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.     

Vibration analysis of pile-supported embankments under high-speed train passage

Soft ground improvement using piles has increasingly been used as a rapid construction technique for railway and highway embankments over soft soil areas. While most studies conducted so far have addressed only issues of stability and settlement of pile-supported embankments under static loading, very limited attention has been paid to understanding their behaviors under transient loading of moving vehicles. In this study, vibration behaviors of this embankment system under high-speed train passage are investigated through three-dimensional finite element simulation. They include (1) characteristics of the surface wave field at high train speeds, (2) the dependence of vibration amplitude on the train speed and the phenomenon of critical speed, and (3) response at some typical locations in the system when the train moves at the critical speed. The study shows that there are breaks in the simulated wave fronts as transiting between different materials due to the difference in the Rayleigh wave speed among the materials relative to the train speed, and that the increase in train speed is accompanied by the increase in phase shift between the train load and the displacement pattern beneath the load. It is shown that the critical speed of the system is governed by the embankment, instead of the soft soil as commonly observed in previous studies in which the ground is not improved. Namely the vibration amplitude is maximally amplified when the train speed approaches the characteristic Rayleigh wave speed of the embankment material. In addition, the results also suggest that the sloping surfaces on the ballast and embankment along with the piles form a ‘trapping’ effect by which most of the train-induced waves, especially higher-frequency waves, incident to the sloping surfaces are trapped and dissipated within the pile-supported embankment system, and thus significantly reducing vibration amplitudes outside the embankment.     

高铁震源地震信号的挤压时频分析应用

我国每天有数千趟高铁列车驰骋在纵横交错的高铁线路上,构成了十分理想的均布震源,但寻找适合高铁震源地震信号的处理方法是充分挖掘信息的关键.传统的频谱分析结果表明高铁震源所产生的地震信号具有明显的窄带分立谱特征,但无法精确获得高铁震源地震信号的时频变化规律.本文首次将挤压时频分析这种分析工具引入到高铁震源地震信号处理中,对中国南方某高铁沿线采集到的高铁震源地震数据进行了分析.处理结果表明:利用挤压时频分析能够更加精确地刻画频率成分随时间的变化,能够利用单检波器精确刻画高铁列车的运行状态(匀速、加速等);同时利用挤压时频变换还可高精度地重构出所需频带的信号,为提取高铁震源地震信号的特征成分提供了一种有力工具.     

Field vibration mitigation by honeycomb WIB for pile foundations of a high-speed train viaduct

Environmental vibrations from recent high-speed trains are becoming a special concern in the civil and environmental engineering field since they can give detrimental effects to residents, sensitive equipments and high-tech production facilities in the vicinity of train tacks. Herein, aiming at the vibration mitigation for a specific high-tech industrial area, the low-frequency vibrations from a train viaduct are targeted over an anticipated range. A theoretically designed innovative countermeasure, called honeycomb wave impeding barrier (WIB) for a wave impeding barrier, is introduced and its effects are investigated by computer simulation. The present WIB is based on the wave dispersion phenomenon that can modulate the incoming wavelengths into the shorter wavelengths, creating an apparent wave cut-off characteristic in the wave field across WIB installation area. The shorter wavelengths are further impeded due to the impedance ratio of the WIB walls and in-fill materials and absorbed by the in-fills more. The three-dimensional FEM simulation demonstrates a dramatic reduction effect that is difficult to achieve by conventional measures.     

饱和多孔介质三维时域黏弹性人工边界与动力反应分析的显式有限元法

本文基于Biot的饱和多孔介质本构方程,考察具有辐射阻尼的外行球面波,推导了饱和多孔介质三维黏弹性人工边界的法向和切向边界方程;在已有的饱和多孔介质二维显式有限元数值计算方法基础上,提出该理论的三维方法,并开发了实现该三维方法的有限元程序.算例表明饱和多孔介质三维时域黏弹性人工边界与动力反应分析的显式有限元法具有较好的精度和稳定性.     

Finite difference modeling of contaminant transport using analytic element flow solutions

The two-dimensional implementation of the analytic element method (AEM) is commonly used to simulate steady-state saturated groundwater flow phenomena at regional and local scales. However, unlike alternative groundwater flow simulation methods, AEM results are not ordinarily used as the basis for simulation of reactive solute transport. The use of AEM-simulated flow fields is impeded by the discrepancy between a continuous representation of flow and a typically discrete representation of transport, and requires translation of the flow solution to a discrete analog. This paper presents a variety of methods for analytically calculating conservative discrete water fluxes and integrated components of the dispersion tensor across cell interfaces. An Eulerian finite difference method based on these AEM-derived parameters is implemented for use in simulation of 2D (vertically averaged) solute transport. This implementation is first benchmarked against existing methods that use standard finite difference flow solutions, then used to investigate the effects of an inaccurate discrete water balance. It is shown that improper translation of AEM fluxes leads to significant water balance errors and inaccurate simulation of contaminant transport.     

移动线源的Green函数求解及辐射能量分析:高铁地震信号简化建模

在基于人工主动源的勘探地震学中,往往采用固定位置和激发时间的点源数学模型来描述爆炸型震源或可控震源,因此就有了描述单点力源作用下的弹性全空间或半空间中弹性波传播的Green函数,成为了勘探地震学的重要理论基础.而如今,行进中的高速列车（高铁）是一种全新的主动源,其接近匀速的运行速度、确定的长度和荷载使其可以被重复利用.本文将行进中的高铁在数学上简化建模为一个移动线源来进行研究,给出了这一震源作用下的弹性半空间和全空间中Green函数的计算方法,并分别讨论了全空间中远场Green函数的频谱特征和空间辐射能量的方向性特点,以及半空间中Green函数与近场观测数据的对比结果,为高铁震源下的地震波传播规律和振动信号的研究与利用提供帮助.

     

Diagnosis and prediction of vibration from railway trains

In the North West of France, more particularly in the region of the Somme Bay, where the ground is constituted mainly of peat, observation of the surface of the soil near railway tracks has revealed high levels of displacement. This paper, contains a prediction model and diagnosis of vibration near the track. A model of a railway track on layered ground subjected to a moving train has been built and the calculation method uses Fourier transform formalism for a semi-analytical solution in the wave number domain. It includes all elements of the track and allows a parametric analysis of its different elements and evaluation of vertical displacement according to the speed, weight and composition of each train. The diagnosis has been performed with in situ measurements and with the aim of the validation of the model. A parameter study of the ground undertaken by seismic measurements shows a critical speed close to 100 m/s while the studied trains are moving with sub-Rayleigh speeds. Measurements give us a lot of information about lateral and vertical acceleration on the soil's surface and parts of the track. For high speeds and freight trains, displacement reaches more than 10 mm.     

Three-dimensional finite element analysis of the seismic behavior of inclined micropiles

This paper presents a thorough study of the behavior of inclined micropiles under seismic loading. Analysis is carried out using a full three-dimensional finite element modeling. The soil media is assumed to be elastic with Rayleigh damping, while micropiles are modeled as 3D elastic beam elements. The structure is described by a single degree of freedom system composed of a concentrated mass and a column. The paper is composed of four parts. The first part includes a literature survey on the behavior of inclined micropiles. The second part presents the numerical model used in this study. The third part concerns analysis related to the influence of micropiles inclination on the seismic behavior of a group of micropiles embedded in a homogeneous soil with a uniform stiffness. The last part deals with the seismic behavior of inclined micropiles embedded in a soil layer with a depth-based increasing stiffness. The results of this study provide valuable information about the influence of micropiles inclination on dynamic amplification and on the seismic-induced internal forces in micropiles.     

Boundary element simulation of scattering of elastic waves by 3-D cracks

Numerical modelling techniques are now becoming common for understanding the complicated nature of seismic wave propagation in fractured rock. Here the Indirect Boundary Element Method (IBEM) is applied to study scattering of elastic waves by cracks. The problem addressed in this paper is the diffraction of P and S waves by open 3-D cracks of arbitrary shape embedded in a homogeneous isotropic medium. The IBEM yields the value of the jump of displacements between opposite surfaces of the crack, often called Crack Opening Displacement (COD). This is used to evaluate the solution away from the crack. We use a multi-regional approach which consists of splitting a surface S into two identical surfaces S⁺ and S⁻ chosen such that the crack lies at the interface. The resulting integral equations are not hyper-singular and wave propagation within media that contain open cracks can be rigorously solved. In order to validate the method, we compare results of displacements of a penny-shaped crack for a vertical incident P-wave with the classic results by Mal (1970) obtaining excellent agreement. This comparison gives us confidence to study cases where no analytic solutions exist. Some examples of incidence of P or S waves upon cracks with various shapes are depicted and the salient aspects of the method are also discussed. Both frequency and time-domain results are included.     

天兴洲公铁两用斜拉桥主梁纵向列车制动振动反应分析

本文对天兴洲公铁两用斜拉桥主梁纵向列车制动的振动反应进行了研究。天兴洲大桥是目前在建的世界上跨度最大的公铁两用斜拉桥,由于具有四线铁路,其主梁在列车制动及行车移动荷载作用下会沿纵向产生大幅振动,因此对其列车制动及行车移动荷载反应进行研究尤为必要。文中,首先根据车辆动力学的原理建立了列车制动动力学模型,获得了列车制动力纵向荷载及在制动过程中列车行走所产生的竖向荷载,并建立制动力传递有限元模型,应用有限元分析软件来获取钢轨上制动力及列车行走时引起的桥梁结构节点上的作用力时程。最后对天兴洲公铁两用斜拉桥主梁纵向列车制动及行车移动荷载的振动反应进行了仿真分析,发现了其主梁纵向列车制动反应具有位移大且速度极小的特点。     

江口水库诱发地震的有限元分析

本文利用有限元方法计算了武隆江口水库蓄水后可能引起的水库诱发地震。在水库底部有断裂通过时,对江口水库在不同的假设宽度情况下进行了分析,给出了水库底部各处的最大剪应力。结果表明,水库底部岩石发生破坏的可能性很大,极可能引起水库的诱发地震,其最大震级为5级左右。     

断层破裂速度对地震动及其地震灾害影响的有限单元法模拟

断层破裂传播速度通常会影响强地面运动加速度的空间分布及地震的灾害程度,但究竟是如何影响的,目前未见全面的定量分析.为此,本研究设断层破裂速度从小到大发生改变(从亚剪切波速度到超剪切破裂速度),同时利用有限元方法计算在不同破裂传播速度的情况下,破裂产生的地震动及强地面运动峰值加速度(PGA)的空间分布,计算时保持在所有情况下其断层上的最终位错相等,即所有不同破裂情况下产生的地震矩震级保持不变,都为MW=7.0.计算结果显示：总体上,破裂传播的速度越快,PGA的幅值越大并且高值区分布的范围也越广,其地震灾害会越严重;超剪切破裂相对于亚剪切破裂会加剧地震灾害.但是,当破裂速度正好等于介质的剪切波速度时,断层面附近PGA峰值最大,断层附近的地震灾害最为严重.此外,研究中还发现,当破裂传播速度等于倍剪切波速度时(该速度称为Eshelby速度),不产生剪切马赫波;这与超剪切破裂产生剪切马赫波的普遍现象不一致;但此时PGA并没有大幅度减小,其震害也不会有显著改变.因此,本研究对于深入认识地震震源过程、地震动效应以及灾害评估有着重要的科学意义及实用价值.     

Numerical modelling of drop load tests

Assessment of the attenuation of induced vibrations in the ground plays an important role in evaluating comfort and structural safety. Analytical and empirical wave attenuation relationships of increasing complexity and detail are presented in the paper, as well as a numerical model that accurately reproduces wave attenuation for a well-documented site, namely the one of the Tower of Pisa, Italy. A new source model is calibrated on near-field data and used as input for the dynamic coupled consolidation finite element analysis to achieve a satisfactory simulation. The accuracy of simpler analytical and empirical approaches is then comprehensively assessed through comparison with the validated numerical model and the field data obtained from geophones at various distances from the impact source.     

Wave dispersion in dry granular materials by the distinct element method

Numerical studies are conducted to investigate the existence of wave dispersion in resonant column tests on dry granular soil. To this end, the two-dimensional distinct element method (DEM) in the time domain is employed. The investigations focus on the effect of sample width, voids ratio, viscous damping and wavelength, on propagation velocities of longitudinal harmonic waves in rectangular samples of uniform grains. It is shown that granular materials may exhibit anomalous dispersion that is, wave velocities that increase with increasing excitation frequency. This increase may exceed 20% for squatty samples, but becomes less pronounced for slender samples. Similar findings have been reported in some experiments on granular materials, but have not been systematically explored by numerical means. Results are presented in the form of dimensionless graphs and charts that elucidate the salient features of the problem. Comparisons with findings from gradient elastodynamic and viscoelastic theories are discussed.     

Transient mechanical wave propagation in semi-infinite porous media using a finite element approach

In this study, we propose a numerical investigation in the time domain of the mechanical wave propagation of an impulsional load on semi-infinite soil. The ground is modelled as a porous saturated viscoelastic medium involving complete Biot theory. All the couplings and a hysteretic Rayleigh damping are taken into consideration. An accurate and efficient finite element method using a matrix-free technique and an expert multigrid system are applied. Our results present the displacements of the fluid and solid particles over the surface and in depth. The arrival times of body and surface waves are studied. Particularly, the compressional wave of the second kind is highlighted. The influence of the different couplings and more specifically, the influence of the permeability on the response of the soil are analyzed.     

地下隧道-土体系地震反应分析的有限元与无限元耦合法

本文采用有限元－无限元耦合法进行地下隧道－土相作用分析,阐述了有无限与无限元耦合模式的基本原理,耦合分析方法具有精度高,省机时的特点。     

福州盆地强地面运动特征的有限元数值模拟

区域性地震波强地面运动的量化数值模拟分析结果可以用来指导城市规划建设,并在防震减灾中发挥重要作用. 本文采用有限元数值模拟方法来模拟由地震激发的区域地震波强地面运动过程,并得到地表峰值速度和加速度的分布特征.考虑到福州是东南沿海的重要省会城市,其明显的盆地结构特征使它很容易遭受强地震灾害的影响. 因此本文以福州盆地为主要研究对象,假定盆地的主要断层某一位置在未来可能发生灾害性地震,则该地震会激发地震波的强地面运动,并由于地形、沉积层等主要影响,在盆地内部发生放大.通过对地震波传播过程的数值模拟和后处理分析,给出了该盆地的地表峰值位移、峰值速度和峰值加速度分布图谱.该图谱可为未来的福州城市规划和抗震减灾提供定量科学参考依据.     

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.