穿越断层隧道纵向地震响应规律解析解

Analytical Solution for Longitudinal Seismic Responses of Fault-crossing Tunnels

隧道穿越断层区域在地震中易受到严重破坏,是隧道抗震设防的重点控制区域。针对现有设计方法很少考虑隧道穿越断层的现状,基于穿越断层隧道地震响应特点,将隧道沿纵向简化为3段位于不同地层条件的黏弹性地基上的剪切梁,推导了地震动下穿越断层隧道纵向地震稳态响应的解析表达式,建立了面向工程设计的穿越断层隧道纵向抗震简化分析方法。首先,采用Kelvin黏弹性地基上的剪切梁模拟衬砌节段,基于格林函数法、拉普拉斯正逆变换和留数法推导衬砌节段在荷载激励下沿纵向的响应。其次,结合衬砌连续性条件获得穿越断层隧道纵向响应解析解。然后,通过与数值分析结果的对比,验证了本文方法的有效性和可行性。最后,采用该解析方法进行了敏感性参数分析,探究了边界条件、结构刚度、断层破碎带性质、围岩阻尼等关键因素对穿越断层隧道结构地震响应的影响规律。结果表明:(1)增大衬砌的弯曲刚度会减小衬砌上的位移响应,但同时会显著增大衬砌上的内力响应值;(2)加固断层围岩可减小衬砌在地震动作用下的位移响应,也使衬砌的内力响应减小,并减小断层对隧道沿纵向地震响应的影响范围;(3)阻尼的存在使衬砌的振动沿隧道纵向出现异步性,加载波的频率越高,异步性越明显。该解析方法能够快速计算得到穿越断层隧道的地震响应,为相关隧道工程的抗减震设计提供参考。

The areas where tunnels run through faults are the key areas for seismic design and easily to be seriously damaged in earthquakes.Since the current design methods seldom considered tunnels passing through faults, the tunnel was simplified to three shear beams on a viscoelastic foundation under different strata along the longitudinal direction, and the analytical solution of the longitudinal seismic steady-state responses of tunnels passing through the faults was derived. A simplified analysis method was proposed for the longitudinal seismic responses of tunnels passing through faults. First, a shear beam on Kelvin’s viscoelastic foundation was utilized to simulate the lining segment. The longitudinal responses of a lining segment under external loads were derived by using Green’s function method, Laplace transform, Laplace inverse transform,and residue theorem. Then, the analytical solution of longitudinal responses of the tunnel crossing the fault was obtained by combining with the continuity condition of the lining segment. Next, the validity and feasibility of the proposed method were verified by comparing with the numerical analysis. Finally, the sensitivity analysis of parameters was conducted using the proposed method to reveal the influences of parameters on seismic responses of tunnels through faults. The results showed that increasing the bending stiffness of the lining could reduce the displacement responses of the lining, but at the same time significantly increased the internal forces of the lining. Reinforcing the fault surrounding rock could reduce the displacement responses of the lining, as well as the internal force responses of the lining, and reduce the influence range of the fault on the seismic responses of the tunnel along the tunnel axis under the action of ground motion. The damping made the vibration of the tunnel lining appear asynchronous along the longitudinal direction. The higher the frequency of the wave was, the more obvious the vibration asynchrony of tunnel lining was. The proposed method could make a quick calculation of the seismic responses of fault-crossing tunnels, which provided a reference for the seismic design of related tunneling projects.