地下结构抗震分析的振动法与波动法对比研究
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摘要
针对地下结构抗震分析中应用广泛的波动方法与振动方法,从物理方程和有限元格式出发,明确了两种方法的区别与联系。通过标准数值试验,证明了振动方法是波动方法采用下卧刚性基岩假设和地层水平无限延伸假设,仅考虑SV波垂直向上入射的一种特例。采用波动方法模拟弹性地基,对比振动方法结果,表明弹性地基和刚性地基上地表位移响应和隧道结构内力响应均有显著差异。建议应根据具体场地条件,选择振动或波动方法进行地下结构抗震设计研究。
The wave and vibration methods of seismic analysis are widely employed with underground structures. Comparisons between the two approaches were conducted in the paper. First, the wave method, i.e., the viscoelastic artificial boundary and pertinent equivalent nodal force method, is introduced briefly. Second, the governing equation and finite element formulation of the problem are presented to clarify the interrelation and distinction between the two methods. On the basis of standard numerical tests, it was proved that the vibration method is only applicable to degraded cases, with assumptions of a rigid base and an SV propagating vertically upward. Then, the comparison between the rigid base and the elastic base was conducted. The rigid base was simulated through the vibration method, while the elastic base was simulated using the equivalent nodal force method. The results showed that there are significant differences between elastic and rigid bases in terms of ground surface displacement response and internal force response of tunnel structures. Therefore, the influence of different site conditions was far from negligible, and the analysis method should be carefully selected based on site conditions and whether a rigid or elastic base is incorporated into the seismic design of underground structures.
The wave and vibration methods of seismic analysis are widely employed with underground structures. Comparisons between the two approaches were conducted in the paper. First, the wave method, i.e., the viscoelastic artificial boundary and pertinent equivalent nodal force method, is introduced briefly. Second, the governing equation and finite element formulation of the problem are presented to clarify the interrelation and distinction between the two methods. On the basis of standard numerical tests, it was proved that the vibration method is only applicable to degraded cases, with assumptions of a rigid base and an SV propagating vertically upward. Then, the comparison between the rigid base and the elastic base was conducted. The rigid base was simulated through the vibration method, while the elastic base was simulated using the equivalent nodal force method. The results showed that there are significant differences between elastic and rigid bases in terms of ground surface displacement response and internal force response of tunnel structures. Therefore, the influence of different site conditions was far from negligible, and the analysis method should be carefully selected based on site conditions and whether a rigid or elastic base is incorporated into the seismic design of underground structures.
引文
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[16] 同济大学.地下铁道建筑结构抗震设计规范:DG/TJ08-2064-2009[S].上海:上海市建筑建材业市场管理总站,2009.Tongji University.Code for Seismic Design of Subway Structures:DG/TJ08-2064-2009[S].Shanghai:Shanghai Construction Building Materials Market Management Station,2009.
[2] 闫静茹,路德春,杜修力,等.港珠澳大桥工程人工岛三维非线性地震反应分析[J].世界地震工程,2016,32(1):161-168.YAN Jingru,LU Dechun,DU Xiuli,et al.Three-Dimensional Nonlinear Seismic Response Analysis of Artificial Island of Hong Kong-Zhuhai-Macao Bridge Project[J].World Earthquake Engineering,2016,32(1):161-168.
[3] 庄海洋,龙慧,陈国兴,等.可液化地基中地铁车站周围场地地震反应分析[J].岩土工程学报,2012,34(1):81-88.ZHUANG Haiyang,LONG Hui,CHEN Guoxing,et al.Seismic Responses of Surrounding Site of Subway Station in Liquefiable Foundation[J].Chinese Journal of Geotechnical Engineering,2012,34(1):81-88.
[4] 刘晶波,吕彦东.结构-地基动力相互作用问题分析的一种直接方法[J].土木工程学报.1998(3):55-64.LIU Jingbo,Lü Yandong.ADirect Method for Analysis of Dynamic Soil-Structure Interaction[J].China Civil Engineering Journal,1998(3):55-64.
[5] HUANG J Q,DU X L,ZHAO M,et al.Impact of Incident Angles of Earthquake Shear (S) Waves on 3-D Non-Linear Seismic Responses of Long Lined Tunnels[J].Engineering Geology,2017,222:168-185.
[6] 杜修力,黄景琦,赵密,等.SV波斜入射对岩体隧道洞身段地震响应影响研究[J].岩土工程学报,2014,36(8):1400-1406.DU Xiuli,HUANG Jingqi,ZHAO Mi,et al.Effect of Oblique Incidence of SV Waves on Seismic Response of Portal Sections of Rock Tunnels[J].Chinese Journal of Geotechnical Engineering,2014,36(8):1400-1406.
[7] HUANG J Q,ZHAO M,DU X L.Non-Linear Seismic Responses of Tunnels within Normal Fault Ground under Obliquely Incident P Waves[J].Tunnelling and Underground Space Technology,2017,61:26-39.
[8] LI P,SONG E X.Three-Dimensional Numerical Analysis for the Longitudinal Seismic Response of Tunnels under an Asynchronous Wave Input[J].Computers and Geotechnics,2015,63:229-243.
[9] 刘晶波,李彬.Rayleigh波作用下地下结构的动力反应分析[J].工程力学,2006,23(10):132-135,131.LIU Jingbo,LI Bin.Dynamic Response Analysis of Underground Structures during Propagation of Rayleigh Waves[J].Engineering Mechanics,2006,23(10):132-135,131.
[10] 刘晶波,王文晖,刘祥庆,等.Rayleigh波作用下地下结构地震反应影响分析[J].振动与冲击,2013,32(16):95-99.LIU Jingbo,WANG Wenhui,LIU Xiangqing,et al.Influence Analysis on Seismic Response of Underground Structures under Propagation of Rayleigh Waves[J].Journal of Vibration and Shock,2013,32(16):95-99.
[11] 赵源,杜修力,赵密,等.地下结构地震响应中的地震动输入探讨[J].土木建筑与环境工程,2010,32(增刊2):192-197.ZHAO Yuan,DUXiuli,ZHAOMi,et al.Discussion on Ground Motion Input in Seismic Response of Underground Structures[J].Journal of Civil,Architectural and Environmental Engineering,2010,32(Supp 2):192-197.
[12] 赵武胜,陈卫忠,郑朋强,等.地下工程数值计算中地震动输入方法选择及实现[J].岩石力学与工程学报,2013,32(8):1579-1587.ZHAO Wusheng,CHEN Weizhong,ZHENG Pengqiang,et al.Choice and Implementation of SeismicwaveInput Method in Numerical Calculation for Underground Engineering[J].Chinese Journal of Rock Mechanics and Engineering,2013,32(8):1579-1587.
[13] 黄景琦.岩体隧道非线性地震响应分析[D].北京:北京工业大学,2015.HUANG Jingqi.Study on Nonlinear Seismic Response of Rock Tunnels[D].Beijing:Beijing University of Technology,2015.
[14] 杜修力,李洋,赵密,等.下卧刚性基岩条件下场地土-结构体系地震反应分析方法研究[J].工程力学,2017,34(5):52-59.DU Xiuli,LI Yang,ZHAO Mi,et al.Seismic Response Analysis Method for Soil-Structure Interaction System of Underlying Rigid Rock Base Soil Condition[J].Engineering Mechanics,2017,34(5):52-59.
[15] Zienkiewicz O C,Chan A H C,Pastor M,et al.Computational Geomechanic with Special Reference to Earthquake Engineering[M].Chichester:Wiley,1999.
[16] 同济大学.地下铁道建筑结构抗震设计规范:DG/TJ08-2064-2009[S].上海:上海市建筑建材业市场管理总站,2009.Tongji University.Code for Seismic Design of Subway Structures:DG/TJ08-2064-2009[S].Shanghai:Shanghai Construction Building Materials Market Management Station,2009.