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用解析法研究了移动列车荷载作用下下卧成层地基的路轨系统的动力响应问题。将整个系统分为上覆路轨系统和下卧土体。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,同时考虑由Cosserat模型描述的道渣层。在实际工程中,地下水位往往位于地表以下几米处,因此将下卧土体考虑为成层土,其中,上层为弹性介质,下层为由Biot波动方程描述的饱和弹性半空间。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,孔压表达式。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,孔压在时域内的表达式。着重研究了弹性层厚度、密度、刚度和道渣层质量对钢轨动力响应的影响。计算结果表明,在低速情况下,这些参数对钢轨动力响应影响都很有限,但在高速情况下,这些参数对钢轨动力响应的影响都很大。
The dynamic response of the rail system under the stratified subsoil under moving train load is studied by analytical method. The whole system is divided into overlying rail system and the next soil. For rail systems, the rails are reduced to an infinitely long elastic Euler beam, which reduces the sleepers to a continuous mass, taking into account the ballast layer described by the Cosserat model. In practical engineering, the groundwater table is often located a few meters below the earth’s surface. Therefore, the underlying soil is considered as the layered soil, where the upper layer is the elastic medium and the lower layer is the saturated elastic half-space described by Biot’s wave equation. In the Fourier transform domain, the dynamic equation of the simultaneous railway system and the underlying soil is solved to solve the displacement, acceleration, soil displacement, acceleration and pore pressure expressions under train load. The numerical integral method is used to inverse Fourier transform of the expressions to get the expressions of the displacement, acceleration, soil displacement, acceleration and pore pressure in the time domain. The effects of the elastic layer thickness, density, stiffness and the quality of the ballast layer on the dynamic response of the rail are emphatically studied. The calculation results show that these parameters have a limited influence on the dynamic response of the rail at low speed, but these parameters have a great influence on the dynamic response of the rail at high speed.