高速交通荷载作用下饱和土体与线路系统的动力响应
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摘要
移动荷载动力响应问题很早就被注意到并加以研究,近年来随着高速铁路的兴建和发展,以及已有铁路线路的提速,高速列车的移动速度已经开始超过土体的Rayleigh波速,因此这个问题再次被重视起来。如何利用基础理论成果,分析研究高速交通荷载作用下饱和地基和交通线路系统的变形特性和工程的耐久性,及对周围环境振动的影响,是十分必要的。
本文在平面应变条件下研究了移动条形荷载作用下横观各向同性饱和土体和上覆弹性梁有限厚饱和土体的动力响应问题。在求解移动条形荷载作用下横观各向同性饱和土体的动力响应问题时。由忽略土粒压缩和土体自重的Biot波动方程出发,对荷载进行Fourier级数展开,假设了响应函数的级数形式,利用土体表面边界条件,由待定系数法求解了考虑固液耦合作用的两相介质在移动荷载作用下的土体位移、有效应力及孔压表达式。在求解移动条形荷载作用下上覆弹性梁有限厚饱和土体的动力响应问题时,将土体表面的应力边界条件与弹性梁动力方程结合,由待定系数法求解了土体位移、孔压表达式。着重研究了荷载移动速度、横观各向同性性、弹性梁刚度等参数对土体位移、孔压响应的影响。
接下来本文研究了移动矩形荷载作用下三维饱和土体的动力响应问题。由忽略土粒压缩和土体自重的Biot波动方程出发,利用Fourier变换将土体波动方程转化为四个常微分方程组。利用待定系数法对方程进行求解并给出了土体位移,加速度,孔压表达式。数值算例给出了土体表面沿x,y,z方向的位移,沿x,z方向的加速度和土体孔压的时程曲线。计算结果表明,荷载移动速度和土体渗透系数都对土体动力响应有很大影响。
本文进一步研究了交通荷载作用下上覆无限大板的三维饱和土体的动力响应问题。将交通荷载简化为四个矩形荷载来模拟车轮与路面的接触,采用Kirchoff小变形薄板理论来模拟路面,并通过改变板的刚度分别模拟柔性路面与刚性路面。在Fourier变换域内,通过联立板与三维饱和土体的动力方程对问题进行了求解,并着重研究了路面刚度、荷载移动速度和土体渗透系数对路面动力响应的影响。
而后,本文利用Fourier变换对移动列车荷载作用下铁路系统和饱和半空间土体的动力响应问题进行研究。将整个系统分为上覆路轨系统和下卧土体分别求解,并通过应力、位移边界条件进行耦合。对于路轨系统,将钢轨简化为无限长弹性Euler梁;将枕木简化为连续质量块;对道渣层采用Cosserat模型。对于下卧饱和土体,由忽略土体自重的Biot波动方程出发,利用Fourier变换对Biot波动方程进行求解。在Fourier变换域内,联立铁路系统和下卧土体的动力方程,求解列车荷载作用下钢轨位移、加速度,土体位移、加速度及孔隙水压力表达式。利用数值积分方法对表达式进行Fourier逆变换,得到钢轨位移、加速度,土体位移、加速度及孔隙水压力在时域内的表达式。计算结果表明,轨道刚度,水相介质与荷载移动速度都对路轨系统和土体动力响应有很大影响。
由于对于多数实际工程而言,地下水位并非位于地表,而是在地表以下一定深度。因此,本文将饱和半空间模型进一步改进,利用Fourier变换对移动列车荷载作用下铁路系统和成层半空间土体的动力响应问题进行研究。采用与前文相同的轨道系统模型,对于下卧土体,采用了成层土体模型,模型分为两层,上层为弹性土体,下层为饱和半空间。结算结果表明在高速情况下了上层弹性土体的参数对轨道和土体动力响应的影响很大。
最后,研究了饱和土体、轨道系统和复杂列车荷载耦合动力响应。对于下卧土体基于Biot动力方程,采用与前文相同解法进行求解;采用Euler-Bernoulli梁模拟轨道系统;对于列车荷载模型,采用考虑前后转向架与车体之间相互作用及车轮与转向架之间的相互作用和由轨道不平顺引起的荷载简谐振动的列车模型。考虑车轮与铁轨之间的线性接触,联立列车荷载模型运动控制方程、轨道系统和饱和半空间控制方程,在Fourier变换域内求解车轮与轨道之间的作用力表达式,将表达式代入轨道系统和土体的动力方程,求解轨道系统和土体频域内的动力响应表达式,利用Fourier逆变换,得出列车、轨道和饱和土体振动的时域表达式。数值计算着重研究了耦合振动和轨道不平顺对轨道系统和土体动力响应的影响。
Studies of the dynamic response of railway track and adjoining ground under the action of moving train has received considerable attention in a number of engineering fields such as civil engineering, transportation engineering and environmental engineering. Recently high-speed trains are becoming increasingly popular and freight trains becoming heavier. Combined with this finding and the observation that Rayleigh wave speeds are slow in soft soils, it can be seen that the study of the dynamic response subjected to moving train load is important for environmental sense of the along side built-in area.
The dynamic response of a transversely isotropic poroelastic half-space soil medium and soil medium under elastic beam on rigid rock subjected to moving loads are studied analytically/ numerically under conditions of plane strain. The full dynamic poroelastic theory of Biot is employed, under the assumption of an incompressible solid grain and neglecting the apparent mass density. The loading function is presented by a Fourier series expansion. By using the boundary condition at the surface of the soil, the governing equations of motion are then solved. The effect of transversely isotropic on soil vertical displacement is discussed under different parameters such as load speed and coefficient of permeability. Numerical results of vertical displacements are given and indicate that transversely isotropic have much effect on the response of the soil. While investigating the dynamic response of soil medium under elastic beam on rigid rock, the effect of the beam is considered by jointing the governing equation of the beam with the boundary condition of the soil medium. The effect of the rigidity of the beam on soil vertical displacement and pore pressure is studied particularly.
The three dimensional steady state responses of a poroelastic half-space soil medium subjected to a moving rectangular load are investigated analytically/numerically. The full dynamic poroelastic theory of Biot is employed, under the assumption of an incompressible solid grain and neglecting the apparent mass density. Using the triple Fourier transform, the governing equations of motion are then reduced to a system of four coupled ordinary differential equations which are solved semi-analytically. Soil vertical displacements, accelerations and pore water pressures induced by moving load are calculated. Computed result shows that load velocity and intrinsic permeability of the soil medium shows an apparent effect on its dynamic responses and pore water pressures.
Further more the three dimensional steady state responses of pavement systems subjected to a moving traffic load are investigated. The traffic loads are simulated by four rectangular load pressures, and the rigid and flexible pavement systems are regarded as an infinite plate resting on a poroelastic half-space soil medium. The contact surface between the plate and the poroelastic half-space is assumed to be smooth and fully permeable. Kirchhoff small-deflection thin-plate theory is employed to analyze the plate; while Biot's fully dynamic poroelastic theory is used to characterize the poroelastic half-space. The frequency wave number domain solution of the pavement system is obtained by the compatibility condition between the plate and the poroelastic half-space. By applying the inverse fast Fourier transform, the time domain solution is obtained. Also, the influences of the load speed, the permeability of the soil, and the flexural rigidity of the plate on the response of the pavement system are investigated. The numerical results show that the influences of these parameters on the dynamic response of the pavement system are significant.
Based on solution of the Biot's theory given in the former part, the dynamic responses of a track system and poroelastic half-space soil medium subjected to moving point load and train passages are investigated by the substructure method. The whole system is divided into two separately formulated substructures, the track and the ground, and the rail is described by introducing the Green function for an infinitely long Euler beam subjected to the action of moving axle loads of the train and the reactions of the sleeper. Sleepers are represented by a continuous mass and the effect of the ballast is considered by introducing the Cosserat model for granular medium. Using the triple Fourier transform, the governing equations of motion are then solved analytically in the frequency-wave-number domain. The time domain responses are evaluated by the inverse Fourier transform computation for a certain train speed. Computed results show that the shape of the rail displacements of the elastic and poroelastic soil medium are in good agreement with each other of the low train velocity, but the result of the poroelastic soil medium is significantly different to that of the elastic soil medium for the high train velocity which is higher than Rayleigh-wave speed in the soil. The influence of the soil intrinsic permeability on soil responses is discussed with great care in both time domain and frequency domain. The dynamic responses of the soil medium are considerably affected by the fluid phase as well as the load velocity.
Practically, due to the ground water table being of several meters beneath the ground surface, the soil profile can be divided into two layers: the upper layer modeled by elastic medium and the lower layer by fully saturated poroelastic medium governed by Biot's theory. In this part, the former rail track model and train model is introduced. The influences of the thickness, the mass and the rigidity of the elastic layer and the mass of the ballast on rail's displacement responses are carefully investigated. Numerical results show that the influences of these parameters are significant for high train velocity, while vanishes for low velocity.
Finally, the vibration of a vehicle-rail-ground coupled system is studied semi-analytically. The theoretical model incorporates vehicles, a track and a saturated poroelastic half-space soil medium, and a Hertizian contact spring is introduced between each wheelset and the rails to consider the dynamic forces. The source of vibration excitation is divided into two components: the moving axle loads and the dynamic loads caused by the vertical rail irregularities. Biot's fully dynamic poroelastic theory is used to characterize the poroelastic half-space soil medium, and the rail is modeled by infinite Euler-Bernoulli beam. The governing equations for the vehicle, the track and poroelastic soil are solved by Fourier transform. The effect of the vehicle-rail couple and the rail irregularity is studied.
本文在平面应变条件下研究了移动条形荷载作用下横观各向同性饱和土体和上覆弹性梁有限厚饱和土体的动力响应问题。在求解移动条形荷载作用下横观各向同性饱和土体的动力响应问题时。由忽略土粒压缩和土体自重的Biot波动方程出发,对荷载进行Fourier级数展开,假设了响应函数的级数形式,利用土体表面边界条件,由待定系数法求解了考虑固液耦合作用的两相介质在移动荷载作用下的土体位移、有效应力及孔压表达式。在求解移动条形荷载作用下上覆弹性梁有限厚饱和土体的动力响应问题时,将土体表面的应力边界条件与弹性梁动力方程结合,由待定系数法求解了土体位移、孔压表达式。着重研究了荷载移动速度、横观各向同性性、弹性梁刚度等参数对土体位移、孔压响应的影响。
接下来本文研究了移动矩形荷载作用下三维饱和土体的动力响应问题。由忽略土粒压缩和土体自重的Biot波动方程出发,利用Fourier变换将土体波动方程转化为四个常微分方程组。利用待定系数法对方程进行求解并给出了土体位移,加速度,孔压表达式。数值算例给出了土体表面沿x,y,z方向的位移,沿x,z方向的加速度和土体孔压的时程曲线。计算结果表明,荷载移动速度和土体渗透系数都对土体动力响应有很大影响。
本文进一步研究了交通荷载作用下上覆无限大板的三维饱和土体的动力响应问题。将交通荷载简化为四个矩形荷载来模拟车轮与路面的接触,采用Kirchoff小变形薄板理论来模拟路面,并通过改变板的刚度分别模拟柔性路面与刚性路面。在Fourier变换域内,通过联立板与三维饱和土体的动力方程对问题进行了求解,并着重研究了路面刚度、荷载移动速度和土体渗透系数对路面动力响应的影响。
而后,本文利用Fourier变换对移动列车荷载作用下铁路系统和饱和半空间土体的动力响应问题进行研究。将整个系统分为上覆路轨系统和下卧土体分别求解,并通过应力、位移边界条件进行耦合。对于路轨系统,将钢轨简化为无限长弹性Euler梁;将枕木简化为连续质量块;对道渣层采用Cosserat模型。对于下卧饱和土体,由忽略土体自重的Biot波动方程出发,利用Fourier变换对Biot波动方程进行求解。在Fourier变换域内,联立铁路系统和下卧土体的动力方程,求解列车荷载作用下钢轨位移、加速度,土体位移、加速度及孔隙水压力表达式。利用数值积分方法对表达式进行Fourier逆变换,得到钢轨位移、加速度,土体位移、加速度及孔隙水压力在时域内的表达式。计算结果表明,轨道刚度,水相介质与荷载移动速度都对路轨系统和土体动力响应有很大影响。
由于对于多数实际工程而言,地下水位并非位于地表,而是在地表以下一定深度。因此,本文将饱和半空间模型进一步改进,利用Fourier变换对移动列车荷载作用下铁路系统和成层半空间土体的动力响应问题进行研究。采用与前文相同的轨道系统模型,对于下卧土体,采用了成层土体模型,模型分为两层,上层为弹性土体,下层为饱和半空间。结算结果表明在高速情况下了上层弹性土体的参数对轨道和土体动力响应的影响很大。
最后,研究了饱和土体、轨道系统和复杂列车荷载耦合动力响应。对于下卧土体基于Biot动力方程,采用与前文相同解法进行求解;采用Euler-Bernoulli梁模拟轨道系统;对于列车荷载模型,采用考虑前后转向架与车体之间相互作用及车轮与转向架之间的相互作用和由轨道不平顺引起的荷载简谐振动的列车模型。考虑车轮与铁轨之间的线性接触,联立列车荷载模型运动控制方程、轨道系统和饱和半空间控制方程,在Fourier变换域内求解车轮与轨道之间的作用力表达式,将表达式代入轨道系统和土体的动力方程,求解轨道系统和土体频域内的动力响应表达式,利用Fourier逆变换,得出列车、轨道和饱和土体振动的时域表达式。数值计算着重研究了耦合振动和轨道不平顺对轨道系统和土体动力响应的影响。
Studies of the dynamic response of railway track and adjoining ground under the action of moving train has received considerable attention in a number of engineering fields such as civil engineering, transportation engineering and environmental engineering. Recently high-speed trains are becoming increasingly popular and freight trains becoming heavier. Combined with this finding and the observation that Rayleigh wave speeds are slow in soft soils, it can be seen that the study of the dynamic response subjected to moving train load is important for environmental sense of the along side built-in area.
The dynamic response of a transversely isotropic poroelastic half-space soil medium and soil medium under elastic beam on rigid rock subjected to moving loads are studied analytically/ numerically under conditions of plane strain. The full dynamic poroelastic theory of Biot is employed, under the assumption of an incompressible solid grain and neglecting the apparent mass density. The loading function is presented by a Fourier series expansion. By using the boundary condition at the surface of the soil, the governing equations of motion are then solved. The effect of transversely isotropic on soil vertical displacement is discussed under different parameters such as load speed and coefficient of permeability. Numerical results of vertical displacements are given and indicate that transversely isotropic have much effect on the response of the soil. While investigating the dynamic response of soil medium under elastic beam on rigid rock, the effect of the beam is considered by jointing the governing equation of the beam with the boundary condition of the soil medium. The effect of the rigidity of the beam on soil vertical displacement and pore pressure is studied particularly.
The three dimensional steady state responses of a poroelastic half-space soil medium subjected to a moving rectangular load are investigated analytically/numerically. The full dynamic poroelastic theory of Biot is employed, under the assumption of an incompressible solid grain and neglecting the apparent mass density. Using the triple Fourier transform, the governing equations of motion are then reduced to a system of four coupled ordinary differential equations which are solved semi-analytically. Soil vertical displacements, accelerations and pore water pressures induced by moving load are calculated. Computed result shows that load velocity and intrinsic permeability of the soil medium shows an apparent effect on its dynamic responses and pore water pressures.
Further more the three dimensional steady state responses of pavement systems subjected to a moving traffic load are investigated. The traffic loads are simulated by four rectangular load pressures, and the rigid and flexible pavement systems are regarded as an infinite plate resting on a poroelastic half-space soil medium. The contact surface between the plate and the poroelastic half-space is assumed to be smooth and fully permeable. Kirchhoff small-deflection thin-plate theory is employed to analyze the plate; while Biot's fully dynamic poroelastic theory is used to characterize the poroelastic half-space. The frequency wave number domain solution of the pavement system is obtained by the compatibility condition between the plate and the poroelastic half-space. By applying the inverse fast Fourier transform, the time domain solution is obtained. Also, the influences of the load speed, the permeability of the soil, and the flexural rigidity of the plate on the response of the pavement system are investigated. The numerical results show that the influences of these parameters on the dynamic response of the pavement system are significant.
Based on solution of the Biot's theory given in the former part, the dynamic responses of a track system and poroelastic half-space soil medium subjected to moving point load and train passages are investigated by the substructure method. The whole system is divided into two separately formulated substructures, the track and the ground, and the rail is described by introducing the Green function for an infinitely long Euler beam subjected to the action of moving axle loads of the train and the reactions of the sleeper. Sleepers are represented by a continuous mass and the effect of the ballast is considered by introducing the Cosserat model for granular medium. Using the triple Fourier transform, the governing equations of motion are then solved analytically in the frequency-wave-number domain. The time domain responses are evaluated by the inverse Fourier transform computation for a certain train speed. Computed results show that the shape of the rail displacements of the elastic and poroelastic soil medium are in good agreement with each other of the low train velocity, but the result of the poroelastic soil medium is significantly different to that of the elastic soil medium for the high train velocity which is higher than Rayleigh-wave speed in the soil. The influence of the soil intrinsic permeability on soil responses is discussed with great care in both time domain and frequency domain. The dynamic responses of the soil medium are considerably affected by the fluid phase as well as the load velocity.
Practically, due to the ground water table being of several meters beneath the ground surface, the soil profile can be divided into two layers: the upper layer modeled by elastic medium and the lower layer by fully saturated poroelastic medium governed by Biot's theory. In this part, the former rail track model and train model is introduced. The influences of the thickness, the mass and the rigidity of the elastic layer and the mass of the ballast on rail's displacement responses are carefully investigated. Numerical results show that the influences of these parameters are significant for high train velocity, while vanishes for low velocity.
Finally, the vibration of a vehicle-rail-ground coupled system is studied semi-analytically. The theoretical model incorporates vehicles, a track and a saturated poroelastic half-space soil medium, and a Hertizian contact spring is introduced between each wheelset and the rails to consider the dynamic forces. The source of vibration excitation is divided into two components: the moving axle loads and the dynamic loads caused by the vertical rail irregularities. Biot's fully dynamic poroelastic theory is used to characterize the poroelastic half-space soil medium, and the rail is modeled by infinite Euler-Bernoulli beam. The governing equations for the vehicle, the track and poroelastic soil are solved by Fourier transform. The effect of the vehicle-rail couple and the rail irregularity is studied.
引文
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