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In this study, a refined finite element model was built that represented the structural and mechanical properties of railway bridges. A coupled vehicle–bridge vibration model was established to simulate the dynamic behavior of the bridge under moving trains. Field tests were then conducted to determine the free vibration characteristics as well as...

## Contexts in source publication

**Context 1**

... addition, torsional deformation of the bogies is also ignored, as is the effect of the transverse gap between wheel-sets and bogies on the system response. These assumptions mean that the car body and each of the bogies have 5 degrees-of-freedom (5 DOF); namely, vertical move- ment, yaw, roll, shaking, and nodding (see Figure 1). However, for each wheel-set, it is only necessary to consider vertical movement, yaw, roll, and shaking deformations. ...

**Context 2**

... is performed in accordance with the actual working conditions. The coordinate system selected is shown in Figure 1. The DOF of the car body fU b g ¼ ½z b y b b b b T , the DOF of the bogie fU tj g ¼ ½z tj y tj tj tj tj T j ¼ 1, 2 (j ¼1, 2), and the DOF of the wheel-set fU i g ¼ ½z i y i i i T i ¼ 1, 2, 3, 4 (j ¼ 1, 2, 3, 4) can be derived on this basis. ...

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... is an important index used to evaluate the dynamic performance of a structure. Figure 10 therefore shows the typical time-history curves for the vertical acceleration of the bridge when a freight train passes over it on a single line at 80 km/h. Figures 11 and 12 also show respectively the vertical and transverse acceleration at the middle of the span with freight trains running on single and double lines at speeds ranging from 40 to 90 km/h at intervals of 10 km/h. ...

**Context 4**

... 11 and 12 also show respectively the vertical and transverse acceleration at the middle of the span with freight trains running on single and double lines at speeds ranging from 40 to 90 km/h at intervals of 10 km/h. As shown in Figure 11, we see that the vari- ation in the vertical acceleration with the speed of a freight train running on a single line generally follows a pattern of initial increase to a maximum value on the right-hand side of 0.59 m/s 2 at 90 km/h, followed by a decrease. Figure 9. Transverse amplitude at the middle of the span under freight trains running on single and double lines. ...

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... vertical stability and transverse stability indi- ces for a freight train passing over the bridge on a single or double line at speeds ranging from 40 to 90 km/h at intervals of 10 km/h are presented in Figures 13 and 14, respectively. As illustrated in these two figures, the stability index of the locomo- tives and vehicles show a similar tendency to increase with the train speed, but the stability index of the vehicles is larger than that of the locomotives. ...

**Context 6**

... indicates that the stability of the vehicles is worse than that of the locomotives. The maximum values of the vertical stability index and transverse stability index obtained from Figures 13 and 14 are 3.00 and 3.08, respectively. A stability index of less than 3.5 is con- sidered Grade 1, 29 meaning that the vertical and transverse stabilities of the locomotives and vehicles are all excellent (i.e. ...

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... load testing of the Shizikou Bridge was per- formed using a freight train running on a single line and two freight trains running on double lines in opposite directions. The axle load and wheelbase of the loading locomotives and vehicles for the up line, and down line of the dynamic loading tests and brak- ing tests are shown in Figure 15. After calibrating the speed of the train at 5 km/h, dynamic loading tests were performed with increasing train speeds of 20, 40, 60, and 80 km/h. ...

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... vibration characteristics Figure 15. Axle load and wheelbase distribution diagrams of the loading locomotives and vehicles (unit: m). ...

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... tests were conducted with test trains operating at different speeds and running on either a single line or double lines in opposite directions. When one of these trains passed over the bridge in a down-line dir- ection at a speed of 60 km/h, a dynamic strain time- history curve was obtained for the main beam section A-A at the top of pier No. 2, as shown in Figures 21 and 22. Through an analysis of these curves, the dynamic strain coefficients at different sections were obtained and are listed in Table 3. ...

**Context 10**

... values obtained from the analysis of these curves are listed in Tables 4 and 5. It is evi- dent from these test results that the vertical and trans- verse accelerations at the mid-span of the main girder increases with the train speed reaching a maximum of Figure 16. Measured transverse natural frequency. ...

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## Citations

... However, as a number of weld joints exist in OSD, it is sensitive to fatigue, especially at the welded joints from the rib to deck and U rib to transverse diaphragm [8][9][10][11]. Large numbers of fatigue cracks were found in the existing bridge [12][13][14]. Fatigue cracks are typical problems for OSD and seriously endanger the durability and safety of steel bridge structures. ...

The orthotropic steel deck is widely used in long-span steel bridges due to its simplicity and efficiency. The welded joint of the U-rib to e deck panel area is extremely sensitive to fatigue cracks. In this study, an orthotropic steel deck with an arc-shape stiffener was proposed that aimed to alleviate the fatigue cracks and enhance the fatigue resistance in long-span steel bridges. Based on the Mingzhu Bay steel bridge, the proposed steel deck FE model was first established. Then, the moving vehicle load was applied to investigate the impact of the arc-shape stiffener on the fatigue stress amplitude and distribution. The Miner fatigue cumulative damage theory was employed to evaluate the fatigue life of the orthotropic steel deck with arc-shaped stiffener, and comparative analyses were carried out. Finally, the results show the maximum stress of the orthotropic steel deck with an arc-shaped stiffener is reduced by 15%, and the fatigue life is improved by 40% compared with the OSD.

... The peak pointing model retains the basic hysteresis rule and adds the degraded section and the residual strength section after the peak, and the model is shown in Figure 3 [18]. ...

... Among them, n = E s /E c . If the reason for the section yielding is formula (1), then, the calculation formulas of A and B are formula (18) and (19). If the cause of section yielding is equation (2), then, the calculation formulas for A and B are equations (20) and (21). ...

After the fragility curve is established, the probability of structural damage reaching each level of damage under the action of the ground motion can be determined according to the ground motion parameters, so as to calculate the direct and indirect loss caused by the structural damage and complete the earthquake damage prediction. This paper combines the improved IMK resilience model to study the seismic vulnerability of high-pier and long-span bridges. Moreover, this paper obtains the parameter calculation model based on the regression analysis of PEER’s 255 column specimen data. The improved IMK model needs to modify the elastic stiffness and strain hardening rate of the rotating spring to ensure the accuracy of the lateral stiffness of the component. The experimental research shows that the seismic vulnerability research model of high-pier and long-span bridges based on the improved IMK restoring force model has a certain analytical effect.

... The effects of the bridge deformations, subgrade settlement and various parameters of the bridge are also taken into account. Considering the accuracy and rationality of the finite element results, Jiang et al. [18][19][20][21][22] did lots of experiments and compared with the results of the finite element models. The problems of the track irregularities caused by structural deformations and the dynamic responses of the track structure under the action of trains were studied in detail. ...

This paper examines the effect of structural deformation on the unit slab-type ballastless track structure of high-speed railway. The principle of stationary potential energy was used to map the relation between girder vertical deformation and rail deformation considering the effect of subgrade boundary conditions and the nonlinear contact of interlayer. The theoretical model was verified by comparing with the finite element analysis and experimental results. The theoretical model was used to analyze the effects of several key parameters on the rail deformation, such as vertical deformation amplitude, elastic modulus of the mortar layer, and vertical stiffness of the fasteners. The results show that the track slabs suffered significant disengagement, which makes the deformation of the track structure at the position of the beam joint tend to be gentle when nonlinear contact between the mortar layer and the track slabs was considered. The track slabs disengagement mainly occurs near the beam joints (the side of the deformed beam). As the deflection amplitude of the girder increases, the track deformation, the fastener forces and the disengagement length of the track slabs are obviously nonlinear. When the vertical stiffness of the fastener and/or the elastic modulus of the mortar layer increase, the fastener force and the track plate disengagement length increase monotonically and nonlinearly, which will adversely affect the life and safety of the track structure.

... The maximum de°ection is calculated to be 0.557 mm, which is close to the result (0.556 mm) obtained from the method reported in previous research and tests. 29 For further validation, the train-track-bridge coupled multi-body model is used to analyze the acceleration of the train at the speed of 350 km/h. The analysis results are compared with the analysis results reported in the literature. ...

... The analysis results are compared with the analysis results reported in the literature. 29 The vertical acceleration of the train-track-bridge model is 0.0325 g while the reference model is 0.0345 g. As for the lateral acceleration, this train-trackbridge model and the reference model are 0.0295 g and 0.0309 g, respectively. ...

... The maximum de°ection is calculated to be 0.557 mm, which is close to the result (0.556 mm) obtained from the method reported in previous research and tests. 29 For further validation, the train-track-bridge coupled multi-body model is used to analyze the acceleration of the train at the speed of 350 km/h. The analysis results are compared with the analysis results reported in the literature. ...

... The analysis results are compared with the analysis results reported in the literature. 29 The vertical acceleration of the train-track-bridge model is 0.0325 g while the reference model is 0.0345 g. As for the lateral acceleration, this train-trackbridge model and the reference model are 0.0295 g and 0.0309 g, respectively. ...

The Lanzhou-Xinjiang High-speed Railway runs through a region of over 500[Formula: see text]km that is amenable to frequent winds. The strong wind and rainfall pose a great threat to the safe operation of high-speed trains. To tackle the aforementioned climate challenges, this paper investigates the dynamic response of the high-speed train-track-bridge coupling system under the simultaneous action of winds and rains for the safe operation of trains. Specifically, there are four main objectives: (1) to develop a finite element model to analyze the dynamic response of the train-track-bridge system in windy and raining conditions; (2) to investigate the aerodynamic loads posed to the train-track-bridge system by winds and rains; (3) to evaluate the effects of wind speed and rainfall intensity on the train-track-bridge system; and (4) to assess the safety of trains at different train speeds and under various wind-rain conditions. To this end, this paper first establishes a train-track-bridge model via ANSYS and SIMPACK co-simulation and the aerodynamics models of the high-speed train and bridge through FLUENT to form a safety analysis system for high-speed trains running on the bridge under the wind-rain conditions. Then, the response of the train-track-bridge system under different wind speeds and rainfall intensities is studied. The results show that the effects of winds and rains are coupled. The rule of variation for the train dynamic response with respect to various wind and rain conditions is established, with practical suggestions provided for control of the safe operation of high-speed trains.

... Recently, high-speed railways have developed rapidly and the China Railway Track System (CRTS) II slab track has been widely used [1][2][3]. With increasing train speed, requirements for the smoothness and stability of railways have also increased [4]. However, differential subgrade settlement commonly occurs under the long-term effects of train load [5]. ...

Slab track structures become deformed under the effects of differential subgrade settlement. According to the properties of the China Railway Track System (CRTS) II slab track on a subgrade, a three-dimensional (3D) coupled model based on both the discrete element method (DEM) and finite difference method (FDM) was developed. The slab track and subgrade were simulated using the FDM and DEM, respectively. The coupled model was verified. The deformation of the slab track and contact forces of gravel grains in the surface layer of the subgrade were studied under differential subgrade settlement. The effects of settlement wavelength, settlement amplitude, and other types of settlements were also discussed. The results demonstrate that the settlement amplitude and settlement wavelength of the subgrade have significant effects on track deformation. The deformation amplitude of the slab track increases nonlinearly with an increasing settlement amplitude of the subgrade. Increases in the settlement wavelength and amplitude of the subgrade significantly increase the maximum value of the contact force of the gravel grains in the subgrade. The maximum contact force of gravel grains near the boundaries of the settlement section can reach two to three times that of the unsettled condition, which makes it easy to accelerate the plastic settlement of the subgrade.

... Therefore, scholars at home and abroad have made in-depth research on the relationship between bridge alignment change and train running performance analysis by means of vehicle-bridge coupling numerical simulation and experimental analysis. [4][5][6][7] For example, Gou et al. 8,9 analyzed the dynamic performance of railway bridges and studied the influence of bridge deformation on the geometric alignment of high-speed railway tracks. Esveld 10 studied the relationship between train dynamic response and track irregularity and obtained the transfer function of track irregularity to vibration acceleration. ...

With the continuous service time, long-span track cable-stayed bridges are inevitably affected by material time-varying and fatigue load periodic effects, and permanent down-deflection phenomenon is inevitable. The down-deflection of the main girder would lead to the irregularity of bridge deck, which would directly affect the running comfort and safety of the train. The permanent deformation control value should be set reasonably. In this paper, based on the research and analysis of domestic and foreign codes and standards, the evaluation criteria for the service performance of long-span track cable-stayed bridges was determined, aiming at the problem of deformation classification control in the service stage of the long-span track cable-stayed bridge. The limit of permanent deformation of main girder was analyzed, and the decision processing was put forward and applied to an engineering example. According to the vehicle-bridge coupling vibration analysis, the maximum vertical deformation safety control value in the service stage is L/400, and the pre-warning control value is L/500. With the non-permanent deformation value β deducted, the permanent deformation safety control value is L/400- β, and the pre-warning control value is L/500- β. The rationality of the grading control limit of permanent deformation based on service performance analysis has been verified by application analysis.

... In recent years, high-speed railways have rapidly developed, and the train speeds have increased [1][2][3]. To ensure the safety and comfort of high-speed trains, there are increasingly higher requirements railway smoothness and stability [4]. Under the impact of shrinkage and creep of concrete after bridge completion [5], dynamic load of multiple trains, foundation settlement, and seismic load, the bridge structures would suffer unpredictable residual deformation [6,7]. ...

In order to study the effect of the vertical deformation of continuous beam structure of CRTS Ι slab ballastless track on rail deformation, this paper analyzes the mapping mechanism of the structural vertical deformation-rail deformation. Based on the principle of stationary potential energy, the work derives an analytical expression for a mapping between the vertical deformation of continuous beam structure and rail deformation by considering the effect of the subgrade. Then, the mapping relation between the vertical deformation of various typical bridge structures and rail deformation was calculated using analytical method. The results were compared with those obtained using ANSYS finite element method. The effects of four factors on rail deformation were investigated, namely, pier settlement, staggered steps on girder, rotation angles on beam ends, and number of spans of simply supported beam. The calculation results obtained via analytical method and those obtained using finite element method fit well with each other, verifying the rationality and correctness of the analytical method. The expression for analytical method is concise and can easily obtain the mapping relation between the structural vertical deformation and rail deformation using the displacement boundary conditions. The vertical deformation of the rail was proportional to the vertical deformation of same typical structure. Both inside and outside the rail deformation area, the length of rail deformation section did not change with structural vertical deformation. When there were simply supported beams at both ends of the continuous beam, the number of spans of simply supported beams had no significant effect on the rail deformation caused by the vertical deformation of typical continuous beam structures. When there were no simply supported beams, the settlement of side pier of continuous beam caused rail deformation similar to the staggered step of girder.

... The fast running train demands a strict requirement for track regularity and train dynamic stability. Research about dynamic interaction of trainbridge system 1,2,3,4 and in-situ tests of bridge structure 5,6 have been carried out. How to ensure the function of the HSR line under earthquake is a challenging research topic and massive work is needed to find out whether the techniques formerly applied in building, highway bridge and pipeline 7,8 , including numerical simulation method, sensor monitoring technology 9,10,11,12 and vibration control method 13,14,15 are suitable for seismic protection of HSR bridge. ...

This paper evaluates seismic performance of a three-span high-speed railway (HSR) simply supported bridge-track system equipped with multi-joints rotational friction damper (MRFD) using pseudodynamic hybrid simulation. In hybrid simulation, a simplified nonlinear model based on the reference of high-speed railway model is used as a numerical substructure. The experimental substructure is a rotational friction damper (RFD) specimen consisting of two rotational joints. The feedback-force of the RFD specimen is multiplied in different multiples to consider the different clamping force of MRFD with more rotational joints. Results of cyclic tests indicate that the RFD specimen has a good ability to mitigate seismic damage of bridge-track system. Then, pseudodynamic hybrid simulations were performed in the longitudinal direction of the bridge to examine the seismic performance of MRFD. The effect of various ground motions and the influence of different clamping forces of MRFD were investigated. Test results confirmed the applicability of MRFD in HSR bridge-track system.

... In the wake of development in heavy-haul and high-speed railways over the world, the problems of train-bridge dynamic interaction have become increasingly prominent, and considerable progress has been made in this field over the recent decades. Most researchers used field tests and numerical simulations to investigate the vehicle-bridge dynamic interaction [4][5][6][7][8][9]. Numerical models such as moving load models [10,11] and dynamic interaction models [12][13][14][15][16][17][18] have been developed for the train-bridge system (TBS) dynamic interaction. ...

In the freight railway bridge, the increase of the train running speed and train axle loads can enlarge dynamic response (DR) of the railway bridges, which leads to excessive vibration of bridges and endangers the structural safety. In this paper, a three-dimensional coupled finite element (FE) model of a heavy-haul freight train-track-bridge (HHFTTB) is established using multibody dynamics theory and FE method, and the DR for the coupled system of HHFTTB are solved by ABAQUS/Explicit dynamic analysis method. The field-measured data for a 32 m simply supported prestressed concrete beam of a heavy-haul railway in China are analyzed, and the validity of the FE model is verified. Finally, the effects of train formation number, train running speed, and train axle loads on DR of the heavy-haul railway bridge structures are studied. The results show that increasing the train formation number only has an influence on DR duration of the bridge structure, rather than the peak value of DR, when the train formation number exceeds a certain number; besides, the train axle loads and train running speed have significant influence on DR of the bridge structure. The results of this study can be used as reference for the design of heavy-haul railway bridges and the reinforcement transformation of existing railway bridges.