Train-bridge Interaction Research Articles

Seismic Retrofit of Monorail Bridges Considering Soil–Pile–Bridge–Train Interaction

Abstract Monorail bridges play an important role in urban transportation networks, and their proper seismic performance is an issue of great concern in earthquake-prone countries. Seismic isolation...

Longitudinal Seismic Response of Train–Bridge Interaction System With Slip in Moderate Earthquakes

Abstract This study assesses the seismic responses of viaduct structures in the Japanese high-speed rail system under moderate earthquake forces considering the slip between tracks and wheels. Equations of motion for the train–bridge interaction system were derived, where the track–wheel interaction was described by the Coulomb friction law. A full train–bridge finite element model incorporating nonslip and stick–slip interaction models was built using commercial finite element analysis software: abaqus. Simulation results indicate that the slip phenomenon might occur under a moderate earthquake and that a conventional nonslip model with an infinitely large friction coefficient is inappropriate. A parametric study revealed that the braking-train-induced slip friction little influenced the bridge response to moderate earthquake forces. The bridge's dynamic motions were dominated by ground motion irrespective of the values assigned as the train's initial speed and track–wheel friction coefficient. A computationally efficient method was proposed for calculating the longitudinal seismic responses of a bridge interacting with a braking train, following the linear superposition principle. As illustrated, this method could be helpful in reliability or uncertainty analysis when a great number of computationally expensive seismic analyses are required for train–bridge interaction systems.

An improved dynamic model of suspended monorail train-bridge system considering a tyre model with patch contact

This study aims to elaborately investigate the dynamic performance of suspended monorail train-bridge system (SMTBS) by establishing an improved train-bridge interaction model considering a tyre model with patch contact. First, to reasonably model the contact behaviour between tyre and bridge, a tyre model with patch contact is established by using the continuous radial spring-damping elements. Subsequently, the stiffness and damping performances of a driving tyre used in the SMTBS are studied based on a full-scale laboratory experiment, and then the parameter identification of the established patch contact tyre model is accordingly conducted with the test data. On this base, an improved integrated train-bridge interaction model considering the tyre model with patch contact is developed by using ANSYS parameter design language (APDL), and its reliability is also validated by the field test. Further, by a comparison of train-bridge dynamic responses between the point-contact tyre model and the patch contact tyre model under different conditions, some obvious discrepancies are pointed out, and the advantage and significance of the patch contact model are also revealed. Finally, by applying the proposed model, the train-bridge dynamic performance is studied systematically when a train travels on the curve bridge, revealing the curve negotiation characteristics of vehicle as well as the bridge vibration performance. Meanwhile, several key design parameters of vehicle subsystem are selected optimally by comprehensively considering all vehicle-bridge dynamic indices. The research results may be beneficial to the dynamic performance improvement and optimal design of the SMTBS.

Running safety assessment of a train traversing a three-tower cable-stayed bridge under spatially varying ground motion

To explore the influence of spatially varying ground motion on the dynamic behavior of a train passing through a three-tower cable-stayed bridge, a 3D train–track–bridge coupled model is established for accurately simulating the train–bridge interaction under earthquake excitation, which is made up of a vehicle model built by multi-body dynamics, a track–bridge finite element model, and a 3D rolling wheel–rail contact model. A conditional simulation method, which takes into consideration the wave passage effect, incoherence effect, and site-response effect, is adopted to simulate the spatially varying ground motion under different soil conditions. The multi-time-step method previously proposed by the authors is also adopted to improve computational efficiency. The dynamic responses of the train running on a three-tower cable-stayed bridge are calculated with differing earthquake excitations and train speeds. The results indicate that (1) the earthquake excitation significantly increases the responses of the train–bridge system, but at a design speed, all the running safety indices meet the code requirements; (2) the incoherence and site-response effects should also be considered in the seismic analysis for long-span bridges though there is no fixed pattern for determining their influences; (3) different train speeds that vary the vibration characteristics of the train–bridge system affect the vibration frequencies of the car body and bridge.

Dynamic effects on a train-bridge system caused by stochastically generated turbulent wind fields

The present paper presents a methodology for evaluating the possibility of derailment of trains running over bridges subjected to crosswinds. The dynamic model consists of a train–bridge interaction coupling system that takes into account the contact interface between wheel and rail from which the contact forces arise. These contact forces are the inputs for the safety criteria that are later used to evaluate derailment. The wind fluctuating component is accurately considered through a stochastic process that generates correlated wind velocity fields, which are later converted into wind loads that are applied to both the bridge and the train. Before evaluating the running safety, the dynamic response of the train–bridge system is assessed to understand the influence of the train speed and wind velocity on it. Then, the running safety is analyzed based on three criteria, namely the Nadal, Prud’homme and unloading indexes, being the influence of the bridge lateral flexibility in the derailment risk also discussed. Finally, the results obtained with the stochastic wind model are compared with those obtained with a simplified discrete gust model proposed by the European normative. The maximum wind velocities, obtained through the stochastic and simplified formulations, for which no derailment criteria allowance is exceeded are computed and a comparative critical analysis between the models is presented.

Finite Element Analysis Framework for Dynamic Vehicle-Bridge Interaction System Based on ABAQUS

This paper presents a unified framework for dynamic analysis of vehicle-bridge interaction (VBI) systems using a commercial finite element software suite (ABAQUS[Formula: see text]). This framework can provide bridge designers and engineering practitioners with a general platform to analyze the coupled system with high modeling efficiency and accuracy in modeling and outputting. Moreover, it has readily available nonlinear material/element models and nonlinear dynamic analysis functions for complex structures. This analysis framework was first validated with a classical VBI problem involving a sprung mass moving on a simply supported beam, whose closed-form solution is readily available. Validation for the application on complex structure was then presented with a typical 16-car Japanese high-speed train (Shinkansen) and a three-block bridge. The cars comprised car bodies, bogies and wheelsets, which were all modeled as rigid bodies and which were connected with springs and dashpots. The bridge was modeled with typical three-dimensional solid elements. Interaction between wheelsets and tracks was realized using the penalty method. Rail irregularity was also considered in the analysis. The consistency between calculated dynamic responses and field experiment data of certain pre-specified observation points validated the proposed method. Furthermore, ease in analyzing VBI problems involving nonlinear material properties and with high spatial resolutions was demonstrated with a classical cracked beam problem: a point mass moving on a simply supported cracked beam. Both linear and nonlinear crack models were employed. The former model assigned crack surfaces with a mechanical contact property and showed its accuracy in comparison to the reference model. The latter assigned a nonlinear material model in crack-prone zones and illustrated the potential applicability to dynamic crack propagation simulation in VBI problems. The present framework was further applied to seismic response analysis of a train-bridge interaction system involving material nonlinearity and separation between track and wheel under a strong earthquake.

Stochastic Analysis of Train–Bridge System Using the Karhunen–Loéve Expansion and the Point Estimate Method

This paper presents a new method for analyzing the dynamic behavior of train–bridge systems with random rail irregularity aimed at its simplicity, efficiency and accuracy. A vertical train–bridge system is considered, in which the bridge is regarded as a series of simply supported beams, and the train is regarded as a multibody system with suspensions. The Karhunen–Loéve expansion (KLE) is used to simulate the stochastic vertical rail irregularities, and the mean and standard deviation of the system response are calculated by the point estimate method (PEM), based on the Gaussian integration and the dimension reduction method. The proposed KLE–PEM method, which combines the key features of the KLE and PEM, is validated by comparing the results obtained with existing ones. The Monte Carlo simulation (MCS) is used to verify the rationality of the results obtained by the KLE–PEM approach. The results show that the KLE–PEM approach can accurately calculate the response of the vertical train–bridge interaction system with random irregularity. This paper further discusses the responses of the train and bridge system with different speeds for the train.

Approaches for predicting the probability of failure of bridges subjected to high-speed trains

The scope of this paper is to evaluate different approaches for the prediction of the probability of failure of uncertain railway bridges subjected to high-speed trains. The peak acceleration of a bridge, which is commonly the governing response quantity for dynamic bridge design and failure, depends strongly on the type of train and the train speed. Since in many cases the critical speeds related to response maximums are below the design speed and failure, and during operation the speed varies up to the design speed, the assessment of the probability of failure is not straightforward. In this contribution, several more sophisticated measures of the probability of failure of the bridge-train interaction problem are proposed, considering the peak acceleration as a function of the speed in a certain interval and the distribution of the actual train speed. These measures are tested on two random test bridges, taking into account the main sources of uncertainty, i.e. damping, track irregularities, and the environmental impact. The mechanical model used for the prediction of the dynamic bridge response is composed of a beam bridge crossed by a planar mass-spring-damper model of the train. In this simplest approach that considers explicitly dynamic bridge-train interaction, random irregularity profiles capture the effect of track irregularities. It is shown that in certain speed intervals the predicted probability of failure strongly depends on the underlying measure of the probability of failure. In the first example bridge, whose response is governed by a pronounced resonance peak, exceedance of the serviceability limit state is predicted by all measures at virtually the same speed. The second example problem, where track irregularities lead to considerable response amplifications, only some of the measures predict failure. The results of this study may serve as an impulse for a more in-depth discussion on the appropriate prediction of the probability of failure of bridge-train interaction.

An efficient analysis framework for high-speed train-bridge coupled vibration under non-stationary winds

The consideration of train-bridge system under winds has been attracted extensive attentions, but the winds are typically treated as stationary. This stationary assumption clearly presents a departure from the field observations during extreme storms (e.g., tropical cyclones, thunderstorms and tornadoes). The assurance of structural safety and reliability requires accurate modeling of the non-stationary features in the coupled high-speed train-bridge vibration system. In this study, an efficient analysis framework for high-speed train-bridge coupled vibrations under non-stationary winds based on the pseudo excitation method (PEM) has been developed, in which the non-stationary winds were transformed into a series of pseudoharmonic excitation vectors. The high simulation fidelity and computational efficiency of the established analysis framework were verified based on a case study where the train run over a seven-span continuous girder high-speed railway bridge. A number of transient durations and maximum wind speeds associated with various extreme events are investigated to comprehensively examine the non-stationary effects on the high-speed train-bridge coupled vibrations. It has been demonstrated that the non-stationary characteristics of winds presented important contributions to the dynamic performance of the coupled train-bridge interaction system.

Nonlinear dynamic analysis of Qom Monorail Bridge considering Soil-Pile-Bridge-Train Interaction

Railway tracks experience has shown that considering the effects of Soil-Structure Interaction (SSI) especially for soft soil sites is necessary. These effects can also be important for monorail bridges on soft soil beds. The main aim of this study is to investigate the effects of Soil-Pile-Bridge-Train Interaction (SPBTI) on the Qom Monorail Bridge (QMB) responses. In spite of many studies on the effects of monorail train-bridge (fixed-base structure) interaction, very little information is available in the literature on the effects of monorail trains on SPB systems. In this paper, an advanced three-dimensional (3D) continuum finite element analysis of QMB subjected to train moving loads was developed. The SPBT models have been validated using three case studies (two bridge-monorail train studies and a soil-pile-structure study) available in the literature. The maximum displacements of the guideway beam at the different train speeds were obtained for various SPBT system conditions. The effects of the stiffness and thickness of the soil, the bridge span length, and the amplitude, length, and geometry of the train loading on the critical speed of the SPBT system are discussed in detail. Finally, the results have been synthesized into simple design charts to select the appropriate straddle-type monorail train and determine its critical speed for a particular soil-bridge condition. In addition, a new simple method for simulating the behavior of the finger-bands (as one of the excitation source of vertical bridge vibrations) in commercial software was presented. The results show that the position of a monorail train bogies plays an important role in determining critical speed so that with uniformity the spacing between the bogies decreases the critical speed in the vertical direction.

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.

Dynamic Response of High Speed Train Moving on Consecutive Bridges

This research demonstrates how to analyse the dynamic response of a high-speed train moving over consecutive bridges. The authors explain in detail how to apply the uncoupled iterative method to consecutive bridges, by deriving the complete motion history for one bridge segment at a time, using the solution of the train as an initial condition for the next bridge. This algorithm is a highly cost-effective approach to analysing the train-bridge interaction for a high speed railway (HSR). The authors perform this analysis on two existing bridges: a simply supported Taiwan HSR bridge, and a three-span continuous Korea HSR bridge. The results show that both types of bridges are capable of supporting HSR trains at speeds up to 400 km/h with negligible carbody displacements and accelerations. This speed is greater than the current service speed of 300 km/h.

On the optimal strategy of stochastic-based reliability assessment of railway bridges for high-speed trains

The scope of this paper is to evaluate the performance and computational efficiency of various stochastic simulation methods for a stochastic based reliability assessment of railway bridges subjected to high-speed trains. Depending on the degree of sophistication, application of crude Monte Carlo simulation to a realistic mechanical model of the uncertain bridge-train interacting dynamical system can be prohibitively expensive. Thus, three alternative stochastic methods, i.e. line sampling, subset simulation, and asymptotic sampling, are tested on two example problems. These examples represent two classes of bridges with different dynamic response characteristics. While in the one class of bridges distinctive resonance peaks govern the dynamic peak response, the random response amplification of the second group of bridges is primarily induced by track irregularities. The studies are conducted on a simplified mechanical model, composed of a plain beam representing the bridge and a planar mass-spring-damper system representing the train. This modeling strategy captures the fundamental characteristics of dynamic bridge-train interaction, and thus, facilitates the desired assessment of the stochastic methods with reasonable computational effort. It is shown that both line sampling and subset simulation reduce significantly the computational expense for the first class of bridges, while maintaining the accuracy of the predicted bridge reliability. To ensure accuracy and efficiency, these methods need to be modified when applied to systems where track irregularities dominate the random response. For the latter class of bridges, subset simulation proved to be a suitable method for assessing the reliability of this dynamic interacting system when appropriately modified.

Validation of a vertical train–track–bridge dynamic interaction model based on limited experimental data

This article focuses on the calibration and validation of a numerical model of a steel-concrete composite railway bridge considering the vehicle–track–structure interaction. The calibration of the numerical model of the bridge-track system involved the use of a genetic algorithm, and was based on modal parameters obtained from an ambient vibration test, which was performed with significant limitations regarding the sensors placement. The model updating results demonstrated a considerable degradation of the ballast in the interfaces between the decks, particularly in the longitudinal joint between half-decks, essentially due to the movements induced by rail traffic. The validation of the dynamic behaviour of the train-bridge system was performed based on the comparison between experimental responses obtained from a dynamic test under railway traffic and numerical responses, based on train–bridge interaction analysis. A good agreement was achieved between experimental and numerical records regarding the displacements at the supports and deck, and the accelerations at the deck. In case of the deck accelerations, the damping coefficient values adopted in the dynamic analysis, estimated from the logarithmic decrement method, were decisive for reaching the best adjustment between experimental and numerical records.

Uncertainty and sensitivity analysis for train-ballasted track–bridge system

ABSTRACTThis paper is devoted to present an integrated uncertainty and sensitivity procedure for use in performance assessments for train–bridge interactions. Firstly, a train-ballasted track–bridge dynamic model with proper consideration of the nonlinear wheel–rail contact geometries is constructed in three-dimensional space; and then the uncertainties related to this system are illustrated, in which the material, geometry, structural damping of bridge superstructure and the temporal–spatial ergodic properties of track irregularities are highlighted; and furthermore, the probability density evolution method accompanied with an advanced number theoretical method is introduced to describe the transmission of probability from excitation input to response output for the uncertainty analysis; finally, the key factors affecting the dynamic behaviours of system components are clarified by the variance-based global sensitivity analysis which has taken the interactions between factors into account. Numerical examples show that the uncertainty analysis algorithm is of high efficiency and accuracy by comparing with the robust Monte-Carlo simulation method; the variability of bridge parameters and track irregularities show remarkable effects on the dynamic indices; and the most sensitive factors are rather different with regard to varied dynamic indices.

Vector Form Intrinsic Finite Element Method for Analysis of Train–Bridge Interaction Problems Considering The Coach-Coupler Effect

In this paper, the vector form intrinsic finite element (VFIFE) method is presented for analysis the train–bridge systems considering the coach-coupler effect. The bridge is discretized into a group of mass particles linked by massless beam elements and the multi-body coach with suspension systems is simulated as a set of mass particles connected by parallel spring-dashpot units. Then the equation of motion of each mass particle is solved individually and the internal forces induced by pure deformations in the massless beam elements are calculated by a fictitious reverse motion method, in which the structural stiffness matrices need not be updated or factorized. Though the vector-form equations resulting from the VFIFE method cannot be used to compute the structural frequencies by the eigenvalue approach, this study proposes a numerical free vibration test to identify the bridge frequencies for evaluating the bridge damping. Numerical verifications demonstrate that the present VFIFE method performs as accurately as previous numerical ones. The results show that the couplers play an energy-dissipating role in reducing the car bodies’ response due to the bridge-induced resonance, but not in their response due to the train-induced resonance because of the bridge’s intense vibration. Meanwhile, a dual-resonance phenomenon in the train–bridge system occurs when the coach-coupler effect is considered in the vehicle model.

Justification of the bridge span vertical stiffness on high-speed railways

When designing bridges on high-speed railways, special attention should be paid to ensuring the safety of train traffic and the comfort of passengers. Excessive structure deformations (both elastic and non-elastic) result in unfavorable irregularities in the train movement pattern on the bridge and so can lead to violation of the traffic safety requirements as well as to vibration and acceleration of the train body, which is inadmissible due to its effect on the human body or the transported goods. In this paper, based on numerical simulation, the results of the study of the motion of a high-speed train along bridge structures of the dynamic bridgetrain interaction was performed with respect to various models of high-speed trains running along the bridges. The obtained dependences help to provide a practical assessment of high-speed passenger car dynamics and passenger comfort under the most unfavorable conditions, when the train is running along a multi-span bridge. For these purposes, the dependences of the admissible value of the relative vertical deflection are presented, based on the envelope curves that show the typical dynamic passenger car parameters (natural frequency of car oscillations) and Corresponding with their oscillations on the multi-span girder bridges with various lengths

Vehicle–bridge interaction analysis modeling derailment during earthquakes

A realistic simulation of train derailment is crucial when assessing the safety of a train running over a bridge during earthquake excitation. This paper presents a seismic vehicle–bridge interaction analysis that simulates directly different wheel–rail contact states including flange contact, detachment, uplifting, wheel–rail climbing-up, recontact, and ultimately, derailment. The proposed model determines the contact point and the direction of the contact forces over practical nonlinear profiles of wheels and rails. It then classifies the wheel–rail contact, as double contact, single contact or double detachment, and tackles accordingly the kinematics. The modeling of the wheel–rail contact along the normal direction hinges upon the principles of nonsmooth dynamics and accounts for continuous contacts of finite duration, impacts (instantaneous duration) and transitions from continuous contacts to detachments. The modeling of the tangential contact forces follows the nonlinear creep theory. The results verify that well-known force-based metrics such as derailment factor and offload factor yield conservative estimations of train operational safety. The analysis stresses the key role of flange contact under a large contact angle that could lead to the detachment of the other wheel of the same wheelset, and underlines the importance of a more realistic train–bridge interaction modeling during earthquakes. For the examples examined, which involve a complete three-dimensional vehicle running on simply supported bridge units, derailment occurs when a wheel rolls over the rail head (wheel–rail climbing-up). The results unveil that both the amplitude and the frequency of the earthquakes are important to the safety of trains running over bridges.

Impact of track irregularities and damping on the fatigue damage of a railway bridge deck slab

The structural response of reinforced concrete slabs in railway bridges is strongly influenced by local dynamic effects and, therefore, detailed calculations of internal forces have to be performed for a realistic fatigue assessment. In this context, this paper discusses the influence of track irregularities and modal damping coefficients in the dynamic response and fatigue behaviour of a railway bridge deck slab. For that purpose, track irregularities were measured (at different instants of time) and damping coefficients were determined based on acceleration records for passing trains in a real bridge. The bridge behaviour was calculated using a train–bridge interaction methodology, considering calibrated numerical models of the viaduct and the train. The fatigue damage was quantified through the linear damage accumulation method. This methodology allowed to understand the way track irregularities and damping coefficients affect the magnitude of applied bending moments and fatigue damage in the slab.

Simulation of train–bridge interaction under wind loads: a rigid-flexible coupling approach

ABSTRACTThis study proposed a rigid-flexible coupling method to simulate the train–bridge vibration under the actions of wind loads. Specifically, the numerical models of a rigid train and a flexible bridge were first established in the Multibody Dynamics Software SIMPACK and the Finite Element Software ANSYS, respectively. The bridge model was then integrated, using the virtual rigid body as an intermediate object, into the SIMPACK as a flexible body through the interface module FlexModal. The wind loads were applied to the coupled train–bridge system in the SIMPACK, and then the dynamic responses were obtained. The accuracy and efficiency of the proposed rigid-flexible coupling approach was verified by calculating the responses of the train–bridge system under various train speeds and comparing the results with those from FlexTrack module. The Xijiang Bridge on the Nanning–Guangzhou railway was employed as a case study to evaluate the dynamic indices under various combinations of the train and wind speeds.