圆形隧道抗震分析若干近似解析方法比较研究
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摘要
为避免盾构隧道抗震设计动力时程分析的复杂性和减小计算工作量,对圆形隧道抗震设计的3种近似解析方法进行了比较.第1种是基于复变函数的近似解析方法,并用成层地层振动方程获得的地层剪切力进行了改进;第2种是基于贝塞尔函数的近似解析方法;第3种是基于弹性力学的近似解析方法.分别采用上述3种近似解析方法和反应位移法对某隧道进行了抗震分析.结果表明:前2种近似解析方法的计算结果较接近,规律大致相同,因此可用二者计算结果的最不利组合进行抗震分析;第3种近似解析方法较为粗略,只可用于圆形隧道抗震设计的前期估算.
In order to cut down the complexity and workload of seismic analyses,three approximate analytical methods for seismic design of circular tunnels were discussed.The first one is based on the function of complex variable and improved by using shear stresses in strata gained by the vibration equation for stratification strata,the second one is founded on the Bessel function,and the third method is grounded on the theory of elasticity mechanics.Seismic analyses of a circular tunnel were carried out respectively using the three analytical methods and by numerical calculation based on the seismic deformation method.The results show that the first two analytical methods can obtain relatively close results,so it is feasible to carry out the seismic analysis by the worst combination of their calculation results,and the third analytical method can be only used at the preliminary stage of seismic design.
In order to cut down the complexity and workload of seismic analyses,three approximate analytical methods for seismic design of circular tunnels were discussed.The first one is based on the function of complex variable and improved by using shear stresses in strata gained by the vibration equation for stratification strata,the second one is founded on the Bessel function,and the third method is grounded on the theory of elasticity mechanics.Seismic analyses of a circular tunnel were carried out respectively using the three analytical methods and by numerical calculation based on the seismic deformation method.The results show that the first two analytical methods can obtain relatively close results,so it is feasible to carry out the seismic analysis by the worst combination of their calculation results,and the third analytical method can be only used at the preliminary stage of seismic design.
引文
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[14]周健,苏燕,董鹏.软土地层地铁及地下构筑物抗震动力分析研究现状[J].地下空间,2003,23(2):173-178.ZHOU Jian,SU Yan,DONG Peng.Current situationof earthquake resistance of subway and undergroundstructures in soft soil[J].Underground Space,2003,23(2):173-178.
[15]林皋.地下结构的抗震设计[J].土木工程学报,1996,29(1):15-24.LIN Gao.Aseismic design of underground structure[J].China Civil Engineering Journal,1996,29(1):15-24.
[16]王俊民,江理平.弹性力学复习及解题指导[M].上海:同济大学出版社,2003:93.
[17]刘如山,胡少卿,石宏彬.地下结构抗震计算中拟静力法的地震荷载施加方法研究[J].岩土工程学报,2007,29(2):237-242.LIU Rushan,HU Shaoqing,SHI Hongbin.Study onseismic loading of pseudo-static approach used in theseismic design of underground structure[J].ChineseJournal of Geotechnical Engineering,2007,29(2):237-242.
[18]HE Chuan,KOIZUMI A.Study on seismic behaviorand seismic design methods in transverse direction ofshield tunnels[J].Structural Engineering andMechanics,2001,11(6):651-662.
[2]吕和林.一种用于浅埋隧道抗震分析的拟静力数值方法[J].西南交通大学学报,1999,36(3):316-319.L Helin.A pseudo-static numerical method used inaseismic analysis on shallow-buried tunnel[J].Journalof Southwest Jiaotong University,1999,36(3):316-319.
[3]吴林.基于反应位移法的隧道结构抗震计算与分析[J].路基工程,2010(5):142-144.WU Lin.Calculation and analysis of tunnel structureearthquake resistance based on response displacementmethod[J].Subgrade Engineering,2010(5):142-144.
[4]晏启祥,马婷婷,何川,等.盾构隧道抗震分析近似解析解及其应用[J].西南交通大学学报,2010,45(3):341-345.YAN Qixiang,MA Tingting,HE Chuan,et al.Theapproximate formula method and application of aseismicanalysis on shield tunnel[J].Journal of SouthwestJiaotong University,2010,45(3):341-345.
[5]川島一彦.地下构造物の耐震设计[M].東京:鹿岛出版会,1994:31-33.
[6]VERRUIJT A.A complex variable solution for adeforming circular tunnel in an elastic half plane[J].International Journal for Numerical and AnalyticalMethod in Geomechanics,1997,21(2):77-89.
[7]VERRUIJTA.Deformation of an elastic half plane witha circular tunnel[J].International Journal of Solids andStructures,1998,35(21):2795-2804.
[8]EXADAKTYLOS G E,LIOLIOS P A,STAVRO-POULOU M C.Asemi-analytical elastic stressdisplacement solution for notched circular openings inrocks[J].International Journal of Solids andStructures,2003,40(5):1165-1187.
[9]HUO H,BOBETA,FERNANDEZ G,et al.Analyticalsolution for deep rectangular structures subjected to far-field shear stresses[J].Tunneling and UndergroundSpace Technology,2006,21(6):613-625.
[10]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):544-549.ZHANG Dongliang,YANG Linde,XIE Yongli,et al.Analytical solution for seismic design calculation ofshield tunnels[J].Chinese Journal of Rock Mechanicsand Engineering,2008,27(3):544-549.
[11]边金,陶连金,张印涛,等.地下结构抗震设计方法的比较与分析[J].现代隧道技术,2008,45(6):50-55.BIAN Jin,TAO Lianjin,ZHANG Yintao,et al.Thecomparisons and analysis of underground structure saseismic design[J].Modern Tunneling Technology,2008,45(6):50-55.
[12]黄先锋.地下结构的抗震计算:位移响应法[J].铁道建筑,1999(6):3-6.HUANG Xianfeng.Seismic calculation of undergroundstructure:the displacement response method[J].Railway Engineering,1999(6):3-6.
[13]耿萍,何川,晏启祥.盾构隧道纵向地震响应分析[J].西南交通大学学报,2007,42(3):283-287.GENG Ping,HE Chuan,YAN Qixiang.Analysis oflongitudinal seismic response of shield tunnel[J].Journal of Southwest Jiaotong University,2007,42(3):283-287.
[14]周健,苏燕,董鹏.软土地层地铁及地下构筑物抗震动力分析研究现状[J].地下空间,2003,23(2):173-178.ZHOU Jian,SU Yan,DONG Peng.Current situationof earthquake resistance of subway and undergroundstructures in soft soil[J].Underground Space,2003,23(2):173-178.
[15]林皋.地下结构的抗震设计[J].土木工程学报,1996,29(1):15-24.LIN Gao.Aseismic design of underground structure[J].China Civil Engineering Journal,1996,29(1):15-24.
[16]王俊民,江理平.弹性力学复习及解题指导[M].上海:同济大学出版社,2003:93.
[17]刘如山,胡少卿,石宏彬.地下结构抗震计算中拟静力法的地震荷载施加方法研究[J].岩土工程学报,2007,29(2):237-242.LIU Rushan,HU Shaoqing,SHI Hongbin.Study onseismic loading of pseudo-static approach used in theseismic design of underground structure[J].ChineseJournal of Geotechnical Engineering,2007,29(2):237-242.
[18]HE Chuan,KOIZUMI A.Study on seismic behaviorand seismic design methods in transverse direction ofshield tunnels[J].Structural Engineering andMechanics,2001,11(6):651-662.
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