饱和土隧道内集中荷载作用下振动位移反应的Green函数解答
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摘要
饱和土隧道在集中荷载作用下的隧道底面振动位移反应关系着饱和土的液化、震陷。根据饱和土中方形隧道的断面特征,采用两相饱和介质边界元法Green函数以及推导出的Lamb积分方程,计算出机车的集中振动引起的隧道底面振动反应表达式。结合具体算例,数值计算后表明结果可信。
Saturated soil under a concentrated dynamic load in a tunnel will cause vibration displacements, which concerns the liquefaction, and shaked subsidence. The paper will be based on the tunnel’s section feature located in saturation soil, adopting a two-phase saturated medium’s Green function in BEM and Lamb integral equation to infer from Betti theorem to figure out the displacement function of the underside in the tunnel arose by vehicle-engine vibrations. Combined with the exact example, the value after being calculated indicates that the result is reliable.
Saturated soil under a concentrated dynamic load in a tunnel will cause vibration displacements, which concerns the liquefaction, and shaked subsidence. The paper will be based on the tunnel’s section feature located in saturation soil, adopting a two-phase saturated medium’s Green function in BEM and Lamb integral equation to infer from Betti theorem to figure out the displacement function of the underside in the tunnel arose by vehicle-engine vibrations. Combined with the exact example, the value after being calculated indicates that the result is reliable.
引文
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[9]苗天德,朱久江,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.Miao Tiande,Zhu Jiujiang,Ding Boyang.Essay on constitutive relation of wave propagation in saturated porous media[J].Acta Mechanica Sinica,1995,27(5):536―543.(in Chinese)
[10]De Hoop A T.The surface line source problem[J].Applied Scientific Research,1958,B:349―356.
[11]Manolis G D A.Comparative study on three boundary element approaches to problems in elastodynamics[J].International Journal of Numerical Methods in Engineering,1983,19:73―91.
[12]丁伯阳,丁翠红,陈禹.集中力作用下两相饱和介质二维位移场Green函数[J].应用数学和力学,2004,25(8):869―874.Ding Boyang,Ding Cuihong,Chen Yu.Green function on two-phase saturated medium by concentrated force in two-dimensional displacement field[J].Applied Mathematics and Mechanics,2004,25(8):951―956.(in Chinese)
[2]Biot M A.Mechanics of deformation and acoustic propagation in porous media[J].Journal of Applied Physics,1962,33:1482―1498.
[3]Biot M A.Theory of propagation of elastic wave in a fluid-saturated soil[J].Journal of the Acoustical Society America,1956,28:168―178.
[4]刘银斌,李幼铭,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.Liu Yinbin,Li Youming,Wu Rushan.Seismic wave propagation in transversely isotropic porous media[J].Acta Geophysica Sinica,1994,37(4):499―514.(in Chinese)
[5]丁伯阳,樊良本,吴建华.两相饱和介质中的集中力点源位移场解与应用[J].地球物理学报,1999,42(6):800―808.Ding Boyang,Fan Liangben.Wu Jianhua.The Green function and wave field on two-phase saturated medium by concentrated force[J].Chinese Journal of Geophysics,1999,42(6):800―808.(in Chinese)
[6]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.Ding Boyang,Ding Cuihong,Meng Fanli.The Green function on two-phase saturated medium by concentrated force[J].Acta Mechanica Sinica,2001,33(2):234―241.(in Chinese)
[7]艾龙根,舒胡毕.弹性动力学[M].戈革,译.北京:石油工业出版社,1984.Erigen A C,Suhubi E S.Elastic dynamics Vol.2linear theory[M].New York:Academic Press,1975.(in English)
[8]丁伯阳,孟凡丽,胡敏云.两相饱和介质的弹性位错震源矢量与静态位移场[J].地震学报,2001,23(3):239―245.Ding Boyang,Meng Fanli,Hu Minyun.The source vector and static displacement field by elastic dislocation on the two-phase saturated medium[J].Acta Seismologica Sinica,2001,14(3):251―258.(in Chinese)
[9]苗天德,朱久江,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.Miao Tiande,Zhu Jiujiang,Ding Boyang.Essay on constitutive relation of wave propagation in saturated porous media[J].Acta Mechanica Sinica,1995,27(5):536―543.(in Chinese)
[10]De Hoop A T.The surface line source problem[J].Applied Scientific Research,1958,B:349―356.
[11]Manolis G D A.Comparative study on three boundary element approaches to problems in elastodynamics[J].International Journal of Numerical Methods in Engineering,1983,19:73―91.
[12]丁伯阳,丁翠红,陈禹.集中力作用下两相饱和介质二维位移场Green函数[J].应用数学和力学,2004,25(8):869―874.Ding Boyang,Ding Cuihong,Chen Yu.Green function on two-phase saturated medium by concentrated force in two-dimensional displacement field[J].Applied Mathematics and Mechanics,2004,25(8):951―956.(in Chinese)
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