A simple finite element to consider the non-linear influence of the ballast on vibrations of railway bridges

This article proposes a new and simple finite element which can be used to analyze vertical vibrations in railway bridges. The main feature of the element is that the effect of the ballast is introduced through a non-linear longitudinal stiffness associated to the slip at the interface between the bridge and the ballast. Two numerical applications show that this element can be used to model the variation of the natural frequencies of the bridge as a function of the amplitude of vibration.     

铁路钢桥环氧沥青柔性保护层受力控制指标值研究

研究轨道高低动态不平顺引起的列车随机动荷载作用下铁路钢桥柔性保护层的力学行为。采用有限单元法,建立高速列车-轨道-柔性保护层-桥梁耦合体系有限元模型,其中轨道体系采用一次梁(单层)轨道模型和离散支撑体系。将轨道高低不平顺作为列车随机动荷载的激励源输入,通过典型铁路钢桥面系算例分析可见,轨枕两侧、纵肋上方及轨枕下方对应的保护层区域较易出现开裂破坏;钢板和保护层之间较容易发生横向剪切滑移;考虑轨道高低动态不平顺的柔性保护层力学响应明显大于静载计算结果。研究成果表明铁路钢桥柔性保护层设计时应重点考虑轨道随机不平顺的影响。     

Fatigue analysis of long-span suspension bridges under multiple loading: Case study

Long-span suspension bridges are often subject to multiple types of dynamic loads, especially those located in wind-prone regions and carrying both trains and road vehicles. Fatigue assessment shall be performed to ensure the safety and functionality of the bridges. This paper proposes a framework for fatigue analysis of a long-span suspension bridge under multiple loading by integrating computer simulation with structural health monitoring system. By taking the Tsing Ma Bridge in Hong Kong as an example, a computationally efficient engineering approach is first proposed for dynamic stress analysis of the bridge under railway, highway and wind loading. The fatigue-critical locations are then determined for key bridge components, and databases of the dynamic stress responses at the critical locations are established. The time histories of dynamic stresses induced by individual loading during the design life of the bridge are generated based on the databases. The corresponding stress time histories due to the combined action of multiple loading are also compiled. Finally, fatigue analysis is performed to compute the cumulative fatigue damage over the design life of 120 years. The results indicate that it is necessary to consider the combined effect of multiple loading in the fatigue analysis of long-span suspension bridges.     

Vibration of subgrade and evaluation of derailment coefficient of train under combined earthquake- moving train load

Vibration response of track and foundation subjected to dynamic loading is one of the key issues to solve on-track safety of high-speed train. The previous pioneering works commonly only considered the train moving load, however, in reality, trains are likely to be on track when an earthquake occurs due to the high frequency and widespread distribution of earthquake activities. Hence, a three-dimensional FEM of track-subgrade- foundation interaction system with bidirectional seismic and moving loads is established for investigating the differences and relations of vibration responses of subgrade in such two immensely disparate loads: train moving load and earthquake-moving load. As a case study, the vibration characteristics of the Beijing-Shanghai High-speed Railway of the China, excited by moving load and seismic-moving composite load are analyzed respectively, with various velocity (v = 50 m/s, 70 m/s, 100 m/s, 130 m/s). On the other hand, the increases in operational train speeds mean that critical velocity effects are becoming more common on high speed rail lines. If unaddressed, critical velocity issues can cause safety concerns and elevated maintenance costs. Based on the derailment coefficient and lateral deformation of the rail, the critical speed of the model is discussed, which is a reasonable improvement to the derailment mechanism of the train.     

抛物线拱桥在移动荷载作用下的动力响应分析

建立抛物线双铰拱桥的强迫振动的运动微分方程,分析了拱桥在移动荷载作用下的横向振动问题,将运动微分方程解耦,得到拱桥在移动荷载作用下振动时的动力响应并加以分析,通过实例计算,得到了拱桥在移动荷载不同行驶速度时的动力挠度曲线,并进行了比较分析。     

Fragility analysis of track-on steel-plate-girder railway bridges in Korea

More than 40% of the bridges in conventional Korean railway lines are track-on steel-plate-girder (TOSPG) bridges. They are characterized by a superstructure consisting of railway tracks sitting directly on steel plate girders without any ballast system. Most of these bridges have been designed with little or no consideration given to seismic loading. In this paper, seismic fragility curves of TOSPG bridges in Korea are developed. Fragility curves are developed first for the components, by using the probabilistic seismic demand model. The developed component fragility curves show that the bearings are the most vulnerable components of the TOSPG bridges against seismic loading. On the other hand, the piers are much less vulnerable, although they contain no reinforcing bars. This is because the superstructure mass is very light, and therefore horizontal loading transferred from the superstructure to the piers is minimal. A generic damage measure is introduced for measuring the system-level damage of structures out of the component-level damages. The system fragility curves are then developed, using the generic damage measure. Finally, representation of seismic risk in terms of expected seismic losses is demonstrated. This demonstration shows how the fragility analysis is utilized for risk assessment and support in decision-making.     

Fatigue evaluation of riveted railway bridges through global and local analysis

This paper presents an overview of recent research efforts by the authors and co-workers on the fatigue assessment of old metallic railway bridges. The investigation focuses on the behaviour of riveted stringer-to-cross-girder connections in a typical, short-span bridge. A generic methodology, which is based on nominal stresses and the S-N method, is presented first, followed by a more detailed analysis using a recently developed fatigue assessment theory, which is based on local stress distributions. The discussion is made within a deterministic as well as a probabilistic context and typical results are presented in terms of fatigue damage and remaining fatigue life.     

A shakedown limit calculation method for geogrid reinforced soils under moving loads

A method to calculate the elastic shakedown limit of transportation systems (e.g. pavements and railways) supported by geogrid reinforced soils is presented. For the first time, lower-bound shakedown theory is combined with a strength-based geogrid simulation approach, resulting in a rapid method to quantify the benefit of geogrids on the elastic shakedown limit. It allows decoupling of elastic stress generation and shakedown calculations, meaning it is straightforward to implement, and requires minimal computational effort. Therefore it presents a useful tool to optimise geogrid design for transportation structures such as highway pavements and railways. To show the capability of the method, shakedown limits are calculated for a variety of geogrid configurations using elastic stresses induced by a moving Hertz load. The effect of geogrid depth, soil cohesion, soil friction angle and loading type (normal versus tangential) are investigated for reinforced and non-reinforced soils. It is found that the optimum depth is sensitive to the soil strength properties. Regarding loading, it is shown that for highly tangential loads, shallower geogrids are effective, while for loads with a minimal tangential component, deeper geogrids are effective.     

船撞作用下斜桩基础动力响应研究

东海大桥100MW海上风电示范项目中风机采用斜桩基础,必须考虑船撞作用。本文利用有限元方法,研究了斜桩基础在船撞作用下的动力响应。模拟不同工况,研究船舶吨位、船舶速度、倾斜角、桩径、桩周土体等因素对桩基的动力响应的影响。研究表明:船舶吨位和船舶速度对斜桩的动力学响应影响最大;桩的倾斜角会影响最大桩项位移,最优倾斜角约为10°;在既定的土质条件下,桩径增大到某一值后,桩基动力响应基本不变;土体较软时,桩身的最大应力较小,但最大桩顶位移较大。因此,进行斜桩设计时,必须在理论分析的基础上,选取合适的倾斜角与桩径。本文研究结果对斜桩基础在考虑船撞作用下的设计和施工有一定参考价值。     

Recent developments of high-speed railway bridges in China

China’s high-speed railway (HSR) construction industry has been experiencing a golden period of opportunities in the recent decades. Due to the necessity of protecting arable lands and the advantage of rapid construction, bridges (elevated structures) are predominantly used in China’s HSRs, which must meet the critical small settlement requirement. This article first reviews the main technical standards of small- to medium-span HSR bridges, where their comparison with the Japanese standard and International Union of Railway standards is highlighted. Then, the long-span HSR steel bridges are described and discussed case by case. Based on the engineering practice of HSRs, the main achievements and key technologies of HSR bridges in China are provided, followed by the opportunities and challenges of the current and future developments of HSR bridges.     

Reliability-based strength limit state for steel railway bridges

Railway bridges require special attention to provide safe and economical service. To assess the reliability of a structure, all critical parameters need to be specified. Load and resistance are random in nature; hence, the probabilistic approach is the best method for accurate evaluation of the performance of a bridge. In this study, identification of critical parameters was conducted on a typical through-plate girder, riveted, open deck railway bridge. This type of structure is a weakest link system. In such a system, the failure of one component can lead to failure of the entire structural system. This research involved identification of the basic load and resistance parameters and the development of analytical procedures for modelling the structural behaviour. The finite element method (FEM) was used to investigate the structural performance characteristics of the evaluated bridge. A three-dimensional structural model was developed to determine stress distribution in the members and connections. Based on the results of FEM analysis, the reliability indices were calculated for critical components.     

Simulation of dynamic linear thermal bridges using a boundary element method model in the frequency domain

Heat losses through thermal bridges often lead to building pathologies generated by moisture condensation. Thus, thermal bridges need to be considered in the building design phase in order to avoid both heat loss and the occurrence of these pathologies later on. The linear thermal bridge is often taken into account at the design stage by using a pre-defined ψ coefficient. This ψ factor is listed in several national regulation/standards for various types of linear thermal bridges on the assumption of a steady state condition.This paper studies linear thermal bridges more realistically by assuming a dynamic behavior that allows the simulation of transient states where the external and internal temperatures may vary over time. The problem is solved by a boundary element model (BEM), formulated in the frequency domain. Time solutions are obtained afterwards by means of inverse Fourier transformations, which can simulate any external temperature variations. After an experimental validation of the BEM model, a series of linear thermal simulations was performed to illustrate the applicability of the proposed model. It further allows the importance of computing thermal bridges to be verified dynamically.     

Assessment of European railway bridges for future traffic demands and longer lives – EC project “Sustainable Bridges”

A European Integrated Research Project has recently been started within the 6th Framework Program of the European Commission. The project aims at improved methods for the upgrading of existing railway bridges within the European railway network. The main objectives of the project are to increase the transport capacity by allowing higher axle loads and by increasing the maximum speeds. Other objectives are to increase the residual lifetime of existing bridges and to enhance management, strengthening and repair systems. The overall goal is to enable the delivery of improved capacity without compromising the safety and economy of the working railway. A consortium consisting of railway bridge owners, consultants, contractors, research institutes and universities will carry out the project, having a gross budget of more than 10 million Euros. Funding from the European Commission covers a major portion of the four-year project costs.     

System reliability of suspension bridges

Provisions for the design of existing suspension bridges often rely on a deterministic basis. Consequently, the reliability of these bridges cannot be assessed if current provisions are applied. In order to develop cost-effective design and maintenance strategies for suspension bridges a system reliability-based approach has to be used. This is accomplished by a probabilistic finite element geometrically nonlinear analysis approach. This study forms part of an investigation into the system reliability evaluation of geometrically nonlinear large span bridges recently undertaken at the University of Colorado. A brief review of reliability analysis of geometrically nonlinear elastic structures allows for the determination of its relevance to the assessment of suspension bridges. A probabilistic finite element geometrically nonlinear elastic code is used for system reliability evaluation of suspension structures. The allowable stress design procedures used by the Honshu Shikoku Bridge Authority for the design of suspension bridges are presented along with their application to the design of an existing bridge. This bridge is studied from a system reliability viewpoint to evaluate its reliability under different loading and damage scenarios. Such information calls attention to the fact that the reliability of cables, hanger ropes and girders are very different. Therefore, optimal maintenance decisions for suspension bridges designed according to allowable stress method are not consistent with those based on equal component reliability values.     

Finite element method failure analysis of a pressurized FRP cylinder under transverse impact loading

Safety is vital in transport vehicles, especially in case of accidents. The fuel tank must particularly be free from failure. This study discusses impact analyses of pressurized fibre-reinforced plastic (FRP) cylinders by simulation, using the finite element method. The FRP material is defined as orthotropic, and different failure conditions are defined for every failure mode. After failure, the elastic moduli are reduced, based on the appropriate damage mechanics. To represent a fluid-filled vessel, inner pressure is added to the cylinder, and nodal forces are loaded on the inner surface and side section nodes. A bar impactor hits the centre of the cylinder, vertical to the axis. As a result, the relationship between burst mode and inner pressure can be clarified.     

Dynamic response analysis of monorail bridges under moving trains and riding comfort of trains

This paper introduces an analytical procedure to derive equations of motion for the monorail train–bridge interaction based on Lagrange’s formulation to investigate riding comfort of moving monorail trains on bridges. A 15 degrees-of-freedom dynamic model is assumed for a car in a monorail train that consists of driving, steering, and stabilizing wheels. It is based on the finite element method for modal analysis using three-dimensional models for a monorail bridge. Dynamic behaviors of a rationalized monorail bridge with a simplified structural system are investigated in comparison with those of a conventional monorail bridge using the developed analytical method. The riding comfort of running trains on the rationalized monorail bridge based on ISO 2631 is estimated using 1/3 octave band spectral analysis. Observations indicate that a rational type bridge does not engender difficulties related to the riding comfort of the monorail train, even when considering the longest traveling time of passengers between terminals.     

Neural networks for prediction of deflection in composite bridges

Neural networks have been developed for prediction of deflections, at service load, in steel-concrete composite bridges incorporating flexibility of shear connectors, shear lag effect and cracking in concrete slabs. Three neural networks have been presented to cover simply supported bridges, two span continuous bridges and three span continuous bridges. The use of the neural networks requires a computational effort almost equal to that required for the simple beam analysis (neglecting flexibility of shear connectors, shear lag effect and cracking of concrete). The training and testing data for neural networks are generated using finite element software ABAQUS. The neural networks have been validated for number of bridges and the errors are found to be small. Closed form solutions are also proposed based on the developed neural networks. The networks/ closed form solutions can be used for rapid prediction of deflection for everyday design.     

Static and dynamic stability assessment of slopes or dam foundations using a rigid body–spring element method

A rigid body–spring element method is used to evaluate the static and dynamic stability of slopes or dam foundations. The versatility of the method applies well to both static and dynamic problems for blocks of arbitrary polyhedral shape with various re-entrant surface features. Examples show that the safety factor obtained in this way agrees well with theoretical solutions. The dynamic safety factor determined with this method varies with time, which differentiate it from the results of the limit equilibrium method or the finite element method. The method also makes it possible to search for the most probable sliding mass.     

Dynamic behavior of hybrid framed arch railway bridge under moving trains

In this study, the dynamic behavior of a concrete-filled steel tube (CFST) hybrid framed arch railway bridge under moving trains are investigated through an in-site dynamic test. The bridge was tested under train loadings in different scenarios and at different speeds of the trains. The free vibration characteristics, strain, displacement, and acceleration of the bridge structure were measured to evaluate the dynamic responses of the train-bridge coupling system. A three-dimensional finite element model, which took into account the train-bridge coupling and track irregularities, was established to analyze the behaviors of the train-bridge system. The model was validated against the in situ test results. The impact effect on the girder was greater than that of the arch frame. The acceleration responses of the trains on the bridge increased with the train’s speed. The riding comfort of the trains was evaluated based on the measured dynamic responses of trains.     

Vibration analysis of toroidal panels using the differential quadrature method

The free vibration characteristics of linear elastic toroidal shell panels are determined. A solution based on the Mushtari–Vlasov–Donnell shell equations is developed using the Differential Quadrature Method. The work represents the first application of this method to problems in shell theory with variable coefficients in the governing equations. Numerical results are calculated using the method, and these are compared with results found using a Fourier series and a finite element solution.