Xiaozhen Li

High-speed train-track-bridge dynamic interactions - Part I: theoretical model and numerical simulation

This paper presents a framework to systematically investigate the high-speed train–track–bridge dynamic interactions, aiming to provide a method for analysing and assessing the running safety and the ride comfort of trains passing through bridges, which are critically important for the design of new high-speed railway bridges. Train–track–bridge interactive mechanism is illustrated. A fundamental model is established for analysing the train–track–bridge dynamic interactions, in which the vehicle subsystem is coupled with the track subsystem through a spatially interacted wheel–rail model; and the track subsystem is coupled with the bridge subsystem by a track–bridge dynamic interaction model. Modelling of each subsystem and each interactive relationship between subsystems are presented. An explicit–implicit integration scheme is adopted to numerically solve the equations of motion of the large non-linear dynamic system in the time domain. Computer simulation software named the train–track–bridge interaction simulation software (TTBSIM) is developed to predict the vertical and lateral dynamic responses of the train–track–bridge coupled system.

Experimental research on noise emanating from concrete box-girder bridges on intercity railway lines

Simply supported pre-stressed concrete box-girder bridges are the most common bridge type found on high-speed railway and urban rail transit lines in China. A field experiment has been conducted on the Pixian Viaduct of the Chengdu–Dujiangyan Intercity Railway, where two kinds of simply supported pre-stressed concrete box-girder bridges with a standard span of 32 m are used, one single track and the other double track. Characteristics of the noise underneath the box-girder, far from the bridge, and near the bridge gap were measured and analyzed in the time and frequency domains during high-speed train passage, as was the vibration of the box-girder’s bottom plate. The variations of noise with distance and train speed at locations 1.5 and 9 m above ground level were measured and fitted using mathematical formulae. A simplified formula to predict near-field bridge-borne noise was proposed and verified. The peak bridge-borne noise frequency and its tonal characteristic at 50 and 63 Hz for the double-track and single-track box-girders, respectively, were interpreted in terms of bridge vibration and sound radiation efficiency, respectively. The vibration/noise transfer function and coherence were evaluated, showing that vibration resonance is more significant than acoustic coincidence and that the former is more important in terms of noise reduction.

A hybrid model for the prediction of low–frequency noise emanating from a concrete box-girder railway bridge

Concrete box-girder bridges are widely used on high-speed railway and urban rail transit lines; however, the low-frequency noise generated by these systems has not been intensively studied. The prediction of bridge-radiated noise is a complicated procedure and can require prohibitively long computational times. This paper presents a hybrid finite element and statistical energy analysis (hybrid FE–SEA) procedure for the prediction of bridge-radiated noise, with the aim of reducing computational time while still guaranteeing accuracy. A simplified train–bridge coupling model is first introduced and solved in the frequency range 20–200 Hz; the wheel–rail interaction force is calculated and taken as the vibration excitation. The hybrid FE–SEA model is then constructed, in which the rail and ballastless track are modeled as the SEA subsystems and the bridge girder components as the FE subsystems. The bridge-radiated noise is finally estimated by considering each vibrating component of the bridge as a flat plate. The procedure is applied to predict the vibration and noise emanating from a simply supported concrete box-girder bridge with a standard span of 32 m, and the computed results are compared with those obtained from in-situ measurements. The numerical results are in good agreement with measured data, and comparisons between computed and measured results reveal that the noise radiation from adjacent spans needs to be considered at a perpendicular distance of 25 m from the track’s centerline. Furthermore, the vibration transmission mechanism and the acoustic contribution performance are investigated, based on the validated numerical model. The results show that the vibrational energy of the top slab has the highest value; however, the vibration of the flange cannot be ignored. Therefore, the top slab and the flange, which may respectively account for 50% and 25% of the overall noise contribution at far-field points, should be given priority when formulating noise-mitigation measures.

Influences of Soil-Structure Interaction on Coupled Vibration of Train-Bridge System: Theoretical and Experimental Study

A numerical solution for the dynamic response of train-track-bridge coupled system taking into account the influence of soil-structure interaction is studied and verified by field experiments. A three-dimensional vehicle–track-bridge coupling dynamics model is developed, in which the vehicle subsystem, the track subsystem and the bridge subsystem are coupled through wheel-rail interaction and track-bridge interaction, respectively. The soil-structure interaction between the bridge foundation and the soil is simulated by spring stiffness exerted on group-pile foundation. In a case study, the dynamic responses of a high-speed train and a continuous beam bridge are calculated by three models, that is fixed-base model, equivalent-stiffness model and the proposed whole-pile model. The comparison of simulated and experimental results show that soil-structure interaction has significant influence on the lateral dynamic response of the bridge; The whole-pile model is proposed to study the coupled vibration of bridge and vehicle, which gives more reasonable simulation result than the other two models.

Vehicle-Induced Lateral Vibration of Railway Bridges: An Analytical-Solution Approach

AbstractThe lateral vibration of railway bridges induced by moving trains has traditionally been solved through numerical integration. Although it provides practical prediction, the numerical approach does not explicitly reveal the underlying driving mechanism of the train–bridge interaction. In this paper, a closed-form solution is derived for the lateral vibration of a simply supported bridge subjected to hunting forces from running wheel sets. Through complex Fourier expansion, this solution leads to the formulation of three influential factors with explicit physical meanings, namely, the effective unit moving load on the bridge, the arrangement of all moving wheel sets, and the frequency response function of the bridge. On the basis of these factors, a simplified formula to estimate the maximum vibration of the bridge is proposed. The closed-form solution and the simplified formula are validated through comparison with results from numerical integration. The resonance conditions of the bridge due to m...

Vibrational and acoustical performance of concrete box-section bridges subjected to train wheel-rail excitation: Field test and numerical analysis

For the sustainable development of high-speed railway (HSR) networks, it is becoming increasingly important to tackle usability problems, one of which is the bridge noise generated by high-frequency vibrations of bridge members owing to train wheel-rail excitation. Although concrete box-section bridges predominate in HSR infrastructures, their vibrational and acoustical performance has not been well studied. Field tests on two concrete box-section bridges, one dual-track and the other single-track, are carried out simultaneously during high-speed train passbys. Time-history and spectral characteristics of vibration velocity levels (VVLs) and sound pressure levels (SPLs) are measured and analyzed. Measured data show that the highest peaks of VVLs and SPLs for dual and single-track bridges appear at 50 and 63 Hz, respectively. High-frequency vibrations are independent of longitudinal location for bridges with uniform cross-section. The average difference between the magnitudes of VVLs (with a reference velocity of 10_9 m/s) and SPLs (with a reference pressure of 2_10-5 Pa) is about 28 dB at each frequency. A train-track-bridge dynamic interaction model is applied to determine the vibration of bridge members and the statistical relation between VVL and SPL is used to estimate the near-field bridge noise. The computed results match the measurement results. The cross-sectional bending vibration modes of box-section bridges are of two types: a top-slab-dominated mode and a bottom-slab-dominated mode. Numerical analyses show that the levels of vibration and associated noise are jointly determined by the wheel-rail contact force and cross-sectional bending vibration modes, which reach their highest peaks when the modal frequencies coincide with the frequencies of the wheel-rail contact force at high values. Adjusting the cross-sectional bending vibration modes to the frequency range of the wheel-rail contact force at low values is a feasible method to mitigate bridge vibrations and noise; for example, numerical results show that the addition of a third web in the center of the bridge cross section is effective.

Analysis of bridge response to barge collision: Refined impact force models and some new insights:

This article presents finite element simulations of bridge–barge collision using a representative Jumbo Hopper barge model and a bridge pier model with a squared cross section. Based on the simulation results and also the conservation principles of kinetic energy and linear momentum, refined simplified impact force history models for both elastic and inelastic collisions are developed. The simplified force models take into account the influences of barge impact velocity, barge loading tonnage and pier size. The proposed force models are validated through comparisons on the impact force time histories and response spectra with other impact force models. With a three-span continuous girder bridge, the participation of different bridge modal responses and modal combination rules are also investigated. A new modal combination rule is proposed for quantifying the maximum responses due to barge impact load.

Nonstationary Random Vibration Performance of Train-Bridge Coupling System with Vertical Track Irregularity

In order to study the random vibration performance of trains running on continuous beam bridge with vertical track irregularity, a time-domain framework of random analysis on train-bridge coupling system is established. The vertical rail irregularity is regarded as a random process. A multibody mass-spring-damper model is employed to represent a moving railway car and the bridge system is simulated by finite elements. By introducing the pseudo excitation algorithm into the train-bridge interaction dynamic system, expressions of the mean value, standard deviation, and power spectral density of the nonstationary random dynamic responses of bridge and vehicles are derived. Monte-Carlo simulations are implemented to validate the presented method. A comprehensive analysis of the train-bridge coupling system with vertical track irregularity is conducted focusing on the effect of the randomness of the vertical rail irregularity on the dynamic behavior of the running train and the three-span continuous concrete bridge. Moreover, stochastic characteristics of the indicator for assessing the safety and the riding quality of the railway cars running on continuous beam bridge are carried out, which may be a useful reference in the dynamic design of the bridge.

Coupled Vibration Analysis of Railway Continuous BEAM Bridge and Vehicles with Soil-Structure Interaction

Simulation computation of vehicle-bridge coupling vibration and field experiment are carried out in a long-span continuous beam bridge of an intercity railway. And the effect of soil-structure interaction on the coupled vibration of continuous beam bridges and vehicles under high speed vehicle load was discussed in this paper. With BDAP V2.0(Bridge Dynamic Analysis Program), which is certificated by National Copyright Administration, the natural frequencies and dynamic responses of the bridge under vehicle load are calculated by using a more complex bridge FEM model(whole-pile model), which can take account of the interaction of lateral displacement and bending angle on group-piles. In order to assess the influence of soil-structure interaction on bridge dynamic response and evaluate the actual dynamic response of a long-span continuous beam high speed railway bridge, dynamic loading tests were made at the speed varying from 200km/h to 380km/h to get the vertical dynamic displacements in the mid-span and the lateral and vertical amplitude and acceleration of some typical points in the beam and pier. With a comparison of simulation computation results of different bridge FEM models and field experiment results, we can draw some conclusions, which is beneficial to research and design of long-span continuous beam bridges in high speed railway: Compared with commonly used consolidation model and equivalent-stiffness model, the dynamic response of the bridge with whole-pile model, especially the lateral dynamic response, varies a lot by considering soil-structure interaction. While the maximum dynamic accelerations get lower, the maximum lateral amplitudes become higher. And the results of field experiment show that with whole-pile model, a precise and reasonable simulation computation result can be gained because soil-structural interaction is also taken into account. For a high speed railway bridge located in soft ground with group-piles foundation, whole-pile model is proposed to analysis the coupled vibration of vehicle and bridge.

Three-dimensional random vibrations of a high-speed-train–bridge time-varying system with track irregularities

Three-dimensional random vibrations of a high-speed-train–bridge time-varying system with track irregularities are studied in this paper. The rail irregularity is regarded as a random process. By extending the pseudo-excitation method, three kinds of rail irregularity are transformed into a pseudo load vector of the coupled system. A finite element model is used to describe the bridge and a spatial multi-body mass–spring–damping model is adopted to represent a moving railway car. Monte Carlo simulations are implemented to validate the presented method. A detailed case study on the train–bridge coupled system is conducted; it is focused on the effects of three kinds of rail irregularity on the stochastic characteristics of the dynamic responses of the system. The effect of randomness on the level of safety and the riding comfort created by the coupled system are also discussed. The results demonstrate that track irregularities may have a greater impact on the transverse response of the coupled system than on the vertical responses.