基于饱和土的Biot波动方程和边界条件,利用Fourier变换和Galerkin法推导出频域内的u-w格式的2.5维有限元方程.把轨道视为饱和地基上的Euler梁,通过沿轨道方向的波数变换将三维空间问题降为平面应变问题.通过解方程首先获得饱和土体频域-波数域的位移解答,然后通过快速Fourier逆变换求得三维时域-空间域内的位移解答.通过计算实例验证了计算模型.建立轨道-地基模型,对饱和地基上列车运行引起的地面振动进行了分析,详细讨论了动力渗透系数、孔隙率、土骨架密度和剪切波速等参数对地面振动传播与衰减的影响规律分析.研究表明:在垂直轨道方向,随着与轨道中心距离增加,加速度幅值和主频迅速衰减;饱和土体动力渗透系数、孔隙率、剪切波速和土骨架密度对地表位移幅值均有较大的影响.%Based on Biot' s wave propagation equations and boundary conditions, Galerkin method was applied to derive the u-w format finite element equation in frequency domain by use of Fourier transform. The track and the attached sleepers were simplified as Euler beams resting on saturated half-space and the wave-number transform in the load moving direction was adopted to reduce the three-dimensional (3D) dynamic problem to a two-dimensional (2D) problem. The displacement in frequency-wave-number domain was obtained by solving the equations, and the 3D time-space domain displacement of the track and the ground was obtained by the fast Fournier transform. The model of 2.5D FEM was verified by a calculation example. A track-ground interaction model was presented and the dynamic response was given out to evaluate the ground vibration induced by a moving train on the saturated ground. The effects of the soil parameters (such as permeability coefficient, porosity, soil skeleton density and shear wave velocity) on the attenuation of ground vibration were investigated in detail. The results show that the acceleration amplitude and the dominant frequency decay quickly with the increase of distance from the track. It is also found that the permeability coefficient of soil, porosity,shear wave velocity and soil skeleton density have great influences on the ground vibrations.
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