In the Netherlands, there is a large and widely used railway system that includes numerous railway bridges. This master thesis investigates the problems caused by these railway bridges. Since World War II, continu- ous welded rails have been used extensively throughout the Netherlands. These rails offer several advantages on embankments, such as reduced maintenance due to less vibration, increased passenger comfort, and reduced noise. However, continuous welded rails can cause problems when they run continuously over a bridge, as is the case in the Dutch railway system. Bridges are not continuous structures and have joints between the decks or between the deck and the transition structure. These joints allow the bridge deck to expand and contract due to temperature changes, move due to longitudinal forces from train braking and acceleration, and deflect due to the vertical load of the train, causing rotations at the ends of the bridge decks. This relative displacement between the bridge deck and the continuously welded rails creates addi- tional stresses in the rails. These additional stresses must not exceed the maximum allowable stress of the rail material, as this could cause the rails to buckle or fracture. Fixed points are often used in practice to limit the movement of the bridge deck and keep additional rail stresses within acceptable limits. This investiga- tion, however, focuses on understanding the interaction between the rails and the structure without the use of fixed points. The study assumes a railway bridge in the Netherlands with a ballast bed and uses concrete precast bridge decks. To gain initial knowledge of the problem and the various railway components and bridges, a literature review was conducted, and two existing railway bridge projects were analysed. It quickly became evident that there are two different bridge types relevant to the study of additional rail stresses: those without embankment influence and those with embankment influence. The study then identified parameters that could influence the magnitude of additional rail stresses to use them as variables in further investigations. Two longitudinal force models were created in SCIA Engineer: one without embankment influence (Model 1) and one with embankment influence (Model 2). These models are spring models where the stiffness of connections and elements is schematised as springs. The models were validated with hand calculations and used to obtain results for the influence of various parameters such as bridge deck span length, elastomeric bearings, bridge pier length, and foundation stiffness. The results of the two models were compared to understand the influence of the embankment. Additionally, the spring elongations of the non-linear springs between the bridge deck and the rails, representing the ballast bed, were examined to determine if they were in the linear or non-linear part of the spring characteristic to see if the springs slipped enforcing stress redis- tribution. Finally, the models assessed the individual contributions of three load cases (thermal, longitudinal traffic load, and vertical traffic load) to the combined additional rail stress. The results lead to the following conclusions: • When a structure is not influenced by the embankment, the magnitude of additional rail stresses depends on the stiffness of the substructure. The stiffness of the weakest component, in this case, the elastomeric bearings, has a significant influence. • When a structure is influenced by the embankment, the magnitude of additional rail stresses mainly depends on the dominant stiffness of the embankment, with the stiffness of the substructure having little to no influence. • Structures with embankment influence experience lower additional rail stresses due to the additional stiffness provided by the embankment. Problems with exceeding maximum permissible rail stresses occur mainly in relatively long railway bridge structures without embankment influence. • The vertical load has the largest contribution to the combined additional rail stresses for both structure types. • The thermal load has a larger influence on structures with embankment influence because these structures are more constrained by the embankment and thus more vulnerable to thermal deformations. • Linear summation of individual stress contributions from different load cases generally results in higher or equal stresses compared to non-linear combinations, making linear summation a conservative approach. The stress difference between linear summation and non-linear combination is usually only a few megapascals. If the springs between the bridge deck and the rails slip into the non-linear branch, this difference increases slightly but remains small. Based on these conclusions, the following recommendations can be made to prevent additional rail stresses from exceeding maximum permissible stresses without the use of fixed points and to streamline the process of longitudinal force analysis for engineers: • To prevent exceeding the maximum permissible stress in structures without embankment influence, consider using larger elastomeric bearings or less slender bridge decks that are less susceptible to deflection, thereby reducing additional rail stress, especially from vertical loads. • Since linear summation of individual contributions to additional rail stresses results in conservative and faster calculations, it is recommended to use linear calculations in the initial phase. Then, perform a final design review with non-linear calculations to ensure accuracy. This approach will significantly speed up the design process, as models will not need to run for hours or days each time.

In the Netherlands, there is a large and widely used railway system that includes numerous railway bridges. This master thesis investigates the problems caused by these railway bridges. Since World War II, continu- ous welded rails have been used extensively throughout the Netherlands. These rails offer several advantages on embankments, such as reduced maintenance due to less vibration, increased passenger comfort, and reduced noise. However, continuous welded rails can cause problems when they run continuously over a bridge, as is the case in the Dutch railway system. Bridges are not continuous structures and have joints between the decks or between the deck and the transition structure. These joints allow the bridge deck to expand and contract due to temperature changes, move due to longitudinal forces from train braking and acceleration, and deflect due to the vertical load of the train, causing rotations at the ends of the bridge decks. This relative displacement between the bridge deck and the continuously welded rails creates addi- tional stresses in the rails. These additional stresses must not exceed the maximum allowable stress of the rail material, as this could cause the rails to buckle or fracture. Fixed points are often used in practice to limit the movement of the bridge deck and keep additional rail stresses within acceptable limits. This investiga- tion, however, focuses on understanding the interaction between the rails and the structure without the use of fixed points. The study assumes a railway bridge in the Netherlands with a ballast bed and uses concrete precast bridge decks. To gain initial knowledge of the problem and the various railway components and bridges, a literature review was conducted, and two existing railway bridge projects were analysed. It quickly became evident that there are two different bridge types relevant to the study of additional rail stresses: those without embankment influence and those with embankment influence. The study then identified parameters that could influence the magnitude of additional rail stresses to use them as variables in further investigations. Two longitudinal force models were created in SCIA Engineer: one without embankment influence (Model 1) and one with embankment influence (Model 2). These models are spring models where the stiffness of connections and elements is schematised as springs. The models were validated with hand calculations and used to obtain results for the influence of various parameters such as bridge deck span length, elastomeric bearings, bridge pier length, and foundation stiffness. The results of the two models were compared to understand the influence of the embankment. Additionally, the spring elongations of the non-linear springs between the bridge deck and the rails, representing the ballast bed, were examined to determine if they were in the linear or non-linear part of the spring characteristic to see if the springs slipped enforcing stress redis- tribution. Finally, the models assessed the individual contributions of three load cases (thermal, longitudinal traffic load, and vertical traffic load) to the combined additional rail stress. The results lead to the following conclusions: • When a structure is not influenced by the embankment, the magnitude of additional rail stresses depends on the stiffness of the substructure. The stiffness of the weakest component, in this case, the elastomeric bearings, has a significant influence. • When a structure is influenced by the embankment, the magnitude of additional rail stresses mainly depends on the dominant stiffness of the embankment, with the stiffness of the substructure having little to no influence. • Structures with embankment influence experience lower additional rail stresses due to the additional stiffness provided by the embankment. Problems with exceeding maximum permissible rail stresses occur mainly in relatively long railway bridge structures without embankment influence. • The vertical load has the largest contribution to the combined additional rail stresses for both structure types. • The thermal load has a larger influence on structures with embankment influence because these structures are more constrained by the embankment and thus more vulnerable to thermal deformations. • Linear summation of individual stress contributions from different load cases generally results in higher or equal stresses compared to non-linear combinations, making linear summation a conservative approach. The stress difference between linear summation and non-linear combination is usually only a few megapascals. If the springs between the bridge deck and the rails slip into the non-linear branch, this difference increases slightly but remains small. Based on these conclusions, the following recommendations can be made to prevent additional rail stresses from exceeding maximum permissible stresses without the use of fixed points and to streamline the process of longitudinal force analysis for engineers: • To prevent exceeding the maximum permissible stress in structures without embankment influence, consider using larger elastomeric bearings or less slender bridge decks that are less susceptible to deflection, thereby reducing additional rail stress, especially from vertical loads. • Since linear summation of individual contributions to additional rail stresses results in conservative and faster calculations, it is recommended to use linear calculations in the initial phase. Then, perform a final design review with non-linear calculations to ensure accuracy. This approach will significantly speed up the design process, as models will not need to run for hours or days each time.

In the Netherlands, there is a large and widely used railway system that includes numerous railway bridges. This master thesis investigates the problems caused by these railway bridges. Since World War II, continu- ous welded rails have been used extensively throughout the Netherlands. These rails offer several advantages on embankments, such as reduced maintenance due to less vibration, increased passenger comfort, and reduced noise. However, continuous welded rails can cause problems when they run continuously over a bridge, as is the case in the Dutch railway system. Bridges are not continuous structures and have joints between the decks or between the deck and the transition structure. These joints allow the bridge deck to expand and contract due to temperature changes, move due to longitudinal forces from train braking and acceleration, and deflect due to the vertical load of the train, causing rotations at the ends of the bridge decks. This relative displacement between the bridge deck and the continuously welded rails creates addi- tional stresses in the rails. These additional stresses must not exceed the maximum allowable stress of the rail material, as this could cause the rails to buckle or fracture. Fixed points are often used in practice to limit the movement of the bridge deck and keep additional rail stresses within acceptable limits. This investiga- tion, however, focuses on understanding the interaction between the rails and the structure without the use of fixed points. The study assumes a railway bridge in the Netherlands with a ballast bed and uses concrete precast bridge decks. To gain initial knowledge of the problem and the various railway components and bridges, a literature review was conducted, and two existing railway bridge projects were analysed. It quickly became evident that there are two different bridge types relevant to the study of additional rail stresses: those without embankment influence and those with embankment influence. The study then identified parameters that could influence the magnitude of additional rail stresses to use them as variables in further investigations. Two longitudinal force models were created in SCIA Engineer: one without embankment influence (Model 1) and one with embankment influence (Model 2). These models are spring models where the stiffness of connections and elements is schematised as springs. The models were validated with hand calculations and used to obtain results for the influence of various parameters such as bridge deck span length, elastomeric bearings, bridge pier length, and foundation stiffness. The results of the two models were compared to understand the influence of the embankment. Additionally, the spring elongations of the non-linear springs between the bridge deck and the rails, representing the ballast bed, were examined to determine if they were in the linear or non-linear part of the spring characteristic to see if the springs slipped enforcing stress redis- tribution. Finally, the models assessed the individual contributions of three load cases (thermal, longitudinal traffic load, and vertical traffic load) to the combined additional rail stress. The results lead to the following conclusions: • When a structure is not influenced by the embankment, the magnitude of additional rail stresses depends on the stiffness of the substructure. The stiffness of the weakest component, in this case, the elastomeric bearings, has a significant influence. • When a structure is influenced by the embankment, the magnitude of additional rail stresses mainly depends on the dominant stiffness of the embankment, with the stiffness of the substructure having little to no influence. • Structures with embankment influence experience lower additional rail stresses due to the additional stiffness provided by the embankment. Problems with exceeding maximum permissible rail stresses occur mainly in relatively long railway bridge structures without embankment influence. • The vertical load has the largest contribution to the combined additional rail stresses for both structure types. • The thermal load has a larger influence on structures with embankment influence because these structures are more constrained by the embankment and thus more vulnerable to thermal deformations. • Linear summation of individual stress contributions from different load cases generally results in higher or equal stresses compared to non-linear combinations, making linear summation a conservative approach. The stress difference between linear summation and non-linear combination is usually only a few megapascals. If the springs between the bridge deck and the rails slip into the non-linear branch, this difference increases slightly but remains small. Based on these conclusions, the following recommendations can be made to prevent additional rail stresses from exceeding maximum permissible stresses without the use of fixed points and to streamline the process of longitudinal force analysis for engineers: • To prevent exceeding the maximum permissible stress in structures without embankment influence, consider using larger elastomeric bearings or less slender bridge decks that are less susceptible to deflection, thereby reducing additional rail stress, especially from vertical loads. • Since linear summation of individual contributions to additional rail stresses results in conservative and faster calculations, it is recommended to use linear calculations in the initial phase. Then, perform a final design review with non-linear calculations to ensure accuracy. This approach will significantly speed up the design process, as models will not need to run for hours or days each time.

In the Netherlands, there is a large and widely used railway system that includes numerous railway bridges. This master thesis investigates the problems caused by these railway bridges. Since World War II, continu- ous welded rails have been used extensively throughout the Netherlands. These rails offer several advantages on embankments, such as reduced maintenance due to less vibration, increased passenger comfort, and reduced noise. However, continuous welded rails can cause problems when they run continuously over a bridge, as is the case in the Dutch railway system. Bridges are not continuous structures and have joints between the decks or between the deck and the transition structure. These joints allow the bridge deck to expand and contract due to temperature changes, move due to longitudinal forces from train braking and acceleration, and deflect due to the vertical load of the train, causing rotations at the ends of the bridge decks. This relative displacement between the bridge deck and the continuously welded rails creates addi- tional stresses in the rails. These additional stresses must not exceed the maximum allowable stress of the rail material, as this could cause the rails to buckle or fracture. Fixed points are often used in practice to limit the movement of the bridge deck and keep additional rail stresses within acceptable limits. This investiga- tion, however, focuses on understanding the interaction between the rails and the structure without the use of fixed points. The study assumes a railway bridge in the Netherlands with a ballast bed and uses concrete precast bridge decks. To gain initial knowledge of the problem and the various railway components and bridges, a literature review was conducted, and two existing railway bridge projects were analysed. It quickly became evident that there are two different bridge types relevant to the study of additional rail stresses: those without embankment influence and those with embankment influence. The study then identified parameters that could influence the magnitude of additional rail stresses to use them as variables in further investigations. Two longitudinal force models were created in SCIA Engineer: one without embankment influence (Model 1) and one with embankment influence (Model 2). These models are spring models where the stiffness of connections and elements is schematised as springs. The models were validated with hand calculations and used to obtain results for the influence of various parameters such as bridge deck span length, elastomeric bearings, bridge pier length, and foundation stiffness. The results of the two models were compared to understand the influence of the embankment. Additionally, the spring elongations of the non-linear springs between the bridge deck and the rails, representing the ballast bed, were examined to determine if they were in the linear or non-linear part of the spring characteristic to see if the springs slipped enforcing stress redis- tribution. Finally, the models assessed the individual contributions of three load cases (thermal, longitudinal traffic load, and vertical traffic load) to the combined additional rail stress. The results lead to the following conclusions: • When a structure is not influenced by the embankment, the magnitude of additional rail stresses depends on the stiffness of the substructure. The stiffness of the weakest component, in this case, the elastomeric bearings, has a significant influence. • When a structure is influenced by the embankment, the magnitude of additional rail stresses mainly depends on the dominant stiffness of the embankment, with the stiffness of the substructure having little to no influence. • Structures with embankment influence experience lower additional rail stresses due to the additional stiffness provided by the embankment. Problems with exceeding maximum permissible rail stresses occur mainly in relatively long railway bridge structures without embankment influence. • The vertical load has the largest contribution to the combined additional rail stresses for both structure types. • The thermal load has a larger influence on structures with embankment influence because these structures are more constrained by the embankment and thus more vulnerable to thermal deformations. • Linear summation of individual stress contributions from different load cases generally results in higher or equal stresses compared to non-linear combinations, making linear summation a conservative approach. The stress difference between linear summation and non-linear combination is usually only a few megapascals. If the springs between the bridge deck and the rails slip into the non-linear branch, this difference increases slightly but remains small. Based on these conclusions, the following recommendations can be made to prevent additional rail stresses from exceeding maximum permissible stresses without the use of fixed points and to streamline the process of longitudinal force analysis for engineers: • To prevent exceeding the maximum permissible stress in structures without embankment influence, consider using larger elastomeric bearings or less slender bridge decks that are less susceptible to deflection, thereby reducing additional rail stress, especially from vertical loads. • Since linear summation of individual contributions to additional rail stresses results in conservative and faster calculations, it is recommended to use linear calculations in the initial phase. Then, perform a final design review with non-linear calculations to ensure accuracy. This approach will significantly speed up the design process, as models will not need to run for hours or days each time.

Sustainable railway systems with less disturbance are highly desired. Insulated rail joint (IRJ) is one important structural component in a railway track. IRJs serve the railway system with two crucial functions: dividing track into sections for signal control and enable the detection of broken rails. An IRJ generally consists of two fishplates, insulation layers between the rails and the fishplates, and an end-post layer between two rails. The fishplates are assembled using pre-tensioned bolts. Although the IRJ plays an important role in the railway system, it introduces discontinuities in stiffness and geometry to wheel-rail rolling contact and is thus considered one of the weakest parts of the railway track. Maintenance of IRJs has been an issue of great concern for the rail operators worldwide. Over the past few years many studies have been conducted on monitoring, modelling and analysis of IRJs. Both numerical and experimental studies have been performed in order to gain better understanding of the behaviour of IRJs under static and dynamic loads. Considering that dynamic wheel-rail impacts occur at IRJs, the dynamic behaviour of IRJs should be carefully examined. This M.Sc. thesis studies the dynamic behaviour of the IRJ experimentally and numerically. Two three-dimensional finite element (FE) track models with different types of IRJ, i.e. a new NRG-joint and normal joint, are developed. Rails, fishplates, insulation layer and sleepers are represented in the models as detailed as possible, while the rail-pads and the ballast are simplified as spring and damper elements. The NRG-joint consists of two fishplates and six pretensioned bolts, while the normal joint consists of two shorter fishplates and four bolts. Implicit FE analyses are first performed to calculate the initial stresses and displacements of the track models, which are then used as initial conditions for the explicit dynamic FE analysis. Field hammer tests are performed on the track line between Zwolle and Meppel. The tests are used on one hand to calibrate the stiffness and damping parameters involved in the rail-pad and ballast models, and on the other hand to validate the dynamic behaviour reproduced by the FE IRJ models. The comparison between the simulation and the measurements shows reasonable agreement of the results. Based on the validated FE models, optimisation strategies of the dynamic behaviour of the IRJ are proposed by a parametric study. The varied parameters include stiffness and damping of the rail-pads and the ballast as well as sleeper span. Implementation of non-uniform sleeper span seems effective for reducing pinned-pinned resonance. Finally, conclusions are drawn and recommendations for further research are made.

For railway travel the Insulated Rail Joint (IRJ) is a critical part in most railway safety systems but at the same time also considered a weak link. The IRJ creates a discontinuity in stiffness and geometry that leads to wheel-rail impact forces. The angled IRJ is a proposal to reduce these impact forces. Despite the real-world experiences with angled IRJs the research on the topic is marginal. In this thesis a study is presented into the dynamic behaviour of the wheel-rail impact occurring at IRJs. Numerical models are established to simulate a wheel rolling over IRJs with angles of 0, 15, 30 and 45 degrees, using the implicit-explicit sequential finite element method with the software ANSYS/LS-DYNA. The impact forces are the main output and analysed. Three variations of the IRJ models were used for simulations. The basic version IRJ model is built up with a fully constrained rail foot to simulate an infinite support stiffness condition. The second version is supported by spring and damper elements to simulate supports such as ballast and rail pads. Height differences between the rail ends are generated when a wheel passes the joint, which corresponds to a real-world scenario. Different degrees of support degradation are simulated by varying the support stiffness, using the spring and damper element parameters. The third version also incorporates the spring and damper elements as support but couples some nodes between the fish plate and rail web in vertical displacement to reduce the rail height difference caused by wheel pass-by, aiming to simulate a ‘factory-new’ condition joint. The established models were validated in terms of wheel-rail contact solution and contact force amplitude. In comparison with existing FE wheel-rail impact models the proposed models in this thesis are less time consuming and more flexible for joint angle adjustments. The second version simulating degraded joint conditions provided the most interesting findings and was used in a sensitivity analysis by varying the velocity and wheel load. The simulation results show that angled IRJs are advantageous when degradation is present, whereas in ‘new joint’ conditions the gap width plays a significant role and angled IRJs with larger gaps produce higher impact forces. Based on the results the recommendation is given to consider angled IRJs on tracks with a low maintenance scheme and further research is suggested.

Transition zones in railway tracks are locations with an abrupt change in stiffness in the vertical rail supporting structure. These locations are typically located as approaches near engineering structures where there is a sudden change in track substructure. Due to these abrupt changes the dynamic forces of the wheel-rail interaction on the railway track are significantly amplified resulting in the deterioration of track geometry. With higher operational velocities, the degradation process of the track is accelerated. The goal of this research is the investigation of the relationship between vertical acceleration from the axle box of the vehicle bogie (axle box accelerations - ABA) and track geometry changes at transition zones. While most studies investigate the behavior of railway transition zones making use of finite element models, this study focuses on the use of a more computational efficient multi body simulation (MBS) software (VI-Rail flextrack). After the software is tested and the results validated, different stages of the service life of a transition zone (new - used - heavily used) are simulated. From the results two main conclusion can be drawn. First, the vertical acceleration is able to show the changes in differential settlement and stiffness that are occurring at transition zones. The indicators for these changes are the frequency responses with a wavelength between 1.2 < 𝜆 < 5 meters. This shows that ABA is a powerful non-invasive monitoring technique for long wavelength track irregularities. Second, the multi body simulation software is able to model complex railway tracks. The software shows the same characteristic frequencies as the measurement data does. The results of this investigation could especially be of interest for asset owners and contractors. By showing that ABA measurements tends to be an effective way of monitoring transition zones, predictive maintenance could be implemented which saves time and high costs.