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.@en

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.

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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.@en

In this paper, we delve into the dynamics of an electromagnetically suspended mass from a rigid support. The study employs a 1.5-degrees-of-freedom system which serves as a simplified model for a Hyperloop vehicle traveling in a tube. Through linear stability analysis, we analytically uncover three distinct regions for the physically significant equilibrium point. Further inspection reveals that the system exhibits limit-cycle vibrations in one of these regions. Employing the harmonic balance method, we determine the properties of the limit cycle, thus unravelling the frequency and amplitude characterizing the periodic oscillations of system’s variables. We also present preliminary findings regarding the influence of the steady aeroelastic force on the stability of the system.@en

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.@en

The current study is concerned with ground-borne vibrations induced by railways and their impact on nearby structures and inhabitants. More specifically, it explores the efficacy of the so-called metawedge, a novel mitigation measure, in reducing ground-borne vibrations along the propagation path. A metawedge comprises a series of periodically arranged resonators along the propagation direction positioned either on the ground surface or embedded into the soil at varying depths. The difference between the metawedge and a classical locally-resonant metamaterial is that the metawedge resonators have a smooth variation of the resonance frequency with longitudinal direction. This arrangement enables the conversion of incoming Rayleigh waves into body waves, effectively channeling the energy deeper into the ground. While a theoretical proof-of-concept has been previously presented by the authors, this study makes a step forward by proposing a realizable design. Simulations indicate that a metawedge with realistic properties can significantly diminish vibration levels. Unlike conventional single trenches, which are effective only against incoming waves beyond a specific angle (outside a critical cone), the metawedge proves efficient also within this cone. This work aims to showcase the potential and feasibility of metamaterials to address present and future challenges in railway transportation.@en

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.@en

In recent times, railway transportation has received increasing attention, particularly for its ability to operate entirely on electricity sourced from renewable sources. However, the growing demand for railway services has transformed previously acceptable issues into significant challenges, disrupting normal traffic operations. One such issue is ground-borne vibration especially in urban and inter-urban locations. This study explores the efficacy of a novel mitigation technique, termed a "metawedge," in reducing ground-borne vibration at the receiving end. The metawedge consists of a series of periodically arranged barriers that act as resonators. Unlike traditional metamaterials, each resonator within the metawedge possesses slightly different natural frequencies compared to its neighbours. With an appropriate choice of this variation, incoming Rayleigh (surface) waves are converted into body waves, redirecting energy deeper into the ground. Simulation results demonstrate that the metawedge can significantly diminish vibration levels with just a few resonators. Additionally, unlike conventional single trenches, which effectively mitigate vibrations only at specific angles of incoming waves (outside the critical cone), the metawedge remains efficient within this cone. While a theoretical proof-of-concept has been previously presented by the authors, this study makes a step forward by proposing a realizable design. Consequently, this work showcases the potential and feasibility of metamaterials to address present and future challenges in railway transportation.@en

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.@en

The reliable design of high-rise buildings subject to wind-induced vibrations is important for ensuring comfort and safety. However, the Eurocode recommendations and common design practices used to estimate natural frequency and damping parameters in the design stage have been found to be inaccurate, leading to unreliable predictions of building accelerations. Previous studies have shown that soil-structure interaction (SSI) can have a significant influence on these parameters, especially for high-rise buildings on soft soils. This study presents a formulation of a simple model to include soil-structure interaction effects in the natural frequency and damping parameters. It also demonstrates the compatibility of this model with the current Eurocode procedures. The study compares the results of the simple SSI model with those of a continuous model of the New Orleans tower under design wind loading. In previous work, this continuous model was validated against in-situ measurements on the New Orleans tower. The results demonstrate that the simple SSI model significantly improves the accuracy of the predicted building accelerations under wind loading for the New Orleans tower, compared to accelerations determined in the original design and accelerations computed with the Eurocode guidelines.@en

The Hyperloop, a developing transportation system, reduces air resistance by housing the vehicle within a depressurized tube and eliminates contact friction through an electro-magnetic suspension/levitation system. Maintaining system stability poses a challenge due to the exceptionally high target velocities. The interplay between electro-magnetic and wave-induced instability has been previously studied by the authors, showing that stability domains drastically change above a certain vehicle velocity. The current study demonstrates that the anomalous Doppler waves (i.e., wave-induced instability) are causing this drastic change. This investigation offers physical insight into the mechanisms that can cause instability in the Hyperloop system.@en

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.@en

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.@en

Railway transition zones are critical regions in railway infrastructure that are subjected to excessive operation-driven degradation due to energy concentration within these zones. This work presents a heuristic approach to optimise the geometry of the transition structure and investigate its influence on the strain energy distribution in the railway transition zones (RTZs), with a specific focus on embankment-bridge transitions equipped with a newly proposed ’Safe Hull-Inspired Energy Limiting Design (SHIELD)’ transition structure. For this purpose, a number of three-dimensional finite element models are used to analyze different geometric profiles of SHIELD in a systematic manner. By altering SHIELD's geometry across longitudinal, transversal, and vertical directions, the influence of the different geometric profiles on the total strain energy distribution across the trackbed layers (ballast, embankment, and subgrade) is studied in terms of spatial and temporal variations. The results establish the contribution of geometry to energy redistribution in all three directions and present an optimum geometry for the type of transition under study. It is found that among all the profiles, the longitudinal geometric profile of SHIELD has the most significant impact on the strain energy distribution, while the transversal profile primarily influences the ballast layer, and the alteration of vertical profiles enhance the local redistribution of strain energy in the vicinity of the transition interface. The preliminary optimisation (heuristic approach) presented in this work provides the starting point for full-scale optimisation to obtain tailored shapes of transition structures such that there is neither a concentration of energy nor an obstruction in the flow of energy in RTZs.@en

Railway transition zones are the most critical part of the railway infrastructures that experience 4-8 times more degradation compared to open tracks. Despite several attempts to reduce the maintenance and operation costs in these critical zones, a robust and comprehensive solution remains unknown. In recent studies, a robust safe hull inspired energy limiting design of a transition structure was proposed for an embankment-bridge transition (without ballast layer over the bridge) to deal with operation-induced degradation. However, this solution was investigated in detail for only this particular type of transition. In this work, the scope of this mitigation measure is extended for an embankment-bridge transition with ballast running over the bridge and its performance is evaluated using a strain-energy criterion. It was concluded in the end that the safe hull inspired energy limiting design can effectively mitigate the operation-induced dynamic amplification for more than one type of railway transition zones. @en

The authors have previously introduced a novel gradient elasticity model for seismic wave predictions. The said model combines (i) the higher-order gradient terms that capture the influence of small-scale soil heterogeneity and/or microstructure and (ii) the nonlinear softening soil behaviour through the use of the hyperbolic soil model. The current study presents an in-depth analysis of the proposed model. The findings indicate that as nonlinearity increases, the bulk of the wave slows down, and its shape becomes more distorted in comparison to the response of the linear system. Furthermore, the wavenumber spectrum of the nonlinear-elastic response presents peaks at large wavenumbers. However, these are eliminated when a small amount of linear viscous damping is added indicating that they are not physically relevant. One model feature that does not disappear with the presence of damping is the formation of small-amplitude waves travelling in the opposite direction to the main wave. These findings shed light on the characteristics of the proposed nonlinear gradient elasticity model and its applicability for predicting the seismic site response.@en

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.@en

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.@en

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.@en

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.@en