流体饱和层状半空间中沉积谷地对地震波的散射—IBIEM求解
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摘要
针对流体饱和层状半空间中任意形状沉积谷地对地震波的散射问题,基于单层位势理论,建立一种新的间接边界积分方程法(IBIEM):首先推导饱和层状半空间中两类膨胀波源和剪切波源动力格林函数,进而由分布在沉积谷地和层状半空间交界面附近两虚拟波源面上的PI、PII和SV波源分别构造沉积内外的散射波场。由交界面连续性条件建立方程并求解确定虚拟波源密度,总波场即可由自由波场和散射波场叠加而得。然后通过边界条件验算、退化解答与现有结果的比较,验证了方法的计算精度。通过一组典型算例,初步探讨了平面SV波在饱和层状半空间中沉积谷地周围散射的基本规律。研究表明:饱和层状沉积对地震波的散射和相应干土情况存在显著差异,边界渗透条件对沉积内部地震响应具有重要影响;饱和层状场地中波的散射和均质半空间情况有着本质不同,总体反应体现了饱和土层的共振放大效应和沉积谷地对波的散射效应。实际场地中地震波传播的精确模拟需考虑岩土介质的多相性和层理特征。
A new indirect boundary integral equation method for numerically solving the scattering of seismic waves by a two-dimensional alluvial valley of arbitrary shape in poroelastic layered half-space is proposed based on the single layer potential approach.The Green's functions of compressional and shear wave sources in poroelastic layered half-space are derived firstly,then the scattered waves in alluvial valley and layered half-space are constructed by using the fictitious wave sources close to the interface between the valley and the half-space respectively,and the magnitude of the fictitious wave sources is determined through continuous boundary conditions,and the total response can be obtained by the superposition of the free field and the scattered field.The precision of the proposed method is verified by the satisfaction extent of boundary conditions and the comparison between the degenerated solutions of single-phased half-space and the well-known solutions.The diffraction of plane SV waves around an alluvial valley in poroelastic layered half-space is studied with a typical example.It is illustrated that there exists significant difference between the scattering of waves around the poroelastic alluvial valley and the dry soil valley,and the drainage condition has large impact on earthquake ground motion in the valley.The wave scattering in layered sites and that in homogenous half-space are different in nature,and the total response characteristics combine the resonant behavior of the soil layers and the characteristics of scattering waves around the alluvial valley.Hence,to simulate the propagation of seismic waves more accurately,it is necessary to consider the multi-phased and layered characteristics of soil medium in reality.
A new indirect boundary integral equation method for numerically solving the scattering of seismic waves by a two-dimensional alluvial valley of arbitrary shape in poroelastic layered half-space is proposed based on the single layer potential approach.The Green's functions of compressional and shear wave sources in poroelastic layered half-space are derived firstly,then the scattered waves in alluvial valley and layered half-space are constructed by using the fictitious wave sources close to the interface between the valley and the half-space respectively,and the magnitude of the fictitious wave sources is determined through continuous boundary conditions,and the total response can be obtained by the superposition of the free field and the scattered field.The precision of the proposed method is verified by the satisfaction extent of boundary conditions and the comparison between the degenerated solutions of single-phased half-space and the well-known solutions.The diffraction of plane SV waves around an alluvial valley in poroelastic layered half-space is studied with a typical example.It is illustrated that there exists significant difference between the scattering of waves around the poroelastic alluvial valley and the dry soil valley,and the drainage condition has large impact on earthquake ground motion in the valley.The wave scattering in layered sites and that in homogenous half-space are different in nature,and the total response characteristics combine the resonant behavior of the soil layers and the characteristics of scattering waves around the alluvial valley.Hence,to simulate the propagation of seismic waves more accurately,it is necessary to consider the multi-phased and layered characteristics of soil medium in reality.
引文
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[2]汶川8.0级地震工程震害概览[J].地震工程与工程振动,2008,28(增刊):22–27.(General introduction toengineering damage of the Wenchuan Earthquake[J].Journalof Earthquake Engineering and Engineering Vibration,2008,28(S0):22–27.(in Chinese))
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[6]廖振鹏.工程波动理论导论[M].2版.北京:科学出版社,2002.(LIAO Zheng-peng.Introduction to wave motiontheories in engineering[M].2nd ed.Beijing:Science Press,2002.(in Chinese))
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[10]SANCHEZ-SESMA F J,PALENCIA V J,LUZON F.Estimation of local site effects during earthquakes:anoverview[J].Journal of Earthquake Technology,2002,39(3):167–193.
[11]李伟华,赵成刚.饱和土沉积谷场地对平面SV波的散射问题的解析解[J].地球物理学报,2004,47(5):911–919.(LI Wei-hua,ZHAO Cheng-gang.Scattering of plane SVwaves by circular-arc alluvial valleys with saturated soildeposits[J].Chinese Journal of Geophysics,2004,47(5):911–919.(in Chinese))
[12]LI W H,ZHAO C G,SHI P X.Scattering of plane P waves bycircular-arc alluvial valleys with saturated soil deposits[J].Soil Dynamics and Earthquake Engineering,2005,25(12):997–1014.
[13]梁建文,刘中宪.饱和半空间中沉积谷地对平面SV波的散射[J].地震工程与工程振动,2010(3):12–21.(LIANGJian-wen,LIU Zhong-xian.Diffraction of plane SV waves byan alluvial valley in poroelastic half-space[J].Journal ofEarthquake Engineering and Engineering Vibration,2010(3):12–21.(in Chinese))
[14]GOLBERG M A,CHEN C S.The method of fundamentalsolutions for potential,Helmholtz and diffusion problems.Boundary Integral Methods:Numerical and MathematicalAspects[C]//Golberg M A,ed.WIT Press&ComputationalMechanics Publications,Boston,Southampton,1998:103–176.
[15]GRAEME FAIRWEATHERA,ANDREAS KARAGEO-RGHISB,MARTIN P A.The method of fundamentalsolutions for scattering and radiation problems[J].Engineering Analysis with Boundary Elements,2003,27(7):759–769.
[16]DE BARROS F C P,LUCO J E.Amplification of obliquelyincident waves by a cylindrical valley embedded in a layeredhalf-space[J].Soil Dynamics and Earthquake Engineering,1995,14(3):163–175.
[17]DRAVINSKI M.Scattering of waves by a sedimentary basinwith a corrugated interface[J].Bulletin of the SeismologicalSociety of America,2007,97(1B):256–264.
[18]LIANG J,LIU Z.Diffraction of plane P waves by a canyon ofarbitrary shape in poroelastic half-space(I):Formulation[J].Earthquake Science,2009,22(3):215–222.
[19]BIOT M A.Mechanics of deformation and acousticpropagation in porous media[J].Journal of Applied Physics,1962,33(4):1482–1498.
[20]LIANG Jian-wen,YOU Hong-bing.Dynamic stiffness matrixof a poroelastic multi-layered site and its Green's functions[J].Earthquake Engineering and Engineering Vibration,2004,3(2):273–282.
[21]DERESIEWICZ H.On uniqueness in dynamicporoelasticity[J].Bulletin of Seismological Society ofAmerica,1963,53(4):595–626.
[22]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 SVwaves around an alluvial valley in layered half-space[J].Journal of Earthquake Engineering and Engineering Vibration,2011,31(3):18–26.(in Chinese))
[2]汶川8.0级地震工程震害概览[J].地震工程与工程振动,2008,28(增刊):22–27.(General introduction toengineering damage of the Wenchuan Earthquake[J].Journalof Earthquake Engineering and Engineering Vibration,2008,28(S0):22–27.(in Chinese))
[3]TRIFUNAC M D.Surface motion of a semi cylindricalalluvial valley for incident plane SH waves[J].Bulletin ofSeismological Society of America,1971,61(6):1755–l770.
[4]YUAN X M,LIAO Z P.Scattering of plane SH waves by acylindrical alluvial valley of circular-arc cross-section[J].Earthquake Engineering and Structural Dynamics,1995,24(10):1303–1313.
[5]BOORE D M,LARNER K L,AKI K.Comparison of twoindependent methods for the solution of wave scatteringproblems:response of a sedimentary basin to incident SHwaves[J].Journal of Geophysical Research,1971,76(2):558–569.
[6]廖振鹏.工程波动理论导论[M].2版.北京:科学出版社,2002.(LIAO Zheng-peng.Introduction to wave motiontheories in engineering[M].2nd ed.Beijing:Science Press,2002.(in Chinese))
[7]SANCHEZ-SESMA F J,RAMOS-MARTINEZ J,CAMPILLOM.An indirect boundary element method applied to simulatethe seismic response of alluvial valleys for incident P,S andRayleigh waves[J].Earthquake Engineering and StructuralDynamics,1993,22(4):279–295.
[8]KAWASE H,KEIITI A K.A study on the response of a softbasin for incident P,S,Rayleigh waves with special referenceto the long duration observed in Mexico city[J].Bulletin ofSeismological Society of America,1989,79(5):1361–1382.
[9]金峰,张楚汉,王光纶.半椭圆形河谷上沉积层地震响应研究[J].清华大学学报,1993,33(5):23–30.(JIN Feng,ZHANG Chu-han,WANG Guang-lun.Seismic response ofalluvial soil deposit on a semi-elliptical canyon[J].Journal ofTsinghua University,1993,33(5):23–30.(in Chinese))
[10]SANCHEZ-SESMA F J,PALENCIA V J,LUZON F.Estimation of local site effects during earthquakes:anoverview[J].Journal of Earthquake Technology,2002,39(3):167–193.
[11]李伟华,赵成刚.饱和土沉积谷场地对平面SV波的散射问题的解析解[J].地球物理学报,2004,47(5):911–919.(LI Wei-hua,ZHAO Cheng-gang.Scattering of plane SVwaves by circular-arc alluvial valleys with saturated soildeposits[J].Chinese Journal of Geophysics,2004,47(5):911–919.(in Chinese))
[12]LI W H,ZHAO C G,SHI P X.Scattering of plane P waves bycircular-arc alluvial valleys with saturated soil deposits[J].Soil Dynamics and Earthquake Engineering,2005,25(12):997–1014.
[13]梁建文,刘中宪.饱和半空间中沉积谷地对平面SV波的散射[J].地震工程与工程振动,2010(3):12–21.(LIANGJian-wen,LIU Zhong-xian.Diffraction of plane SV waves byan alluvial valley in poroelastic half-space[J].Journal ofEarthquake Engineering and Engineering Vibration,2010(3):12–21.(in Chinese))
[14]GOLBERG M A,CHEN C S.The method of fundamentalsolutions for potential,Helmholtz and diffusion problems.Boundary Integral Methods:Numerical and MathematicalAspects[C]//Golberg M A,ed.WIT Press&ComputationalMechanics Publications,Boston,Southampton,1998:103–176.
[15]GRAEME FAIRWEATHERA,ANDREAS KARAGEO-RGHISB,MARTIN P A.The method of fundamentalsolutions for scattering and radiation problems[J].Engineering Analysis with Boundary Elements,2003,27(7):759–769.
[16]DE BARROS F C P,LUCO J E.Amplification of obliquelyincident waves by a cylindrical valley embedded in a layeredhalf-space[J].Soil Dynamics and Earthquake Engineering,1995,14(3):163–175.
[17]DRAVINSKI M.Scattering of waves by a sedimentary basinwith a corrugated interface[J].Bulletin of the SeismologicalSociety of America,2007,97(1B):256–264.
[18]LIANG J,LIU Z.Diffraction of plane P waves by a canyon ofarbitrary shape in poroelastic half-space(I):Formulation[J].Earthquake Science,2009,22(3):215–222.
[19]BIOT M A.Mechanics of deformation and acousticpropagation in porous media[J].Journal of Applied Physics,1962,33(4):1482–1498.
[20]LIANG Jian-wen,YOU Hong-bing.Dynamic stiffness matrixof a poroelastic multi-layered site and its Green's functions[J].Earthquake Engineering and Engineering Vibration,2004,3(2):273–282.
[21]DERESIEWICZ H.On uniqueness in dynamicporoelasticity[J].Bulletin of Seismological Society ofAmerica,1963,53(4):595–626.
[22]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 SVwaves around an alluvial valley in layered half-space[J].Journal of Earthquake Engineering and Engineering Vibration,2011,31(3):18–26.(in Chinese))
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