Track-bridge Interaction Research Articles

A comprehensively overall track-bridge interaction study on multi-span simply supported beam bridges with longitudinal continuous ballastless slab track

Track-bridge interaction has become an essential part in the design of bridges and rails in terms of modern railways. As a unique ballastless slab track, the longitudinal continuous slab track (LCST) or referred to as the China railway track system Type-II (CRTS II) slab track, demonstrates a complex force mechanism. Therefore, a comprehensive track-bridge interaction study between multi-span simply supported beam bridges and the LCST is presented in this work. In specific, we have developed an integrated finite element model to investigate the overall interaction effects of the LCST-bridge system subjected to the actions of temperature changes, traffic loads, and braking forces. In that place, the deformation patterns of the track and bridge, and the distributions of longitudinal forces and the interfacial shear stress are studied. Our results show that the additional rail stress has been reduced under various loads and the rail's deformation has become much smoother after the transition of the two continuous structural layers of the LCST. However, the influence of the temperature difference of bridges is significant and cannot be ignored as this action can bend the bridge like the traffic load. The uniform temperature change causes the tensile stress of the concrete track structure and further induce cracks in them. Additionally, the influences of the friction coefficient of the sliding layer and the interfacial bond characteristics on the LCST's performance are discussed. The systematic study presented in this work may have some potential impacts on the understanding of the overall mechanical behavior of the LCSTbridge system.

A real-time co-simulation solution for train–track–bridge interaction

This study develops a real-time co-simulation solution that combines ANSYS and MATLAB for investigating of the train–track–bridge dynamic interactions, with the aim of providing an effective and robust method for analyzing and assessing the dynamic responses of running train and bridge, considering their complex nonlinear behaviors under extreme excitations such as earthquake and strong wind. The train–track–bridge coupled system consists of the train subsystem, the track subsystem, and the bridge subsystem. With the adoption of a previously developed efficient multi-time-step method, the train subsystem and the track subsystem are analyzed in MATLAB with a small time-step, whereas the bridge subsystem is analyzed in ANSYS using a large time-step. At each large time-step, the train–track subsystem in MATLAB and the bridge subsystem in ANSYS are coupled by communication of the track reaction forces calculated in MATLAB and the dynamic responses at the track–bridge connecting points calculated in ANSYS. The co-simulation procedure is validated through a comparison of the numerical results from computer coding developed by the authors and the measurement data of a cable-stayed bridge. To demonstrate the effectiveness and robustness of the proposed solution, the responses of a train passing through a cable-stayed bridge under earthquake excitation are analyzed, with consideration of the geometrical nonlinearity of the bridge, using the co-simulation solution.

Sequential Track–Bridge Interaction Analysis of Quick-Hardening Track on Bridge Considering Interlayer Friction

A quick-hardening track (QHT) was developed by injecting quick-hardening mortar into an existing ballast track to rapidly substitute the ballast track with a slab track, thereby improving maintainability and running safety. QHT tracks on a bridge undergo track–bridge interactions similar to other track systems. This paper presents a model to analyze the interaction between the QHT and the bridge. This model considers the longitudinal resistances of rail fasteners and anchors, as well as the interlayer friction between the track and the bridge. A sequential analysis method was applied to systematically consider such effects, revealing that rail additional stress will be high if the track slips over the bridge for a very low frictional coefficient of 0.1. Furthermore, a track segment without an anchor can slip under train traction load when the frictional coefficient is 0.3 or lower. For low friction cases, low-speed operation is advised to prevent the accumulation of the resulting longitudinal slip displacements of the track. An anchor should be installed immediately after the quick-hardening mortar provides sufficient bearing strength to the anchors. The proposed sequential analysis is useful for determining the critical friction coefficient and appropriate longitudinal resistance of a rail fastener, as well as for verifying track safety.

Long-term monitoring of the track–bridge interaction on an extremely skew steel arch bridge

This paper presents the results of long-term monitoring of the track–bridge interaction on a 100-m-long net-arch bridge with the MW steering bar system. Monitoring track–bridge interaction phenomena is a specific type of structural health monitoring (SHM). The paper begins with a thorough description of the configuration of the track and the bridge, and of the monitoring methods that were used. The real behaviour of the track and the bridge during the daily temperature cycles and during train crossings was investigated and the results are presented, together with an evaluation of the plastic shear resistance of the track. In addition, a summary of the measured extreme values and other interesting findings from an evaluation of the long-term monitoring campaign are presented. Recommendations are given on sensor application and on data evaluation. The results are discussed with reference to the requirements of transport management for safe track behaviour, to prevent buckling or cracking of the rail.

교량상 급속경화궤도의 종방향 거동을 고려한 궤도-교량 상호작용해석

궤도틀림 발생을 방지하기 위하여 기존 자갈궤도에 급속경화 모르타르를 주입하여 단시간 내에 콘크리트궤도로 치환할 수 있는 급속경화궤도가 개발되었다. 급속경화궤도를 교량에 부설할 때는 교량의 신축 변위 및 열차 시제동 하중에 의한 궤도-교량 상호작용이 발생한다. 교량상 급속경화궤도는 세그먼트 형식을 취하며 부설 초기에는 급속시공을 위하여 앵커가 설치되지 않아 궤도와 교량 사이 마찰만으로 지지되고, 앵커 설치 후에는 앵커의 전단저항력이 전체 궤도를 지지한다. 본 연구는 후설치 앵커 설치여부, 급속경화궤도와 교량 사이의 마찰 계수, 급속경화 콘크리트의 재령을 변수로 궤도-교량 상호작용해석을 수행하였으며, 해석 결과 교량과 궤도 사이의 마찰계수가 0.3 이상이면 앵커 시공전후에 모두 구조적 안전성을 확보할 수 있는 것으로 확인되었다.

A New Bilinear Resistance Algorithm to Analyze the Track-Bridge Interaction on Long-Span Steel Bridge under Thermal Action

In this paper, an analytical algorithm, based on the bilinear resistance model, was proposed to analyze the track-bridge interaction on long-span steel bridges under thermal action. Calculation results show that the proposed algorithm is more accurate than previous analytical algorithms and can achieve nearly the same accuracy as the finite-element method (FEM), but is more efficient than FEM. Based on the algorithm, this paper explained why the longitudinal force (LF) in the middle of the bridges doesn't increase as bridge length increases, then proposed a manual LF calculation formula. Researchers and engineers can use this formula to easily estimate the maximum LF on bridges which have rail expansion devices (REDs). A parametric study was performed. The result shows that LF is not a matter of concern on the bridges with REDs. Besides, the relationships between track resistance distribution, track-bridge relative displacement and boundary conditions were revealed, and the difference between LF on bridge and on embankment were discussed. The outcomes of this paper can be applied to long-span centrosymmetric continuous bridge as well as cable-stayed bridges.

Resonance Analysis of Train–Track–Bridge Interaction Systems with Correlated Uncertainties

Over the last decades, the resonance-related dynamics for bridge systems subjected to a moving train has been researched and discussed from mechanics, physics and mathematics. In the current work, new perspectives of train-induced resonance analysis are investigated through introducing random propagation process into the train–bridge dynamic interactions. Besides, the Nataf-transformation-based point estimation method is applied to generate pseudorandom variables following arbitrarily correlated probability distributions. A three-dimensional (3D) nonlinear train-ballasted track–bridge interaction model founded on fundamental physical and mechanical principles is employed to convey and depict train–bridge interactions with random properties considered. After that, extensive applications are illustrated in detail for revealing the statistical characteristics of the so-called “random resonance”. Numerical results show that the critical train speeds associated with resonance and cancelation are random in essence owing to the variability of system parameters; the correlation between parameters exerts obvious influences on system dynamic behaviors; the last vehicle of a train will be in more violent vibrations compared to the front vehicles; the influences of track irregularities on the wheel–rail interactions are significantly greater than those of resonance.

Experimental and numerical investigations of rail behaviour under compressive force on ballastless track systems

Aiming to verify the behaviour of ballastless track systems under high compressive rail forces occurring in the vicinity of bridge joints due to track bridge interaction, numerical and experimental studies are described in this paper. At first, a short summary of background information on the allowable rail stresses under compressive force on ballasted track systems is presented. Subsequently, a numerical pre-study for ballastless systems is performed. The unfavourable imperfection cases and loading procedures in transverse direction for experimental tests are determined. Based on these results, two rails are experimentally tested to achieve practical results. To ensure safety and reliability of the system, a specific testing program and a measurement concept are developed. Main testing results including the rail geometry, deformation and stress development are compared and discussed. Additionally, numerical models to evaluate the rail behaviour are improved and verified. A good consistency between the finite element model and the testing results could be achieved. The performed investigations give a scientific basis in order to increase the allowable rail compressive stresses in comparison with the existing values in the codes. A higher allowable rail stress considerably improves the design conditions for long railway bridges.

Interaction Analysis of Sliding Slab Track on Railway Bridge Considering Behavior of End-Supporting Anchors

Railway bridges with a continuously welded rails are subject to track-bridge interactions due to temperature changes and train load, which cause an additional axial force on the rail. The recently developed sliding slab track can significantly reduce the axial force on the rail caused by such interactions by placing a low frictional sliding layer between the track slab and the bridge deck and separating the longitudinal movement of the bridge from that of the track. In this study, the anchor in the fixed support region, which is an important component of the sliding slab track, was analytically evaluated to derive the load–displacement relationship, and the track-bridge interaction of the continuous bridge with the sliding slab track was analyzed considering the derived relationship. The anchor was examined for the cases of infinite stiffness, consistent stiffness, and damaged state; the stiffness of the anchor reached 10% of the original. There were no significant differences in the rail stress, track slab axial force, and rail displacement when the stiffness of the anchor was interpreted as infinite. Although the displacement of the rail increased when the anchor was damaged, there was no significant increase in the rail stress or the track slab axial force. It was confirmed, however, that the damaged anchor must be repaired as early as possible because the damage can develop rapidly as the displacement of the damaged anchor significantly increases.

무도상 교량 레일 장대화시 침목고정장치 강성에 따른 궤도-교량 상호작용 영향 분석

무도상 교량 레일 장대화시 침목고정장치 강성에 따른 궤도-교량 상호작용 영향 분석

Train–track–bridge dynamic interaction: a state-of-the-art review

ABSTRACTTrain–track–bridge dynamic interaction is a fundamental concern in the field of railway engineering, which plays an extremely important role in the optimal design of railway bridges, especially in high-speed railways and heavy-haul railways. This paper systematically presents a state-of-the-art review of train–track–bridge dynamic interaction. The evolution process of train–bridge dynamic interaction model is described briefly, from the simplest moving constant force model to the sophisticated train–track–bridge dynamic interaction model (TTBDIM). The modelling methodology of the key elements in the TTBDIM is systematically reviewed, including the train, the track, the bridge, the wheel–rail contact, the track–bridge interaction, the system excitation and the solution algorithm. The significance of detailed track modelling in the whole system is highlighted. The experimental research and filed test focusing on modelling validation, safety assessment and long-term performance investigation of the train–track–bridge system are briefly presented. The practical applications of train–track–bridge dynamic interaction theory are comprehensively discussed in terms of the system dynamic performance evaluation, the system safety assessment and train-induced environmental vibration and noise prediction. The guidance is provided on further improvement of the train–track–bridge dynamic interaction model and the challenging research topics in the future.

Experimental Determination of the Longitudinal Pier Stiffness of a Long Railway Viaduct

Track–bridge interaction plays a decisive role in the design of long railway bridges due to the high braking and acceleration forces that occur and the fact that the continuous rail is attached to the superstructure. A fundamental parameter for the calculation of the effects of track–bridge interaction is the equivalent longitudinal stiffness of piers and abutments with fixed bearings. The equivalent horizontal stiffness is commonly calculated using a pile group model. The static and ‘dynamic’ stiffnesses of the Itz valley railway viaduct were determined experimentally by using a static diagnostic load test and a braking test, which allowed for the verification of the additional rail stresses and the bearing forces with realistic input parameters. Furthermore, numerical 3D FE analyses of the deep foundation system were carried out to provide class-A predictions of the experimental results. In this article, the experimental setup and the execution and evaluation of the two tests are presented. A comparison of the experimental results and the numerical predictions is also carried out

Evaluation of seismic behaviour of railway bridges considering track-bridge interaction

Railway bridges have historically performed well in the previous earthquakes. Although this performance has qualitatively been studied in some references such as AREMA code, no quantitative criteria has been proposed for it. Thus, this study aims to present quantitative criteria for railway bridge performance under seismic loads. In the paper, seismic behaviour of railway bridges, with and without track-bridge interaction (TBI), is calculated through finite element modeling. Pushover and incremental dynamic analyses, are utilized to assess the proposed method, considering fourteen records of the past earthquakes. The results clearly show superior performance of the proposed model with track system, in which the deck displacement, base shear, and plastic rotation decrease by 70%-90%, 20%-83%, and 85%-100%, respectively. Finally, two equations are proposed to calculate deck displacement and base shear of railway bridges without performing track-bridge interaction (TBI) by Peak Ground Acceleration (PGA) of the applied record approximately.

Quantification of ballasted track-bridge interaction behavior due to the temperature variation through field measurements

Additional axial stresses in the rail are developed due to the influence of the track-bridge interaction (TBI) when the CWR (Continuous Welded Rail) track is used in the railway bridge. This is the main reason of the length limitation of railway bridge and an increase in the construction cost. Also, the track-bridge interaction analysis should be performed in order to examine the influence of track-bridge interaction. Several standards specifies analysis methods and limit values for TBI to guarantee the safety design of railway track. However, the interaction effects are not fully understood yet due to the uncertainty of ballasted track. Thus, the interaction effects should be investigated and verified based on the field test results. In this paper, the measurement and analysis method for the track-bridge interaction was proposed. For this, the measurement system was developed considering the parameters causing the track-bridge interaction, and the track-bridge interaction response caused by temperature change was measured and analyzed. From the results, the track-bridge interaction phenomenon can be fully analyzed and quantified through the measurement system presented in this study. In addition, finite element analysis was conducted and the results were compared with the measured track-bridge interaction response.

A novel algorithm for longitudinal track-bridge interactions considering loading history and using a verified mechanical model of fasteners

The mechanical behavior of fasteners has considerable influence on track–bridge interaction (TBI) analysis, and a consensus has been gradually reached that their loading history and nonlinear characteristics should be taken into account. In this study, we present a new variation pattern of the longitudinal resistance of the fasteners considering loading history, which was experimentally verified based on the Dahl friction model. The model’s mechanical behavior was more consistent with measured results compared with previously proposed Ruge’s model and the double-spring model. According to the new model, an algorithm for TBI analysis considering loading history was derived based on the Ritz method and the principle of minimum potential energy, which was applied in a case study of an N-span, simply-supported girder bridge in a high-speed railway with a typical loading sequence: (1) the seasonal temperature change of the bridge; (2) the bending of the bridge structure under a vertical train load; (3) the braking of the train. Additionally, some significant conclusions were obtained by comparing the numerical results and adopting the mechanical parameters of the fasteners specified in various codes, according to both the linear superposition method (LSM) and loading history method (LHM).

무도상 철도교 레일 장대화를 위한 궤도-교량 상호작용 해석 및 개량방안 분석

무도상 철도교 레일 장대화를 위한 궤도-교량 상호작용 해석 및 개량방안 분석

Installation of CWR on Long-Span Bridges of Ballastless Tracks

In Korea, ballastless track bridges have been built since the early 1900s and are one of the most popular railway bridges. However, because the self-weight of the upper structure is relatively lightweight compared to the train, severe noise and vibration occur, and it is difficult to increase the train speed, owing to a 20-50 m long rail being connected by the seam plate. To overcome these problems, welded rails for ballastless track bridges are urgently required. This study preliminarily investigates the installation of continuous welded rails (CWR) for ballastless tracks in order to analyze the effects of and issues due to the track-bridge interaction in this configuration and determine solutions. Keywords: Ballastless Track, Continuous Welded Rail, Additional Axial Stress

Reconstruction of low-frequency bridge noise using an inverse modal acoustic transfer vector method

Low-frequency noise emitted by elevated viaducts in light rail transit lines has considerable adverse effects on inhabitants living nearby. Reliable prediction of the acoustic field radiating from the viaduct using forward numerical models is challenging because the model parameters that influence viaduct vibration are difficult to obtain. To avoid directly quantifying these parameters, such as wheel–rail combined roughness, an inverse method is presented to reconstruct the acoustic field using modal acoustic transfer vectors and the sound pressures at a small number of measurement points. First, a forward numerical method based on the train–track–bridge interaction analysis is performed to predict the structure-borne noise of a concrete box girder viaduct. Then, the calculated sound pressures are treated as virtual measurement results to illustrate the inverse method procedure. Both QR decomposition and singular value decomposition with Tikhonov regularisation are used in the inverse analysis. Third, the proposed inverse method is validated by comparing the sound pressure levels computed using the inverse method with the results simulated using the forward prediction method. Finally, the reliability of the inverse procedure is further validated through field tests of two U-shaped girder viaducts.

"Track-Bridge" Interaction Problems in High Speed Bridge Design

Track-bridge interaction problems have a main role in the design of bridges on high speed railways (HSR). In this paper, a technique is described for performing calculations of the interaction of the elements of the "bridge-jointless track" system. The complexity of these calculations lies in the nonlinear relationship between the bridge spans and the railway track. The characteristics of these relationships are largely determined by climatic factors (summer and winter conditions), as well as the presence of temporary loading on the bridge. The results of the interaction "bridge-jointless track" system are presented at temperature and train impacts for the characteristic types of bridge structures in the form of multi-span beams and continuous beams. The influence of the length, the construction scheme, the longitudinal stiffness of the intermediate supports on the magnitude of the forces arising in the rails of the continuous path is shown. Based on the performed calculations, conclusions were drawn about the characteristic modes of operation of the "bridge-jointless track" system and recommendations were made on constructive measures reducing efforts in rails.

Estimation of Longitudinal Resistance of Concrete Tracks on Bridge Considering Longitudinal Resistance Characteristics of Rail Fastening System

The longitudinal resistance of a railway track is one of the most important factors indicating the track-bridge interaction (TBI). However, it is difficult to consider the actual resistance of an installed fastening system of a rail because the longitudinal resistance of the concrete track on the bridge for analyzing TBI is presented as a single resistance-displacement curve in design standards. In this study, the resistance that can satisfy the design requirements from the point of view of safety was calculated through experiments of the fastening system of rails. For this purpose, laboratory experiments were performed, and it was confirmed that the resisting force increases linearly with the vertical load. Further, the confidence interval of the resistance was calculated by establishing a relation that accounts for the increase in resistance due to the vertical load. Moreover, the TBI analysis was performed considering the resistance within the confidence interval, and the results were analyzed. It is thus confirmed that safe design is possible when the upper limit of the resistance value used is within the confidence interval. Keywords: Track-bridge Interaction (TBI), Rail Fastening System, Longitudinal Resistance of Track, Concrete Track