The settlement of piers and subgrade bending deformation are widely recognized as common issues in the transition zones of high-speed railway bridges. This study aims to investigate the settlement behavior within these transition zones and its impact on the dynamic interaction between trains and the track. To achieve this, a vehicle-track-transition zone mapping relationship model is developed to analyze both the settlement behavior and the resulting dynamic response characteristics. The study employs the finite element method and multi-body dynamics to construct the simulation model. Settlement effects are simulated using the Newton-Raphson iterative method, with the additional rail deformation caused by foundation settlement serving as the excitation for the vehicle-track-transition zone dynamic interaction system. In the numerical analysis, the dynamic effects of three key factors—train speed, transition zone length, and the amplitude of foundation settlement—are examined based on the performance of the vehicle-track-transition zone interaction. The time-frequency technique is utilized to comprehensively reveal and clarify the spatial-frequency characteristics of system responses influenced by settlement excitation. Moreover, the relationship between the safety-based settlement threshold and these three factors is calibrated.

In light of two wheel-rail contact relations, i.e., displacement compatibility and force equilibrium, a newly developed three-dimensional (3D) model for vehicle-track interactions is presented in this paper. This model is founded on the basis of an assumption: wheel-rail rigid contact. Unlike most of the dynamic models, where the interconnections between the vehicle and the track entirely depend on the wheel-rail contact forces, the subsystems of the vehicle and the tracks in the present study are effectively united as an entire system with interactive matrices of stiffness, damping and mass by the energy-variational principle and wheel-rail contact geometry. With wheel-rail nonlinear creepage/equivalent stiffness, this proposed model can derive dynamic results approaching to those of vehicle-track coupled dynamics. However, it is possible to apply a relatively large time integral step with numerical stability in computations. By simplifying into a linearized model, pseudo-excitation method (PEM) can be theoretically implemented to characterize the dominant vibration frequencies of vehicle-track systems due to random excitations. Finally, a trail method is designed to achieve the wheel climbing derailment process and a full derailment case where the bottom of the wheel flange has completely reached the rail top to form a complete derailment is presented.

To efficiently select track irregularity random samples for satisfying the ergodicity requirements of excitation sources in stochastic dynamics and reliability analysis in vehicle-track system, the weak-stationarity and similarity spectral of track irregularities were introduced to propose a track irregularity probabilistic model. Using the discrete probability integration and statistical approaches, the massively measured track irregularity time histories were divided into multiple time-domain sequences. The statistical power spectral density distribution of each sequence was calculated by the spectral analysis method. Then, using the matrix-based method, the set representation of the power spectral density function of track irregularities was obtained. It was assumed that the power spectral densities could be linearly accumulated at different frequencies, allowing the probabilities of entire spectra line to be obtained using the power spectral density probability distribution of a single frequency. The representative track irregularity spectra were selected through the commonly random simulation methods, and the track random irregularities were inversely simulated. The height and direction track irregularities of high-speed railway about 269 km were measured. Based on the vehicle-track coupled dynamics theory, the calculation results between the track irregularity probabilistic model and track irregularity stochastic model was compared from the aspects of the simulated amplitude of track irregularity and the probability density distribution for dynamic response in the vehicle-track system to verify the validity and high efficacy of the track irregularity probabilistic model. Calculation result shows that when taking the track random irregularities caused by the two models as excitation sources, the difference of the obtained probability entropies of vehicle-track system dynamic response between the two models is less than 2%. Both models can accurately express the excitation characteristics of track irregularities. The stochastic and probabilistic models need 131 and 33 random samples, respectively, to guarantee the consistent probability density distributions between the simulation and measurement, and the probabilistic model has higher computation efficiency. Under the presented computational condition, the wheel-rail forces and car body accelerations are 38-152 kN and -0.042g-0.043g, respectively, and are respectively less than the limits of wheel-rail forces (170 kN) and car body accelerations (0.25g) in Code for High Speed Railway Design (TB 10621-2014). The track irregularity status of the investigated high-speed line is sufficient to guarantee the running safety and riding comfort of the vehicle.

The randomness of track irregularities directly leads to the random vibration of the vehicle–track systems. To assess the dynamic performance of a railway system in more comprehensive and practical ways, a framework for probabilistic assessment of vehicle-curved track systems is developed by effectively integrating a vehicle–track coupled model (VTCM), a track irregularity probabilistic model (TIPM) with a probability density evolution method (PDEM). In VTCM, the railway vehicle and the curved track are coupled by the nonlinear wheel–rail interaction forces, and through TIPM, the ergodic properties of random track irregularities on amplitudes, wavelengths and probabilities can be properly considered in the dynamic calculations. Lastly, PDEM, a newly developed method for solving probabilistic transmissions between stochastic excitations and deterministic dynamic responses, is introduced to this probabilistic assessment model. Numerical examples validate the correctness and practicability of the proposed models. In this paper, the results of probabilistic assessment are presented to illustrate the dynamic behaviours of a high-speed railway vehicle subject to curved tracks with various radii, and to demonstrate the importance of considering the actual status of wheel–rail contacts and curve negotiation effects in vehicle-curved track interactions.

Due to random characteristics of system parameters and excitations, the dynamic assessment and prediction for the train-track-bridge interaction systems become rather complex issues needing to be addressed, especially considering the longitudinal inhomogeneity and uncertainty of dynamic properties in physics and correspondingly their temporal evolutions. In this paper, a temporal-spatial coupled model is developed to fully deal with the deterministically/non-deterministically computational and analytical matters in the train-track-bridge interactions with a novelty, where a train-track-bridge interaction model is newly developed by effectively coupling the three-dimensional nonlinear wheel-rail contact model and the finite element theory, moreover, the Monte-Carlo method (MCM) and Karhunen–Loève expansion (KLE) are effectively united to model the random field of track-bridge systems, and a spectral evolution method accompanied by a track irregularity probabilistic model are introduced to select the most representative track irregularity sets and to characterize their random evolutions in temporal dimension. In terms of random vibration analysis, the high-efficiency and effectiveness of this developed model is validated by comparing to a robust method, i.e., MCM. Apart from validations, multi-applications of the temporal-spatial coupled model from aspects of deterministic computation, random vibration, resonant analysis and long-term dynamic prediction, etc., have been fully presented to illustrate the universality of the proposed model.

The dynamic performance of the railway vehicles and the guiding tracks is mainly governed by the wheel-rail interactions, particularly in cases of track irregularities. In this work, a united model was developed to investigate the track portions subject to violent wheel/rail forces triggered by track irregularities at middle-low frequencies. In the modeling procedures, a time-frequency unification method combining wavelet transform and Wigner-Ville distribution for characterizing time-frequency characteristics of track irregularities and a three-dimensional nonlinear model for describing vehicle-track interaction signatures were developed and coupled, based on which the method for predicting track portions subject to deteriorated wheel/rail forces was proposed. The theoretical models developed in this paper were comprehensively validated by numerical investigations. The significance of this present study mainly lies on offering a new path to establish correlation and realize mutual prediction between track irregularity and railway system dynamics.