SH波作用下各向异性弹性半空间中浅埋圆孔附近的动应力集中研究
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摘要
研究了稳态水平剪切(SH)波作用下含有圆柱形孔洞的各向异性弹性半空间的动力响应问题,探讨介质的各向异性对孔附近动应力的影响规律。运用复变函数和多极坐标方法在变换空间中构造出各向异性弹性半空间中圆孔的散射波函数,所构造的散射波函数能够自动满足半空间水平表面上应力自由的边界条件和无穷远处的Sommerfeld辐射条件。根据圆孔表面应力自由的边界条件,采用最小二乘法求解所构造的散射波函数的系数。分析了SH波以不同角度自弹性半空间内入射时,不同介质特性、入射波数和埋深对圆孔附近动应力集中系数的影响。数值结果表明,各向异性弹性半空间中孔附近的动应力比各向同性情况有明显增高。
The problem of dynamic stress concentration around a shallow cylindrical cavity incident by steady-state shear horizontal SH wave in an anisotropically elastic half-space ware solved;and the rules that anisotropy of the medium influenced dynamic stress concentration around the cavity were investigated.By using the function of complex variable and multi-polar coordinate system,we constructed scattering wave function of the cylindrical cavity,which automatically satisfied the zero-stress boundary condition on the horizontal surface in elastic half-space and the Sommerfeld radiation condition at infinity.According to zero-stress boundary condition of the cylindrical cavity,we solved coefficients of the scattering wave function by least square method.Finally,the effects of different media characteristics,wave numbers,and embedded depth on dynamic stress concentration factors around the cylindrical cavity were analyzed,when SH wave incident with different angles.Numerical results show that: the dynamic stress concentration factor around cylindrical cavity increases obviously in anisotropically elastic half-space in contrast with isotropic one.
The problem of dynamic stress concentration around a shallow cylindrical cavity incident by steady-state shear horizontal SH wave in an anisotropically elastic half-space ware solved;and the rules that anisotropy of the medium influenced dynamic stress concentration around the cavity were investigated.By using the function of complex variable and multi-polar coordinate system,we constructed scattering wave function of the cylindrical cavity,which automatically satisfied the zero-stress boundary condition on the horizontal surface in elastic half-space and the Sommerfeld radiation condition at infinity.According to zero-stress boundary condition of the cylindrical cavity,we solved coefficients of the scattering wave function by least square method.Finally,the effects of different media characteristics,wave numbers,and embedded depth on dynamic stress concentration factors around the cylindrical cavity were analyzed,when SH wave incident with different angles.Numerical results show that: the dynamic stress concentration factor around cylindrical cavity increases obviously in anisotropically elastic half-space in contrast with isotropic one.
引文
[1]刘殿魁,林宏.浅埋的圆柱形孔洞对SH波的散射与地震动[J].爆炸与冲击,2003,23(1):6-12.LIU Dian-kui,LIN Hong.Scattering of SH waves by ashallow buried cylindrical cavity and the groundmotion[J].Explosion and Shock Waves,2003,23(1):6-12.
[2]WANG Guo-qing,LIU Dian-kui.Scattering of SH waveby multiple circular cavities in half space[J].EarthquakeEngineering and Engineering Vibration,2002,1(1):36-44.
[3]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,2006,38(2):209-218.LIU Dian-kui,WANG Guo-qing.Antiplane SHdeformation of a semi-cylindrical hill above a subsurfacecavity[J].Acta Mechanica Sinica,2006,38(2):209-218.
[4]刘刚,刘殿魁.SH波入射时浅埋圆孔附近等腰三角形凸起地形的地震动[J].固体力学学报,2007,28(1):60-66.LIU Gang,LIU Dian-kui.Ground motion of an isoscelestriangular hill above a subsurface cavity with incident SHwaves[J].Acta Mechanica Solida Sinica,2007,28(1):60-66.
[5]梁建文,纪晓东,Vincent W LEE.地下圆形衬砌隧道对沿线地震动的影响(I):级数解[J].岩土力学,2005,26(4):520-524.LIANG Jian-wen,JI Xiao-dong,Vincent W LEE.Effectsof an underground lined tunnel on ground motion(I):Series solution[J].Rock and Soil Mechanics,2005,26(4):520-524.
[6]梁建文,纪晓东,Vincent W LEE.地下圆形衬砌隧道对沿线地震动的影响(II):数值结果[J].岩土力学,2005,26(5):687-692.LIANG Jian-wen,JI Xiao-dong,Vincent W LEE.Effectsof an underground lined tunnel on ground motion(II):Numerical results[J].Rock and Soil Mechanics,2005,26(5):687-692.
[7]梁建文,张浩,Vincent W Lee.地下洞室群对地面运动影响问题的级数解答——P波入射[J].地震学报,2004,26(3):269-280.LIANG Jian-wen,ZHANG Hao,Vincent W LEE.Aseries solution for surface motion amplification due tounderground group cavities:Incident P waves[J].ActaSeismologica Sinica,2004,26(3):269-280.
[8]LIANG Jian-wen,ZHANG Hao,LEE Vincent W.A seriessolution for surface motion amplification due tounderground twin tunnels:Incident SV waves[J].Earthquake Engineering and Engineering Vibration,2003,2(2):289-298.
[9]LEE V W,TRIFUNAC M D.Response of tunnels toincident SH-wave[J].Journal of the EngineeringMechanics Division,ASCE,1979,105(4):643-659.
[10]LEE V W,KARL J.Diffraction of SV waves byunderground circular cylindrical cavities[J].SoilDynamics and Earthquake Engineering,1992,11(8):445-456.
[11]LEE V W,MANOOGIAN M E,CHEN S.Anti-planeSH-deformations near a surface rigid foundation above asubsurface rigid circular tunnel[J].EarthquakeEngineering and Engineering Vibration,2002,1(1):27-35.
[12]刘殿魁.各向异性介质中SH波引起的圆孔附近的动应力集中[J].力学学报,1988,20(5):443-452.LIU Dian-kui.Dynamic stress concentration around acircular cavity by SH wave in an anisotropic media[J].Acta Mechanica Sinica,1988,20(5):443-452.
[13]刘殿魁,韩峰.SH波对各向异性凹陷地形的散射[J].地震工程与工程振动,1990,10(2):11-24.LIU Dian-kui,HAN Feng.Scattering of plane SH waveby canyon topography in anisotropic medium[J].Earthquake Engineering and Engineering Vibration,1990,10(2):11-24
[14]刘殿魁,袁迎春.各向异性介质中由SH波引起的圆孔周围的远场位移[J].地震工程与工程振动,1988,8(1):50-59.LIU Dian-kui,YUAN Ying-chun.Far field displacementaround a circular cavity caused by SH wave in ananisotropic medium[J].Earthquake Engineering andEngineering Vibration,1988,8(1):50-59.
[15]刘殿魁,许怡燕.各向异性介质中SH波与多个半圆形凹陷地形的相互作用[J].力学学报,1993,25(1):93-102.LIU Dian-kui,XU Yi-yan.Interaction of multiplesemi-cylindrical canyons by plane SH wave in anisotropicmedia[J].Acta Mechanica Sinica,1993,25(1):93-102.
[16]LIU Dian-kui,HAN Feng.Scattering of plane SH waveby noncircular cavity in anisotropic media[J].Journal ofApplied Mechanics,Transactions ASME,1993,60(3):769-772.
[17]钟伟芳,聂国华.各向异性体内多个夹杂对反平面波的散射[J].固体力学学报,1988,9(1):1-14.ZHONG Wei-fang,NIE Guo-hua.The scattering of SHwave by numerous inhomogeneities in an anisotropicbody[J].Acta Mechanica Solida Sinica,1988,9(1):1-14.
[18]钟伟芳,钱维平.各向异性体内含任意孔洞对反平面波散射的边界元方法[J].固体力学学报,1990,11(4):285-297.ZHONG Wei-fang,QIAN Wei-ping.A boundary elementmethod for calculation the SH wave scattering fromarbitrrarily shaped holes in an anisotropic mediun[J].Acta Mechanica Solida Sinica,1990,11(4):285-297.
[19]杜修力,熊建国.各向异性弹性层中SH波传播的边界元法[J].工程力学,1989,6(3):10-18.DU Xiu-li,XIONG Jian-guo.Propagation of SH wave inanisotropic midium and the solution by boundary elementmethod[J].Engineering Mechanices,1989,6(3):10-18.
[20]ESLAMI H,GATMIRIA B.Two formulations fordynamic response of a cylindrical cavity in cross-anisotropic porous media[J].International Journal forNumerical and Analytical Methods in Geomechanics,2010,34(4):331-356.
[21]PAO Y H,MOW C C.Diffraction of elastic waves anddynamic stress concentrations[M].New York:CraneRussak and Company,1973.
[22]林宏,刘殿魁.半无限空间中圆形孔洞周围SH波的散射[J].震工程与工程振动,2002,22(2):9-15.LIN Hong,LIU Dian-kui.Scattering of SH-wave arounda circular cavity in half space[J].Earthquake Engi-neering and Engineering Vibration,2002,22(2):9-15.
[2]WANG Guo-qing,LIU Dian-kui.Scattering of SH waveby multiple circular cavities in half space[J].EarthquakeEngineering and Engineering Vibration,2002,1(1):36-44.
[3]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,2006,38(2):209-218.LIU Dian-kui,WANG Guo-qing.Antiplane SHdeformation of a semi-cylindrical hill above a subsurfacecavity[J].Acta Mechanica Sinica,2006,38(2):209-218.
[4]刘刚,刘殿魁.SH波入射时浅埋圆孔附近等腰三角形凸起地形的地震动[J].固体力学学报,2007,28(1):60-66.LIU Gang,LIU Dian-kui.Ground motion of an isoscelestriangular hill above a subsurface cavity with incident SHwaves[J].Acta Mechanica Solida Sinica,2007,28(1):60-66.
[5]梁建文,纪晓东,Vincent W LEE.地下圆形衬砌隧道对沿线地震动的影响(I):级数解[J].岩土力学,2005,26(4):520-524.LIANG Jian-wen,JI Xiao-dong,Vincent W LEE.Effectsof an underground lined tunnel on ground motion(I):Series solution[J].Rock and Soil Mechanics,2005,26(4):520-524.
[6]梁建文,纪晓东,Vincent W LEE.地下圆形衬砌隧道对沿线地震动的影响(II):数值结果[J].岩土力学,2005,26(5):687-692.LIANG Jian-wen,JI Xiao-dong,Vincent W LEE.Effectsof an underground lined tunnel on ground motion(II):Numerical results[J].Rock and Soil Mechanics,2005,26(5):687-692.
[7]梁建文,张浩,Vincent W Lee.地下洞室群对地面运动影响问题的级数解答——P波入射[J].地震学报,2004,26(3):269-280.LIANG Jian-wen,ZHANG Hao,Vincent W LEE.Aseries solution for surface motion amplification due tounderground group cavities:Incident P waves[J].ActaSeismologica Sinica,2004,26(3):269-280.
[8]LIANG Jian-wen,ZHANG Hao,LEE Vincent W.A seriessolution for surface motion amplification due tounderground twin tunnels:Incident SV waves[J].Earthquake Engineering and Engineering Vibration,2003,2(2):289-298.
[9]LEE V W,TRIFUNAC M D.Response of tunnels toincident SH-wave[J].Journal of the EngineeringMechanics Division,ASCE,1979,105(4):643-659.
[10]LEE V W,KARL J.Diffraction of SV waves byunderground circular cylindrical cavities[J].SoilDynamics and Earthquake Engineering,1992,11(8):445-456.
[11]LEE V W,MANOOGIAN M E,CHEN S.Anti-planeSH-deformations near a surface rigid foundation above asubsurface rigid circular tunnel[J].EarthquakeEngineering and Engineering Vibration,2002,1(1):27-35.
[12]刘殿魁.各向异性介质中SH波引起的圆孔附近的动应力集中[J].力学学报,1988,20(5):443-452.LIU Dian-kui.Dynamic stress concentration around acircular cavity by SH wave in an anisotropic media[J].Acta Mechanica Sinica,1988,20(5):443-452.
[13]刘殿魁,韩峰.SH波对各向异性凹陷地形的散射[J].地震工程与工程振动,1990,10(2):11-24.LIU Dian-kui,HAN Feng.Scattering of plane SH waveby canyon topography in anisotropic medium[J].Earthquake Engineering and Engineering Vibration,1990,10(2):11-24
[14]刘殿魁,袁迎春.各向异性介质中由SH波引起的圆孔周围的远场位移[J].地震工程与工程振动,1988,8(1):50-59.LIU Dian-kui,YUAN Ying-chun.Far field displacementaround a circular cavity caused by SH wave in ananisotropic medium[J].Earthquake Engineering andEngineering Vibration,1988,8(1):50-59.
[15]刘殿魁,许怡燕.各向异性介质中SH波与多个半圆形凹陷地形的相互作用[J].力学学报,1993,25(1):93-102.LIU Dian-kui,XU Yi-yan.Interaction of multiplesemi-cylindrical canyons by plane SH wave in anisotropicmedia[J].Acta Mechanica Sinica,1993,25(1):93-102.
[16]LIU Dian-kui,HAN Feng.Scattering of plane SH waveby noncircular cavity in anisotropic media[J].Journal ofApplied Mechanics,Transactions ASME,1993,60(3):769-772.
[17]钟伟芳,聂国华.各向异性体内多个夹杂对反平面波的散射[J].固体力学学报,1988,9(1):1-14.ZHONG Wei-fang,NIE Guo-hua.The scattering of SHwave by numerous inhomogeneities in an anisotropicbody[J].Acta Mechanica Solida Sinica,1988,9(1):1-14.
[18]钟伟芳,钱维平.各向异性体内含任意孔洞对反平面波散射的边界元方法[J].固体力学学报,1990,11(4):285-297.ZHONG Wei-fang,QIAN Wei-ping.A boundary elementmethod for calculation the SH wave scattering fromarbitrrarily shaped holes in an anisotropic mediun[J].Acta Mechanica Solida Sinica,1990,11(4):285-297.
[19]杜修力,熊建国.各向异性弹性层中SH波传播的边界元法[J].工程力学,1989,6(3):10-18.DU Xiu-li,XIONG Jian-guo.Propagation of SH wave inanisotropic midium and the solution by boundary elementmethod[J].Engineering Mechanices,1989,6(3):10-18.
[20]ESLAMI H,GATMIRIA B.Two formulations fordynamic response of a cylindrical cavity in cross-anisotropic porous media[J].International Journal forNumerical and Analytical Methods in Geomechanics,2010,34(4):331-356.
[21]PAO Y H,MOW C C.Diffraction of elastic waves anddynamic stress concentrations[M].New York:CraneRussak and Company,1973.
[22]林宏,刘殿魁.半无限空间中圆形孔洞周围SH波的散射[J].震工程与工程振动,2002,22(2):9-15.LIN Hong,LIU Dian-kui.Scattering of SH-wave arounda circular cavity in half space[J].Earthquake Engi-neering and Engineering Vibration,2002,22(2):9-15.
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