Substructure Simulation of Inhomogeneous Track and Layered Ground Dynamic Interaction under Train Passage

The vibrations in track and ground induced by train passages are investigated by the substructure method with due consideration to dynamic interaction between an inhomogeneous track system comprising continuous rails and discrete sleepers, and the underlying viscoelastic layered half space ground. Initially, the total system is divided into two separately formulated substructures, i.e., the track and the ground. The rail is described by introducing the Green function for an infinite long Euler beam both for moving axle loads action from a train and for reactions from sleepers. The ground is formulated by the layer transfer matrix approach for wave propagation along the depth. Subsequently, these substructures are integrated to meet the displacement compatibility and force equilibrium via inertia of sleepers and stiffness of railpad springs. The dynamic equations are solved in the frequency–wave-number domain by applying the Fourier transform procedure. Based on the assumption of a constant train speed, the time domain response is evaluated from the inverse Fourier transform computation. The dispersive characteristics of the layered ground and the moving axle loads lead to significantly different response features, depending on the train speed. The response is classified as quasistatic for a low speed, whereas it is dynamic for a high-speed situation. An illustrative case study is presented for Swedish X-2000 train track properties and ground profile.     

Effects of Train Characteristics on the Rate of Deterioration of Track Roughness

Track roughness describes in part the up and down waves in the longitudinal geometry of a railway track. A train passing over rough track experiences a degree of bouncing that generates oscillations in the forces exerted by the train’s wheels on the top of the rail, which in turn cause this roughness to worsen. The rate at which the track roughness deteriorates depends on the response of the track to the weight of the train and to the dynamic oscillations in wheel/rail forces, which in turn are affected by the properties of the train vehicles’ components and the speed of the train. The paper develops relationships between the severity of track roughness and the dynamic wheel/rail forces generated by a moving train using field data, and between those forces and the specific vehicle characteristics of speed, total mass, unsprung mass, suspension stiffness, and damping, using NUCARS simulations. These two relationships in turn are combined to show how the speed of the train and the design of the train vehicle’s bogie suspension can worsen or improve the rate of deterioration of track roughness. The relationships also provide a firm basis for the owner of track to set more representative charges levied on the train operator for using the track.     

Dynamic Stress Analysis of a Ballasted Railway Track Bed during Train Passage

Scientific design of a railway track formation requires an understanding of the subgrade behavior and the factors affecting it. These include the effective resilient stiffness during train passage, which is likely to depend on the stress history and the stress state of the ground, and the stress path followed during loading. This study investigates the last of these, by means of a two-dimensional dynamic finite-element analysis. The effects of train speed, acceleration/braking, geometric variation in rail head level, and a single unsupported sleeper are considered. Results indicate that dynamic effects start to become apparent when the train speed is greater than 10% of the Rayleigh wave speed, vc, of the subgrade. At a train speed of 0.5vc, the shear stresses will be underestimated by 30% in a static analysis, and at train speeds greater than vc the stresses due to dynamic effects increase dramatically. Train acceleration/braking may increase shear stresses and horizontal displacements in the soil, and hence the requirement for track maintenance at locations where trains routinely brake or accelerate. For heavy haul freight trains, long wavelength variations in rail head level may lead to significantly increased stresses at passing frequencies (defined as the train speed divided by the wavelength of the variation in level) greater than 15, and short wavelength variations at passing frequencies of 60–70. Stress increases adjacent to an unsupported sleeper occur in the ballast and subballast layers, but rapidly become insignificant with increasing depth.     

Experimental Study on the Stability of Railroad Silt Subgrade with Increasing Train Speed

The comfort and safety of a moving train is largely determined by the dynamic response of the railway track and its foundation (i.e., subgrade). To study the dynamic stability of a silt subgrade subjected to train traffic loading with increasing speed, cyclic triaxial tests were conducted for compacted silt specimens with varying dry density, water content, dynamic stress, and load frequency. The laboratory test results and field measurements of the subgrade dynamic stress under train loading indicate that with increasing train speed, an increase in dynamic stress and load frequency does not impair the stability of the silt subgrade, provided the subgrade is in sound physical condition (i.e., its natural water content approximates the optimal water content) and the relative compaction is at least 90%. However, if the relative compaction is 85%, the subgrade is stable only at a dynamic stress level that is below 70 kPa, and the subgrade may suffer shear failure at a higher dynamic stress level. The elastic deformation of the subgrade linearly increases with an increase in train speed. However, if the degree of saturation of the silt subgrade increases, the thresholds of both the dynamic stress and resilient modulus decrease markedly, accompanied by sharp increases in elastic deformation and cumulative deformation and can even result in the shear failure of the subgrade. These conditions are unfavorable for the high speeds and stability needed for trains; therefore, train speeds should be limited in wet conditions to reduce subgrade dynamic stress and load frequency.     

Dynamic Response of Suspension Bridge to High Wind and Running Train

A framework is presented for predicting the dynamic response of long suspension bridges to high winds and running trains. A three-dimensional finite-element model is used to represent a suspension bridge. Wind forces acting on the bridge, including both buffeting and self-excited forces, are generated in the time domain using a fast spectral representation method and measured aerodynamic coefficients and flutter derivatives. Each 4-axle vehicle in a train is modeled by a 27-degrees-of-freedom dynamic system. The dynamic interaction between the bridge and train is realized through the contact forces between the wheels and track. By applying a mode superposition technique to the bridge only and taking the measured track irregularities as known quantities, the number of degrees of freedom of the bridge-train system is significantly reduced and the coupled equations of motion are efficiently solved. The proposed formulation is then applied to a real wind-excited long suspension bridge carrying a railway inside the bridge deck of a closed cross section. The results show that the formulation presented in this paper can predict the dynamic response of the coupled bridge-train systems under fluctuating winds. The extent of interaction between the bridge and train depends on wind speed and train speed.     

Experimental Dynamic Response of a Short-Span Composite Bridge to Military Vehicles

A continued desire for increased mobility in the aftermath of natural disasters or on the battlefield has lead to the need for improved lightweight bridging solutions. Currently, within the U.S. military, there is a need for a lightweight bridging system for crossing short-span gaps up to 4 m (13.1 ft) in length. This paper describes the field testing of a newly developed lightweight fiber-reinforced polymer bridging system to meet the U.S. militaries needs. The study investigates dynamic impact loads of track and wheel vehicles at different crossing speeds to increase understanding of appropriate impact factors used in design. It was found that the impact loads for the bridge treadways were most sensitive to vehicle crossing speed and vehicle type (wheel versus track and axle spacing) with observed impact factors as high as 1.71.     

Model Validation for Bridge-Road-Vehicle Dynamic Interaction System

The dynamic response of highway bridges subjected to moving truckloads has been observed to be dependent on (1) dynamic characteristics of the bridge; (2) truck configuration, speed, and lane position on the bridge; and (3) road surface roughness profile of the bridge and its approach. Historically, truckloads were measured to determine the load spectra for girder bridges. However, truckload measurements are either made for a short period of time [for example, weigh-in-motion (WIM) data] or are statistically biased (for example, weigh stations) and cost prohibitive. The objective of this paper is to present results of a 3D computer-based model for the simulation of multiple trucks on girder bridges. The model is based on the grillage approach and is applied to four steel girder bridges tested under normal truck traffic. Actual truckload data collected using a discrete bridge WIM system are used in the model. The data include axle loads, truck gross weight, axle configuration, and statistical data on multiple presence (side by side or following). The results are presented as a function of the static and dynamic stresses in each girder and compared with code provisions for dynamic load factor. The study provides an alternate method for the development of live-load models for bridge design and evaluation.     

Train-Induced Vibration Control of High-Speed Railway Bridges Equipped with Multiple Tuned Mass Dampers

This paper deals with the applicability of multiple tuned mass dampers (MTMDs) to suppress train-induced vibration on bridges. A railway bridge is modeled as an Euler-Bernoulli beam and a train is simulated as a series of moving forces, moving masses, or moving suspension masses. According to the train load frequency analysis, resonant effects will occur as the modal frequencies of a bridge are close to the multiple of the impact frequency of the train load to the bridge. An MTMD system is then designed to alter the bridge dynamic characteristics to avoid excessive vibrations. Numerical results from simply supported bridges of the Taiwan High-Speed Railway (THSR) under real trains show that the proposed MTMD is more effective and reliable than a single TMD in reducing dynamic responses during resonant speeds, as the train axle arrangement is regular. It is also found that the inner space of a bridge box-girder of the THSR is wide and deep enough for installation and movement of MTMDs.     

Full-Scale Field Evaluation of Microelectromechanical System-Based Biaxial Strain Transducer and Its Application in Fatigue Analysis

The objective of this research is to develop a microelectromechanical system (MEMS)-based intelligent hybrid Biaxial Strain Transducer (BiAST) sensor for predicting railroad fatigue life based on strain history. The developed BiAST prototype was deployed to collect real-time strain data from the full-scale test track at the Transportation Technology Center (TTCI), near Pueblo, Colorado. The collected strain data were analyzed using the “Binner” fatigue analysis program for counting the load cycles and estimating the fatigue life of a rail structure. Field-testing results of the BiAST were used to evaluate the BiAST prototype with respect to its repeatability, accuracy, and hybridization. BiAST was effective in detecting the dynamic response of a particular wheel and spurious overload events. BiAST can be used to detect passing wheels, train speed, and track condition.     

Concentrations of Pressure Between an Elastically Supported Beam and a Moving Timoshenko-Beam

The present paper is concerned with the motion of an elastically supported beam that carries an elastic beam moving at constant speed. This problem provides a limiting case to the assumptions usually considered in the study of trains moving on rail tracks. In the literature, the train is commonly treated as a moving line-load with space-wise constant intensity, or as a system of moving rigid bodies supported by single springs and dampers. In extension, we study an elastically supported infinite beam, which is mounted by an elastic beam moving at a constant speed. Both beams are considered to have distributed stiffness and mass. The moving beam represents the train, while the elastically supported infinite beam models the railway track. The two beams are connected by an interface modeled as an additional continuous elastic foundation. Here, we follow a strategy by Stephen P. Timoshenko, who showed that a beam on discrete elastic supports could be modeled as a beam on a continuous elastic Winkler (one-parameter) foundation without suffering a substantial loss in accuracy. The celebrated Timoshenko theory of shear deformable beams with rotatory inertia is used to formulate the equations of motion of the two beams under consideration. The resulting system of ordinary differential equations and boundary conditions is solved by means of the powerful methods of symbolic computation. We present a nondimensional study on the influence of the train stiffness and the interface stiffness upon the pressure distribution between train and railway track. Considerable pressure concentrations are found to take place at the ends of the moving train.     

Computer-Aided Graphical Analysis of Bridges under Vehicular Loading

A computer-based, graphical approach is presented to construct the Influence Profile for determinate bridge structures that are subjected to multiple axle loads. An Influence Profile represents the variation of an internal or external force, or moment, at a specific location of a structure, under loading by an actual vehicle (e.g., AASHTO HS-20 truck, American Railway Engineering and Maintenance-of-Way Association (AREMA) Cooper E-80 train). The technique works by scaling the influence line ordinates by the individual axle weights of the vehicle, and by applying distance delays to account for the horizontal separation between axles. The scaled and shifted influence lines for individual axle loads are then superimposed graphically to obtain the effect of the entire vehicle. Beam and truss examples are given to illustrate the technique. A simple method is also presented for constructing influence profiles for compound systems, where the load is transferred through the deck and floor beams to the superstructure. Because of its graphical concept, the technique provides a practical approach for evaluating the force effects caused by an actual vehicular load; it is also well suited for teaching purposes.     

Model Testing of Two-Layer Railway Track Ballast

Railway track ballast requires regular attention to maintain line and level. A recently developed maintenance method, known as pneumatic ballast injection (PBI) or stoneblowing, re-levels and realigns the track by lifting the sleepers and track and blowing smaller size gravel between the ballast and the base of the sleeper. This creates a two-layer ballast bed. Series of large-scale model tests have been carried out to gain a better understanding of the behavior of such a bed under repeated loading. The results confirm that stoneblowing is a better form of track maintenance than the commonly used ballast tamping method, but the size and type of stone and the thickness of the injected layer are of critical importance in determining the postmaintenance behavior.     

Effects of Principal Stress Rotation on Permanent Deformation in Rail Track Foundations

A realistic assessment of the whole life cost of rail track foundations requires analysis of the effects of the repeated loadings applied by trains. This paper reports the effects of principal stress rotation (PSR) during cyclic loading on the permanent deformations measured in a series of hollow cylinder tests. The tests were carried out on a number of reconstituted soils selected in order to simulate foundation materials on an existing heavy haul railway line. Typical loadings and track geometry together with dynamic finite-element analyses were used to define representative stress changes to be applied to these soils, which were then tested with and without principal stress rotation during loading. It is shown that principal stress rotation has a significant and deleterious impact on permanent deformation of some materials. Therefore, it is concluded that cyclic triaxial testing, which cannot impose principal stress rotation, will not necessarily give good estimates of the long-term performance of rail track foundations. As PSR cannot be ignored when evaluating permanent displacements of rail track foundations, the use of more appropriate (realistic) testing methods such as the cyclic hollow cylinder or the cyclic simple shear apparatus is required.     

机电轨道衡快速改造实践

针对机电结合轨道衡使用年限长、计量精度差、急需更新改造的现状。为缩短工期，在不停秤的情况下设计制造了工字钢及钢板焊接而成的横梁与原基础联接，使停秤时间由30天减少为2天．测试表明，各项功能正常，器件防护良好，为中准确度级合格．应用表明。称重速度快、性能稳定。减少了计量误差，提高了衡器精度，各项技术指标符合要求。     

矿山LT型动态轨道衡的误差调节

对矿山LT型动态轨道衡进行静态和动态误差调节，提高计量精度，控制了矿山原矿和成品矿亏吨，取得了明显经济效果。     

桥式起重机自动防啃轨装置的应用

针对桥式起重机在运行过程中普遍存在的啃轨现象,运用自动防啃轨控制技术对两侧车轮运行速度进行动态实时调整,以消除车轮啃轨现象、延长设备寿命、节约设备成本、提高生产的安全与经济效益.     

Dynamic Response of Elevated High-Speed Railway

The study of the dynamic response of the elevated railway for the high-speed train in the Taiwan area at the preliminary design stage is presented. Two types of the elevated reinforced concrete railway, they being the simple-span and the three-equal-span box girders supported on piers; three types of the high-speed train, namely, the French T.G.V., the German I.C.E., and the Japanese S.K.S.; and the maximum operation speed 350 km∕h are under investigation. The general dynamic stiffness matrix of a damped Timoshenko beam is employed for the structural analysis. The influence line of any dynamic response (also called the dynamic influence line) of the elevated railway subjected to the high-speed train, considered as a series of the moving loads, is calculated by the mode-superposition method. A preliminary design of the section of the railway is proposed for this study.     

Laboratory Evaluation of the Briaud Compaction Device

Soil compaction quality control plays an important role in earthwork construction. Compacted dry density is only loosely related to the actual deformation of the compacted soil. Rather than using dry density as the controlling factor for compacted fills, it would be better to measure properties more closely related to soil compressibility. The Briaud compaction device (BCD) is a simple, small-strain, nondestructive testing apparatus that can be used to evaluate the modulus of compacted soils. The use of the BCD as a field testing device for compacted soil quality control may be more beneficial than the current practice of measuring in situ dry density. In this study, the laboratory procedures of the BCD were evaluated for compacted silt. The modulus determined by the BCD was compared to the dynamic elastic moduli (Young’s and shear moduli) determined from ultrasonic pulse velocity testing on the same compacted silt samples. The BCD modulus correlated well with the ultrasonic pulse velocity results with R2 value of 0.8 or better. Finally, a repeatability and reproducibility study conducted on the BCD showed a variation of 4% from the mean when only the soil properties were altered.     

基于新型趋近律和扰动观测器的永磁同步电机滑模控制

为了提高永磁同步电机的转速控制性能,克服扰动对伺服控制的影响,提出了一种基于新型趋近律和扰动观测器的滑模控制方法.设计了一种新型趋近律,以解决传统趋近律滑模面趋近时间和系统抖振之间的矛盾,提高系统响应快速性.综合考虑系统存在内部参数摄动和外部负载扰动,设计了滑模扰动观测器,并将观测值前馈补偿到速度控制器输出端;将观测器切换增益设计为扰动观测误差的函数,以削弱滑模观测值抖振.仿真结果显示,与传统趋近律相比,采用新型趋近律可有效提高系统的响应速度,快速准确的跟踪速度阶跃信号;滑模观测器可准确的观测系统扰动的变化;当系统加入负载扰动时,PI控制最大转速波动值为75 r·min-1,而基于新型趋近律和扰动观测器的滑模控制最大转速波动值较小为30 r·min-1,鲁棒性更好.实验结果显示,采用基于新型趋近律和扰动观测器的滑模控制方法可以快速跟踪400 r·min-1的速度指令,调节时间为0.12 s,稳态跟踪误差为±4 r·min-1,且转速无超调;滑模观测器可准确无超调的估计系统扰动值,进一步提高系统的抗扰动性能;当电机以400 r·min-1稳速运行时,加入0.6 N·m的负载扰动,基于新型趋近律和扰动观测器的滑模控制方法最大转速波动为23 r·min-1,与PI控制相比,转速波动减小了8%.上述仿真和实验结果具有较好的一致性,表明基于新型趋近律和扰动观测器的滑模控制方法可以有效抑制滑模控制系统的抖振,提高转速控制系统的鲁棒性和动态响应性能.      

Impact of Bituminous Subballast on Railroad Track Deformation Considering Atmospheric Actions

High-speed ballasted track design standards usually require the use of sand and gravel layers as subballast to fulfill an accurate protection of the formation layers, not only against traffic loads, but also against the effects of weather. Seasonal changes in soil water content, or suction changes, are responsible for cyclic volumetric strains on railroad trackbed layers, thus on the infrastructure. Being almost completely water-resistant when compared with granular-only layers, bituminous subballast offers a higher protection of the subgrade, consequently improving its behavior along the infrastructure life cycle. This question is investigated through the comparison of the performance of the track formation against atmospheric actions, taking into consideration the unsaturated state of the geomaterials. The method adopted consists of modeling the vertical displacements of both bituminous and granular subballast designs through a finite-element coupled thermo-hydro-mechanical (THM) analysis. The comparison of the two design solutions confirms that the adoption of a bituminous subballast layer might allow important reductions in seasonal vertical displacements.