跨越V形峡谷的桥梁抗震分析:多水平成层非均匀介质V形场地多点地震动模拟
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摘要
为了解峡谷地形对地震波场分布的特殊影响,重点发展和实现了V形非均匀多层介质峡谷的多点地震动场模拟,其理论依据是在长期假设均匀介质峡谷场地的基础上引入分层效应模型,其优点在于考虑了地下土层分布不均匀对地震动的影响。具体理论包括:稳态波场被分为封闭区和开放区,同时引入波函数展开法和大圆弧法,经推导得到了V形峡谷在SH波入射激励下稳态波场的分布频域解析解,进而得到分布于V形峡谷表面的频域谱;然后,简述导出的基于V形峡谷地形的"平-凹"相干函数模型;进而,利用两步骤传递函数法(水平自由表面→V形峡谷表面→峡谷地下)推导得到地下频域谱;由此,形成并阐明了非均匀多层介质V形峡谷表面和地下的多点地震动具体模拟方法;最后,开发了依据上述途径的V形场地多点地震动模拟程序并实现其可视化,验证了计算结果的合理性和可靠性。分析结果表明:波场幅值在峡谷两侧水平场地与峡谷底部具有明显差异,峡谷效应的多点相干性因各土层分界面与峡谷边界稳态波场中的散射成分存在而被降低。
In order to investigate the specific effect of canyon topography on the seismic wave field,a simulation approach of multi-support seismic motions was proposed and developed based on the theory of spatial variable seismic motions in a multi-layered V-shaped canyon with inhomogeneous media.The homogeneous-media canyon model was improved by introducing the layer model,and the effects of inhomogeneous media were taken into account.Firstly,the steady-state wave field was separated into two regions,namely,the open region and the enclosed region.The wave function expansion method and big-arc boundary method were adopted to obtain the analytical solution of seismic wave field in the V-shaped canyon by a train of plane SH waves.A flat-sunken coherence function model of a V-shape canyon was illuminated.Moreover,the underground power spectral density functions were deduced by a two-step transfer function method(horizontal free surface→V-shaped canyon surface→underground canyon).Then thesimulation approach of spatially variable seismic motions in a multi-layer V-shaped canyon was illuminated.Finally,a visual program of multi-support seismic motions in a V-shaped canyon was developed for the simulation,whilst the rationality of calculation results was verified.The results show that there are great differences of the wave displacement amplitudes between flat terrain and canyon bottom.Influenced by the scattering wave components in the steady-state wave field of the layer interface boundary and the canyon surface boundary,the coherence of canyon effect decreases correspondingly.
In order to investigate the specific effect of canyon topography on the seismic wave field,a simulation approach of multi-support seismic motions was proposed and developed based on the theory of spatial variable seismic motions in a multi-layered V-shaped canyon with inhomogeneous media.The homogeneous-media canyon model was improved by introducing the layer model,and the effects of inhomogeneous media were taken into account.Firstly,the steady-state wave field was separated into two regions,namely,the open region and the enclosed region.The wave function expansion method and big-arc boundary method were adopted to obtain the analytical solution of seismic wave field in the V-shaped canyon by a train of plane SH waves.A flat-sunken coherence function model of a V-shape canyon was illuminated.Moreover,the underground power spectral density functions were deduced by a two-step transfer function method(horizontal free surface→V-shaped canyon surface→underground canyon).Then thesimulation approach of spatially variable seismic motions in a multi-layer V-shaped canyon was illuminated.Finally,a visual program of multi-support seismic motions in a V-shaped canyon was developed for the simulation,whilst the rationality of calculation results was verified.The results show that there are great differences of the wave displacement amplitudes between flat terrain and canyon bottom.Influenced by the scattering wave components in the steady-state wave field of the layer interface boundary and the canyon surface boundary,the coherence of canyon effect decreases correspondingly.
引文
[1]BOORE D M.The Effect of Simple Topography on Seismic Waves:Implications for the Accelerations Recorded at Pacoima Dam,San Fernando Valley,California[J].Bulletin of the Seismological Society of America,1973,63(5):1603-1609.
[2]CELEBI M.Topographical and Geological Amplifications Determined from Strong-motion and Aftershock Records of the 3 March 1985Chile Earthquake[J].Bulletin of the Seismological Society of America,1987,77(4):1147-1167.
[3]邱燕玲,姚令侃.峡谷地形隔震效应及减灾选线对策[J].铁道标准设计,2015,59(11):1-4.QIU Yan-ling,YAO Ling-kan.Effect of Valley on Ground Motion and Disaster Reduction in Route Selection[J].Railway Standard Design,2015,59(11):1-4.
[4]王笃国,赵成刚.地震波斜入射下考虑场地非线性、地形效应和土结动力相互作用的大跨连续刚构桥地震响应分析[J].工程力学,2017,34(4):32-41.WANG Du-guo,ZHAO Cheng-gang.Seismic Analysis of Long-span Continuous Rigid Frame Bridge Considering Site Non-linearity,Topography Effect and Soil Structure Dynamic Interaction Under Oblique Incidence[J].Engineering Mechanics,2017,34(4):32-41.
[5]周国良,李小军.SH波入射下河谷地形对连续刚构桥地震反应影响[J].土木工程学报,2010,43(增2):42-48.ZHOU Guo-liang,LI Xiao-jun.Canyon Topography Effects of Seismic Response of Continuous Rigid Frame Bridge Under SH Incident Waves[J].China Civil Engineering Journal,2010,43(S2):42-48.
[6]谷音,江梦霞,卓卫东,等.考虑地震波斜入射下河谷地形的大跨桥梁动力反应研究[J].福州大学学报:自然科学版,2013,41(4):517-522.GU Yin,JIANG Meng-xia,ZHUO Wei-dong,et al.Seismic Response Analysis of Long-span Bridges Subjected to Spatially Non-uniform Seismic Ground Motions[J].Journal of Fuzhou University:Natural Science Edition,2013,41(4):517-522.
[7]赵密,杜修力,刘晶波,等.P-SV波斜入射时成层半空间自由场的时域算法[J].地震工程学报,2013,35(1):84-90.ZHAO Mi,DU Xiu-li,LIU Jing-bo,et al.Time-domain Method for Free Field in Layered Half Space under P-SV Waves of Oblique Incidence[J].China Earthquake Engineering Journal,2013,35(1):84-90.
[8]TRIFUNAC M D.Scattering of Plane SH Waves by a Semi-cylindrical Canyon[J].Earthquake Engineering&Structural Dynamics,1972,1(3):267-281.
[9]WONG H L,TRIFUNAC M D.Scattering of Plane SH Waves by a Semi-elliptical Canyon[J].Earthquake Engineering&Structural Dynamics,1974,3(2):157-169.
[10]LEE V W.Scattering of Plane SH-waves by a Semiparabolic Cylindrical Canyon in an Elastic Half-space[J].Geophysical Journal International,1990,100(1):79-86.
[11]何钟怡,樊洪明.用波函数展开法求解界面圆孔的SH波散射问题[J].地震工程与工程振动,2000,20(3):1-7.HE Zhong-yi,FAN Hong-ming.Application of Wave Functions Expansion Method to Scattering Problems of SH-wave by an Interface Circular Cavity[J].Earthquake Engineering and Engineering Vibration,2000,20(3):1-7.
[12]TSAUR D H,CHANG K H.An Analytical Approach for the Scattering of SH Waves by a Symmetrical Vshaped Canyon:Shallow Case[J].Geophysical Journal International,2008,174(1):255-264.
[13]TSAUR D H,CHANG K H,HSU M S.An Analytical Approach for the Scattering of SH Waves by a Symmetrical V-shaped Canyon:Deep Case[J].Geophysical Journal International,2010,183(3):1501-1511.
[14]WU Y,GAO Y,ZHANG N,et al.Simulation of Spatially Varying Ground Motions in V-shaped Symmetric Canyons[J].Journal of Earthquake Engineering,2016,20(6):992-1010.
[15]LIU G,FENG X,LIAN J,et al.Simulation of Spatially Variable Seismic Underground Motions in U-shaped Canyons[J/OL].Journal of Earthquake Engineering,2017,DOI:10.1080/13632469.2017.1326427.
[16]潘旦光,楼梦麟.河谷地形对土层地震反应的影响[J].北京科技大学学报,2008,30(11):1217-1222,1248.PAN Dan-guang,LOU Meng-lin.Effect of Valley Topography on the Seismic Responses of Soil Sites[J].Journal of University of Science and Technology Beijing,2008,30(11):1217-1222,1248.
[17]WATSON G N.A Treatise on the Theory of Bessel Functions[M].Cambridge:Cambridge University Press,1922.
[18]ABRAMOWITZ M,STEGUN I A.Handbook of Mathematical Functions with Formulas,Graphs,and Mathematical Tables[M].New York:Dover,1972.
[19]CLOUGH R W,PENZIEN J.Dynamics of Structures[M].Berkeley:Computers&Structures,Inc,1995.
[20]LIU G,LIAN J,LIANG C,et al.An Effective Approach for Simulating Multi-support Earthquake Underground Motions[J].Bulletin of Earthquake Engineering,2017,15(11):4635-4659.
[21]柳国环,赵大海.地震差动与结构非线性输出——方法、程序开发及实践[M].北京:科学出版社,2016.LIU Guo-huan,ZHAO Da-hai.Method,Program Development and Practice for Spatially Variable Earthquake Motions and Structural Nonlinear Analysis[M].Beijing:Science Press,2016.
[22]杜修力,陈厚群.地震动随机模拟及其参数确定方法[J].地震工程与工程振动,1994,14(4):1-5.DU Xiu-li,CHEN Hou-qun.Random Simulation and Its Parameter Determination Method of Earthquake Ground Motion[J].Earthquake Engineering and Engineering Vibration,1994,14(4):1-5.
[23]HAO H,OLIVEIRA C S,PENZIEN J.Multiple-station Ground Motion Processing and Simulation Based on SMART-1 Array Data[J].Nuclear Engineering and Design,1989,111(3):293-310.
[2]CELEBI M.Topographical and Geological Amplifications Determined from Strong-motion and Aftershock Records of the 3 March 1985Chile Earthquake[J].Bulletin of the Seismological Society of America,1987,77(4):1147-1167.
[3]邱燕玲,姚令侃.峡谷地形隔震效应及减灾选线对策[J].铁道标准设计,2015,59(11):1-4.QIU Yan-ling,YAO Ling-kan.Effect of Valley on Ground Motion and Disaster Reduction in Route Selection[J].Railway Standard Design,2015,59(11):1-4.
[4]王笃国,赵成刚.地震波斜入射下考虑场地非线性、地形效应和土结动力相互作用的大跨连续刚构桥地震响应分析[J].工程力学,2017,34(4):32-41.WANG Du-guo,ZHAO Cheng-gang.Seismic Analysis of Long-span Continuous Rigid Frame Bridge Considering Site Non-linearity,Topography Effect and Soil Structure Dynamic Interaction Under Oblique Incidence[J].Engineering Mechanics,2017,34(4):32-41.
[5]周国良,李小军.SH波入射下河谷地形对连续刚构桥地震反应影响[J].土木工程学报,2010,43(增2):42-48.ZHOU Guo-liang,LI Xiao-jun.Canyon Topography Effects of Seismic Response of Continuous Rigid Frame Bridge Under SH Incident Waves[J].China Civil Engineering Journal,2010,43(S2):42-48.
[6]谷音,江梦霞,卓卫东,等.考虑地震波斜入射下河谷地形的大跨桥梁动力反应研究[J].福州大学学报:自然科学版,2013,41(4):517-522.GU Yin,JIANG Meng-xia,ZHUO Wei-dong,et al.Seismic Response Analysis of Long-span Bridges Subjected to Spatially Non-uniform Seismic Ground Motions[J].Journal of Fuzhou University:Natural Science Edition,2013,41(4):517-522.
[7]赵密,杜修力,刘晶波,等.P-SV波斜入射时成层半空间自由场的时域算法[J].地震工程学报,2013,35(1):84-90.ZHAO Mi,DU Xiu-li,LIU Jing-bo,et al.Time-domain Method for Free Field in Layered Half Space under P-SV Waves of Oblique Incidence[J].China Earthquake Engineering Journal,2013,35(1):84-90.
[8]TRIFUNAC M D.Scattering of Plane SH Waves by a Semi-cylindrical Canyon[J].Earthquake Engineering&Structural Dynamics,1972,1(3):267-281.
[9]WONG H L,TRIFUNAC M D.Scattering of Plane SH Waves by a Semi-elliptical Canyon[J].Earthquake Engineering&Structural Dynamics,1974,3(2):157-169.
[10]LEE V W.Scattering of Plane SH-waves by a Semiparabolic Cylindrical Canyon in an Elastic Half-space[J].Geophysical Journal International,1990,100(1):79-86.
[11]何钟怡,樊洪明.用波函数展开法求解界面圆孔的SH波散射问题[J].地震工程与工程振动,2000,20(3):1-7.HE Zhong-yi,FAN Hong-ming.Application of Wave Functions Expansion Method to Scattering Problems of SH-wave by an Interface Circular Cavity[J].Earthquake Engineering and Engineering Vibration,2000,20(3):1-7.
[12]TSAUR D H,CHANG K H.An Analytical Approach for the Scattering of SH Waves by a Symmetrical Vshaped Canyon:Shallow Case[J].Geophysical Journal International,2008,174(1):255-264.
[13]TSAUR D H,CHANG K H,HSU M S.An Analytical Approach for the Scattering of SH Waves by a Symmetrical V-shaped Canyon:Deep Case[J].Geophysical Journal International,2010,183(3):1501-1511.
[14]WU Y,GAO Y,ZHANG N,et al.Simulation of Spatially Varying Ground Motions in V-shaped Symmetric Canyons[J].Journal of Earthquake Engineering,2016,20(6):992-1010.
[15]LIU G,FENG X,LIAN J,et al.Simulation of Spatially Variable Seismic Underground Motions in U-shaped Canyons[J/OL].Journal of Earthquake Engineering,2017,DOI:10.1080/13632469.2017.1326427.
[16]潘旦光,楼梦麟.河谷地形对土层地震反应的影响[J].北京科技大学学报,2008,30(11):1217-1222,1248.PAN Dan-guang,LOU Meng-lin.Effect of Valley Topography on the Seismic Responses of Soil Sites[J].Journal of University of Science and Technology Beijing,2008,30(11):1217-1222,1248.
[17]WATSON G N.A Treatise on the Theory of Bessel Functions[M].Cambridge:Cambridge University Press,1922.
[18]ABRAMOWITZ M,STEGUN I A.Handbook of Mathematical Functions with Formulas,Graphs,and Mathematical Tables[M].New York:Dover,1972.
[19]CLOUGH R W,PENZIEN J.Dynamics of Structures[M].Berkeley:Computers&Structures,Inc,1995.
[20]LIU G,LIAN J,LIANG C,et al.An Effective Approach for Simulating Multi-support Earthquake Underground Motions[J].Bulletin of Earthquake Engineering,2017,15(11):4635-4659.
[21]柳国环,赵大海.地震差动与结构非线性输出——方法、程序开发及实践[M].北京:科学出版社,2016.LIU Guo-huan,ZHAO Da-hai.Method,Program Development and Practice for Spatially Variable Earthquake Motions and Structural Nonlinear Analysis[M].Beijing:Science Press,2016.
[22]杜修力,陈厚群.地震动随机模拟及其参数确定方法[J].地震工程与工程振动,1994,14(4):1-5.DU Xiu-li,CHEN Hou-qun.Random Simulation and Its Parameter Determination Method of Earthquake Ground Motion[J].Earthquake Engineering and Engineering Vibration,1994,14(4):1-5.
[23]HAO H,OLIVEIRA C S,PENZIEN J.Multiple-station Ground Motion Processing and Simulation Based on SMART-1 Array Data[J].Nuclear Engineering and Design,1989,111(3):293-310.