High-speed Train Loads Research Articles

Development of corrosion-fatigue analysis method of cable hangers in tied-arch bridges considering train-bridge interaction

This study proposes an integrated corrosion-fatigue analysis method for bridge hangers by combining the dynamic bridge-train interaction analysis for random train arrivals with various speeds and the linear elastic fracture mechanics (LEFM)-based crack propagation analysis considering the corrosion-fatigue effects. Accordingly, a three-stage process, namely, zinc coating corrosion, pit-crack transition, and corrosion-fatigue crack propagation for wires in hangers, was proposed to simulate the total service life. A train-bridge-interaction analysis was conducted on a tied-arch bridge with multiple cable hangers using the vector form intrinsic finite element method, where the stresses in the hangers were generated under high-speed train loads. The pit-crack transition was analyzed based on the pit growth and fatigue growth; whose rates compete to dominate the transition phenomenon. The fatigue crack growth rate was estimated using a LEFM approach considering the equivalent stress ranges and number of stress cycles. The effects of reducing the cable cross-section and updating the internal stress of the multi-layered wires were investigated. The present method was compared with the continuum damage mechanics model for validation. A relatively short remaining corrosion-fatigue life was found in the cables under the train loads, after corrosion of the zinc coating and pit-crack transition in the steel wires were developed.

Numerical Simulation Study of the Vibrational Response of Continuous Arch Tunnels under the Action of Overlying Train Loads

With the rapid development of transportation infrastructure in China, continuous arch tunnels passing under existing operational railways are increasingly encountered. This paper primarily investigates the mechanical response patterns of the lining of continuous arch tunnels under the vibrational loads generated by trains traveling on railways. To this end, a three-dimensional finite element model of the dynamic response of continuous arch tunnels under train vibrational loads was constructed using Midas GTS/NX software. This model explores the patterns of acceleration, dynamic displacement, and dynamic strain responses of continuous arch tunnels under the action of moving train loads. The study reveals that under train vibrational loads, the vertical acceleration, vertical displacement, and strain time history curves at various monitoring points in the continuous arch tunnel exhibit vibrational characteristics. The acceleration, vertical displacement, and dynamic strain increase as the train enters, fluctuate within a certain range, and then decrease to zero as the train exits. Under high-speed train loads, the acceleration peak values at the arch feet and outer sidewalls of the left and right tunnels are larger, with a greater peak value difference. The vertical displacement peak values at the arch shoulders and crown are larger, whereas those at the middle partition wall and base slab are smaller. During the process from the train's entry to its exit, the dynamic strain exhibits a trend of initially increasing, then stabilizing, and finally decreasing to zero, all while displaying vibrational characteristics. The strain response on the tunnel side where the train enters is greater than that on the side where it exits.

Vibration response prediction and vibration safety assessment method for building structures around viaducts under the action of high-speed railway trains

Concerning the cumulative damage of building structures caused by the long-term effects from high-speed railway train loads and various environmental impacts, and to ensure the service safety of building structures around viaducts, this paper establishes a vibration safety assessment method for the entire life cycle of building structures with less workload and good applicability, while ensuring the accuracy and effectiveness of the prediction of vibration response of building structures. Firstly, the vibration source function is formed based on the mechanical model of the mobile vibration source of high-speed railway trains, and the vibration wave of high-speed railway trains is numerically simulated. Then the time and frequency characteristics of the simulated high-speed railway train vibration waves are verified through on-site monitoring tests. In addition, the peak particle vibration velocity attenuation formula for the foundation site of the viaduct is derived by the dimension analysis method, and it is used to correct the attenuation characteristics of the simulated high-speed railway train vibration waves. Finally, based on the response spectrum method to realize the prediction and assessment of the overall vibration response of the building structures, and using the cumulative damage coefficient to reflect the cumulative degree of the service damage of the building structure, a vibration safety assessment method for the whole lifecycle of the building structure is proposed. The method overcomes the shortcoming that vibration velocity does not reflect the impact of service damage on the vibration safety of building structures, and avoids neglecting localized vibration damage, and is therefore useful for the rapid, overall vibration safety assessment of any long-term service building structure in a viaduct site.

Field Testing and Numerical Simulation of the Dynamic Response of Loess Hill Site under High-Speed Train Load

In this study, the loess hill site of an elevated bridge section in Tongwei-Qin’an of the Baolan high-speed railroad was selected as the research object, and the vibration acceleration of the loess hill site under the elevated bridge was tested in the field under the train operating load. The results show that under the same intensity of train load, the time range of vibration acceleration observed by field test and numerical simulation decays linearly with increasing distance from the source, while the amplification effect appears in the loess hill site at a greater distance, and the vibration duration also appears to increase. The vibration acceleration waveforms at each observation point observed by field tests and numerical simulations are similar, and the peak vertical acceleration at each observation point obtained from numerical simulations is overall greater than the peak acceleration at each point obtained from field tests, with aSimulated− max/aObservated− max values ranging from 1.04 to 1.63. The Fourier spectrum frequencies recorded by numerical simulation and field test are mainly concentrated in the range of 1∼40 Hz, but the difference between the main frequencies recorded by the two is large. The main frequency of the energy spectrum recorded by the numerical simulation is around 15 Hz, which is the same as the main frequency of the energy spectrum vibration of the input vibration wave, and the main frequency of the energy spectrum vibration recorded by the field test is around 25 Hz.

Nonlinear dynamics simulation of the helical gear transmission system for high-speed train

Considering the bending-torsional-axial-coupled vibration of the helical gear transmission system, a 10 degrees of freedom high-speed train gear transmission system model, including motor and load, is established based on the lumped parameter method. In addition, the potential energy method based on the slicing principle is used to accurately calculate the time-varying meshing stiffness of helical gears. Furthermore, the influence of geometric parameters of helical gears on the time-varying meshing stiffness is studied, and the impact of time-varying meshing stiffness on the system is further investigated. Meanwhile, by analyzing the dynamic phenomena of the system under different parameter excitations under different parameter excitations, the influence of internal and external excitation parameters such as gear speed, wheel rail creep force, support stiffness, and support damping on the stability of high-speed train gear transmission system is deeply studied.

Dynamic Response of Bridge–Tunnel Overlapping Structures under High-Speed Railway and Subway Train Loads

With the rapid development of high-speed railroads and subways, there has been an increasing number of bridge–tunnel overlapping structures. To study the dynamic response characteristics of bridge–tunnel structures under the synergistic effects of the vibration generated by high-speed railway and subway trains, the dynamic response characteristics of a bridge–tunnel structure under single-point vibration loading was analyzed by conducting numerical simulations and model tests, with the frequency response function and peak acceleration as the evaluation indices. The dynamic response characteristics of the overlapping structure under moving vibration loads of the high-speed railway and subway trains were further analyzed. The results showed that the dynamic response of the bridge–tunnel overlapping structure increased with the increase in the frequency under the full frequency domain single-point sweep vibration load. The dynamic response of the tunnel hance near the pile foundation side was significantly greater than the vault and invert. Compared with the effect of high-speed train loads alone, the dynamic response of the bridge–tunnel overlapping structure under the synergistic effects of high-speed railways and subways increased significantly and varied at different locations. This investigation provides theoretical support for the design and construction of bridge–tunnel overlapping structures under the synergistic effects of high-speed railways and subways, contributing to improving engineering quality and safety.

NUMERICAL METHODS OF HYDRO-DYNAMIC COUPLING IN SATURATED SOIL AND ITS APPLICATION TO RAILWAY ENGINEERING

Recent field case study shows that the roadbed of ballastless high-speed railway experienced water-induced defect such as excessive fines pumping and even local subgrade-track contact loss affecting the normal operation of highspeed train due to water immersion through gaps of waterproof materials in expansion joints between the concrete base, particularly in rainy seasons. However, the study about the dynamic behavior of high-speed railway subgrade involving water is currently rare. Based on the theory of fluid dynamics in porous medium and the vehicle-track coupling vibration theory, a numerical method of hydraulic-dynamic coupling was established to evaluate the dynamic responses of saturated roadbed surface layer under the high-speed train loading with the validation by comparing the calculated values and field data. The temporal and spatial characteristics of dynamic behaviors (stress, pore water pressure, seepage velocity, displacement) of saturated roadbed surface layer are fully discussed. Also, the effects of train velocity, permeability, on aforementioned dynamic responses of the saturated roadbed surface layer are evaluated. The study shows that improving the drainage of ballastless track roadbed has a significant effect on minimizing the mud pumping of ballastless track, and the influence zone of hydraulic-mechanical coupling is mainly within 0.1 m of the roadbed.

Prediction of ground vibration under combined seismic and high-speed train loads considering earthquake intensity and site category

Based on a two-and-half-dimensional finite element model (2.5D FEM), the layered ground vibration under combined seismic and high-speed train loads was investigated. On this basis, the effect of site category and earthquake intensity on ground vibration under the combined action of two dynamic loads was analyzed. Numerical examples indicated that ground vibration displacement due to combined loads decreases with the increase of soil stiffness, while the influence of soil stiffness on the ground vibration is small when the hardness of the subsoil is large. The peak ground displacement (PGD) is a reasonable seismic intensity index for predicting the ground vibration displacement at the track center under the combined loads, which has a higher accuracy for hard ground. In view of this, an equivalent shear wave velocity and PGD-based prediction formula was proposed to estimate the ground vibration under combined seismic and high-speed train loads. Reliability of the prediction formula was verified through comparison with results of numerical tests, indicating that the prediction formula has good applicability to different site conditions and seismic events. Compared with the previous study, it demonstrated that the prediction method provided an effective means for estimating ground vibration caused by a high-speed train load during earthquakes.

Dynamic response analysis of piled embankment and train derailment evaluation subjected to seismic and high-speed train loads

Based on a train-rail-piled embankment three-dimensional finite element model, the vibration displacement, acceleration and frequency spectrum of the rail and subgrade caused by combined seismic and high-speed train loads was investigated. On this basis, performance of piled embankment under combined seismic and high-speed train loads was analyzed. Numerical examples indicate that the seismic load dominates the ground displacement and the moving train load has negligible effects on the ground displacement. However, the moving train load has a significant effect on the rail vibration displacement during earthquakes. The rail and subgrade vibration displacement of piled embankment under combined seismic and moving train loads is obviously lower than that of ordinary subgrade, and its dominant frequency tends to transfer from high to middle and low frequency compared with ordinary subgrade, indicating that pile embankment has a good vibration reduction effect. Moreover, the derailment coefficient and lateral displacement of piled embankment is obviously decreased, which provides important guidance that pile embankment has significant vibration reduction effect and thus it can effectively prevent derailment or overturning during earthquakes.

Enhancing railway track stiffness and sustainability through flowable dredged soil backfill

This study investigates flowable dredged soil backfill using air-foam technology and simulates a bridge approach structure under high-speed train loads. A comparison between conventional cement-treated soil (CTB) and innovative flowable dredged soil backfill solutions reveals crucial findings: Resilient modulus tests highlight the significant impact of cement and air foam, favoring mixtures with over 210 kg/m3 cement content and less than 10% air-foam, resulting in a resilient modulus of 354 MPa. Finite Element Method (FEM) simulations show CTB compliance with k1/k2 standards for all track options and the effectiveness of lightweight soil, especially Silty Soil (SM), in preventing critical k1/k2 increases. The lightweight soil exhibits superior performance through FEM analysis, settling only 3 mm after 800,000 cyclic train loads compared to nearly 5 mm in conventional CTB systems. This confirms the feasibility of lightweight dredged soil backfill in strengthening weak bridge approach foundations, enhancing railway track infrastructure sustainability and performance.

DYNAMIC ANALYSIS OF A STEEL-CONCRETE RAILWAY BRIDGES OF LANGER TYPE UNDER THE INFLUENCE OF A MOVING LOAD

The studying the dynamic response of steel-concrete railway bridges of Langer type is huge importance of ensuring the safety of such structures under high-speed train loads. Numerical simulations at the design stage require knowledge of the modal characteristics: natural frequencies, shapes and damping. In addition, in the dynamics of railway bridges subjected to high-speed trains, it is important to check the impact of dynamic effects on the ultimate and serviceability limit states. As part of the investigations displacements and accelerations of selected measurement points arising from driving the test rolling stock are analyzed. In the first stage, calculations of the eigenvalues and the corresponding eigenvectors were carried out in the Robot program for two variants of mass description (distributed and discrete). In the second stage, dynamic train passages for various vehicle speeds were examined in terms of displacements and accelerations of measurement points by using the authors’ program MES3D.

Numerical investigation into hydrodynamic behavior of graded aggregates of high-speed ballastless track considering the degree of saturation

The ballastless track inevitably suffers from some functional defects, such as expansion joint cracking, due to the long term combined effect of dynamic train loads and environmental factors. As a result, water can be somehow retained in the graded aggregates of the roadbed surface layer under ballastless track, which is a key structural component subject to high-speed train loads. Accordingly, it is of significance to study the hydrodynamic behavior of roadbed surface layer that can be prone to depend on variation of the degree of saturation (Sr) in graded aggregates. A coupled hydrodynamic model of roadbed surface layer under ballastless track subject to high speed train loads was established based on homogenization theory and elastic wave theory involving Sr of graded aggregates. The proposed model is validated by degrading to Biot's dynamic model in saturated porous medium and analytical method of unsaturated soil. The effect of different Sr on the pore fluid pressure, spatial seepage velocity of graded aggregates is investigated based on this model with the practical seepage boundaries in ballastless track considered. On this basis, the influence of different spatial locations on the dynamic seepage index is discussed, and the differences in the stress paths in the roadbed surface layer under different Sr at different depths are analysed. The numerical results show that the increase of Sr has a spatial and critical effect on the increase of pore water pressure and seepage velocity in the roadbed surface layer. When the expansion joint of ballastless track cracks, the hydrodynamic erosion in the surface layer of ballastless track roadbed has been accumulating continuously. The erosion is more serious within the depth of 15 cm under the surface of roadbed. For Sr above 0.7, extra attention should be given to prevent internal erosion diseases in the roadbed surface layer during maintenance of ballastless track.

Full-scale model tests on ballasted tracks with/without geogrid stabilisation under high-speed train loads

High-speed trains running on ballasted tracks intensify the vibration of ballast layers to a greater extent than conventional passenger trains, with detrimental effects to train operations. The stabilisation effect of the geogrid in real railways under high-speed train moving loads remains unclear. Herein, full-scale model tests on a ballasted trackbed with and without geogrid were conducted, and a novel sequential loading system was adopted to apply the train moving loads. The highest train speeds were 300 km/h for the ballasted track without geogrid, and 360 km/h for the ballasted track with geogrid. To monitor the geogrid tension strain, distributed fibre Bragg grating sensors were mounted on the geogrid ribs. It was found that the maximum geogrid tension strain between neighbouring sleepers was six times larger than that beneath the sleepers. The geogrid influence zone in the ballast layer was identified as being at least 15 cm above the geogrid. The dynamic stress on the subballast surface was decreased by about 49% in the stabilised trackbed. The testing results also showed that geogrid stabilisation could reduce ballast breakage from 14·9% to 2·5% and reduce the permanent settlement of ballast layer by 40%. The experimental results presented in the paper provide a benchmark for geogrid-stabilisation modelling and will be referenced for the optimal design of ballasted tracks.

Dynamic analysis on the structure of metro station under high-speed railway load

High-speed railways often run over underground metro stations. Dynamic load induced by high-speed train can influence the internal force of underground structure and hence can pose danger to the underground structure. Hence, it is necessary to estimate the safety of underground structure due to high-speed train load. In this paper, the effects of dynamic load induced by high-speed train on metro station are investigated by carrying out three-dimensional numerical analysis. Guinan high-speed railway, which is designed to run over Jinqiao metro station in Nanning, Guangxi province of China are adopted as the background of this case study. The hardening soil model with small-strain stiffness was adopted to model the behaviour of soil. Two typical speed of railway train (i.e., 160 km/h and 350 km/h) are considered in this study. Based on the numerical analysis, vertical vibration acceleration and bending moment of the structure of the metro station are presented and analysed.

State of Art for Dynamic interaction of High Speed Bullet Train Load for Cable Stayed Bridge

Cable stayed bridge (CSB) is the center of attraction among all bridges due to aesthetic appearance and structural integrity. Earlier CSB used only for pedestrian and vehicular loads but with time passes it uses more intended towards mass transportation. When a bridge is designed to serve such heavy and rapid load; it should be analyzed for such load intensity. The question is how this high-speed rail load should be applied? The trainload is applied to bridge structure by different approaches by different researchers. In this article, a state of art for high-speed train load applications is discussed.

Numerical modelling of vibration response in loess hills due to a high-speed train on railway viaduct

In order to accurately analyze vibration characteristics and site effects of loess hills under moving load of a high-speed train, four types of loess hill models under railway viaduct was established by ABAQUS of finite element analysis software by field test. The dynamic response and stability of loess hills under two different vibration sources under high-speed train load were studied by using two-dimensional equivalent linear response time-history analysis, and the influence of the mechanical parameters of loess on the vibration of different types of loess hill was analyzed. Results show that there are obvious differences between peak displacement cloud maps of loess hills under the railway viaduct under gravity and train load action. We analyzed the influence of the change of elastic modulus on vibration propagation of soil of foundation and loess knoll, and found that the change of elastic modulus of soil in different position of foundation has more effect on vibration propagation than that of loess knoll soil. At the same time, the vertical acceleration cloud maps of the four types of loess hills are obviously different.

Image-Aided Analysis of Ballast Particle Movement Along a High-Speed Railway

As a core infrastructure of high-speed railways, ballast layers constituted by graded crushed stones feature noteworthy particle movement compared with normal railways, which may cause excessive settlement and have detrimental effects on train operation. However, the movement behavior remains ambiguous due to a lack of effective measurement approaches and analytical methods. In this study, an image-aided technique was developed in a full-scale model test using digital cameras and a color-based identification approach. A total of 1274 surface ballast particles were manually dyed by discernible colors to serve as tracers in the test. The movements of the surface ballast particles were tracked using the varied pixels displaying tracers in the photos that were intermittently taken during the test in the perpendicular direction. The movement behavior of ballast particles under different combinations of train speeds and axle loads was quantitatively evaluated. The obtained results indicated that the surface ballast particle movements were slight, mainly concentrated near sleepers under low-speed train loads and greatly amplified and extended to the whole surface when the train speed reached 360 km·h−1. Additionally, the development of ballast particle displacement statistically resembled its rotation. Track vibration contributed to the movements of ballast particles, which specifically were driven by vertical acceleration near the track center and horizontal acceleration at the track edge. Furthermore, the development trends of ballast particle movements and track settlement under long-term train loading were similar, and both stabilized at nearly the same time. The track performance, including the vibration characteristics, accumulated settlement, and sleeper support stiffness, was determined to be closely related to the direction and distribution of ballast particle flow, which partly deteriorated under high-speed train loads.

Dynamic Response of Pile-Soil Foundation with an Adjacent Tunnel under the High-Speed Train Loads: A Case Study

In order to study the dynamic response characteristics of a pile-soil foundation when an adjacent tunnel exists, both model tests and numerical simulations were performed in this study. Taking the peak vibration acceleration, peak vibration velocity, and peak vibration displacement as the evaluation indexes of the dynamic response, the dynamic response of the pile-soil foundation with an adjacent tunnel under high-speed train loads is studied. A method of dividing the affected zones of the dynamic response based on the safety threshold is provided in this paper, which can evaluate the safety of the adjacent tunnel under the action of train load. Additionally, the effect of train speed on dynamic response is further analyzed. The results show that the dynamic response index inside the foundation decays significantly with increasing distance from the surface when the train load is applied, regardless of the presence or absence of the adjacent tunnel. Compared with an ordinary pile-soil foundation, the dynamic response indexes inside the foundation increase significantly when there is an adjacent tunnel. With the increase in the horizontal distance from the pile foundation, the distribution characteristics of the horizontal transverse direction of each dynamic response index inside the foundation change from a “wavy” distribution to a monotonically decreasing distribution. According to the safety threshold of vibration velocity, the foundation is divided into the hazardous affected zone, strongly affected zone, and weakly affected zone, and then the corresponding vibration reduction measures are adopted. With the increase in train speed, the effect of tunnel structure on the attenuation of dynamic response in a pile-soil foundation becomes more obvious.

A method for defining high speed train loads in time - domain FEM models

This paper presents a method for defining high speed train loads in finite element models to simulate train-induced ground vibrations in time-domain. The method assumes that wheel/rail contact is perfect and that the wheel loads act on the rails as moving forces. These moving forces are then transferred to the ballast surface as a series of equivalent concentrated forces that appear successively depending on the train speed. To verify the presented method, we compare numerical and analytical solution for a case of a track resting on an elastic half space subjected to an axle force moving at a high speed.

A Review of Numerical Models for Slab-Asphalt Track Railways

Higher train speeds and heavier axle loads trigger elevated stresses and vibrations in the track, potentially increasing track deterioration rates and maintenance costs. Alternative track forms made of combinations of reinforced concrete and asphalt layers have been developed. A thorough understanding of the slab and asphalt tracks is needed to investigate track performance. Thus, analytical and numerical models have been developed and validated by many researchers. This paper reviews numerical models developed to investigate railway track performance. The synthesis of major finite element models is described in detail, highlighting the main components and their outputs. For slab track models, the use of a structural asphalt layer within the railway track remains an active research topic and firm conclusions on its efficacy are not yet available. It can be expected that slab track structures will also be affected by train-induced ground vibrations. There is thus a gap in the literature regarding the measurement of dynamic effects on high-speed railway lines, and further research is needed to investigate the dynamic behaviour of slab–asphalt track systems. In this review, novel solutions for mitigating the vibrations in high-speed rail are discussed and compared. The use of asphalt material in railways appears to have beneficial effects, such as increasing the bearing capacity and stiffness of the structure and improving its dynamic performance and responses, particularly under high-speed train loads.