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 analyze more accurately the dynamic response of sleeper and ballast bed under heavy haul railway train load, this paper uses parallel bonded spherical elements to simulate concrete sleeper structure, which can realistically simulate the load transfer from sleeper to load, and rigid clusters with realistic shape to simulate ballast particles. The reliability of the model is tested by verifying the vertical stiffness and lateral resistance and comparing them with the experimental data. The train load is applied to the area on the sleeper in contact with the rail to study the settlement and vibration response of the sleeper and the ballast bed. The results show that the vertical displacement of the sleeper is different at each place under the train load, the displacement of the sleeper in the area under the rail is significantly larger than the shoulder and the center of the sleeper, and the bending deformation of the sleeper is W-shaped; the displacement and vibration amplitude of the sleeper will increase when the train speed increases; the internal stress of the sleeper under the rail is much larger than the center of the sleeper, the influence degree of sleeper center will increase with the increase in train speed. The ballast particle displacement and vibration will decrease with the increase in the ballast bed depth, and the ballast displacement and velocity in the area below the rail action is larger than that in the ballast shoulder and bed center area.

In order to explore the influence of different particle size gradations of dirty materials on the service performance of the ballast bed, the clean track bed, the completely fouled ballast bed polluted by coarse coal and fine coal, respectively, were studied based on the discrete element method. In order to explore the influence of the multi-scale particle size gradation of the dirty material on the service performance of the ballast bed, the clean ballast bed, the completely dirty ballast bed polluted by coarse-particle coal, and the completely dirty ballast bed polluted by coarse-particle coal were simulated, respectively, based on the discrete element method, which are used to analyze the dynamic response of track bed under different working conditions under cyclic load. The model is verified by the lateral resistance and vertical stiffness of the ballast bed to prove the accuracy of the discrete element model. On this basis, the dynamic cyclic load is considered to analyze and study the mechanical response and change law of the ballast bed with different degrees of contamination. Studies have shown that after the ballast bed is contaminated, its lateral resistance and vertical support stiffness are reduced, the amount of settlement increases, the coordination number between ballasts is declined, and the fine-grained dirty material has a worse effect on the ballast bed; The displacement value of the ballast particles decreases with the increase of the depth of the ballast bed; The displacement value of the ballast particles under the rail is the largest, and the ballast particles on the ballast shoulder appear dilatancy; The displacement of the ballast particles at the laterally symmetrical position of the track structure is close to but not completely same; Dirty materials aggravate the frequency of ballast particles, and the impact of fine-particle coal powder is particularly significant.

To explore the impact of seismic intensity on the working performance of ballasted track bed, the seismic acceleration corresponding to earthquakes of magnitude 6, 7, 8, and 9 is obtained through the method of artificial synthetic seismic wave, and the ground motion is added to the discrete element model of the ballasted track to realize loading. The synthetic method of seismic wave adopts the spectrum representation method of the simulation of an essentially non-stationary random process, in which the modulation function is the time–frequency modulation function, and the self-power spectrum is the Kanai–Tajimi spectrum. The feasibility of this method is verified by comparing the mean value, standard deviation and autocorrelation of the generated seismic motion with the target value. The discrete element method is used to establish the ballast bed model, and the reliability of the model is verified by lateral resistance and vertical stiffness. Based on the above research results, the seismic waves under four seismic intensities are added to the bottom wall of the discrete element model, and it is concluded that the seismic intensity has a significant impact on the working performance of the ballast bed. With the increase in the seismic intensity, the lateral and vertical displacement of the sleeper, the lateral and vertical stress of the track bed, and the displacement–velocity–acceleration value of the bottom ballast particles all increase; compared with the other three earthquake intensities, the dynamic impact of the magnitude 9 earthquake intensity is more significant; under different seismic intensities, the displacement, stress and dynamic characteristics of ballast increase with the increase in seismic action time.

The load generated during train operation is transmitted to sleepers through rails, and then from sleepers to trackbeds. As one of the important components of the track structure, sleepers are very important to the service-life and safety of railways. The running speed of the train will produce different load frequencies on the rails. To explore the response of sleepers under cyclical train loads, this research used the discrete element method to simulate rails and sleepers, and realizes the loading of sleepers by applying cyclic loads to the rails. The discrete element method was used to simulate the compression-failure test of the concrete sample to verify the reliability of parameters of the discrete element model. On this basis, the sleeper was simulated by the discrete element, and the change law of the mechanical parameters such as particle displacement, contact force, and stress of the sleeper under different loading frequencies were analyzed. The research results show that the sleeper particles under the rail had a large vertical displacement, and the maximum displacement and the maximum contact force of the particles in the sleeper increased with increasing loading frequency. The stress change trend of the sleeper under the left and right rails was the same, and both showed periodic changes with cyclic loading. The loading frequency had little effect on the stress of the sleeper. The vertical displacement, velocity, and acceleration amplitude of the rail all increased with increasing cyclic loading frequency, thereby increasing the force between the rail and the sleeper, and increasing the dynamic response of the sleeper.

In this work, a model for characterizing the ballasted track–vehicle interaction is presented. The vehicle is modeled as a multirigid-body system consisting of a car body, two bogie frames, and four wheelsets, and the track is modeled by finite elements including the rail, the sleeper, and the track bed. All bodies are connected by spring–dashpot elements. With novelty, the geometric nonlinearity of curved rail beam and mechanical nonlinearity of ballasted bed lateral resistance have been fully considered. Besides, numerical solution procedures including iteration and increment have also been developed to accurately clarify the dynamic nonlinear performance of vehicle–track systems. Apart from model validations in statics and dynamics, the influence of track nonlinearity and curved track radius on vehicle–track dynamic performance has been revealed in detail.