angular particles which are difficult to model due to thelong computational time. As a result, researchers prefer to use spherical orscale-up particles as granular material. Also, it prevents the modeling of thehigher number of loading cycles. Second, the DEM is incapable of includingcontinuous rail beams due to its discrete nature. Therefore, most of the re-search is limited to ignoring the rail beam and other structural elements ofthe track. In this study, a DEM model is calibrated against the measure-ment results of a physical full-scale ballasted track. The model is then used toinvestigate the effect of including the rail beam for high-speed railways sub-jected to 2000 axle passages. The results show that although ignoring therail beam does not substantially affect the results for initial loading cycles,its influence is significant after a couple of hundred axle passages. The modelwithout a rail beam shows more principal stress rotation, more settlement,non-realistic vertical displacement of the sleepers, more particle rearrange-ment and more sleepers’ vibration. Therefore, it is necessary to include therail beam in the long-term analysis of the track to conclude realistic results.