任意多个沉积谷地对平面SV波的散射
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摘要
采用间接边界元法研究了入射平面SV波在层状半空间中多个沉积谷地周围的散射问题。该方法将整体模型分解为各个沉积闭合域和开口的层状半空间域。通过在各沉积闭合边界上施加虚拟均布荷载模拟各闭合域内散射波场,通过在层状半空间开口域所有开口边界上施加虚拟荷载模拟开口域内散射波场,通过引入各沉积与层状半空间的连续条件确定所有施加虚拟荷载的密度。验证了该方法的正确性,并对均匀半空间中不同间距和不同数量的半圆沉积为例进行了数值计算分析,数值结果表明,多个沉积与单一沉积对应的位移幅值及其放大谱均显不同,沉积间的动力相互作用,使得多个沉积情况对应位移幅值显著大于单一沉积情况。沉积间距的改变导致了沉积间动力相互作用机制的改变,进而改变了放大谱的峰值及峰值周期。沉积个数影响主要体现在增强或减弱沉积间的动力相互作用上,而对相互作用机制影响较小,因而不同沉积个数对应的放大谱峰值差异明显而峰值周期较为接近。
Wave scattering of arbitrary alluvial valleys in a layered half-space to incident plane SV waves was studied using the indirection boundary element method( IBEM). The model was divided into multiple independent closed regions and an open layered half-space region. Scattering wave fields of closed regions were simulated with fictitious distributed loads acting on closed boundaries,and scattering wave field of the open layered half-space region was simulated with fictitious distributed loads acting on open boundaries. Then,the densities of distributed loads were determined according to the continuity boundary conditions. The validity of the proposed method was verified by comparing the results using this method with those using the published method. Numerical analyses were performed for semicylindrical valleys with different separation distances and different numbers in an uniformly half-space. The numerical results showed that both surface displacement and amplification spectrum of the observed points are influenced by the above two factors,also frequency and angle of incident SV waves and observation points; the distance between valleys and the number of valleys have a larger influence on surface displacement amplitudes and peak values of amplification spectrum when SV waves propagate with oblique angle; with increase in frequency,the above two factors have a weaker influence on surface displacement amplitudes; displacement amplitudes are influenced severely with decrease in distance between valleys; due to the dynamic interaction among valleys,displacement amplitudes of multiple valleys are bigger than those of a single valley.
Wave scattering of arbitrary alluvial valleys in a layered half-space to incident plane SV waves was studied using the indirection boundary element method( IBEM). The model was divided into multiple independent closed regions and an open layered half-space region. Scattering wave fields of closed regions were simulated with fictitious distributed loads acting on closed boundaries,and scattering wave field of the open layered half-space region was simulated with fictitious distributed loads acting on open boundaries. Then,the densities of distributed loads were determined according to the continuity boundary conditions. The validity of the proposed method was verified by comparing the results using this method with those using the published method. Numerical analyses were performed for semicylindrical valleys with different separation distances and different numbers in an uniformly half-space. The numerical results showed that both surface displacement and amplification spectrum of the observed points are influenced by the above two factors,also frequency and angle of incident SV waves and observation points; the distance between valleys and the number of valleys have a larger influence on surface displacement amplitudes and peak values of amplification spectrum when SV waves propagate with oblique angle; with increase in frequency,the above two factors have a weaker influence on surface displacement amplitudes; displacement amplitudes are influenced severely with decrease in distance between valleys; due to the dynamic interaction among valleys,displacement amplitudes of multiple valleys are bigger than those of a single valley.
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]WONG H L,TRIFUNAC M D.Surface motion of semielliptical alluvial valley for incident plane SH waves[J].Bulletin of the Seismological Society of America,1974,64(15):1389-1408.
[3]TODOROVSKA M I,LEE V W.Surface motion of shallow circular alluvial valleys for incident plane SH ja:math,wavesanalytical solution[J].Soil Dynamics&Earthquake Engineering,1991,10(4):192-200.
[4]YUAN X,LIAO Z.Scattering of plane SH waves by a cylindrical alluvial valley of circular-arc cross section[J].Earthquake Engineering&Structural Dynamics,1995,24(10):1303-1313.
[5]梁建文,严林隽,李军伟,等.圆弧形沉积河谷场地在平面P波入射下的响应[J].岩土力学,2001,22(2):138-143.LIANG Jianwen,YAN Linjun,LI Junwei,et al.Response of circular-arc alluvial valleys under incident plane P waves[J].Rock and Soil Mechanics,2001,22(2):138-143.
[6]梁建文,严林隽,秦东,等.圆弧形沉积河谷场地在平面SV波入射下的动力响应[J].土木工程学报,2003,36(12):74-82.LIANG Jianwen,YAN Linjun,QIN Dong,et al.Dynamic response of circular-arc sedimentary valley site under incident plane SV waves[J].China Civil Engineering Journal,2003,36(12):74-82.
[7]梁建文,张秋红,李方杰.浅圆沉积谷地对瑞雷波的散射——高频解[J].地震学报,2006,28(2):176-182.LIANG Jianwen,ZHANG Qiuhong,LI Fanjie.Scattering of Rayleigh waves by a shallow circular alluvial valley:high frequency solution[J].Acta Seismologica Sinica,2006,28(2):176-182.
[8]梁建文,张郁山,顾晓鲁,等.圆弧形层状沉积河谷场地在平面SH波入射下动力响应分析[J].岩土工程学报,2000,22(4):396-401.LIANG Jianwen,ZHANG Yushan,GU Xiaolu,et al.Surface motion of circular-arc layered alluvial valleys for incident plane SH waves[J].Chinese Journal of Geotechnical Engineering,2000,22(4):396-401.
[9]梁建文,严林隽,LEE V W.圆弧形层状沉积谷地对入射平面P波的散射解析解[J].地震学报,2001,23(2):167-184.LIANG Jianwen,YAN Linjun,LEE V W.Scattering of plane P waves by circular-arc layered alluvial valleys:an analytical solution[J].Acta Seismologica Sinica,2001,23(2):167-184.
[10]梁建文,严林隽,LEE V W.圆弧形层状沉积谷地对入射平面SV波散射解析解[J].固体力学学报,2003,24(2):235-243.LIANG Jianwen,YAN Linjun,LEE V W.Diffraction of plane SV waves by a circular-arc layered alluvial valley:analytical solution[J].Acta Mechanica Solida Sinica,2003,24(2):235-243.
[11]杨彩红,梁建文,张郁山.含多个圆弧状沉积层河谷场地对平面SH波散射问题的解析解[J].地震工程与工程振动,2010,30(3):22-30.YANG Caihong,LIANG Jianwen,ZHANG Yushan.Analytical solution to the scattering problem of valley site containing multiple circular-arc alluvial layers in the case of plane SH waves incidence[J].Earthquake Engineering and Engineering Dynamics.Earthquake Engineering and Engineering Dynamics,2010,30(3):22-30.
[12]WOLF J P.Dynamic soil-structure interaction[M].Englewood Cliffs:Prentice-Hall,1985.
[13]梁建文,巴振宁.弹性层状半空间中沉积谷地对入射平面SH波的放大作用[J].地震工程与工程振动,2007,27(3):1-9.LIANG Jianwen,BA Zhenning.Surface motion of an alluvial valley in layered half-space for incident plane SH waves[J].Earthquake Engineering and Engineering Dynamics,2007,27(3):1-9.
[14]巴振宁,梁建文.平面SV波在层状半空间中沉积谷地周围的散射[J].地震工程与工程振动,2011,31(3):18-26.BA Zhenning,LIANG Jianwen.Diffraction of plane SV waves around an alluvial valley in layered half-space[J].Earthquake Engineering and Engineering Dynamics,2011,31(3):18-26.
[15]张郁山.圆弧状多层沉积谷地在平面P波入射下稳态响应的解析解[J].地球物理学报,2008,51(3):7.ZHANG Yushan.Analytical solution for the stationary response of alluvial valleys containing multiple circular-arc layers to incident plane P waves[J].Chinese Journal of Geophysics,2008,51(3):7.
[16]张郁山.圆弧状多层沉积谷地在平面SV波入射下的动力响应[J].地球物理学报,2009,52(6):1547-1555.ZHANG Yushan.Dynamic response of alluvial valley containing multiple circular-arc layers incident by plane SV waves[J].Chinese Journal of Geophysics,2009,52(6):1547-1555.
[17]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(1):1-6.ZHANG Yushan.Dynamic response of arc-layered alluvial valley under incidence of plane SH waves[J].Chinese Journal of Geotechnical Engineering,2010(1):1-6.
[18]张郁山.圆弧状多层沉积谷地在Rayleigh波入射下动力响应的解析解[J].地球物理学报,2010,53(9):2129-2143.ZHANG Yushan.Analytical solution to dynamic response of circular-arc-shaped multi-layered valley due to incidence of Rayleigh wave[J].Chinese Journal of Geophysics,2010,53(9):2129-2143.
[19]DRAVINSKI M.Scattering of plane harmonic SH wave by dipping layers or arbitrary shape[J].Bulletin of the Seismological Society of America,1983,73(5):1303-1319.
[20]DRAVINSKI M,MOSSESSIAN T K.Scattering of plane P,SV,and Rayleigh waves by dipping layers of arbitrary shape[J].Bulletin of the Seismological Society of America,1987,77(1):15-19.
[21]KAWASE H,AKI K.A study on the response of a soft basin for incident S,P,and Rayleigh waves with special reference to the long duration observed in Mexico City[J].Bulletin of the Seismological Society of America,1989,79(5):1361-1382.
[22]SNCHEZ-SESMA F J,RAMOS-MARTINEZ J,CAMPILLO M.An indirect boundary element method applied to simulate the seismic response of alluvial valleys for incident P,S and Rayleigh waves[J].Earthquake Engineering&Structural Dynamics,1993,22(4):279-295.
[23]SEMBLAT J F.Modal superposition method for the analysis of seismic-wave amplification[J].Bulletin of the Seismological Society of America,2003,93(3):1144-1153.
[24]王慧文,刘殿魁,邱发强,等.SH波入射时多个半圆形沉积谷地附近浅埋圆形孔洞的动力分析[J].地震工程与工程振动,2006,26(4):18-23.WANG Huiwen,LIU Diankui,QIU Faqiang,et al.Dynamic response of shallow-embedded cylindrical lining structure below semi-cylindrical alluvial valleys to incident SH waves[J].Earthquake Engineering and Engineering Vibration,2006,26(4):18-23.
[25]CHEN J T,CHEN P Y,CHEN C T.Surface motion of multiple alluvial valleys for incident plane SH-waves by using a semi-analytical approach[J].Soil Dynamics&Earthquake Engineering,2008,28(1):58-72.
[26]吕晓棠,安静波.半圆形凸起与沉积谷地相连地形对SH波的散射[J].振动与冲击,2014,33(17):127-131.LXiaotang,AN Jingbo.Ground motion of a semicylindrical hill joined with a semi-cylindrical alluvial valley under incident SH-waves[J].Journal of Vibration and Shock,2014,33(17):127-131.
[2]WONG H L,TRIFUNAC M D.Surface motion of semielliptical alluvial valley for incident plane SH waves[J].Bulletin of the Seismological Society of America,1974,64(15):1389-1408.
[3]TODOROVSKA M I,LEE V W.Surface motion of shallow circular alluvial valleys for incident plane SH ja:math,wavesanalytical solution[J].Soil Dynamics&Earthquake Engineering,1991,10(4):192-200.
[4]YUAN X,LIAO Z.Scattering of plane SH waves by a cylindrical alluvial valley of circular-arc cross section[J].Earthquake Engineering&Structural Dynamics,1995,24(10):1303-1313.
[5]梁建文,严林隽,李军伟,等.圆弧形沉积河谷场地在平面P波入射下的响应[J].岩土力学,2001,22(2):138-143.LIANG Jianwen,YAN Linjun,LI Junwei,et al.Response of circular-arc alluvial valleys under incident plane P waves[J].Rock and Soil Mechanics,2001,22(2):138-143.
[6]梁建文,严林隽,秦东,等.圆弧形沉积河谷场地在平面SV波入射下的动力响应[J].土木工程学报,2003,36(12):74-82.LIANG Jianwen,YAN Linjun,QIN Dong,et al.Dynamic response of circular-arc sedimentary valley site under incident plane SV waves[J].China Civil Engineering Journal,2003,36(12):74-82.
[7]梁建文,张秋红,李方杰.浅圆沉积谷地对瑞雷波的散射——高频解[J].地震学报,2006,28(2):176-182.LIANG Jianwen,ZHANG Qiuhong,LI Fanjie.Scattering of Rayleigh waves by a shallow circular alluvial valley:high frequency solution[J].Acta Seismologica Sinica,2006,28(2):176-182.
[8]梁建文,张郁山,顾晓鲁,等.圆弧形层状沉积河谷场地在平面SH波入射下动力响应分析[J].岩土工程学报,2000,22(4):396-401.LIANG Jianwen,ZHANG Yushan,GU Xiaolu,et al.Surface motion of circular-arc layered alluvial valleys for incident plane SH waves[J].Chinese Journal of Geotechnical Engineering,2000,22(4):396-401.
[9]梁建文,严林隽,LEE V W.圆弧形层状沉积谷地对入射平面P波的散射解析解[J].地震学报,2001,23(2):167-184.LIANG Jianwen,YAN Linjun,LEE V W.Scattering of plane P waves by circular-arc layered alluvial valleys:an analytical solution[J].Acta Seismologica Sinica,2001,23(2):167-184.
[10]梁建文,严林隽,LEE V W.圆弧形层状沉积谷地对入射平面SV波散射解析解[J].固体力学学报,2003,24(2):235-243.LIANG Jianwen,YAN Linjun,LEE V W.Diffraction of plane SV waves by a circular-arc layered alluvial valley:analytical solution[J].Acta Mechanica Solida Sinica,2003,24(2):235-243.
[11]杨彩红,梁建文,张郁山.含多个圆弧状沉积层河谷场地对平面SH波散射问题的解析解[J].地震工程与工程振动,2010,30(3):22-30.YANG Caihong,LIANG Jianwen,ZHANG Yushan.Analytical solution to the scattering problem of valley site containing multiple circular-arc alluvial layers in the case of plane SH waves incidence[J].Earthquake Engineering and Engineering Dynamics.Earthquake Engineering and Engineering Dynamics,2010,30(3):22-30.
[12]WOLF J P.Dynamic soil-structure interaction[M].Englewood Cliffs:Prentice-Hall,1985.
[13]梁建文,巴振宁.弹性层状半空间中沉积谷地对入射平面SH波的放大作用[J].地震工程与工程振动,2007,27(3):1-9.LIANG Jianwen,BA Zhenning.Surface motion of an alluvial valley in layered half-space for incident plane SH waves[J].Earthquake Engineering and Engineering Dynamics,2007,27(3):1-9.
[14]巴振宁,梁建文.平面SV波在层状半空间中沉积谷地周围的散射[J].地震工程与工程振动,2011,31(3):18-26.BA Zhenning,LIANG Jianwen.Diffraction of plane SV waves around an alluvial valley in layered half-space[J].Earthquake Engineering and Engineering Dynamics,2011,31(3):18-26.
[15]张郁山.圆弧状多层沉积谷地在平面P波入射下稳态响应的解析解[J].地球物理学报,2008,51(3):7.ZHANG Yushan.Analytical solution for the stationary response of alluvial valleys containing multiple circular-arc layers to incident plane P waves[J].Chinese Journal of Geophysics,2008,51(3):7.
[16]张郁山.圆弧状多层沉积谷地在平面SV波入射下的动力响应[J].地球物理学报,2009,52(6):1547-1555.ZHANG Yushan.Dynamic response of alluvial valley containing multiple circular-arc layers incident by plane SV waves[J].Chinese Journal of Geophysics,2009,52(6):1547-1555.
[17]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(1):1-6.ZHANG Yushan.Dynamic response of arc-layered alluvial valley under incidence of plane SH waves[J].Chinese Journal of Geotechnical Engineering,2010(1):1-6.
[18]张郁山.圆弧状多层沉积谷地在Rayleigh波入射下动力响应的解析解[J].地球物理学报,2010,53(9):2129-2143.ZHANG Yushan.Analytical solution to dynamic response of circular-arc-shaped multi-layered valley due to incidence of Rayleigh wave[J].Chinese Journal of Geophysics,2010,53(9):2129-2143.
[19]DRAVINSKI M.Scattering of plane harmonic SH wave by dipping layers or arbitrary shape[J].Bulletin of the Seismological Society of America,1983,73(5):1303-1319.
[20]DRAVINSKI M,MOSSESSIAN T K.Scattering of plane P,SV,and Rayleigh waves by dipping layers of arbitrary shape[J].Bulletin of the Seismological Society of America,1987,77(1):15-19.
[21]KAWASE H,AKI K.A study on the response of a soft basin for incident S,P,and Rayleigh waves with special reference to the long duration observed in Mexico City[J].Bulletin of the Seismological Society of America,1989,79(5):1361-1382.
[22]SNCHEZ-SESMA F J,RAMOS-MARTINEZ J,CAMPILLO M.An indirect boundary element method applied to simulate the seismic response of alluvial valleys for incident P,S and Rayleigh waves[J].Earthquake Engineering&Structural Dynamics,1993,22(4):279-295.
[23]SEMBLAT J F.Modal superposition method for the analysis of seismic-wave amplification[J].Bulletin of the Seismological Society of America,2003,93(3):1144-1153.
[24]王慧文,刘殿魁,邱发强,等.SH波入射时多个半圆形沉积谷地附近浅埋圆形孔洞的动力分析[J].地震工程与工程振动,2006,26(4):18-23.WANG Huiwen,LIU Diankui,QIU Faqiang,et al.Dynamic response of shallow-embedded cylindrical lining structure below semi-cylindrical alluvial valleys to incident SH waves[J].Earthquake Engineering and Engineering Vibration,2006,26(4):18-23.
[25]CHEN J T,CHEN P Y,CHEN C T.Surface motion of multiple alluvial valleys for incident plane SH-waves by using a semi-analytical approach[J].Soil Dynamics&Earthquake Engineering,2008,28(1):58-72.
[26]吕晓棠,安静波.半圆形凸起与沉积谷地相连地形对SH波的散射[J].振动与冲击,2014,33(17):127-131.LXiaotang,AN Jingbo.Ground motion of a semicylindrical hill joined with a semi-cylindrical alluvial valley under incident SH-waves[J].Journal of Vibration and Shock,2014,33(17):127-131.
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