基于无限元和波场分离法的地震响应数值分析
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摘要
用无限元模拟远场地基,有限元模拟近场区域,并在有限元和无限元接触处施加等效荷载以输入地震作用,从而求解半无限地基的地震响应.通过算例对边界和地震输入方式进行验证,研究剪切波作用下,重力和土与结构相互作用对场地地震响应的影响.结果表明:基于无限元和波场分离法的地震输入,能够有效仿真波动在半无限地基中的传播过程;重力对水平地震运动无影响;土与结构相互作用效应使短周期段加速度反应谱值降低,而长周期段加速度反应谱值增加;土与结构相互作用对岩石地基水平位移无影响,但使结构底部地基的最大主应力和最小主应力幅值增大.
The infinite element is adopted to model the far field and the finite element to model the near field of foundation,and the equivalent load is artificially applied to the interface between the finite element and the infinite element meshes to replace the seismic action.The seismic responses of semi-infinite foundation are then simulated.An example is performed to verify the boundary and seismic input,simultaneously effects of gravity and soil-structure interaction on the seismic response of field under incident shear wave are investigated.Numerical results show that the proposed method based on the infinite element and wave field separation method is feasible and it can effectively simulate the process of wave propagation in semi-infinite foundation.Gravity has nothing to do with horizontal earthquake.Furthermore,the influence of soil-structure interaction reduces the acceleration response spectrum in a short period,while increasing the acceleration response spectrum at long period.Finally,the influence of soil-structure interaction has nothing to do with horizontal displacement of rock foundation,however,it augments the max and min principal stress of groundwork just beneath the structure.
The infinite element is adopted to model the far field and the finite element to model the near field of foundation,and the equivalent load is artificially applied to the interface between the finite element and the infinite element meshes to replace the seismic action.The seismic responses of semi-infinite foundation are then simulated.An example is performed to verify the boundary and seismic input,simultaneously effects of gravity and soil-structure interaction on the seismic response of field under incident shear wave are investigated.Numerical results show that the proposed method based on the infinite element and wave field separation method is feasible and it can effectively simulate the process of wave propagation in semi-infinite foundation.Gravity has nothing to do with horizontal earthquake.Furthermore,the influence of soil-structure interaction reduces the acceleration response spectrum in a short period,while increasing the acceleration response spectrum at long period.Finally,the influence of soil-structure interaction has nothing to do with horizontal displacement of rock foundation,however,it augments the max and min principal stress of groundwork just beneath the structure.
引文
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[15]赵建锋,杜修力,韩强,等.外源波动问题数值模拟的一种实现方式[J].工程力学,2007,24(4):52.ZHAO Jianfeng,DU Xiu1i,HAN Qiang,et al.An approach tonumerical simulation for external source wave motion[J].Engineering Mechanics,2007,24(4):52.
[16]杜修力,赵密.基于黏弹性边界的拱坝地震反应分析方法[J].水利学报,2006,37(9):1063.DU Xiuli,ZHAO Mi.Analysis method for seismic response ofarch dams in time domain based on viscous-spring artificialboundary condition[J].Journal of Hydraulic Engineering,2006,37(9):1063.
[17]Idriss I M,Sun J I.SHAKE 91:a computer program forconducting equivalent linear seismic response analyses ofhorizontally layered soils deposits[EB/OL].[2011-04-20].USA:http://nees.ucdavis.edu/publications/Shak91_manual.pdf.
[2]刘晶波,谷音,杜义欣.一致粘弹性人工边界及粘弹性边界单元[J].岩土工程学报,2006,28(9):1070.LIU Jingbo,GU Yin,DU Yixin.Consistent viscous-springartificial boundaries and viscous-spring boundary elements[J].Journal of Geotechnical Engineering,2006,28(9):1070.
[3]廖振鹏.工程波动理论导论[M].北京:科学出版社,2002.LIAO Zhenpeng.Introduction to wave motion theories inengineering[M].Beijing:Science Press,2002.
[4]Deeks A J,Randolph M F.Axisymmetric time-domaintransmitting boundaries[J].Journal of Engineering MechanicsDivision,ASCE,1994,120(1):25.
[5]Ungless R F.An infinite finite element[D].Vancouver:University of British Columbia,1973.
[6]Bettess P.More on infinite element[J].International Journalfor Numerical Methods in Engineering,1980,15(11):1613.
[7]Beer G,Meek J L.Infinite domain element[J].InternationalJournal for Numerical Methods in Engineering,1981,17(3):43.
[8]Zienkiewicz O C.A novel boundary infinite element[J].International Journal for Numerical Methods in Engineering,1983,19(3):393.
[9]ZHANG Chuhan,ZHAO Chongbin.Coupling method of finiteand infinite elements for strip foundation wave problems[J].Earthquake Engineering and Structural Dynamics,1987,15(7):839.
[10]葛修润,谷先荣,丰定祥.三维无限元和节理无界元[J].岩土工程学报,1986,8(5):9.GE Xiurun,GU Xianrong,FENG Dingxiang.Three-dimensional infinite domain elements and joint infinite domainelements[J].Journal of Geotechnical Engineering,1986,8(5):9.
[11]燕柳斌.用三维映射无限元模拟重力坝地基[J].水利学报,1991,2(10):7.YAN Liubin.Modeling of gravity dam foundation using threedimensional mapped infinite element[J].Journal of HydraulicEngineering,1991,2(10):7.
[12]黄胜,陈卫忠,杨建平,等.地下工程地震动力响应及抗震研究[J].岩石力学与工程学报,2009,28(3):483.HUANG Sheng,CHEN Weizhong,YANG Jianping,et al.Research on earthquake-induced dynamic response and aseismicmeasures for underground engineering[J].Chinese Journal ofRock Mechanics and Engineering,2009,28(3):483.
[13]姜袁,陈灯红,姚艳华.有限元-无限元法在重力坝应力分析中的应用[J].武汉大学学报:工学版,2009,42(3):322.JIANG Yuan,CHEN Denghong,YAO Yanhua.Application offinite element and infinite element method to stress analysis ofgravity dam[J].Engineering Journal of Wuhan University,2009,42(3):322.
[14]SIMULIA Inc.ABAQUS theory manual[EB/OL].[2011-04-20].USA:https://www.sharcnet.ca/Software/Abaqus610/Documentation/ddoc/v6.10/books/stm/default.htm.
[15]赵建锋,杜修力,韩强,等.外源波动问题数值模拟的一种实现方式[J].工程力学,2007,24(4):52.ZHAO Jianfeng,DU Xiu1i,HAN Qiang,et al.An approach tonumerical simulation for external source wave motion[J].Engineering Mechanics,2007,24(4):52.
[16]杜修力,赵密.基于黏弹性边界的拱坝地震反应分析方法[J].水利学报,2006,37(9):1063.DU Xiuli,ZHAO Mi.Analysis method for seismic response ofarch dams in time domain based on viscous-spring artificialboundary condition[J].Journal of Hydraulic Engineering,2006,37(9):1063.
[17]Idriss I M,Sun J I.SHAKE 91:a computer program forconducting equivalent linear seismic response analyses ofhorizontally layered soils deposits[EB/OL].[2011-04-20].USA:http://nees.ucdavis.edu/publications/Shak91_manual.pdf.
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