Numerical prediction of ground vibrations induced by high-speed trains including wheel–rail–soil coupled effects

A simplified analytical model including the coupled effects of the wheel–rail–soil system and geometric irregularities of the track is proposed for evaluation of the moving train load. The wheel–rail–soil system is simulated as a series of moving point loads on an Euler–Bernoulli beam resting on a visco-elastic half-space, and the wave-number transform is adopted to derive the 2.5D finite element formulation. The numerical model is validated by published data in the literature. Numerical predictions of ground vibrations by using the proposed method are conducted at a site on the Qin-Shen Line in China.     

Scoping prediction of re-radiated ground-borne noise and vibration near high speed rail lines with variable soils

This paper outlines a vibration prediction tool, ScopeRail, capable of predicting in-door noise and vibration, within structures in close proximity to high speed railway lines. The tool is designed to rapidly predict vibration levels over large track distances, while using historical soil information to increase accuracy. Model results are compared to an alternative, commonly used, scoping model and it is found that ScopeRail offers higher accuracy predictions. This increased accuracy can potentially reduce the cost of vibration environmental impact assessments for new high speed rail lines.To develop the tool, a three-dimensional finite element model is first outlined capable of simulating vibration generation and propagation from high speed rail lines. A vast array of model permutations are computed to assess the effect of each input parameter on absolute ground vibration levels. These relations are analysed using a machine learning approach, resulting in a model that can instantly predict ground vibration levels in the presence of different train speeds and soil profiles. Then a collection of empirical factors are coupled with the model to allow for the prediction of structural vibration and in-door noise in buildings located near high speed lines. Additional factors are also used to enable the prediction of vibrations in the presence of abatement measures (e.g. ballast mats and floating slab tracks) and additional excitation mechanisms (e.g. wheelflats and switches/crossings).     

Three-dimensional simulation of track on poroelastic half-space vibrations due to a moving point load

An analytical approach is used to investigate dynamic responses of a track system and the poroelastic half-space soil medium subjected to a moving point load under three-dimensional condition. The whole system is divided into two separately formulated substructures, the track sub-system and the ground. The ballast supporting rails and sleepers is placed on the surface of the ground. The rail is modeled by introducing the Green function for an infinitely long Euler beam subjected to the action of the moving point load and the reaction of sleepers represented by a continuous mass. Using the double Fourier transform, the governing equations of motion are then solved analytically in the frequency–wave-number domain. The time domain responses are evaluated by the inverse Fourier transform computation for a certain load velocities. Computed results show that dynamic responses of the soil medium are considerably affected by the fluid phase as well as the load velocity.     

Vibrations induced by HST passage on ballast and non-ballast tracks

The use of ballastless slab track is significantly increasing in HST line technology. This development is due to some structural and operational advantages over ballasted track. In addition, floating slab tracks can be used to control ground-borne vibrations generated by surface and underground rail transportation systems. In this paper, a general and fully three dimensional multi-body-finite element-boundary element model is used to study vibrations due to train passage on ballast and non-ballast tracks. The vehicle is modelled as a multi-body system, the track, in both cases, using finite elements and the soil is represented using boundary elements. The three components of the load are considered; the quasi-static excitation (force generated by moving axle loads), the parametric excitation due to discrete supports of the rails and the excitation due to wheel and rail roughness and track unevenness. Track receptances are computed for both track systems and vibrations induced by high-speed train passage at the track and the free-field are evaluated for different train speeds. Soil behaviour changes significantly with the track system. Finally, a floating slab track is studied to show how this type of solution leads to a significant vibration reduction for surface tracks.     

城轨交通引起的环境振动问题综述研究

随着城市化进程的加快和人们生活质量的提高,城市轨道交通系统引起的沿线地面和建筑物的振动问题越来越引起人们的关注。系统地介绍了城市轨道交通的主要形式,对城市轨道交通所引起环境振动问题的国内外研究进行了综述,同时,全面分析了环境振动对人们生产生活的影响、振动产生的原因、振动预测模拟等方面的问题。对国内外有关环境振动的计算模型也系统深入地作了分析研究。     

Behavior of ground vibrations induced by trains moving on embankments with rail roughness

This study investigates the behavior of ground vibrations induced by trains moving on embankments using theoretical formulations, finite element analyses, and field experiments. The train-induced vibrations are large at the dominant frequencies of nV/L_c, even though the rail is very rough, where n is a positive integer, V is the train speed, and L_c is the carriage interval. For subsonic train speeds, the train-induced ground vibration is extremely small when the rail is perfectly smooth, but with a minor rail irregularity, the train-induced ground vibration can be significantly increased. However, for supersonic train speeds, the ground vibrations with or without rail irregularities are not very different, and the vibration of the first dominant frequency having the longest wavelength is the most obvious wave.     

Model track studies on fouled ballast using ground penetrating radar and multichannel analysis of surface wave

Ballast fouling is created by the breakdown of aggregates or outside contamination by coal dust from coal trains, or from soil intrusion beneath rail track. Due to ballast fouling, the conditions of rail track can be deteriorated considerably depending on the type of fouling material and the degree of fouling. So far there is no comprehensive guideline available to identify the critical degree of fouling for different types of fouling materials. This paper presents the identification of degree of fouling and types of fouling using non-destructive testing, namely seismic surface-wave and ground penetrating radar (GPR) survey. To understand this, a model rail track with different degree of fouling has been constructed in Civil engineering laboratory, University of Wollongong, Australia. Shear wave velocity obtained from seismic survey has been employed to identify the degree of fouling and types of fouling material. It is found that shear wave velocity of fouled ballast increases initially, reaches optimum fouling point (OFP), and decreases when the fouling increases. The degree of fouling corresponding after which the shear wave velocity of fouled ballast will be smaller than that of clean ballast is called the critical fouling point (CFP). Ground penetrating radar with four different ground coupled antennas (500 MHz, 800 MHz, 1.6 GHz and 2.3 GHz) was also used to identify the ballast fouling condition. It is found that the 800 MHz ground coupled antenna gives a better signal in assessing the ballast fouling condition. Seismic survey is relatively slow when compared to GPR survey however it gives quantifiable results. In contrast, GPR survey is faster and better in estimating the depth of fouling.     

A study of the reduction of ground vibrations by an active generator

This paper presents the concept of using an additional generator to prevent ground vibrations. A linear, transversally isotropic three dimensional half-space with the hysteretic damping model, acted upon by a harmonic vertical excitation is assumed. Equations of motion for the transversally isotropic ground model with the absorbing boundary conditions are presented and numerically integrated using FlexPDE software, based on the finite element method. The efficiency of the solution is analysed in terms of reducing the vertical and horizontal components of ground surface vibrations. Results in the form of a dimensionless amplitude reduction factor are presented for four different locations of a generator. The influence of the soil parameters and layers locations on the additional generator's efficiency is investigated. The vibration reduction efficiency in a four-story building is also presented.     

Numerical modelling of ground borne vibrations from high speed rail lines on embankments

A three dimensional numerical model is presented capable of modelling the propagation and transmission of ground vibration in the vicinity of high speed railways. It is used to investigate the effect of embankment constituent material on ground borne vibration levels at various distances from the track.The model is a time domain explicit, dynamic finite element model capable of simulating non-linear excitation mechanisms. The entire model, including the wheel/rail interface is fully coupled. To account for the unbounded nature of the soil structure an absorbing boundary condition (infinite element) is placed at the truncated interfaces. To increase boundary absorption performance, the soil structure is modelled using an elongated spherical geometry.The complex geometries associated with the track components are modelled in detail thus allowing a highly realistic simulation of force transmission from vehicle to embankment. Lastly, quasi-static and dynamic excitation mechanisms of the vehicle locomotives are described using a multi-body approach which is fully coupled to the track using non-linear Hertzian contact theory.The resulting model is verified using experimental ground borne vibration data from high speed trains, gathered through field trials. It is then used to investigate the role of embankments in the transmission of vibration. It is found that soft embankments exhibit large deflections and act as a waveguide for railway vibrations which are trapped within the structure. This results in increased vibration levels both inside the embankment and in the surrounding soil. In contrast it is found that embankments formed from stiffer material reduce vibrations in the near and far fields.     

Combined paraxial-consistent boundary conditions finite element model for simulating wave propagation in elastic half-space media

In this paper, a finite element model of a soil island is coupled to both a consistent transmitting boundary and a paraxial boundary, which are then used to model the propagation of waves in semi-infinite elastic layered media. The formulation is carried out in the frequency domain while assuming plane strain conditions. It is known that a discrete model of this type, while providing excellent results for a wide range of physical parameters in the context of a half-space problem, may deteriorate rapidly at low frequencies of excitation. This is so because at low frequencies the various waves in the model eventually attain characteristic wavelengths which exceed the distance of the bottom boundary, which then causes that boundary to fail. Also, the paraxial boundaries themselves break down at very low frequencies. In this paper, this difficulty is overcome and the model׳s performance is improved upon dramatically by incorporating an artificial buffer layer sandwiched between the bottom of the soil medium and the underlying elastic half-space. Applications dealing with rigid foundations resting on homogenous or layered half-space media are shown to exhibit significant improvement. Following extensive simulations, clear guidelines are provided on the performance of the coupled model and an interpretation is given on the engineering significance of the findings. Finally, clear recommendations are provided for the practical use of the proposed modelling strategy.     

层状半空间中洞室对平面SH波的放大作用

利用间接边界元法,求解了弹性层状半空间中洞室对入射平面SH波的放大作用问题,并以基岩上单一土层中洞室对入射平面SH波的放大作用为例进行了数值计算分析。本文模型的特点之一是考虑了层状场地的动力特性,因而更接近于实际工程;特点之二是计算精度非常高。研究表明,层状半空间中洞室对波的放大作用与均匀半空间中情况有着本质的差别;层状半空间中洞室附近地表动力响应由土层动力特性和洞室对波的散射二者共同决定。土层动力特性不仅影响洞室附近地表位移的幅值,还会影响地表位移的频谱。在土层的前几阶共振频率附近,随着基岩与土层剪切波速比的增大,土层的影响随之增大,而随着土层厚度的增加,土层的影响随之减小,并逐渐趋于均匀半空间情况。     

Reduction in ground vibrations by using shaped landscapes

Reduction in traffic-induced ground vibrations by the use of shaped landscapes is investigated here by shaping the landscape surrounding a high-tech facility, using the landscape thus produced as a wave obstacle. The effects of the geometric parameters of a shaped landscape were examined in parametric studies. An architectural landscape design was also investigated in terms of its effectiveness in reducing traffic-induced ground vibrations. Finite element models, analysed in the frequency domain, were employed. The models involve a layer of soil and the underlying bedrock. It was found that anywhere from an appreciable reduction to an appreciable amplification of the vibrations produced can occur, depending upon the geometric parameters of the shaped landscape involved. The most effective shape was found for a topography that acted as a waveguide that reduced the level of vibration by approximately 35%.     

Transient flexural vibrations of an elastic column supported by an elastic half-space

An analysis is presented of the transient flexural vibrations of an elastic column supported by an elastic half-space under the condition that an arbitrarily shaped free-field lateral acceleration and displacement are given as inputs. Applying Laplace transformations with respect to time and numerical inverse Laplace transformations, the time histories of the column acceleration at the interface and free end, and the column and half-space displacement distributions are obtained. After the input free-field acceleration terminates, slightly damped and almost harmonically variable acceleration is observed. The acceleration frequency after the disappearance of the input acceleration nearly coincides with the resonant frequency of the system. The slight damping with the first resonant frequency, even if the half-space is soft compared with the column, is characteristic of the transient flexural vibrations of a column supported by a half-space. Such a phenomenon is not typical of the transient longitudinal vibration problem. Therefore, it may be concluded: when buildings and structures are subjected to an earthquake or an explosive force, their flexural vibrations will continue with their first resonant frequencies, even if their foundations are soft.     

Stress distribution from railway track over geogrid reinforced ballast underlain by clay

Railway ballast forms a major component of a conventional rail track and is used to distribute the load to the subgrade, providing a smooth running surface for trains. It plays a significant role in providing support for the rail track base and distributing the load to the weaker layer underneath. Ballast also helps with drainage, which is an important factor for any type of transportation structure, including railroads. Over time, ballast progressively deforms and degrades under dynamic loading and loses its strength. In this study, extensive laboratory tests were conducted to investigate the effect of load amplitude, geogrid position, and number of geogrid layers, thickness of ballast layer and clay stiffness on the behavior of the reinforced ballast layer and induced strains in a geogrid. A half full-scale railway was constructed for carrying out the tests, which consisted of two rails 800 mm in length with three wooden sleepers(900 mm × 10 mm × 10 mm). Three ballast thicknesses of 200, 300 and 400 mm were used in the tests. The ballast was overlying 500 mm thickness clay in two states, soft and stiff. The tests were carried out with and without geogrid reinforcement; the tests were performed in a well-tied steel box of 1.5 m length ×1 m width ×1 m height. Laboratory tests were conducted to investigate the response of the ballast and the clay layers where the ballast was reinforced by a geogrid. Settlement in ballast and clay, soil pressure and pore water pressure induced in the clay were measured in reinforced and unreinforced ballast cases. It was concluded that the amount of settlement increased as the simulated train load amplitude increased, and there was a sharp increase in settlement up to cycle 500. After that, there was a gradual increase that leveled out between, 2500 to 4500 cycles depending on the frequency used. There was a slight increase in the induced settlement when the load amplitude increased from 0.5 to 1 ton but it was higher when the load amplitude increased to 2 tons. The increased amount in settlement depended on the existence of the geogrid and other parameters studied. The transmitted average vertical stress for ballast thicknesses of 30 cm and 40 cm increased as the load amplitude increased, regardless of the ballast reinforcement for both soft and stiff clay. The position of the geogrid had no significant effect on the transmitted stresses. The value of the soil pressure and pore water pressure on ballast thicknesses of 20 cm was higher than for 30 cm and 40 cm thicknesses. This meant that the ballast attenuated the induced waves. The soil pressure and pore water pressure for reinforced and unreinforced ballast was higher in stiff clay than in soft clay.     

Prediction of high-speed train induced ground vibration based on train-track-ground system model

The development of analysis on train-induced ground vibration is briefly summarized. A train-track-ground integrated dynamic model is introduced in the paper to predict the ground vibration induced by high-speed trains. Representative dynamic responses of the train-track-ground system predicted by the model are presented. Some major results measured from two field tests on the ground vibration induced by two high-speed trains are reported. Numerical prediction with the proposed train-track-ground model is validated by the high-speed train running experiments. Research results show that the wheel/rail dynamic interaction caused by track irregularities has a significant influence on the ground acceleration and little influence on the ground displacement. The main frequencies of the ground vibration induced by high-speed trains are usually below 80 Hz. Compared with the ballasted track, the ballastless track structure can produce much larger train-induced ground vibration at frequencies above 40 Hz. The vertical ground vibration is much larger than the lateral and longitudinal components.     

A procedure to develop scalable models for the transient response of sleepers in conventional and high-speed railway lines and implementation to the vertical vibration mode

This paper presents a procedure to develop scalable reduced models for the through-the soil interaction and traveling wave effects of distant sleepers in a long railway track. For development purposes, and, without loss of generality, the geometry of the sleepers is consistent with the UIC-60 track system commonly used in European high speed rail and the vertical vibration mode is considered. The ballast and the effects of soil layering are not considered in the present paper; however, it is the subject of ongoing research. The proposed reduced models are based on B-Spline impulse response functions (BIRF) of the sleepers only as computed through boundary element method (BEM) solutions of the full model, preserve the frequency content of the full models, and they are highly accurate within the assumptions of linear isotropic and homogeneous soil media. They are expressed in a scalable form with respect to soil properties and sleeper spacing. In particular, the BIRFs of distant sleepers can be accurately approximated by appropriate scaling operations of time and amplitude of a reference sleeper BIRF while retaining all dynamic characteristics of the full model. Three main scaling parameters are proposed: (i) the apparent propagation velocity, (ii) the geometric damping coefficient, and (iii) the soil properties of a reference soil (i.e., the shear modulus and shear wave velocity). The models are validated through comparisons with other BEM solutions, and the accuracy and efficiency are established. The proposed models are developed as part of an NSF funded research on vibrations induced by high-speed rail traffic and are consistent with the associated train and rail models and a multi-system interface coupling (MSIC) technique that were developed as a part of the project and presented in companion papers. The proposed procedure forms the framework for developing scaled reduced models for other vibration modes and different sleeper geometries and can be generalized to include any foundation type or layered soil profiles.     

Numerical prediction of low-frequency ground vibrations induced by high-speed trains at Ledsgaard, Sweden

The ground vibrations induced by a passenger train at the test site of Ledsgaard, Sweden, have been analysed and numerically simulated through a spectral element discretization of the soil. To calculate the spatial distribution of loading due to train passage, the train is decoupled from the track, and a suitable series of static forces is applied. The track and the embankment are modeled as a beam on elastic foundation, using analytical solutions for loads moving at constant velocity. The results of both 2D and 3D modelling assumptions are thoroughly discussed, in terms of prediction of track motion and of attenuation of peak ground velocity with distance.     

Attenuation of ground vibrations due to different technical sources

The attenuation of technically induced surface waves is studied theoretically and experimentally.In this paper, nineteen measurements of ground vibrations induced by eight different technical sources including road and rail traffic, vibratory and impulsive construction work or pile driving, explosions, hammer impulses and mass drops are described, and it is shown that the technically induced ground vibrations exhibit a power-law attenuation v～r-q where the exponents q are in the range of 0.5 to 2.0 and depend on the source types.Comparisons performed demonstrate that the measured exponents are considerably higher than theoretically expected.Some potential effects on ground vibration attenuation are theoretically analyzed.The most important effect is due to the material or scattering damping.Each frequency component is attenuated exponentially as exp(-kr), but for a broad-band excitation, the sum of the exponential laws also yields a power law but with a high exponent.Additional effects are discussed, for example the dispersion of the Rayleigh wave due to soil layering, which yields an additional exponent of 0.5 in cases of impulsive loading.     

谱时程比方法及其在确定地铁沿线地层场地响应中的应用

利用在北京地铁4号线北京大学东门站附近地铁隧道内和地面场地观测得到的振动数据,提出一种基于独立信号的谱时程比方法,实现了从地铁振动和地面振动数据中提取地层场地响应信息以及土层中的振动衰减信息．该方法对同一观测点不同时间段观测数据的分析结果具有高度的稳定性,经验证与基于钻孔资料地层模型的半无限空间层状介质的理论传递函数的频率响应特征具有良好一致性．同时,基于该方法还对隧道壁与土层振动耦合以及观测点附近浅表土层非弹性吸收带来的综合等效衰减特征进行了评估．研究结果显示,北京大学东门站附近振动场地放大效应的峰值频率主要在3—10 Hz之间,受地铁振动的影响,场地效应在不同测点以及地铁沿线、 切线和铅垂线等3个不同方向显示出一定的差异．      

Study of the train-induced vibration impact on a historic Bell Tower above two spatially overlapping metro lines

There is concern regarding the long-term vibration effects caused by metro trains on historic buildings. In this paper, the impact of metro train-induced vibrations on the Bell Tower in Xi’an above two spatially overlapping tunnels was studied.Metro Line 2 has been operational since 2011, and Line 6 is still under construction. To study and control the effect of micro vibrations on the Bell Tower, a metro train–track–tunnel–soil 3D dynamic FE model was developed. The vibration response generated by Line 2 was then predicted, and the influences of train speed on ground vibration were analysed. In addition, a detailed in situ measurement, which helped calibrate the numerical model and determine the dynamic behaviour of timber structures, was performed. Finally, the calibrated models and measured results were used to predict vibrations caused by road traffic and trains from two spatially overlapping metro lines. This was performed under different route schemes and train operation conditions.The results showed that installing steel spring floating slab tracks (FST) and decreasing train speeds had obvious effects on controlling the ground peak particle velocity (PPV). Simulated results from both the input impulse and output response generated by metro Line 2 matched well with actual measurements. If correct designs are employed, it is possible to resolve the vibration problem on historic buildings caused by metro trains.