具有饱和土沉积层的充水河谷对平面波的散射
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摘要
把波函数展开方法用于地震波散射问题的研究中,首次在频域内给出了具有饱和土沉积层的圆弧形充水河谷对平面P波和SV散射问题的解析解答.其中半空间场地用单相介质弹性动力理论模拟,河谷中的饱和土沉积层用饱和多孔介质的Biot动力学理论模拟,河谷中的水用无黏性流体(理想流体)介质模拟.文中还给出算例,计算了不同高宽比的河谷谷底的位移幅值,分析表明河谷地形的存在使得半空间介质表面的位移幅值随着观察点位置的变化变化较大.
We present an analytic solution of two_dimensional scattering and diffraction of plane P and SV waves by circular_arc alluvial valleys with saturated soil deposits and water. We use the Fourier_Bessel series expansion technique with the deposits simulated by the Biot dynamic theory for saturated porous media, the half space assumed to be elastic single_phase media, and the water in the valleys simulated by perfect fluid. Numerical results are given to show the displacement amplitudes on the valley floor. Our analysis indicates that the surface displacement amplitudes of the valley floor changes with the positions of the observation points apparently.
We present an analytic solution of two_dimensional scattering and diffraction of plane P and SV waves by circular_arc alluvial valleys with saturated soil deposits and water. We use the Fourier_Bessel series expansion technique with the deposits simulated by the Biot dynamic theory for saturated porous media, the half space assumed to be elastic single_phase media, and the water in the valleys simulated by perfect fluid. Numerical results are given to show the displacement amplitudes on the valley floor. Our analysis indicates that the surface displacement amplitudes of the valley floor changes with the positions of the observation points apparently.
引文
[1]Cao H,Lee V W.Scattering and diffraction of plane P waves by circular_cylindrical canyons with variable depth_to_width ratio.Soil Dynamics and Earthquake Engineering,1990,9(3):141~150
[2]Sanchez_sesma F J,Pamos_martinez J,Campillo M.An indirect boundary element method appliedto simulate the seismic response of alluvial valleys for incident P,S and Rayleigh waves.Earthquake Engineering and Structure Dynamics,1993,22:279~295
[3]Todorovska M,Lee V W.Surface motion of shallowcircular alluvial valleys for incident plane SH waves:analytical solution.Soil Dynamics and Earthquake Engineering,1991,4:192~200
[4]Trifunac MD.Surface motion of semi_cylindrical alluvial valley for incident plane SH waves.Bulletin of Seismological Society of America,1971,61:1755~1770
[5]Yuan X,Liao Z.Scatteringof plane SHwave bya cylindrical alluvial valley of circular_arc cross_section.Earthquake Engineering and Structure Dynamics,1995,24(1):1303~1313
[6]李伟华.含饱和土的复杂局部场地波动散射问题的解析解和显式有限元模拟[博士学位论文].北京:北京交通大学,2004Li W H.Analytical solutions and numerical simulation of the scattering of plane waves by local sites with saturated soil(Ph.D.dissertation).Beijing:Beijing Jiaotong Unversity,2004
[7]李伟华,赵成刚.圆弧形凹陷饱和土场地对平面P波散射问题的解答.地球物理学报,2003,46(4):539~546Li WH,Zhao C G.An analytical solutionforthe diffraction of plane P_waves by circular cylindrical canyons in a fluid_saturated porous media half space.Chinese J.Geophys.(in Chinese),2003,46(4):539~546
[8]董俊,赵成刚.三维半球形凹陷饱和土场地对平面P波散射问题的解析解.地球物理学报,2005,48(3):680~688Dong J,Zhao C G.Ananalytic solutionforthe diffractionof plane P_wave bythree_dimensional hemispherical canyons in a fluid_saturated porous media half space.Chinese J.Geophys.(in Chinese),2005,48(3):680~688
[9]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.地球物理学报,2004,47(5):911~919Li W H,Zhao C G.Scattering of plane SV waves by circular_arc alluvial valleys with saturated deposits.Chinese J.Geophys.(in Chinese),2004,47(5):911~919
[10]李伟华,赵成刚.饱和土沉积谷场地对平面P波的散射.岩土工程学报,2003,25(3):346~351Li WH,Zhao C G.Scattering of plane P waves in alluvial valleys with saturated soil deposits.Chinese Journal of Geotechnical Engineering(in Chinese),2003,25(3):346~351
[11]Li Weihua,Zhao Chenggang.Scattering of plane SV waves by cylindrical canyons in saturated porous medium.Soil Dynamics and Earthquake Engineering,in press
[12]王维佳.粘性可压缩流体中的波.地球物理学报,1984,27(1):84~93Wang WJ.The waves in viscous compressible fluid.Chinese J.Geophys.(in Chinese),1984,27(1):84~93
[13]Deresiewicz H.The effect of boundaries wave propagationin aliquid_filled porous solid.Bulletin of Seismological Society of America,1962,52:595~625
[14]Abramowitz M,Stegan I A.Handbook of Mathematical Functions,with Formulas,Graphs and Mathematical Tables.New York:Dover Publication,1972
[15]Л.М.布列霍夫斯基赫著.分层介质中的波.杨训川译.科学出版社,1985Brekhovskikh L M.Waves in Layered Media.Yang X Ctranslated.Beijing:Science Press,1985
[2]Sanchez_sesma F J,Pamos_martinez J,Campillo M.An indirect boundary element method appliedto simulate the seismic response of alluvial valleys for incident P,S and Rayleigh waves.Earthquake Engineering and Structure Dynamics,1993,22:279~295
[3]Todorovska M,Lee V W.Surface motion of shallowcircular alluvial valleys for incident plane SH waves:analytical solution.Soil Dynamics and Earthquake Engineering,1991,4:192~200
[4]Trifunac MD.Surface motion of semi_cylindrical alluvial valley for incident plane SH waves.Bulletin of Seismological Society of America,1971,61:1755~1770
[5]Yuan X,Liao Z.Scatteringof plane SHwave bya cylindrical alluvial valley of circular_arc cross_section.Earthquake Engineering and Structure Dynamics,1995,24(1):1303~1313
[6]李伟华.含饱和土的复杂局部场地波动散射问题的解析解和显式有限元模拟[博士学位论文].北京:北京交通大学,2004Li W H.Analytical solutions and numerical simulation of the scattering of plane waves by local sites with saturated soil(Ph.D.dissertation).Beijing:Beijing Jiaotong Unversity,2004
[7]李伟华,赵成刚.圆弧形凹陷饱和土场地对平面P波散射问题的解答.地球物理学报,2003,46(4):539~546Li WH,Zhao C G.An analytical solutionforthe diffraction of plane P_waves by circular cylindrical canyons in a fluid_saturated porous media half space.Chinese J.Geophys.(in Chinese),2003,46(4):539~546
[8]董俊,赵成刚.三维半球形凹陷饱和土场地对平面P波散射问题的解析解.地球物理学报,2005,48(3):680~688Dong J,Zhao C G.Ananalytic solutionforthe diffractionof plane P_wave bythree_dimensional hemispherical canyons in a fluid_saturated porous media half space.Chinese J.Geophys.(in Chinese),2005,48(3):680~688
[9]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.地球物理学报,2004,47(5):911~919Li W H,Zhao C G.Scattering of plane SV waves by circular_arc alluvial valleys with saturated deposits.Chinese J.Geophys.(in Chinese),2004,47(5):911~919
[10]李伟华,赵成刚.饱和土沉积谷场地对平面P波的散射.岩土工程学报,2003,25(3):346~351Li WH,Zhao C G.Scattering of plane P waves in alluvial valleys with saturated soil deposits.Chinese Journal of Geotechnical Engineering(in Chinese),2003,25(3):346~351
[11]Li Weihua,Zhao Chenggang.Scattering of plane SV waves by cylindrical canyons in saturated porous medium.Soil Dynamics and Earthquake Engineering,in press
[12]王维佳.粘性可压缩流体中的波.地球物理学报,1984,27(1):84~93Wang WJ.The waves in viscous compressible fluid.Chinese J.Geophys.(in Chinese),1984,27(1):84~93
[13]Deresiewicz H.The effect of boundaries wave propagationin aliquid_filled porous solid.Bulletin of Seismological Society of America,1962,52:595~625
[14]Abramowitz M,Stegan I A.Handbook of Mathematical Functions,with Formulas,Graphs and Mathematical Tables.New York:Dover Publication,1972
[15]Л.М.布列霍夫斯基赫著.分层介质中的波.杨训川译.科学出版社,1985Brekhovskikh L M.Waves in Layered Media.Yang X Ctranslated.Beijing:Science Press,1985
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