直角域中凸起和孔洞对SH波的散射与地震动
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摘要
按照波函数展开法和镜像方法,对直角域中半圆形凸起和圆形孔洞对SH波的散射进行了分析,得到其稳态解。对含孔洞和凸起的直角域做分区,等效为一个含孔洞与凹陷的直角域和一个圆域的契合,其在分界面上满足位移和应力的连续性条件,即契合条件,分别构造两个区域内的位移波函数,按照孔洞边界柱面上的应力自由和契合条件定解波函数展开式的系数。按Fourier级数展开法,得到定解条件的线性代数方程组,截断求解,进而得到问题的解析解。数值算例给出圆形孔洞边沿动应力和地表位移幅值的分布情况,得到直角域自由边界、凸起、孔洞对散射和地震动的影响。
By using wave function expansion method and image method, scattering of a salient and a circular cavity with SH wave in an elastic quarter space is analyzed to obtain the steady state solution. The elastic quarter space which contains a salient and a circular cavity is divided into two media, while medium I is a quarter spaces which contain a circular cavity and a semi-circular canyon,medium II is a circular domain. Conjunction condition is introduced to force displacements and stresses of two media continued on the divided bound. Specific expressions of constructed displacement wave in medium I and medium II are determined by employing stress free condition on cavity bound and conjunction condition by using wave function expansion method and Fourier series expansion method. Simultaneously, the analytical solution is presented by solving truncated linear algebraic equations of definite boundary conditions. Numerical results are calculated to describe distribution of dynamic stress around the circular cavity and amplitude of displacement along the horizontal surface, then, effects of salient, cavity and stress free bounds of the quarter space to scattering and seismic ground motion are quantified.
By using wave function expansion method and image method, scattering of a salient and a circular cavity with SH wave in an elastic quarter space is analyzed to obtain the steady state solution. The elastic quarter space which contains a salient and a circular cavity is divided into two media, while medium I is a quarter spaces which contain a circular cavity and a semi-circular canyon,medium II is a circular domain. Conjunction condition is introduced to force displacements and stresses of two media continued on the divided bound. Specific expressions of constructed displacement wave in medium I and medium II are determined by employing stress free condition on cavity bound and conjunction condition by using wave function expansion method and Fourier series expansion method. Simultaneously, the analytical solution is presented by solving truncated linear algebraic equations of definite boundary conditions. Numerical results are calculated to describe distribution of dynamic stress around the circular cavity and amplitude of displacement along the horizontal surface, then, effects of salient, cavity and stress free bounds of the quarter space to scattering and seismic ground motion are quantified.
引文
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[7]LEE V W,TRIFUNAC M D.Response of tunnels to incident SH-waves[J].Journal of Engineering Mechanics,ASCE,1979,105:643-659.
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[10]刘殿魁,王国庆.浅埋圆形孔洞附近的半圆形凸起对SH波的散射[J].力学学报,2006,3(2):209-218.LIU Dian-kui,WANG Guo-qing.Antiplane SHdeformation of a semi-cylindrical hill above a subsurface cavity[J].Acta Mechanica Sinica,2006,3(2):209-218.
[11]赵嘉喜,齐辉,杨在林.含有部分脱胶的浅埋圆夹杂对SH波的散射[J].岩土力学,2009,30(5):1297-1302.ZHAO Jia-xi,QI Hui,YANG Zai-lin.Scattering of SH-waves by a shallow buried cylindrical inclusion with a partially debonded curve in half space[J].Rock and Soil Mechanics,2009,30(5):1297-1302.
[12]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.
[13]张根昌,齐辉,刘平安.SH波对直角平面区域内圆形衬砌的散射与地震动[J].力学与实践,2013,35(1):60-66.ZHANG Gen-chang,QI Hui,LIU Ping-an.Scattering of SH-wave by circular cavity in right-angle plane and seismic ground motion[J].Mechanics in Engineering,2013,35(1):60-66.
[14]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.
[15]孙苗苗.任意排列的空心管桩屏障对SH波的多重散射[J].岩土力学,2014,35(4):943-950.SUN Miao-miao.Multiple scattering of SH waves by rows of arbitrarily arranged tubular piles[J].Rock and Soil Mechanics,2014,35(4):943-950.
[16]何刘,吴光,赵志明.坡面形态对边坡动力变形破坏影响的模型试验研究[J].岩土力学,2014,35(1):111-117.HE Liu,WU Guang,ZHAO Zhi-ming.Model test of influence of slope surface morphology on dynamic deformation failure[J].Rock and Soil Mechanics,2014,35(1):111-117.
[2]POULOS H G,DAVIS E H.Elastic solutions for soil and rock mechanics[M].New Yorker:John Wiley&Sons,1974.
[3]ACHENBACH J D.Wave propagation in elastic solids[M].Amsterdam:North-Holland,1973.
[4]PAO Y H,MOW C C.Diffraction of elastic waves and dynamic stress concentrations[M].New York:Crane and Russak,1973.
[5]LIU D K,GAI B Z,TAO G Y.Applications of the method of complex functions to dynamic stress concentrations[J].Wave Motion,1982,4:293-304.
[6]LEE V W.On deformation near circular underground cavity subjected to incident plane SH waves[C]//Proceedings of the Application of Computer Methods in Engineering Conference.Los Angeles:[s.n.],1977,951-652.
[7]LEE V W,TRIFUNAC M D.Response of tunnels to incident SH-waves[J].Journal of Engineering Mechanics,ASCE,1979,105:643-659.
[8]TRIFUNAC M D.Scattering of plane SH waves by a semi-cylindrical canyon[J].Earth Engineering and Structural Dynamics,1973,1:267-281.
[9]袁晓铭.地表下圆形夹塞区出平面散射对地面运动的影响[J].地球物理学报,1996,39(3):373-381.YUAN Xiao-ming.Effect of a circular underground inclusion on surface motion under incident plane SH waves[J].Acta Geophysica Sinica,1996,39(3):373-381.
[10]刘殿魁,王国庆.浅埋圆形孔洞附近的半圆形凸起对SH波的散射[J].力学学报,2006,3(2):209-218.LIU Dian-kui,WANG Guo-qing.Antiplane SHdeformation of a semi-cylindrical hill above a subsurface cavity[J].Acta Mechanica Sinica,2006,3(2):209-218.
[11]赵嘉喜,齐辉,杨在林.含有部分脱胶的浅埋圆夹杂对SH波的散射[J].岩土力学,2009,30(5):1297-1302.ZHAO Jia-xi,QI Hui,YANG Zai-lin.Scattering of SH-waves by a shallow buried cylindrical inclusion with a partially debonded curve in half space[J].Rock and Soil Mechanics,2009,30(5):1297-1302.
[12]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.
[13]张根昌,齐辉,刘平安.SH波对直角平面区域内圆形衬砌的散射与地震动[J].力学与实践,2013,35(1):60-66.ZHANG Gen-chang,QI Hui,LIU Ping-an.Scattering of SH-wave by circular cavity in right-angle plane and seismic ground motion[J].Mechanics in Engineering,2013,35(1):60-66.
[14]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.
[15]孙苗苗.任意排列的空心管桩屏障对SH波的多重散射[J].岩土力学,2014,35(4):943-950.SUN Miao-miao.Multiple scattering of SH waves by rows of arbitrarily arranged tubular piles[J].Rock and Soil Mechanics,2014,35(4):943-950.
[16]何刘,吴光,赵志明.坡面形态对边坡动力变形破坏影响的模型试验研究[J].岩土力学,2014,35(1):111-117.HE Liu,WU Guang,ZHAO Zhi-ming.Model test of influence of slope surface morphology on dynamic deformation failure[J].Rock and Soil Mechanics,2014,35(1):111-117.
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