Rayleigh波场的数值模拟及其应用
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摘要
本文总结了Rayleigh波场数值模拟的4种思路和各自特点,根据Lamb问题的理论分析成果提出了基于地表激振的Rayleigh波场数值模拟技术,论述了地表集中震源作用下引起地表波动场的特点及主要影响因素。在此基础上,利用Plaxis 2D有限元软件实现了Rayleigh波场的数值模拟,并结合算例验证了所提方法的可行性和结果的合理性。最后,针对多层建筑结构,研究了不同地震动输入模式下结构动力反应的特点。结果表明,Rayleigh波作用下结构的动力反应特性明显区别于在底部输入剪切波时的结果,不同地震动输入模式对结构的振动形态和破坏模式有着明显的影响。
Four different approaches about numerical modeling techniques of Rayleigh wave field were summarized. The techniques base on vertical harmonic point load on the free surface has been proposed in this paper. The main research achievements of Lamb issues, such as the characteristics of Rayleigh wave field under point load and its main influencing factors were discussed. On this basis the numerical modeling of Rayleigh wave field with Plaxis 2 D was conducted and the effectiveness of the approach was verified with an example. The dynamic response of a multi-story building structure during propagation of Rayleigh wave was analyzed using the proposed method, and the results were compared to that from the traditional methods. Numerical analysis results show that different wave motion input methods have great effect on the dynamic response of building structures.The vibration shape and failure modes of the structure were greatly influenced by seismic input modes.
Four different approaches about numerical modeling techniques of Rayleigh wave field were summarized. The techniques base on vertical harmonic point load on the free surface has been proposed in this paper. The main research achievements of Lamb issues, such as the characteristics of Rayleigh wave field under point load and its main influencing factors were discussed. On this basis the numerical modeling of Rayleigh wave field with Plaxis 2 D was conducted and the effectiveness of the approach was verified with an example. The dynamic response of a multi-story building structure during propagation of Rayleigh wave was analyzed using the proposed method, and the results were compared to that from the traditional methods. Numerical analysis results show that different wave motion input methods have great effect on the dynamic response of building structures.The vibration shape and failure modes of the structure were greatly influenced by seismic input modes.
引文
巴振宁,梁建文,2014.瑞雷波斜入射下层状半空间中沉积谷地周围的三维散射研究.地震学报,36(4):571-583.
崔杰,张为,张建国,2008.Rayleigh波对浅地表地基震害的影响.华南地震,28(2):10-18.
高广运,1998.非连续屏障地面隔振理论与应用.杭州:浙江大学.
梁建文,魏新磊,Lee V.W.,2009.圆弧形沉积谷地对Rayleigh波三维散射解析解.天津大学学报,42(1):24-34.
刘广裕,刘凯欣,2007.区域脉冲载荷下二维Lamb问题的精确求解.固体力学学报,28(4):341-346.
刘晶波,李彬,2006.Rayleigh波作用下地下结构的动力反应分析.工程力学,23(10):132-135,131.
刘晶波,谭辉,宝鑫等,2018.土-结构动力相互作用分析中基于人工边界子结构的地震波动输入方法.力学学报,50(1):32-43.
刘凯欣,刘广裕,2004.垂直点源问题的一个精确解.科学通报,49(5):419-423.
刘志祥,张海清,2017.PLAXIS 2D基础教程.北京:机械工业出版社.
罗超,2017.河谷地形及土-结构相互作用对大跨度桥梁地震反应的影响.上海:同济大学,78-94.
萨瓦林斯基,1981.地震波.段星北,译.北京:科学出版社.
佘德平,2004.波场数值模拟技术.勘探地球物理进展,27(1):16-21.
施有志,林树枝,赵花丽,2017a.瑞利阻尼参数对瑞利波作用下场地动力响应的影响.人民长江,48(3):76-80.
施有志,孙爱琴,林树枝等,2017b.Rayleigh波作用下地下综合管廊动力响应三维数值分析.世界地震工程,33(4):196-210.
苏传行,2017.二维起伏地形瑞利面波数值模拟研究,成都:西南交通大学,18-22.
王朝令,刘争平,2012.黏弹性边界条件在ANSYS有限元波场模拟中的实现.大地测量与地球动力学,32(2):28-31.
王朝令,刘争平,黄云艳等,2014.隧道地震预报波场的有限元数值模拟.吉林大学学报(地球科学版),44(4):1369-1381.
王贻荪,1979.关于拉姆问题的精确解.湖南大学学报,6(1):61-76.
王贻荪,1980.半无限体表面在竖向集中谐和力作用下表面竖向位移的精确解.力学学报,12(4):386-391.
王贻荪,1982.地面波动分析若干问题.建筑结构学报,3(2):56-67.
吴世明,1997.土介质中的波.北京:科学出版社.
杨桂通,张善元,1988.弹性动力学.北京:中国铁道出版社.
杨先健,徐建,张翠红,2013.土-基础的振动与隔振.北京:中国建筑工业出版社.
于文福,2017.点源横向非均匀介质瑞利面波波场数值模拟研究.成都:西南交通大学,66-72.
岳庆霞,李杰,2008.近似Rayleigh地震波作用下地下综合管廊响应分析.防灾减灾工程学报,28(4):409-416.
Brinkgreve R.B.J.,Kumarswamy S.,Swolfs,W.M.,2016.PLAXIS 2D reference manual.Delft,The Netherlands:PLAXIS BV,286-290.
Kontoe S.,Zdravkovic L.,Potts D.M.,2009.An assessment of the domain reduction method as an advanced boundary condition and some pitfalls in the use of conventional absorbing boundaries.International Journal for Numerical and Analytical Methods in Geomechanics,33(3):309-330.
Lamb H.,1904.On the propagation of tremors over the surface of an elastic solid.Philosophical Transactions of the Royal Society of London.Series A,Containing Papers of a Mathematical or Physical Character,203:1-42.
Woods R.D.,1968.Screening of surface waves in soils.Journal of Soil Mechanics and Foundations Division ASCE,94(SM4):951-979.
Yu W.F.,Liu Z.P.,2015.A numerical study of the Rayleigh wave particle motions excited by a point source and
Poisson’s ratio for lateral inhomogeneous half-spaces.Journal of Applied Geophysics,123:242-255.
崔杰,张为,张建国,2008.Rayleigh波对浅地表地基震害的影响.华南地震,28(2):10-18.
高广运,1998.非连续屏障地面隔振理论与应用.杭州:浙江大学.
梁建文,魏新磊,Lee V.W.,2009.圆弧形沉积谷地对Rayleigh波三维散射解析解.天津大学学报,42(1):24-34.
刘广裕,刘凯欣,2007.区域脉冲载荷下二维Lamb问题的精确求解.固体力学学报,28(4):341-346.
刘晶波,李彬,2006.Rayleigh波作用下地下结构的动力反应分析.工程力学,23(10):132-135,131.
刘晶波,谭辉,宝鑫等,2018.土-结构动力相互作用分析中基于人工边界子结构的地震波动输入方法.力学学报,50(1):32-43.
刘凯欣,刘广裕,2004.垂直点源问题的一个精确解.科学通报,49(5):419-423.
刘志祥,张海清,2017.PLAXIS 2D基础教程.北京:机械工业出版社.
罗超,2017.河谷地形及土-结构相互作用对大跨度桥梁地震反应的影响.上海:同济大学,78-94.
萨瓦林斯基,1981.地震波.段星北,译.北京:科学出版社.
佘德平,2004.波场数值模拟技术.勘探地球物理进展,27(1):16-21.
施有志,林树枝,赵花丽,2017a.瑞利阻尼参数对瑞利波作用下场地动力响应的影响.人民长江,48(3):76-80.
施有志,孙爱琴,林树枝等,2017b.Rayleigh波作用下地下综合管廊动力响应三维数值分析.世界地震工程,33(4):196-210.
苏传行,2017.二维起伏地形瑞利面波数值模拟研究,成都:西南交通大学,18-22.
王朝令,刘争平,2012.黏弹性边界条件在ANSYS有限元波场模拟中的实现.大地测量与地球动力学,32(2):28-31.
王朝令,刘争平,黄云艳等,2014.隧道地震预报波场的有限元数值模拟.吉林大学学报(地球科学版),44(4):1369-1381.
王贻荪,1979.关于拉姆问题的精确解.湖南大学学报,6(1):61-76.
王贻荪,1980.半无限体表面在竖向集中谐和力作用下表面竖向位移的精确解.力学学报,12(4):386-391.
王贻荪,1982.地面波动分析若干问题.建筑结构学报,3(2):56-67.
吴世明,1997.土介质中的波.北京:科学出版社.
杨桂通,张善元,1988.弹性动力学.北京:中国铁道出版社.
杨先健,徐建,张翠红,2013.土-基础的振动与隔振.北京:中国建筑工业出版社.
于文福,2017.点源横向非均匀介质瑞利面波波场数值模拟研究.成都:西南交通大学,66-72.
岳庆霞,李杰,2008.近似Rayleigh地震波作用下地下综合管廊响应分析.防灾减灾工程学报,28(4):409-416.
Brinkgreve R.B.J.,Kumarswamy S.,Swolfs,W.M.,2016.PLAXIS 2D reference manual.Delft,The Netherlands:PLAXIS BV,286-290.
Kontoe S.,Zdravkovic L.,Potts D.M.,2009.An assessment of the domain reduction method as an advanced boundary condition and some pitfalls in the use of conventional absorbing boundaries.International Journal for Numerical and Analytical Methods in Geomechanics,33(3):309-330.
Lamb H.,1904.On the propagation of tremors over the surface of an elastic solid.Philosophical Transactions of the Royal Society of London.Series A,Containing Papers of a Mathematical or Physical Character,203:1-42.
Woods R.D.,1968.Screening of surface waves in soils.Journal of Soil Mechanics and Foundations Division ASCE,94(SM4):951-979.
Yu W.F.,Liu Z.P.,2015.A numerical study of the Rayleigh wave particle motions excited by a point source and
Poisson’s ratio for lateral inhomogeneous half-spaces.Journal of Applied Geophysics,123:242-255.