Finite element algorithm for jointed concrete pavements subjected to moving aircraft

An algorithm based on the finite element method is developed to analyze the dynamic response of multiple, jointed concrete pavements to moving aircraft loads. In the finite element idealization, the pavement-subgrade system is idealized by thin plate finite elements resting on Winkler-type viscoelastic foundation represented by a series of distributed springs and dashpots. The dowel bars at the transverse joints are represented by beam elements. It i assumed that the dowel bar is fully embedded into the pavement thus neglecting dowel-pavement interaction effects. The longitudinal keyed or aggregate interlock joints are modeled by vertical spring elements. The dynamic aircraft-pavement interaction effects are considered in the analysis by modeling the aircraft by masses supported by spring-dashpot systems representing the landing gear of the aircraft. It is assumed that the aircraft travels along a straight line with a specific initial velocity and acceleration. The aircraft-pavement interaction takes the form of two sets of coupled equations which result ina non-symmetric stiffness matrix. An approximate mixed iteration-direct elimination scheme is used to solve for the dynamic equations. The accuracy of the computer code is verified by the available experimental and analytical solutions. A parametric study is conducted to investigate the effects of various parameters on the dynamic response of pavements.     

Effect of vehicle–pavement interaction on dynamic response of rigid pavements

In the present paper, dynamic response of rigid pavements subjected to moving vehicular loads is presented using an analytical procedure based on the finite element method. The vehicle–pavement interaction effects are taken into account while developing the solution algorithm. The concrete pavement is discretized by finite and infinite beam elements. Infinite elements are helpful in appropriate modeling of end conditions. The main purpose of the development of infinite elements is to model the unbounded domain. The underlying soil medium is modeled by Pasternak model which assumes the existence of shear interaction between the spring elements. The moving vehicle is represented by a mass supported by a spring-dashpot system. The vehicle -pavement interaction force is modeled with Dirac-delta function. Dynamic equilibrium equation is solved with Newmark-Beta integration scheme. It has been observed that the dynamic interaction between the moving load and the pavement has significant effect on pavement response. Parametric study is carried out to investigate the effect of vehicle–pavement interaction (VPI) and soil parameters on the response of pavement.     

Numerical Analysis of Asphalt Pavements under Moving Wheel Loads

INTRODUCTIONThe design methods of asphalt pavement areusually based on the static and elastic analysis sys-tem,though the actual loads such as wheel loads andtemperatureloads are kinetic.The mechanic responseof the pavement is sensitive to the ti me-dependentvariables.Thereis an obvious difference betweentheresults obtainedfromthe kinetic systemandthe stat-ic system.Thus,the dynamic analysisis necessarytodescribe explicitly the working condition of the as-phalt pavement.The dynamic charac…     

不平整路面上的非稳定车流荷载研究及应用

车辆动荷载是引起路面损坏的最主要原因。目前国内外相关研究多集中于单一车辆对路面结构所产生的动荷载,实际上路面结构所承受的是车流荷载,而且车流在行驶过程中各车辆的车速和车辆之间的距离会产生变化,但关于这方面的研究甚少。针对这一工程实际问题,采用微观交通流模型中的跟车模型来模拟车流行驶过程中各车辆的速度以及它们之间车距的变化,车辆振动模型采用1/4车身结构的两自由度模型,并根据国家标准GB7031-86[1]规定生成路面轮廓的时域信号。最后分析了某水泥混凝土路面在生成的车流荷载作用下的动力响应,为研究车流荷载作用下路面结构动力响应提供了基础性成果。     

无拉力双地基参数板在移动荷载作用下的动力响应

求解了无拉力双参数地基上厚、薄板受任意移动荷载作用下的动力响应问题和板的脱离问题。从板-地基接触系统的分区广义势能泛函出发,通过建立和分析板单元区、地基单元区和连接板-地基的接触单元区的势能泛函,给出求解无拉力双参数地基板受任意移动荷载作用下的动力响应问题的分区广义协调元法。利用纽马克（Newmark）法经MATLAB编程叠代数值计算,验证了文中方法分析无拉力双参数地基板的动力响应问题是有效的。     

Numerical analysis of soil vibrations due to trains moving at critical speed

High-speed train induced vibrations of track structure and underlying soils differ from that induced by low-speed train. Determining the critical speed of train operation remains difficult due to the complex properties of the track, embankment and ground. A dynamic analysis model comprising track, embankment and layered ground was presented based on the two-and-half-dimensional (2.5D) finite elements combining with thin-layer elements to predict vibrations generated by train moving loads. The track structure is modeled as an Euler–Bernoulli beam resting on embankment. The train is treated as a series of moving axle loads; the embankment and ground are modeled by the 2.5D finite elements. The dynamic responses of the track structure and the ground under constant and vibrating moving loads at various speeds are presented. The results show that the critical speed of a train moving on an embankment is higher than the Rayleigh wave velocity of the underlying soil, attributed to the presence of the track structure and the embankment. It is found that the dynamic response of ground induced by moving constant loads is mostly dominated by train speed. While for the moving load with vibration frequency, the ground response is mostly affected by the vibration frequency instead of train speed. Mach effect appears when the train speed exceeds the critical speed of the track–embankment–ground system.     

Three dimensional FEM of moving coordinates for the analysis of transient vibrations due to moving loads

This paper is concerned with the transient vibration analysis of railway-ground system under fast moving loads. A 3D finite element method in a convected coordinate system moving with the load is formulated, together with viscous-elastic transmitting boundary conditions in order to limit the finite element mesh. A method is proposed to introduce Rayleigh type material damping in the finite element formulation in the moving coordinate system, while measures have also been taken to improve the numerical stability of the solution procedure. The performance of the transmitting boundary and the entire solution procedure are assessed via comparison with the ordinary finite element solution of some relatively simple problems and through a comparison with field measurements. The reasonable agreement found from these comparisons demonstrates the validity of the proposed method.     

移动荷载作用下土岩组合基坑吊脚桩变形分析

以青岛地区特有的土岩组合地质条件为背景,采用现场监测和Plaxis有限元模拟相结合的方法,研究了土岩基坑中吊脚桩在龙门吊移动荷载作用下的变形规律及动力响应。结果表明：桩身变形模拟结果与实测值吻合较好,基坑的变形主要发生在基坑上部软弱土层,吊脚桩嵌岩处产生应力集中;在龙门吊移动荷载作用下,桩顶水平位移较大,但其动力响应最小,而嵌岩处水平位移较小,但其动力响应最大;嵌岩处、桩身最大正弯矩处及最大负弯矩处的土压力动力响应较大,且移动荷载刚经过时刻影响最大。研究成果可为类似土岩结合地区深基坑支护设计提供参考。     

移动荷载下三维半空间动力安定性下限分析

针对交通移动荷载,基于第一动力安定性理论预测了弹塑性半无限空间动力安定性下限值。通过建立无限元边界的三维动力有限元模型,研究了移动荷载作用下弹塑性半无限空间的动应力分布,构造了稳态动应力下的残余应力场,基于残余应力场的构造提出了动力安定性下限值的预测方法,分析了交通动应力下的安定性下限值以及车辆移动速度对安定性的影响,同时分析了均布荷载和Hertz荷载分布对动力安定性下限值的影响。当荷载移动速度低于Rayleigh波速时,安定性极限值随着速度的增加而增加,而当速度超过Rayleigh波速时,随着速度的增加而减小。研究还发现,当荷载和总重相等时采用圆形均布荷载和Hertz荷载的安定性极限值较为相似。     

Simulating train moving loads in physical model testing of railway infrastructure and its numerical calibration

Ballastless high-speed railways have dynamic performances that are quite different from those of conventional ballasted railways. The essential dynamic characteristics of high-speed railways due to passing train wheels, such as the cyclic effect, moving effect, and speed effect, were put forward and discussed. A full-scale accelerated railway testing platform for ballastless high-speed railways was proposed in this study. The feasibility of the sequential loading method in simulating train moving loads, and the boundary effect of the proposed physical model of ballastless railways, was investigated using three-dimensional finite element models. A full-scale physical model, 5 m long, 15 m wide, and 6 m high, was then established according to practical engineering design methods. Using a sequential loading system composed of eight high-performance hydraulic actuators, loads of a moving train with highest speed of 360 km/h were simulated. Preliminary experimental results of vibration velocities were presented and compared with field measurements of the Wuguang high-speed railway in China. Results showed that the experimental results coincided with the field measurements, demonstrating that the full-scale accelerated railway testing platform can simulate the process of a moving train and realistically reproduce the dynamic behaviors of ballastless high-speed railways.     

水平荷载下导管架平台桩基础的非线性有限元分析

导管架平台桩基础的控制荷载主要为风荷载、波浪荷载、地震荷载等水平荷载,为研究水平荷载下导管架平台桩基础的承载特性,采用非线性有限元分析方法对水平荷载下桩-土之间的相互作用进行研究,提出了有效模拟桩基水平承载特性的有限元模型,分析了模型桩的刚度、直径、土质参数中水平土压力系数、剪胀角对桩基承载特性的影响及水平荷载下群桩承载特性,并将有限元计算结果与API规范及模型试验结果进行对比。研究结果表明,非线性有限元分析方法分析水平荷载下桩-土相互作用是可行的,计算结果可为导管架平台的桩基设计提供参考。     

移动荷载下高铁路基段振动加速度频谱衰减特性

采用精细化和多尺度建模技术,建立了设计速度为350 km/h的双线高速铁路轨道-路基-地基非线性耦合系统的真三维动力分析模型,将地基土和路基填筑材料的非线性纳入分析模型中,采用三维黏弹性静-动力统一人工边界技术对地基无限域进行模拟,采用动接触算法模拟底座板底面和基床表层表面之间的相互作用,考虑移动荷载作用前路基-地基中客观的静应力状态对后续动力计算的影响,依托大规模并行计算技术和单元生死技术,模拟了地基的初始应力场生成、路基结构和轨道系统的施工过程,在此基础上模拟了与8辆编组的某型动车组轮对空间位置相对应的、作用于钢轨顶部的压力荷载的移动过程。基于分析结果,归纳了移动荷载作用下高速铁路轨道-路基-地基系统中振动加速度频谱的衰减特性。     

移动荷载下瞬态振动的三维移动坐标有限元分析

针对移动荷载引起地基振动问题的特点,在随荷载移动坐标系下建立有限元方程进行分析,能够与常规有限元方法较好地符合。建立了可用于移动坐标有限元法的黏弹性边界,从而有效地模拟波在边界的透射。以Euler-Bernoulli梁模拟轨道和路基的作用,以三维实体单元模拟黏弹性分层地基,得到的数值模拟结果能够与瑞典Ledsgård地区高速铁路实测数据较好地吻合,表明移动坐标有限元法可以有效地分析此类问题。     

Dynamic response of double beam rested on stochastic foundation under harmonic moving load

This paper deals with the dynamic response of infinite double Euler–Bernoulli beam supported by elastic foundation with stochastic stiffness subjected to an oscillating moving load, which is the first research in relevant literature review. In this matter, equations of motion for double beam are formulated in a moving frame of reference. Moreover, by employing the first order perturbation theory and calculating contour integration, the response of double beam is obtained analytically and validated by a stochastic finite element model. Sensitivity analyses on the various parameters of closed form solution such as velocity, load frequency, coefficient of variation of soil foundation and rail and slab bending stiffness show the significant effect of load frequency on the dynamic response of the doubled beam. From practical point of view, the obtained results of the present study can be utilized efficiently in analysis and design of slab track systems. Copyright © 2013 John Wiley & Sons, Ltd.     

A BEM–FEM approach for analysis of distresses in pavements

A combined boundary-element–finite-element method is presented for the analysis of distresses in pavements subjected to mechanical and environmental effects. Owing to the spatial dimensions of the problem, the non-homogeneity and the irregular geometry at the pavement joints, a combination of the two methods proves to offer a more realistic solution technique. The advantage of the finite element method (FEM) is in its capabilities of modelling near-field regions at or around the vicinity of the joint, whereas the boundary element method (BEM) is more suitable to model the far-field region at infinity. The three major distresses affecting the serviceability of the pavement system are the temperature, moisture and the applied mechanical loads. The model analyses the stresses and strains resulting from both mechanical and environmental factors in the analysis of a pavement system. Moreover, the infiltration of water through pavement joints, which causes weakening of the subgrade soil, is also analysed. Secondly the curling of the pavement concrete slab under the mechanical and thermal loads and induced friction may cause separation of the pavement structure from its supporting subgrade. Both are treated and modelled in this study. A detailed analysis of the pavement joint with its load transfer device is also performed for the proper assessment of the separation and further extension of the loss of support in the pavement system.     

列车运行时由轨道不平顺引起的地基振动研究

采用半解析法研究了列车荷载作用下列车-轨道-饱和地基系统的耦合振动问题。研究模型共分为3部分：车体简化为一个多刚体系统,在车轮与钢轨之间引入线性Hertizian弹簧接触模型模拟轮轨动力相互作用、采用离散轨枕支撑的弹性Euler梁来模拟轨道系统、下卧土体采用多孔饱和半空间模型。列车荷载分为轴重和由轨道不平顺引起的轮轨动力相互作用力。采用Fourier变换分别求解各子系统的控制方程,并通过动力子结构法对各子系统进行耦合。土体在时域内的动力响应通过快速Fourier变换求得。在分析了轮轨动力相互作用力的基础上,研究了轮轨动力作用力和列车轴重作用下饱和地基的动力响应,并分析了轨枕间距和土体渗透系数对饱和地基振动响应的影响。研究表明,轮轨动力作用力对地基远场振动有重要贡献,同时枕木间距对轨道与地基振动响应有较大影响。     

Propagation and localization of wave in multi‐span Timoshenko beams on elastic foundations under moving harmonic loads

Wave propagation and localization in ordered and disordered multi‐span beams on elastic foundations due to moving harmonic loads are investigated by using the transfer matrix methodology. The transfer matrix, as a function of the frequency and velocity of the moving harmonic load, of the periodic beam is formulated in a coordinate system moving with the load. The expressions of critical velocities, cut‐off frequency of an associated uniform beam without discrete spaced supports, are determined through the analysis of the wavenumbers, and the dynamic responses of the beam are also examined. For the ordered and disordered case, the propagation constants and localization factors are respectively employed to identify the velocity and frequency pass bands and stop bands in order to examine whether the perturbation can propagate along the structure or not. The effects of the periodicity, disorder level, excitation frequency, and moving velocity are studied in detail. The validity of the obtained results is confirmed by evaluating the transverse deformation of the beams through the finite element simulations. Copyright © 2017 John Wiley & Sons, Ltd.     

A simple model for inelastic footing response to transient loading

This paper presents a mechanical analogue which models the response of a rigid circular footing on an ideal elastoplastic half-space to transient loads. In the rational analysis of pile-driving dynamics, the response of soil at the base of a pile is often approximated by a footing on a semi-infinite half-space. Most existing base models employ the well-known Lysmer analogue to model the elastic response of the soil at the pile base, and account for the inelastic soil behaviour through the inclusion of a plastic slider with a slip load equal to the ultimate failure load of the footing. The improved model provides a force response which is significantly closer to the ideal response than existing models. The paper commences with a review of analytical solutions for the dynamic response of a rigid circular footing on an elastic half-space. Existing mechanical analogs for the system are reviewed, and an automatic matching process proposed which improves the accuracy of the analogs under transient loading. The inelastic response is then studied using the finite element method, and the mechanical analogs are modified to allow representation of the observed inelastic behaviour. Examples are presented illustrating close agreement between the proposed models and finite element analyses for a range of Poisson's ratio. The improved models have direct application for one-dimensional models of pile driving, particularly in the back-analysis of data from dynamic testing of piles. They are also applicable to studies of dynamic compaction.     

Dynamic responses of a poroelastic half‐space from moving trains caused by vertical track irregularities

The vibrations of railway tracks on a poroelastic half‐space generated by moving trains are investigated through a vehicle–track–ground coupling model. The theoretical model incorporates a vehicle, a track, and a fully saturated poroelastic half‐space soil medium. The source of vibration excitation is divided into two components: the quasi‐static loads and the dynamic loads. The quasi‐static loads are related to the static component of the axle loads, whereas the dynamic loads are due to the dynamic wheel–rail interaction. A linear Hertizian contact spring is introduced between each wheelset and the rail to consider the dynamic loads. Biot's dynamic theory is used to characterize the poroelastic half‐space soil medium. Using the Fourier transform, the governing equations for the track–ground system are solved and the numerical results are presented for a single axle vehicle model. The different dynamic characteristics of the elastic soil medium and the saturated poroelastic medium are investigated. In addition, the different roles of the moving axle loads and the roughness‐induced dynamic loads are identified. It is concluded that the vibration level of the free field off the track predicted by the poroelastic soil medium is smaller than that predicted by the elastic soil medium for vehicle speed below the Rayleigh wave speed of the poroelastic half‐space, whereas it is larger for vehicle speed above the Rayleigh wave speed. The dynamic loads play an important role in the dynamic responses of the track–ground system. Copyright © 2010 John Wiley & Sons, Ltd.     

重载铁路路基面动应力峰值随机分布特征研究

掌握列车移动荷载作用下路基的动应力响应特性可为路基沉降预测、状态评估提供依据。建立重载铁路车辆-轨道-路基三维动力有限元模型,并在钢轨轨面引入中国三大干线不平顺轨道谱以实现轨道不平顺的模拟。通过数值计算,分析了轨道高低不平顺对路基面动应力分布的影响,统计了4种列车轴重下路基面3个位置（钢轨下方,线路中心）处的动应力峰值沿线路纵向的分布,对路基面动应力峰值的随机分布形式进行了正态性检验,对动应力峰值的最大值进行了预测。结果表明：轨道不平顺导致路基面动应力沿路基面中心不对称,路基面动应力峰值沿线路纵向服从正态分布。随着轴重的增大,动应力峰值离散程度增大,动应力峰值分布曲线变陡。动应力峰值的预测值和现场实测值相吻合,证明了有限元模型及统计分析方法的正确性。研究结果对路基动变形及累积沉降的可靠性分析提供依据。