浅埋的圆柱形孔洞对SH波的散射与地震动
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摘要
研究了浅埋的圆柱形孔洞对以任意方向入射的平面SH波的散射与地震动问题。利用复变函数和多极坐标方法构造了问题的位移解。当入射波的波长与圆孔的半径相比较小时,地震动将受到较大的影响。影响地震动有三个主要参数:(1)SH波的入射角α0;(2)入射波波数η,即圆柱形孔洞的半径与入射波半波长之比;(3)h/R,即圆柱形孔洞至表面的距离与圆孔半径之比。当η较大时,地震动幅值变化激烈,位移幅值可出现跳动和放大的现象。当h/R增大至10～12时,位移幅值变化恢复至半空间的情况,表明圆柱形孔洞的影响可被忽略。
The problem of scattering of SH waves by a buried cylindrical cavity and the ground motion is investigated at arbitrary in cident angle in this paper. The displacement solution is constructed by applying the methods of complex function and multi polar coordinates system. When wavel ength of the incident wave is smaller compared with radius of the cylindrical ca vity, the ground motion will be influenced greatly. There are three main factors that influence the ground motion. The first one is incident angle α 0 , th e second one is incident wave number η , i.e. the ratio of radius of the cyl indrical cavity to the half wavelength of incident wave, and the last one is h /R , that is the ratio of the distance of the center of the cylindrical cavity from the horizontal interface to the radius of the cylindrical cavity. When η is larger, the amplitude of the ground motion varies fiercely and sometimes w ill leap and enlarge sharply. If the value of h/R increases to 10～12, the v a riation of amplitude of the displacement recovers to that of half space, which s hows that the influence of cylindrical cavity can be ignored.
The problem of scattering of SH waves by a buried cylindrical cavity and the ground motion is investigated at arbitrary in cident angle in this paper. The displacement solution is constructed by applying the methods of complex function and multi polar coordinates system. When wavel ength of the incident wave is smaller compared with radius of the cylindrical ca vity, the ground motion will be influenced greatly. There are three main factors that influence the ground motion. The first one is incident angle α 0 , th e second one is incident wave number η , i.e. the ratio of radius of the cyl indrical cavity to the half wavelength of incident wave, and the last one is h /R , that is the ratio of the distance of the center of the cylindrical cavity from the horizontal interface to the radius of the cylindrical cavity. When η is larger, the amplitude of the ground motion varies fiercely and sometimes w ill leap and enlarge sharply. If the value of h/R increases to 10～12, the v a riation of amplitude of the displacement recovers to that of half space, which s hows that the influence of cylindrical cavity can be ignored.
引文
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[14] 黎在良,刘殿魁.固体中的波[M].北京:科学出版社,1995.
[2] 胡聿贤.地震工程学[M].北京:地震出版社,1998.
[3] 胡聿贤,周锡元.地震工程跨世纪发展趋势[J].工程抗震,1999(1):3 9.HUYi xian,ZHOUXi yuan.Proceedingofearthquakeengineeringspancentury[J].EngineringPrecautionsAgainstEarthquake,1999(1):3 9.
[4] TrifunacMD.ScatteringofplaneSH wavesbyasemi cylindricalcanyon[J].EarthquakeEngineeringandStructuralDynamics,1973(1):267 281.
[5] LIUDian kui,HANFeng.ScatteringofplaneSH wavesbycylindricalcanyonofarbitraryshapeinanisotropicmedia[J].ActaMechanicsSinica,1990,6(3):256 260.
[6] LIUDian kui,HANFeng.ScatteringofplaneSH wavesbyacylindricalcanyonofarbitraryshape[J].IntJSoilDynamicandEarthquakeEngineering,1991,10(5):249 255.
[7] YUANXiao ming,MENFu lu.ScatteringofplaneSH wavesbyasemi cylindricalhill[J].EarthqEngandStructDynamics,1992,21:1091 1098.
[8] 崔志刚,曹新荣,刘殿魁.SH波对半圆形凸起地形的散射[J].地震工程与工程振动,1998,18(1):140 146.CUIZhi gang,CAOXin rong,LIUDian kui.ScatteringofSH wawesbysemi cylindricalhill[J].EarthquakeEngiandEngiVibration,1998,18(1):140 146.
[9] 袁晓铭,廖振鹏.任意圆弧形凸起地形对平面SH波的散射[J].地震工程与工程振动,1996,16(2):1 13.YUANXiao ming,LIAOZhen peng.ScatteringofplaneSH wavesbyasemi cylindricalhillofarbitraryshapes[J].EarthquakeEngiandEngiVibration,1996,16(2):1 13.
[10] 刘殿魁,刘宏伟.曲线坐标在弹性波散射研究中的应用SH波对不等深度凹陷地形的散射[J].地震工程与工程振动,1996,16(2):14 24.LIUDian kui,LIUHong wei.TheApplicationofcurvecoordinatetoscatteringofelasticwaves[J].EarthquakeEngiandEngiVibration,1996,16(2):14 24.
[11] 刘殿魁,刘宏伟.P波对具有不等深凹陷地形散射[J].固体力学学报,1997,18(4).LIUDian kui,LIUHong wei.ScatteringofP wavesbycanyonswithvariabledepth to widthratio[J].ActaMechancsSolidSinica,1997,18(4).
[12] 刘殿魁,曹新荣,崔志刚.多个半圆形凸起地形对平面SH波散射[J].固体力学学报,1998,19(4):178 185.LIUDian kui,CAOXin rong,CUIZhi gang.ScatteringofSH wavesbysemi cylindricalhills[J].ActaMechancsSolidSinica,1998,19(4):178 185.
[13] 刘殿魁,许贻燕.各向异性介质中SH波与多个半圆形凹陷地形的相互作用[J].力学学报,1993,25(1):93 102.LIUDian kui,XUYi yan.Interactionmultiplesemi cylindricalcanyonsbyplaneSH waveinanisotropicmedia[J].ActaMechanicaSinica,1993,25(1):93 102.
[14] 黎在良,刘殿魁.固体中的波[M].北京:科学出版社,1995.
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