软土隧道横向抗震分析的简化响应位移法
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摘要
响应位移法能够反映软土隧道在地震荷载作用下的动力反应特性,是一种简便实用的隧道抗震设计简化分析方法。以方形截面隧道为例,采用地层-结构整体动力有限元方法,验证了响应位移法的准确性与合理性;为了简化响应位移法的计算过程,基于平面应变假定,采用弹性理论的复变函数方法推导了土弹簧刚度的解析表达式,并与有限元解进行了对比分析。将土弹簧刚度的解析表达式应用到响应位移法的计算中,同时采用地层剪应力及自由场地震反应位移的简化计算模式,将简化后的响应位移法和整体动力有限元法进行了对比分析,验证了简化方法的可行性。
Response displacement method is a kind of simple and practical analysis method for aseismic design of soft soil tunnel,for the method can reflect dynamic reaction behavior of soft soil tunnel under aseismic load.Taking square section tunnel for example,the accuracy of the method has been verified by comparing its predictions with results from a soil-structure whole dynamic finite element method.Based on plane strain assumption,the analytical expression for soil spring stiffness has been deduced from the function of complex variable method in elastic theory for the purpose of simplifying the calculation process of response displacement method.The analytical solution for soil spring stiffness has been verified by comparing its predictions with results from finite element method.The analytical expression for soil spring stiffness has been applied to response displacement method.Meanwhile,simplified calculation models for shear stress and seismic response displacement of free soil field have been adopted.The whole dynamic finite element method has been used to validate the accuracy of simplified response displacement method for transverse secion aseismic analysis of soft soil tunnel.
Response displacement method is a kind of simple and practical analysis method for aseismic design of soft soil tunnel,for the method can reflect dynamic reaction behavior of soft soil tunnel under aseismic load.Taking square section tunnel for example,the accuracy of the method has been verified by comparing its predictions with results from a soil-structure whole dynamic finite element method.Based on plane strain assumption,the analytical expression for soil spring stiffness has been deduced from the function of complex variable method in elastic theory for the purpose of simplifying the calculation process of response displacement method.The analytical solution for soil spring stiffness has been verified by comparing its predictions with results from finite element method.The analytical expression for soil spring stiffness has been applied to response displacement method.Meanwhile,simplified calculation models for shear stress and seismic response displacement of free soil field have been adopted.The whole dynamic finite element method has been used to validate the accuracy of simplified response displacement method for transverse secion aseismic analysis of soft soil tunnel.
引文
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[10]黄茂松,曹杰.隧道地震响应简化分析与动力离心试验验证[J].岩石力学与工程学报,2010,29(2):271-280.HUANG Mao-song,CAO Jie.Simplified analysis oftunnel earthquake response and centrifuge modelingcalibration[J].Chinese Journal of Rock Mechanics andEngineering,2010,29(2):271-280.
[11]WANG J N.Seismic design of tunnels:A state-of-the-artapproach[M].New York:[s.n.],1993.
[12]Newark N M.Problems in wave propagation in soil androck[C]//Proceedings of the International Symposium onWave Propagation and Dynamic Properties of EarthMaterials.Albuquerque:[s.n.],1968:7-26.
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[14]THOMAS R K.Earthquake design criteria for subways[J].Journal of the Structural Division,ASCE,1969,(6):1213-1231.
[15]BURNS J Q,RICHARD R M.Attenuation of stresses forburied cylinders[C]//Proceedings of the Symposium onSoil-Structure Interaction.Arizona:University of Arizona,1964:378-392.
[16]吴家龙.弹性力学[M].北京:高等教育出版社,2002.
[2]PENZIEN J,WU C.Stresses in linings of boredtunnels[J].Earthquake Engineering and StructuralDynamics,1998,27:283-300.
[3]PENZIEN J.Seismically induced cracking of tunnellinings[J].Earthquake Engineering and StructuralDynamics,2000,29:683-691.
[4]DAVIS C A,LEE V W,BARDET J P.Transverseresponse of underground cavities and pipes to incident SVwaves[J].Earthquake Engineering and StructuralDynamics,2001,30:383-410.
[5]HASHASH Y M A,PARK D,YAO J I.Ovalingdeformations of circular tunnels under seismic loading,anupdate on seismic design and analysis of undergroundstructures[J].Tunnelling and Underground SpaceTechnology,2005,20:435-441.
[6]HUO H,BOBET A,FERNANDEZ G,et al.Analyticalsolution for deep rectangular structures subjected tofar-field shear stresses[J].Tunnelling and UndergroundSpace Technology,2006,21:613-625.
[7]张栋梁,杨林德,谢永利,等.盾构隧道抗震设计计算的解析解[J].岩石力学与工程学报,2008,27(3):543-549.ZHANG Dong-liang,YANG Lin-De,XIE Yong-li,et al.Analytical solution for aseismic design calculation ofshield tunnels[J].Chinese Journal of Rock Mechanicsand Engineering,2008,27(3):543-549.
[8]GIL L M,HERNANDEZ E,FUENTE P.Simplifiedtransverse seismic analysis of buried structures[J].SoilDynamic and Earthquake Engineering,2001,21:735-740.
[9]PAKBAZ M C,YAREEVAND A.2-D analysis of circulartunnel against earthquake loading[J].Tunnelling andUnderground Space Technology,2005,20:411-417.
[10]黄茂松,曹杰.隧道地震响应简化分析与动力离心试验验证[J].岩石力学与工程学报,2010,29(2):271-280.HUANG Mao-song,CAO Jie.Simplified analysis oftunnel earthquake response and centrifuge modelingcalibration[J].Chinese Journal of Rock Mechanics andEngineering,2010,29(2):271-280.
[11]WANG J N.Seismic design of tunnels:A state-of-the-artapproach[M].New York:[s.n.],1993.
[12]Newark N M.Problems in wave propagation in soil androck[C]//Proceedings of the International Symposium onWave Propagation and Dynamic Properties of EarthMaterials.Albuquerque:[s.n.],1968:7-26.
[13]川岛一彦.地下构筑物の耐震设计[M].日本:鹿岛出版会,1994.
[14]THOMAS R K.Earthquake design criteria for subways[J].Journal of the Structural Division,ASCE,1969,(6):1213-1231.
[15]BURNS J Q,RICHARD R M.Attenuation of stresses forburied cylinders[C]//Proceedings of the Symposium onSoil-Structure Interaction.Arizona:University of Arizona,1964:378-392.
[16]吴家龙.弹性力学[M].北京:高等教育出版社,2002.
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