西安建筑科技大学学报(自然科学版)

基于弹性地基杆理论建立了考虑竖井结构初衬和二次衬砌竖向地震响应力学模型。将竖井初衬和二次衬砌简化为两根平行的杆,采用均布的弹簧模拟竖井初衬与二次衬砌间的切向相互作用,推导了竖向地震作用下的竖井振动微分控制方程,通过将场地地震自由场位移转换为施加在初衬上的简谐荷载实现了地震动作用施加,结合分布传递函数法基本理论实现了竖井初衬和二次衬砌竖向地震响应快速求解,并通过与有限元数值模拟方法对比,验证了本文解析解的可行性。最后应用该解析解表达式分别从地基弹簧刚度、二次衬砌刚度和竖井外径的角度出发对竖井顶部地震响应开展参数化分析。结果发现:随着地基弹簧刚度增大,初衬顶部的竖向位移响应会略微增大,二次衬砌响应却会减小; 二次衬砌刚度的变化对竖井顶部竖向位移响应无显著影响; 随着竖井外径的增大,初衬和二次衬砌顶部竖向位移响应均会减小,其中二次衬砌减小更为明显.研究方法和结论可为竖井抗震设计提供一定参考,并为今后竖井的抗震研究提供理论方法和科学依据。

In this paper, a mechanical model of the vertical seismic response of shaft with considering primary lining and secondary lining is established based on the elastic foundation rod theory. The primary lining and secondary lining of the shaft are simplified into two parallel rods, a homogeneous spring is used to simulate the tangential interaction between the primary lining and the secondary lining of the shaft, and the differential control equation of the vibration of the shaft under vertical earthquake is derived. The ground motion is realized by converting the free field displacement of the site earthquake into a simple harmonic load applied to the primary lining. Combined with the basic theory of the distributed transfer function method, the vertical seismic response of the primary lining and the secondary lining of the shaft is quickly solved. The feasibility of the analytical solution is verified by comparison with the finite element numerical simulation method. Finally, the expressions of the analytical solution are applied to parametrically analyze the top seismic response of the shaft from the perspectives of the foundation spring stiffness, secondary liner stiffness and shaft outer diameter respectively. The results show that with the increase of foundation spring stiffness, the vertical displacement response at the top of the primary lining will increase slightly, while the response of the secondary lining will decrease. The change of secondary lining stiffness has no significant effect on the vertical displacement response at the top of the shaft. With the increase of the outer diameter of the shaft, the vertical displacement response at the top of the primary lining and the secondary lining will decrease, and the decrease of the secondary lining is more obvious. The research methods and conclusions can provide some reference for seismic design of shaft, and provide theoretical methods and scientific basis for seismic research of shaft in the future.

引言
1 竖井模型与假定
2 解析解推导
3 数值验证
4 参数化分析
5 结论

图1 简化计算模型示意图<br/>Fig.1 Diagram of simplified calculation modal

图1 简化计算模型示意图
Fig.1 Diagram of simplified calculation modal

图2 有限元分析模型示意图<br/>Fig.2 Finite element analysis model

图2 有限元分析模型示意图
Fig.2 Finite element analysis model

图3 El-Centro波时程曲线<br/>Fig.3 Time history curve of El-Centro

图3 El-Centro波时程曲线
Fig.3 Time history curve of El-Centro

图4 z=30 m竖井响应对比验证<br/>Fig.4 Shaft response of z=30 comparison verification

图4 z=30 m竖井响应对比验证
Fig.4 Shaft response of z=30 comparison verification

表1 解析解数值解最大值对比<br/>Tab.1 Maximum value comparison between analytical solution and numerical solution

表1 解析解数值解最大值对比
Tab.1 Maximum value comparison between analytical solution and numerical solution

图5 地基弹簧刚度对竖井响应的影响<br/>Fig.5 Influence of foundation spring stiffness on shaft response

图5 地基弹簧刚度对竖井响应的影响
Fig.5 Influence of foundation spring stiffness on shaft response

图6 二次衬砌刚度对竖井响应的影响<br/>Fig.6 Influence of secondary lining stiffness on shaft response

图6 二次衬砌刚度对竖井响应的影响
Fig.6 Influence of secondary lining stiffness on shaft response

图7 竖井外径对竖井响应的影响<br/>Fig.7 Influence of shaft outer diameter on shaft response

图7 竖井外径对竖井响应的影响
Fig.7 Influence of shaft outer diameter on shaft response

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备注

引言

1 竖井模型与假定

2 解析解推导

3 数值验证

4 参数化分析

5 结论

期刊信息