Wave Barriers for Reduction of Train-Induced Vibrations in Soils

This paper is aimed at studying the effectiveness of different vibration countermeasures in isolating the ground vibrations induced by trains moving at sub- and supercritical speeds, with respect to the Rayleigh wave speed of the supporting soils. The vibration countermeasures considered herein include the installation of open trenches, in-filled trenches, and wave impeding blocks. The 2.5D finite/infinite element approach developed previously by the authors is employed in this study. This approach allows us to consider the load-moving effect of the train in the direction normal to the two-dimensional profile considered, and therefore to obtain three-dimensional results using only two-dimensional elements. The moving train is simulated as a sequence of moving wheel loads that may vibrate at some specific frequencies. The performance of the three types of wave barriers in isolating soil vibrations for trains moving at sub- and supercritical speeds with various excitation frequencies is evaluated with respect to some key parameters, along with suggestions made for enhancing the isolation efficiency.     

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.     

Effects of Space Distribution of Excitation on Seismic Response of Arch Dams

The effects of the ground motion spatial variation and of the canyon geometry on the dynamic response of arch dams during the event of an earthquake is studied in this paper. The seismic response of a dam subject to time harmonic longitudinal, shear, and Rayleigh waves impinging the dam site from different directions is analyzed. Several canyon and reservoir geometries are considered. A three-dimensional boundary element model which allows for the rigorous representation of the dynamic interaction between the dam, the foundation rock, and the water is used. The foundation rock is modeled as a uniform viscoelastic boundless domain where the incident traveling wave field is defined by its analytical expression, which may include any spatial variation. The obtained results show the importance of three-dimensional effects which are many times neglected.     

Undrained Lateral Pile Response in Sloping Ground

Three-dimensional finite element analyses were performed to study the behavior of piles in sloping ground under undrained lateral loading conditions. Piles of different diameter and length in sloping cohesive soils of different undrained shear strength and several ground slopes were considered. Based on the results of the finite element analyses, analytical formulations are derived for the ultimate load per unit length and the initial stiffness of hyperbolic p-y curves. New p-y criteria for static loading of piles in clay are proposed, which take into account the inclination of the slope and the adhesion of the pile-slope interface. These curves are used through a commercial subgrade reaction computer code to parametrically analyze the effect of slope inclination and pile adhesion on lateral displacements and bending moments. To validate the proposed p-y curves, a number of well documented lateral load tests are analyzed. Remarkable agreement is obtained between predicted and measured responses for a wide range of soil undrained shear strength and pile diameter, length, and stiffness.     

Determination of Dynamic Track Modulus from Measurement of Track Velocity during Train Passage

The measurement of track stiffness, or track modulus, is an important parameter for assessing the condition of a railway track. This paper describes a method by which the dynamic track modulus can be determined from the dynamic displacements of the track during normal train service, measured using geophones. Two techniques are described for calculating the track modulus—the inferred displacement basin test (DBT) method and a modified beam on an elastic foundation (BOEF) method. Results indicate that the viscoelastic response of the soil will influence the value of track modulus determined using the DBT method. The BOEF method was therefore used to calculate the apparent increase in axle load due to train speed. Hanging or partly supported sleepers were associated with a relatively small increase in dynamic axle loads with train speed.     

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.     

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.     

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.     

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.     

Doubly Spectral Stochastic Finite-Element Method for Linear Structural Dynamics

Uncertainties in complex dynamic systems play an important role in the prediction of a dynamic response in the mid- and high-frequency ranges. For distributed parameter systems, parametric uncertainties can be represented by random fields leading to stochastic partial differential equations. Over the past two decades, the spectral stochastic finite-element method has been developed to discretize the random fields and solve such problems. On the other hand, for deterministic distributed parameter linear dynamic systems, the spectral finite-element method has been developed to efficiently solve the problem in the frequency domain. In spite of the fact that both approaches use spectral decomposition (one for the random fields and the other for the dynamic displacement fields), very little overlap between them has been reported in literature. In this paper, these two spectral techniques are unified with the aim that the unified approach would outperform any of the spectral methods considered on their own. An exponential autocorrelation function for the random fields, a frequency-dependent stochastic element stiffness, and mass matrices are derived for the axial and bending vibration of rods. Closed-form exact expressions are derived by using the Karhunen-Loève expansion. Numerical examples are given to illustrate the unified spectral approach.     

Liquefaction-Induced Softening of Load Transfer between Pile Groups and Laterally Spreading Crusts

Laterally spreading nonliquefied crusts can exert large loads on pile foundations causing major damage to structures. While monotonic load tests of pile caps indicate that full passive resistance may be mobilized by displacements on the order of 1–7% of the pile cap height, dynamic centrifuge model tests show that much larger relative displacements may be required to mobilize the full passive load from a laterally spreading crust onto a pile group. The centrifuge models contained six-pile groups embedded in a gently sloping soil profile with a nonliquefied crust over liquefiable loose sand over dense sand. The nonliquefied crust layer spread downslope on top of the liquefied sand layer, and failed in the passive mode against the pile foundations. The dynamic trace of lateral load versus relative displacement between the “free-field” crust and pile cap is nonlinear and hysteretic, and depends on the cyclic mobility of the underlying liquefiable sand, ground motion characteristics, and cyclic degradation and cracking of the nonliquefied crust. Analytical models are derived to explain a mechanism by which liquefaction of the underlying sand layer causes the soil-to-pile-cap interaction stresses to be distributed through a larger zone of influence in the crust, thereby contributing to the softer load transfer behavior. The analytical models distinguish between structural loading and lateral spreading conditions. Load transfer relations obtained from the two analytical models reasonably envelope the responses observed in the centrifuge tests.     

Dynamic growth of tensile cracks by ductile and brittle fracture mechanisms in a viscoplastic material

In this paper, a finite element analysis of steady-state dynamic crack growth under Mode I, plane strain, small-scale yielding conditions is performed in a rate dependent plastic material characterized by the over-stress model. The main objective of the paper is to obtain theoretically the dependence of dynamic fracture toughness on crack speed. Crack propagation due to a ductile (micro-void) mechanism or a brittle (cleavage) mechanism, as well as transition from one mode to another are considered. The conversion from ductile to brittle has been observed experimentally but has received very little attention using analytical methods. Local fracture criteria based on strains and stresses are used to describe ductile and brittle fracture mechanisms. The results obtained in this paper are in general agreement with micro-structural observations of mode conversion during fracture initiation. Finally, the particular roles played by material rate sensitivity and inertia are examined in some detail.     

Effect of Vehicle Velocity on the Dynamic Amplification of Two Vehicles Crossing a Simply Supported Bridge

The effect of multiple vehicles on a bridge’s dynamic amplification is a complex problem. Previously writers have examined multiple vehicle presence by constructing elaborate finite element models or undertaking field tests. Although both these methods give valuable information regarding the magnitude of dynamic amplification, the results tend to be site specific and give limited insight into how large amplifications occur. This paper examines the dynamic amplification factor of a simply supported bridge being crossed by two loads traveling in both the same and opposing directions. Simple numerical point load models are used to determine the critical load velocities and load positions that result in high amplifications. An experimentally validated finite element model is used to examine the applicability of the conclusions to real bridge/vehicle systems.     

考虑土―结构相互作用的运转状态风电塔抗震分析

针对某陆上风电场1.5 MW风电塔结构,建立了"塔筒-基础-地基"整体三维精细有限元模型,研究土-结构相互作用对风机运转状态下风电塔结构地震动力响应的影响规律.在风机运转状态下,使用FAST程序把风速时程转化为风荷载时程输入模型,并使用EERA程序进行土层地震反应分析得到模型土层底部的地震波,作为地震激励进行输入,对风电塔进行模态分析并计算风电塔地震动力响应.研究表明,考虑土-结构相互作用效应会引起风电塔体系自振频率降低,并显著增加风电塔的结构动力响应.      

Dynamic Characteristics of Infinite and Finite Railways to Moving Loads

Some fundamental dynamic characteristics of a railway subjected to a harmonic or constant moving load are established and presented in this paper. The railway is modeled as an infinite or finite Timoshenko beam on viscoelastic foundation. The dynamic-stiffness matrices characterized by the complex wave numbers are employed to deal with this problem. The relationship between the forced frequency and the resonant velocity of the moving load, and the resonant frequency of the railway are especially emphasized and intensively discussed. The fundamental dynamic characteristics of a railway modeled as a Bernoulli-Euler Beam on viscoelastic foundation are also included for comparison.     

Effects of Seismically Induced Pounding at Expansion Joints of Concrete Bridges

This paper presents the result of a study on the effect of pounding at expansion joints on concrete bridge response to earthquake ground motions. An engineering approach, rather than continuum mechanics approach, is emphasized. First, the dynamic behavior of a damped multidegree-of-freedom bridge system separated by an expansion joint involving an impact is examined by means of the finite element method. Second, the sensitivity analysis of the stiffness in gap elements is performed. Third, usefulness of the analysis method for simulation of pounding phenomena is demonstrated and the effect of pounding on the ductility demands measured in terms of the rotation of column ends is investigated. Two-dimensional finite element analysis using a bilinear hysterestic model for bridge substructure joints and a nonlinear gap element for the expansion joint is performed on a realistic bridge with an expansion joint. The effects of the primary factors on the ductility demand such as gap sizes and characteristics of earthquake ground motion are investigated through a parametric study. The major conclusions are (1) the effect of impact most directly depends on the size of momentum (or pounding magnitude); and (2) the pounding effect is generally found to be negligible on the ductility demand for wide practical ranges of gap size and peak ground acceleration, but is potentially significant at the locations of impact.     

铜锍包吊耳断裂的有限元分析

对某企业铜锍包吊耳断裂的原因进行分析,通过解析分析、静态有限元计算、动态有限元模拟及断口形貌的综合分析,最终判断频繁碰撞是造成铜锍包吊耳失效的主要原因,对日常的管理及操作提出了改进建议。     

3D Finite Element Model for Asphalt Concrete Response Simulation

An extensive experimental, analytical, and numerical investigation on the response of asphalt concrete is currently in progress at Delft University of Technology. The objectives of this Asphalt Concrete Response (ACRe) project are: (a) the formulation and finite element implementation of a three‐dimensional, strain‐rate sensitive, temperature‐ and loading history‐dependent constitutive model, and (b) the development of the necessary experimental set‐ups, testing procedures, and data analysis methods for determination of the model parameters. These objectives are strongly interrelated: on the one hand, the model dictates what should be measured in a test, while on the other hand, the response observed in the tests sets the requirements for the model. As a result, model development/verification and experimental testing have been progressing in parallel throughout the project. In this contribution both the finite element and the experimental aspects of the project will be presented. The constitutive model has been implemented in the finite element system INSAP. The system has been used to simulate the initiation and propagation of damage in two flexible pavement structures due to repeated loading. The simulations illustrate the influence of geometry and material characteristics on the development of damage.     

Collapse Loads for a Cylinder Embedded in Trench in Cohesive Soil

This study investigates the relationship between the sediment resisting force and embedment depth for horizontal cylinders in a vertical trench. Plane-strain calculations of collapse loads are performed for a series of trench depths. Collapse load predictions are based on finite element predictions validated by upper and lower bound solutions from classical plasticity theory. This study extends work by previous investigators by considering variable soil shear strength profiles and embedment depths exceeding one cylinder radius. Curve fits are applied to the finite element predictions to develop simplified equations relating collapse load to trench depth. The predictions are relevant to a number of applications, including pipeline penetration, waste disposal, and mine detection.