竖井结构初衬及二次衬砌水平地震响应解析解  

Analytical solution for horizontal seismic response of shaft structure primary lining and secondary lining

作　　者：张卜 卢立东 钟紫蓝 姬若愚 杜修力[1,2] ZAHNG Bu;LU Li-dong;ZHONG Zi-lan;JI Ruo-yu;DU Xiu-li(Faculty of Architecture,Civil and Transportation Engineering,Beijing University of Technology,Beijing 100124,China;Key Laboratory of Urban Security and Disaster Engineering,Ministry of Education,Beijing University of Technology,Beijing 100124,China)

机构地区：[1]北京工业大学城市建设学部,北京100124 [2]北京工业大学城市与工程安全减灾教育部重点实验室,北京100124

出　　处：《振动工程学报》2024年第12期2003-2011,共9页Journal of Vibration Engineering

基　　金：国家自然科学基金联合基金资助项目(U1839201);中国博士后科学基金资助项目(2021M700311);朝阳区博士后工作经费资助项目;北京市博士后国际交流培养资助派出项目(2022-PC-03)。

摘　　要：基于弹性地基梁理论建立了考虑竖井初衬与二次衬砌相互作用的地震响应力学模型,将竖井初衬和二次衬砌简化为欧拉-伯努利梁,采用均布弹簧模拟竖井初衬与二次衬砌的法向相互作用,推导了水平地震作用下的竖井振动微分控制方程。通过分布传递函数法实现了竖井初衬和二次衬砌水平地震响应的快速求解,并通过与有限元模拟数值解进行对比,验证了本文解析解的正确性。应用该解析解表达式分别从地基刚度、二次衬砌刚度、竖井外径和初衬与二次衬砌之间连接层刚度的角度出发,对竖井顶部峰值地震响应开展参数化分析,结果发现二次衬砌顶部的峰值地震响应大于初衬顶部,随着地基刚度的增大,初衬与二次衬砌顶部峰值响应均减小;二次衬砌刚度增加会导致二次衬砌顶部峰值响应明显增大;随着竖井外径的增大,初衬和二次衬砌顶部峰值响应均会明显增大;当弹性连接层刚度增大时,初衬顶部峰值响应会略微增大,而二次衬砌顶部峰值响应会显著减小。Based on the elastic foundation beam theory,the mechanical model for the seismic response of the vertical shaft is established.The shaft primary lining and secondary lining are simplified as Euler Bernoulli beams and the normal interaction between the primary lining and secondary lining is simulated by using uniformly distributed springs.The differential governing equations of the shaft under the horizontal seismic excitation are derived.The rapid solution of the horizontal seismic response of the primary lining and secondary lining is achieved through the distributed transfer function method and the correctness of the analytical solution is verified by comparison with the finite element numerical simulation method.The peak seismic response at the top of the shaft is parametrically analyzed from the perspectives of elastic foundation stiffness,secondary lining stiffness,shaft outer diameter,and stiffness of the elastic connection layer between the primary and secondary linings,respectively.The results show that the peak seismic response at the top of the secondary lining is greater than that of the primary lining.With the increase of the elastic foundation stiffness,the peak response of the top of the primary lining and the secondary lining decreases.The increase of secondary lining stiffness leads to the obvious increase of peak response at the top of secondary lining.With the increase of the shaft outer diameter,the peak response of both the primary and secondary linings increase significantly.When the elastic connection layer stiffness increases,the peak response of the primary lining increases slightly,but the peak response of the secondary lining decreases significantly.

关 键 词：地下结构抗震 竖井地震响应 竖井衬砌 弹性地基梁 

分 类 号：TU352.1[建筑科学—结构工程] TU91