土岩变化地层长隧道纵向地震响应解析解

Analytical solution for longitudinal seismic responses of long tunnels crossing soil-rock stratum

土岩地层交界面是制约长隧道结构抗震安全的关键控制节点,但现有设计方法均未考虑隧道沿其纵向的地层变化。基于隧道的动力响应特点提出力学模型,将隧道沿纵向简化为两段处于不同地层条件中的半无限长弹性地基梁。通过求解结构的位移微分控制方程,推导出土岩变化地层长隧道纵向地震响应的解析表达式,并引入位移相位角模拟行波效应,提出了面向工程设计的土岩变化地层长隧道纵向抗震简化分析方法。通过与有限元基准模型在相同条件下的对比分析,验证了该方法的有效性。最后应用该解析公式进行参数敏感性分析,揭示了结构刚度、地层剪切波速比等关键因素对土岩变化地层隧道结构地震响应的影响规律:隧道结构刚度越大,结构内力响应越剧烈,隧道地层突变段的内力峰值差越大,地层突变的影响范围也随之变宽;地层剪切波速比越大,隧道地层突变段的内力峰值差越大,但地层突变的影响范围却不受影响。

The contact between soil and rock is the controlling point in the seismic design of long tunnels, which has not been considered in any design methods yet. The mechanical model for a long tunnel crossing soil-rock stratum is proposed with assumptions based on its dynamic response characteristics, in which two semi-infinite elastic foundation beams in different soils are assumed to model the behaviors of the tunnel. An analytical solution for longitudinal seismic responses of tunnels crossing soil-rock stratum is derived by solving the displacement differential governing equations. The simplified method for longitudinal seismic responses of tunnels crossing soil-rock stratum is proposed. The traveling wave effect can be considered by introducing the displacement phase angle. A benchmark model, a finite element model for a long tunnel crossing soil-rock stratum, is used to calibrate the proposed method. Comparison under the same parameters shows a high degree of consistency between them, which verifies the efficiency of the innovative method. Finally, sensitivity analyses of parameters are carried out using the proposed analytic formulas, and the influences of parameters on seismic response of tunnels crossing soil-rock stratum are revealed. The results suggest that with the increase of the structural stiffness, the internal force response of the tunnel becomes larger, the difference of the values of the peak internal forces becomes greater, and the zone of influence of the transition becomes wider. With the increase of shear velocity ratio of soils, the difference of the values of the peak internal forces becomes greater but the zone of in fluence of the transition remains unchanged.