斜入射地震波在土体中产生的动应力路径及试验模拟
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摘要
针对地震波传播时并非垂直的情况,基于半无限弹性空间地震波的传播理论,对地震波进行简化,考虑斜入射时地震波在自由界面处的反射,推导了地震波斜入射时地震应力的计算公式,并通过计算实例分析了不同入射角度下,P波、SV波单独斜入射时在土单元体中所产生的地震应力以及所形成的应力路径。结果表明:当P波、SV波单独斜入射时,土单元体在平面应力差–剪应力平面上形成的应力路径均为一个倾斜椭圆,斜椭圆的倾角和长短轴之比随地震波入射角度、频率、波速等影响因素在一定范围内变化。文中还针对如何实现倾斜椭圆形应力路径的室内试验模拟进行了初步探讨分析。
Considering the fact that seismic waves do not vertically propagate near the surface especially under near field earthquakes,a simplified model is deduced to analyze the seismic response under obliquely incident waves based on the propagation theory in elastic half-space.It is considered the incident waves are harmonic,reflected at the free surface.The seismic stresses at arbitrary depth and the corresponding dynamic stress paths are estimated to investigate the effect of the incident angle of input waves.Under the single incidence of P-waves or SV-waves,it is shown that in the coordinate plane((y x) /2,xy),the stress path will be a fluctuating ellipse,the angular betweenX axis and the longaxis of the ellipse,and the ratio of long axis to short axis of the ellipse are related to the incident angle,frequency,wave velocity,etc.Moreover,preliminary discussion is also made on the way to simulate such a dynamic stress path in laboratory tests.
Considering the fact that seismic waves do not vertically propagate near the surface especially under near field earthquakes,a simplified model is deduced to analyze the seismic response under obliquely incident waves based on the propagation theory in elastic half-space.It is considered the incident waves are harmonic,reflected at the free surface.The seismic stresses at arbitrary depth and the corresponding dynamic stress paths are estimated to investigate the effect of the incident angle of input waves.Under the single incidence of P-waves or SV-waves,it is shown that in the coordinate plane((y x) /2,xy),the stress path will be a fluctuating ellipse,the angular betweenX axis and the longaxis of the ellipse,and the ratio of long axis to short axis of the ellipse are related to the incident angle,frequency,wave velocity,etc.Moreover,preliminary discussion is also made on the way to simulate such a dynamic stress path in laboratory tests.
引文
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[18]GB50011—2010中华人民共和国国家标准建筑抗震设计规范[S].(GB50011—2010Code for seismic design ofbuildings of the People's Republic of China[S].(in Chinese))
[19]程守洙,江之永.普通物理学(第三册)[M].北京:高等教育出版社,1979.(CHENG Shou-zhu,JIANG Zhi-yong.General physics(volume No.three)[M].Beijing:ChinaHigher Education Press,1979.(in Chinese))
[20]ISHIHARA K,TOWHATA I.Sand response to cyclic rotationof principal stress directions as induced by wave loads[J].Soils and Foundations,1983,23(4):11–26.
[21]ALLEN R M,KANAMORI H.The potential for earthquakeearly warning in southern California[J].Science,2003,300(2):786–789.
[22]HIGHT D W,GENS A,SYMES M J.Development of a newhollow cylinder apparatus for investigating the effects ofprincipal stress rotation in soils[J].Géotechnique,1983,33(4):355–383.
[2]SEED H B,PEACOCK W H.Test procedures for measuringsoil liquefaction characteristics[J].Journal of the SoilMechanics and Foundation Division,ASCE,1971,97(8):1099–1119.
[3]SEED H B,IDRISS I M.Simplified procedure for evaluatingsoil liquefaction potential[J].Journal of the Soil Mechanicsand Foundation Division,ASCE,1971,97(9):1249–1273.
[4]ISHIHARA K J.Soil behaviour in earthquake geotechnics[M].Oxford:Oxford University Press,1996.
[5]SCHROEDER W L,SCHUSTER R L.Laboratory simulationof seismic activity in saturated sands[M].Vibration Effects ofEarthquakes on Soils and Foundations,1969,ASTM STP 450:57–70.
[6]JIN Xing,LIAO Zhen-peng.Statistical research on S-waveincident angle[J].Annuals of Disas Prev Res Inst,1997,40:91–97.
[7]TAKAHIRO S,KAZUHIKO K,etc.Estimation of earthquakemotion incident angle at rock site[C]//Proceedings of 12thWorld Conference Earthquake Engineering,New Zealand,2000.
[8]潘旦光,楼梦麟,董聪.P、SV波作用下层状土层随机波动分析[J].工程力学,2006,23(2):66–71.(PANDang-guang,LOU Meng-lin,DONG Cong.Randomwave-theory analysis of layered soil sites under P-andSV-wave excitations[J].Engineering Mechanics,2006,23(2):66–71.(in Chinese))
[9]李山有,马强,韦庆海.地震体波斜入射下的断层台阶地震反应分析[J].地震研究,2005,28(3):277–281.(LIShan-you,MA Qiang,WEI Qing-hai.Seismic responseanalysis of fault step subjected to obliquely incident bodywaves[J].Journal of Seismological Research,2005,28(3):277–281.(in Chinese))
[10]HRYNIEWICZ Z,HERMANS A J.Free-field response frominclined body waves in a viscoelastic random medium[J].Earthquake Engineering and Structural Dynamics,1989,18:1025–1040.
[11]WOLF J P,OBERNHUBER P.Free-field response frominclined SV-and P-waves and rayleigh-waves[J].EarthquakeEngineering and Structural Dynamics,1982,10:847–869.
[12]刘月红,刘涛,宋金龙.土层性质对入射平面P波场地放大效应的影响[J].山东建筑大学学报,2007,22(3):198–202.(LIU Yue-hong,LIU Tao,SONG Jin-long.Influenceof properties of soil layer on site amplification effect for Pwaves[J].Journal of Shandong Jianzhu University,2007,22(3):198–202.(in Chinese))
[13]李山有,王学良,周正华.地震波斜入射情形下水平成层半空间自由场的时域计算[J].吉林大学学报(地球科学版),2003,33(3):372–376.(LI Shan-you,WANG Xue-liang,ZHOU Zheng-hua.The time-step numerical simulation offree field motion of layered half-space for inclined seismicwaves[J].Journal of Jilin University,2003,33(3):372–376.(in Chinese))
[14]尤红兵,赵凤新,荣棉水.地震波斜入射时水平层状场地的非线性地震反应[J].岩土工程学报,2009,31(2):234–240.(YOU Hong-bing,ZHAO Feng-xin,RONG Mian-shui.Nonlinear seismic response of horizontal layered site due toinclined wave[J].Chinese Journal of GeotechnicalEngineering,2009,31(2):234–240.(in Chinese))
[15]吴世明.土动力学[M].北京:中国建筑工业出版社,2000.(WU Shi-ming.Soil dynamics[M].Beijing:ChinaArchitecture and Building Press,2000.(in Chinese))
[16]牛滨华,孙春岩.半空间介质与地震波传播:地震波传播理论与应用[M].北京:石油工业出版社.2002.(NIUBin-hua,SUN Chun-yan.Half space medium and seismicwave propagation[M].Beijing:Petroleum Industry Press,2002.(in Chinese))
[17]徐仲达.地震波理论[M].上海:同济大学出版社,1997.(XU Zhong-da.Seismic wave theory[M].Shanghai:TongjiUniversity Press,1997.(in Chinese))
[18]GB50011—2010中华人民共和国国家标准建筑抗震设计规范[S].(GB50011—2010Code for seismic design ofbuildings of the People's Republic of China[S].(in Chinese))
[19]程守洙,江之永.普通物理学(第三册)[M].北京:高等教育出版社,1979.(CHENG Shou-zhu,JIANG Zhi-yong.General physics(volume No.three)[M].Beijing:ChinaHigher Education Press,1979.(in Chinese))
[20]ISHIHARA K,TOWHATA I.Sand response to cyclic rotationof principal stress directions as induced by wave loads[J].Soils and Foundations,1983,23(4):11–26.
[21]ALLEN R M,KANAMORI H.The potential for earthquakeearly warning in southern California[J].Science,2003,300(2):786–789.
[22]HIGHT D W,GENS A,SYMES M J.Development of a newhollow cylinder apparatus for investigating the effects ofprincipal stress rotation in soils[J].Géotechnique,1983,33(4):355–383.
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