层状半空间中洞室对入射平面SV波的散射
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摘要
利用间接边界元法,在频域内求解了层状弹性半空间中洞室对入射平面SV波的散射问题。通过自由场反应分析,求得假想洞室边界上各点位移和各单元应力响应。在洞室边界各个单元上施加虚拟分布荷载,求得位移和应力的格林函数。根据应力边界条件确定虚拟分布荷载,将自由场位移响应和虚拟分布荷载产生的位移响应叠加起来,即得到问题的解答。比较了层状半空间和均匀半空间中洞室对入射平面SV波的放大作用。结果表明,层状半空间情况有可能导致较大的地表位移幅值,尤其是对于较低频率入射波。
Scattering of SV waves by a cavity in a layered half-space was analyzed by indirect boundary element method in frequency domain.The free-field displacements and stresses were calculated on the line which will form the surface of the cavity.Then fictitious distributed loads were applied on the same line to calculated Green’s functions for displacements and stresses.The amplitudes of the fictitious distributed loads were determined by the boundary conditions,and the displacement response arising from the waves in the free field and from the fictitious distributed loads were then summed up to obtain the solution.The amplification of the incident SV waves by a cavity in a homogeneous and a layered half-space were compared;and numerical results showed that larger surface displacement amplitude may be resulted in the case of layered half-space,especially for low-frequency waves.
Scattering of SV waves by a cavity in a layered half-space was analyzed by indirect boundary element method in frequency domain.The free-field displacements and stresses were calculated on the line which will form the surface of the cavity.Then fictitious distributed loads were applied on the same line to calculated Green’s functions for displacements and stresses.The amplitudes of the fictitious distributed loads were determined by the boundary conditions,and the displacement response arising from the waves in the free field and from the fictitious distributed loads were then summed up to obtain the solution.The amplification of the incident SV waves by a cavity in a homogeneous and a layered half-space were compared;and numerical results showed that larger surface displacement amplitude may be resulted in the case of layered half-space,especially for low-frequency waves.
引文
[1]Liang J,Zhang H,Lee V W.A series solution for surface motion amplification due to underground twin tunnels:incident SV waves[J].Earthquake Engineering and Engineering Vibration,2003,2(2):289-298.
[2]梁建文,张浩,Lee V W.地下洞室群对地面运动影响问题的级数解答-P波入射[J].地震学报,2004,26(3):269-280.LIANG Jian-wen,ZHANG Hao,Vincent W Lee.A series solution for surface motion amplification due to underground group cavities:incident P waves[J].Acta Seismologica Sinica,2004,26(3):269-280.
[3]Pao Y H,Mow C C.Diffraction of Elastic Waves and Dynamic Stress Concentrations[M].New York:Crane Russak and Company Inc.,1973.
[4]Lee V W.On deformations of near a circular underground cavity subjected to Incident SH-waves[A].Proceedings of Symposium on Applications of Computer Methods in Engineering[C].Los Angeles:University of Southern California,1977,951-962.
[5]Lee V W,Karl J.Diffraction of SV waves by underground,circular,cylindrical cavities[J].Soil Dynamics and Earthquake Engineering,1992,11:445-456.
[6]Lee V W,Karl J.On deformations of near a circular underground cavity subjected to incident plane P waves[J].European Journal of Earthquake Engineering,1993,(1):29-36.
[7]Davis C A,Lee V W,Bardet J P.Transverse response of underground cavities and pipes to incident SV waves[J].Earthquake Engineering and Structural Dynamics,2001,30:383-410.
[8]Wolf J P.Dynamic Soil-Structure Interaction[M].Englewood Cliffs:Prentice-Hall,1985.
[9]Vogt R F,Wolf J P,Bachmann H.Wave scattering by a canyon of arbitrary shape in a layered half space[J].Earthquake Engineering and Structural Dynamic,1988,16:803-812.
[10]梁建文,纪晓东,Lee V W.地下圆形衬砌隧道对沿线地震动的影响:(I)级数解[J].岩土力学,2005,26(4):520-524.LIANG Jian-wen,JI Xiao-dong,Vincent W lee.Effects of an underground lined tunnel on ground motion(I):series solution[J].Rock and Soil Mechanics,2005,26(4):520-524.
[11]梁建文,纪晓东,Lee V W.地下圆形衬砌隧道对沿线地震动的影响:(II)数值结果[J].岩土力学,2005,26(5):687-692.LIANG Jian-wen,JI Xiao-dong,Vincent W lee.Effects of an underground lined tunnel on ground motion(II):numerical results[J].Rock and Soil Mechanics,2005,26(5):687-692.
[2]梁建文,张浩,Lee V W.地下洞室群对地面运动影响问题的级数解答-P波入射[J].地震学报,2004,26(3):269-280.LIANG Jian-wen,ZHANG Hao,Vincent W Lee.A series solution for surface motion amplification due to underground group cavities:incident P waves[J].Acta Seismologica Sinica,2004,26(3):269-280.
[3]Pao Y H,Mow C C.Diffraction of Elastic Waves and Dynamic Stress Concentrations[M].New York:Crane Russak and Company Inc.,1973.
[4]Lee V W.On deformations of near a circular underground cavity subjected to Incident SH-waves[A].Proceedings of Symposium on Applications of Computer Methods in Engineering[C].Los Angeles:University of Southern California,1977,951-962.
[5]Lee V W,Karl J.Diffraction of SV waves by underground,circular,cylindrical cavities[J].Soil Dynamics and Earthquake Engineering,1992,11:445-456.
[6]Lee V W,Karl J.On deformations of near a circular underground cavity subjected to incident plane P waves[J].European Journal of Earthquake Engineering,1993,(1):29-36.
[7]Davis C A,Lee V W,Bardet J P.Transverse response of underground cavities and pipes to incident SV waves[J].Earthquake Engineering and Structural Dynamics,2001,30:383-410.
[8]Wolf J P.Dynamic Soil-Structure Interaction[M].Englewood Cliffs:Prentice-Hall,1985.
[9]Vogt R F,Wolf J P,Bachmann H.Wave scattering by a canyon of arbitrary shape in a layered half space[J].Earthquake Engineering and Structural Dynamic,1988,16:803-812.
[10]梁建文,纪晓东,Lee V W.地下圆形衬砌隧道对沿线地震动的影响:(I)级数解[J].岩土力学,2005,26(4):520-524.LIANG Jian-wen,JI Xiao-dong,Vincent W lee.Effects of an underground lined tunnel on ground motion(I):series solution[J].Rock and Soil Mechanics,2005,26(4):520-524.
[11]梁建文,纪晓东,Lee V W.地下圆形衬砌隧道对沿线地震动的影响:(II)数值结果[J].岩土力学,2005,26(5):687-692.LIANG Jian-wen,JI Xiao-dong,Vincent W lee.Effects of an underground lined tunnel on ground motion(II):numerical results[J].Rock and Soil Mechanics,2005,26(5):687-692.
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