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With the continuous development of high‐speed railway (HSR) construction technology, many HSR bridges are close to near‐fault earthquake zones. Due to the short warning time for earthquakes occurring in these areas, the scene of trains running on the HSR bridges under earthquakes will become more and more common. In order to effectively evaluate the train running safety performance on the HSR bridge under earthquakes, an improved model for the nonlinear simulation of the high‐speed vehicle‐track‐bridge (VTB) coupling system under seismic shaking is proposed. The commercial finite element software was utilized for the general modeling of track‐bridge structure, and nonlinear hysteric behaviors of key components were realized by using the local nonlinearity correction method. By adopting the unconditional stable explicit dynamic integration algorithm and an efficient wheel–rail contact model, an explicit dynamic solution framework is established. It can efficiently solve the nonlinear coupled vibration of the VTB system under earthquakes. Finally, based on the improved model developed in this paper, the influence of hysteretic behaviors of bridge bearings on the nonlinear coupling vibration of the VTB system under near‐fault earthquakes is discussed. [ABSTRACT FROM AUTHOR]

As an important part of the boundary conditions on both sides of the high-speed railway track–bridge system, the seismic response of the subgrade structure is different from that of the bridge structure. This difference has become increasingly significant with the widespread adoption of continuous welded rail technology in bridge construction. Therefore, investigating the seismic response of the bridge system, with a specific focus on the longitudinal constraint effects of the subsequent subgrade track structure, is of paramount importance. Utilizing finite element software, two distinct bridge models are developed: one incorporating the subsequent subgrade track structure and another excluding it. Through nonlinear time history analysis under varying seismic intensities, it is demonstrated that the longitudinal constraint of the subsequent subgrade track structure mitigates the longitudinal displacements and internal forces in critical components of the high-speed railway track–bridge system. Concurrently, acknowledging the heightened complexity and cost associated with post-earthquake repairs of the bridge structure compared to subgrade structure, this study uses a risk transfer connecting beam device. This device can redirect seismic damage from bridge structure to subgrade structure, thereby potentially reducing post-seismic repair expenses for the bridge. [ABSTRACT FROM AUTHOR]

Track irregularity is an important factor affecting the train-track-bridge system interaction, and for the seismic design of the track-bridge system, the study of the law of the influence of track irregularity on the train dynamic effect is of great theoretical significance. Based on this, the finite element models of China railway track structure (CRTS) II plate high-speed railway simple-supported girder bridge and CRH2C high-speed train model are developed and compared with the shaking table test results to verify their validity. Considering track irregularity and earthquake randomness, a sample library of the train dynamic effect of the track-bridge system under earthquake is established, the probabilistic statistical characteristics of the train dynamic effect are analyzed, and the influence level of track irregularity on the train dynamic effect of the track-bridge system under earthquake is studied, and the standard value of track irregularity influence coefficient of train dynamic effect based on probability guarantee rate is proposed. The results indicate that: the influence of track irregularity on the seismic response of bridge structure is slight, with their greatest impact not exceeding 1%. However, it has a significant impact on the seismic response of track structures. The standard values of the sliding and mortar layers' track irregularity influence coefficients are 1.49 and 1.71, respectively, at 0.1 g. Under various peak ground acceleration (PGA) settings, the fasteners' standard values for the track irregularity influence coefficient are less than 1.1. Additionally, the degree of influence of track irregularity on the seismic response of track structure decreases significantly as the PGA increases. [ABSTRACT FROM AUTHOR]

The track structure has an effect on the dynamic characteristics of the bridge structure, which makes the seismic response of the bridge structure complicated. In this paper, an assessment method is proposed to evaluate the seismic risk of bridge structure, including over-limit risk and over-limit scale. Based on a newly proposed simplified model with high accuracy and high computational efficiency, a total of 3000 calculation conditions are analyzed and the sample stability of response is validated to ensure the reliability of the seismic risk analysis. The seismic risks in the longitudinal direction of the track-bridge model are compared with that of the trackless model, and the influence of the constraint effect of China Railway Track System II ballastless track structure on the seismic risk of the structure is obtained. The influence of the number of spans and PGA on track constraints is also revealed. The analysis results, based on a large number of samples, show that although track constraints can reduce the seismic risk of some phenomenon, such as girders' collision, the expected enhancement of longitudinal seismic safety of the system cannot be guaranteed in general, especially when the number of spans is large. However, it is noted that the track constraint can effectively control the over-limit scale of the system, which can reduce the expected repair cost after an earthquake. Therefore, it can be considered that the positive effect of the track constraints is more significant in economy than in structural safety when the bridge is subjected to a longitudinal earthquake excitation. [ABSTRACT FROM AUTHOR]

Seismic duration significantly impacts the structural seismic response. In order to obtain a correct time history analysis result of structural seismic design, determining a reasonable seismic duration scheme is imperative. In this paper, a five-span simply supported beam bridge and China Railway Track System (CRTS) II slab ballastless track system is taken as the research focus. A finite-element model for a high-speed railway track-bridge system was developed. The influence mechanism of starting and end threshold on seismic response was analyzed. Different bracketed duration schemes were put forward, and their applicability was assessed. The optimal bracketed duration scheme of time history analysis for a high-speed railway track-bridge system was determined. The results indicate a response curve deviation between the full duration and partial duration in the starting part due to the inconsistent structural movement trends and a deviation in the end part because of the structure entering a free vibration state in advance. When calculating the seismic peak response, the starting threshold A and end threshold B at both ends should be taken as5% of peak acceleration. When calculating seismic residual response, the starting threshold C at the left end should be taken as 25% of peak acceleration. [ABSTRACT FROM AUTHOR]

An efficient model of high-speed railway simply supported bridge with China Railway Track Structure II (CRTS II) ballastless track structure, setup on ANSYS platform, is proposed in this article. The goal is to improve the low computational efficiency and reduce the high computer memory consumption caused by complex bridge models of numerous spans. Programming language and modeling procedures are utilized to ensure that all spans in the proposed model of a large multispan simply supported railway bridge have consistent boundary conditions. Hence, only the middle span is simulated. The comparison of the first longitudinal vibration modes and first natural frequencies of the proposed model and the conventional simply supported bridge model preliminarily validates the feasibility of the model. It also confirms the range of the span number that the proposed model can simulate with accuracy. Taking into account eight different seismic excitations, the results further prove that the proposed model can significantly improve the computational efficiency of the seismic analyses, and can decrease the modeling complexity and calculation time cost without loss of accuracy. The design verification of three different heights of pier groups and the consideration of nonlinear springs enables the proposed model to be utilized in a wide range of applications. As a conclusion, for seismic simulation of high-speed railway simply supported bridges, the proposed model is a reliable alternative for practical engineering simulation. [ABSTRACT FROM AUTHOR]

CRTS II ballastless track is more commonly used in railway operations since it can meet the railway comfort and smoothness requirements. The effects of track constraint on the seismic response of high-speed railway simply-supported bridges can not be neglected. However, refined track structure modeling can significantly increase the computational time. Therefore, adopting a reasonably simplified model (SM) can improve computational efficiency effectively. Based on the principle of virtual work, the equivalent system is adopted instead of the track structure, and build a simplified model of bridge-track system. And on the basis of considering the randomness of the earthquake, the seismic response of the track-bridge model, the simplified model and the trackless model with different span numbers are compared, the over-capacity ratio and track constraint effect of the high-speed railway bridge-track system under the earthquake are analyzed. The analysis shows that the simplified efficiency of simplified model is up to 85% under longitudinal and transverse ground motions, and the seismic responses are in good agreement with those of the bridge-track system model; The track structure has a greater influence on the safety of the over-capacity probability (SPO) of the bridge structure under the longitudinal ground motion, particularly when the number of spans is high and ignoring the track structure may underestimate the over-capacity probability of some structures. [ABSTRACT FROM AUTHOR]

The deformation of the track on bridge after the earthquake mainly includes bridge creep and seismic-induced deformation, which poses a serious threat to the running safety of trains. In order to study the influence of the comprehensive deformation on the train-bridge system, a three-dimensional model of train-bridge coupling analysis was established. New point estimation method was used to solve the stochastic problem of initial track irregularity, aiming to study the changes of system motion under different parameters including deformation degrees and train speed. Results show that system motion increases with the increase of track parameters, and the earthquake intensity has the greatest influence on the train the motion, which reaches the peak in 0.4 g. The train speed has the greatest influences on the bridge when the train speed reaches the peak value of 400 km/h, while the impact of bridge creep is the smallest. Conclusion was obtained that the results of random analysis are of more general significance, and that in the vehicle-bridge system considering comprehensive track deformation after earthquake, the damage effect of track deformation induced by earthquake intensity is mainly considered for train, and the impact of train speed shall be mainly considered in bridge design. [ABSTRACT FROM AUTHOR]

When the high-speed railway (HSR) bridge is subjected to earthquakes, some components in the HSR bridge are damaged, and these components' damages will be reflected in the deterioration of the rail unevenness. In this study, a framework to address the lateral seismic rail unevenness corresponding to the damages of different components in the HSR track-bridge subjecting to earthquakes is developed. In the first place, a benchmark HSR track-bridge system is selected to conduct the nonlinear dynamic analysis, and the distribution law of the seismic residual drifts in the HSR track-bridge system subjecting to different earthquake intensity levels is proposed. Next, a refined mapping model is developed to assess the additional rail unevenness corresponding to the damages of different components in the system. The seismic rail unevenness sample is established by combining the initial and additional rail unevenness. Finally, the assessment method for the power spectrum density (PSD) of the seismic rail unevenness is introduced, and the PSD assessments of rail unevenness corresponding to the seismic damages of different components in the HSR track-bridge system are developed. The proposed methodology provides an innovative approach to assessing the seismic damage status of the HSR track-bridge subjecting to random earthquakes. [ABSTRACT FROM AUTHOR]

In the dynamic analysis of railway lines, both lateral and vertical track irregularities should be considered. In addition, uncertainties in the bridge structure and train load will have different effects on the train-bridge coupled system (TBCS). This paper presents a three-dimensional model of the TBCS to study the influence of various sources of randomness on the response of the TBCS. The Karhunen–Loéve expansion is combined with the point estimate method (KLE-PEM) to calculate the statistical moment of the system response with high accuracy and efficiency. Furthermore, applicability of KLE-PEM method is discussed and the influence of different combinations of sources of randomness on the train and bridge responses under different speeds is analyzed according to the maximum range of probability values. Random track irregularities are found to have a much greater influence on the train response than uncertain parameters, whereas uncertain parameters have the greatest influence on the displacement of the bridge. [ABSTRACT FROM AUTHOR]

In this paper, the Difference of Seismic Response across Different Spans (DSR) in the longitudinal distribution of High-Speed Railway Multi-spans Simply Supported Bridge (HSRSB) under longitudinal earthquake excitation is investigated, and an evaluation method which can intuitively reflect the difference of seismic response is proposed. A feasible way to strengthen the connection stiffness between adjacent girders is proposed to control DSR. The rationality of the finite element model used is verified by comparing the numerical results with the experimental ones, showing a satisfactory agreement. Comparing the seismic response of a bridge model considering the subgrade-track constraints (BCTM) and a bridge model without subgrade-track constraints (BWTM), it is found that the DSR in the longitudinal distribution causes some new disadvantages, which are neglected in BWTM. The BCTM considering the Difference Level Controller (DLC) generates a model called BCDM. The effect of the number of span on DSR are studied based on BCDM. The analysis of this model showed that DLC suppresses the DSR and reduces the seismic response of most bridge components. It also transfers the seismic disadvantage from the bridge part to the subgrade-track structure. As it is more convenient and cost-effective to repair the base plate of the subgrade than the bridge components after earthquake seismic event, this disadvantage transfer is in favor of forming a new anti-seismic system that subgrade-track structure is used to protect the bridge part. [ABSTRACT FROM AUTHOR]

A simplified calculation model for the integration of tracks and bridges of multi-span simply supported beam bridge on high-speed railway is proposed by considering the longitudinal connecting effects of adjoining structure. Using this simplified calculation model, the seismic response of multi-span standard simply supported beam bridges of multiple high-speed railways was calculated and compared with the seismic response using the corresponding full-bridge model. Based on the above calculation results, the simplification efficiency and equivalent stiffness of simplified calculation model was studied. Seven earthquake records were selected for calculation, and the growth rates of seismic responses with the increase of number of spans were analyzed in detail. The analysis results show that the seismic response using the simplified calculation model and corresponding full-bridge model are identical with each other; the simplified calculation model greatly reduces the calculation time and the efficiency of reducing calculation time is up to a maximum of 86%. The order of arrangements of interlayer components such as shear teeth and support significantly affects the equivalent stiffness of adjoining structures. The equivalent stiffness of adjoining structures becomes stable with the increase in the number of spans of simply supported beam in adjoining structures. The adjoining structures has an amplification effect on the seismic response of target structures, and the amplification effect becomes stable with the increase in the number of spans of simply supported beam in adjoining structures. Without considering the restraint effect of adjoining structures, the seismic response of multi-span simply supported beam bridge on high-speed railway becomes unsafe, that is, the result is smaller than that of considering adjoining structures. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The systematic running safety assessment of railway bridges presents lots of challenges, one of which is estimating the uncertainty bounds of the structural responses of bridges under vehicle loads with multisource randomness. In this study, a probability safety assessment method is proposed for evaluating the uncertainty bounds of random time-history responses for the stochastic train-bridge coupled system. First, a refined probabilistic model for the train-bridge coupled system (TBS) in heavy haul railway is established with the multi-excitations of random track irregularities, random vehicle loads and stochastic structural parameters. The probability density evolution method (PDEM) is employed to obtain the solution of the time-varying probability transferred between the stochastic excitations and the output of the dynamic responses. Then, to establish a rapid and straightforward approach for the systematic running safety assessment of the TBS, the quantiles of the probability distribution are used to estimate the time-history uncertainty bounds of random responses of interest distributed in real probability functions. Case studies by the field test and numerical simulation are presented to verify and investigate the accuracy and reliability of the proposed method. The results show that the quantiles of the probability distribution proposed are suitable for the systematic running safety assessment of the TBS. [ABSTRACT FROM AUTHOR]

High-speed railways are “lifeline projects” that shoulder the heavy responsibility of transporting relief supplies and medical forces for the first time after earthquakes. To ensure the train’s safety after earthquakes, it is of great urgency to ascertain a post-earthquake speed threshold. To that end, a target model for seismic irregularity emerges as a key parameter. In this paper, a null phase assumption-based technique for the mutual conversion between evolutionary power spectral density and non-stationary signal was proposed. Taking a high-speed railway track-bridge system as the research object, the target model of seismic irregularities was constructed based on the proposed technique. The rationality of the target model of seismic irregularities was verified, and the construction parameter settings were discussed. Moreover, a simplified frequency-domain fitting method for the target model of seismic irregularities was proposed based on the spectral decomposition theory. According to the research findings, the null phase assumption-based technique is capable of performing interconversion between seismic irregularity and its evolutionary power spectral density with satisfactory accuracy. It is recommended to set the minimum number of seismic irregularities, spatial sampling interval, hop size, and length of window function as 50, 0.25m, 1, and 40 to 100, respectively. [ABSTRACT FROM AUTHOR]

The friction pendulum bearings (FPB) begin to be used in railway bridges in China. In one earthquake region in China, the shear pins of FPB are required to be well to provide the enough shear force and stiffness under service loads (such as the vehicle forces being less than 170 kN in the longitudinal direction and 40 kN in the transverse direction) or small earthquake loads with a peak ground acceleration (PGA) being less than 0.1 g, however, are cut off to isolate seismic energy under large earthquake loads with a PGA being larger than 0.2 g. It is necessary to identify the appropriate strength of FPB shear pin to satisfy the above requirements. This paper selected the simply supported bridges on a single-line railway in the above earthquake region as the study object, which had a span length of 32 m and two height types of piers (8 m and 25 m). A prototype finite element model (FEM) and a scaled FEM were numerically analyzed, and a scaled experimental model was tested on shake table for each bridge. The results of them were compared with each other to validate the rationality of all models and to achieve the appropriate strength of FPB shear pin. The results show that the appropriate strengths of FPB shear pins are 540 kN in the longitudinal direction and 300 kN in the transverse direction for the bridge with the pier height of 8 m. Likewise, 350 kN and 270 kN are determined as the appropriate strengths of FPB shear pins for the bridge with the pier height of 25 m in the longitudinal and transverse directions, respectively. The numerical method of FEM is correct based on the experimental validation, and can be used to identify the appropriate strengths of FPB shear pins for other railway bridges. [ABSTRACT FROM AUTHOR]

• An elaborated vehicle-bridge-coupled system is modelled with the consideration of elastoplasticities of supports and shear keys. • Running safety assessment of vehicles over bridge under near-fault pulse-type earthquakes based on geometric derailment is conducted. • The influence of different excitations input times of near-fault pulse-type earthquakes is discussed. • A preliminary running safety assessment limitation zone is proposed. In this study, the running safety assessment (RSA) of high-speed railways is carried out, with the wheel lift being the derailment criterion. Seventy near-fault pulse-type earthquakes (NFPTEs) are imposed on an elastoplastic vehicle-track-bridge coupled model with elastoplastic supports and shear keys. Since the bridge length in the simulation model is limited by the 14-span high-speed railway simply supported bridge prototype with subgrades and a CRTS II track plate, it is difficult for the vehicles going through the full time-history of ground motions while passing over the bridge. Therefore, the excitation-input-time (EIT) analysis is conducted herein, and it is found that the effects of EIT on RSA under NFPTEs are significant and, as such, cannot be ignored. The EIT analysis also shows that the appearance times and EITs of peak ground acceleration and peak ground velocity of NFPTEs significantly affect the RSA results. In order to reveal and describe the potential relationship between dynamic responses of rail and wheel lift, dynamic contact point responses (DCPRs) are also proposed, and after comparison with the traditional dynamic responses, including rail deformations and displacements, the dynamic contact point velocity in Y-direction (DCPV-Y) are selected for developing of relationship with wheel lift and RSA limitation zone proposal. [ABSTRACT FROM AUTHOR]

In this paper, the responses of high-speed railway bridge subjected to seismic load were investigated by numerical simulation. Elastic deformation will occur in the bridge system under low-level earthquake; however, the bridge system may enter a nonlinear stage under high-level earthquake. The whole finite element model of the bridge system was set up by means of ANSYS software and self-compiled moment-curvature relationship program, the elastic seismic responses of bridge system and the elastic-plastic deformation of piers considering different vehicle speeds are calculated respectively. The calculation results show that, the earthquake responses of bridge system are increase in general with the increase of vehicle speed and earthquake intensity, and the bottom of piers step into elastic-plasticity stage under high-level earthquake, the plastic hinges occurred at the pier bottom, the pier bottom step into the plastic stage, some measures such as lateral reinforced steel encryption should be taken into account to ensure safety. [ABSTRACT FROM AUTHOR]

Dynamic response analysis of a nonlinear train-track-bridge system under earthquakes is a time-consuming task. In this paper, a fast computing strategy is proposed to reduce the simulation time by solving the shortcomings of classical time integration algorithms in the computation of the coupled system. The core of the strategy focuses on completely explicit computational processes and unconditional stability. Based on the loosely coupling scheme, the model of the train-track-bridge system is divided into two parts, namely, the train substructure established using multibody dynamics and the track-bridge substructure established using the finite element method. Track-bridge substructure and train substructure are separately integrated by the unconditionally stable explicit algorithm, CQ3, and its degenerate form, respectively. The interaction of the two substructures depends on wheel-rail forces. The track-bridge substructure is further decoupled to describe its nonlinear behavior and to improve the speed of solving algebraic equations. The proposed strategy not only avoids the complex iterative process of the nonlinear train-track-bridge system but also eliminates the limitation of the integration time step caused by the minimum natural period of the track-bridge substructure. This paper first simulates the dynamic response of a train under a sinusoidal displacement excitation and extends the simulation strategy to analyze the vibration of the coupling system under an earthquake. The applicability, efficiency, and accuracy of the strategy are illustrated through three numerical analyses. The strategy proposed in this paper provides a convenient and greatly computationally efficient option for simulating the nonlinear dynamic response of a large-scale train-track-bridge system. • The unconditionally stable explicit algorithm is introduced to the large-scale nonlinear train-track-bridge system. • Compared with using the classical algorithms, the proposed method achieves the same accuracy and higher efficiency. • The proposed method can greatly improve the computational efficiency of train-track-bridge coupling simulation. [ABSTRACT FROM AUTHOR]

• KLE-PEM can calculate train-bridge system with both random irregularity and parameters; • Sensitivities of random irregularities and parameters to the system response are analyzed. • Train-bridge system responses with different random factors and speeds is analyzed. The train-bridge system is complex and presents many random factors, including stochastic track irregularities as well as random parameters of bridge and train. Moreover, the entire train-bridge system may contain more than one hundred random variables. Herein, we proposed a new random analysis method that comprehensively considers two random sources of the system. Irregularities are represented using the Karhunen–Loéve expansion and the response of the system is then calculated using the point estimate method based on a two-dimensional reduction technique. The solution of the Monte Carlo simulation is regarded as the exact solution to verify the proposed method. Comparing to the Monte Carlo simulation method, the proposed method demonstrates high precision and efficiency. Moreover, sensitivities of random irregularities and parameters of the bridge and train to the system responses are analyzed. The bridge response demonstrates the highest sensitivity to Young's modulus and mass of the car-body, whereas the responses of the train exhibit the highest sensitivity to stochastic irregularities. Further, the influence of different random source combinations on the system response at different speeds is analyzed. The results suggest that it is sufficient to consider only random track irregularities for the train response, whereas random sources from both the bridge and train must be considered for the bridge response. [ABSTRACT FROM AUTHOR]

• Traditional damage index (DI) is inappropriate to high-speed railway (HSR) piers. • New DI is proposed for HSR piers under earthquakes and is validated by tests. • New DI is affected by longitudinal bar ratio and axial compression ratio. • HSR piers are more vulnerable to cumulative damage under earthquakes. The traditional Park–Ang damage index (DI) has been devised for damage assessment of highway bridge piers and building columns, but is inappropriate for high-speed railway (HSR) bridge piers, which have much larger cross sections, much less longitudinal bar ratios and much less axial compression ratios under earthquakes. In order to obtain the appropriate DI for HSR bridge piers, numerical analysis of 144 HSR bridge piers and quasi-static test of 7 HSR bridge piers was done to study the combined parameter β in DI. The new DI was subsequently validated by pseudo-dynamic testing of 2 HSR bridge piers. The results show that the new combined parameter β in the reformulated DI for HSR bridge piers is mainly affected by the longitudinal bar ratio and the axial compression ratio; however, the traditional β and DI are significantly affected by the stirrup reinforcement ratio. It is suggested that 0.06, 0.19, 0.49 and 1.0 should be taken as the critical values for the new DI among the basically intact, slightly damaged, moderately damaged, severely damaged and collapsed states of HSR bridge piers with axial compression ratio being less than 0.09, while values 0.11, 0.33, 0.49 and 1.0 are recommended for HSR piers with an axial compression ratio from 0.09 to 0.15. As for the collapse state of HSR bridge piers, the cumulative damage contribution of energy to the full DI (of value 1.0) is 0.64. It is a large value and indicates that HSR bridge piers are vulnerable to cumulative damage from earthquakes. [ABSTRACT FROM AUTHOR]

• Vibration of train-bridge couple system with random parameters is calculate. • The efficiency and accuracy of NPEM in train-bridge couple vibration is evaluated. • Response with random parameter and different coefficient of variation is discussed. In the analysis of train-bridge coupled vibration system, randomness of parameters of high-speed railway bridge cannot be ignored. The new point estimate method (NPEM) is a kind of accurate and efficient method to calculate the random response and reliability. In this paper, NPEM is applied to analyze the random dynamic responses of 3D train-bridge coupled system with random parameters, including parameters of bridge materials, environment factor and prestressing parameters. Newmark-β approach is applied as the integration algorithm, and the Monte Carlo method is used to validate the feasibility of the NPEM. The results show that NPEM can be combined with random system accurately and efficiently. Furthermore, the influences of different random parameters distributions are discussed. [ABSTRACT FROM AUTHOR]

• Pure LSTM-based temporal learning or CNN-based feature extraction networks are inadequate for accurately predicting the seismic damage level in high-speed railway track-bridge systems. • The VHXLA model exhibits high prediction accuracy, with the accuracy of predicting the damage level of the supports approaching 100% and the accuracy of predicting the damage level of the sliding layers approaching 95%. The model can be used for real-time discrimination of damages in high-speed railway systems and structural damage analysis, requiring a large amount of seismic data. • The VHXLA model demonstrates consistent prediction accuracy for various positions of the same predicted component, with slightly lower accuracy for the track structures than the bridge structures. • The VMD decomposition and HT transformation of seismic motion effectively capture the time–frequency features of the seismic data, reducing the network's complexity and improving the model's predictive capability. The timely and accurate prediction of post-earthquake damage is critically important for ensuring the safety of high-speed railway track-bridge systems. The study introduces a novel method known as the VHXLA model. This innovative model blends variational mode decomposition (VMD) with a hybrid neural network for predicting non-linear multi-component post-earthquake damage in high-speed railways. The VHXLA model comprises a signal processing module and a deep learning module. The signal processing module utilises VMD decomposition, and the Hilbert transform (HT) to transform two-dimensional seismic signals into four-dimensional complex time–frequency signals, thus simplifying the task of identifying seismic time–frequency characteristics via the neural network. The deep learning module integrates diverse types of neural network components, such as the Xception CNN feature extraction submodule, the LSTM RNN temporal learning submodule, and the multi-head attention mechanism submodule. A Bayesian self-optimisation method is implemented to determine the number of decomposition layers in VMD and select essential hyperparameters. The model's effectiveness is evaluated by predicting the damage of an experimentally validated finite element model, subjecting it to seismic loads, and thus gauging its performance. The results indicated that the signal processing module, based on VMD decomposition, significantly improves the neural network's signal processing capability. In addition, the synergistic integration of different modules in the VHXLA model provides superior prediction accuracy compared to pre-existing damage prediction models. Notably, the prediction accuracy is consistent across different positions of the same predicted component in the high-speed railway track-bridge system. [ABSTRACT FROM AUTHOR]

This study proposes a simplified analysis method that couples the bridge and train-track subsystem in a weak form to facilitate the dynamic analysis of the train-track-bridge coupled system (TTBS) under earthquakes. The method includes three main steps: (i) performing dynamic analysis of the bridge under seismic conditions to obtain the response of the bridge deck; (ii) interpolating the bridge displacement beneath each wheelset based on the train's velocity, departure time, and the initial positions of the wheelsets; and (iii) assessing the running safety of the train by incorporating the interpolated bridge response as track irregularity into the train-track coupled system. Steps (i) and (iii) can be analyzed separately using finite element and multibody dynamics software, eliminating the need to create a complex TTBS model that is challenging to achieve within a single software platform. Additionally, based on the method's assumptions, the earthquake excitation on the train can be separated into the seismic inertial effect and seismic-induced bridge deformation, enabling a quantitative analysis of the impact of these two types of excitations on train safety. Taking a 10-span simply supported bridge and a long-span cable-stayed bridge as examples, the proposed method's assumptions are verified by comparing its results with those obtained from a complex TTBS model. Furthermore, the impact characteristics of inertial effects and seismic-induced bridge deformation on train safety for these two types of bridges are analyzed. The proposed method offers robust support for seismic design of bridges and facilitates a comprehensive analysis of the mechanisms through which seismic excitations affect train safety. • Proposal and validation of a simplified method for running safety evaluation of train on bridges under earthquake excitation. • Separation of seismic excitation on the train into seismic inertial effect and seismic-induced bridge deformation. • Analysis of impact characteristics of inertial effects and seismic-induced bridge deformation on train running safety. [ABSTRACT FROM AUTHOR]

The safety of high-speed railway trains running on bridges during stochastic near-fault pulse-type earthquakes is of utmost importance in designing railway bridges. This paper presents an efficient and feasible approach for analyzing the train-bridge coupling system (TBCS) during random near-fault ground motions using the number theory method with dimensionality reduction (NTM-DR). The method's validity is demonstrated through Monte Carlo simulations, which calculate the probabilistic maximum of the system response and the derailment coefficient under various conditions, such as different bridge heights, seismic intensities, and train speeds. Additionally, the response sensitivity to changes in seismic randomness is discussed by comparing it with the deterministic maximum. The results show that the proposed method achieves high accuracy and efficiency in analyzing the TBCS under random near-fault earthquakes. The ratio between the probabilistic and deterministic maximum is consistently above 1.3, highlighting the significance of considering earthquake randomness. [ABSTRACT FROM AUTHOR]

• This paper proposed a simplified seismic model of track structure on HSR bridges. • The simplified track model provides an alternative for seismic analysis of HSR bridges. • The simplified track model can be used for seismic performance evaluation and collision judgement. 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. [ABSTRACT FROM AUTHOR]