非均质无限地基上高拱坝的动力响应分析
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摘要
地震作用下拱坝-无限地基的动力相互作用将对拱坝的地震响应产生重要影响。虽然很多学者曾经提出过各种相互作用的计算模型,但是绝大多数都是基于均质地基或有限地基假定的。利用比例边界有限元方法能够方便地模拟非均质无限域的优点,研究非均质无限地基对双曲高拱坝动力响应的影响。拱坝、地基和库水都利用比例边界有限元方法模拟,从而减少大量的计算量。在假定地基弹性模量随深度按指数变化的前提下,分析研究210 m高的大岗山双曲拱坝分别坐落在无质量地基、均质无限地基和非均质无限地基3种情况下的拱坝加速度频响曲线。通过与刚性较大的重力坝结构对比发现,无限地基的远场非均质特性对拱坝的动力响应影响较小。这是因为与重力坝不同,双曲高拱坝坝体与坝基之间的连接相对较为柔性,所以远场地基刚度变化对拱坝地震响应的影响较小。经进一步对近场地基刚度变化的分析发现,近场地基对拱坝地震响应产生一定影响。分析结果具有普遍意义,对强震区的高拱坝建设可以提供重要参考。
Dynamic interaction between arch dam and unbounded foundation has great significance on the seismic response of dam structure.Although various computational models for arch dam-foundation interaction have been developed by researchers,most of these models were based on the assumption of uniform homogeneous foundation medium.Taking advantages of the scaled boundary finite element method(SBFEM),the influence of the foundation inhomogeneity on the seismic response of high arch dams is studied.The arch dam,the unbounded foundation and the reservoir are all modeled by the SBFEM.Discretization is carried out only on dam-foundation interface and the surfaces of dam structure,thus the computational effort is reduced to a great extent.Assuming that the elastic modulus of the unbounded foundation varies according to an exponential law along the depth,complex frequency-response functions of a 210 m high double curvature arch dam are calculated.Three cases have been studied and compared,namely,massless foundation,homogeneous unbounded foundation and inhomogeneous unbounded foundation.It is found that,in contrast with the case of gravity dams,the foundation inhomogeneity brings little influence on the seismic response of arch dams.This phenomenon can be physically explained as follows.Unlike the gravity dam,where the connection between the dam and the foundation is very massive,the connection between the arch dam and the foundation is more flexible;far-field foundation impedance has little influence on the seismic response of the dam,only the near-field impedance affects the arch dam response to some extent.In order to get a better understanding of the effects of the near-field impedance,some cases of the variation of the near-field foundation models have been examined.The general tend of the conclusions is applicable for the design of high arch dams located in high seismic area.
Dynamic interaction between arch dam and unbounded foundation has great significance on the seismic response of dam structure.Although various computational models for arch dam-foundation interaction have been developed by researchers,most of these models were based on the assumption of uniform homogeneous foundation medium.Taking advantages of the scaled boundary finite element method(SBFEM),the influence of the foundation inhomogeneity on the seismic response of high arch dams is studied.The arch dam,the unbounded foundation and the reservoir are all modeled by the SBFEM.Discretization is carried out only on dam-foundation interface and the surfaces of dam structure,thus the computational effort is reduced to a great extent.Assuming that the elastic modulus of the unbounded foundation varies according to an exponential law along the depth,complex frequency-response functions of a 210 m high double curvature arch dam are calculated.Three cases have been studied and compared,namely,massless foundation,homogeneous unbounded foundation and inhomogeneous unbounded foundation.It is found that,in contrast with the case of gravity dams,the foundation inhomogeneity brings little influence on the seismic response of arch dams.This phenomenon can be physically explained as follows.Unlike the gravity dam,where the connection between the dam and the foundation is very massive,the connection between the arch dam and the foundation is more flexible;far-field foundation impedance has little influence on the seismic response of the dam,only the near-field impedance affects the arch dam response to some extent.In order to get a better understanding of the effects of the near-field impedance,some cases of the variation of the near-field foundation models have been examined.The general tend of the conclusions is applicable for the design of high arch dams located in high seismic area.
引文
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[12]Genes M C,Kocak S.Dynamic soil-structure interaction analysis of layered unbounded media via a coupled finite element/boundary element/scaled boundary finite element model[J].International Journal for Numerical Methods in Engineering,2005,62(6):798-823.
[13]Doherty J P,Deeks A J.Scaled boundary finite-element analysis of a non-homogenous elastic half-space[J].International Journal for Numerical Methods in Engineering,2003,57(7):955-973.
[14]Doherty J P,Deeks A J.Elastic response of circular footings embedded in a non-homogeneous half-space[J].Geotechnique,2003,53(8):703-714.
[15]Doherty J P,Deeks A J.Scaled boundary finite-element analysis of a non-homogeneous axisymmetric domain subjected to general loading[J].International Journal for Numerical and Analytical Methods in Geomechanics,2003,27(10):813-835.
[16]杜建国,林皋,钟红.基于锥体理论的三维拱坝无限地基SBFEM模型[J].水电能源科学,2006,24(1):25-29.(Du Jianguo,Lin Gao,Zhong Hong.Scaled boundary finite element method model of three-dimensional unbounded foundation of arch dams based on cone theory[J].Water Resources and Power,2006,24(1):25-29.(in Chinese))
[17]Bartels R H,Stewart G W.Solution of the matrix equation AX+XB=C[J].Communication of the ACM,1972,15(9):820-826.
[18]林皋,杜建国.基于SBFEM的坝-库水相互作用分析[J].大连理工大学学报,2005,45(5):723-729.(Lin Gao,Du Jianguo.Analysis of dam-reservoir interaction based on SBFEM[J].Journal of Dalian University of Technology,2005,45(5):723-729.(in Chinese))
[19]吴健,金峰,张楚汉,等.无限地基辐射阻尼对溪洛渡拱坝地震响应的影响[J].岩土工程学报,2002,24(6):716-719.(Wu Jian,Jin Feng,Zhang Chuhan.Effects of radiation damping of infinite foundation on seismic response of the Xiluodu arch dam[J].Chinese Jounal of Geotechnical Engineering,2002,24(6):716-719.(in Chinese))
[20]Proulx J,Darbre G R,Kamileris N.Analytical and experimental investigation of damping in arch dams based on recorded earthquakes[A].In:Proc.the 13th World Conf.on Earthquake Engineering[C].Vancouver,Canada,[s.n.],2004.68.
[2]金峰,张楚汉,王光纶.结构地基相互作用的FE-BE-IBE耦合模型[J].清华大学学报,1993,33(2):17-24.(Jin Feng,Zhang Chuhan,Wang Guanglun.A coupling FE-BE-IBE model for structure-foundation interactions[J].Journal of Tsinghua University,1993,33(2):17-24.(in Chinese))
[3]杜修力,陈厚群,侯顺载.拱坝系统三维非线性地震波动分析[J].地震工程与工程振动,1996,16(3):39-47.(Du Xiuli,Chen Houqun,Hou Shunzai.Three-dimensional nonlinear seismic wave analysis of dam system[J].Earthquake Engineering and Engineering Vibration,1996,16(3):39-47.(in Chinese))
[4]Wolf J P,Song C H.Finite-element Modelling of Unbounded Media[M].New York:John Wiley and Sonslnc,1996.
[5]Doherty J P,Deeks A J.Application of the scaled boundary finite-element method to offshore foundation systems[A].In:Proc.the 12th Int.Offshore and Polar Eng.Conf.[C].Kitakyusha:[s.n.],2002.706-711.
[6]Li B,Cheng L,Deeks A J.Wave diffraction by vertical cylinder using the scaled boundary finite element method[A].In:World Congress on Computational Mechanics VI[C].Beijing:[s.n.],2004.313.
[7]Chidgzey S R,Deeks A J.Higher order terms of elastic crack tip field using the scaled boundary finite element method[A].In:World Congress on Computational Mechanics VI[C].Beijing:[s.n.],2004.310.
[8]Ekevid T,Wiberg N E.Wave propagation related to high-speed train—a scaled boundary FE-approach for unbounded domain[J].Comput.Methods Appl.Mech.Engrg.,2002,191(36):3 947-3 964.第25卷增2杜建国等.非均质无限地基上高拱坝的动力响应分析?4111?
[9]Zhang X,Wegner J L,Haddow J B.Three-dimensional dynamic soil-structure interaction analysis in the time domain[J].Earthquake Engineering and Structural Dynamics,1999,28(12):1 501-1 524.
[10]Wegner J L,Zhang X.Free-vibration analysis of a three-dimensional soil-structure system[J].Earthquake Engineering and Structural Dynamics,2001,30(1):43-57.
[11]Yan J Y,Zhang C H,Jin F.A coupling procedure of FE and SBFE for soil-structure interaction in time domain[J].International Journal for Numerical Methods in Engineering,2004,59(11):1 453-1 471.
[12]Genes M C,Kocak S.Dynamic soil-structure interaction analysis of layered unbounded media via a coupled finite element/boundary element/scaled boundary finite element model[J].International Journal for Numerical Methods in Engineering,2005,62(6):798-823.
[13]Doherty J P,Deeks A J.Scaled boundary finite-element analysis of a non-homogenous elastic half-space[J].International Journal for Numerical Methods in Engineering,2003,57(7):955-973.
[14]Doherty J P,Deeks A J.Elastic response of circular footings embedded in a non-homogeneous half-space[J].Geotechnique,2003,53(8):703-714.
[15]Doherty J P,Deeks A J.Scaled boundary finite-element analysis of a non-homogeneous axisymmetric domain subjected to general loading[J].International Journal for Numerical and Analytical Methods in Geomechanics,2003,27(10):813-835.
[16]杜建国,林皋,钟红.基于锥体理论的三维拱坝无限地基SBFEM模型[J].水电能源科学,2006,24(1):25-29.(Du Jianguo,Lin Gao,Zhong Hong.Scaled boundary finite element method model of three-dimensional unbounded foundation of arch dams based on cone theory[J].Water Resources and Power,2006,24(1):25-29.(in Chinese))
[17]Bartels R H,Stewart G W.Solution of the matrix equation AX+XB=C[J].Communication of the ACM,1972,15(9):820-826.
[18]林皋,杜建国.基于SBFEM的坝-库水相互作用分析[J].大连理工大学学报,2005,45(5):723-729.(Lin Gao,Du Jianguo.Analysis of dam-reservoir interaction based on SBFEM[J].Journal of Dalian University of Technology,2005,45(5):723-729.(in Chinese))
[19]吴健,金峰,张楚汉,等.无限地基辐射阻尼对溪洛渡拱坝地震响应的影响[J].岩土工程学报,2002,24(6):716-719.(Wu Jian,Jin Feng,Zhang Chuhan.Effects of radiation damping of infinite foundation on seismic response of the Xiluodu arch dam[J].Chinese Jounal of Geotechnical Engineering,2002,24(6):716-719.(in Chinese))
[20]Proulx J,Darbre G R,Kamileris N.Analytical and experimental investigation of damping in arch dams based on recorded earthquakes[A].In:Proc.the 13th World Conf.on Earthquake Engineering[C].Vancouver,Canada,[s.n.],2004.68.
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