Train–track–bridge dynamic interaction is a fundamental concern in the field of railway engineering, which plays an extremely important role in the optimal design of railway bridges, especially in high-speed railways and heavy-haul railways. This paper systematically presents a state-of-the-art review of train–track–bridge dynamic interaction. The evolution process of train–bridge dynamic interaction model is described briefly, from the simplest moving constant force model to the sophisticated train–track–bridge dynamic interaction model (TTBDIM). The modelling methodology of the key elements in the TTBDIM is systematically reviewed, including the train, the track, the bridge, the wheel–rail contact, the track–bridge interaction, the system excitation and the solution algorithm. The significance of detailed track modelling in the whole system is highlighted. The experimental research and filed test focusing on modelling validation, safety assessment and long-term performance investigation of the train–track–bridge system are briefly presented. The practical applications of train–track–bridge dynamic interaction theory are comprehensively discussed in terms of the system dynamic performance evaluation, the system safety assessment and train-induced environmental vibration and noise prediction. The guidance is provided on further improvement of the train–track–bridge dynamic interaction model and the challenging research topics in the future.

This paper presents a method to analyse the influence of multi-pier settlement on the train–track–bridge coupled dynamic system, and to determine the safe value of the continuous multi-pier settlement for simply supported girder bridges in Chinese high-speed railways. Firstly, the mapping relationship between the multi-pier settlement and the rail deformation is derived theoretically. Then, taking the superposition of the rail deformation and the track random irregularity as excitation, the variations of vehicle dynamic indices are analysed based on the train–track–bridge dynamic interaction theory. Further, the relationships between the pier settlement and the change amounts of vehicle dynamic indices are obtained. The multi-pier settlement safe value is determined according to the limits of vehicle dynamic indices. Results show that the rail deformation caused by multi-pier settlement agrees well with the settlement data. When passing through the 32.6 m-long simply supported girder bridge with multi-pier settlement, the train suffers a low-frequency excitation. Only considering the influence of pier settlement, the settlement value difference between two adjacent piers should be less than 26.3 mm at China’s highest operation speed of 350 km/h from the perspective of dynamics, which is much larger than the pier settlement limit in the current code for Chinese high-speed railways.

Sichuan–Tibet Railway plays a vital role in China’s transportation system by connecting Tibet and Central China, whose design and construction are extremely difficult due to numerous seismic zones and deep valleys along the railway line. This paper systematically presents a framework to control seismic vibration of T-beam bridges with high-piers in Sichuan–Tibet Railway using tuned mass dampers (TMDs). Firstly, a finite element model of the widely used high-pier bridge is established to reveal its vibration modes subject to earthquakes. On this basis, optimal installation locations and optimal parameters of the TMDs are determined. Then, vibration reduction effects of the designed TMDs on the high-pier bridge subject to actual earthquake samples are investigated and compared with that of using some other vibration absorption measures. Finally, a detailed train-track-bridge dynamic model with attached TMDs is established to study the effects of the designed TMDs on the seismic responses of the running trains. The results indicate that, for the high-pier T-beam bridges, the first bending vibration mode of the high-pier is most likely to be excited by earthquakes, which should be restrained. With the designed optimal parameters, the attached TMDs are effective to control seismic vibrations of the concerned high-pier bridges. Tuned mass damper is the best one among all the investigated measures to absorb vibrations subject to earthquakes from the perspective of vibration absorption performance, installation and maintenance.

This paper investigates a more advanced vertical vehicle–slab track interaction model (VTIM) by considering the discontinuity of track slabs, besides, it can be degenerated to the traditional two-dimensional model conveniently. Moreover, a cyclic calculation method (CCM) is further developed to solve infinite length calculations. On this basis, the proposed dynamic model and CCM are validated by comparing with the more comprehensive three-dimensional train–track model and fixed-point excitation method. Then, from aspects of probability statistics and frequency analysis, an illustrative example is particularly conducted to comprehensively characterize the dynamic responses of vehicle–slab track systems, in which the representative and realistic rail irregularity sets simulated by the track irregularity probabilistic model are used as the loading inputs. Results show that, with a low consumption of computational time and computer memory, the dynamic results derived from VTIM and CCM have a high accuracy, which indicates that the proposed dynamic model and calculation method can be efficiently and accurately used to analyze train–slab track interactions.

A tuned mass damper (TMD) is a widely used vibration reduction measure in bridge engineering, whose design is based on the modal property of bridge structure. As a consequence, bridge vibrations in certain frequencies are reduced, while vibrations in some other frequencies may be amplified according to the design methodology of the TMD. This paper systematically investigates the influence of these amplified frequencies on the dynamic performance of running trains subject to earthquake loads. Primarily, the design methodology of bridge-based designed TMD (BBD-TMD) is introduced. On this basis, a detailed train–track–bridge coupled dynamic model with attached BBD-TMD is established based on the multi-body dynamics theory and the finite element method. Finally, aiming at a practical engineering problem in China, the influence of BBD-TMD on running trains subject to earthquake loads is investigated. The results indicate that, for the bridge structure adopted in this study, the amplified frequency bands are similar to the natural frequencies of the car body in the train system. To design TMDs for railway bridges, the dynamic performance of running trains caused by these external installations should be seriously considered.