SH波在浅埋多个圆孔处的散射与地震动
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摘要
研究了以任意方向入射的平面SH波在浅埋多个圆孔处的散射与地震动问题。利用SH散射的对称性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,即圆形孔洞的半径与入射波半波长之比;(3)诸圆孔的埋置情况,诸孔的埋深hi/ai、孔心距Di/ai,即圆形孔洞至表面距离与圆半径之比和圆形孔洞中心的距离与半径之比。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。当诸圆孔的最小埋深量hi/ai和孔心距Di/ai超过10-12时,位移幅值恢复至半空间单一圆孔散射的情况,表明圆形孔洞的影响可被忽略。
The problem of scattering of SH-waves by shallow fill multiple circular cavities and the ground motion is investigated for arbitrary incident angle in this paper. The displacement solution is constructed by applying the symmetry of scattering of SH-wave and the method of multi-polar coordinate system. When wavelength of the incident wave is smaller than the radius of the circular cavities, 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 and the second one is incident wave number η, i.e. the ratio of radius of the circular cavities to the half wavelength of incident wave. And the last one is h_i/a_i and D_i/a_i, those are the ratio of the distance of center of the circular cavities from the horizontal interface and the distance between the centers to the radius of the circular cavities respectively. When η is larger, the amplitude of the ground motion varies fiercely and sometimes will leap and enlarge sharply. If the value of h_i/a_i increases to 10～12, and the value of D_i/a_i increases to 10, the amplitude of displacement approaches to that of the half space with single cavity, which shows that the influence of circular cavity can be ignored.
The problem of scattering of SH-waves by shallow fill multiple circular cavities and the ground motion is investigated for arbitrary incident angle in this paper. The displacement solution is constructed by applying the symmetry of scattering of SH-wave and the method of multi-polar coordinate system. When wavelength of the incident wave is smaller than the radius of the circular cavities, 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 and the second one is incident wave number η, i.e. the ratio of radius of the circular cavities to the half wavelength of incident wave. And the last one is h_i/a_i and D_i/a_i, those are the ratio of the distance of center of the circular cavities from the horizontal interface and the distance between the centers to the radius of the circular cavities respectively. When η is larger, the amplitude of the ground motion varies fiercely and sometimes will leap and enlarge sharply. If the value of h_i/a_i increases to 10～12, and the value of D_i/a_i increases to 10, the amplitude of displacement approaches to that of the half space with single cavity, which shows that the influence of circular cavity can be ignored.
引文
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[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
[4] M.D.Trifunac.ScatteringofPlaneSH-wavesbyaSemi-CylindricalCanyon[J].EarthquakeEngineeringandStructuralDynamics.1973(1):267-281
[5] V.W.Lee,M.E.Manoogian.SurfaceMotionaboveanArbitraryShapeUndergrandCavityforIncidentSHWave[J].EuropeanEarthqueEngineering1995,8(1):3-11
[6] V.W.Lee,S.ChenandI.R.Hsu.AntiplaneDiffractionfromCanyonAboveSubsurfaceUnlinedTunner[J].ASCEEng.Mech.Div.1999
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