柱面SH波在地下圆形衬砌洞室周围散射解析解
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摘要
采用波函数展开法给出了半空间中柱面SH波在圆形衬砌洞室周围散射的解析解,并对解答的精度进行了分析。通过数值算例分析了入射频率、波源与洞室的距离、洞室埋深、衬砌刚度等对洞室衬砌动应力集中因子的影响。研究表明,柱面波在地下衬砌洞室周围的散射与平面波情况有着显著的差别,衬砌动应力集中因子和波源与洞室的距离密切相关;柱面波在全空间衬砌洞室周围的散射与半空间情况有着显著的差别,半空间地表对动应力集中因子有着重要影响。
An analytical solution to the cylindrical SH wave diffraction around circular lined cavity is presented using wave function expansion method,and the precision of the solution is verified.Effects of the incident frequency,the distance between the wave source and the cavity,the buried depth of the cavity,and the lined stiffness on DSCF(dynamic stress concentration factor) are discussed by numerical results.It is shown that,there is distinct difference between the cylindrical wave diffraction and the plane wave diffraction around lined cavity and the DSCF is significantly dependent on the distance between the wave source and the cavity;there is a notable difference between cylindrical wave diffraction around lined cavity in half-space and that in whole-space,and the DSCF is closely related to the surface of half-space.
An analytical solution to the cylindrical SH wave diffraction around circular lined cavity is presented using wave function expansion method,and the precision of the solution is verified.Effects of the incident frequency,the distance between the wave source and the cavity,the buried depth of the cavity,and the lined stiffness on DSCF(dynamic stress concentration factor) are discussed by numerical results.It is shown that,there is distinct difference between the cylindrical wave diffraction and the plane wave diffraction around lined cavity and the DSCF is significantly dependent on the distance between the wave source and the cavity;there is a notable difference between cylindrical wave diffraction around lined cavity in half-space and that in whole-space,and the DSCF is closely related to the surface of half-space.
引文
[1]Pao Y H,Mow C C.Diffraction of elastic waves and dynamic stress concentrations[M].New York:Crane Russak and Company,Inc.,1973:239-363.
[2]Lee V W,Trifunac M D.Response of tunnels to incident SH-waves[J].Journal of Engineering Mechanics,ASCE,1979,105:643-659.
[3]Lee V W,Karl J.Diffraction of SV waves by underground,circular,cylindrical cavities[J].Soil Dynamics and Earthquake Engineering,1992,11:445-456.
[4]Lee V W,Karl J.On deformation near a circular underground cavity subjected to incident plane P waves[J].European Earthquake Engineering,1993,(1):29-36.
[5]Davis C A,Lee V W,Bardet J P.Transverse response of underground cavities and pipes to incident SV waves[J].Earthquake Engineering andStructural Dynamics,2001,30:383-410.
[6]林宏,刘殿魁.半无限空间中圆形洞室周围SH波的散射[J].地震工程与工程振动,2002,22(2):9-16.LIN Hong,LIU Diankui.Scattering of SH-wave around a cavity in half space[J].Journal of Earthquake Engineering and Engineering Vibration,2002,22(2):9-16.(in Chinese)
[7]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 Diankui,LIN Hong.Scattering of SH-waves by a shallow buried cylindrical cavity and the ground motion[J].Explosion and Shock Waves,2003,23(1):6-12.(in Chinese)
[8]梁建文,张浩,Lee V W.平面P波入射下地下洞室群动应力集中问题解析解[J].岩土工程学报,2004,26(6):815-819.LIANG Jianwen,ZHANG Hao,Lee V W.An analytical solution for dynamic stress concentration of underground cavities under incident plane Pwaves[J].Chinese Journal of Geotechnical Engineering,2004,26(6):815-819.(in Chinese)
[9]梁建文,张浩,Lee V W.地下双洞室在SV波入射下动力响应问题解析解[J].振动工程学报,2004,17(2):132-140.LIANG Jianwen,ZHANG Hao,Lee V W.An analytical solution for dynamic streess concentration of underground twin cavities due to incident SVwaves[J].Journal of Vibration Engineering,2004,17(2):132-140.(in Chinese)
[10]纪晓东,梁建文,杨建江.地下圆形衬砌洞室在平面P波和SV波入射下动应力集中问题的级数解[J].天津大学学报,2006,39(5):511-517.JI Xiaodong,LIANG Jianwen,YANG Jianjiang.On dynamic stress concentration of an underground cylindrical lined cavity subjected to incidentplane P and SV waves[J].Journal of Tianjin University,2006,39(5):511-517.(in Chinese)
[11]梁建文,刘中宪.柱面波在半空间中洞室周围的散射[J].地震工程与工程振动,2008,28(5):27-37.LIANG Jianwen,LIU Zhongxian.Scattering of cylindrical waves around a cavity in a half-space[J].Journal of Earthquake Engineering and Engi-neering Vibration,2008,28(5):27-37.(in Chinese)
[12]袁晓铭.散射问题中柱面坐标波函数的全域变换公式[J].地震工程与工程振动,2010,30(4):1-7.YUAN Xiaoming.A complete-domain transform formula of cylindrical wave functions for scattering problems[J].Journal of Earthquake Engi-neering and Engineering Vibration,2010,30(4):1-7.(in Chinese)
[13]梁建文,张浩,Lee V W.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 Jianwen,ZHANG Hao,Lee V W.A series solution for surface motion amplification due to underground group cavities:incident P waves[J].Acta Seismologica Sinica,2004,17(3):296-307.(in Chinese)
[14]丁美.地下圆形衬砌隧洞对柱面SH波的散射解析解[D].天津:天津大学,2004.DING Mei.On scattering and diffraction of underground,circular,lined tunnels subjected to incident cylindrical SH waves[D].Tianjin:TianjinUniversity,2004.(in Chinese)
[2]Lee V W,Trifunac M D.Response of tunnels to incident SH-waves[J].Journal of Engineering Mechanics,ASCE,1979,105:643-659.
[3]Lee V W,Karl J.Diffraction of SV waves by underground,circular,cylindrical cavities[J].Soil Dynamics and Earthquake Engineering,1992,11:445-456.
[4]Lee V W,Karl J.On deformation near a circular underground cavity subjected to incident plane P waves[J].European Earthquake Engineering,1993,(1):29-36.
[5]Davis C A,Lee V W,Bardet J P.Transverse response of underground cavities and pipes to incident SV waves[J].Earthquake Engineering andStructural Dynamics,2001,30:383-410.
[6]林宏,刘殿魁.半无限空间中圆形洞室周围SH波的散射[J].地震工程与工程振动,2002,22(2):9-16.LIN Hong,LIU Diankui.Scattering of SH-wave around a cavity in half space[J].Journal of Earthquake Engineering and Engineering Vibration,2002,22(2):9-16.(in Chinese)
[7]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 Diankui,LIN Hong.Scattering of SH-waves by a shallow buried cylindrical cavity and the ground motion[J].Explosion and Shock Waves,2003,23(1):6-12.(in Chinese)
[8]梁建文,张浩,Lee V W.平面P波入射下地下洞室群动应力集中问题解析解[J].岩土工程学报,2004,26(6):815-819.LIANG Jianwen,ZHANG Hao,Lee V W.An analytical solution for dynamic stress concentration of underground cavities under incident plane Pwaves[J].Chinese Journal of Geotechnical Engineering,2004,26(6):815-819.(in Chinese)
[9]梁建文,张浩,Lee V W.地下双洞室在SV波入射下动力响应问题解析解[J].振动工程学报,2004,17(2):132-140.LIANG Jianwen,ZHANG Hao,Lee V W.An analytical solution for dynamic streess concentration of underground twin cavities due to incident SVwaves[J].Journal of Vibration Engineering,2004,17(2):132-140.(in Chinese)
[10]纪晓东,梁建文,杨建江.地下圆形衬砌洞室在平面P波和SV波入射下动应力集中问题的级数解[J].天津大学学报,2006,39(5):511-517.JI Xiaodong,LIANG Jianwen,YANG Jianjiang.On dynamic stress concentration of an underground cylindrical lined cavity subjected to incidentplane P and SV waves[J].Journal of Tianjin University,2006,39(5):511-517.(in Chinese)
[11]梁建文,刘中宪.柱面波在半空间中洞室周围的散射[J].地震工程与工程振动,2008,28(5):27-37.LIANG Jianwen,LIU Zhongxian.Scattering of cylindrical waves around a cavity in a half-space[J].Journal of Earthquake Engineering and Engi-neering Vibration,2008,28(5):27-37.(in Chinese)
[12]袁晓铭.散射问题中柱面坐标波函数的全域变换公式[J].地震工程与工程振动,2010,30(4):1-7.YUAN Xiaoming.A complete-domain transform formula of cylindrical wave functions for scattering problems[J].Journal of Earthquake Engi-neering and Engineering Vibration,2010,30(4):1-7.(in Chinese)
[13]梁建文,张浩,Lee V W.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 Jianwen,ZHANG Hao,Lee V W.A series solution for surface motion amplification due to underground group cavities:incident P waves[J].Acta Seismologica Sinica,2004,17(3):296-307.(in Chinese)
[14]丁美.地下圆形衬砌隧洞对柱面SH波的散射解析解[D].天津:天津大学,2004.DING Mei.On scattering and diffraction of underground,circular,lined tunnels subjected to incident cylindrical SH waves[D].Tianjin:TianjinUniversity,2004.(in Chinese)
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