Soil Vibrations Caused by Underground Moving Trains

The wave propagation problems caused by the underground moving trains are analyzed by the 2.5-dimensional finite/infinite-element approach. The near field of the half-space, including the tunnel and parts of the soil, is simulated by finite elements, and the far field extending to infinity by infinite elements. The train is simulated as a sequence of wheel loads moving at constant speeds. Using the present approach, a two-dimensional profile with three degrees per node is used to simulate the three-dimensional behavior of the half-space, which is valid for the case when the material and geometry of the system are invariant along the tunnel direction. The factors considered in the analysis of ground-borne vibrations include the damping ratio and stratum depth of the supporting soils, the depth and thickness of the tunnel, and the moving speed and excitation frequency of the trains. It was found that moving train loads with nonzero excitation frequencies can induce significantly higher vibrations than the static moving loads. The effect of stratum depth depends highly on the excitation frequency. For a tunnel constructed in a stiffer soil, the ground surface vibrations can be greatly reduced. Other conclusions useful to practical engineers are contained in the parametric study.     

Three-Dimensional Analyses of Wave Barriers for Reduction of Train-Induced Vibrations

This paper explores the use of a three-dimensional finite-element analysis to model soil vibrations due to high-speed trains on bridges. Finite-element meshes include the bridge superstructure, bridge foundations, nearby building foundations, and piles. Wheel elements represented by appropriate mass, damping and stiffness factors were used to simulate a moving high-speed train. Along the mesh boundaries, absorbing boundary conditions were employed to avoid fictitious wave reflections. Isolation methods to reduce soil vibrations were investigated including construction of open and infilled trenches and soil improvement. Vibration isolation effects due to building foundations and piles were also studied. The finite-element results indicate that suitable axial stiffness between two simple beams can reduce vibration significantly, especially at a near-resonance condition. Operating with an appropriate train velocity to avoid resonance can be another way to reduce vibrations. Suitable mat foundations can significantly reduce soil horizontal vibration, but cannot isolate vertical vibration. Soil improvements near the bridge do not effectively attenuate low-frequency vibrations. Infilled and open trenches can isolate soil vertical vibration; however, their efficiency seems disproportionate to their cost.     

Studying Characteristics of Train-Induced Ground Vibrations Adjacent to an Elevated Railway by Field Experiments

This paper investigates the characteristics of the ground vibration induced by moving trains on elevated railways using a number of field measurements at various train speeds. The experimental results indicate that the vibration at the dominant frequencies is quite large in both the vertical and horizontal directions, where the dominant frequencies and their influence factors can be evaluated using two simple theoretical equations deducted from the trainload in the frequency domain. Furthermore, the vibration at the dominant frequencies increases almost proportionally to the train speed, except at the resonance condition, which can be found both in field experiments and using the equation of the influence factor.     

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.     

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.     

Surface Wave Tests for Vibration Mitigation Studies

Wave barriers (open or in-filled trenches) are often used in engineering practice to reduce ground vibrations caused by industrial activities or transportation systems. Typically, most of the energy is transmitted in the form of Rayleigh waves so that information related to their propagation can be very useful in the design process. This technical note presents a case study in which both active and passive surface wave tests have been used in the design of a vibration mitigation barrier. It is shown that several pieces of information can be inferred from these tests for specific applications: source characterization in terms of dominant frequencies and direction of propagation; dominant wavelength for the preliminary design; and soil characterization for the construction of a numerical model aimed at analyzing the performance of the wave barrier.     

Wave Propagation in Orthogonally Supported Periodic Curved Panels

In the present paper, a two-dimensional periodic curved panel which rests on an orthogonal array of equispaced simple line supports has been analyzed by a FEM. A periodic unit of the system is represented by an accurate high-precision curved triangular shallow shell finite-element model to find out frequencies of plane wave motion in terms of propagation constants for the two-dimensional periodic shell. The natural frequencies of vibration of a full cylindrical shell have been obtained for different propagation constants in the axial and circumferential directions. The propagation surface is found using the optimum periodic curved panel in the analysis. It is observed that the lowest frequency can be found out at the lower bound of first propagation surface, by choosing an optimum periodic angle of curved panel. All the natural frequencies of orthogonally multisupported open curved panel of (Nx×Ny) elements have been found out from the propagation surface and compared with NASTRAN results. It is shown that by this approach the order of the resulting matrices in the FEM is considerably reduced leading to a significant decrease in computational effort.     

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.     

Ground Motion Induced by Train Passage

Two methods are illustrated to effectively calculate the ground motion induced by constant speed moving loads. On the one hand, the dynamic Betti–Rayleigh reciprocity theorem allows one to take full advantage of the availability of Green’s functions for a homogeneous or a horizontally layered half-space. On the other hand, the spectral element method allows one to deal with complicated configurations, including dynamic soil-structure interaction, with an accuracy that is significantly higher than classical finite element or finite difference methods. Both the Betti–Rayleigh and spectral element methods are considered in three dimensions. After validating both methods, the decay of peak ground motion with distance is analyzed as a function of load speed and frequency. For speeds lower than the Rayleigh wave velocity in the soil, the decay turns out to be much faster than for a stationary point load. This effect is studied in detail by an analytical approach and interpreted in terms of destructive interference. Finally, the previous analytical and numerical results are checked against the records obtained at Ath, Belgium, during a field experiment to study ground motion induced by high-speed trains in soft soil conditions.     

Generation of Three-Dimensional Fully Nonlinear Water Waves by a Submerged Moving Object

This paper describes a numerical investigation on the generation of three-dimensional (3D) fully nonlinear water waves by a submerged object moving at speeds varied from subcritical to supercritical conditions in an unbounded fluid domain. Considering a semispheroid as the moving object, simulations of the time evolutions of 3D free-surface elevation and flow field are performed. The present 3D model results are found to agree reasonably well with other published vertical two-dimensional (2D) and quasi-3D numerical solutions using Boussinesq-type models. Different from the 2D cases with near critical moving speeds, the 3D long-term wave pattern suggests that in addition to the circularly expanded upstream advancing solitonlike waves, a sequence of divergent and transverse waves are also developed behind the moving object. The velocity distributions and associated fluid-particle trajectories at the free-surface and middle layers are presented to show the 3D feature of the motion. The results under various vertical positions (referred as gap) of a moving object are also compared. It is found the gap has shown a substantial influence on the generated waves, especially in the wake region, when an object moves at a near critical or subcritical speed. However, the results under the case with a high supercritical moving speed indicate the gap has a negligible effect on the generated upstream and downstream waves.     

Ground Vibration from High-Speed Trains: Prediction and Countermeasure

This paper outlines a test program in southern Sweden for measurement of the vibration induced in the ground and railway embankment by high-speed trains, together with a rigorous numerical model developed for the prediction of embankment/ground response. In this formulation the ground is modeled as a layered viscoelastic half-space, and the railway embankment is modeled as a viscoelastic beam excited by the moving loads of the train. The model uses the Kausel-Ro?sset Green's functions to calculate the soil stiffness matrix at the ground-embankment interface and assembles it with the dynamic stiffness matrix of the embankment. The solution is carried out in the frequency domain, and the time histories of the motions are derived through a Fourier synthesis of the frequency components. Numerous simulations of train-induced vibration are presented for the ground conditions and embankment parameters at the test site and compared with measured records. The simulations agree well with the measurements, both in qualitative and quantitative terms. In particular, the large ground deformations registered for train speeds exceeding 140 km∕h are reproduced by the simulations. With the help of the prediction model, the effectiveness of a remediation measure for the mitigation of ground vibration is explored.     

连轧机振动控制重要进展综述

阐述连轧机振动控制的新思路和对策。提出了轧机存在垂扭耦合振动、液机耦合振动、弯扭耦合振动和机电耦合振动现象。确定了轧机振动性质为机电液界多态耦合振动,找到了抑制轧机振动的通用技术,发明了“轧机耦合振动解耦抑振器”并在某连轧机组上成功应用,取得了良好的抑振效果。     

Effects of Induced Vibrations on Early Age Concrete

The purpose of this investigation was to conduct a laboratory test program on how much induced vibrations on concrete during the period between initial set and final set affect the attainable strength of concrete. To achieve this purpose, a laboratory test program was conducted. The laboratory program consisted of casting 144 76?mm by 152?mm (3×6?in.) concrete cylinders and subjecting them to one of two levels of vibration for either 1 or 2?min at five different ages ranging in time from before, during, and after the setting period for the concrete. The levels of vibration correspond to typical frequencies of vibratory soil compactors and the peak particle velocity produced by the compactors. Both compression and splitting tensile tests were performed. The results of the laboratory study indicate that vibratory soil compaction should not be considered a significant hazard to foundation strength as long as the vibrations are within the limits in this study.     

Validation of a Source–Receiver Model for Road Traffic-Induced Vibrations in Buildings. I: Source Model

This work focuses on the coupling of a validated source model for free field traffic-induced vibrations to a receiver model that enables one to predict the response of buildings, accounting for dynamic soil–structure interaction. The resulting model is validated by means of in situ measurements, that have been performed in and around a single-family dwelling during the passage of a truck with known characteristics at speeds between 23?km/h and 58?km/h on joints between plates of the concrete pavement and on a plywood unevenness installed on the road. Simultaneous vibration measurements have been performed with a mobile data acquisition system on the truck’s axles. The objective of part I of this paper is to present the validation of the source model. The characteristics of the vehicle and the road unevenness are discussed, and the vehicle response is validated. The response is independent of the vehicle speed for the passage on the joints, whereas, for the passage on the plywood unevenness, the vibrations increase with the vehicle speed. The dynamic road–soil interaction problem is subsequently solved. Special consideration is given to the determination of the dynamic soil characteristics using the spectral analysis surface wave and seismic cone penetration test methods and to the validation of the transfer functions in the soil. The free-field incident wave field is finally validated. This incident wave field is used in part II of the paper to predict and validate the response of the single family dwelling.     

Timoshenko Beam-Column with Generalized End Conditions and Nonclassical Modes of Vibration of Shear Beams

The main objective of this publication is to derive, in a classic manner, the characteristic equations for the undamped natural frequencies and the corresponding modes of vibration of a two-dimensional (2D) Timoshenko beam–column with generalized support conditions (i.e., with semirigid flexural restraints and lateral bracings as well as lumped masses at both ends) and subjected to a constant axial load along its span. The model includes the simultaneous effects (or couplings) of bending and shear deformations, translational and rotational inertias of all masses considered. The proposed model is general, showing that the natural frequencies and the corresponding modes of vibration of 2D beam–columns are highly sensitive to the coupling effects just mentioned. This is particularly true in members with low shear stiffness and with the end flexural restraints and lateral bracing approaching those of free–free and pinned–free conditions. A second objective of this paper is to show that the obtained solution reproduce, as a special case, the nonclassical modes of shearbeams, including the inversion of modes of vibration (i.e., higher modes crossing lower modes) in shear beams with pinned–free and free–free end conditions, and the phenomena of double frequencies at certain values of beam slenderness (r/L).     

Vibration Control of Railway Bridges under High-Speed Trains Using Multiple Tuned Mass Dampers

In this paper, multiple tuned mass dampers (MTMDs) are considered for suppressing the vibration of railway bridges under high-speed trains. The interaction equations of motion between the vehicle and the bridge with MTMDs have been developed. The effectiveness of MTMDs on suppressing resonant vibration of railway bridges is examined and the optimum parameters of MTMDs for suppressing the resonant vibration are proposed. The results indicate that the use of the MTMD with the optimum parameters reduces the displacement and acceleration responses of railway bridges significantly.     

Different Approaches for Estimating Ground Strains from Pile Driving Vibrations at a Buried Archeological Site

Ground strains were estimated from vibrations measured during pile driving operations at a buried, prehistoric archeological site to monitor potential construction impacts. Subsurface characteristics of the site were investigated using multiple cone penetration test (CPT) soundings and the shear wave velocity profile was measured using the seismic CPT method. Embedded geophones and surface accelerometers were then used to measure ground vibrations during pile driving. Displacement gradients were estimated from the vibrations using the following three methods: (1) the difference between adjacent displacements divided by sensor spacing; (2) peak particle velocity divided by depth-dependent wave velocity (i.e., at the depth where the sensor was placed); and (3) peak particle velocity divided by frequency-dependent wave velocity from a measured dispersion curve. Methods (1) and (3) agreed well, while method (2) caused errors that depended on depth of embedment of the sensors and distance from pile driving. Errors in (2) were attributed to a mismatch between the depth-dependent wave velocity and the wave velocity on the frequency band that carried the largest velocity pulse through the dispersive soil profile. Ground strains were related to displacement gradients based on theoretical solutions of harmonic body waves and Rayleigh waves in dispersive elastic media. The peak estimated ground strains were smaller than the threshold volumetric shear strain, but a few centimeters of settlement were nevertheless observed at the site. The spatial extent of the settlement is characterized using attenuation rules fit to the vibration data, and by calibration with a settlement gauge. Ground cracking and vertical offsets that could potentially mask the archaeological history of the site were neither observed nor predicted from the observed vibration amplitudes. Estimated impact on archeological interpretation of artifacts in their stratigraphic context was likely insignificant except in the immediate region where the piles were driven. This insight will assist in future planning at sites with similar subsurface stratigraphy.     

Vehicle Induced Dynamic Behavior of Short-Span Slab Bridges Considering Effect of Approach Slab Condition

In this paper the vehicle induced dynamic bridge responses are calculated by modeling the bridge and vehicle as one coupled system. The dynamic behavior of short slab bridges with different span lengths induced by the AASHTO HS20 truck is investigated. A parametric study is conducted to analyze the effects of different truck speeds and different road surface conditions. Critical truck speeds that result in peaks of dynamic response are found to follow the rule that describes the resonant vibration of bridges due to train loading. The approach slab condition that consists of faulting at the ends and deformation along the span is considered in the analysis. Although the effect of the along-span deformation on the dynamic response of bridges is trivial, the faulting condition of the approach slab is found to cause significantly large dynamic responses in short-span slab bridges. Impact factors obtained from numerical analyses are compared with those values specified in the AASHTO codes.     

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.     

Forced Vibrations of Single-Degree-of-Freedom Systems with Nonperiodically Time-Varying Parameters

A new exact approach for forced vibration analysis of single-degree-of-freedom (SDOF) systems with nonperiodically time-varying parameters (mass and stiffness) is presented. In this paper, the variations of mass and stiffness, relative to time, are described by the selection of suitable expressions such as power functions and exponential functions. More general cases, such as the variation of mass is described by an arbitrary continuous real-valued function and the variation of stiffness is expressed as a functional relation with the variation of mass and vice versa, are also considered in this study. Using appropriate functional transformation, the governing differential equations for vibrations of SDOF systems with nonperiodically time-varying parameters are reduced to Bessel’s equations or other solvable equations for several important cases. Thus, classes of exact solutions for the free and forced vibrations of SDOF systems with arbitrarily time-varying parameters (mass and stiffness) are obtained. Numerical examples show that the proposed procedure is a simple, efficient, and exact method.