横观各向同性凸起地形对平面qP-qSV波的散射
|
摘要
为研究横观各向同性(TI)介质的凸起地形对平面qP-qSV波的散射问题,采用间接边界元法进行数值模拟,并且分别给出该问题在时域和频域内的解答。在求解过程中将计算模型分解为开口层状半空间域和闭合凸起域,同时将波场分解为自由波场和散射波场,自由波场可通过直接刚度法求得,散射波场由斜线荷载动力格林函数来模拟。频域结果表明,TI介质参数的改变导致了凸起和层状半空间动力特性的改变,进而导致了凸起与层状半空间动力相互作用机制的改变,使得不同TI介质参数对应的地表位移幅值显著不同。而时域结果表明,TI介质参数与波的传播方向均对qP波和qSV波的在凸起地形中的传播有着显著影响。另外,时域结果更为清晰地展示入射波、反射波和散射波的传播过程。
To investigate scattering of plane qP-qSV waves induced by a convex topography with the transversely isotropic(TI) medium, the indirect boundary element method(IBEM) is used for the numerical simulation and the solutions of the plane qP-qSV waves scattering problem in both the frequency and time domain are given, respectively. In the process of solving, the calculation model is divided into open layered half-space region and close hill region, and the wave field is decomposed into free wave field and scattered wave field, the first of which can be solved by the direct stiffness method, and the second can be simulated by the dynamic Green's function by applying the fictitious inclined uniformly distributed load. The results in frequency domain show that the different TI media can change the dynamic characteristics of hill and layered half-space, and alter the dynamic interaction mechanism between hill and layered half-space, making the surface displacements significantly different. The results in time domain indicate that the parameters of the TI media and incident directions of plane waves have significant effects on the propagation of qP-qSV waves around the hill. In addition, time domain results clearly show the transmission process of incident, reflected and scattered waves.
To investigate scattering of plane qP-qSV waves induced by a convex topography with the transversely isotropic(TI) medium, the indirect boundary element method(IBEM) is used for the numerical simulation and the solutions of the plane qP-qSV waves scattering problem in both the frequency and time domain are given, respectively. In the process of solving, the calculation model is divided into open layered half-space region and close hill region, and the wave field is decomposed into free wave field and scattered wave field, the first of which can be solved by the direct stiffness method, and the second can be simulated by the dynamic Green's function by applying the fictitious inclined uniformly distributed load. The results in frequency domain show that the different TI media can change the dynamic characteristics of hill and layered half-space, and alter the dynamic interaction mechanism between hill and layered half-space, making the surface displacements significantly different. The results in time domain indicate that the parameters of the TI media and incident directions of plane waves have significant effects on the propagation of qP-qSV waves around the hill. In addition, time domain results clearly show the transmission process of incident, reflected and scattered waves.
引文
[1]瓦尔夫J P.土与结构相互作用[M].北京:地震出版社,1989.WOLF J P.Dynamic soil-structure Interaction[M].Beijing:Earthquake Publishing Press,1989.
[2]YUAN XIAOMING,MEN FULU.Scattering of plane SH waves by a semi cylindrical hill[J].Earthquake Engineering and Structural Dynamic,1992,21(12):1091-1098.
[3]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-acrosssection[J].Earthquake Engineering and Engineering Vibration,1996,16(2):1-13.
[4]梁建文,张彦帅.平面SV波入射下半圆凸起地形地表运动解析解[J].地震学报,2006,28(3):238-239.LIANG Jian-wen,ZHANG Yan-shuai.Analytical solution of ground motion of semi convex topography under plane SV wave incidence[J].Acta Seismologica Sinica,2006,28(3):238-239.
[5]LIANG J W,ZHANG Y S,LEE V W.Scattering of plane P waves by a semi-cylindrical hill:analytical solution[J].Earthquake Engineering and Engineering Vibration,2005,4(1):27-36.
[6]LEE V W,LUO H,LIANG J W.Diffraction of anti-plane SH waves by a semi-circular cylindrical hill with an inside concentric semi-circular tunnel[J].Earthquake Engineering and Engineering Vibration,2004,3(2):249-262.
[7]齐辉,蔡立明,潘向南.直角域中凸起和孔洞对SH波的散射与地震动[J].岩土力学,2015,36(2):347-353.QI Hui,CAI Li-ming,PAN Xiang-nan.Scattering and seismic ground motion of circular cavity and salient with SH wave in a quarter space[J].Rock and Soil Mechanics,2015,36(2):347-353.
[8]AMORNWONGPAIBUN A,LEE V W.Scattering of anti-plane(SH)waves by a semi-elliptical hill:I-shallow hill[J].Soil Dynamics and Earthquake Engineering,2013,52(13):116-125.
[9]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(13):126-137.
[10]SANCHEZ-SESMA F J,CAMPILLO M.Topographic effects for incident P,SV and Rayieigh waves[J].Tectonophysics,1993,218(1-3):113-125.
[11]梁建文,巴振宁.弹性层状半空间中凸起地形对入射平面SH波的放大作用[J].地震工程与工程振动,2008,28(1):1-10.LIANG Jian-wen,BA Zhen-ning.Surface motion of hill in layered half-space subjected to incident plane SHwave[J].Earthquake Engineering and Engineering Vibration,2008,28(1):1-10.
[12]张季,梁建文,巴振宁.SH波入射时凸起场地的地形和土层放大效应[J].地震工程与工程振动,2016,1(2):56-67.ZHANG Ji,LIANG Jian-wen,BA Zhen-ning.Topography and soil amplification for hill site when incident SH wave[J].Earthquake Engineering and Engineering Vibration,2016,1(2):56-67.
[13]ALVAREZ-RUBIO S,SANCHEZ-SESMA F J,ALARCóN E,et al.The direct boundary element method:2D site effects assessment on laterally varying layered media(methodology)[J].Soil Dynamics and Earthquake Engineering,2004,24(2):167-180.
[14]ZAHRADNíK J,URBAN L.Effect of a simple mountain range on underground seismic motion[J].Geophysical Journal International,2010,79(1):167-183.
[15]BOORE D M.A note on the effect of simple topography on seismic SH waves[J].Bulletin of the Seismological Society of America,1972,62(1):275-284.
[16]CHEN J T,LEE J W,WU C F,et al.SH-wave diffraction by a semi-circular hill revisited:a null-field boundary integral equation method using degenerate kernels[J].Soil Dynamics and Earthquake Engineering,2011,31(5-6):729-736.
[17]CHEN J T,LEE J W,SHYU W S.SH-wave scattering by a semi-elliptical hill using a null-field boundary integral equation method and a hybrid method[J].Geophysical Journal International,2015,118(1):177-194.
[18]LIU G,CHEN H,LIU D,et al.Surface motion of a half-space with triangular and semicircular hills under incident SH waves[J].Bulletin of the Seismological Society of America,2010,100(3):1306-1319.
[19]巴振宁,黄棣旸,梁建文,等.层状半空间中周期分布凸起地形对平面SH波的散射[J].地球物理学报,2017,60(3):1039-1052.BA Zhen-ning,HUANG Di-yang,LIANG Jian-wen,et al.Scattering and diffraction of plane SH waves by periodically distributed hill topographies[J].Chinese Journal of Geophysics,2017,60(3):1039-1052.
[20]SANCHEZ-SESMA F J.Diffraction of elastic waves by three-dimensional surface irregularities[J].Bulletin of the Seismological Society of America,1983,73(6A):1621-1636.
[21]ESHRAGHI H,DRAVINSKI M.Scattering of plane harmonic SH,SV,P and Rayleigh waves by non-axisymmetric three-dimensional canyons:a wave function expansion approach[J].Earthquake Engineering and Structural Dynamics,1989,18(7):983-998.
[22]BOUCHON M,SCHULTZ C A,TOKSOS M N.Effect of three-dimensional topoghraphy on seismic motion[J].Journal of Geophysical Research,1996,101(B3):583-546.
[23]OHMINATO T,CHOUET B A.A free-surface boundary condition for including 3D topography in the finite difference method[J].Bulletin of the Seismological Society of America,1997,87(2):494-515.
[24]PEDERSEN H,SANCHEZ-SESMA F J,CAMPILLO M.Three-dimensional scattering by two-dimensional topographies[J].Bulletin of the Seismological Society of America,1994,84(4):1169-1183.
[25]LUZON F,SANCHEZ-SESMA F J,RODRGUEZ-ZUIGA J L,et al.Diffraction of P,S and Rayleigh waves by three dimensional topographies[J].Geophysical Journal International,1997,129(3):571-578.
[26]REINOSO E,WROBEL L C,POWER H.Three-dimensional scattering of seismic waves from topographical structures[J].Soil Dynamics and Earthquake Engineering,1997,16(1):41-61.
[27]KOMATITSCH D,VILOTTE J P.The spectral element method:an efficient tool to simulate the seismic response of 2D and 3D geological structures[J].Bulletin of the Seismological Society of America,1998,88(2):368-392.
[28]SOHRABI-BIDAR A,KAMALIAN M,JAFARI M K.Time-domain BEM for three dimensional site response analysis of topographic structures[J].International Journal for Numerical Methods in Engineering,2009,79(12):1467-1492.
[29]SOHRABI-BIDAR A,KAMALIAN M,JAFARI M K.Seismic response of 3D Gaussian shaped valleys to vertically propagating incident waves[J].Geophysical Journal International,2010,183(3):1429-1442.
[30]SOHRABI-BIDAR A,KAMALIAN M,JAFARI M K.Seismic waves scattering in three dimensional homogeneous media using time-domain boundary element method[J].Journal of Earth and Space Physics,2011,38(1):23-40.
[31]巴振宁,梁建文.Rayleigh波斜入射下层状场地中凸起地形的三维响应分析[J].中国科学(技术科学),2015,45(8):874-888.BA Zhen-ning,LIANG Jian-wen.Three dimensional responses of a hill in a layered half-space for obliquely incident Rayleigh waves[J].Science China(Technological Sciences),2015,45(8):874-888.
[32]丁浩江.TI弹性力学[M].杭州:浙江大学出版社,1997.DING Hao-jiang.TI elasticity mechanics[M].Hangzhou:Zhejiang University press,1997.
[33]陈镕,陈竹昌,薛松涛.横观各项同性层状场地对入射SH波的响应分析[J].上海力学,1998,19(3):213-220.CHEN Rong,CHEN Zhu-chang,XUE Song-tao.The response analysis of transversely isotropic elastic strata to incident SH waves[J].Shanghai Journal of Mechanics,1998,19(3):213-220.
[34]薛松涛,陈军,陈镕.有阻尼TI层状场地对平面入射SH波的响应分析[J].振动与冲击,2000,19(4):54-56.XUE Song-tao,CHEN Jun,CHEN Rong.The response analysis of damped TI layered soil for incident SH-waves[J].Journal of Vibration and Shock,2000,19(4):54-56.
[35]薛松涛,陈镕,秦岭.TI层状场地在SH波入射时共振特性的响应分析[J].同济大学学报,2002,30(2):127-132.XUE Song-tao,CHEN Rong,QIN ling.Resonant character of transversely isotropic stratified media[J].Journal of Tongji University,2002,30(2):127-132.
[36]巴振宁,张艳菊,梁建文.横观各向同性层状半空间中凹陷地形对平面SH波的散射[J].地震工程与工程振动,2015,35(2):9-21.BA Zhen-ning,ZHANG Yan-ju,LIANG Jian-wen.Scattering of SH wave by a canyon in transversely isotropic layered half-space[J].Earthquake Engineering and Engineering Vibration,2015,35(2):9-21.
[37]BA Z N,LIANG J W,ZHANG Y J.Scattering of SHwave by a canyon in transversely isotropic layered half-space[J].Earthquake Engineering and Engineering Vibration,2015,35(2):9-21.
[38]巴振宁,张艳菊,梁建文.基于TI介质模型的沉积谷地对平面SH波的放大效应[J].振动工程学报,2016,29(4):666-678.BA Zhen-ning,ZHANG Yan-ju,LIANG Jian-wen.Amplification of plane SH waves by an alluvial valley based on the TI medium model[J].Journal of Vibration Engineering,2016,29(4):666-678.
[39]BA Z N,LIANG J W,ZHANG Y J.Diffraction of SH-waves by topographic features in a layered transversely isotropic half-space[J].Earthquake Engineering and Engineering Vibration,2017,16(1):11-22.
[40]BA Z N,LEE V W,LIANG J W,et al.Scattering of plane q P-and q SV-waves by a canyon in a multi-layered transversely isotropic half-space[J].Soil Dynamics and Earthquake Engineering,2017,98:120-140.
[41]DESAI C S,CHRISTIAN J T.Numerical methods in geotechnical engineering[M].Manchester:Mc Graw-Hill,1979.
[42]AI Z Y,ZHANG Y F.Plane strain dynamic response of a transversely isotropic multilayered half-plane[J].Soil Dynamics and Earthquake Engineering,2015,75:211-219.
[2]YUAN XIAOMING,MEN FULU.Scattering of plane SH waves by a semi cylindrical hill[J].Earthquake Engineering and Structural Dynamic,1992,21(12):1091-1098.
[3]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-acrosssection[J].Earthquake Engineering and Engineering Vibration,1996,16(2):1-13.
[4]梁建文,张彦帅.平面SV波入射下半圆凸起地形地表运动解析解[J].地震学报,2006,28(3):238-239.LIANG Jian-wen,ZHANG Yan-shuai.Analytical solution of ground motion of semi convex topography under plane SV wave incidence[J].Acta Seismologica Sinica,2006,28(3):238-239.
[5]LIANG J W,ZHANG Y S,LEE V W.Scattering of plane P waves by a semi-cylindrical hill:analytical solution[J].Earthquake Engineering and Engineering Vibration,2005,4(1):27-36.
[6]LEE V W,LUO H,LIANG J W.Diffraction of anti-plane SH waves by a semi-circular cylindrical hill with an inside concentric semi-circular tunnel[J].Earthquake Engineering and Engineering Vibration,2004,3(2):249-262.
[7]齐辉,蔡立明,潘向南.直角域中凸起和孔洞对SH波的散射与地震动[J].岩土力学,2015,36(2):347-353.QI Hui,CAI Li-ming,PAN Xiang-nan.Scattering and seismic ground motion of circular cavity and salient with SH wave in a quarter space[J].Rock and Soil Mechanics,2015,36(2):347-353.
[8]AMORNWONGPAIBUN A,LEE V W.Scattering of anti-plane(SH)waves by a semi-elliptical hill:I-shallow hill[J].Soil Dynamics and Earthquake Engineering,2013,52(13):116-125.
[9]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(13):126-137.
[10]SANCHEZ-SESMA F J,CAMPILLO M.Topographic effects for incident P,SV and Rayieigh waves[J].Tectonophysics,1993,218(1-3):113-125.
[11]梁建文,巴振宁.弹性层状半空间中凸起地形对入射平面SH波的放大作用[J].地震工程与工程振动,2008,28(1):1-10.LIANG Jian-wen,BA Zhen-ning.Surface motion of hill in layered half-space subjected to incident plane SHwave[J].Earthquake Engineering and Engineering Vibration,2008,28(1):1-10.
[12]张季,梁建文,巴振宁.SH波入射时凸起场地的地形和土层放大效应[J].地震工程与工程振动,2016,1(2):56-67.ZHANG Ji,LIANG Jian-wen,BA Zhen-ning.Topography and soil amplification for hill site when incident SH wave[J].Earthquake Engineering and Engineering Vibration,2016,1(2):56-67.
[13]ALVAREZ-RUBIO S,SANCHEZ-SESMA F J,ALARCóN E,et al.The direct boundary element method:2D site effects assessment on laterally varying layered media(methodology)[J].Soil Dynamics and Earthquake Engineering,2004,24(2):167-180.
[14]ZAHRADNíK J,URBAN L.Effect of a simple mountain range on underground seismic motion[J].Geophysical Journal International,2010,79(1):167-183.
[15]BOORE D M.A note on the effect of simple topography on seismic SH waves[J].Bulletin of the Seismological Society of America,1972,62(1):275-284.
[16]CHEN J T,LEE J W,WU C F,et al.SH-wave diffraction by a semi-circular hill revisited:a null-field boundary integral equation method using degenerate kernels[J].Soil Dynamics and Earthquake Engineering,2011,31(5-6):729-736.
[17]CHEN J T,LEE J W,SHYU W S.SH-wave scattering by a semi-elliptical hill using a null-field boundary integral equation method and a hybrid method[J].Geophysical Journal International,2015,118(1):177-194.
[18]LIU G,CHEN H,LIU D,et al.Surface motion of a half-space with triangular and semicircular hills under incident SH waves[J].Bulletin of the Seismological Society of America,2010,100(3):1306-1319.
[19]巴振宁,黄棣旸,梁建文,等.层状半空间中周期分布凸起地形对平面SH波的散射[J].地球物理学报,2017,60(3):1039-1052.BA Zhen-ning,HUANG Di-yang,LIANG Jian-wen,et al.Scattering and diffraction of plane SH waves by periodically distributed hill topographies[J].Chinese Journal of Geophysics,2017,60(3):1039-1052.
[20]SANCHEZ-SESMA F J.Diffraction of elastic waves by three-dimensional surface irregularities[J].Bulletin of the Seismological Society of America,1983,73(6A):1621-1636.
[21]ESHRAGHI H,DRAVINSKI M.Scattering of plane harmonic SH,SV,P and Rayleigh waves by non-axisymmetric three-dimensional canyons:a wave function expansion approach[J].Earthquake Engineering and Structural Dynamics,1989,18(7):983-998.
[22]BOUCHON M,SCHULTZ C A,TOKSOS M N.Effect of three-dimensional topoghraphy on seismic motion[J].Journal of Geophysical Research,1996,101(B3):583-546.
[23]OHMINATO T,CHOUET B A.A free-surface boundary condition for including 3D topography in the finite difference method[J].Bulletin of the Seismological Society of America,1997,87(2):494-515.
[24]PEDERSEN H,SANCHEZ-SESMA F J,CAMPILLO M.Three-dimensional scattering by two-dimensional topographies[J].Bulletin of the Seismological Society of America,1994,84(4):1169-1183.
[25]LUZON F,SANCHEZ-SESMA F J,RODRGUEZ-ZUIGA J L,et al.Diffraction of P,S and Rayleigh waves by three dimensional topographies[J].Geophysical Journal International,1997,129(3):571-578.
[26]REINOSO E,WROBEL L C,POWER H.Three-dimensional scattering of seismic waves from topographical structures[J].Soil Dynamics and Earthquake Engineering,1997,16(1):41-61.
[27]KOMATITSCH D,VILOTTE J P.The spectral element method:an efficient tool to simulate the seismic response of 2D and 3D geological structures[J].Bulletin of the Seismological Society of America,1998,88(2):368-392.
[28]SOHRABI-BIDAR A,KAMALIAN M,JAFARI M K.Time-domain BEM for three dimensional site response analysis of topographic structures[J].International Journal for Numerical Methods in Engineering,2009,79(12):1467-1492.
[29]SOHRABI-BIDAR A,KAMALIAN M,JAFARI M K.Seismic response of 3D Gaussian shaped valleys to vertically propagating incident waves[J].Geophysical Journal International,2010,183(3):1429-1442.
[30]SOHRABI-BIDAR A,KAMALIAN M,JAFARI M K.Seismic waves scattering in three dimensional homogeneous media using time-domain boundary element method[J].Journal of Earth and Space Physics,2011,38(1):23-40.
[31]巴振宁,梁建文.Rayleigh波斜入射下层状场地中凸起地形的三维响应分析[J].中国科学(技术科学),2015,45(8):874-888.BA Zhen-ning,LIANG Jian-wen.Three dimensional responses of a hill in a layered half-space for obliquely incident Rayleigh waves[J].Science China(Technological Sciences),2015,45(8):874-888.
[32]丁浩江.TI弹性力学[M].杭州:浙江大学出版社,1997.DING Hao-jiang.TI elasticity mechanics[M].Hangzhou:Zhejiang University press,1997.
[33]陈镕,陈竹昌,薛松涛.横观各项同性层状场地对入射SH波的响应分析[J].上海力学,1998,19(3):213-220.CHEN Rong,CHEN Zhu-chang,XUE Song-tao.The response analysis of transversely isotropic elastic strata to incident SH waves[J].Shanghai Journal of Mechanics,1998,19(3):213-220.
[34]薛松涛,陈军,陈镕.有阻尼TI层状场地对平面入射SH波的响应分析[J].振动与冲击,2000,19(4):54-56.XUE Song-tao,CHEN Jun,CHEN Rong.The response analysis of damped TI layered soil for incident SH-waves[J].Journal of Vibration and Shock,2000,19(4):54-56.
[35]薛松涛,陈镕,秦岭.TI层状场地在SH波入射时共振特性的响应分析[J].同济大学学报,2002,30(2):127-132.XUE Song-tao,CHEN Rong,QIN ling.Resonant character of transversely isotropic stratified media[J].Journal of Tongji University,2002,30(2):127-132.
[36]巴振宁,张艳菊,梁建文.横观各向同性层状半空间中凹陷地形对平面SH波的散射[J].地震工程与工程振动,2015,35(2):9-21.BA Zhen-ning,ZHANG Yan-ju,LIANG Jian-wen.Scattering of SH wave by a canyon in transversely isotropic layered half-space[J].Earthquake Engineering and Engineering Vibration,2015,35(2):9-21.
[37]BA Z N,LIANG J W,ZHANG Y J.Scattering of SHwave by a canyon in transversely isotropic layered half-space[J].Earthquake Engineering and Engineering Vibration,2015,35(2):9-21.
[38]巴振宁,张艳菊,梁建文.基于TI介质模型的沉积谷地对平面SH波的放大效应[J].振动工程学报,2016,29(4):666-678.BA Zhen-ning,ZHANG Yan-ju,LIANG Jian-wen.Amplification of plane SH waves by an alluvial valley based on the TI medium model[J].Journal of Vibration Engineering,2016,29(4):666-678.
[39]BA Z N,LIANG J W,ZHANG Y J.Diffraction of SH-waves by topographic features in a layered transversely isotropic half-space[J].Earthquake Engineering and Engineering Vibration,2017,16(1):11-22.
[40]BA Z N,LEE V W,LIANG J W,et al.Scattering of plane q P-and q SV-waves by a canyon in a multi-layered transversely isotropic half-space[J].Soil Dynamics and Earthquake Engineering,2017,98:120-140.
[41]DESAI C S,CHRISTIAN J T.Numerical methods in geotechnical engineering[M].Manchester:Mc Graw-Hill,1979.
[42]AI Z Y,ZHANG Y F.Plane strain dynamic response of a transversely isotropic multilayered half-plane[J].Soil Dynamics and Earthquake Engineering,2015,75:211-219.