行波效应下曲线隧道动力响应解析解  

Analytical solution for dynamic response of curved tunnels under travelling wave effect

作　　者：禹海涛[1] 李心熙 李攀[2,3] YU Hai-tao;LI Xin-xi;LI Pan(Key Laboratory of Geotechnical and Underground Engineering of Ministry of Education,Tongji University,Shanghai 200092,China;Department of Geotechnical Engineering,Tongji University,Shanghai 200092,China;School of Rail Transportation,Soochow University,Suzhou 215131,China)

机构地区：[1]同济大学岩土及地下工程教育部重点实验室,上海200092 [2]同济大学地下建筑与工程系,上海200092 [3]苏州大学轨道交通学院,江苏苏州215131

出　　处：《岩土工程学报》2021年第1期69-76,共8页Chinese Journal of Geotechnical Engineering

基　　金：国家重点研发计划项目(2018YFC1504305,2017YFC0805501,2017YFC1500703);国家自然科学基金项目(41922059,51978431,51678438);上海市科委重点课题(18DZ1205103&18DZ1205106,17DZ1203804);中央高校基本科研业务费专项项目。

摘　　要：隧道曲率变化段是制约隧道结构抗震安全性的关键控制区段,但目前隧道抗震设计仅以横断面剪切变形为主,未考虑隧道沿纵向的曲率半径变化,缺乏针对曲线隧道的纵向抗震简化分析方法。将曲线隧道沿纵向简化为作用在黏弹性地基上的变曲率有限长均质Euler-Bernoulli梁,基于Hamilton原理及黏弹性地基梁理论建立了结构的微分动力控制方程及边界条件,并通过模态叠加法进行求解,推导出任意动载作用下曲线隧道的位移、速度、加速度、弯矩、剪力等动力响应的解析表达式,以行波荷载为例,给出行波效应下曲线隧道动力响应的退化解答。通过与有限元基准模型在相同条件下的对比分析,验证了所推导解析解的正确性。最后应用该解析公式进行参数敏感性分析,揭示了隧道曲率半径、行波波速、行波频率及地层–结构相对刚度比等关键因素对曲线隧道结构动力响应的影响规律。The tunnel section with curvature variation that restricts the seismic safety of a tunnel is one of the critical sections for structural design.However,the current seismic design of tunnel structures only focuses on the shear deformation of the tunnel cross-section and the longitudinal curvature is not considered.The most important issue is that there are no available simplified methods in the current literatures for longitudinal seismic analysis of curved tunnels.It is therefore necessary to solve the forward problem with the purpose of obtaining an analytical solution for the dynamic response of curved tunnels under travelling loads.Firstly,a curved tunnel is assumed as a finite homogeneous beam with variable curvature resting on a viscoelastic foundation,and the governing differential equation and boundary conditions of the dynamic problem are established based on the Hamilton principle and the viscoelastic foundational beam theory.Then,the modal superposition method is employed to solve the dynamic problem,and thus the analytical solutions of dynamic responses for curved tunnels subjected to arbitrary dynamic loads are derived.Finally,the degraded solution for travelling loads is obtained with the proposed solution.The solutions of tunnel responses investigated are deflection,velocity,acceleration,bending moment,and shear force.The validation of the analytical solution is verified by providing comparisons between its results and those from the finite element method.The parametric analyses are performed to investigate the influences of the radius of curvature,the velocity and frequency of travelling loads and soil-structure relative stiffness ratio on the dynamic responses of the curved tunnel.

关 键 词：曲线隧道 动力响应 行波效应 解析解 影响因素分析 

分 类 号：TU435[建筑科学—岩土工程]