Track Bridge System Research Articles

Experimental and numerical investigations of the dynamic responses of low and medium speed maglev train-track-bridge coupled system

In recent years, low and medium speed maglev (LMSM) transportation system has been greatly promoted in China to meet different social demands. Accordingly, a LMSM train using levitation frames with mid-set air springs has been developed, and it is necessary to investigate the dynamic characteristics of its train-track-bridge coupled system. First, environmental vibration tests were conducted on the bridge to study its self-vibration characteristics. Then, field tests were carried out on this coupled system within the 60 km/h speed range. Subsequently, a three-dimensional rigid-flexible coupled dynamics model of the system was developed to evaluate its dynamic behavior at higher speeds. Results show that the first-order vertical and lateral bending frequencies of the bridge are 7.32 Hz and 6.00 Hz, respectively; train speed has little effect on the vertical dynamic displacement of the track-bridge system, yet has a significant impact on the acceleration responses of the coupled system; key dynamic indicators of the bridge meet the relevant requirements; the vertical ride quality of car body is not so good as that in the lateral direction, but on the whole the train has “Good” ride quality. These results can provide a useful reference for the optimal design of LMSM transportation systems.

Effect of seismic isolation on random seismic response of High-Speed railway bridge based on probability density evolution method

In order to evaluate the effect of seismic isolation on random seismic response characteristics of a track-bridge system, in this paper, a three-dimensional detailed nonlinear dynamic model consists of rail, CRTS II slab ballastless track, high-speed railway simple supported bridges, isolated bearings, piers, pile foundations from top to bottom, is established by OpenSEES. The stochastic process of ground motion constructed by the random harmonic function is taking as random excitation, and the probability density evolution method (PDEM) is applied to investigate and analyze the system from the random perspective. On this basis, the influence of FPB bearing and the different FPB parameters (such as equivalent radius) on the random seismic response of the track-bridge system is studied. Thereby, aplenty probabilistic information (probability density evolution function, mean value and standard deviation) can be gained of seismic response of isolated bridges with different isolation parameters and non-isolated bridges of the high-speed railway track-bridge system under the excitation of random earthquakes by case study. Through the comparison of random seismic responses of non-isolated bridge and isolated bridges with different parameters under random ground motions, the favorable and unfavorable effects of seismic isolation for high-speed railway bridges are explored and demonstrated from a random point of view. The comparison of the random seismic response under different cases are discussed and significant outcomes are drawn. Results show that: The use of isolation bearing can reduce the response of track structure and pier, but meanwhile, increase the response of bearings. The change of the equivalent radius of the isolation bearing has no obvious influence on the random response of the pier and the track structure, but will to some extent bring the change of the bearing response. The results can be used for the seismic design and maintenance of the railway high-speed bridge.

The seismically induced failure sequence of multiple components of high-speed railway bridges under different earthquake intensities

Though seismic vulnerability analysis of highway bridges is mature, there is little corresponding research on high-speed railway (HSR) bridges. The seismic vulnerability analysis of HSR bridges is very different to and more difficult than for highway bridges because the multiple components of the track structure are very complex. To fill this research gap, the authors establish a finite element (FE) model of an HSR bridge with the China railway track system II (CRTS II), which includes sliding layers, cement asphalt (CA) layers and fasteners, base plates, track plates and rails. Analytical results show that seismic responses of multiple bridge components have a linear correlation. Thus, the overall track-bridge system can be assumed to operate like a serial system. Here, the seismic response and vulnerability of various bridge components are first analyzed using the incremental dynamic analysis (IDA) method. Afterwards, the failure sequence is found by comparing the seismic vulnerability of critical bridge components. Finally, the seismic vulnerability of the overall track-bridge system is evaluated according to the upper and lower first-bounds. Results illustrate that the system vulnerability of HSR bridges, which is very different to that of highway bridges, is mainly determined by the sliding layers and fixed bearings. In particular, the serious damage of a sliding layer is caused by the uncoordinated deformation of beam ends, and fixed bearings may break down when they are exposed to strong earthquakes. The overall track-bridge system is prone to severe seismic damage when peak ground acceleration (PGA) is larger than 0.2 g.

Dynamic Performance of the LMS Maglev Train–Track–Bridge System Under Uneven Settlement for Two Typical Bridges

To investigate the dynamic performance of the low-to-medium-speed (LMS) maglev train and bridge system under uneven ground settlement, a refined vertical dynamic interaction model of the LMS maglev train–track–bridge system with uneven settlement is proposed. Firstly, the numerical model is verified based on the field test. Secondly, the dynamic performances of the system induced by uneven settlements are numerically analyzed. Furthermore, numerical studies are carried out to investigate the effect of various uneven settlement types, to compare the performances of the two typical bridges, and to assess the contribution of the F-rail in the presence of uneven settlement. The results show that uneven settlement has a significant enlargement effect on the dynamic responses of the car body and levitation module, but a very weak influence on the bridge. Both the patterns of uneven settlement and bridge types significantly affect the dynamic response of the maglev train to various levels. The numerical model excluding the track structure will overestimate the dynamic responses of the levitation module. It is suggested that the dynamic interaction model for the maglev train–track–bridge system be selected to simulate the influence of uneven settlement for better accuracy.

A Modified Numerical Substructure Method for Dynamic Analysis of Vehicle–Track–Bridge Systems

This paper presents a modified numerical substructure method for simulating the dynamic response of vehicle–track–bridge (VTB) systems. The method can be used to analyze large-scale VTB systems accurately and efficiently. Based on the principle of virtual work, the equations of motion are derived for two separate subsystems, i.e. a small-scale of finely modeled VTB substructure and a coarsely meshed large main bridge subsystem using different level of refinement. Different from the conventional dynamic substructuring approaches, the bridge spans close to the vehicle are modeled in both the main and substructure models, and the contradiction of repeatedly modeling is solved using a “nonlinear force corrector”. A special wheel–rail interaction (WRI) element is used to simulate the fast-moving interaction force between the vehicle and rail. In this way, the two models remain unchanged while the vehicle moves forward, and the computational accuracy is the same as the large-scale purely refined model, while the efficiency is significantly improved, particularly, for the large-scale long VTB systems. Two examples of realistic VTB systems with either smooth or un-smooth rails are used to verify the proposed method. The results demonstrate that the presented method has remarkable advantages of computational efficiency and accuracy, providing a practically useful tool for analysis of large-scale VTB systems.

Applicability analysis of high-speed railway system under the action of near-fault ground motion

Studying the applicability of existing bridge and track systems of high-speed railway in near-fault areas is crucial and urgent, because the current seismic design methods seldom consider the characteristics of the near-fault ground motion. By comprehensively considering the uncertainties in ground motion and structural parameters, a large-sample analysis method for near-faults area was proposed. In addition, an integrated finite element model for beam bridge-track system of high-speed railway was used to calculate the seismic response of the structure under the action of near-fault ground motion. The over-limit state and applicability of seismic response of key components and systems were predicted and evaluated. The analysis results indicate that the statistical characteristics of structural seismic response and over-limit state tend to be stable with increasing number of samples. Under the near-fault ground motion: (i) the piers of high-speed railway are hard to yield (ii) bearings are damaged severely, and (iii) the piers have insufficient shear capacity and the characteristics of structural seismic damage are not in accordance with the concept of ductility design. The sliding layer of the track structure is severely damaged by the transverse and longitudinal ground motions, while the CA mortar layer and fastener are mainly damaged by the transverse ground motion. The applicability of bearings, the anti-shearing behavior of piers, and the inter-layer structure of tracks make it difficult to achieve the goal of the near-fault fortification against ground motion.

Study on the dynamic response correction factor of a coupled high-speed train–track–bridge system under near-fault earthquakes

The extension of high-speed railway construction to earthquake-prone regions has significantly increased the probability of trains encountering an earthquake while running on a bridge. Therefore, it is urgent to explore the applicability of the additional static quality method (ASQM) of train load simulation specified in the Code for seismic design of railway engineering. Based on comprehensively considering the uncertainty of ground motions, this paper builds spatial analysis models for train–track–bridge systems based on ASQM and the moving spring-mass column method (MSMCM), respectively. Next, it calculates the seismic responses of structures under near-fault earthquakes using a large number of samples and evaluates the applicability of ASQM through large-sample analysis. As the analysis results revealed, the statistical characteristics of over-standard ratios tend to stabilize with the increase of sample size. Under near-fault earthquakes, bearing deformation, pier shear strength, and maximum ductility all have high over-standard ratios. The seismic checking computations of bridge structures based on ASQM have failed to meet the applicability requirements, and the calculation results of the seismic responses of track structures are severely distorted. Introducing a reasonable dynamic response correction factor based on ASQM helps to effectively lower over-standard ratios, thus meeting the applicability requirements for the seismic checking computations of bridges.

Relationship between track stiffness and dynamic performance of vehicle–track–bridge system

Track stiffness irregularity is superficially invisible on rail surface, while causes dynamical impact and track deformation when trains running through. Aiming at this issue, this work presents an investigation on the influence of track stiffness on dynamic behaviours of the high-speed vehicle–track–bridge dynamic system. Primarily, a determination method of track stiffness irregularity is analytically deduced, in which a novel solution of deformation of free beam is proposed. Then a high-speed vehicle–track–bridge dynamic interaction model is established based on the vehicle–track–bridge dynamic interaction theory. On this basis, the influence of track stiffness on the dynamic behaviours of the coupled system is investigated both in time domain and in frequency domain. Results show that the distribution of track stiffness in longitudinal direction indeed affects the vibrations of the system. More vibration details of system in full frequency bands can be revealed by considering track elasticity. The most sensitive indicator to different track types is the pitch acceleration of bogie. The wave amplitude caused by length of slab is very small, however its influence on vehicle vibrations is great, indicating that tiny track stiffness change caused by length of slab cannot be ignored in dynamic investigations.

Seismic response of high-speed railway bridge-track system considering unequal-height pier configurations

The unequal-height pier configurations commonly exist in bridge engineering for the adaptation of the varying topography. However, this makes the stiffness of unequal-height piers fluctuating due to the pier's height difference. As piers are the main seismic-resisting components under earthquakes, the irregular stiffness distribution induced by unequal-height pier configurations are unfavorable to the seismic performance of bridge structures. Especially, the high-speed railway (HSR) bridges, which are designed to satisfy strict requirements of structural stability, integrity and smoothness allowing for high velocity, high comfort, high security, are more likely to be adversely affected by the unequal-height pier configuration. Additionally, previous study showed that the track structure that built on the HSR bridge girders is prone to be seismically damaged. Based on this, this paper studies the influence of the unequal-height pier configurations on the seismic displacement responses of HSR bridge-track system, and investigates the damage mechanism. The seismic performance of HSR bridges with different pier configurations are also evaluated from the perspective of probability. Piers with 8 m, 16 m and 24 m are utilized to constitute the symmetric and asymmetric layouts of equal-height and unequal-height pier configurations. Six numerical models of bridge-track system (BTS) are established based on the test data and previous researches. The analysis on seismic responses of six BTS models shows that seismic displacement responses of moveable bearings, sliding layer and shear alveolar rises with the increase of adjacent pier's height difference; It is found that unequal-height piers are more likely to produce large nonuniform displacement responses, which further causes larger displacement responses of components above piers. The moveable bearings are the least fragile in the equal-height pier configuration. However, the sliding layer and the shear alveolar are the most vulnerable with considerable displacement responses in the layout of 8 m and 24 m piers, and become less fragile in the unequal-height pier configuration of 8 m and 16 m piers. In terms of structural safety, the equal-height pier configuration has the least adverse influence on the seismic performance of HSR bridges.

Pseudodynamic Hybrid Simulation of High-Speed Railway Bridge-Track System with Rotational Friction Damper

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.

Impact characteristics of railway bridge with double-block supported track considering carriage oscillation loads

In this study, the impact characteristics of a typical railway bridge with ballastless double-block supported track under moving train considering carriage oscillation load is investigated. The train load is modelled as a constant force superimposed with a harmonic force whose frequency is the heaving oscillation frequency of the carriage. The bridge-track system is discretized and modelled using the double-beam elements connected using the elastic springs and viscous dampers. Numerical computations are conducted to investigate the bending moment impact characteristics of the supporting bridge considering the variations of moving speed and oscillating frequency of the moving load. The result shows that the harmonic loads due to the carriage heaving oscillation will induce some important bending moment impact amplification and peak response offset for the studied bridge in operation.

8 th Symposium on Mechanics of Slender Structures 2019 (MoSS2019)

8 th Symposium on Mechanics of Slender Structures 2019 (MoSS2019)

Vibration Analysis of Coupled Multilayer Structures with Discrete Connections for Noise Prediction

It is often necessary to calculate the vibration of noise from multilayer structures comprising several substructures coupled with discrete connections. A dynamic flexibility method (DFM) is adopted to decouple the multilayer substructures, which allows the interface forces among the substructures to be directly solved using a linear equation of deformation compatibility. The structural vibrations and power flows into each substructure can then be calculated. To illustrate the use of the DFM, a coupled train–track–bridge system for urban rail transit traffic is investigated as a case study. Two infinite plate models are used to model the U-shaped bridge substructure to improve the computing efficiency compared with the finite element models in calculating high-frequency vibration. The applicability of the infinite plate models is discussed in terms of various rail positions on the bridge, the thickness of the rail support blocks, and multiple wheels that interface with the rail. The results show that the Mindlin plate model has similar accuracy but much greater computing efficiency than the finite element models. With the vibration results from the DFM, the associated wheel–rail noise and structure-borne noise from the bridge are then calculated together with a 2D acoustic model. Good agreement is observed between the predicted noises and the measured data.

Analysis of the Vibration Characteristics of Ballastless Track on Bridges Using an Energy Method

Although the high-speed railway (HSR) system has been widely agreed to be a sustainable and convenient means of transportation, the vibration induced has already been deemed an urgent environmental problem. For the sake of investigating the vibration characteristics of the ballastless track on bridges in the HSR system from the point of view of energy, a numerical model of the vehicle–track–bridge coupled system is developed herein and the energy method based on power flow theory is employed. In addition, a corresponding evaluation method of the power flow theory is developed to evaluate the vibration characteristics of the track–bridge system. The conclusions indicate that (1) the vibration energy gradually attenuates from top to bottom of the track–bridge system in its transfer process. Moreover, the attenuation effects are mainly the result of the elasticity and damping effects of the fasteners and the slab mat layer. (2) With increasing slab mat layer stiffness, the vibration energy of the rail slightly decreases; on the contrary, that of the slab track and the bridge obviously increases. (3) With increasing fastener stiffness, the vibration energy of the entire track–bridge system increases. (4) With increasing running speed, the vibration energy of the entire track–bridge system rises obviously. The results reveal that the reasonable stiffness levels of the fasteners and the slab mat layer are 40 to 60 kN/mm and 40 to 60 MPa/m, respectively, under the investigated condition in this work. This work also presents a novel way to study the vibration characteristics of the ballastless track on bridges of HSRs in terms of energy.

Simplified seismic model of CRTS II ballastless track structure on high-speed railway bridges in China

An effective simplified model of CRTS II ballastless track structure is proposed in this paper and is expected to applied into the practical seismic design and analysis of high-speed railway (HSR) bridges in China. The bridge model (BM), as recommended in Chinese seismic design code, simplifies modelling procedures to cater for practical designs and constructions without considering the constraint of track structure on the bridges. Although the BM possesses great computational efficiency, it may produce unreasonable results as compared with the bridge-track system model (BTM) that incorporates the influence of track structure. Nevertheless, the BTM is actually not an effective practical-orientated alternative applied into the seismic design and analysis of HSR bridges due to the demand of massive computation. Therefore, this paper concentrates on the improvement of HSR bridge models applied into the practical seismic design and analysis. A simplified seismic model of China Railway Track Structure II (CRTS II) ballastless track structure on China’s HSR bridges is proposed. The proposed simplified track model is computationally effective and significantly improves the calculation accuracy of the code-recommended BM as it can accurately simulate the longitudinal constraint influence of track structure on bridges. Additionally, the proposed simplified track model can be applied into capturing evaluating performance stateof track structure and judgingearthquake-induced collision of adjacent girders. By comparing seismic responses of the BM, BTM and the bridge-simplified track model (BSTM), results validate that the simplified track model possess computational effectiveness and calculation accuracy.

Nonlinear random seismic analysis of 3D high-speed railway track-bridge system based on OpenSEES

A new nonlinear track-bridge random model was established based on OpenSEES, of which the random seismic responses is systematically studied by using probability density evolution method (PDEM). First, a three-dimensional detail nonlinear random dynamic model of the track-bridge coupled system in high-speed railway is established considering the earthquake as the random excitation. The dynamic model is composed with the rail, CRTS II slab ballastless track, the simple supported bridges, bearing, pier and the pile foundation, from which the random dynamic equation of the random model is formulated. In order to evaluate the seismic performance of track structures from a random perspective, the random seismic responses of high-speed railway bridge under random seismic excitations are investigated and analyzed by using the PDEM. Eventually, the Newmark β integration method and the double edge difference method of TVD format are adopted to obtain the random responses involving the probability functions, which can be translated to get the mean value and the standard deviation of responses. Thus, the abundant probability information of seismic responses of the high-speed railway bridge under random seismic excitations can be obtained. The PDF and CDF of the sliding layer are obtained; thus, the failure probability and reliability of different damage grades of sliding layer are obtained. Discussions and significant conclusions on the random dynamic responses are presented.

Seismic damage features of high-speed railway simply supported bridge–track system under near-fault earthquake

Seismic loads pose a potential threat to the high-speed railway bridges in China, which have been rapidly developing in recent years, especially for those subjected to the near-fault earthquakes. The previous researches on high-speed railway bridges usually concern the far-field earthquake, and the damage of high-speed railway bridge–track system subjected to the near-fault earthquake has not been well studied. In this article, a seven-span high-speed railway simply supported bridge–track system is selected to explore the seismic damage features under the excitation of near-fault earthquake which possesses characteristics of obvious velocity pulse and high-frequency vibration. First, a detailed finite element model of the selected bridge–track system is established and calibrated by the experimental data and design code. Then the low-frequency pulse-type portion and the high-frequency background portion are separated from the selected eight original near-fault records, and a series of nonlinear dynamic analysis is conducted. The results show that the background portion leads to more serious damage of the bridge–track system than the pulse-type portion. Due to the high stiffness of high-speed railway bridge–track system, the background portion with high-frequency vibration characteristic produces the main part of seismic response of system. As for the damage part of system, the weakest component of the bridge–track system is the sliding layer, followed by the shear alveolar.

Seismic Damage Mechanism of CRTS-II Slab Ballastless Track Structure on High-Speed Railway Bridges

China Railway Track System II (CRTS II) slab ballastless track structure is one of commonly adopted track systems on the high-speed railway bridge, which has been found seismically vulnerable under strong earthquakes. To investigate the earthquake-induced damage mechanism of the CRTS II slab ballastless track structure, a nonlinear numerical model of typical 7-span simply supported bridge–track system was established by the finite element software OpenSees and well calibrated by the test data and relative literatures. The nonlinear time history analysis was employed to calculate seismic responses of bridge and track parts under a suite of 10 seismic records. Results demonstrate that the sliding layer in the track structure is the most damage-prone component, especially at the bridge-subgrade transition section, and the shear alveolar may also sustain earthquake-induced fail. By analyzing the seismic damage mechanism of the track structure, this paper reveals that the nonuniform displacement responses of the girders and friction plate at the bridge-subgrade transition section are main factors that result in the extensive damage of the sliding layer and failure of the shear alveolar. However, the damage of these two components are beneficial to reduce the seismic responses of other components in the track structure and protect them from being damaged. From the perspective of engineering safety, the sliding layer and shear alveolar should be rigorously designed because the residual displacement of the sliding layer increases along with the maximum displacement and the failure of the shear alveolar may make the whole track structure failed.

Mapping the relationship between the structural deformation of a simply supported beam bridge and rail deformation in high-speed railways

By considering the effect of the constraints of the rails on the subgrade section on both sides of a bridge, analytical expressions are derived to study the mapping relationship between the rail deformation and changes in the condition of the supporting beam(s), based on the principle of minimum potential energy. Rail deformations in a slab track–bridge system induced by the subsidence of piers and beam faults are investigated in detail. Results are compared with the finite element calculations to assess the main factors that influence rail deformation. The results show that the rail deformation curves under different working conditions (single or multiple pier subsidence and beam faults) determined using the analytical model fit well with those from the finite element models. With increasing subsidence of piers, the rail deformed more significantly in the subsidence zone. Moreover, both the maximum downward and upward deformations of the rail changed linearly with the subsidence of piers. Use of fasteners or a mortar layer with greater vertical stiffness caused the rail to become more irregular.

Reliability assessment of a curved heavy-haul railway track-bridge system

In such curved sections, parameters of a track-bridge system have significant influences on the dynamic performance of the vehicle, track and bridge. Based on two-stage technique, 3D dynamic behaviors of a curved track-bridge system under heavy-haul train are simulated. The stochastic parameters to which the dynamic responses are sensitive are extracted by means of factorial experimental design, and the response surface methodology is adopted to study the influence of each sensitive random parameter on the probability of the failure of system, and the reliability of track-bridge structure in curved sections can then be evaluated. The results show that 1) the damping ratio and elastic modulus of bridge, and the interaction of the thickness of ballast bed and the elastic modulus of beam concrete are the key parameters affecting the reliability of track-bridge system; 2) when the radius of the curved section is less than 800 m, the lateral failure probability of the track-bridge system is increased rapidly; 3) maintaining good track quality can effectively improve the reliability of the track-bridge system; and the heavy-haul bridge designed according to the 30t standard can satisfy the requirements for the operation of train with 35t axle load.