Track Bridge System Research Articles

Integration of Light Rail on the I-90 Floating Bridge across Lake Washington

Installing light rail transit across a floating roadway bridge presents many unique challenges, foremost of which is how to design the multidimensional moving joints at both ends of transition spans between the fixed and floating structures. A technical solution to this technical challenge has been proposed, analyzed, modeled, designed, and prototype tested in the context of the East Link Extension, a light rail transit project being carried out by Central Puget Sound Regional Transit Authority (Sound Transit). Described are the planning, execution, and results of a full-scale prototype testing program of the proposed Curved Element Supported Rail (CESuRa) Track Bridge System, based on the relationship of curved rail supports in two independent planes that adjust in response to the movements of the Interstate 90 (I-90) Bridge. The prototype CESuRa track bridges performed as expected; the information gathered and lessons learned will greatly benefit the final design, the production track-bridge fabrication, and the installation process. Also discussed is the anticipated performance of these track bridges on the I-90 structure in conjunction with the proposed direct fixation track system, fixed rail anchors, and sliding rail expansion joints to be strategically located across the 1.1-mi I-90 Bridge. Built in 1989, the I-90 Bridge is the fifth-longest floating bridge in the world and carries three westbound and two reversible lanes of traffic between Seattle and Mercer Island, Washington. The bridge will be reconfigured to carry four westbound lanes, and the reversible lanes will be converted to light rail transit.

Analysis of structural stresses of tracks and vehicle dynamic responses in train–track–bridge system with pier settlement

Pier settlement causes deformation of bridge structures, and further distorts the track structures placed on bridge decks, which may greatly affect the service life of the tracks and safe operation of trains. This study analyzes track stresses and vehicle dynamic responses in train–track–bridge system with pier settlement and determines the pier settlement safe value for high-speed railways with China Railway Track System (CRTS) II slab tracks. First, a detailed train–track–bridge dynamic model is established based on the train–track–bridge dynamic interaction theory. Verified with field experimental results, the model is utilized to calculate the dynamic responses of the vehicle–track–bridge system with different pier settlement values. Finally, the safe value of the pier settlement in the CRTS II slab track railway line is determined according to the limit of the vehicle dynamic indicators and the structural stresses of tracks. The results show that the vertical acceleration of the car body is more sensitive to pier settlement among all the vehicle dynamic indicators. Structural stresses of tracks caused by pier settlement appear at the positions of the pier with settlement and its two adjacent piers. The effect of train loads on the track stresses is much smaller than that of the pier settlement. It is important to adopt the structural stresses of tracks as the evaluation criteria of the pier settlement safe value than the vehicle dynamic indicators. Taking the effects of the bridge pier settlement, the vehicle load, the prestress effect, and the self-weight into consideration, the pier settlement safe value for the high-speed railway lines with the CRTS II slab track is 11.5 mm.

A combined power flow and infinite element approach to the simulation of medium-frequency noise radiated from bridges and rails

In elevated urban rail transit systems, it can be difficult to distinguish between rail and bridge noise in the medium-frequency range (200Hz–1kHz). The former has been well investigated using line source models or two-dimensional boundary element models, whereas the latter has usually been simulated with either statistical energy analysis-based methods, which achieve only a rough accuracy, or with three-dimensional boundary element methods, which have low efficiency. This study combines the power flow and infinite element approaches to form a new method for simulating rail and bridge noise that makes a trade-off between accuracy and efficiency. The power flow method is first applied to obtain the spatially averaged vibration of the track–bridge system due to wheel–rail interaction in the frequency domain. An analytical model of the infinite Timoshenko beam is used to represent the rail, and the finite element method is adopted to model the bridge structure. A two-dimensional acoustical model comprising finite and infinite elements is then used to calculate the noise field that considers the boundary effects of the rails, bridge, and car bodies with constant sections. The proposed combined method is validated by the comparison with existing vehicle–track–bridge dynamic interaction analysis method in the time domain and acoustical computation method via three-dimensional boundary element model. The proposed approach is then used to compute the vibration and noise from an urban rail transit U-shaped bridge with field measurements. The measured rail vibrations are utilized to estimate the nominal wheel–rail roughness input to the numerical vibration model. The simulated noise in the frequency region where rail noise dominated agreed well with the measured one. However, the bridge noise was underestimated above 400Hz due to the uncertainties and simplifications within the vibrational and acoustical models. Even so, the total noise is primarily dominated by bridge noise in the field underneath the bridge. Both rail noise and bridge noise should be considered in environmental noise evaluation for the lower floors of buildings.

Numerical evaluation of the mid-span assumption in the calculation of total load effects in railway bridges

Maximum load effects in simply supported railway bridges traversed by trains are generally investigated at the mid-span section. However, this assumption is not necessarily correct. The true maximum load effect might occur at some other bridge section and its magnitude could be significantly greater. This paper quantifies the underestimation of the load effects as a result of exclusively considering the middle section, with special emphasis on resonant situations. A 2D numerical model of a vehicle–track–bridge system was used to evaluate different vehicle velocities, bridge properties and track irregularity conditions. The error due to the mid-span assumption depends on the particular case considered but can be related to the relative energy content of the higher modes of vibration. The results show that the error is greatest for accelerations, smaller for bending moments and is almost negligible for displacements.

Train–track–bridge modelling and review of parameters

This study gathers all necessary information to construct a model to calculate the coupled dynamic response of train–track–bridge systems. Each component of the model is presented in detail together with a review of possible sources for the parameter values, including a collection of vehicle models, a variety of track configurations and general railway bridge properties. Descriptions of the most important track irregularity representations are also included. The presented model is implemented in MATLAB and validated against a commercially available finite element package for a range of speeds, paying particular attention to a resonant speed. Finally, the potential of the described model is illustrated with two numerical studies that address interesting aspects of train and bridge dynamic responses. In particular, the effect of the presence of a vehicle on the bridge’s fundamental frequency is studied, as well as the influence of the wavelength of the rail irregularities on the dynamic effects of the bridge and the vehicle.

A linear complementarity method for dynamic analysis of bridges under moving vehicles considering separation and surface roughness

In the present paper, a linear complementarity method for a vehicle-bridge dynamic system considering separation and random roughness is established. By introducing the linear complementarity relationship between the relative displacement of the wheels and the bridge at the contact points, the dynamic interaction problem of the vehicle-bridge coupled system is transformed into a standard linear complementarity problem, and two models with different connection relations between the wheels and the bridge are proposed. The presented models characterize the system with one unified formulation whether the wheels separate from the bridge or not, and the conventional trial-and-error iterative process in numerical simulation is avoided. In the numerical examples, the proposed method is verified by comparing it with the conventional method, and it is found that the velocity, the vehicle to bridge mass ratio and the road roughness have a significant influence on separation. By considering a vehicle model of three rigid bodies with four wheels and the randomness of the rail roughness in train–track–bridge system, the possibility of separation and the expectation of the maximum separation distance at different velocities are studied. The results show that it is very useful to carry out a stochastic analysis of the system and consider the influence of separation in vehicle and bridge design.

Loading-history-based track–bridge interaction analysis with experimental fastener resistance

Track–bridge interaction (TBI) analysis is usually required to determine the longitudinal stresses and displacements of a coupled system under various temperatures and trainloads and to guarantee the serviceability and safety of track structures. Its results can be used to determine the installation of rail expansion devices and even the structural designs of bridges. To improve calculation accuracy and assist with bridge design and construction investment decisions, this study proposed a nonlinear TBI analysis framework that accounted for the loading-history effects and changes in the longitudinal resistance of rail fasteners in various load cases. Laboratory experiments were conducted to determine the accurate nonlinear features of a kind of rail fastener commonly used in elevated urban rail transit traffic in China. The proposed method was applied in a case study to calculate the longitudinal stresses and displacements of a seven-span track–bridge system in comparison with the conventional linear superposition method. The results obtained using experimental longitudinal resistance displacement curves (RDCs) were also compared with those obtained using curves in the Eurocode. Both the calculation methods and the RDCs of rail fasteners were found to have considerable effects on longitudinal additional rail stresses and the relative longitudinal displacements between beam ends.

Safety threshold of high-speed railway pier settlement based on train-track-bridge dynamic interaction

This paper presents a method to determine the safety threshold of bridge pier settlement in high-speed railways. An analytical expression of the mapping relationship between the pier settlement and the rail deformation is derived theoretically for the double block ballastless track-bridge system. By adopting the superposition of the track random irregularity and the rail deformation caused by the pier settlement as the excitation inputs, the variations of vehicle dynamics indices with pier settlement are comparatively analyzed. Then, the safety threshold of the bridge pier settlement is obtained according to the limit of vehicle running safety and ride comfort indices of the high-speed trains. Results show that the dynamics indices of different trains have different sensitivities to the pier settlement, and the train CRH2C is the most sensitive one among all the types of Chinese high-speed trains. When passing through the bridges in common span with pier settlement at the speed of 250–350 km/h, the trains suffer the low-frequency excitations, and the vertical acceleration of car body is most sensitive to the pier settlement of all the dynamics indices. When the car body vertical acceleration just exceeds the allowable limit, the critical settlement value is 23.4 mm, which is much bigger than the pier differential settlement limit in the current code for Chinese high-speed railways.

Analysis of Dynamic Behavior for Ballastless Track-Bridge with a Hybrid Method

A hybrid method combining finite element method (FEM) and statistical energy analysis (SEA) was recently presented for predicting the steady-state response of vibro-acoustic systems. Based on the structural characteristics of vehicle-CRTS II ballastless track-bridge system, the hybrid method of vehicle-track-bridge elements was presented. Using finite element method and Hamilton Theory, the coupled equation of vehicle-track-bridge can be established. Computational software is coded with Matlab. As an application, the vibration characteristics of the track-bridge system vertical profile assumed as random irregularity were calculated and the effect of random irregularity wavelength was analyzed. The computational results show that (1) The changes of the rail random irregularity wavelength have little influences on vertical displacement of track structure. (2) While it has very significant influences on vertical wheel/rail contact forces, and vertical acceleration amplitude of rail and slab, and the influenc...

Probabilistic safety assessment of a short span high-speed railway bridge

A probabilistic methodology for the safety assessment of short span railway bridges for high-speed traffic is presented. The purpose is to create a simple, efficient and automatic procedure that allows identifying the critical train speeds over the bridge and assessing the safety of the train–bridge system. The methodology combines simulation techniques with the extreme value theory in order to minimise the required computational time and guarantee accurate results. Stochastic simulation is employed as it allows reflecting the real variability of the parameters that characterise the dynamic response of the train–bridge system. As a case study the safety of a short span filler beam railway bridge crossed by a TGV double train is assessed. The behaviour of short span railway bridges is known to be particularly difficult to predict due to the complexity of the coupled train–track–bridge system, as well as for being particularly sensitive to resonant phenomena. The variability of the bridge, the track and the train was accounted for, as well as the existence of track irregularities. The proposed probabilistic methodology proved to be efficient as it allowed identifying the critical train speeds with a reduced computational cost. Furthermore, for these critical train speeds two different methods were used to estimate the probability of failure. The obtained results showed a good agreement guaranteeing the accuracy of the methodology.

Analysis of the lateral dynamic response of high pier viaducts under high-speed train travel

With the development of high-speed railways in the last decade, the dynamic behaviour of trains and bridges has been studied more thoroughly. However, it is difficult to find papers in the scientific literature about the lateral response of high-speed trains travel over long viaducts with high piers. In order to evaluate the riding comfort or vehicle dynamic response of a train over this kind of bridges, an efficient nonlinear dynamic interaction model of the train–track–bridge system was developed and checked. In that model, a three-dimensional multi-body train and a finite element bridge and track system are considered. Ballast stiffness and rail flexibility are taken into account in the finite element model. For reproducing the interaction between wheel and rail, a simplified nonlinear creep contact model has been included. In this study, track irregularities and wheel-hunting movement are considered as the system lateral excitation. The influence of pier height on the response of train and bridge is also studied. Continuous bridges, straight and constant section deck viaducts with variable height and tapered piers are the structures which have been considered. The height of the tested viaduct ranges between 60 and 120m. The results of this study show that train behaviour is in accordance with riding comfort standards. And, although some bridge response values obtained are not allowed in the currently recognized train traffic safety standards of bridges, they can be easily improved.

Analysis of the dominant vibration frequencies of rail bridges for structure-borne noise using a power flow method

The use of concrete bridges in urban rail transit systems has raised many concerns regarding low-frequency (20–200Hz) structure-borne noise due to the vibration of bridges when subjected to moving trains. Understanding the mechanism that determines the dominant frequencies of bridge vibrations is essential for both vibration and noise reduction. This paper presents a general procedure based on the force method to obtain the power flows within a coupled vehicle–track–bridge system, the point mobility of the system and the dynamic interaction forces connecting various components. The general coupling system consists of multi-rigid-bodies for the vehicles, infinite Euler beams representing the rails, two-dimensional or three-dimensional elements of the concrete bridges, and spring-dashpot pairs to model the wheel–rail contacts, the vehicle suspensions, the rail pads and the bridge bearings. The dynamic interaction of the coupled system is solved in the frequency domain by assuming the combined wheel–rail roughness moves forward relative to the stationary vehicles. The proposed procedure is first applied to a rail on discrete supports and then to a real urban rail transit U-shaped concrete bridge. The computed results show that the wheel–rail contact forces, the power flows to the rail/bridge subsystem and the accelerations of the bridge are primarily dominated by the contents around the natural frequency of a single wheel adhered to the elastically supported rail.

The Characteristic Analysis of Vibration for High-Speed Train-Ballastless Track-Bridge System Base on A Hybrid FE-SEA Method

A hybrid method combining FE and SEA was recently presented for predicting the steady-state response of vibro-acoustic systems. The new method is presented for the analysis of complex dynamic systems which is based on partitioning the system degrees of freedom into a ‘‘global’’ set and a ‘‘local’’ set. The global equations of motion are formulated and solved by using the finite element method (FEM).The local equations of motion are formulated and solved by using statistical energy analysis (SEA). The power input from the global degrees of freedom. This paper deduces the theory for the beam element , and Train-Ballastless Track-Bridge System provides an application, and it showed that the method yields very good results .

Spatial Coupling Vibration of Vehicle-Track-Bridge System due to Different Track Irregularities

Track irregularity is one of the most important factors that induce vehicle-track-bridge coupling vibration. In this paper, spatial model of vehicle- track-bridge system is established. The track irregularity sample in time domain are established by power spectrum density and taken as the exciting source to analyze the spatial coupling vibration of vehicle-track-bridge system. By comparing the vibration responses of the model excited by vertical profile irregularity and the model excited by four different irregularities, the change of track irregularities have mostly influence on the vibration of the parts above the rail and nearly no influence on the parts under the rail and bridge.

Longitudinal forces in continuously welded rails on bridgedecks due to nonlinear track–bridge interaction

In this contribution longitudinal forces in continuously welded rails on railway bridges are addressed. Here, the interaction between track and structure cannot be neglected. European codes recommend an independent treatment of different longitudinal loading cases taking a nonlinear stiffness law into account. The final rail stresses are obtained by a summation of the results of the above independent calculations. The influence of the load history is completely neglected in this conventional approach. Based on an explanation of the track–bridge interaction problem a truly nonlinear description is proposed in this paper. Here, the deformation history is of essential importance. Exact stiffness formulations are derived for the loading cases ‘temperature change’, ‘sudden change of ballast stiffness when the train reaches the bridge’, ‘bending of the supporting structure’ and ‘braking’. Numerical results are presented for a typical track–bridge system and different combinations of the above loading cases. Extensive parameter studies enable a general comparison of the rail stresses obtained using the conventional approach to the results of the proposed truly nonlinear analysis based on a correct combination of loading cases.

A substructure approach for the dynamic analysis of train–track–bridge system

The dynamic interaction between a running train, the track structure and the supporting bridge is investigated resorting to substructure technique. The train is idealised as a sequence of identical vehicles moving at constant speed. Both the rails and the bridge are modelled as Bernoulli–Euler beams, while the ballast is characterised as a viscoelastic foundation. A variant of the component-mode synthesis method is proposed to couple the continuous (rails and bridge) and discrete (train) substructures. Numerical investigations have demonstrated the accuracy and efficiency of the procedure, which allows to compute simultaneously the dynamic responses of the train, rails and bridge.