Rayleigh波作用下圆形隧洞衬砌横向内力的解析解

 考虑土–结构相互作用，Rayleigh面波入射下隧洞衬砌的横向内力解析解至今比较少见。采用拟静力法，基于地下结构力学和平面弹性波动理论，推导出均匀介质中Rayleigh波以任意角度入射时圆形隧洞衬砌的横向内力解析解，考察土–结构交界面之间存在完全滑移和无滑移2种极限接触状态。算例表明，在Rayleigh波作用下，当其传播方向与隧洞轴向垂直时，衬砌的横向内力取得最大值，且内力在2种极限接触状态下的差别不大；与SV波作用效应相比，Rayleigh波作用下的衬砌横向内力均要大，尤其是轴力要大很多，这是由于Rayleig波中的P波分量造成的。浅埋隧洞衬砌的抗震设计，应充分重视Rayleigh波的作用效应。

Analytical solution of lateral internal forces in circular tunnel lining due to Rayleigh wave

Considering soil-structure interaction，few analytical solutions of lateral internal forces in tunnel lining due to Rayleigh wave(R wave) have been obtained at present. In this paper，the closed-form analytical solutions for internal forces in circular tunnel lining due to R wave at any propagation angle were derived based on mechanics of underground structure and theory of elastic waves using the pseudo-static method. Two ultimate contact conditions，i.e.，the full-slippage and no-slippage along the soil-lining interface，were considered respectively. A numerical example showed that the lateral internal forces in circular tunnel lining reached the maximum values if the propagation of R wave was perpendicular to the tunnel axis and the internal force differences between two contact conditions were minor. In addition，the internal forces resulted from R wave were much higher than those from SV wave，especially the lateral axial force which was induced mainly by the component P wave contained in R wave. In seismic design of shallow tunnels，the lateral internal forces in the lining caused by R wave should be paid adequate attentions.