水平成层场地动剪应变与震动速度关系解析
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摘要
以SHAKE2000为代表的频域等效线性化是目前主流的土层地震动计算方法。由于该方法在软土场地计算结果严重不合理,其改进方法成为目前研究热点,主要采用频率相关法,但一直没有取得实效。对频率相关法中土体动剪应变和震动速度成恒定比例关系的基本假定进行研究,从波动方程推导出了均匀全空间单向行波、单一均匀半无限场地、成层场地等3种典型场地中土体剪应变与震动速度关系的精确解答,通过数值试验研究了这一假定的合理性与偏差程度。结果表明:动剪应变和震动速度成恒定比例关系这一假定只有在无边界均匀介质单向行波情形下才成立,对于实际成层土场地,动剪应变与震动速度关系强烈依赖于波的频率和观察点的位置,如果在土层地震反应分析中忽略反射波而采用单向行波恒定比例假定将会使计算结果产生显著偏差;动剪应变与震动速度成恒定比例关系的假定导致的偏差达4个量级,即使对于单一均匀半无限空间模型偏差也十分显著;对实际土层地震动的求解,该假定在理论上定性错误,定量上偏差不可接受,必须放弃而另寻其他途径。
Equivalent linearization in frequency domain, represented by SHAKE2000, is the mainstream approach for seismic response analysis of soil layers. Due to the severe unreasonable results in soft soil sites, its improvement becomes a research hotspot, which mainly adopts frequency-dependent method(FDM), but there has been no substantial improvement. This paper assumes that dynamic shear strain and vibration velocity present a constant proportional relationship in FDM. Based on wave equation, exact solutions for the relationship of the two variables were derived on three typical site models, i.e., the homogeneous half space with one-way traveling wave, the single uniform soil layer, and the layered soil site. The reasonability and deviation degree of the assumption were studied through numerical experiments. Results show that the constant proportional hypothesis only applies in the case of unbounded homogeneous medium with one-way traveling wave. For actual layered soil sites, the relationship between dynamic shear strain and vibration velocity strongly depends on the frequency of the wave and the location of the observation point. If we ignore the reflection wave in ground seismic response analysis, the use of constant proportion assumption under one-way traveling wave will make significant deviation to the results. The deviation caused by the assumption may span four orders of magnitude. Even for a single uniform deposit, the deviation is also very significant. For practical ground motion calculation, this assumption clearly exists qualitative error in theory, and the quantitative deviation can not be acceptable, so it must be abandoned and need to find another more reasonable approach.
Equivalent linearization in frequency domain, represented by SHAKE2000, is the mainstream approach for seismic response analysis of soil layers. Due to the severe unreasonable results in soft soil sites, its improvement becomes a research hotspot, which mainly adopts frequency-dependent method(FDM), but there has been no substantial improvement. This paper assumes that dynamic shear strain and vibration velocity present a constant proportional relationship in FDM. Based on wave equation, exact solutions for the relationship of the two variables were derived on three typical site models, i.e., the homogeneous half space with one-way traveling wave, the single uniform soil layer, and the layered soil site. The reasonability and deviation degree of the assumption were studied through numerical experiments. Results show that the constant proportional hypothesis only applies in the case of unbounded homogeneous medium with one-way traveling wave. For actual layered soil sites, the relationship between dynamic shear strain and vibration velocity strongly depends on the frequency of the wave and the location of the observation point. If we ignore the reflection wave in ground seismic response analysis, the use of constant proportion assumption under one-way traveling wave will make significant deviation to the results. The deviation caused by the assumption may span four orders of magnitude. Even for a single uniform deposit, the deviation is also very significant. For practical ground motion calculation, this assumption clearly exists qualitative error in theory, and the quantitative deviation can not be acceptable, so it must be abandoned and need to find another more reasonable approach.
引文
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[2]胡聿贤,孙平善,章在墉,等.场地条件对震害和地震动的影响[M]//廖振鹏.地震小区划:理论与实践.北京:地震出版社,1989:12-18.HU Yu-xian,SUN Ping-shan,ZHANG Zai-yong,et al.Effect of site conditions on earthquake damage and ground motion[M]//LIAO Zhen-peng.Seismic microzonation:Theory and practice.Beijing:Seismological Press,1989:12-18.
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[4]李瑞山.新一代土层地震反应分析方法研究[D].哈尔滨:中国地震局工程力学研究所,2016.LI Rui-shan.Research on a new generation technique for ground seismic response analysis[D].Harbin:Institute of Engineering Mechanics,CEA,2016.
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[9]廖振鹏.工程波动理论导论[M].第2版.北京:科学出版社,2002:51.LIAO Zhen-peng.Introduction to wave motion theories for engineering[M].2nd ed.Beijing:Science Press,2002:51.
[10]邢海灵,蒋通,姚东生,等.成层场地由基岩反应谱直接计算地表反应谱的等效线性化方法[J].岩土工程学报,2012,34(12):2337-2344.XING Hai-ling,JIANG Tong,YAO Dong-sheng,et al.Calculation of free field response spectrum form bed rock response spectrum directly for horizontally-layered site using equivalent linear method[J].Chinese Journal of Geotechnical Engineering,2012,34(12):2337-2344.
[11]IWASAKI Y,TAI M.Strong motion records at Kobe Port Island[J].Soils and Foundations,1996,36:29-40.
[12]GIBBS J F,FUMAL T E,BOORE D M,et al.Seismic velocities and geologic logs from borehole measurements at seven strong-motion stations that recorded the Loma Prieta earthquake[R].[S.l.]:U.S.Geological Survey,1992.
[13]中国建筑科学研究院.GB 50011-2010建筑抗震设计规范[S].北京:中国建筑工业出版社,2010.China Academy of Building Research.GB 50011-2010Code for seismic design of buildings[S].Beijing:China Archi-tecture&Building Press,2010.
[14]袁晓铭,李瑞山,孙锐.新一代土层地震反应分析方法[J].土木工程学报,2016,49(10):95-102.YUAN Xiao-ming,LI Rui-shan,SUN Rui.A new generation method for earthquake response analysis of soil layers[J].China Civil Engineering Journal,2016,49(10):95-102.
[15]李瑞山,陈龙伟,袁晓铭,等.荷载频率对动模量阻尼比影响的试验研究[J].岩土工程学报,2017,39(1):71-80.LI Rui-shan,CHEN Long-wei,YUAN Xiao-ming,et al.Experimental study on influences of different loading frequencies on dynamic modulus and damping ratio[J].Chinese Journal of Geotechnical Engineering,2017,39(1):71-80.
[2]胡聿贤,孙平善,章在墉,等.场地条件对震害和地震动的影响[M]//廖振鹏.地震小区划:理论与实践.北京:地震出版社,1989:12-18.HU Yu-xian,SUN Ping-shan,ZHANG Zai-yong,et al.Effect of site conditions on earthquake damage and ground motion[M]//LIAO Zhen-peng.Seismic microzonation:Theory and practice.Beijing:Seismological Press,1989:12-18.
[3]杨洋,孙锐,杨洪搏,等.国际上两种典型土层地震反应分析程序对比研究[J].世界地震工程,2017,33(3):17-23.YANG Yang,SUN Rui,YANG Hong-bo,et al.Contrasting study between two international typical soil layers seismic response analysis programs[J].World Earthquake Engineering,2017,33(3):17-23.
[4]李瑞山.新一代土层地震反应分析方法研究[D].哈尔滨:中国地震局工程力学研究所,2016.LI Rui-shan.Research on a new generation technique for ground seismic response analysis[D].Harbin:Institute of Engineering Mechanics,CEA,2016.
[5]YOSHIDA N,KOBAYASHI S,SUETOMI I,et al.Equivalent linear method considering frequency dependent characteristics of stiffness and damping[J].Soil Dynamics and Earthquake Engineering,2002,22(3):205-222.
[6]ASSIMAKI D,KAUSEL E.An equivalent linear algorithm with frequency-and pressure-dependent moduli and damping for the seismic analysis of deep sites[J].Soil Dynamics and Earthquake Engineering,2002,22(9-12):959-965.
[7]KAUSEL E,ASSIMAKI D.Seismic simulation of inelastic soils via frequency-dependent moduli and damping[J].Journal of Engineering Mechanics,2002,128(1):34-47.
[8]蒋通,邢海灵.水平土层地震反应分析考虑频率相关性的等效线性化方法[J].岩土工程学报,2007,29(2):218-224.JIANG Tong,XING Hai-ling.An equivalent linear method considering frequency-dependent soil properties for seismic response analysis[J].Chinese Journal of Geotechnical Engineering,2007,29(2):218-224.
[9]廖振鹏.工程波动理论导论[M].第2版.北京:科学出版社,2002:51.LIAO Zhen-peng.Introduction to wave motion theories for engineering[M].2nd ed.Beijing:Science Press,2002:51.
[10]邢海灵,蒋通,姚东生,等.成层场地由基岩反应谱直接计算地表反应谱的等效线性化方法[J].岩土工程学报,2012,34(12):2337-2344.XING Hai-ling,JIANG Tong,YAO Dong-sheng,et al.Calculation of free field response spectrum form bed rock response spectrum directly for horizontally-layered site using equivalent linear method[J].Chinese Journal of Geotechnical Engineering,2012,34(12):2337-2344.
[11]IWASAKI Y,TAI M.Strong motion records at Kobe Port Island[J].Soils and Foundations,1996,36:29-40.
[12]GIBBS J F,FUMAL T E,BOORE D M,et al.Seismic velocities and geologic logs from borehole measurements at seven strong-motion stations that recorded the Loma Prieta earthquake[R].[S.l.]:U.S.Geological Survey,1992.
[13]中国建筑科学研究院.GB 50011-2010建筑抗震设计规范[S].北京:中国建筑工业出版社,2010.China Academy of Building Research.GB 50011-2010Code for seismic design of buildings[S].Beijing:China Archi-tecture&Building Press,2010.
[14]袁晓铭,李瑞山,孙锐.新一代土层地震反应分析方法[J].土木工程学报,2016,49(10):95-102.YUAN Xiao-ming,LI Rui-shan,SUN Rui.A new generation method for earthquake response analysis of soil layers[J].China Civil Engineering Journal,2016,49(10):95-102.
[15]李瑞山,陈龙伟,袁晓铭,等.荷载频率对动模量阻尼比影响的试验研究[J].岩土工程学报,2017,39(1):71-80.LI Rui-shan,CHEN Long-wei,YUAN Xiao-ming,et al.Experimental study on influences of different loading frequencies on dynamic modulus and damping ratio[J].Chinese Journal of Geotechnical Engineering,2017,39(1):71-80.