隧道-轨道系统竖向地震响应解析解

Analytical solution for vertical seismic response of tunnel-track system

  • 摘要: 随着城市轨道交通的快速发展,隧道-轨道系统在地震作用下的安全性至关重要。已有研究大多忽略轨道结构与隧道之间的相互作用,难以准确评估隧道-轨道系统的地震响应。本文基于弹性地基梁理论,建立了由钢轨、复合板、隧道和文克勒地基组成的三层梁-弹簧模型,通过杜哈梅积分及傅里叶级数展开实现了竖向地震作用下隧道-轨道系统的动力响应的求解。并通过与数值模拟结果的对比验证了解析解的准确性。然后从地基弹簧刚度、隧道衬砌刚度、钢轨与复合板连接刚度及复合板与隧道连接刚度四个角度出发进行参数分析,结果表明:地基弹簧刚度增大可显著降低各层梁的峰值响应;隧道衬砌刚度提升会导致峰值位移响应先增大后趋于稳定,而峰值转角呈逐步上升趋势;钢轨与复合板连接刚度对系统峰值地震响应影响较小;复合板与隧道连接刚度增大可减小钢轨和复合板的峰值地震响应,但对隧道峰值地震响应无显著影响。

     

    Abstract: With the rapid development of urban rail transit, the seismic safety of the tunnel-track system remains critically important. Most existing studies overlook the interaction between the track structure and the tunnel, which limits accurate assessment of the tunnel-track system’s seismic response. In this paper, a three-layer beam-spring model comprising rails, composite slabs, tunnels, and a Winkler foundation is established based on elastic foundation beam theory. The dynamic response of the tunnel-track system under vertical seismic action is solved using Duhamel integral and Fourier series expansion. The analytical solution’s accuracy is verified through comparison with numerical simulation results. Parameter analysis is then conducted on four aspects: foundation spring stiffness, tunnel lining stiffness, rail-composite slab connection stiffness, and composite slab-tunnel connection stiffness. Results show that increasing foundation spring stiffness significantly reduces the peak response of each beam layer. Increasing tunnel lining stiffness causes peak displacement response to increase initially and then stabilize, while peak rotation angle exhibits a gradually increasing trend. Rail-composite slab connection stiffness has a minimal effect on the system’s peak seismic response. Enhancing composite slab-tunnel connection stiffness reduces the peak seismic response of rails and composite slabs but does not significantly affect the tunnel’s peak seismic response.

     

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