移动列车荷载作用下路轨系统及饱和半空间土体动力响应

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,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。当列车移动速度较低时,饱和多孔介质和弹性介质的位移响应仅在幅值上有区别,但当列车移动速度超过土体Rayleigh波速时,饱和多孔介质与弹性介质的动力响应有很大区别。

DYNAMIC RESPONSES OF TRACK SYSTEM AND SATURATED SOIL IN HALF SPACE SUBJECTED TO A MOVING TRAIN LOAD

The dynamic responses of track system and saturated soil in half space subjected to a moving train load are investigated analytically. The system is divided into two parts,the track and the ground. The track system consists of three parts:rail,sleepers and ballast. The rail is modeled by introducing the Green function for an infinitely long Euler beam subjected to the action of the moving train load and the reaction of sleepers. The sleepers are represented by the continuous masses. The effect of the ballast is considered by introducing the Cosserat model. Neglecting the gravity of the soil medium,the Biot theory of a fully saturated poroelastic half-space is employed. By making use of the double Fourier transform,the governing equations of motion are solved in the frequency-wave-number domain. The governing equations of the soil medium and the track system are coupled by the boundary condition on the surface of the ground. The time domain responses are evaluated by the inverse Fourier transform computation for the cases that train velocity is lower or higher than soil Rayleigh-wave velocity .Computed results show that the dynamic responses of soil medium and rail are considerably affected by the fluid phase as well as train velocity. At low train velocity,whether the soil is considered as poroelastic medium or elastic medium only influences the amplitude of the soil and rail displacement. However,the responses for poroelastic medium are quite different from those for elastic medium when the train velocity exceeds Rayleigh-wave velocity of the soil medium.