Analysis of train-induced vibrations and vibration reduction schemes above and below critical Rayleigh speeds by finite element method

This paper simulates soil vibration under the train speed below and over the soil Rayleigh speed using the three-dimensional finite element method. Two vibration isolation schemes were studied including the soil improvement around the railway and the concrete slab constructed between the rail and soil. Numerical results indicate that the vibration increases considerably and decays slowly when the train speed exceeds the soil Rayleigh speed. The wave direction and dominant frequencies are the simple functions of the train speed, the soil Rayleigh speed and the train compartment length. When the train speed exceeds the shear wave speed, the vibration magnitude is critical and not sensitive to the train speed. To reduce this vibration, the two isolation schemes investigated in this study are useful for the train speed over the soil Rayleigh speed, but they are not efficient for the train speed below the soil Rayleigh speed.     

Effect of topography and subsurface inhomogeneity on seismic rayleigh waves

The effect of topography and subsurface inhomogeneity on surface motion is investigated in the case of Rayleigh waves. In the previous paper, the same effect was investigated in the case of SV waves. Several types of topography, such as cliffs both with and without a soft layer at the foot of the slope, are considered. Computations are made using a new hybrid method combining a particle model with a finite element method. In cases of harmonic Rayleigh waves, surface motions with amplitudes as large as 1.5 to 5 times the horizontal surface displacement of the incident Rayleigh waves are produced near the slope and the sloping interface. When a Rayleigh wave propagating through a hard single-layered ground encounters a sloping interface where hard ground and soft ground make contact with each other, Rayleigh waves having two different, phase velocities are produced and they correspond to the fundamental mode, and the first mode determined by Haskell's method. In addition, the transient response when Rayleigh waves propagate through the cliff is also simulated. Assuming the vertical component of the Tokachi-oki Earthquake (1968) measured on the surface to be a Rayleigh wave, the incident Rayleigh wave can be obtained by a Fourier synthesis of eigenfunctions of Rayleigh waves.     

轨道附近地面振动模型中的饱和地层动力格林函数

列车引起场地振动的建模需要能够表达地层的动力格林函数.本文兼顾饱和土的流固两相耦合性、场地土的分层性和波动的三维传播性,构建了半解析的场地动力格林函数.首先,基于Biot方程,在傅里叶变换域求解固体骨架和流体的位移和应力.然后采用传递矩阵方法建立地表位移和应力间的关系,得到格林函数矩阵.进而讨论矩阵的一些固有特征,提出改善竖向位移计算效率的措施.最后利用推导的格林函数计算了几个典型算例.数值结果与文献中其他方法得到的结果十分接近,与场地振动的现场观测试验基本符合.软土场地振动的计算结果高于饱和砂土场地,高速列车场地振动强度高于低速列车.当车速接近场地瑞利波速,模拟结果中显示出马赫锥.数值结果还显示,即使车速略低于瑞利波速,马赫锥也可能出现.本文推导的格林函数将有助于深入理解列车等移动激励作用下层状饱和土场地的振动特征.     

Model tests on XCC-piled embankment under dynamic train load of high-speed railways

Piled embankments, which offer many advantages, are increasingly popular in construction of high-speed railways in China. Although the performance of piled embankment under static loading is well-known, the behavior under the dynamic train load of a high-speed railway is not yet understood. In light of this, a heavily instrumented piled embankment model was set up, and a model test was carried out, in which a servo-hydraulic actuator outputting M-shaped waves was adopted to simulate the process of a running train. Earth pressure, settlement, strain in the geogrid and pile and excess pore water pressure were measured. The results show that the soil arching height under the dynamic train load of a high-speed railway is shorter than under static loading. The growth trend for accumulated settlement slowed down after long-term vibration although there was still a tendency for it to increase. Accumulated geogrid strain has an increasing tendency after long-term vibration. The closer the embankment edge, the greater the geogrid strain over the subsoil. Strains in the pile were smaller under dynamic train loads, and their distribution was different from that under static loading. At the same elevation, excess pore water pressure under the track slab was greater than that under the embankment shoulder.     

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.     

地震-列车移动荷载耦合作用下高铁路基振动特性研究

基于轨道结构-路基-地基动力相互作用理论,建立考虑地震-列车移动荷载耦合输入的轨道结构-路基-地基动力学模型,研究高速铁路路基及轨道在耦合荷载作用下的振动响应问题.通过编制DLOAD子程序并与ABAQUS有限元计算程序联立,实现地震荷载与列车移动荷载耦合作用的施加,以高速铁路桩承式路基及自由式路基为研究对象,对地震-列...     

Ground surface response induced by shallow buried explosions

Based on the spherical cavity expansion theory in the elastic half space,the ground surface movement characteristics of shallowly buried explosions are analyzed.The results show that the induced seismic wave is a longitudinal wave in the near zone and a Rayleigh wave in the far zone.The maximum displacement(velocity) of the longitudinal wave and the Rayleigh wave are inversely proportional to the scaled distance,and can be described by exponential function with exponents equal to 1.4 and 0.5,respectively.The vibration frequencies of the waves have almost no change.The vibration frequency of the longitudinal wave approximates the natural vibration frequency of the cavity in the broken area,and the vibration frequency of the Rayleigh wave is about half that of the longitudinal wave.On the same reduced buried depth and reduced distance,the particle displacement is directly proportional to the product of the boundary loading and cavity radius,and is inversely proportional to the transversal wave velocity.Meanwhile,the particle velocity is directly proportional to the boundary loading and inversely proportional to the wave velocity ratio.In the far zone,the buried depth of the explosive only has a slight effect on the longitudinal wave,but has a larger effect on the Rayleigh wave.     

Effect of lateral inhomogeneity on seismic waves,II. Observations and analyses

Observation has been conducted on soft surface ground with a sloping basement to clarify the effects of lateral inhomogeneity on ground motions and strains induced by seismic waves and to examine the frequency characteristics of the ground surface motions. The scattered Rayleigh wave from the vicinity of the sloping basement has been detected on seismograms and is observed to have a large influence on the ground motions and strains. In this paper the response of the ground is simulated using a hybrid method which combines a particle model and finite element method (FEM). The computed seismograms are in good agreement with observed ones. It is found from the calculations that large ground strains are produced by the scattered Rayleigh waves as well as by the incident shear waves in the surface ground overlying the sloping basement. In addition, the effects of lateral inhomogeneity on an embedded pipeline are examined. The present results are considered to be significant from the viewpoint of earthquake engineering.     

Evaluation of the dynamic <Emphasis Type="Italic">p</Emphasis>–<Emphasis Type="Italic">y</Emphasis><Subscript>p</Subscript> loops of pile-supported structures on sloping ground

A key issue in the design of pile-supported structures on sloping ground is soil–pile interaction, which becomes more complicated in case of dynamic loading. This study aimed to evaluate the effect of slope on the dynamic behavior of pile-supported structures by performing a series of centrifuge tests. Three models were prepared by varying the slope and soil density of dry sand grounds. The mass supported on 3 by 3 group piles was shaken applying sinusoidal wave with various amplitudes. Test results showed that the location of maximum values and distribution shape of the bending moment below the ground surface varied noticeably with the pile position in the slope case. The relationship between the soil resistance and pile deflection (p–y_p loops) was carefully evaluated by applying the piecewise cubic spline method to fit the measured bending moment curves along piles. It was found that the shape of the p–y_p loops was irregular due to the effect of slope, and immensely influenced by the movement of the unstable zone. In addition, the effect of the pile group in the horizontal case was evaluated by comparing with the previously suggested curves that represent the relationship between the soil resistance and pile–soil relative displacement (p–y curves) to propose the multiplier coefficients.     

Modelling of ground motion in the vicinity of massive structures

A two-dimensional elastic Chebyshev spectral element method (SPEM) is used to model the seismic wavefield within a massive structure and in its vicinity. We consider 2-D models where a linear elastic structure, with quadrangular cross-section, resting on an elastic homogeneous half-space, is impinged upon by the waves generated by a surface impulse at some distance. The scattering of Rayleigh waves and the response of the structure are extensively analysed in a parametric way, varying size, mechanical parameters and shape of the load. Some of the models considered are representative of embankments and earth dams. The simulation shows that some models resonate, storing part of the incoming energy. With realistic parameters, the lowest resonance frequency is due to pure shear deformation and is controlled by the shear velocity and height of the load. Flexural modes are excited only at higher frequencies. The acceleration at the top of the structure may be five/seven times higher than at the base, depending on the mass of the structure. The gradual release of trapped energy produces a ground roll lasting several seconds after the wave front has passed. The ground-roll amplitude depends on the sturcture's mass and can be as large as 30% of the peak acceleration. Outside resonance conditions, the ground motion is almost unaffected by the presence of the artefact; the horizontal motion on top of it is nearly twice the motion at ground level. Similar results should be expected when the incident field is an upcoming shear wave. A qualitative discussion shows that the presence of anelastic attenuation in the embankment does not significantly alter the preceding conclusions, unless it is of very low values (e.g. Q < 15).The modelling results that we discuss indicate that the soil-structure interaction may substantially alter the ‘free-field’ ground motion. From a practical point of view, the main conclusions are: (1) careful analysis is necessary when interpreting seismic records collected in the vicinity of large artefacts; (2) seismic hazard at a site may depend on the presence of man-made structures such as embankments, dams, tall and massive buildings.     

Experimental investigation into ground vibrations induced by very high speed trains on a non-ballasted track

A field measurement of ground vibration was performed on the Beijing−Shanghai high-speed railway in China. In this paper, the experimental results of vertical ground vibration accelerations induced by very high speed trains running over a non-ballasted track on embankment with speeds from 300 to 410 km/h are reported and analyzed in detail for the first time. Characteristics of ground vibration accelerations in both time and frequency domains are analyzed based on the test data. It is shown that the periodic exciting action of high-speed train bogies can be identified in time histories of vertical accelerations of the ground within the range of 50 m from the track centerline. The first dominant sensitive frequency of the ground vibration acceleration results from the wheelbase of the bogie, and the center distance of two neighboring cars plays an important role in the significant frequencies of the ground vibration acceleration. Variations of time–response peak value and frequency-weighted vertical acceleration level of ground vibration in relation with train speed as well as the distance from the track centerline are also investigated. Results show that the time-domain peak value of ground vibration acceleration exhibits an approximately linear upward tendency with the increase of train speed. With the increasing distance from the track centerline, the frequency-weighted vertical acceleration level of the ground vibration attenuates more slowly than the time-domain peak value of the ground vibration acceleration does. Severe impact of high-speed railway ground vibration on human body comfort on the ground occurs at the speed of 380–400 km/h. The results given in the paper are also valuable for validating the numerical prediction of train induced ground vibrations.     

两种不同势函数下半空间饱和多孔介质中Rayleigh波求解比较

分别对"考虑两种压缩波和幅值比例系数"和"考虑一种压缩波(P1或P2波)但不考虑幅值比例系数"两种不同势函数下的半空间饱和多孔介质中Rayleigh波求解进行详细推导,理论分析表明"考虑两种压缩波和幅值比例系数"下Rayleigh波求解推导更为严密,与饱和多孔介质中存在两种压缩波的事实相一致。在研究半空间饱和多孔介质中Rayleigh波时应采用"考虑两种压缩波和幅值比例系数"的势函数。     

地震体波斜入射情形下台阶地形引起的波型转换

本文首次对地震体波斜入射情形下竖直、倾斜台阶地形引起的波型转换进行了数值模拟，结果表明：地震波的斜入射会使台阶上角点引起更强的转换面波；转换Rayleigh面波最大振幅可达弹性半空间表面自由场位移的1.1倍左右。     

机车动荷载作用下多年冻土区铁路路基动力响应的试验研究

青藏铁路穿越多年冻土区因地温和含冰量的不同而采取了不同的路基结构形式,以减小或避免气温和工程扰动对其下部多年冻土的影响。为了把握多年列车振动荷载作用下多年冻土区不同结构路基的动力响应特征,对青藏铁路北麓河段典型结构路基进行了实时强震动测试,得到了多年冻土区铁路路基的振动加速度衰减规律,对于研究机车动荷载对青藏铁路多年冻土区路基变形的定量影响规律,保障青藏铁路安全运营具有重要的科学意义。     

Flexible support of a pile embedded in unsaturated soil under Rayleigh waves

Under the action of Rayleigh waves, pile head is easy to rotate with a concrete pile cap, and pure fixed-head condition is rarely achieved, which is a common phenomenon for it usually occurs on the precast piles with insufficient anchorage. In addition, the propagation characteristics of Rayleigh wave have been changed significantly due to the existence of capillary pressure and the coupling between phases in unsaturated soil, which significantly affects the pile-soil interaction. In order to study the above problems, a coupled vibration model of unsaturated soil–pile system subjected to Rayleigh waves is established on the basis that the pile cap is equivalent to a rigid mass block. Meanwhile, the soil constitution is simplified to linear-elastic and small deformations are assumed to occur during the vibration phase of soil–pile system. Then, the horizontal dynamic response of a homogeneous free-field unsaturated soil caused by propagating Rayleigh waves is obtained by using operator decomposition theory and variable separation method. The dynamic equilibrium equation of a pile is established by using the dynamic Winkler model and the Timoshenko beam theory, and the analytical solutions of the horizontal displacement, rotation angle, bending moment and shear force of pile body are derived according to the boundary conditions of flexible constraint of pile top. Based on the present solutions, the rationality of the proposed model is verified by comparing with the previous research results. Through parametric study, the influence of rotational stiffness and yield bending moment of pile top on the horizontal dynamic characteristics of Rayleigh waves induced pile is investigated in detailed. The analysis results can be utilized for the seismic design of pile foundation under Rayleigh waves.     

Train-induced wave propagation in layered soils using finite/infinite element simulation

In this paper, the transmissibility of soils for vibrations induced by trains moving at different speeds is studied. The 2.5 D finite/infinite element approach adopted herein allows us to consider the load-moving effect of the train in the direction normal to the two-dimensional profile of the soils considered, and, therefore, to obtain three-dimensional responses for the soils using only plane elements. The moving train is simulated by a sequence of moving wheel loads that may vibrate with certain frequency. Two train speeds are considered, one is smaller and the other is greater than the Rayleigh wave speed of the layered soils, to represent the effects of speed in the sub-critical and super-critical ranges. In order to evaluate the effect of each parameter on the ground response induced by moving trains, parametric studies are conducted for the following parameters: the shear wave speed, damping ratio and stratum depth of the supporting soils, and the moving speed and vibration frequency of the traveling trains. Conclusions concerning the mechanism of wave propagation in layered soils are drawn from the parametric studies, which should prove useful to practicing engineers.     

Numerical and test study on vertical vibration characteristics of pile group in slope soil topography

Topography effects on the vertical vibration responses of pile group are revealed though numerical analysis and model tests.First,a series of model tests with different topography of ground and bedrock are conducted.The results indicate that displacement amplitude of the pile head in sloping ground topography is larger than in horizontal ground.Differential displacement at various positions of the pile cap is observed in non-horizontal topography.Afterwards,a numerical algorithm is employed to further explore the essential response characteristics in group piles of different topography configurations,which has been verified by the test results.The lengths of the exposed and frictional segment,together with the thickness of the subsoil layer,are the dominant factors which cause non-axisymmetric vibration at the pile cap.     

Green’s function of multi-layered poroelastic half-space for models of ground vibration due to railway traffic

This study proposes a Green’s function,an essential representation of water-saturated ground under moving excitation,to simulate ground borne vibration from trains.First,general solutions to the governing equations of poroelastic medium are derived by means of integral transform.Secondly,the transmission and reflection matrix approach is used to formulate the relationship between displacement and stress of the stratified ground,which results in the matrix of the Green’s function.Then the Green’s function is combined into a train-track-ground model,and is verified by typical examples and a field test.Additional simulations show that the computed ground vibration attenuates faster in the immediate vicinity of the track than in the surrounding area.The wavelength of wheel-rail unevenness has a notable effect on computed displacement and pore pressure.The variation of vibration intensity with the depth of ground is significantly influenced by the layering of the strata soil.When the train speed is equal to the velocity of the Rayleigh wave,the Mach cone appears in the simulated wave field.The proposed Green’s function is an appropriate representation for a layered ground with shallow ground water table,and will be helpful to understand the dynamic responses of the ground to complicated moving excitation.     

场地条件对高速铁路地基土振动影响的研究

发展高速铁路是解决城市间交通问题的有效途径,但其所产生的振动和噪声引起的环境问题,对铁路沿线居民及周围建筑等造成不利影响。在对高速铁路引起的振动问题进行的研究中,关于高速列车引起的地基土振动随深度变化的相对较少。因此,本文针对Ⅱ、Ⅲ和Ⅳ类场地条件下的路堤式和高架桥式高速铁路,对0—5m不同深度处地基土的振动加速度响应进行了现场测试,并以测试数据为基础,分析了不同场地条件下高速列车引起的地基土振动加速度响应随深度的变化规律。结果表明,不同场地条件下,高速列车引起的振动加速度响应随深度的变化规律具有显著差异;Ⅱ类和Ⅲ类场地条件下,高速列车引起的地基土振动加速度响应总体随深度的增加而逐渐减小,并呈先快后慢的衰减趋势;而Ⅳ类场地条件下,高速列车引起的地基土振动加速度响应随深度的增加呈现先减小后放大的趋势,在深3m处加速度达到最大值。高速列车运行引起的振动频带随深度的变化特征与场地相关。     

Three-dimensional analysis of rows of piles as passive barriers for ground vibration isolation

This paper presents a theoretical study on the ground vibration isolation efficiency by multi-rows of piles as passive barrier in a three-dimensional context. Integral equations governing Rayleigh wave scattering are derived according to the Green's solution of Lamb problem. The integral equations are solved accurately and efficiently with an iteration technique. They are used to predict the complicated Rayleigh wave field that is generated by a number of irregular scatterers embedded in an elastic half-space solid. The method is verified with a numerical solution available in the literature for a simplified Rayleigh wave scattering problem. Passive isolation effectiveness of ground vibration with two or three rows of small piles is further studied in detail. Effects of relevant parameters on the effectiveness of vibration isolation are analyzed and presented.