楔形空间中圆弧形沉积对平面SH波的散射解析解
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摘要
为揭示楔形空间中沉积谷地对地震动的显著影响,基于大圆弧假定,利用Fourier-Bessel波函数展开,采用一种新方法求解了楔形空间中圆弧形沉积对平面SH波的散射问题.首先利用2个大圆弧面模拟地表面,以方便构造地表面引起的散射波场.然后由连续性边界条件建立方程并求解得出该问题的解析解,通过同现有结果的对比,验证该方法的计算精度,进而进行详细的参数分析.计算结果表明,楔形空间中沉积附近地表位移反应特征依赖于波入射角、入射波频率、楔形夹角及沉积内外的材料特性,位移放大效应比半空间情况更为显著,因而需适当提高此类场地上建筑物的抗震设防标准.
In order to understand the significant effect of the alluvial valley in wedge-shaped space on earthquake ground motion,a new method has been proposed in this paper to study the diffraction of plane SH waves by a circular alluvial valley in wedge-shaped space on the basis of large circle assumption with Fourier-Bessel series expansion technique.With two large curved surfaces simulating the ground surface,the scattering field was conveniently constructed.An equation was established with continuous boundary conditions and the analytic solution was derived.The accuracy of the proposed method was verified by comparison with the available results,and then detailed parametric analysis was carried out.The numerical results indicate that the surface displacement characteristics around the alluvial valley in wedge-shaped space depend on the angle of incidence,the frequency of the incident wave,the angle of the wedge,and the material properties of the media,and the displacement amplification effect on ground motion is more significant than that of the half space.It is suggested that the earthquake resistant level of the buildings built in such site should be properly enhanced.
In order to understand the significant effect of the alluvial valley in wedge-shaped space on earthquake ground motion,a new method has been proposed in this paper to study the diffraction of plane SH waves by a circular alluvial valley in wedge-shaped space on the basis of large circle assumption with Fourier-Bessel series expansion technique.With two large curved surfaces simulating the ground surface,the scattering field was conveniently constructed.An equation was established with continuous boundary conditions and the analytic solution was derived.The accuracy of the proposed method was verified by comparison with the available results,and then detailed parametric analysis was carried out.The numerical results indicate that the surface displacement characteristics around the alluvial valley in wedge-shaped space depend on the angle of incidence,the frequency of the incident wave,the angle of the wedge,and the material properties of the media,and the displacement amplification effect on ground motion is more significant than that of the half space.It is suggested that the earthquake resistant level of the buildings built in such site should be properly enhanced.
引文
[1]Trifunac M D.Surface motion of a semi-cylindrical allu-vial valley for incident plane SH waves[J].Bulletin of Seismological Society of America,197l,61(6):1755-l770.
[2]Wong H L,Trifunac M D.Surface motion of a semi-elliptical alluvial valley for incident plane SH waves[J].Bulletin of Seismological Society of America,1974,64(5):1389-1408.
[3]Todorovska M,lee V W.Surface motion of shallow circu-lar alluvial valleys for incident plane SH waves:Analytical solution[J].Soil Dynamics and Earthquake Engineering,1991,10(4):192-200.
[4]Yuan Xiaoming,Liao Zhenpeng.Scattering of plane SH waves by a cylindrical alluvial valley of circular-arc cross-section[J].Earthquake Engineering and Structural Dynamics,1995,24(10):1303-1313.
[5]梁建文,张郁山,顾晓鲁.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 Jianwen,Zhang Yushan,Gu Xiaolu.Surface mo-tion 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]李伟华,赵成刚.具有饱和土沉积层的充水河谷对平面波的散射[J].地球物理学报,2006,49(1):212-224.Li Weihua,Zhao Chenggang.Scattering of plane waves by circular arc alluvial valleys with saturated soil depos-its and water[J].Chinese Journal of Geophysics,2006,49(1):212-224(in Chinese).
[7]Boore D M,Larner K L,Aki K.Comparison of two inde-pendent methods for the solution of wave scattering prob-lems:response of a sedimentary basin to incident SH waves[J].Journal of Geophysical Research,1971,76(2):558-569.
[8]Dravinski M.Scattering of plane harmonic SH wave by dipping layers or arbitrary shape[J].Bulletin of Seismol-ogical Society of America,1983,73(5):1303-1319.
[9]杜修力,熊建国,关慧敏.平面SH波散射问题的边界积分方程分析法[J].地震学报,1992,15(3):331-338.Du Xiuli,Xiong Jianguo,Guan Huimin.The boundary in-tegration equation methods in scattering of plane SH waves[J].Acta Seismologica Sinica,1992,15(3):331-338(in Chinese).
[10]Sanchez-Sesma F J,Ramos-Martinez J,Campillo M.An indirect boundary element method applied to simulate the seismic response of alluvial valleys for incident P,S and Rayleigh waves[J].Earthquake Engineering and Struc-tural Dynamics,1993,22(4):279-295.
[11]廖振鹏.工程波动理论导论[M].2版.北京:科学出版社,2002.Liao Zhenpeng.Introduction to Wave Motion Theories in Engineering[M].2nd ed.Beijing:Science Press,2002(in Chinese).
[12]Sanchez-Sesma F J.Diffraction of elastic SH-waves by wedges[J].Bull Seismological Soc of Am,1985,75(5):1435-1446.
[13]Lee V W,Sherif R I.Diffraction around circular canyon in elastic wedge space[J].Journal of Engineering Me-chanics,1996,122(6):539-544.
[14]Lee V W,Sherif R I.Diffraction around a circular allu-vial valley in an elastic wedge-shaped medium due to plane SH-waves[J].European Earthquake Engineering,1996,10(3):21-28.
[15]Dermendjian N,Lee V W,Liang Jianwen.Anti-plane deformation around arbitrary-shaped canyons in wedge-shape half space:Moment-method solutions[J].Earth-quake Engineering and Engineering Vibration,2003,2(2):281-287.
[16]Dermendjian N,Lee V W,Moment solutions of anti-plane(SH)wave diffraction around arbitrary-shaped rigid foundations on a wedge-shape half space[J].ISET Jour-nal of Earthquake Technology,2003,40(2):161-172.
[17]史文谱,刘殿魁,禇京莲,等.二维直角平面内固定圆形夹杂对稳态入射反平面剪切波的散射[J].爆炸与冲击,2007,27(1):57-62.Shi Wenpu,Liu Diankui,Chu Jinglian,et al.Scattering of fixed cirucular inclusion in right-angled plane to steady incident planar shearing horizontal wave[J].Explosion and Shock Waves,2007,27(1):57-62(in Chinese).
[18]史文谱,刘殿魁,宋永涛,等.直角平面内圆孔对稳态SH波的散射[J].应用数学和力学,2006,27(12):1417-1423.Shi Wenpu,Liu Diankui,Song Yongtao,et al.Scattering of circular cavity in right-angular planar space to steady SH-wave[J].Applied Mathematics and Mechanics,2006,27(12):1417-1423(in Chinese).
[2]Wong H L,Trifunac M D.Surface motion of a semi-elliptical alluvial valley for incident plane SH waves[J].Bulletin of Seismological Society of America,1974,64(5):1389-1408.
[3]Todorovska M,lee V W.Surface motion of shallow circu-lar alluvial valleys for incident plane SH waves:Analytical solution[J].Soil Dynamics and Earthquake Engineering,1991,10(4):192-200.
[4]Yuan Xiaoming,Liao Zhenpeng.Scattering of plane SH waves by a cylindrical alluvial valley of circular-arc cross-section[J].Earthquake Engineering and Structural Dynamics,1995,24(10):1303-1313.
[5]梁建文,张郁山,顾晓鲁.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 Jianwen,Zhang Yushan,Gu Xiaolu.Surface mo-tion 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]李伟华,赵成刚.具有饱和土沉积层的充水河谷对平面波的散射[J].地球物理学报,2006,49(1):212-224.Li Weihua,Zhao Chenggang.Scattering of plane waves by circular arc alluvial valleys with saturated soil depos-its and water[J].Chinese Journal of Geophysics,2006,49(1):212-224(in Chinese).
[7]Boore D M,Larner K L,Aki K.Comparison of two inde-pendent methods for the solution of wave scattering prob-lems:response of a sedimentary basin to incident SH waves[J].Journal of Geophysical Research,1971,76(2):558-569.
[8]Dravinski M.Scattering of plane harmonic SH wave by dipping layers or arbitrary shape[J].Bulletin of Seismol-ogical Society of America,1983,73(5):1303-1319.
[9]杜修力,熊建国,关慧敏.平面SH波散射问题的边界积分方程分析法[J].地震学报,1992,15(3):331-338.Du Xiuli,Xiong Jianguo,Guan Huimin.The boundary in-tegration equation methods in scattering of plane SH waves[J].Acta Seismologica Sinica,1992,15(3):331-338(in Chinese).
[10]Sanchez-Sesma F J,Ramos-Martinez J,Campillo M.An indirect boundary element method applied to simulate the seismic response of alluvial valleys for incident P,S and Rayleigh waves[J].Earthquake Engineering and Struc-tural Dynamics,1993,22(4):279-295.
[11]廖振鹏.工程波动理论导论[M].2版.北京:科学出版社,2002.Liao Zhenpeng.Introduction to Wave Motion Theories in Engineering[M].2nd ed.Beijing:Science Press,2002(in Chinese).
[12]Sanchez-Sesma F J.Diffraction of elastic SH-waves by wedges[J].Bull Seismological Soc of Am,1985,75(5):1435-1446.
[13]Lee V W,Sherif R I.Diffraction around circular canyon in elastic wedge space[J].Journal of Engineering Me-chanics,1996,122(6):539-544.
[14]Lee V W,Sherif R I.Diffraction around a circular allu-vial valley in an elastic wedge-shaped medium due to plane SH-waves[J].European Earthquake Engineering,1996,10(3):21-28.
[15]Dermendjian N,Lee V W,Liang Jianwen.Anti-plane deformation around arbitrary-shaped canyons in wedge-shape half space:Moment-method solutions[J].Earth-quake Engineering and Engineering Vibration,2003,2(2):281-287.
[16]Dermendjian N,Lee V W,Moment solutions of anti-plane(SH)wave diffraction around arbitrary-shaped rigid foundations on a wedge-shape half space[J].ISET Jour-nal of Earthquake Technology,2003,40(2):161-172.
[17]史文谱,刘殿魁,禇京莲,等.二维直角平面内固定圆形夹杂对稳态入射反平面剪切波的散射[J].爆炸与冲击,2007,27(1):57-62.Shi Wenpu,Liu Diankui,Chu Jinglian,et al.Scattering of fixed cirucular inclusion in right-angled plane to steady incident planar shearing horizontal wave[J].Explosion and Shock Waves,2007,27(1):57-62(in Chinese).
[18]史文谱,刘殿魁,宋永涛,等.直角平面内圆孔对稳态SH波的散射[J].应用数学和力学,2006,27(12):1417-1423.Shi Wenpu,Liu Diankui,Song Yongtao,et al.Scattering of circular cavity in right-angular planar space to steady SH-wave[J].Applied Mathematics and Mechanics,2006,27(12):1417-1423(in Chinese).
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