Green函数对饱和土隧道内集中荷载作用振动位移反应的计算
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摘要
由于快速列车与城市地铁的发展,饱和土隧道内集中荷载作用的反应问题日显重要。G reen函数对辐射条件的满足,积分方程的精确解答,D irichlet条件下的通用性,使它对隧道内动荷载作用的土动力反应问题计算有着特有的优越性,作者根据已求得两相饱和介质G reen函数,利用Lamb积分公式,结合隧道断面特征,以解析积分法推导了集中冲击荷载与简谐荷载圆形断面隧道内振动位移反应表达式闭合解、反应时程曲线、瞬态和稳态的振动形态;并根据它们的单位脉冲响应函数结合Duham el积分求得隧道在地震荷载作用下的动力反应。另外窗形隧道受集中冲击荷载作用相关弹性波时程曲线也在文中给出。
The Green function has particular superiority in calculation of soil dynamic behavior due to that it meets the requirement of radiation condition,and it is an accurate solution of the concerned integral equation,so that it is widely used in BEM.Based on the sectional feature of tunnel located in saturated soil,the displacement tremor was analysed by use of analytic integration method.With Green function,the closed solutions of vibration displacement response under impact or harmonic loads acting on inside of saturated soil tunnel,the travel time history of elastic wave and the transient and ordinary modes of vibration were obtained.Moreover on the basis of impulse response function and with Duhamel's integration,the seismic response of tunnel was acquired.The results with respect to the tunnel of common window shape were also presented.
The Green function has particular superiority in calculation of soil dynamic behavior due to that it meets the requirement of radiation condition,and it is an accurate solution of the concerned integral equation,so that it is widely used in BEM.Based on the sectional feature of tunnel located in saturated soil,the displacement tremor was analysed by use of analytic integration method.With Green function,the closed solutions of vibration displacement response under impact or harmonic loads acting on inside of saturated soil tunnel,the travel time history of elastic wave and the transient and ordinary modes of vibration were obtained.Moreover on the basis of impulse response function and with Duhamel's integration,the seismic response of tunnel was acquired.The results with respect to the tunnel of common window shape were also presented.
引文
[1]Burk M,Kingsbury HB.Response of Poroelastic Layers to Mov-ing Loads[J].Int.J.Solid Struct,1984,20:499-511.
[2]Siddharthan R,Zafir Z,Norris,G M.Moving Load Responseof Layered Soil.I.Formulation[J].J.Eng.Mech,1993,119:2052-2071.
[3]Lu Jian-Fei,Jing Dong-Sheng,Lee Tsung L L.Dynamic re-sponse of a piecewise circular tunnel embedded in a poroelasticmedium[J].Soil Dyn.and Earthq.Eng,2007,27:875-891.
[4]Forrest J A,Hunt H E M.Ground vibration generated bytrains in underground tunnels[J].Journal of Sound and Vi-bration,2006,294:706-736.
[5]Gupta S,Hussein MF M,Degrande G,et al.A comparisonof two numerical models for the prediction of vibrations fromunderground railway traffic[J].Soil Dyn.and Earthq.Eng,2007,27:608-624.
[6]Biot MA.Mechanics of deformation and acoustic propagationin porous media[J].J.Appl.phys,1962,33:1482-1498.
[7]Biot MA.Theory of propagation of elastic wave in a fluid-satu-rated soi[J].l.J.Acoust.Soc.Amer.,1956,28:168-178.
[8]刘银屏,李幼民,吴如山.地震波在横观同性介质中的传播[J].地球物理学报,1994,37:499-514.
[9]Erigen A C,Suhubi E S.Elastic dynamics Vol.2 linear theo-ry[M].New York:Academic Press,1975.(中译本)弹性动力学戈革译(1984)石油工业出版社.
[10]苗天德,朱久佳,丁伯阳.对饱和多孔介质弹性波动问题中本构关系探讨[J].力学学报,1995.27(5):538-543.
[11]Ding Boyang,Fan Liangben,Wu Jianhua.The Green functionand wave field on two-phase saturated medium by concentratedforce[J].Chi.J.Geophys,1999,42(6):800-808.
[12]丁伯阳,丁翠红,孟凡丽.集中力作用下的两相饱和介质位移场Green函数[J].力学学报,2001,33(2):234-241.
[13]Ding Bo-yang,Meng Fan-li,HUMin-yun.The source vectorand static displacement field by elastic dislocation on the two-phase saturated medium[J].Acta Seis Mologica Sinica,14(3):251-258.
[14]De Hoop A T.The surface line source problem[J].Appl.Sci.Res.1958,B:349-356.
[15]Manolis G D A.Comparative study on three boundary elementapproaches to problems in elastodynamics[J].Int.J.Num.Meth Engng.,1983,19:73-91.
[16]Ding Boyang Ding Cuihong Chen Yu.Green function on two-phase saturated medium by concentrated force in two-dimen-sional displacement field[J].App.Math.Mech.2004.25(8):951-956.Springer-DOI:10.1007/BF02438804.
[17]Clough R W,Penzien J.Dynamics of Structures[M].NewYork:McGraw-Hill.1993
[2]Siddharthan R,Zafir Z,Norris,G M.Moving Load Responseof Layered Soil.I.Formulation[J].J.Eng.Mech,1993,119:2052-2071.
[3]Lu Jian-Fei,Jing Dong-Sheng,Lee Tsung L L.Dynamic re-sponse of a piecewise circular tunnel embedded in a poroelasticmedium[J].Soil Dyn.and Earthq.Eng,2007,27:875-891.
[4]Forrest J A,Hunt H E M.Ground vibration generated bytrains in underground tunnels[J].Journal of Sound and Vi-bration,2006,294:706-736.
[5]Gupta S,Hussein MF M,Degrande G,et al.A comparisonof two numerical models for the prediction of vibrations fromunderground railway traffic[J].Soil Dyn.and Earthq.Eng,2007,27:608-624.
[6]Biot MA.Mechanics of deformation and acoustic propagationin porous media[J].J.Appl.phys,1962,33:1482-1498.
[7]Biot MA.Theory of propagation of elastic wave in a fluid-satu-rated soi[J].l.J.Acoust.Soc.Amer.,1956,28:168-178.
[8]刘银屏,李幼民,吴如山.地震波在横观同性介质中的传播[J].地球物理学报,1994,37:499-514.
[9]Erigen A C,Suhubi E S.Elastic dynamics Vol.2 linear theo-ry[M].New York:Academic Press,1975.(中译本)弹性动力学戈革译(1984)石油工业出版社.
[10]苗天德,朱久佳,丁伯阳.对饱和多孔介质弹性波动问题中本构关系探讨[J].力学学报,1995.27(5):538-543.
[11]Ding Boyang,Fan Liangben,Wu Jianhua.The Green functionand wave field on two-phase saturated medium by concentratedforce[J].Chi.J.Geophys,1999,42(6):800-808.
[12]丁伯阳,丁翠红,孟凡丽.集中力作用下的两相饱和介质位移场Green函数[J].力学学报,2001,33(2):234-241.
[13]Ding Bo-yang,Meng Fan-li,HUMin-yun.The source vectorand static displacement field by elastic dislocation on the two-phase saturated medium[J].Acta Seis Mologica Sinica,14(3):251-258.
[14]De Hoop A T.The surface line source problem[J].Appl.Sci.Res.1958,B:349-356.
[15]Manolis G D A.Comparative study on three boundary elementapproaches to problems in elastodynamics[J].Int.J.Num.Meth Engng.,1983,19:73-91.
[16]Ding Boyang Ding Cuihong Chen Yu.Green function on two-phase saturated medium by concentrated force in two-dimen-sional displacement field[J].App.Math.Mech.2004.25(8):951-956.Springer-DOI:10.1007/BF02438804.
[17]Clough R W,Penzien J.Dynamics of Structures[M].NewYork:McGraw-Hill.1993
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