Vector Form Intrinsic Finite Element Method for Stochastic Analysis of Train–Track–Bridge Coupling System

In this paper, a train–track–bridge (TTB) interaction model that can account for coach-coupler effect is presented for stochastic dynamic analysis of a train traveling over a bridge. Based on the vector form intrinsic finite element (VFIFE) method, both the bridge and non-ballasted track are discretized into a set of mass particles connected by massless beam elements, in which the fasteners that fixed the tracks on the bridge deck are modeled as a series of linear spring-dashpot units. The multi-body train car is regarded as seven mass particles (1 for car body, 2 for bogies and 4 for wheelsets) connected by parallel spring-dashpot units. Considering the random nature of rail irregularities, the Karhunen–Loéve expansion (KLE) method is used to simulate the vertical profile of the tracks. To calculate the mean and standard deviation of the stochastic response of the TTB system, the point estimated method (PEM) based on the Gaussian integration and dimension reduction method is adopted. The proposed VFIFE–TTB interaction model is then applied to stochastic resonance analyses of a train moving on a bridge. It is shown that the present VFIFE–TTB model is able to analyze the dynamic interaction of the TTB system simply and efficiently. The influence of rail irregularity-induced stochastic vibration on the train and bridge would become significant once the resonant vibration takes place on the TTB system.

Earthquake Influence on the Rail Irregularity on High-Speed Railway Bridge

Rail irregularity is the leading cause of enhancing train-track coupling vibration and, therefore, should be studied in detail for safety requirements. In this study, the differences between existing rail irregularities without being subjected to an earthquake between different countries were first studied. Results show that existing power spectrum density and time-domain displacement samples of rail irregularities in the American code are the largest, while the irregularities of the Germany railway are higher than those of China in a specific range of rail wavelengths. Afterward, the effects of earthquake intensity, soil site, and duration on the rail irregularity of a Chinese typical high-speed railway bridge were investigated. For this purpose, a finite element model was established and validated by the shaking table test of a 1/12-scaled high-speed railway bridge experimental specimen. The calculation results indicated that the influences of earthquakes on the rail alignment irregularity were evident.

Influence of out-of-round wheels on the vehicle–flexible track interaction at rail welds

The dynamic analysis of the vehicle–flexible track interaction involves the study of vehicle motion and its dynamic impact transmitted to the track structure. This paper studies the influence of the out-of-round vehicle wheels running over rail welds on a flexible ballast track. The rails are modeled as an Euler-Bernoulli beam discretely supported by a spring-damper force element that represents the flexibility of the track structure. The dynamic behavior of the vehicle–flexible track interaction is studied using the combination of the finite element method and the multi-body system. In this paper, the simulation of the vehicle with the out-of-roundness wheel running over rail welds on a flexible ballast track in the high-frequency range and the vehicle–track interaction is coupled by a non-linear wheel–rail contact model. The effects of the out-of-roundness wheel on the vehicle–flexible track interaction at rail welds are investigated by comparing the effects of the round wheel under different vehicle speeds. Results indicate that the out-of-roundness wheel at rail welds creates a high magnitude dynamic effect on the vehicle and track components. The obtained simulation results were used to set a safety limitation for the wheel and rail irregularity size.

Theoretical investigation into the measurability of rail unevenness and corrugation using the dynamic response of axle box and bogie

Monitoring track unevenness is important for noise and vibration control and track maintenance. Rail corrugation and shorter wavelength track unevenness can be measured using the corrugation analysis trolley, but it is not suitable for measurement over long distance. It is of great significance to study the dynamic behavior of the response of the axle box and bogie to the unevenness excitation for a better understanding of the measurement results. In this paper, the dynamic response of the axle box and bogie to the unevenness excitation is analyzed in the frequency domain by taking account of multiple wheel–rail interactions, which is the case in practice. The response of the axle box and bogie is found to be affected by the so-called P2 resonances at low and medium frequencies and the standing waves of rail vibration at higher frequencies due to the multiple wheel–rail interactions. Based on the analysis of the response of the axle box and bogie, the measurability of track unevenness is discussed. Results show that the measurement of rail unevenness using the axle box response is mainly limited by the P2 resonance. The frequency range of measurement for the ballasted track studied is estimated to be 1–35 Hz, corresponding to the measurable unevenness wavelength of 0.6–20 m (or longer) at a vehicle speed of 20 m/s. Above 200 Hz, the standing waves of rail vibration will cause serious uncertainty in the measurement of short wavelength rail irregularity using the axle box response for the resilient track. Short pitch rail corrugation, however, can be evaluated using the axle box response due to its strong correlation with certain modes of the wheel–track system.

Stochastic Analysis of Train–Bridge System Using the Karhunen–Loéve Expansion and the Point Estimate Method

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.

Evaluation of longitudinal connected track under combined action of running train and long-term bridge deformation

With long-term operation of high-speed railways, bridge deformation is hard to avoid, which directly affects the mechanical property of longitudinal connected track. To ensure the structural stability of longitudinal connected track and operation safety of train, this work proposes a work to evaluate longitudinal connected track under combined action of running train and long-term bridge deformation. First, the methodology of evaluating longitudinal connected track subject to train load and long-term bridge deformation has been proposed, in which an accurate train–track–bridge dynamic model and the method to determine long-term bridge deformation are settled. Then, the long-term bridge deformations caused by concrete creep, shrinkage, temperature, and pier settlement are investigated. On this basis, the evaluation of longitudinal connected track subject to long-term bridge deformation and running train is conducted, and the safety value of pier settlement for Chinese high-speed railways with longitudinal connected track is suggested. Results show that the long-term bridge deformations are even larger than the amplitude of random rail irregularity. With smaller settlement, influences of creep, shrinkage, and temperature play the leading role in affecting the mechanical behavior of longitudinal connected track, while influence of pier settlement occupies the dominant position with larger settlement. It is suggested that the pier settlement for Chinese high-speed railways with longitudinal connected track should be less than 7.7 mm to ensure structural stability of track and operation safety of train.

Effect of Rail Irregularities on Ride Comfort of Train Moving Over Ballast-Less Tracks

Rail irregularities are the main factors influencing the ride comfort of trains moving over tracks. Despite various investigations made in this regard for the ballasted tracks, there is a lack of studies for the ballast-less tracks. This limitation is addressed in this study. To this end, a vehicle/slab-track interaction numerical model was developed, which was validated by comparison of the results obtained herein with those of the field tests carried out in this study. The effects of rail irregularities with various amplitudes and wavelengths on the ride comfort were studied by a comprehensive parametric analysis. Particularly, the effects of the wavelengths and amplitudes of rail irregularity on the ride comfort were investigated. Contrary to the current understanding, it was shown that rail irregularities with short wavelength have considerable effects on the ride comfort for the slab-tracks. In addition, the ride comfort decreases significantly when the wavelengths of rail irregularity become less than 0.75[Formula: see text]m in the metro lines. The critical speed of the train (at which the lowest ride comfort is obtained) was derived as a function of rail irregularity. The results obtained indicate that the amplitude of rail irregularity has negligible influence on the critical speed of the train.

A Practical Wheel-Rail Interaction Element for Modeling Vehicle-Track-Bridge Systems

A novel practical element is presented for simulating the vertical wheel-rail interaction (WRI) of vehicle-track-bridge (VTB) coupling systems. The WRI is time- and location-varying, which makes the simulation of the VTB system complicated. The new element simulates the WRI using a location dependent internal resisting force, which enables the finite element (FE) model of the VTB system to remain unchanged in analysis. This element is capable of simulating the nonlinear WRI, the rail irregularity and the ‘additional’ displacement of the rail. The ‘additional’ displacement is the extra displacement caused by the WRI besides that interpolated from the element nodal displacements, which is usually ignored by existing models, but may be non-negligible in some cases. The WRI element is implemented into a general FE software framework, OpenSees, and verified by the dynamic analysis of a simply-supported beam subjected to a moving sprung mass. Furthermore, a realistic VTB system with a moving four-wheel vehicle is investigated to evaluate the cases where the additional displacement and nonlinear WRI should be considered. Finally, using another realistic VTB system subjected to rail irregularities and earthquakes, the effects of rail irregularity and earthquake on the dynamic responses of the WRI system are studied and compared.