含半圆形凸起的直角域对平面SH波的地震动
|
摘要
按Green函数和积分方程方法,分析了含半圆形凸起的直角域对平面SH波的稳态响应,讨论了由凸起散射所造成的地震动。对含半圆形凸起的直角域做分区,分为直角域和半圆域,按镜像方法构造直角域的Green函数,按Graf加法公式和波函数展开法构造半圆域的Green函数。对直角域和半圆域做契合,在契合界面施加一组分布力,使直角域和半圆域中的位移场和应力场满足契合界面上的连续性条件,得到分布力的定解积分方程组。数值求解,得到契合界面上的应力分布和地表位移幅值,结果表明入射波的波数和角度以及凸起与直角域垂直边界的距离对凸起散射的影响。
Steady state responses in a right-angle domain with a semi-circular cylindrical hill to plane SH waves are analyzed, and the ground motion caused by hill scattering is discussed by using the Green function method and the integral equation method. The right-angle domain with a semi-circular hill is divided into two domains: Domain Ⅰ is right-angle space and Domain Ⅱ is semi-circular space. Green functions for the two domains are established, respectively: the image method is employed in Domain Ⅰ, and the Graf addition formula and wave function expansion method are employed in Domain Ⅱ. The conjunction condition is introduced between Domain Ⅰ and Domain Ⅱ. Distributed forces along conjunctive interface are adopted to formulate displacement and stress fields in the two domains which are continuous on the interface, and an integral equation for unknown forces is presented. Distribution of stress on the conjunctive interface and displacement amplitude on the horizontal surface are numerically solved to present the effects of incident wave number, angle and distance between hill and vertical bound of the right-angle domain on SH wave scattering of hill.
Steady state responses in a right-angle domain with a semi-circular cylindrical hill to plane SH waves are analyzed, and the ground motion caused by hill scattering is discussed by using the Green function method and the integral equation method. The right-angle domain with a semi-circular hill is divided into two domains: Domain Ⅰ is right-angle space and Domain Ⅱ is semi-circular space. Green functions for the two domains are established, respectively: the image method is employed in Domain Ⅰ, and the Graf addition formula and wave function expansion method are employed in Domain Ⅱ. The conjunction condition is introduced between Domain Ⅰ and Domain Ⅱ. Distributed forces along conjunctive interface are adopted to formulate displacement and stress fields in the two domains which are continuous on the interface, and an integral equation for unknown forces is presented. Distribution of stress on the conjunctive interface and displacement amplitude on the horizontal surface are numerically solved to present the effects of incident wave number, angle and distance between hill and vertical bound of the right-angle domain on SH wave scattering of hill.
引文
[1]TRIFUNAC M D.Surface motion of a semi-cylindrical alluvial valley for incident plane SH waves[J].Bulletin of the Seismological Society of America,1971,61(6):1755–1770.
[2]TRIFUNAC M D.Scattering of plane SH waves by a semicylindrical canyon[J].Earth Engineering and Structural Dynamics,1973,1:267–281.
[3]WONG H L,TRIFUNAC M D.Surface motion of a semi-elliptical alluvial valley for incident plane SH waves[J].Bulletin of the Seismological Society of America,1974,64(5):1389–1403.
[4]WONG H L,TRIFUNAC M D.Scattering of plane SH waves by a semi-elliptical canyon[J].Earth Engineering and Structural Dynamics,1974,3:157–169.
[5]袁晓铭,廖振鹏.圆弧形凹陷地形对平面SH波散射问题的级数解答[J].地震工程与工程振动,1993,13(2):1–11.(YUAN Xiao-ming,LIAO Zhen-peng.Series solution for scattering of plane SH waves by a canyon of circular-arc cross section[J].Earthquake Engineering and Engineering Vibration,1993,13(2):1–11.(in Chinese))
[6]YUAN X,LIAO Z P.Scattering of plane SH waves by a cylindrical canyon of circular-arc cross-section[J].Soil Dynamics and Earthquake Engineering,1994,13(6):407–412.
[7]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.(YUAN Xiao-ming,LIAO Zhen-peng.Scattering of plane SH waves by a cylindrical hill of circular-arc cross section[J].Earthquake Engineering and Engineering Vibration,1996,16(2):1–13.(in Chinese))
[8]YUAN X,LIAO Z P.Surface motion of a cylindrical hill of circular-arc cross-section for incident plane SH waves[J].Soil Dynamics and Earthquake Engineering,1996,15(3):189–199.
[9]崔志刚,邹永超,刘殿魁.SH波对圆弧形凸起地形的散射[J].地震工程与工程振动,1998,18(4):8–14.(CUI Zhi-gang,ZHOU Yong-chao,LIU Dian-kui.Scattering of plane SH wave by a cylindrical hill of circular arc cross section[J].Earthquake Engineering and Engineering Vibration,1998,18(4):8–14.(in Chinese))
[10]曹欣荣,宋天舒,刘殿魁.任意形状凸起地形对平面SH波的散射[J].应用数学和力学,2001,22(9):976–982.(CAO Xin-rong,SONG Tian-shu,LIU Dian-kui.Scattering of plane SH wave by a cylindrical hill of arbitrary shape[J].Applied Mathematics and Mechanics,2001,22(9):976–982.(in Chinese))
[11]张郁山.圆弧状沉积谷地在平面SH波入射下的动力响应[J].岩土工程学报,2010,32(1):1–6.(ZHANG Yu-shan.Dynamic response of arc-layered alluvial valley under incidence of plane SH waves[J].Chinese Journal of Geotechnical Engineering,2010,32(1):1–6.(in Chinese))
[12]LEE V W,AMORNWONGPAIBUN A.Scattering of anti-plane(SH)waves by a semi-elliptical hill:Ⅰ—Shallow hill[J].Soil Dynamics and Earthquake Engineering,2013,52:116–125.
[13]AMORNWONGPAIBUN A,LEE V W.Scattering of anti-plane(SH)waves by a semi-elliptical hill:Ⅱ—deep hill[J].Soil Dynamics and Earthquake Engineering,2013,52:126–137.
[14]巴振宁,梁建文,梅雄一.斜入射平面SH波在层状饱和半空间中沉积谷地周围的三维散射[J].岩土工程学报,2013,35(3):476–486.(BA Zhen-ning,LIANG Jian-wen,MEI Xiong-yi.Three-dimensional scattering of obliquely incident plane SH waves in alluvial valley embedded in layered saturated half-space[J].Chinese Journal of Geotechnical Engineering,2013,35(3):476–486.(in Chinese))
[15]齐辉,郭晶,杨杰.直角域非等腰三角形凸起对SH波的散射与地震动[J].振动与冲击,2012,31(18):157–162.(QI Hui,GUO Jing,YANG Jie.Scattering of SH-wave and ground motion induced by scalene triangular hill on a right-angle field[J].Journal of Vibration and Shock,2012,31(18):157–162.(in Chinese))
[16]折勇,齐辉,杨在林.SH波对直角平面区域内圆形孔洞的散射与地震动[J].应用力学学报,2008,25(3):392–398.(SHI Yong,QI Hui,YANG Zai-lin.Scattering of SH-wave by circular cavity in right-angle plane and seismic ground motion[J].Chinese Journal of Applied Mechanics,2008,25(3):392–398.(in Chinese))
[2]TRIFUNAC M D.Scattering of plane SH waves by a semicylindrical canyon[J].Earth Engineering and Structural Dynamics,1973,1:267–281.
[3]WONG H L,TRIFUNAC M D.Surface motion of a semi-elliptical alluvial valley for incident plane SH waves[J].Bulletin of the Seismological Society of America,1974,64(5):1389–1403.
[4]WONG H L,TRIFUNAC M D.Scattering of plane SH waves by a semi-elliptical canyon[J].Earth Engineering and Structural Dynamics,1974,3:157–169.
[5]袁晓铭,廖振鹏.圆弧形凹陷地形对平面SH波散射问题的级数解答[J].地震工程与工程振动,1993,13(2):1–11.(YUAN Xiao-ming,LIAO Zhen-peng.Series solution for scattering of plane SH waves by a canyon of circular-arc cross section[J].Earthquake Engineering and Engineering Vibration,1993,13(2):1–11.(in Chinese))
[6]YUAN X,LIAO Z P.Scattering of plane SH waves by a cylindrical canyon of circular-arc cross-section[J].Soil Dynamics and Earthquake Engineering,1994,13(6):407–412.
[7]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.(YUAN Xiao-ming,LIAO Zhen-peng.Scattering of plane SH waves by a cylindrical hill of circular-arc cross section[J].Earthquake Engineering and Engineering Vibration,1996,16(2):1–13.(in Chinese))
[8]YUAN X,LIAO Z P.Surface motion of a cylindrical hill of circular-arc cross-section for incident plane SH waves[J].Soil Dynamics and Earthquake Engineering,1996,15(3):189–199.
[9]崔志刚,邹永超,刘殿魁.SH波对圆弧形凸起地形的散射[J].地震工程与工程振动,1998,18(4):8–14.(CUI Zhi-gang,ZHOU Yong-chao,LIU Dian-kui.Scattering of plane SH wave by a cylindrical hill of circular arc cross section[J].Earthquake Engineering and Engineering Vibration,1998,18(4):8–14.(in Chinese))
[10]曹欣荣,宋天舒,刘殿魁.任意形状凸起地形对平面SH波的散射[J].应用数学和力学,2001,22(9):976–982.(CAO Xin-rong,SONG Tian-shu,LIU Dian-kui.Scattering of plane SH wave by a cylindrical hill of arbitrary shape[J].Applied Mathematics and Mechanics,2001,22(9):976–982.(in Chinese))
[11]张郁山.圆弧状沉积谷地在平面SH波入射下的动力响应[J].岩土工程学报,2010,32(1):1–6.(ZHANG Yu-shan.Dynamic response of arc-layered alluvial valley under incidence of plane SH waves[J].Chinese Journal of Geotechnical Engineering,2010,32(1):1–6.(in Chinese))
[12]LEE V W,AMORNWONGPAIBUN A.Scattering of anti-plane(SH)waves by a semi-elliptical hill:Ⅰ—Shallow hill[J].Soil Dynamics and Earthquake Engineering,2013,52:116–125.
[13]AMORNWONGPAIBUN A,LEE V W.Scattering of anti-plane(SH)waves by a semi-elliptical hill:Ⅱ—deep hill[J].Soil Dynamics and Earthquake Engineering,2013,52:126–137.
[14]巴振宁,梁建文,梅雄一.斜入射平面SH波在层状饱和半空间中沉积谷地周围的三维散射[J].岩土工程学报,2013,35(3):476–486.(BA Zhen-ning,LIANG Jian-wen,MEI Xiong-yi.Three-dimensional scattering of obliquely incident plane SH waves in alluvial valley embedded in layered saturated half-space[J].Chinese Journal of Geotechnical Engineering,2013,35(3):476–486.(in Chinese))
[15]齐辉,郭晶,杨杰.直角域非等腰三角形凸起对SH波的散射与地震动[J].振动与冲击,2012,31(18):157–162.(QI Hui,GUO Jing,YANG Jie.Scattering of SH-wave and ground motion induced by scalene triangular hill on a right-angle field[J].Journal of Vibration and Shock,2012,31(18):157–162.(in Chinese))
[16]折勇,齐辉,杨在林.SH波对直角平面区域内圆形孔洞的散射与地震动[J].应用力学学报,2008,25(3):392–398.(SHI Yong,QI Hui,YANG Zai-lin.Scattering of SH-wave by circular cavity in right-angle plane and seismic ground motion[J].Chinese Journal of Applied Mechanics,2008,25(3):392–398.(in Chinese))