Railway tracks are subjected to constant degradation over the operational period leading to high maintenance and operation costs. To add to this railway transition zones experience 4–8 times more degradation and need more frequent maintenance compared to normal tracks. Railway transition zones are areas where the railway tracks cross a different transportation modality (road, waterway, etc.) or where the rail experiences major changes in the type of track support structure. Several studies have pointed out that the transition zones show amplified dynamic responses due to abrupt changes in stiffness and differential settlement in these zones. Consequently, an increased deterioration of geometry and material is observed in these zones. Numerous attempts have been made to address the abovementioned factors at the superstructure and substructure level. However, an effective intervention to mitigate the amplified degradation in these zones is missing. In this chapter, an overview of the problem and existing solutions is presented. Moreover, a novel design methodology to design railway transition zones is proposed and discussed in detail. The design methodology includes the formulation of a design criterion, identification of design parameters, investigation of key phenomena governing design and proposing an optimized design solution.

Railway transition zones (RTZs) are subjected to amplified degradation leading to high maintenance costs and reduced availability of tracks for operation. Over the years, several mitigation measures have been investigated to deal with the amplified degradation of these zones. However, to ensure the robustness of a design solution, it must be evaluated for critical conditions arising due to certain loading and track conditions. In this paper, the critical load conditions arising due to different velocities (sub-critical, critical and super-critical), the direction of the moving load, the combination of inertial effects and track imperfections (non-straight rail and hanging sleepers) and passage of multiple axles (using a comprehensive vehicle model) are investigated for an embankment-bridge transition. The results are then compared against the recently proposed design of a transition structure called SHIELD (Safe Hull Inspired Energy Limiting Design) to evaluate its performance under these critical conditions using various vehicle models and finite element models of the RTZs. It was found that the novel design of the transition structure effectively mitigates dynamic amplifications and results in smooth strain energy distribution across sub-critical, critical, and super-critical velocity regimes in both directions of movement implying that the expected operation-induced degradation will be as uniform as possible in longitudinal direction. Furthermore, even though this transition structure is designed to deal with initial track conditions (perfectly straight track), its superior performance is not confined to tracks in perfect condition; it also efficiently addresses adverse effects from track imperfections such as hanging sleepers and non-straight rail. In the end, this work demonstrates the robustness of the design solution for all the critical conditions under study.

Accurate prediction of train-induced settlement in railway transition zones is of paramount importance for ensuring the safety and serviceability of high-speed railway (HSR) infrastructure. The inherent complexity of mechanical properties and settlement distribution in these zones stems from the significant stiffness variation between different track structures. This study presents a novel iterative framework for long-term settlement prediction specifically tailored to ballastless track transition zones of HSR systems. The framework couples a dynamic Train-Track-Transition Zone (TTTZ) model with a plastic strain prediction model for soil, enhanced by a jump-step iterative algorithm that improves computational efficiency while maintaining accuracy. The model's validity has been verified through comprehensive comparisons with in-situ measurements and existing analytical solutions. Numerical results demonstrate that the iterative updating of track irregularities is crucial for accurate settlement prediction, as it accounts for the time-dependent dynamic characteristics of the TTTZ system. Furthermore, a wavelet transform-short energy method is developed to identify high-density vibration energy distributions in the spatial domain, establishing a robust correlation between dynamic responses and settlement evolution. This study underscores the importance of iterative modeling and advanced time-frequency analysis in settlement prediction and track quality assessment, offering valuable insights for the design, maintenance, and evaluation of HSR transition zones.

In this paper, we study the stability of a simple model of a hyperloop vehicle resulting from the interaction between electromagnetic and aeroelastic forces for both constant and periodically varying coefficients (i.e., parametric excitation). For the constant coefficients, through linear stability analysis, we analytically identify three distinct regions for the physically significant equilibrium point. Further inspection reveals that the system exhibits limit-cycle vibrations in one of these regions. Using the harmonic balance method, we determine the properties of the limit cycle, thereby unraveling the frequency and amplitude that characterize the periodic oscillations of the system's variables. For the varying coefficients case, the stability is studied using Floquet analysis and Hill's determinant method. The part of the stability boundary related to parametric resonance has an elliptical shape, while the remaining part remains unchanged. One of the major findings is that a linear parametric force can suppress or amplify the parametric resonance induced by another parametric force depending on the amplitude of the former. In the context of the hyperloop system, this means that parametric resonance caused by base excitation—in other words by the linearized parametric electromagnetic force—can be suppressed by modulating the coefficient of the aeroelastic force in the same frequency. The effectiveness is also highly dependent on the phase difference between the modulation and the base excitation. The origin of the suppression is attributed to the stabilizing character of the parametric aeroelastic force as revealed through energy analysis. We provide analytical expressions for the stability boundaries and for the stability's dependence on the phase shift of the modulation. Finally, we emphasize that suppressing parametric resonance through an added, linear state-dependent force with the coefficient having the same period as the original force can be achieved in other physical systems too.

Transition zones, characterized by significant variation in track properties (e.g., foundation stiffness) near rigid structures like bridges and tunnels, necessitate more frequent maintenance compared to standard track sections due to higher levels of differential settlements observed at transition zones. Field measurements on one-way tracks reveal asymmetric settlement patterns (i.e., different settlement in the soft-to-stiff vs. stiff-to-soft transitions), yet existing literature often investigate either one or the other transition type without investigating the potential limited validity of results. This study investigates the similar aspects as well as the dissimilar ones regarding the behaviour of soft-to-stiff and stiff-to-soft transitions. Modelling results show that the behaviour of the two transitions can be considerably different. These results strongly suggest that for a mitigation measure to be efficient, it may be necessary to have different designs for the two types of transition wherever possible (i.e., in one-way tracks). This study can help researchers and engineers understand the different degradation patterns obtained using more complex models or from field measurements.

Several studies have been dedicated to altering friction forces, with external excitation being one of the approaches explored. When the latter is considered, its influence has primarily been studied within the context of discrete systems. Therefore, in this study, a moving oscillator in frictional contact with an elastic rod of finite length subjected to distributed damping is considered, to study the influence of external excitation in the presence of support flexibility on friction modulation. The modal expansion method is used to derive the modal equations of motion, which are then solved numerically. Two cases are investigated, one with the load acting on the mass and the other with the load acting on the rod. It is found that, for both cases, friction modulation varies along the rod's length, and it differs from that obtained assuming a rigid rod. Moreover, for the load-on-mass scenario, a critical velocity is defined, providing direct insight into the friction modulation differences between flexible and rigid rod cases. For the load-on-rod scenario, large deformations are observed close to and above resonance, and geometric nonlinearity is accounted for to describe the system dynamics accurately. To link theoretical results to applications, the findings are used to qualitatively interpret slip-joint vibration-assisted decommissioning tests, and are compared with experimental results in which friction force reduction is explained through the use of elasto-plastic friction models that account for surface deformability, showing good qualitative agreements between the theoretical and experimental outcomes.

In this paper, we investigate the response of a cavity embedded in an elastic half-plane (2D) subjected to a harmonic SH wave. In previous work, the method of conformal mapping and the indirect boundary element method (indirect BEM) were employed to solve the 3D wave scattering from a cylindrical tunnel embedded in a half-space. Inaccurate results were obtained particularly at high frequencies (method of conformal mapping). Therefore, in this study we focus on a comparison of the two methods with the method of images, which serves as a benchmark solution. Through a systematic evaluation, we confirm that the two methods accurately work within the complete considered ranges of the dimensionless frequency and the embedded cavity depth. This suggests that representing the waves scattered from the free surface by cylindrical waves in the method of conformal mapping is the cause of the inaccuracies at high frequency in the 3D problem; the cylindrical waves are probably not able to fully capture all wave conversions taking place at the free surface. The presented results reveal significant effects of the system parameters on the responses. The system's response curves display nearly equally spaced resonances, which is in line with those of the 1D shear layer subject to bedrock motion, while similar response curves for the 3D case do not have this feature.

Railway transition zones (RTZs), where rail tracks undergo abrupt changes in foundation types, represent critical challenges in railway infrastructure due to their higher degradation rates compared to open tracks. This study synthesizes insights from multiple research efforts to propose a robust design solution and an energy-based design criterion for RTZ management. We present a two-step approach to establish the design criterion based on a systematic analysis of each RTZ component, focusing on variations in kinematic responses, stresses, and energies. Based on this analysis, the energy-based design criterion is proposed, asserting that minimizing the total strain energy within the trackbed layers and uniformly distributing it in the longitudinal direction can significantly mitigate uneven track geometry and reduce degradation. A novel safe hull-inspired energy limiting design (SHIELD) is introduced and evaluated against traditional transition structures like approach slabs and transition wedges. SHIELD’s effectiveness in managing energy flow at RTZs is demonstrated, highlighting its potential as a transformative solution in RTZ design. Further, we explore the impact of stiffness variations in both vertical and longitudinal track directions and the temporal changes in material properties on RTZ dynamics, suggesting permissible stiffness ratios to control strain energy amplification. A detailed investigation is thus performed to understand the role of geometry in energy management. The influence of different geometric profiles of SHIELD and standard embankment-bridge transitions on strain energy distributions is studied using 3D finite element models. The findings emphasize the strategic use of geometry to channel and scatter energy, and thus mitigate energy concentrations, enhancing the performance and lifespan of RTZs. In conclusion, this comprehensive research not only highlights the importance of an energy-based design criterion and the innovative SHIELD structure in RTZ management but also underscores the need for further research into the geometric profiles and their interplay with energy flow and mechanical properties. This study lays a foundation for future explorations aimed at optimizing RTZ design, ensuring robustness, and extending the operational life of these crucial railway sections.

Maglev and the newer Hyperloop technologies are advanced transportation systems that eliminate wheel–rail friction using electromagnetic suspension/levitation. The electromagnetic suspension is inherently unstable and requires a control strategy for safe operation, which has been previously studied in the context of Maglev. However, the interaction between electromagnetic instability and another instability mechanism, known as wave-induced instability, occurring at high vehicle velocities, has not been explored. This interaction between two distinct instability mechanisms is the focus of this study. From a practical perspective, this study examines the stability of magnetically suspended vehicles (e.g., Maglev or Hyperloop) in relation to vehicle velocity and control gains. To account for this, this study properly includes the infinite guideway, thus allowing vehicle velocity to influence system stability. The results show that at sub-critical velocities, the guideway's reaction force helps suppress perturbations and stabilize the system, with instability driven solely by improper electromagnetic control. However, at super-critical velocities, wave-induced instability drastically reduces the stable parameter space. This study further proposes a methodology to distinguish the contribution of each instability mechanism to the overall system stability, which is important for efficient mitigation measures. The findings reveal that beyond a certain super-critical velocity, wave-induced instability dominates much of the control-gain plane, with the control strategy effective in only limited regions. In conclusion, the study recommends revising control design strategies, as solely focusing on maximizing energy dissipation through control can trigger wave-induced instability. A more effective approach balances energy dissipation with avoiding the activation of wave-induced instability by steering clear of problematic vibration frequencies. These insights provide guidance for improving control strategies.

A two degree of freedom mass on a moving belt system has been considered to study the effect of friction-induced oscillations, due to nonlinear contact properties and external excitation, on friction modulation. Both tangential and normal excitation are present and the Hertz-Damp model governs the normal contact. The combined presence of the normal-tangential coupling through friction and of the external excitation, results in a parametric excitation and triggers friction-induced oscillations. Using a numerical analysis, the occurrence of such oscillations is explained through the inspection of the friction force versus relative velocity plots, which indicate the presence of a negative damping effect in the tangential direction, despite considering Amontons-Coulomb law. Hence, a linearized stability analysis of the steady sliding state, by taking advantage of the Method of Direct Separation of Motion, is employed to predict the bifurcation point as function of system parameters. It is shown that the linearized stability analysis provides a good qualitative agreement for the occurrence of the friction-induced oscillations for the investigated system, while the quantitative match varies depending on the system parameters and their values. Lastly, the effect of the observed friction-induced oscillations on the friction modulation is studied. Through a numerical analysis, a significant degree of scatteredness in friction force modulation is observed. Such scatteredness is significantly linked to the emergence of friction-induced oscillations, and it also depends on the averaging procedure used to quantify the effective friction reduction.

The Hyperloop, a developing transportation system, reduces air resistance by housing the vehicle within a depressurized tube and eliminates contact friction by using an electro-magnetic suspension/levitation system. Maintaining system stability poses a challenge due to the exceptionally high target velocities. Consequently, it is important to know apriori the velocity regimes in which the system can be unstable. The authors have recently investigated this aspect by, unlike previous studies, properly accounting for the frequency and velocity dependent reaction force provided by the infinite guideway. Furthermore, that study focused on the interplay between two fundamentally different instability sources, namely (i) the electro-magnetic suspension, and (ii) wave-induced instability, showing that stability domains drastically change above a certain vehicle velocity. The current study presents a methodology to distinguish the contribution of each instability mechanism to the overall system stability, and demonstrates that the wave-induced instability mechanism is causing the drastic stability change at large vehicle velocities. This investigation offers physical insight into the mechanisms that can cause instability in the Maglev/Hyperloop systems, and can help engineers that develop this novel transportation system to avoid excessive vibrations and, in extreme cases, derailment.

Railway transition zones present a major challenge in railway track design mainly due to abrupt jumps in stiffness and differential settlements that result from crossing stiffer structures such as bridges or culverts. Despite numerous efforts to mitigate these transition effects at both the superstructure and substructure levels, a comprehensive solution remains elusive. Substructure-level interventions have demonstrated some effectiveness but are often cost-prohibitive and challenging to implement in existing operational railway transition zones. In contrast, mitigation measures at the superstructure (rail, sleepers, rail-pads, under-sleeper pads) level can be easily installed but have shown limited improvement in site measurements. This study evaluates the influence of different sleeper configurations in transition zones and reduced sleeper spacings on the operation-driven dynamic amplifications in railway transition zones, employing a recently proposed criterion based on the total strain energy in the track-bed layers (ballast, embankment, and subgrade). In addition to this, the influence of the loss of contact between sleepers and ballast (i.e., hanging sleepers), which typically results from the differential settlement, is studied. The first part of the paper provides useful insights regarding the interventions (and/or initial design) in the sleeper configuration and spacing, whereas the second part of the work highlights the need for interventions to deal with the loss of contact between sleeper and ballast. A 2-dimensional finite element model of an embankment-bridge transition was used for the analysis. The results show that it is not possible to mitigate the transition effects completely using the interventions involving sleeper spacing and configuration.

Railway transition zones (RTZs) experience higher rates of degradation compared to open tracks, which leads to increased maintenance costs and reduced availability. Despite existing literature on railway track assessment and maintenance, effective design solutions for RTZs are still limited. Therefore, a robust design criterion is required to develop effective solutions. This paper presents a two-step approach for the formulation of a preliminary-design criterion to delay the onset of processes leading to uneven track geometry in RTZs. Firstly, a systematic analysis of each track component in a RTZ is performed by examining spatial and temporal variations in kinematic responses, stresses and energies using a finite element model of an embankment-bridge transition. Secondly, the study proposes an energy-based criterion to be assessed using a model with linear elastic material behavior and states that an amplification in the total train energy in the proximity of the transition interface is an indicator of increased (and thus non-uniform) degradation in RTZs compared to the open tracks. The correlation between the total strain energy (assessed in the model with linear material behaviour) and the permanent irreversible deformations is demonstrated using a model with non-linear elastoplastic material behavior of the ballast layer. In the end, it is claimed that minimising the magnitude of total strain energy will lead to reduced degradation and a uniform distribution of total strain energy in each trackbed layer along the longitudinal direction of the track will ensure uniformity in the track geometry.

The Hyperloop is an innovative transportation system that is currently under development. It minimizes air resistance by enclosing the vehicle in a de-pressurized tube and eliminates wheel-rail contact friction through the use of an electromagnetic suspension/levitation, similar to Maglev trains. This design can potentially achieve much higher velocities compared to traditional railways, positioning the Hyperloop as an environmentally friendly alternative to air transportation.

A potential challenge for Hyperloop is ensuring the dynamic stability at large velocities, where multiple instability sources can be present. An apparent source is the electro-magnetic suspension (adopted by some designs) making a control strategy mandatory to ensure stability even at quasi-static velocities. A less obvious instability mechanism is that the vibration of a vehicle on an elastic guideway can become unstable when surpassing a critical velocity.

The authors have previously investigated the interplay between the electro-magnetic and wave-induced instability mechanisms and showed that the stability space changes significantly above a certain velocity. In other words, the control strategy can ensure the overall system stability only for a very limited range of its gains. The cause for this drastic change was attributed to the wave-induced instability mechanism. Metrikin demonstrated that this instability arises with the radiation of anomalous Doppler waves, which introduce more energy to the vehicle's vibration than normal Doppler waves radiate away from the vehicle. The current study demonstrates that the change of stability domain is indeed caused by the anomalous Doppler waves. While identifying unstable velocity regimes is practical for Hyperloop design, gaining insight into the contribution of individual instability mechanisms can be crucial for efficient mitigation.

This study examines the impact of railway-induced ground-borne vibrations on nearby structures and residents, focusing on the effectiveness of the metawedge, a novel mitigation measure. The metawedge consists of a series of periodically arranged resonators along the propagation path, either placed on the ground surface or embedded at various depths. Unlike classical locally-resonant metamaterials, the metawedge features resonators with smoothly varying resonance frequencies in the longitudinal direction. Two metawedge designs, the forward and inverse metawedge, have been proposed in the literature. Despite their similarities, they operate on different principles: the forward metawedge decelerates incoming surface waves, localizing energy, while the inverse metawedge accelerates the waves, converting Rayleigh waves into body waves. This study compares the performance of both designs in mitigating train-induced ground-borne vibrations. Results indicate that both the forward and inverse metawedge exhibit remarkably similar performance for the specific design adopted. If this similarity holds across different designs, it offers engineers flexibility in choosing the appropriate measure based on practical needs. More generally, this work demonstrates the potential and feasibility of using metamaterials to address current and future challenges in railway transportation.

The railway transition zone where the track transitions from a ballasted track to a slab track, is a crucial area that can experience amplified dynamic responses. This work aims to develop a deeper insight into the mechanisms leading to the amplified dynamic response in railway transition zones. The study employs a finite element model to investigate the amplification of total strain energy due to the phenomena of reflection and redistribution of energy close to the transition interface. The results of the study are obtained for three case studies involving non-reflecting boundary (representing an energy sink) and homogeneous material along the vertical direction of the track, and the responses are studied for individual and combined effects in comparison to a benchmark case. The findings of the study show that eliminating the phenomena results in no dynamic amplification in total strain energy in railway transition zones. The conclusion highlights the importance of understanding these phenomena in order to design an efficient railway transition structure.

Railway transition zones (RTZs) are regions where abrupt track stiffness changes occur that may lead to dynamic amplifications and subsequent track deterioration. The design challenges for these zones arise due to variations in material properties in both the depth (trackbed layers composed of different materials) and longitudinal directions of the track, as well as temporal variations in mechanical properties of materials due to several external factors over the operational period. This research aims to investigate the effects of these variations in material properties (i.e., of the resulting stiffness distributions in vertical and longitudinal directions) on the behaviour of RTZs, assess from this perspective the performance of a novel transition structure called the SHIELD, and establish a methodology for designing a robust solution to mitigate the dynamic amplifications in these zones. Results indicate that stiffness variations in both vertical and longitudinal directions significantly influence the dynamic behaviour of the RTZs. The study also suggests a permissible range of stiffness ratios to control the amplification of strain energy in the most critical components of RTZs, both in the initial state as well as during the operational phase (where material properties may vary over time). Moreover, the proposed methodology offers a valuable tool for the design and evaluation of RTZs and is applicable to various transition types and a broad spectrum of material properties.

The paper of Krylov [1] demonstrates that radiation of plane Rayleigh waves excited by a constant load moving on a beam with discrete, periodic supports that rest on an elastic half-space can take place at speeds of the moving load smaller than the Rayleigh-wave velocity and at angles that are different from the conventional Mach angle. This discussion paper presents an expression for the frequency-dependent radiation angle as well as conditions for the existence of the plane Rayleigh waves, it further clarifies the mechanism of the radiation of the waves, and it demonstrates their physical significance. First, an alternative closed-form representation for the response in the space-frequency domain is presented to reveal expressions for the wavenumbers in horizontal directions (and thus for the angles of the radiated waves) as well as the conditions for existence based on those. Then, by comparing with the wave field excited in the canonical case of an harmonically varying load moving directly on the surface of the half-space (at sub-Rayleigh velocity), it is found that the basic mechanism of plane-wave generation is not fundamentally different. In both cases, the plane Rayleigh waves are radiated due to the time-periodic nature of the loading moving/progressing on the half-space surface. More specifically, all harmonic components representing the set of sequentially exerted sleeper forces continuously radiate Rayleigh waves leading to the occurrence of plane waves, just like the harmonic load moving directly on the half-space surface creates them. It is therefore claimed that the plane Rayleigh waves demonstrated in [1] are not unconventional; they are simply the elementary components of the well-known curved Rayleigh-wave pattern excited by the harmonic load moving directly on the half-space surface, as well as of the very similar Rayleigh-wave pattern excited by the set of sleeper forces. The radiated plane waves do not add up to the classical Mach cone – which is indeed due to the frequency dependence of the radiation angle [1] – but together constitute the curved wave patterns. The destructive interference of the plane Rayleigh waves is therefore only partial and their physical significance is evident.

Transition zones, characterized by significant variation in track properties (e.g., foundation stiffness) near rigid structures like bridges and tunnels, necessitate more frequent maintenance compared to standard track sections due to higher levels of differential settlements observed at transition zones. Field measurements on one-way tracks reveal asymmetric settlement patterns (i.e., different settlement in the soft-to-stiff vs stiff-to-soft transitions), yet existing literature often investigate either one or the other transition type without investigating the potential limited validity of results. This study investigates the similar aspects as well as the dissimilar ones regarding the behaviour of soft-to-stiff and stiff-to-soft transitions. Modelling results show that the behaviour of the two transition can be considerably different. These results strongly suggest that for a mitigation measure to be efficient, it may be necessary to have different designs for the two types of transition wherever possible (i.e., in one-way tracks). This study can help researchers and engineers understand the different degradation patterns obtained using more complex models or from field measurements.

Railway induced ground vibrations are of increasing importance for structures and inhabitants in the vicinity of railway tracks. This study investigates the capabilities of a novel mitigation measure, a so-called metawedge, in reducing the ground-borne vibration at the receiver end. A metawedge is series of barriers (i.e., resonators) arranged periodically in the longitudinal direction and each one is offset with respect to the others in depth direction (i.e., while the first barrier is completely on the surface, the last barrier can be completely embedded). The advantage of this countermeasure is that it can convert the incoming Rayleigh (surface) waves into body ones, redirecting the energy content deep into the ground. Simulation results show that the metawedge is capable of significantly reducing the vibration levels with as few as five resonators. Furthermore, while conventional single trenches are efficient as mitigation measures only at a certain angle of the incoming waves (outside the critical cone), the metawedge is efficient inside this cone. Although the metawedge solution is promising, this paper serves solely as a proof of concept, and additional studies are necessary to design realistic resonators that can comply with the low frequencies of the railway induced ground vibrations. Nonetheless, this study shows that metamaterials-inspired solutions can play an important role in addressing present and future challenges of the railway transportation.