地铁列车荷载作用下轨道系统及饱和土体动力响应分析

 为研究地铁列车运行引起的轨道系统及饱和土体动力响应问题，建立了地铁列车–轨道结构–衬砌–饱和土体耦合分析模型，其中列车荷载用一系列符合列车几何尺寸的移动常荷载或移动简谐荷载模拟，轨道结构中的钢轨和浮置板简化为无限长弹性Euler梁。基于弹性理论和Biot多孔介质理论，采用2.5维有限元法分别模拟衬砌和饱和土体，结合轨道与衬砌仰拱处的力和位移连续条件，实现浮置板轨道系统与衬砌及周围饱和土体的耦合，并通过快速Fourier逆变换(IFFT)进行波数展开获得三维时域–空间域内的动力响应。研究结果表明，随着常荷载移动速度和移动简谐荷载自振频率的提高，地表振动水平显著增大；移动常荷载产生的地表响应最大值在荷载正上方，其空间衰减率保持恒定；移动简谐荷载产生的地基振动大于移动常荷载产生的地基振动，响应最大值在列车运行线路两侧一定范围内；在移动简谐荷载作用下，钢轨速度谱与地表速度谱分布在以简谐荷载自振频率为中心的一段范围内。

DYNAMIC RESPONSE ANALYSIS OF TRACK SYSTEM AND UNDERGROUND RAILWAY TUNNEL IN SATURATED SOIL SUBJECTED TO A MOVING TRAIN LOAD

The underground railway coupling analysis model was established and used to study the dynamic response of track systems and saturated soil. The model was divided into four parts，the moving train，floating-slab tracks，liner and saturated ground. The train load was simulated by a series of moving constant or harmonic load in accordance with the geometry of a real train. The tracks consisted of an upper Euler-Bernoulli beam to account for the rails and a lower Euler-Bernoulli beam to account for the slab. By adopting the method of 2.5D FEM，the elastic theory and the Biot’s theory were used to simulate the liner and saturated porous medium respectively. The floating-slab tracks and soil medium were coupled by the boundary conditions at the tunnel invert. The three-dimensional time-space domain dynamic response was obtained from the fast inverse Fourier transform (IFFT). Computed results show that with increasing train velocity and self-vibration frequency of the moving harmonic load，the dynamic responses of the ground surface increase obviously. The maximum ground surface responses generated by the moving constant load are located directly over the tunnel centerline with a constant space attenuation rate. The dynamic responses of ground surface induced by moving harmonic load are larger than those induced by moving constant load and become the strongest at certain distances from the tunnel centerline. The distribution of velocity spectrum for the rail and ground surface is centered on self-vibration frequency of the harmonic load.