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Realistic vibration predictions of railway bridges during high-speed train crossings require reliable dynamic input parameters for the applied calculation model. In particular, the dynamic stiffness and damping properties of the ballast superstructure for the mathematical consideration of the vertical track–bridge interaction (TBI) significantly influence the generated calculation results. However, due to a striking scattering of model-related characteristic values available in the literature, adequate and realistic consideration of the dynamic properties of the vertical TBI in vibration predictions is associated with considerable uncertainties. This uncertainness illustrates the need to determine experimental-based and reliable characteristic values. For targeted and isolated research of dynamic characteristics of vertical TBI, a unique large-scale test facility was developed at the Institute of Structural Engineering at TU Wien, which replicates a section of ballast superstructure on a railway bridge on a scale of 1:1 and excited to vertical movements. This paper presents the essential results and findings from the experiments, focusing on determining the ballast superstructure’s dynamic stiffness and damping characteristics, which can subsequently be implemented in practical applications for vibration predictions. As a result of the experiments, model-related dynamic stiffness and damping parameters are provided to describe the vertical TBI. In addition, the experiments are used to identify destabilization processes occurring in the ballast superstructure as a result of vertical vibrations. The investigations include the vertical TBI’s displacement and acceleration behavior and the track’s settlement behavior due to the entire structure’s vertical movements. These investigations allow for assessing the currently valid, internationally, and nationally normatively prescribed permissible accelerations for railway bridges due to train crossings. The conclusion is that short-term excessive vertical accelerations of the ballast superstructure caused by train passage do not destabilize the ballast bed or considerably change the track position.

Increasing the operating speed of the trains on modern networks necessitates performing dynamic analyses to assess the performance of bridges under passage of trains. The detailed investigation of their responses requires constructing complex computational models capable to take the train–track–bridge interaction effects into account. Such models have successfully been developed; however, employing those elaborated models for practical engineering applications, or to perform studies that require a large number of analyses may become infeasible. Among such situations are conducting probabilistic investigations, screening of entire networks, or sensitivity analyses. These concerns have been addressed by employing simplified models mostly relying on moving load modeling strategy which disregards the train–track–bridge interaction effects. Those neglected contributions can be compensated by implementing additional correction factors. The distribution of loads within track is one of those disregarded effects where a reduction factor is recommended by design guidelines to take its contribution into account. It has been shown that the existing relationship for these reduction factors delivers an acceptable performance for vertical accelerations, while showing a less favorable performance for displacements. Then, a data-driven strategy is adopted in this study to propose easy-to-apply relationships for reduction factors of deflections, due to load distribution within the track. In this context, three different distributive lengths of triangular load footprints have been considered, namely 2.0, 2.5 and 3.0m. The procedure employed has trained and tested for more than 1200 train configurations, comprising conventional, articulated and regular vehicles, and including several tens of thousand data points for each distributive length. The performance observed in the new models revealed a considerable improvement with respect to the existing relationship.

In this paper, the mechanism of train derailment on bridge is developed by applying the system dynamics stability concepts. The theory of energy random analysis for train derailment on bridge is put forward. The contents of the theory are as follows: (1) establishing vibration equation set for the train–bridge system; (2) determining exciting source of transverse vibration of the system; (3) method of energy random analysis of transverse vibration of the system; (4) geometric rules of derailment; (5) calculation of the whole process of train derailment on bridge; (6) criteria of energy increment for judging train derailment on bridge. Finally, three cases concerning train derailment on bridges are treated that coincide with actual conditions. Some main conclusions obtained are: (1) insufficient transversal rigidity of bridge is the reason causing train derailment on bridge and (2) enhancing transversal rigidity of bridge is the main preventive measure against train derailment on bridge.

The safety of railway vehicles running on bridges needs to be evaluated in the seismic design of bridges. This study examined the spectral intensity calculated from the lateral vibration of the bridge deck during earthquakes, a Japanese code-based index to measure bridge vibration’s strength. In addition, the effect of the torsion of the bridge deck on vehicle derailment is investigated using a nonlinear vehicle–track–bridge model. The bridge deck torsion increases the derailment risk, especially for bridges with a low natural frequency. The reason lies in that the lateral and torsional deck motions are highly correlated for bridges with lower frequency. Based on this observation, a code-type formula was proposed to evaluate the vehicle running safety including both lateral and torsional motions of the bridge deck. The accuracy of the proposed formula was demonstrated by comparison with vehicle–track–bridge simulation excited by ground motion records. The new procedure overcomes the non-conservative assessment of derailment caused by ignoring bridge torsion.

When an earthquake occurs, railway bridges will suffer from different degrees of seismic damage, and it is necessary to assess the seismic risk of bridges. Unfortunately, the majority of studies were done on highway bridges without taking into account railway bridge characteristics; hence they are not applicable to railway bridges. Furthermore, current research methods for risk assessment cannot be performed quickly, and suffer from the problems of subjective personal experience, complicated calculations, and time-consuming. This paper we use machine learning for earthquake damage prediction and empirical vulnerability curves to represent risk assessment results, creating a rapid risk assessment procedure. We gathered and tallied seismic damage data from 335 railway bridges that were damaged in the Tangshan and Menyuan earthquakes, found six variables that had a substantial impact on seismic risk outcomes, and categorized the damage levels into five categories. It is essentially a multi-classification and prediction problem. In order to solve this problem, four algorithms were tested: Random Forest (RF) Back Propagation Artiifcial Neural Network (BP-ANN), PSO-Support Vector Machine (PSO-SVM), and K Nearest Neighbor (KNN). It was found that RF is the most effective method, with an accuracy rate of up to 93.31% for the training set and 89.39% for the test set. Then this study describes the new procedure in detail for rapidly assessing seismic risk to 269 bridges chosen at random from the sample pool. Firstly, the seismic damage data of bridges are collated, then the seismic damage rating is predicted using RF, and finally the empirical vulnerability curve is drawn using a two-parameter normal distribution function for the purpose of seismic damage risk assessment. The study’s findings can be used as a guide for choosing a machine learning approach and its inputs to build a rapid assessment model for railway bridges.

Accurately identifying the axle loads of the moving train on the railway bridge can provide reliable information for assessing the safety of the train–bridge system. Bridge weigh-in-motion, namely, BWIM, is an effective approach for identifying the positions and weights of the train axles based on the monitored bridge responses. Existing BWIM methods generally focus on identifying the probable value of the axle weights instead of quantifying the identification uncertainty. To address this issue, a novel two-stage train load identification framework for the medium-small railway bridge is developed by combining the virtual axle theory and Bayesian inference. In the first stage, the axle configuration including the axle number, axle spacing and axle weight of the moving train, are estimated according to the modified virtual axle theory in which a clustering algorithm is embedded to automatically determine the axle number. In the second stage, the most probable value (MPV) and the uncertainty of the train axle weight are accurately identified using the Bayesian inference method which takes five types of error patterns into consideration. Finally, the proposed framework is verified using the data from numerical simulations and an in-situ railway bridge. Results show that the proposed framework can improve the accuracy of train load identification after quantifying the uncertainty of estimated axle weights and can confirm the confidence interval of the individual axle weight and gross train weight.