Numerical analysis of high‑speed railway slab tracks using calibrated and validated 3D time‑domain modelling

Concrete slabs are widely used in modern railways to increase the inherent resilient quality of the tracks,provide safe and smooth rides,and reduce the maintenance frequency.In this paper,the elastic performance of a novel slab trackform for high-speed railways is investigated using three-dimensional finite element modelling in Abaqus.It is then compared to the performance of a ballasted track.First,slab and ballasted track models are developed to replicate the full-scale testing of track sections.Once the models are calibrated with the experimental results,the novel slab model is developed and compared against the calibrated slab track results.The slab and ballasted track models are then extended to create linear dynamic models,considering the track geodynamics,and simulating train passages at various speeds,for which the Ledsgard documented case was used to validate the models.Trains travelling at low and high speeds are analysed to investigate the track deflections and the wave propagation in the soil,considering the issues associated with critical speeds.Various train loading methods are discussed,and the most practical approach is retained and described.Moreover,correlations are made between the geotechnical parameters of modern high-speed rail and conventional standards.It is found that considering the same ground condition,the slab track deflections are considerably smaller than those of the ballasted track at high speeds,while they show similar behaviour at low speeds.

Dynamic analysis of slab track on multi-layered transversely isotropic saturated soils subjected to train loads

The dynamic responses of a slab track on transversely isotropic saturated soils subjected to moving train loads are investigated by a semi-analytical approach. The track model is described as an upper Euler beam to simulate the rails and a lower Euler beam to model the slab. Rail pads between the rails and slab are represented by a continuous layer of springs and dashpots. A series of point loads are formulated to describe the moving train loads. The governing equations of track-ground systems are solved using the double Fourier transform, and the dynamic responses in the time domain are obtained by the inverse Fourier transform. The results show that a train load with high velocity will generate a larger response in transversely isotropic saturated soil than the lower velocity load, and special attention should be paid on the pore pressure in the vicinity of the ground surface. The anisotropic parameters of a surface soil layer will have greater influence on the displacement and excess pore water pressure than those of the subsoil layer. The traditional design method taking ground soil as homogeneous isotropic soil is unsafe for the case of RE 〈 1 and RG 〈 1, so a transversely isotropic foundation model is of great significance to the design for high train velocities.

Analysis of vibration reduction characteristics and applicability of steel-spring floating-slab track

A coupled dynamics computation model for metro vehicles, along with a steel-spring floating-slab track, is developed based on the theory of vehicle-track coupled dynamics. Using the developed model, the influences of the thickness, length and mass of floating-slab, spring rate and its arrangement space, running speed, etc. on the time and frequency domain characteristics of steel-spring fulcrum force are analyzed. The applicability of steel-spring floatingslab track is discussed through two integrated example cases of metro and buildings possessing distinct natural vibra- tion characteristics. It is concluded that, it is quite significant, in the optimization modular design of the parameters of steel-spring floating-slab track, to take the matching relationship of both the amplitude-frequency characteristics of steel-spring fulcrum force and natural vibration characteristics of integrated structures into comprehensive consideration. In this way the expensive steel-spring floating-slab track can be economically and efficiently utilized according to the site condition, and at the same time, the economic losses and bad social impact resulted from the resonance during usage of steel-spring floating-slab track can be avoided.

Slab Tracking and Controlling on Hot Plate Rolling Line

By studying the slab moving in detail in the plate rolling process, the problem of slab tracking and controlling was solved by using the distributed control system. The problems of rhythm control for the big-complex system, the exchange of manual and automatic operations, the data exchange between the levelⅠ, TCS (technology control system) and levelⅡ, PCS (process control system), are solved. By this way, the automatic level of the plate production line is improved.

Testing and Approval Procedures for New Slab Track Systems in Europe

This paper describes the required testing and approval procedures of new track systems operated in Europe. To begin with, test methods and performance specifications according to European Standard （EN） are outlined. These include the repeated loading test, the determination of the static and dynamic stiffness of rail pads, clamping force and longitudinal rail resistance. The fact that labor tests are unable to simulate all the conditions in situ shows that these labor tests are not sufficient for the evaluation of the long term behaviour of a new track system： a test track of sufficient length must be constructed and exposed to traffic loads. In Europe to be accredited as a new system, a new slab track system must have a trial time of more than two years, during which the features of the whole system can be recognized. In the second part of this paper, the experience of the Institute of Road, Railway and Airfield Construction of TUM concerning the measuring methods of slab track systems carrying traffic are outlined. Also the approval procedure of the new slab tracks in Germany is discussed.

Analysis theory of spatial vibration of high-speed train and slab track system

The motor and trailer cars of a high-speed train were modeled as a multi-rigid body system with two suspensions. According to structural characteristic of a slab track, a new spatial vibration model of track segment element of the slab track was put forward. The spatial vibration equation set of the high-speed train and slab track system was then established on the basis of the principle of total potential energy with stationary value in elastic system dynamics and the rule of "set-in-right-position" for formulating system matrices. The equation set was solved by the Wilson-θ direct integration method. The contents mentioned above constitute the analysis theory of spatial vibration of high-speed train and slab track system. The theory was then verified by the high-speed running experiment carried out on the slab track in the Qinghuangdao-Shenyang passenger transport line. The results show that the calculated results agree well with the measured results, such as the calculated lateral and vertical rail displacements are 0.82 mm and 0.9 mm and the measured ones 0.75 mm and 0.93 mm, respectively; the calculated lateral and vertical wheel-rail forces are 8.9 kN and 102.3 kN and the measured ones 8.6 kN and 80.2 kN, respectively. The interpolation method, that is, the lateral finite strip and slab segment element, for slab deformation proposed is of simplification and applicability compared with the traditional plate element method. All of these demonstrate the reliability of the theory proposed.

Transfer relation between subgrade frost heave and slab track deformation and vehicle dynamic response in seasonally frozen ground

Subgrade frost heave in seasonally frozen ground can greatly influence the safety and smooth running of high-speed trains and the service performance of track structures.In this study,we used a static model to:(1)investigate track-subgrade frost heave and develop a dynamic model of vehicle-track-subgrade frost heave;(2)explore the transfer relation between subgrade frost heave and track structure deformation;(3)examine the characteristics of interlayer debonding;(4)study the influence of subgrade frost heave on the dynamic response of vehicles in high-speed railways in seasonally frozen regions.A Fourier series was used to fit the frost heave waveform and simulate the behavior of subgrade uneven frost heave using data collected on-site.The results show:(i)The position of frost heave significantly affects the transfer of deformation to a slab track.The largest deformation of the track slab,with the amplitude transfer ratio reaching 20%,was recorded when the frost heave occurred near the joint of the base plate.(ii)At the same frost heave amplitude,long-wave frost heave causes smaller deformation and debonding of the track structure than short-wave frost heave.In the wavelength range of 10-30 m,the main frequency of the acceleration spectral density was concentrated between 3.5 and 3.7 Hz,with larger frost heave wavelengths producing smaller superposition on the vertical acceleration of the vehicle.(ii)The maximum wheel-rail force occurs when the front bogie passes the frost heave peak,with greater frost heave amplitudes producing greater wheel-rail force.From these results,we conclude there is a clear need to control the frost heave deformation of the track to reduce the dynamic response of the vehicle and in turn improve train operatSubgrade frost heave in seasonally frozen ground can greatly influence the safety and smooth running of high-speed trains and the service performance of track structures.In this study,we used a static model to:(1)investigate track`-subgrade frost heave and develop a dynamic model of vehicle`-track`-subgrade frost heave;(2)explore the transfer relation between subgrade frost heave and track structure deformation;(3)examine the characteristics of interlayer debonding;(4)study the influence of subgrade frost heave on the dynamic response of vehicles in high-speed railways in seasonally frozen regions.A Fourier series was used to fit the frost heave waveform and simulate the behavior of subgrade uneven frost heave using data collected on-site.The results show:(i)The position of frost heave significantly affects the transfer of deformation to a slab track.The largest deformation of the track slab,with the amplitude transfer ratio reaching 20%,was recorded when the frost heave occurred near the joint of the base plate.(ii)At the same frost heave amplitude,long-wave frost heave causes smaller deformation and debonding of the track structure than short-wave frost heave.In the wavelength range of 10-30 m,the main frequency of the acceleration spectral density was concentrated between 3.5 and 3.7 Hz,with larger frost heave wavelengths producing smaller superposition on the vertical acceleration of the vehicle.(iii)The maximum wheel`-rail force occurs when the front bogie passes the frost heave peak,with greater frost heave amplitudes producing greater wheel`-rail force.From these results,we conclude there is a clear need to control the frost heave deformation of the track to reduce the dynamic response of the vehicle and in turn improve train operations.ions.

A method for support stiffness failure identification in a steel spring floating slab track of urban railway: a case study in China

The extensive use of steel spring floating slab tracks has effectively addressed the challenge of alleviating the environmental vibrations induced by urban rail transit systems.However,under the combined action of train dynamic loads and complex environmental factors,problems,such as the fracture of steel spring vibration isolators and suspension vibrations induced by the uneven settlement of the base,often occur.The failure of isolator support stiffness is often hidden in its early stages and is challenging to identify by conventional detection methods.At the same time,it will aggravate the wheel-rail interaction,accelerate the deterioration of track structure,and even affect the driving safety.This study first establishes a detailed coupled train-floating slab track-foundation analytical model.Then the influence of the vibration isolator support stiffness failure on the dynamic indices of the floating slab track system response is analyzed.A set of defect identification methods that can detect the number of failed steel springs,severity of damage,and their location is proposed.Finally,an intelligent monitoring system for support stiffness of floating slab track is built by combining the density-based spatial clustering of applications with noise algorithm and statistical data analysis and is applied to a rail line in southern China.During a three-year monitoring campaign,a suspension failure and a fracture of a steel spring were each successfully detected and detailed failure information was obtained.Field investigation results were consistent with the damage identification results.After repair,the track structure dynamic response returned to the average pre-damage level and further deterioration had been arrested.The proposed damage identification methods and monitoring system provide an approach for intelligent identification of track structure support stiffness failures.

Two-stage identification of interlayer contact loss for CRTS Ⅲ prefabricated slab track based on multi-index fusion

To accurately identify the potential contact loss of the China railway track system(CRTS)III prefabricated slab track,a finite element model with contact loss of self-compacting concrete(SCC)under transient impact was established.Then the vertical accelerations near impact points on the track slab surface were extracted to obtain damage-sensitive indices in the time and frequency domains.The indices were initially normalized to obtain independent items of evidence before the Dempster-Shafer(D-S)evidence theory was used to fuse these into one.Finally,a two-stage identification was performed to identify the damaged SCC area,comprising a rough identification(Stage I)and a precise identification(Stage II).The research results show that the damage indices extracted based on the transient impact response change abruptly at the damage location,and that can be used for damage identification.However,the use of a single index to determine the damage of the impact point may be misjudged.In Stage I,five damage indices of acceleration were fused to magnify the difference between the damaged point and undamaged point,thereby improving the accuracy of finding damage.In Stage II,in the area where more impact points were added,a fusion of three indices of acceleration response,that is,the absolute mean of the time domain,the maximum amplitude of the frequency domain,and the power density ratio,further narrowed down the area where damage exists.As a result,when the contact loss of SCC is greater than 50%along the thickness direction,the identification accuracy can be as high as 70%to 80%.The two-stage identification method proposed in this study can greatly improve the efficiency of interlayer damage detection of slab tracks and is expected to provide effective technical support for damage identification of track structures in the future.

Influences of cement asphalt emulsified mortar construction on track slab geometry status

Purpose–The construction of cement asphalt(CA)emulsified mortar can obviously disturb the slab status after the fine adjustment.To decrease or eliminate the influence of CA mortar grouting on track slab geometry status,the effects of grouting funnel,slab pressing method,mortar expansion ratio,seepage ratio and grouting area on China Railway Track System Type(CRTS I)track slab geometry status were discussed in this paper.Design/methodology/approach–Combined with engineering practice,this paper studied the expansion law of filling layer mortar,the liquid level height of the filling funnel,the pressure plate device and the amount of exudation water and systematically analyzed the influence of filling layer mortar construction on the state of track slab.Relevant precautions and countermeasures were put forward.Findings–The results showed that the track slab floating values of four corners were different with the CA mortar grouting and the track slab corner near CA mortar grouting hole had the maximum floating values.The anti-floating effect of“7”shaped slab pressing device was more efficient than fixed-joint angle iron,and the slab floating value could be further decreased by increasing the amount of“7”shaped slab pressing devices.After CA mortar grouting,the track slab floating pattern had a close correlation with the expansion rate and water seepage rate of CA mortar over time and the expansion and water seepage rate of the mortar were faster when the temperature was high.Furthermore,the use of strip CA mortar filling under the rail bearing platform on bothsides could effectively reduce the float under the track slab,and it could also save mortar consumption and reduce costs.Originality/value–This study plays an important role in controlling the floating values,CA mortar dosage and the building cost of projects by grouting CA mortar at two flanks of filling space.The research results have guiding significance for the design and construction of China’s CRTS I,CRTS II and CRTS III track slab.

Experimental study of temperature gradient in track slab under outdoor conditions in Chengdu area

Temperature is one of the important loads for designing slab track. The characteristic of slab track tem- perature varies greatly with different regional climates. In this work, a bi-block slab track model was built under outdoor conditions in Chengdu area; the statistical characteristic of temperature gradient in track slab and the relationship between temperature gradient and surface air temperature were tested and analyzed. The results show that the track slab temperature gradient will vary periodically according to the surface air temperature, and show a clear nonlinearity along the height direction. The temperature gradient distribution is extremely uneven： the temperature gradient in the top part of the track slab is larger than that in the bottom part; the most frequently occurring temperature gradient of the track slab is around -3.5 ℃/m and more than 75 % locates in the level -10 to 10 ℃/m; concrete with a relatively good heat exchange condition with the surrounding air has a narrower band distribution. In addition, the frequency distribution histogram should exclude the time zone from 00：00 to 06：00 because there is almost no traffic in this period. The amplitude of track slab temperature variation is obviously lower than that of the air temperature variation, and the former is approximately linear with the latter.

Low frequency vibration tests on a floating slab track in an underground laboratory

Low frequency vibrations induced by underground railways have attracted increasing attention in recent years. To obtain the characteristics of low frequency vibrations and the low frequency performance of a floating slab track (FST), low frequency vibration tests on an FST in an underground laboratory at Beijing Jiaotong University were carried out. The FST and an unbalanced shaker SBZ30 for dynamic simulation were designed for use in low frequency vibration experiments. Vibration measurements were performed on the bogie of the unbalanced shaker, the rail, the slab, the tunnel invert, the tunnel wall, the tunnel apex, and on the ground surface at distances varying from 0 to 80 m from the track. Measurements were also made on several floors of an adjacent building. Detailed results of low frequency vibration tests were reported. The attenuation of low frequency vibrations with the distance from the track was presented, as well as the responses of different floors of the building. The experimental results could be regarded as a reference for developing methods to control low frequency vibrations and for adopting countermeasures.

Vibration response analysis of floating slab track supported by nonlinear quasi-zero-stiffness vibration isolators

To improve the low-frequency vibration reduction effect of a steel spring floating slab track(FST),nonlinear quasizero-stiffness(QZS)vibration isolators composed of positive stiffness elements(PSEs)and negative stiffness elements(NSEs)were used to support the FST.First,considering the mechanical characteristics of the nonlinear QZS vibration isolators and the dynamic displacement limit(3 mm)of the FST,the feasible parameter groups were studied with the nonlinear stiffness variation range and bearing capacity as evaluation indices.A vertical vehicle quasi-zero-stiffness floating slab track(QZS-FST)coupled dynamic model was then established.To obtain a reasonable nonlinear stiffness within a few millimeters,the original length of the NSEs must be analyzed first,because it chiefly determines the stiffness nonlinearity level.The compression length of the NSEs at the equilibrium position must be determined to obtain the low stiffness of the floating slab without vehicle load.Meanwhile,to meet the dynamic displacement limit of the FST,the PSE stiffness must be increased to obtain a higher stiffness at the critical dynamic displacement.Various stiffness groups for the PSEs and NSEs can provide the same dynamic bearing capacity and yet have a significantly different vibration reduction effect.Excessive stiffness nonlinearity levels cannot effectively improve the vibration reduction effect at the natural frequency.Furthermore,they also significantly amplify the vibrations above the natural frequency.In this paper,the vertical vibration acceleration level(VAL)of the floating slab and the supporting force of the FST can be decreased by 6.9 dB and 55%,respectively,at the resonance frequency.

Design theories and maintenance technologies of slab tracks for high-speed railways in China:a review

The durability and reliability of slab track structures are essential for the long-term safety and stable operation of high-speed railways.In order to provide a solid theoretical basis and technical reference for the advancement of high-speed railway quality,this paper comprehensively discusses design theories of slab track structures,service performance evolution and maintenance technologies,and reviews the innovation happening in the industry.On top of that,the damage evolution,fatigue features and durability of slab tracks,which are highly relevant to serviceability,are summarized,and the future research trend of slab track service behaviours is pointed out.In addition,this paper summarizes the rules of establishing standards for damage maintenance,typical solutions for repairing damage and methods of evaluating the maintenance outcomes that combine field tests and numerical simulations.It also envisions a future direction where advanced testing technologies would assist the evaluation of maintenance effects.

Fatigue damage analysis of ballastless slab track in heavy-haul railway tunnels

A ballastless slab track,which is commonly used in the track structures of heavy-haul railway tunnels,was analysed based on field measurement data of the Fuyingzi Tunnel on the Zhangtang Railway.In accordance with the measured data,the dynamic load thresholds and distributions on the surface and bottom of the ballastless slab track were investigated.A fatigue damage analysis of the ballastless slab track was performed based on the dynamic load time–history curve.The results show that the ballastless slab track can accomplish train load attenuation and reduce the dynamic load from heavy-haul trains by 47.22%from the surface to the bottom.In addition,the distribution at the bottom of the ballastless slab track exhibited a triangular shape,and the dynamic load threshold at the line centre accounted for 78.67%of that at the track position.Meanwhile,the distribution at the surface was saddle-shaped;the dynamic load threshold at the track position accounted for 79.55%of that at the line centre position.The fatigue damage of the ballastless slab track was analysed effectively by combining the measured data and the linear fatigue damage theory.Moreover,the accuracy of the calculation results was verified based on the measured dynamic stress of the ballastless slab track structure.The dynamic action of the train load led to more-concentrated damage to the track bed,and the damage occurred earlier than that in the ordinary line.The axle load was the primary influencing factor of the track bed fatigue damage,and the damage mainly occurred in the track position.These results provide a theoretical basis for performing stress analysis and designing parameters for ballastless slab tracks in heavy-haul railway tunnels.

Critical Velocity of Short Floating Slab Track Using Alterable Element Method Considering Wheel-Rail Contact Loss

In actual line operation,the critical velocity is one of the key physical quantities of rail design owing to its great infuence on the riding comfort and safety of vehicles due to the wheel-rail contact loss caused by the abrupt change of rail foundation rigidity,rail wear,or abruptness irregularities on rail.In this study,the short floating slab track(SFST)structure is regarded as a double-layer system.The Euler beam and the rigid body model are adopted for the rail and the floating slab,respectively.and the dispersion equation and the theoretical critical velocity of the rail structure under ideal conditions are deduced.Besides,this st udy considers the implementation of the SFST in the vehicle-structure coupling system.The alterable element method is introduced for accurately simulating the change of the whee-rail contact state and coding a vehicle-structure dynamic analysis program(VSDAP)to calculate the critical velocity of rail structures from the dynamic response of vehicles and rail structures.The principle of its design at the beginning of the design is given on the basis of the theoretical value of the critical velocity and the simulation of the dynamic response,which can provide reference for practical engineering design.

Damage evolution and dynamic response of cement asphalt mortar layer of slab track under vehicle dynamic load

The damage evolution and dynamic performance of a cement asphalt(CA)mortar layer of slab track subjected to vehicle dynamic load is investigated in this paper.Initially,a statistical damage constitutive model for the CA mortar layer is developed using continuous damage mechanics and probability theory.In this model,the strength of the CA mortar elements is treated as a random variable,which follows the Weibull distribution.The inclusion of strain rate dependence affords considering its influence on the damage development and the transition between viscosity and elasticity.Comparisons with experimental data support the reliability of the model.A three-dimensional finite element(FE)model of a slab track is then created with the commercial software ABAQUS,where the devised model for the CA mortar is implemented as a user-defined material subroutine.Finally,a vertical vehicle model is coupled with the FE model of the slab track,through the wheel-rail contact forces,based on the nonlinear Hertzian contact theory.The evolution of the damage and of the dynamic performance of the CA mortar layer with various initial damage is investigated under the train and track interaction.The analysis indicates that the proposed model is capable of predicting the damage evolution of the CA mortar layer exposed to vehicle dynamic load.The dynamic compressive strain,the strain rate,and the induced damage increase significantly with an increase in the initial damage,whereas the dynamic compressive stress exhibits a sharp decrease with the increasing initial damage.Also,it is found that the strain rate dependence significantly influences the damage evolution and the dynamic behavior of the CA mortar layer.

Temperature-induced deformation of CRTS II slab track and its effect on track dynamical properties

Two finite-element models of the CRTS II slab track are presented to simulate temperature-induced deformations of the concrete track slab with no deterioration or with a deteriorated cement asphalt mortar(CAM).One model,which considers the fully bonding interface between the slab and the CAM layer,could applied to a track that is in good condition;the other model uses cohesive zone elements to simulate the deteriorated CAM with some possible interfacial separation and slip.Utilizing both of the models,temperature-induced warp deformations of track under various temperature loads are investigated.The influence of temperature deformation on the dynamic properties of the track is analyzed based on the train-track coupled dynamics.Numerical results show that the deteriorated CAM layer can significantly increase temperature deformations of a CRTS II track slab,which would produce tiny rail irregularities.There are clear differences between the deformation shapes of the track slabs that have an inseparable mortar layer and those have a separable mortar layer.The track slab with a deteriorated mortar layer showed more open curl distortion than the track slab in good condition.The dynamical response index of the slab track is intensified to a certain level due to the temperature deformation;with an increase of the train speed,the track dynamical responses increased linearly.However,rail irregularities due to the temperature deformations are very tiny.Even if a track is exposed to extreme temperature loads and the mortar layer is deteriorated,temperature deformation can have a negligible effect on the track’s dynamical properties.

Design method of pile-slab structure roadbed of ballastless track on soil subgrade

堆积平板结构路基是为高速度铁路的无碎石的轨道的一种新形式。由于相应设计代码的缺乏，基于它的结构特征和应用程序要求的分析，根据最终的限制状态和有用性限制状态执行负担效果联合被建议，并且每个状态的最相反的联合被选择为堆积平板结构完成设计计算。堆积平板结构的空间模型能作为一个飞机框架模型被简化，由用直角的测试方法，和堆积平板的设计参数，结构被优化。而且基于 Suining 重庆高速度的铁路的设计背景，堆积平板结构路基的动态变丑特征被继续室内的动态模型测试进一步研究。测试结果证明在路基的建设以后的解决满足解决控制的要求为高速度的铁路在土壤路基上造无碎石的轨道。当负担从平板被传给堆积，平板结构起拱门壳的作用，并且路基土壤的垂直动态压力是近似有深度的 K 形式分发。应力是的堆积的分发仔细与土壤特征，它有一个不安的三角形有关塑造大动态压力在顶在哪儿。与土壤份额相比堆很有活力的应力。堆积结构扩展路基的动态反应的深度并且改进火车的路基土壤，和速度的压力在动态反应上限制了效果。这些结果能为在土壤路基上使用的堆积平板结构路基提供科学基础。

Horizontal Push Plate Test and Simulation of CRTS II Slab Ballastless Track

Good interlayer interface performance is the key to maintaining the stability of CRTSⅡslab ballastless track structure.In a project,the tangential cohesion parameters of CRTSⅡslab ballastless track structure are generally measured by horizontal push plate test,so as to measure the interlayer interface performance.Horizontal push plate contraction scale and full scale tests of CRTSⅡslab ballastless track structure are carried out to obtain the tangential force-displacement relation curve of the interlayer interface,thus obtaining the parameters of cohesion model.A threedimensional progressive damage analysis model for CRTSⅡslab ballastless track structure is established,the whole process inversion of the horizontal push plate test is carried out,and the reliability of the contraction scale test results is verified by means of simulation and comparative analysis of test results.The results show that the greater the tangential stiffness of the interlayer interface of the track structure,the weaker the interlayer deformation coordination capability;the more significant the non-uniformity of the interface damage,the more likely the stress concentration;the greater the fracture toughness,the less likely the disjoint in the interlayer interface of the track structure.