Study on the safe value of multi-pier settlement for simply supported girder bridges in high-speed railways

This paper presents a method to analyse the influence of multi-pier settlement on the train–track–bridge coupled dynamic system, and to determine the safe value of the continuous multi-pier settlement for simply supported girder bridges in Chinese high-speed railways. Firstly, the mapping relationship between the multi-pier settlement and the rail deformation is derived theoretically. Then, taking the superposition of the rail deformation and the track random irregularity as excitation, the variations of vehicle dynamic indices are analysed based on the train–track–bridge dynamic interaction theory. Further, the relationships between the pier settlement and the change amounts of vehicle dynamic indices are obtained. The multi-pier settlement safe value is determined according to the limits of vehicle dynamic indices. Results show that the rail deformation caused by multi-pier settlement agrees well with the settlement data. When passing through the 32.6 m-long simply supported girder bridge with multi-pier settlement, the train suffers a low-frequency excitation. Only considering the influence of pier settlement, the settlement value difference between two adjacent piers should be less than 26.3 mm at China’s highest operation speed of 350 km/h from the perspective of dynamics, which is much larger than the pier settlement limit in the current code for Chinese high-speed railways.     

32m双线简支箱梁在对开列车作用下梁体竖向动力响应规律研究

将列车、双线简支箱梁分别简化为二系悬挂多刚体体系和模态函数,推导车桥系统动力方程,建立并验证车桥相互作用模型,对双线简支箱梁在对开列车作用下梁体竖向动力响应规律进行研究。研究表明:对开列车作用下,桥梁动力响应与列车运行速度及入桥距离差密切相关;列车以共同速度对开时,可引起的梁体最大挠度动力系数与单线行车作用下基本一致,但梁体动力响应值约为单线行车引起的梁体动力响应值的2倍。     

An iterative interacting method for dynamic analysis of the maglev train-guideway/foundation-soil system

This paper presents an iterative interacting method for analyzing the dynamic response of a maglev train traveling on an elevated guideway supported by piers embedded in soil. The maglev train is idealized as a row of 2D rigid beams each suspended by levitation forces and controlled by onboard PID controllers. The guideway is modeled as a series of simple beams supported by rigid piers embedded in an elastic half-space. To address the structure interactions from the train to the soil and vice versa, the entire model is decomposed into two subsystems, i.e., the maglev train-guideway and foundation-soil subsystems, each interacting with the other via the rigid piers. The procedure of analysis is as follows: First, the train-guideway subsystem is computed, and the support reactions are used as excitations to the elastic half space. Next, the ground vibrations induced by the pier excitations are computed and fed back via the supports for computing the train-guideway response. The procedure is repeated until the convergence condition is satisfied. The solution obtained for a 2-degree-of-freedom system under a harmonic force is compared with the analytical one to verify the validity of the method proposed herein. The effects of ground wave propagation on the vehicle-guideway response will be evaluated in the numerical examples.     

An analytical approach to train-induced site vibration around Shinkansen viaducts

This study is intended to establish an analytical approach to evaluate the site vibration caused by the passage of bullet trains over Shinkansen viaducts. In this approach, to simplify the problem the entire train–bridge–ground interaction system is divided into two subsystems: train–bridge interaction and foundation–ground interaction. In the train–bridge interaction problem, the analytical programme to simulate the traffic-induced bridge vibration is developed. Then, the dynamic responses of the viaducts are calculated to obtain the dynamic reaction forces at the bottoms of the piers. Applying these reaction forces as input excitation forces in the foundation–ground interaction problem, the site vibration around the viaducts is simulated and evaluated using a general-purpose programme.     

Response of suspended beams due to moving loads and vertical seismic ground excitations

In this paper, the vibration of a suspension bridge due to moving loads of equidistant, identical forces and shaken by vertical support motions caused by earthquake is studied. The suspension bridge is modelled as a single-span suspended beam. To conduct the beam vibration with time-dependent boundary conditions, the total response of the suspended beam is decomposed into two parts: the quasistatic component and the dynamic part based on the decomposition method. Since the quasi-static component of the suspended beam under the static action of multiple support motions has been obtained analytically, the remaining dynamic part can be solved using Galerkin’s method. The numerical results indicate that the contribution of higher modes on the maximum acceleration of the suspended beams to moving loads will become significant as the propagation effect and multiple support motions of seismic waves in the subsoil of bridge supports has been taken into account.     

Vibration of railway bridges under a moving train by using bridge-track-vehicle element

During the last two decades, much attention has been paid to various vibration problems associated with railways. They include the dynamic response of railway bridges and railway tracks at grade under the action of moving trains. However, studies on the role of track structures on the vibration of railway bridges are rather limited. In this paper, a new element called bridge-track-vehicle element is proposed for investigating the interactions among a moving train, and its supporting railway track structure and bridge structure. The moving train is modelled as a series of two-degree-of-freedom mass-spring-damper systems at the axle locations. A bridge-track-vehicle element consists of vehicles modelled as mass-spring-damper systems, an upper beam element to model the rails and a lower beam element to model the bridge deck. The two beam elements are interconnected by a series of springs and dampers to model the rail bed. The investigation shows that the effect of track structure on the dynamic response of bridge structure is insignificant. However, the effect of the bridge structure on the dynamic response of the track structure is considerable.     

Numerical simulation based heuristic investigation of inertia-induced phenomena and theoretical solution based verification by the damped wave equation for the dynamic deformation of saturated soil based on the u–w–p governing equation

The theoretical and numerical solutions for the one-dimensional dynamic deformation of saturated ground were obtained using the u–w–p governing equation. The numerical analysis was performed based on the finite element method, and the occurrence of superficially peculiar phenomena, i.e., S-shaped settlement–time relation, non-harmonic oscillation in the settlement/pressure–time relation in highly permeable soil, and inconsistency in the vertical load and immediate pressure was identified heuristically. The theoretical solution of the damped wave equation was derived from the original governing equation expressed as the superposition of several modes with different eigenvalues, and this solution could successfully explain the phenomena observed heuristically. It was noted that the phenomena were induced by the presence of inertia, because the static solution and u–p analysis did not exhibit such phenomena. The verification of the analysis was conducted owing to the correspondence of the theoretical solutions of the damped wave equation and the u–w–p analysis results.     

A multidisciplinary approach for fatigue assessment of a steel–concrete high-speed railway bridge on Sesia river

Steel–concrete composite bridge solutions have been more and more exploited in the new high-speed (HS) lines of European railway networks. New design solutions, introduced during a period of quick expansion for railway networks, amplified open problems related to dynamic effects, train–bridge interaction phenomena, fatigue loadings, structural modelling, fatigue life and comfort. In this article, results obtained by long-term dynamic monitoring of Sesia viaduct, a medium span double-box composite bridge of the new Italian HS network, are described and analysed. Structural modal properties were determined in order to evaluate the real-time dynamic behaviour and its correlation with environmental conditions. A suitable numerical procedure was then implemented in order to identify typology, length and velocity of trains crossing the bridge, to evaluate the intensity of deck vertical accelerations as a function of train speed and to obtain a reliable evaluation of real traffic spectra. A final fatigue assessment on welded connections was executed evaluating fatigue spectra by the aforementioned real traffic spectra and assuming S–N curves obtained by suitably executed experimental tests.     

Probabilistic assessment of the train running safety on a short-span high-speed railway bridge

In this work the running safety of high-speed trains on a short-span bridge is assessed. A probabilistic approach that combines Monte Carlo simulation with the extreme value theory is used and the existence of track irregularities is taken into account along with the variability of parameters related to the bridge, the track and the train. As case study, a 12 m span filler beam bridge was selected as the train–bridge interaction effects are most significant for short spans. The running safety is assessed for the case of loss of contact between the wheel and the rail, taking into consideration only the vertical wheel–rail interaction and assuming that no lateral forces act on the train. This research enables the characterisation of the wheel unloading coefficient, the identification of the critical wheel and also the definition of the maximum allowable speed for trains to run safely on the bridge.     

中低速磁浮列车-桥梁系统竖向耦合振动#br# 理论分析与试验验证

为探讨中低速磁浮列车-桥梁系统竖向动力相互作用特性,文章将中低速磁浮列车进行两种方式的简化,考虑PID主动悬浮控制系统,基于模态叠加法,建立2种类型的中低速磁浮列车-桥梁系统竖向耦合振动分析模型。随后基于长沙中低速磁浮运营线桥梁动载试验,对建立的2种仿真模型进行对比与验证。基于仿真模型2,以不同梁高的桥A、桥B、桥C为研究对象,对中低速磁浮列车-桥梁系统耦合振动特性进行分析。研究表明：将磁浮列车简化为均布荷载的方式能较为准确的模拟实际状况;桥梁刚度的减小会导致作用于车辆和桥梁上的电磁悬浮力增大,使得车体和桥梁的动力响应变大;磁浮列车低速运行时悬浮力频谱分布较离散,而正常速度运行时较集中;中低速磁浮列车-桥梁系统竖向存在着由电磁悬浮力自身频率引起的共振现象,该共振频率较低。     

桥墩沉降下纵连板式轨道与桥面间动态#br# 接触行为及其对列车动态特性的影响

桥墩沉降在高速铁路运营过程中不可避免,其会导致纵连板式轨道与桥面之间的变形不协调,进而引起底座与桥面之间的动态接触行为,恶化轨道力学性能并最终影响列车正常运行。这对这一问题,文章首先研究该动态接触过程的产生机制,并基于列车-轨道-桥梁动力相互作用理论提出纵连板式轨道和桥面间动态接触行为的研究方法;借助该方法从静态与动态两个角度研究桥墩沉降下轨道-桥梁动态接触行为;在此基础上探讨列车通过时的动态特性。结果表明：桥墩沉降和列车荷载会导致底座与桥面出现三处明显的动态接触区域;桥墩沉降导致的相邻桥墩处梁体上拱位移远小于沉降桥墩处的梁体下沉,但是沉降对上拱区域力学特性的影响却不可忽略;轨道的纵向连接特性可以在一定程度上缓解高速列车通过沉降区域时的振动;轨道随机不平顺不能完全掩盖桥墩沉降对系统动态特性的影响,表明沉降对系统的影响是不可忽视的。     

Dynamic response of a long span suspension bridge and running safety of a train under wind action

A dynamic analysis model of a wind-train-bridge system is established. The wind excitations of the system are the buffeting and self-excited forces simulated in time domain using measured aerodynamic coefficients and flutter derivatives. The proposed formulations are then applied to a long rail-cum-road suspension bridge. The dynamic responses of the bridge and the train under wind action are analyzed. The results show that the lateral and rotational displacements of the bridge are dominated by wind, while the vertical by the gravity loading of the moving train. The running safeties of the train vehicles are much affected by wind. Under wind conditions of 30–40 m/s, the offload factors, derail factors and overturn factors of the train vehicles exceed the safety allowances, to which great attention should be paid. Translated from Engineering Mechanics, 2006, 23(2): 103–110 [译自: 工程力学]     

列车运行引起高架桥群桩基础地面振动分析

采用半解析数值方法分析列车运行引起高架桥群桩基础地面振动,研究合理设计桩基减小地面振动。半解析数值模型包括列车–轨道模型、高架桥模型、群桩模型。列车轨道模型中采用多质点弹簧–阻尼模型模拟列车,采用美国功率谱描述轨道随机不平顺,使用Euler梁模拟钢轨,采用Hertzian非线性公式描述轮轨接触,采用振型分解法求解轮轨作用力。铁路高架桥采用弹性支座简支梁模拟,采用传递系数矩阵和群桩影响因子分析桥墩下群桩的动力阻抗,根据桥墩的动力平衡方程求得桥墩–地基相互作用力,采用Green函数求得弹性半空间地面振动。研究铁路高架桥下群桩参数对地面振动的影响,分析不同桩长、桩直径、桩间距和轨道不平顺条件下地面振动速度1/3倍频程的大小。结果表明:轨道不平顺对桥墩作用力有较大影响,对小于6 Hz的地面振动影响较小,对大于6 Hz的地面振动影响较大。合适调整桥梁跨度与车速组合可减小地面振动。车速小于260 km/h时,桩径对地面振动影响较小;车速大于260 km/h时,增加桩径可减小地面振动。适当增加桩间距可避开振动增大区、减小地面振动随车速的增加。合理设计桩长可减小地面振动的增大区域。     

Effectiveness of Soil–Structure Interaction and Dynamic Characteristics on Cable-Stayed Bridges Subjected to Multiple Support Excitation

The purpose of the study is to determine the effects of multiple support excitations (MSE) and soil–structure interaction (SSI) on the dynamic characteristics of cable-stayed bridges founded on pile foundation groups. In the design of these structures, it is important to consider the effects of spatial variability of earthquake ground motions. To do this, the time histories of the ground motions are generated based on the spatially varying ground motion components of incoherence, wave-passage, and site-response. The effects of SSI on the response of a bridge subjected to the MSE are numerically illustrated using a three-dimensional model of Quincy Bayview cable-stayed bridge in the USA. The soil around the pile is linearly elastic, homogeneous isotropic half space represented by dynamic impedance functions based on the Winkler model of soil reaction. Structural responses obtained from the dynamic analysis of the bridge system show the importance of the SSI and the MSE effects on the dynamic responses of cable-stayed bridges.     

The time dimension in site layout planning

With regard to incorporation of the time factor, site layout models are traditionally grouped into two categories of static models (with no considerations of the changes over time), and dynamic models (reflecting the changes on the construction sites). This paper demonstrates that there are in fact fundamental differences in the assumptions and the final outcome of models that are currently all categorized under dynamic site layout planning models, and proposes that these should in fact be divided into two groups of phased and dynamic models. The paper provides a comparative analysis of the three approaches of static, phased and dynamic site layout planning. The strengths, limitations, and differences in the final results of the three approaches are demonstrated through numerical examples. Finally, existing methods for the 2D representation of dynamic site layouts are compared, and an improved algorithm is provided to represent dynamic site layouts in minimum number of overlap-free drawings.     

Vereinfachte Methoden zur Berechnung der dynamischen Antwort von Eisenbahnbrücken bei Zugüberfahrt

Simplified methods to calculate the dynamic response of railway‐bridges under crossing trains. In this paper, two different methods to calculate the dynamic response of single‐span bridges under moving forces are presented. The work is focused on beam bridges with constant cross‐section in underdamped condition. In the first method, referred to as “Impulse‐method”, the effective impulse resulting from the load is approximated by simple analytical functions. The bridge is modelled as a single degree of freedom system by means of modal analysis. For this simplified system describing bridge and load, closed analytical formulae to calculate the dynamic response can be set up. The “Impulse‐method” is exemplified by the HSLM‐A1 load train given in Eurocode 1 (EC1). In the second method the response spectrum analysis widely used in earthquake engineering is adopted for the present problem. The calculation of response spectra for beam bridges under the HSLM‐A load models is demonstrated. An example shows how this method is deployed.     

Dynamic analysis of three-dimensional bridge–high-speed train interactions using a wheel–rail contact model

A formulation of three-dimensional dynamic interactions between a bridge and a high-speed train using wheel–rail interfaces has been developed. In the interface, contact loss is allowed, the vertical contact is represented by finite tensionless stiffness and the lateral contact is idealized by finite contact stiffness and creepage damping. Such stiffness and damping are nonlinearly dependent on normal contact force. The relative rotations of a wheelset to the rails about its vertical and longitudinal axes are included. Bridge eccentricities and deck displacement due to torsion are accounted for in bridge deck modeling. A numerical algorithm using separate integrations for bridges and trains, and iterations for interface compatibilities is established. A case study of a ten-car train passing over a two-span continuous bridge at various speeds and rail irregularity wavelength ranges is analyzed. The responses of the bridge, car-bodies and wheelsets are investigated for their behavior, acceptability and relations with the wavelengths. Analytical and numerical evaluations of resonant speeds are in good agreement, and the exit span vibration is more amplified than the entrance one at those speeds. The computed relative displacements of all wheelsets to the rail facilitate an explicit assessment for derailment risk.     

浅埋大跨洞桩隧道变形监测与控制分析

针对采用洞桩法施工的北京地铁10号线工体北路站,介绍了浅埋大跨洞桩隧道的变形监测与控制措施。根据监测数据,对洞桩法隧道导洞开挖,主体扣拱的拱顶沉降与洞周收敛以及地表和上部立交桥基础的沉降变形规律进行了分析研究。结果表明：1)采用洞桩施工方法能有效控制浅埋大跨隧道地表沉降和地层变形;2)隧道埋深和跨度、导洞开挖对浅埋大跨洞桩隧道变形影响显著;3)设置超前小导管注浆,及时施作初期支护和二衬,可以有效的控制变形的发展。     

地铁列车荷载作用下轨道系统及饱和土体动力响应分析

 为研究地铁列车运行引起的轨道系统及饱和土体动力响应问题,建立了地铁列车–轨道结构–衬砌–饱和土体耦合分析模型,其中列车荷载用一系列符合列车几何尺寸的移动常荷载或移动简谐荷载模拟,轨道结构中的钢轨和浮置板简化为无限长弹性Euler梁。基于弹性理论和Biot多孔介质理论,采用2.5维有限元法分别模拟衬砌和饱和土体,结合轨道与衬砌仰拱处的力和位移连续条件,实现浮置板轨道系统与衬砌及周围饱和土体的耦合,并通过快速Fourier逆变换(IFFT)进行波数展开获得三维时域–空间域内的动力响应。研究结果表明,随着常荷载移动速度和移动简谐荷载自振频率的提高,地表振动水平显著增大;移动常荷载产生的地表响应最大值在荷载正上方,其空间衰减率保持恒定;移动简谐荷载产生的地基振动大于移动常荷载产生的地基振动,响应最大值在列车运行线路两侧一定范围内;在移动简谐荷载作用下,钢轨速度谱与地表速度谱分布在以简谐荷载自振频率为中心的一段范围内。