斜入射平面SH波在层状饱和半空间中沉积谷地周围的三维散射
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摘要
为研究层状饱和场地中沉积谷地对斜入射地震波的三维散射问题,建立了求解问题的2.5维间接边界元方法。通过沿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,进而在沉积谷地的截面内进行边界单元的离散和求解,求得沉积谷地截面内的动力响应,然后再将截面内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。通过与弹性情况的比较验证了方法的正确性,并以均匀饱和半空间和基岩上单一饱和土层中沉积谷地对斜入射平面SH波的三维散射为例进行了数值计算和分析。研究发现沉积谷地对SH波的三维散射与二维散射之间存在显著差异;饱和情况(透水或不透水)与干土情况沉积谷地附近地表位移的差别很大;另外层状饱和半空间中沉积谷地和均匀饱和半空间中沉积谷地对斜入射SH波的放大作用也存在显著差别。
The indirect boundary element method(IBEM) is proposed to study the three-dimensional scattering problem by a two-dimensional valley embedded in a fluid-saturated,poroelastic layered half-space for obliquely incident seismic waves.The wave-number transform is applied in the axial direction of the valley to reduce the three-dimensional problem to a two-dimensional plane strain problem.Then the dynamic problem is solved in one section perpendicular to the axis of the valley,and finally the three-dimensional responses of the valley and of the layered site are obtained through the inverse wave-number expansion.The validity of the method is confirmed by comparison with the results of the corresponding dry poroelastic case,and numerical calculation and analyses are performed by taking the amplification of obliquely incident plane waves by an alluvial valley in a uniformly saturated poroelastic half space and in a single saturated poroelastic soil layer overlying on elastic bedrock as examples.The results show that the three-dimensional responses are distinctively different from the two-dimensional responses,that the surface displacement amplitudes near the valley in dry poroelastic and saturated poroelastic half-spaces are very different,and that the displacement amplitudes around the valley in a uniform saturated poroelastic half space are obviously different from those in a saturated,poroelastic layered half-space.
The indirect boundary element method(IBEM) is proposed to study the three-dimensional scattering problem by a two-dimensional valley embedded in a fluid-saturated,poroelastic layered half-space for obliquely incident seismic waves.The wave-number transform is applied in the axial direction of the valley to reduce the three-dimensional problem to a two-dimensional plane strain problem.Then the dynamic problem is solved in one section perpendicular to the axis of the valley,and finally the three-dimensional responses of the valley and of the layered site are obtained through the inverse wave-number expansion.The validity of the method is confirmed by comparison with the results of the corresponding dry poroelastic case,and numerical calculation and analyses are performed by taking the amplification of obliquely incident plane waves by an alluvial valley in a uniformly saturated poroelastic half space and in a single saturated poroelastic soil layer overlying on elastic bedrock as examples.The results show that the three-dimensional responses are distinctively different from the two-dimensional responses,that the surface displacement amplitudes near the valley in dry poroelastic and saturated poroelastic half-spaces are very different,and that the displacement amplitudes around the valley in a uniform saturated poroelastic half space are obviously different from those in a saturated,poroelastic layered half-space.
引文
[1]TRIFUNAC M D.Surface motion of a semi-cylindrical alluvial valley for incident plane SH waves[J].Bull Seism Soc Am,1976,61(6):1755–1770.
[2]WONG H L,TRIFUNAC M D.Surface motion of a semi-elliptical alluvial valley for incident plane SH waves[J].Bull Seism Soc Am,1974,64(5):1389–1408.
[3]DRAVINSKI M.Scattering of plane harmonic SH wave by dipping layers or arbitrary shape[J].Bull Seism Soc Am,1983,73(5):1303–1319.
[4]YUAN X M,LIAO Z P.Scattering of plane SH waves by a cylindrical alluvial valley of circular-arc cross-section[J].Earthq Eng Struct Dynam,1995,24(10):1303–1313.
[5]梁建文,张郁山,顾晓鲁,等.圆弧形层状沉积河谷场地在平面SH波入射下动力响应分析[J].岩土工程学报,2000,22(4):396–401.(LIANG Jian-wen,ZHANG Yu-shan,GU Xiao-lu,et al.Surface motion of circular arc layered alluvial valleys for incident plane SH waves[J].Chinese Journal of Geotechnical Engineering,2000,22(4):396–401.(in Chinese))
[6]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 Jian-wen,BA Zhen-ning,Surface motion of an alluvial valley in layered half-space for incident plane SH waves[J].Journal of Earthquake Engineering and Engineering Vibration,2007,27(3):1–9.(in Chinese))
[7]巴振宁,梁建文.平面SV波在层状半空间中沉积谷地周围的散射[J].地震工程与工程振动,2011,31(3):18–26.(BA Zhen-ning,LIANG Jian-wen.Diffraction of plane SV waves around an alluvial valley in layered half-space[J].Journal of Earthquake Engineering and Engineering Vibration,2011,31(3):18–26.(in Chinese))
[8]LI Wei-hua,ZHAO Chen-gang.Scattering of plane P waves by circular-arc alluvial valleys with saturated soil deposits[J].Soil Dyn Earthquake Eng,2005,25(12):997–1014.
[9]LI Wei-hua,ZHAO Chen-gang.Scattering of plane SV waves by circular-arc alluvial valleys with saturated soil deposits[J].Soil Dyn Earthquake Eng,2005,25(12):981–995.
[10]韩铮,赵成刚,半球形沉积谷场地对入射平面Rayleigh波的三维散射解析解[J].岩土力学,2007,28(12):260–2613.(HAN Zheng,ZHAO Cheng-gang.Analytical solution of three-dimensional scattering and diffraction of plane Rayleigh-waves bya hemispherical alluvial valley with saturated soil deposit[J].Rock and Soil Mechanics,2007,28(12):461–470.(in Chinese))
[11]ZHOU Xian-lian,JIANG Ling-fa,WANG Jian-hua.Scattering of plane wave by circular-arc alluvial valley in a poroelastic half-space[J].Journal of Sound and Vibration,2008,318(5):1024–1049.
[12]LIU Zhong-xian,LIANG Jian-wen.Diffraction of plane P waves around an alluvial valley in poroelastic half-space[J].Earthquake Science,2010,23(1):35–43.
[13]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 Jian-wen,WEI Xin-lei,LEE V W.3D scattering of plane SV waves by a circular-arc alluvialvalley[J].Chinese Journal of Geotechnical Engineering,2009,31(9):1345–1353.(in Chinese))
[14]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 Jian-wen,WEI Xin-lei,LEE V W.3-D scattering of plane P waves by a circular-arc alluvial valley[J].Rock and Soil Mechanics,2010,31(2):461–470.(in Chinese))
[15]DE Barros FCP,LUCO J E.Amplication of obliquely incident waves by a cylindrical valley embedded in a layered half-space[J].Soil Dyn Earthq Engng,1995,14(3):163–175.
[16]KHAIR K R,DATTA S K,SHAH A H.Amplification of obliquely incident seismic waves by cylindrical alluvial valleys of arbitrary cross-sectional shape Part II:Incident SH and Rayleigh waves[J].Bull Seismol Soc Am,1991,81(1):346–357.
[17]PEDERSEN H,SANCHEZ-SESMA F J,CAMPILLO M.Three-dimensional scattering by two-dimensional topographies[J].Bull Seism Soc Am,1994,84(4):1169–1183.
[18]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,2008.(BA Zhen-ning,Green's Functions for layered half space and elastic wave scattering by local sites[D].Tianjin:Tianjin University,2008.(in Chinese))
[19]BIOT M A.The theory of propagation of elastic waves in a fluid-saturated porous solid I:Low-frequency range[J].J Acoust Soc Am,1956,28(2):168–178.
[20]BIOT M A.The theory of propagation of elastic waves in a fluid-saturated porous solid II:Higher-frequency range[J].J Acoust Soc Am,1956,28(2):179–191.
[21]LIN C H,LEE V W,TRIFUNAC M D.The reflection of plane waves in a poroelastic half-space fluid saturated with inviscid fluid[J].Soil Dyn Earthquake Eng,2005,25(3):205–223.
[2]WONG H L,TRIFUNAC M D.Surface motion of a semi-elliptical alluvial valley for incident plane SH waves[J].Bull Seism Soc Am,1974,64(5):1389–1408.
[3]DRAVINSKI M.Scattering of plane harmonic SH wave by dipping layers or arbitrary shape[J].Bull Seism Soc Am,1983,73(5):1303–1319.
[4]YUAN X M,LIAO Z P.Scattering of plane SH waves by a cylindrical alluvial valley of circular-arc cross-section[J].Earthq Eng Struct Dynam,1995,24(10):1303–1313.
[5]梁建文,张郁山,顾晓鲁,等.圆弧形层状沉积河谷场地在平面SH波入射下动力响应分析[J].岩土工程学报,2000,22(4):396–401.(LIANG Jian-wen,ZHANG Yu-shan,GU Xiao-lu,et al.Surface motion of circular arc layered alluvial valleys for incident plane SH waves[J].Chinese Journal of Geotechnical Engineering,2000,22(4):396–401.(in Chinese))
[6]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 Jian-wen,BA Zhen-ning,Surface motion of an alluvial valley in layered half-space for incident plane SH waves[J].Journal of Earthquake Engineering and Engineering Vibration,2007,27(3):1–9.(in Chinese))
[7]巴振宁,梁建文.平面SV波在层状半空间中沉积谷地周围的散射[J].地震工程与工程振动,2011,31(3):18–26.(BA Zhen-ning,LIANG Jian-wen.Diffraction of plane SV waves around an alluvial valley in layered half-space[J].Journal of Earthquake Engineering and Engineering Vibration,2011,31(3):18–26.(in Chinese))
[8]LI Wei-hua,ZHAO Chen-gang.Scattering of plane P waves by circular-arc alluvial valleys with saturated soil deposits[J].Soil Dyn Earthquake Eng,2005,25(12):997–1014.
[9]LI Wei-hua,ZHAO Chen-gang.Scattering of plane SV waves by circular-arc alluvial valleys with saturated soil deposits[J].Soil Dyn Earthquake Eng,2005,25(12):981–995.
[10]韩铮,赵成刚,半球形沉积谷场地对入射平面Rayleigh波的三维散射解析解[J].岩土力学,2007,28(12):260–2613.(HAN Zheng,ZHAO Cheng-gang.Analytical solution of three-dimensional scattering and diffraction of plane Rayleigh-waves bya hemispherical alluvial valley with saturated soil deposit[J].Rock and Soil Mechanics,2007,28(12):461–470.(in Chinese))
[11]ZHOU Xian-lian,JIANG Ling-fa,WANG Jian-hua.Scattering of plane wave by circular-arc alluvial valley in a poroelastic half-space[J].Journal of Sound and Vibration,2008,318(5):1024–1049.
[12]LIU Zhong-xian,LIANG Jian-wen.Diffraction of plane P waves around an alluvial valley in poroelastic half-space[J].Earthquake Science,2010,23(1):35–43.
[13]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 Jian-wen,WEI Xin-lei,LEE V W.3D scattering of plane SV waves by a circular-arc alluvialvalley[J].Chinese Journal of Geotechnical Engineering,2009,31(9):1345–1353.(in Chinese))
[14]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 Jian-wen,WEI Xin-lei,LEE V W.3-D scattering of plane P waves by a circular-arc alluvial valley[J].Rock and Soil Mechanics,2010,31(2):461–470.(in Chinese))
[15]DE Barros FCP,LUCO J E.Amplication of obliquely incident waves by a cylindrical valley embedded in a layered half-space[J].Soil Dyn Earthq Engng,1995,14(3):163–175.
[16]KHAIR K R,DATTA S K,SHAH A H.Amplification of obliquely incident seismic waves by cylindrical alluvial valleys of arbitrary cross-sectional shape Part II:Incident SH and Rayleigh waves[J].Bull Seismol Soc Am,1991,81(1):346–357.
[17]PEDERSEN H,SANCHEZ-SESMA F J,CAMPILLO M.Three-dimensional scattering by two-dimensional topographies[J].Bull Seism Soc Am,1994,84(4):1169–1183.
[18]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,2008.(BA Zhen-ning,Green's Functions for layered half space and elastic wave scattering by local sites[D].Tianjin:Tianjin University,2008.(in Chinese))
[19]BIOT M A.The theory of propagation of elastic waves in a fluid-saturated porous solid I:Low-frequency range[J].J Acoust Soc Am,1956,28(2):168–178.
[20]BIOT M A.The theory of propagation of elastic waves in a fluid-saturated porous solid II:Higher-frequency range[J].J Acoust Soc Am,1956,28(2):179–191.
[21]LIN C H,LEE V W,TRIFUNAC M D.The reflection of plane waves in a poroelastic half-space fluid saturated with inviscid fluid[J].Soil Dyn Earthquake Eng,2005,25(3):205–223.
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