斜入射平面SH波在层状半空间中沉积谷地周围的三维散射
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摘要
采用直接刚度法计算自由场动力响应,以层状半空间中移动斜线均布荷载动力格林函数模拟散射波场,采用间接边界元方法求解了层状半空间中沉积谷地对斜入射平面SH波的三维散射问题。由于文中采用的层状场地三维动力刚度矩阵是精确的,且用于模拟散射波场的均布移动斜线荷载可以直接施加在沉积交界面处而不存在奇异性,所以本文方法具有很高精度。文中以均匀半空间和基岩上单一土层中沉积谷地对入射SH波的散射为例进行了数值计算,研究表明,沉积谷地对地震波的三维散射与二维散射之间存在本质差别;层状半空间中沉积谷地与均匀半空间中沉积谷地附近地表位移存在显著差异。
The indirect boundary element method(IBME) is used to study three-dimensional scattering by an alluvial valley embedded in a layered half-space for obliquely incident plane SH waves;by using the direct stiffness method to calculate the free-field responses and dynamic Green's functions of moving distributed loads acting on inclined lines in a layered half-space to simulate the scatter wave filed responses.The presented method yields very accurate results for the 3D dynamic stiffness matrixes and the fictitious uniform moving loads can be acted directly on the interface between the alluvial valley and the layered half-space without singularity.Numerical results and analyses are performed by taking the amplification of incident plane SH waves by an alluvial in a uniform half space and in one layer over half-space.The results show that the three-dimensional responses are distinctively different from the two-dimensional responses,and the displacement amplitudes around the valley in a uniform half-space are obviously different from those of in a layered half-space.
The indirect boundary element method(IBME) is used to study three-dimensional scattering by an alluvial valley embedded in a layered half-space for obliquely incident plane SH waves;by using the direct stiffness method to calculate the free-field responses and dynamic Green's functions of moving distributed loads acting on inclined lines in a layered half-space to simulate the scatter wave filed responses.The presented method yields very accurate results for the 3D dynamic stiffness matrixes and the fictitious uniform moving loads can be acted directly on the interface between the alluvial valley and the layered half-space without singularity.Numerical results and analyses are performed by taking the amplification of incident plane SH waves by an alluvial in a uniform half space and in one layer over half-space.The results show that the three-dimensional responses are distinctively different from the two-dimensional responses,and the displacement amplitudes around the valley in a uniform half-space are obviously different from those of in a layered half-space.
引文
巴振宁、梁建文,2010,2.5D scattering of incident plane SH waves by a canyon in layered half-space,Earthquake Science,23,25～33。
梁建文、巴振宁,2007,弹性层状半空间中沉积谷地对入射平面SH波的放大作用,地震工程与工程振动,27(3),1～9。
梁建文、魏新磊,Lee V W,2009,圆弧型沉积谷地对平面SV波三维散射解析解,岩土工程学报,31(9),1345～1353。
梁建文、魏新磊,Lee V W,2010,圆弧型沉积谷地对平面P波三维散射解析解,岩土力学,31(2),461～470。
梁建文、严林隽、秦东,2003,圆弧形沉积河谷场地在平面SV波入射下的动力响应,地震学报,26(12),74～82。
De Barros FCP,Luco J E,1995,Amplication of obliquely incident waves by a cylindrical valley embedded in a layered half-space,Soil Dyn Earthq Engng,14,163～175.
Dravinski M,1983,Scattering of plane harmonic SH wave by dipping layers or arbitrary shape,Bull Seism Soc Am,73,1303～1319.
Dravinski M,Mossessian T K,1987,Scattering of plane harmonic P,SV,and Rayleigh waves by dipping layers of arbitraryshape,Bull Seism Soc Am,77,212～235.
Kawase H,Aki K,1989,A study on the response of a soft basin for incident S,P and Rayleigh waves with special reference to thelong duration observed in Mexico city,Bull Seism Soc Am,79(5),1361～1382.
Pedersen H,Campillo M,Sanchez-Sesma F J,1995,Azimuth dependent wave amplification in alluvial valleys,Soil Dyn EarthqEngng,14,289～300.
Sanchez-Sesma F J,Ramos-Martinez J,Campillo M,1993,An indirect boundary element method applied to simulate the seismicresponse of alluvial valleys for incident P,S and Rayleigh waves,Earthq Eng Struct Dyn,22,279～295.
Trifunac M D,1971,Surface motion of a semi-cylindrical alluvial valley for incident plane SH waves,Bull Seism Soc Am,61,1755～1770.
Wong H L,Trifunac M D,1974,Surface motion of a semi-elliptical alluvial valley for incident plane SH waves,Bull Seism SocAm,64,1389～1408.
Yuan X,Liao Z,1995,Scattering of plane SH waves by a cylindrical alluvial valley of circular-arc cross-section,Earthq EngStruct Dynam,24,1303～1313.
梁建文、巴振宁,2007,弹性层状半空间中沉积谷地对入射平面SH波的放大作用,地震工程与工程振动,27(3),1～9。
梁建文、魏新磊,Lee V W,2009,圆弧型沉积谷地对平面SV波三维散射解析解,岩土工程学报,31(9),1345～1353。
梁建文、魏新磊,Lee V W,2010,圆弧型沉积谷地对平面P波三维散射解析解,岩土力学,31(2),461～470。
梁建文、严林隽、秦东,2003,圆弧形沉积河谷场地在平面SV波入射下的动力响应,地震学报,26(12),74～82。
De Barros FCP,Luco J E,1995,Amplication of obliquely incident waves by a cylindrical valley embedded in a layered half-space,Soil Dyn Earthq Engng,14,163～175.
Dravinski M,1983,Scattering of plane harmonic SH wave by dipping layers or arbitrary shape,Bull Seism Soc Am,73,1303～1319.
Dravinski M,Mossessian T K,1987,Scattering of plane harmonic P,SV,and Rayleigh waves by dipping layers of arbitraryshape,Bull Seism Soc Am,77,212～235.
Kawase H,Aki K,1989,A study on the response of a soft basin for incident S,P and Rayleigh waves with special reference to thelong duration observed in Mexico city,Bull Seism Soc Am,79(5),1361～1382.
Pedersen H,Campillo M,Sanchez-Sesma F J,1995,Azimuth dependent wave amplification in alluvial valleys,Soil Dyn EarthqEngng,14,289～300.
Sanchez-Sesma F J,Ramos-Martinez J,Campillo M,1993,An indirect boundary element method applied to simulate the seismicresponse of alluvial valleys for incident P,S and Rayleigh waves,Earthq Eng Struct Dyn,22,279～295.
Trifunac M D,1971,Surface motion of a semi-cylindrical alluvial valley for incident plane SH waves,Bull Seism Soc Am,61,1755～1770.
Wong H L,Trifunac M D,1974,Surface motion of a semi-elliptical alluvial valley for incident plane SH waves,Bull Seism SocAm,64,1389～1408.
Yuan X,Liao Z,1995,Scattering of plane SH waves by a cylindrical alluvial valley of circular-arc cross-section,Earthq EngStruct Dynam,24,1303～1313.
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