层状场地中二维沉积谷地对弹性波的三维散射
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摘要
为研究层状场地中二维沉积谷地对斜入射弹性波的三维散射问题,建立了求解问题的移动间接边界元方法。方法通过沿二维沉积谷地轴线方向的傅里叶变换将三维问题降为二维问题,进而在沉积谷地截面内进行边界单元的离散和求解,求得截面内的三维动力响应,然后将截面内的计算结果沿沉积谷地轴线方向进行波数展开即可求得任意位置动力响应。文中通过与前人结果的比较验证了方法的正确性,并以均匀半空间场地和基岩上单一土层场地为例进行了数值计算和分析,给出了一些有益的结论。
The indirect boundary element method(IBEM) is proposed to study the three-dimensional scattering by a two-dimensional valley embedded in a layered half-space.The wave-number transform has been applied in the valley's axis direction to reduce the three-dimensional problem to a plane strain problem.The dynamic problem is solved in a section perpendicular to the axis of the valley,and the three-dimensional responses of the valley and the layered site are obtained from the inverse wave-number expansion.The validity of the method is confirmed by comparison with related results,and numerical results and analyses are performed by taking the amplification of obliquely incident plane waves by an alluvial valley in a uniform half space and in one soil layer over half-space as examples to give some useful conclusions.
The indirect boundary element method(IBEM) is proposed to study the three-dimensional scattering by a two-dimensional valley embedded in a layered half-space.The wave-number transform has been applied in the valley's axis direction to reduce the three-dimensional problem to a plane strain problem.The dynamic problem is solved in a section perpendicular to the axis of the valley,and the three-dimensional responses of the valley and the layered site are obtained from the inverse wave-number expansion.The validity of the method is confirmed by comparison with related results,and numerical results and analyses are performed by taking the amplification of obliquely incident plane waves by an alluvial valley in a uniform half space and in one soil layer over half-space as examples to give some useful conclusions.
引文
[1]Trifunac M D.Surface motion of a semi-cylindrical alluvialvalley for incident plane SH waves[J].Bull Seism SocAm,1971,61:1755-1770
[2]Yuan X,Liao Z.Scattering of plane SH waves by a cylindricalalluvial valley of circular-arc cross-section[J].Earthq EngStruct Dynam,1995,24:1303-1313
[3]梁建文,严林隽,秦东.圆弧形沉积河谷场地在平面SV波入射下的动力响应[J].土木工程学报,2003,26(12):74-82(Liang Jianwen,Yan Linjun,Qin Dong.Dynamic response of circular-arc sedimentary valley siteunder incident plane SV waves[J].China CivilEngineering Journal,2003,26(12):74-82(in Chinese))
[4]梁建文,严林隽,李军伟,等.圆弧形沉积河谷场地在平面P波入射下的响应[J].岩土力学,2001,2:18-23(Liang Jianwen,Yan Linjun,Li Junwei,et al.Responseof circular-arc alluvial valleys under incident plane P waves[J].Rock and Soil Mechanics,2001,2:18-23(inChinese))
[5]Wong H L.Effect of surface topography on the diffractionof P,SV,and Rayleigh waves[J].Bull Seism Soc Am,1982,72:1167-1183
[6]Dravinski M,Mossessian T K.Scattering of plane harmonicP,SV,and Rayleigh waves by dipping layers of arbitraryshape[J].Bull Seism Soc Am,1987,77:212-235
[7]梁建文,巴振宁.弹性层状半空间中沉积谷地对入射平面SH波的放大作用[J].地震工程与工程振动,2007,27(3):1-9(Liang Jianwen,Ba Zhenning.Surface motionof an alluvial valley in layered half-space for incident planeSH waves[J].Journal of Earthquake Engineering andEngineering Vibration,2007,27(3):1-9(in Chinese))
[8]Sainchez-Sesma F J,Ramos-Martinez J,Campillo M.Anindirect boundary element method applied to simulate theseismic response of alluvial valleys for incident P,S andRayleigh Waves[J].Earthq Eng Struct Dyn,1993,22:279-295
[9]Kawase H,Aki K.A study on the response of a soft basinfor incident S,p and Rayleigh waves with special referenceto the long duration observed in Mexico city[J].BullSeism Soc Am,1989,79(5):1361-1382
[10]Geli L,Bard P Y,Bouchon M.The effect of topography onearthquake ground motion:a review and new results[J].Bull Seismol Soc Am,1988,78:42-63
[11]梁建文,魏新磊,Lee V W.圆弧型沉积谷地对平面SV波三维散射解析解[J].岩土工程学报,2009,31(9):1345-1353(Liang Jianwen,Wei Xinlei,Lee V W.3Dscattering of plane SV waves by a circular-arc alluvialvalley[J].Chinese Journal of Geotechnical Engineering,2009,31(9):1345-1353(in Chinese))
[12]梁建文,魏新磊,Lee V W.圆弧型沉积谷地对平面P波三维散射解析解[J].岩土力学,2010,31(2):461-470(Liang Jianwen,Wei Xinlei,Lee V W.3D scattering ofplane p waves by a circular-arc alluvial valley[J].Rockand Soil Mechanics,2010,31(2):461-470(in Chinese))
[13]Pedersen H,Campillo M,Sanchez-Sesma F J.Azimuthdependent wave amplification in alluvial valleys[J].SoilDyn Earthq Engng,1995,14:289-300
[14]De Barros F C P,Luco J E.Amplication of obliquelyincident waves by a cylindrical valley embedded in alayered half-space[J].Soil Dyn Earthq Engng,1995,14:163-175
[15]梁建文,巴振宁.三维层状场地精确动力刚度矩阵及格林函数[J].地震工程与工程振动,2007,27(5):7-17(Liang Jianwen,Ba Zhenning.Exact dynamic stiffnessmatices of 3-D layered site and its Green’s functions[J].Journal of Earthquake Engineering and EngineeringVibration,2007,27(5):7-17(in Chinese))
[16]巴振宁.层状半空间中格林函数和局部场地对弹性波的散射[D].天津:天津大学(Ba Zhenning.Green’sfunctions for layered half space and elastic wave scatteringby local sites[D].Tianjin:Tianjin University(inChinese))
[2]Yuan X,Liao Z.Scattering of plane SH waves by a cylindricalalluvial valley of circular-arc cross-section[J].Earthq EngStruct Dynam,1995,24:1303-1313
[3]梁建文,严林隽,秦东.圆弧形沉积河谷场地在平面SV波入射下的动力响应[J].土木工程学报,2003,26(12):74-82(Liang Jianwen,Yan Linjun,Qin Dong.Dynamic response of circular-arc sedimentary valley siteunder incident plane SV waves[J].China CivilEngineering Journal,2003,26(12):74-82(in Chinese))
[4]梁建文,严林隽,李军伟,等.圆弧形沉积河谷场地在平面P波入射下的响应[J].岩土力学,2001,2:18-23(Liang Jianwen,Yan Linjun,Li Junwei,et al.Responseof circular-arc alluvial valleys under incident plane P waves[J].Rock and Soil Mechanics,2001,2:18-23(inChinese))
[5]Wong H L.Effect of surface topography on the diffractionof P,SV,and Rayleigh waves[J].Bull Seism Soc Am,1982,72:1167-1183
[6]Dravinski M,Mossessian T K.Scattering of plane harmonicP,SV,and Rayleigh waves by dipping layers of arbitraryshape[J].Bull Seism Soc Am,1987,77:212-235
[7]梁建文,巴振宁.弹性层状半空间中沉积谷地对入射平面SH波的放大作用[J].地震工程与工程振动,2007,27(3):1-9(Liang Jianwen,Ba Zhenning.Surface motionof an alluvial valley in layered half-space for incident planeSH waves[J].Journal of Earthquake Engineering andEngineering Vibration,2007,27(3):1-9(in Chinese))
[8]Sainchez-Sesma F J,Ramos-Martinez J,Campillo M.Anindirect boundary element method applied to simulate theseismic response of alluvial valleys for incident P,S andRayleigh Waves[J].Earthq Eng Struct Dyn,1993,22:279-295
[9]Kawase H,Aki K.A study on the response of a soft basinfor incident S,p and Rayleigh waves with special referenceto the long duration observed in Mexico city[J].BullSeism Soc Am,1989,79(5):1361-1382
[10]Geli L,Bard P Y,Bouchon M.The effect of topography onearthquake ground motion:a review and new results[J].Bull Seismol Soc Am,1988,78:42-63
[11]梁建文,魏新磊,Lee V W.圆弧型沉积谷地对平面SV波三维散射解析解[J].岩土工程学报,2009,31(9):1345-1353(Liang Jianwen,Wei Xinlei,Lee V W.3Dscattering of plane SV waves by a circular-arc alluvialvalley[J].Chinese Journal of Geotechnical Engineering,2009,31(9):1345-1353(in Chinese))
[12]梁建文,魏新磊,Lee V W.圆弧型沉积谷地对平面P波三维散射解析解[J].岩土力学,2010,31(2):461-470(Liang Jianwen,Wei Xinlei,Lee V W.3D scattering ofplane p waves by a circular-arc alluvial valley[J].Rockand Soil Mechanics,2010,31(2):461-470(in Chinese))
[13]Pedersen H,Campillo M,Sanchez-Sesma F J.Azimuthdependent wave amplification in alluvial valleys[J].SoilDyn Earthq Engng,1995,14:289-300
[14]De Barros F C P,Luco J E.Amplication of obliquelyincident waves by a cylindrical valley embedded in alayered half-space[J].Soil Dyn Earthq Engng,1995,14:163-175
[15]梁建文,巴振宁.三维层状场地精确动力刚度矩阵及格林函数[J].地震工程与工程振动,2007,27(5):7-17(Liang Jianwen,Ba Zhenning.Exact dynamic stiffnessmatices of 3-D layered site and its Green’s functions[J].Journal of Earthquake Engineering and EngineeringVibration,2007,27(5):7-17(in Chinese))
[16]巴振宁.层状半空间中格林函数和局部场地对弹性波的散射[D].天津:天津大学(Ba Zhenning.Green’sfunctions for layered half space and elastic wave scatteringby local sites[D].Tianjin:Tianjin University(inChinese))
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