Track-bridge Interaction Research Articles

Lateral Reinforcing Plate Field Test of a Sliding Track Panel System for a Ballastless Track Bridge

The Sliding Track Panel (STP) System is a method for installing Continuous Welded Rail (CWR) in a long-span ballastless track bridge, such as a truss bridge. The STP system aims to reduce additional stress generated on the rail due to track-bridge interactions. However, as the STP system eliminates longitudinal resistance by eliminating the sleeper fastener device installed on the existing ballastless track bridge, there is no buckling stability in the vertical and lateral directions. Therefore, a plan was devised to install a lateral reinforcement plate to increase the lateral resistance. This paper investigated the effect of increasing the lateral resistance of the reinforcing plate through a field test to determine the lateral resistance performance of the track panel.

Dynamic analysis of train and bridge in crosswinds based on a coupled wind-train-track-bridge model

The dynamic performance and safety of both the train and the bridge are great concerns for long-span bridges subjected to crosswinds. For railway bridges, there is track laid on the bridge deck. The wind, train, track, and bridge subsystems form a complicated coupling system. This paper presents the dynamic responses of both the train and the bridge under crosswinds based on a wind-train-track-bridge coupled model, in which the vibration effect of the track structure involved in the coupling system is especially considered. For studying the dynamic responses of both the train and the bridge, models of railway vehicle dynamics are used for the train and a three-dimensional finite element model is used for the bridge. The train-track interaction and the track-bridge interaction are respectively considered. The wind action on the train and the bridge consists of a steady-state force and an unsteady-state force. Based on an in-situ test, the proposed numerical wind-train-track-bridge model involving the vibration effect of the track is validated. Then, the application of this proposed model on a long-span cable-stayed bridge on the Shanghai-Suzhou-Nantong HSR (high-speed railway) is presented as a case study. The typical running train and track currently serving in the Chinese railway transportation system are modeled in this study. Excitations from track irregularities are also taken into account. Finally, with the proposed wind-train-track-bridge coupled model, the dynamic performance of both the train and the bridge subjected to crosswinds are investigated.

Investigating the impact of typical bridge transverse dislocations on the running performance of high-speed trains

Bridge dislocations are hard to be voided in the operation of high-speed trains, which will lead to abnormal vibration of trains. In this study, the train–track–bridge interaction theory was adopted to develop and validate a three-dimensional coupled train–track–bridge vibration model using the finite element method. Thereafter, the influence of the dislocation amplitude on the dynamic performance of high-speed trains under five typical bridge additional transverse dislocation modes was investigated utilizing the overrun probability analysis approach. The results showed that the dislocation amplitude significantly affects the transverse dynamic behavior of high-speed trains, but it has a considerably smaller impact in the vertical direction when exposed to five typical bridge transverse dislocation modes. Moreover, under constant dislocation amplitude, the transverse parallel misalignment of the girders has the greatest influence on the running performance of high-speed trains. Although all the running performance indicators did not exceed the limit in the transverse unilateral cornering condition of the girder, speed control was suggested to guarantee operational stability. At various vehicle speeds, dislocation thresholds for the transverse symmetrical cornering, transverse parallel cornering, transverse misalignment, and transverse parallel misalignment were provided based on probabilistic guarantee rates utilizing the transverse Sperling index as the control index.

The longitudinal track-bridge interaction of ballasted track in railway bridges: Experimental determination of dynamic stiffness and damping characteristics

Considering the longitudinal track-bridge interaction (TBI) of ballasted track significantly influences the corresponding calculation results in dynamic analyses of railway bridges. However, there is still a need for realistic and test-based characteristic parameters (dynamic stiffness and damping values). This paper focuses on an experimental determination of the dynamic properties of the longitudinal track-structure interaction. Based on extensive experiments using a large-scale test facility, the ballasted track's dynamic stiffness and damping values are determined for practical applications. The test spectrum covers a wide frequency and amplitude range, whereby influences due to vertical load of the track (loaded/unloaded) and climatic conditions (summer/winter) are also examined. The tests show that the dynamic properties change significantly with the vertical load and climatic influence. Different damping mechanisms occur depending on the excitation frequency regarding the damping properties. Both friction-based and viscous damping mechanisms appear in the lower frequency range, while only viscous damping occurs in the upper frequency range. The resulting damping characteristics act frequency-dependent and also slightly amplitude-dependent. The stiffness characteristics of the longitudinal track-structure interaction show for each configuration (loaded/unloaded, summer/winter) a non-linear behaviour deviating from the normative specifications, which acts primarily displacement-dependent and almost frequency-independent. Concerning the frozen ballast bed, EN 1991-2 equates the state of the frozen ballast bed with a fixed (ballastless) track. The tests show that this assumption (‘frozen = ballastless’) does not correspond to reality, whereby the temperature level fundamentally influences the longitudinal stiffness in this respect. While at temperatures just below zero (-2°C), no significant differences to the non-frozen ballast bed are discernible; the dynamic properties change considerably at temperatures far below zero (−10 °C). Furthermore, the tests also allow observing the ballast bed liquefaction phenomenon, which occurs at resonance when the excitation frequency matches the natural frequency.

Ballast shear effects on the dynamic response of railway bridges

Single-track railway bridges are susceptible of experiencing high levels of vertical acceleration on the deck that may be dangerously accentuated at resonance. This is especially critical for short-to-medium span simply supported bridges. This problem can compromise the safety of the trains and increase the maintenance costs of the track. The main objective of this work is to investigate the influence of the ballasted track on the dynamic behaviour of these structures. The present contribution provides a detailed sensitivity analysis over a wide single-track bridge catalogue covering span lengths from 10 to 25 m and considering two common deck structural typologies: girder-deck and slab-deck bridges. The effect of the vertical stiffness of the neoprene bearings is also evaluated. A 2D Finite-Element track–bridge interaction model is implemented and used to analyse the effect of the track on the modal parameters, harmonic response and vertical acceleration of the bridges under train passages. Additionally, the weak coupling exerted by the track is studied for structures with an increasing number of consecutive spans. The results obtained reveal a notable influence of the mobilised ballast shear transfer mechanism on the dynamic response of the structures, especially for the shortest girder bridges. Finally, a track–bridge interaction model of an existing short girder bridge from a conventional railway line is updated and used to predict the experimental response measured under operating conditions. The adequacy of the numerical tool and influence of the ballast shear parameters on the dynamic response are shown.

Track–Bridge Interaction of CWR on Chinese Large-Span Bridge of High-Speed Railway

The track–bridge interaction is a fundamental concern in the field of railway engineering, which plays an important role in the optimization design of railway bridges, especially for heavy-haul railway and high-speed railway bridges. This paper systematically introduces the research status of the CWR track–bridge interaction for large-span bridges of high-speed railway in China. The evolution process of the track–bridge interaction model from the simplest elastic bar and linear longitudinal resistance model to the complex beam–rail interaction model considering the loading history is described. In this paper, the modeling methods of the track–bridge interaction model for five types of long-span railway bridges, namely simply supported beam bridge, continuous beam bridge, cable-stayed bridge, arch bridge, and suspension bridge, are systematically introduced, and the characteristics of longitudinal force distribution under the track–bridge interaction are analyzed. This paper discusses the practical application of the theory of the track–bridge interaction on extra-large-span bridges from the aspects of system dynamic performance evaluation and system safety evaluation. The practical application of track–bridge interaction theory under special conditions such as earthquake load, complex temperature load, shrinkage and creep load, and superposition of multiple loads is emphasized. It provides guidance for the further improvement of the track–bridge interaction model and the design of large-span high-speed railway bridges in the future.

Slab track-bridge interaction subjected to a moving train: an improved matrix formulation and truncation method

ABSTRACT Modelling slab track-bridge interaction subject to a moving train usually involves solving complex high-dimensional matrix equations which is time-consuming. This research works to optimize the auto-assembling process in the slab track-bridge coupling matrices formulation and improve the computational efficiency by truncating the dynamic matrices used in time integral scheme. To achieve the above goals, the key issue is to appropriately couple the systems’ dynamic matrices in conditions where the elemental sizes of the track slab and the bridge are inconsistent in 3-D space. Besides, by firstly clarifying the degrees of freedom vector of the rail, the track slab and the bridge girder participated in each time step, dynamic matrices characterizing the train-slab track-bridge interaction are truncated with time to reduce the matrix size. This present study has demonstrated the solutions for above problems. Apart from model validations, some numerical examples are presented to show applicability of the proposed methods.

Dynamic Response of Spatial Train-Track-Bridge Interaction System Due to Unsupported Track Using Virtual Work Principle

An improved spatial vehicle–track–bridge interaction system considering the unsupported track is proposed using the virtual work principle. When the track fails to be supported due to the defects under the track, the corresponding bridge–rail connection coupled matrix should be removed. Using the proposed dynamic model, a novel numerical analysis of the unilateral and bilateral unsupported sleepers in the bridge and the subgrade is carried out. The results indicate that the wheel–rail contact force changes dramatically when the vehicles pass through the unsupported track. The unsupported track has a little effect on the displacement of the bridge, but it increases the acceleration of the bridge. The displacement and acceleration of the track increase significantly with the expansion of the supported defects under the track and the increase of driving speed. For unilateral unsupported sleepers, the dynamic response on the unsupported side is slightly smaller than that of the bilateral unsupported sleeper, while the unsupported side has a limited effect on the other side of the normal support.

Long-term friction performance monitoring of sliding layer in China railway track system Ⅱ slab track on bridge superstructure

The sliding layer is an important component of the China Railway Track System (CRTS) Ⅱ slab track on bridges, and its friction performance has a significant influence on the intensity of track–bridge interaction (TBI). However, the friction performance deterioration of this sliding layer under actual repeated abrasion and harsh environmental conditions is difficult to grasp since structural health monitoring implementation into in-service high-speed railway tracks is extremely hard to be permitted and only limited valuable monitoring datasets are available at present. In this study, the friction performance degradation of the sliding layer was therefore investigated using long-term monitoring data from a multi-span simply supported box girder bridge. First, the friction-induced strain in the base plate was decoupled using the monitored strain at the fixing point and mid-span based on mechanical properties of TBI. Then, structural health monitoring and finite element analysis both indicated an approximately linear relationship between the decoupled friction-induced strain and the temperature of the investigated bridge under certain circumstances. Furthermore, the correspondence between the slope of this linear relationship and the friction coefficient was modelled. Finally, the friction coefficients of the sliding layers on target spans were identified using 4 years of monitoring data and the established correspondence model to analyse the statistical characteristics and degradation performance of the layers. This investigation of the friction performance degradation of the sliding layer in the CRTS II slab track system provides guidance for future maintenance and replacement decision making.

On the vertical coupling effect of ballasted tracks in multi–span simply–supported railway bridges under operating conditions

This contribution investigates the vertical coupling exerted by ballasted tracks on the vertical response of bridges composed either of (i) several successive simply-supported spans with weak coupling between them due to the continuous track; or (ii) adjacent single-track decks conforming a double-track bridge, in which interaction effects are induced due to the transverse continuity of the ballast layer. To this end, 2 D and 3 D track-bridge interaction Finite Element models are implemented, which consider a three-layer discrete and explicit idealization of the track. The 2 D track-bridge interaction model is used to perform sensitivity analyses on the track parameters, which have revealed that the ballast shear mechanisms along the track may significantly affect the train-induced vibrations under resonant conditions. Then, the influence of the ballast coupling on the response of twin adjacent decks is investigated with a 3 D track-bridge interaction model. To this end, this model is updated based on the results of an experimental campaign performed on a real bridge composed of two SS spans and two single track twin adjacent decks. The numerical-experimental comparison shows an evident dynamic vertical coupling between the bridge decks and reveals the importance of including the ballasted track in the modelling process of these structures.

Coupling Effects of the Ballast Track Infrastructure on the Dynamic Response of Structurally Independent Railway Bridges

This paper is devoted to track-bridge interaction phenomena in railway bridges of short simply-supported (SS) spans composed by ballasted tracks. These structures may experience high vertical acceleration levels under operating conditions. In particular, the coupling effect exerted by the ballast track shared by structural parts that are theoretically independent, such as consecutive simply-supported spans or twin adjacent single-track decks, is investigated. Experimental evidence shows that in these cases there may be an important vibration transmission from the loaded to the unloaded track, and that the interlocked ballast granules couple some of the lowest modes of vibration to an important extent. To this end a detailed three- dimensional (3D) Finite Element (FE) model of an existing bridge is implemented where the ballast in weakly connected regions is simulated as transversely isotropic material, in order to represent in a simplified manner, the degraded state due to the relative motion between the disconnected structural parts. First, the bridge numerical model is updated from the ambient vibration response of the structure previously measured by the authors. Second, a sensitivity analysis is performed on the properties of the degraded ballast and their effect on the first five modes of vibration of the bridge is discussed. Finally, the response of the bridge under operating conditions is computed numerically, compared with the response measured experimentally in the time and frequency domains and conclusions are extracted regarding the model adequacy.

Effects of the highway live load on the additional forces of the continuously welded rails of a long-span suspension bridge

High-speed running trains have higher regularity requirements for rail tracks. The track-bridge interaction of long-span bridges for high-speed railways has become a key factor for engineers and researchers in the last decade. However, studies on the track-bridge interaction of long-span bridges are rare because the bridges constructed for high-speed railways are mainly short- or moderate-span bridges, and the effects of the highway live load on the additional forces of continuously welded rails (CWRs) have not been reported. In the present study, the effects of the highway live load on the additional forces of a CWR of a long-span suspension bridge are investigated through numerical simulations. A track-bridge spatial analysis model was established using the principle of the double-layer spring model and the bilinear resistance model. The additional stress and displacement of the rail are calculated, and the effects of the highway live load are analyzed and compared with those without a highway live load. The results show that the highway live load has an obvious effect on the additional forces of a CWR. Under a temperature force, the highway live load increases the maximum tensile stress and compressive stress by 10 and 13%, respectively. Under a bending force, the highway live load increases the maximum compressive rail stress and maximum displacement by 50 and 54%, respectively. Under a rail breaking force, when the highway live load is taken into consideration, the rail displacement at both sides of the broken rail varies by 50 and 42%, respectively. The highway live load must be taken into consideration when calculating the additional forces of rails on highway-railway long-span bridges.

Additional forces on continuously welded rails of a long-span high-speed railway suspension bridge under single effect and multiple effects: A case study

This paper investigates the track–bridge interactions of the Wufengshan Yangtze Bridge, the longest high-speed railway suspension bridge in China. A finite element model of the track and bridge is built using the commercial software ANSYS. The longitudinal additional forces of the track under a single effect and combination effects of temperature rising load, bending load, and braking load are calculated. The numerical results show that strong additional forces appear in the continuously welded rail of the Wufengshan Yangtze Bridge. Temperature effect is the dominant factor for the residual internal forces. The maximum tensile stress is 115.5 MPa and the extreme compressive stress reaches 329.9 MPa. Rail expansion joints are needed for this long-span suspension bridge.

Vibrational Energy Properties of Twin-Block Ballastless Track with Anti-vibration Structure on Bridge by Power Flow Analysis

This article aims to investigate the vibrational energy properties of the twin–block ballastless track with anti–vibration structure (TBTAS) by mobility power flow method. Power flow of the components in TBTAS and bridge are deduced and power flow transfer rate is proposed to present the vibrational energy transmission property of the TBTAS–bridge system. Power flow of rail, twin–block slab and bridge in frequency domain is calculated based on a train–track–bridge interaction model. The effect of the stiffness of the elastic pad on power flow is discussed. The results show that the power flow of the rail exhibits a broad peak in the frequency range of 100 – 400 Hz which corresponds to the broad peak of the rail mobility and exhibits another peak around 1,000 Hz which is the pinned–pinned vibration frequency of the rail. By using elastic pad, the power flow of the bridge reduces by a maximum of 43 dB in the frequency range of 1 – 1,000 Hz. The power flow transfer rate shows that the vibrational energy concentrates in the slab. The vibrational energy of slab and bridge reaches the balance when the stiffness of the elastic pad is 40 MPa/m.

Stability of continuous welded rail on steel bridge subjected to thermal loading

Continuous Welded Rail (CWR) forms a smooth high-speed rail track. However, its stability has been a cause of worry for being a slender structural element and its tendency to buckle about the weaker axis. Track-Bridge Interaction (TBI) phenomenon results in additional axial rail stress, creating local high-stress zones in the track. Since TBI is the main reason for rail stress and track displacements of CWR on railway bridges, more confidence needs to be developed by quantifying the stability of CWR-on-bridge. In this study, a simplified numerical model is proposed to study the effect of TBI on the stability of CWR-on-bridge due to temperature loading. Boundary elements are utilized to reduce the number of elements in the model. The model predicts the state of the stress in CWR due to thermal loading. Stability analysis of CWR on a single span bridge employing nonlinear buckling analysis reveals a significant influence of TBI on CWR stability. The two critical buckling parameters of CWR, the maximum buckling temperature (Tmax) and safe temperature increase (Tmin), are affected by TBI. Tmin drops more rapidly compared to Tmax and needs to be kept below the safe limits to ensure track safety.

Running Safety Assessment of Trains on Bridges under Earthquakes Based on Spectral Intensity Theory

The main goal of this paper is to perform the safety assessment of high-speed trains (HSTs) on the simply supported bridges (SSBs) under low-level earthquakes, which are frequently encountered by HSTs, utilizing spectral intensity (SI) index. First, the HST’s limit displacements, which are calculated by using the multi-body train model with detailed wheel–rail relationship, varying with train speed, frequency and amplitude of a sinusoidal base excitation are obtained. Then, based on the obtained HST’s limit displacements, the spectral intensity limits (SIL) graded by the train’s running speed are calculated, and the relationship between the bridge seismic dynamic responses and the train’s running safety was established. Next, the method that utilizes the SI and the SIL indexes to evaluate the HST’s running safety was proposed and verified by comparing with the evaluation result of the train–track–bridge interaction model. Based on the proposed SI index, the HST’s running safety on the SSBs was evaluated under earthquakes, considering different pier heights and site types. The results showed that the low-frequency components of the ground motions are unfavorable to the HST’s running safety, and the height of bridge piers has a significant impact on running safety.

Investigation on the Maximum Expansion Length of Urban Rail Transit Double-Tower Cable-Stayed Bridges Without Rail Expansion Device

Cable-stayed bridges carrying urban rail transit are often equipped with rail expansion devices (REDs) to avoid possible breaking or buckling of the rails. Such devices not only increase construction and maintenance budgets of the track system, but also endanger ride comfort and safety of the trains. Therefore, the maximum expansion length of cable-stayed bridges without the adoption of RED is investigated and presented in this paper. Finite element models of cable-stayed bridges with various lengths are developed based on design parameters of existing bridges with similar lengths. A friction-spring model is utilized to simulate the nonlinear resistance history of fasteners under various loading cases. Track–bridge interactions are then studied by varying the longitudinal restraint conditions for the cable-stayed bridges. The investigation reveals that the admissible overall rail stress allows a maximum expansion length of about 400[Formula: see text]m for urban rail transit double-tower cable-stayed bridge paved with the ballastless track and WJ-2 small resistance fasteners. This finding provides theoretical bases and practical guidelines for the saving of REDs for many large-span urban rail transit bridges in future design.

Ballasted track interaction effects in railway bridges with simply-supported spans composed by adjacent twin single-track decks

This paper is devoted to track-bridge interaction phenomena in railway bridges of short simply-supported (SS) spans composed by ballasted tracks. These structures may experience high vertical acceleration levels under operating conditions. In particular, the coupling effect exerted by the ballast track shared by structural parts that are theoretically independent, such as consecutive simply-supported spans or twin adjacent single-track decks, is investigated. Experimental evidence shows that in these cases there may be an important vibration transmission from the loaded to the unloaded track, and that the interlocked ballast granules couple some of the lowest modes of vibration to an important extent. To this end a detailed three-dimensional (3D) Finite Element (FE) model of an existing bridge is implemented where the ballast in weakly connected regions is simulated as transversely isotropic material, in order to represent in a simplified manner the degraded state due to the relative motion between the disconnected structural parts. First, the bridge numerical model is updated from the ambient vibration response of the structure previously measured by the authors. Second, a sensitivity analysis is performed on the properties of the degraded ballast and their effect on the first five modes of vibration of the bridge is discussed. Finally, the response of the bridge under operating conditions is computed numerically, compared with the response measured experimentally in the time and frequency domains and conclusions are extracted regarding the model adequacy.

무도상 교량의 레일 장대화에 따른 궤도-교량 상호작용 영향 저감 방안

이 연구에서는 무도상 교량의 레일 장대화 시 발생하는 궤도-교량 상호작용(track-bridge interaction, TBI)의 영향을 저감하기 위한 방안을 제시하기 위하여 주요 영향 인자인 궤도의 종저항력과 교량 하부구조의 종방향 강성 특성에 따른 레일 부가축응력, 변위, 교각 작용력을 분석하였다. 연구 결과에 따르면, 무도상 교량에 장대레일을 설치하면 교량 위에서 침목과 거더 간 상대변위와, 교량 접속부에서 침목과 노반의 상대변위가 한계변위를 초과하여 침목의 슬립이 발생할 가능성이 높다. 이는 레일체결장치의 종저항력이 교량 위와 교량 접속부의 적정 길이에 걸쳐 침목고정장치의 종저항력보다 작은 종저항력을 갖는 레일체결장치를 설치하면 침목의 슬립을 방지할 수 있는 것으로 나타났다. 또한 교각의 종방향 강성이 클수록, 교대의 종방향 강성이 작을수록 교각에 작용하는 힘이 증가하였다. 이는 교각과 교대의 종방향 강성을 정확히 산정하기가 쉽지 않은 노후 교량에서의 교각 작용력 계산 결과에는 매우 큰 오차가 포함될 가능성이 크다는 점을 시사한다. 이 경우 2단 선형 탄성을 가지는 면진받침을 설치함으로써 교각 작용력과 레일 부가축응력을 일정 크기 이하로 억제할 수 있다.

Numerical Study on Track–Bridge Interaction of Integral Railway Rigid-Frame Bridge

Track–bridge interaction (TBI) is an increasingly essential consideration for the design and operation of railway bridges, especially for the innovative bridge structure systems that constantly spring up over the years. This paper focuses on the characteristics of additional forces in continuous welded rails (CWRs) on the 3 × 70 m integral rigid-frame bridge of the Fuzhou–Xiamen High-Speed Railway, which is a novel high-speed railway (HSR) bridge structure system in China. The differential equations of rail stress and displacement are first investigated and an integrative analysis model comprising of rail, track, bridge and piers is then established. Secondly, the characteristics of representative additional forces are illustrated and the influences of different design parameters are discussed in detail. Furthermore, suitable rail fasteners, optimal layout schemes of adjacent bridges and reasonable stiffness of piers are also studied. The results indicate that the additional expansion force accounts for the largest proportion of additional forces in integral rigid-frame bridges and that resistance reduction obviously weakens the various additional forces caused by the TBI effect, while the broken gap of the rail increases greatly. Small resistance fasteners are recommended to be applied onto this new type of HSR line as these provide reductions in additional stresses of CWRs compared to WJ-8 fasteners. The additional rail stresses after adopting an adjacent span scheme of 4 × 32 m simply supported beams are less than the corresponding stresses in other schemes. The results also show that there is a strong correlation between the minimum threshold value of the pier stiffness and the longitudinal resistance of HSR lines for the integral rigid-frame bridge. This work could serve as a valuable reference for detailed design and safety evaluation of integral rigid-frame bridges.