剪切模量沿深度按指数规律增大的场地土的地震放大效应
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摘要
采用一维波动模型分析基岩上、受竖直向上传播的稳态剪切地震波激振下剪切模量沿深度按指数规律增长的场地土的横向自由振动问题,求得位移的闭合解,并由该解得到反映地震放大效应的场地的放大系数。通过对此类场地土的算例分析,讨论了剪切模量沿深度按指数规律增长的场地土的地震放大效应,并从讨论中总结了场地土土质特性、基岩与场地土底面之间的阻抗比及振动频率对地震放大效应的影响规律,同时验证了广泛使用的场地卓越周期简化估算公式仍可应用于剪切模量沿深度非线性变化的场地土。
For the one-dimensional analysis of sites on a bedrock subjected to the excitation of steady-state and vertically propagating shear seismic waves,closed-form solutions for the displacements are presented for a single layer with exponentially increasing shear modulus with depth.A general form of analytical solution of the seismic amplification is developed.The study of an example shows that the characteristics of soil sites,the vibration frequency and the impedance ratio of the half-space and the bottom surface of the soil layer affect the seismic amplification.The predominant period of a nonlinear site,i.e.four times the total shear wave travel time through the layer,is proved to be a good estimate.
For the one-dimensional analysis of sites on a bedrock subjected to the excitation of steady-state and vertically propagating shear seismic waves,closed-form solutions for the displacements are presented for a single layer with exponentially increasing shear modulus with depth.A general form of analytical solution of the seismic amplification is developed.The study of an example shows that the characteristics of soil sites,the vibration frequency and the impedance ratio of the half-space and the bottom surface of the soil layer affect the seismic amplification.The predominant period of a nonlinear site,i.e.four times the total shear wave travel time through the layer,is proved to be a good estimate.
引文
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[5]Zhao J X.Modal analysis of soft-soil sites including radiation damping[J].Earthquake Engineering and Structure Dynamics,1997,26(1):93~113.
[6]熊建国,许贻燕.分层土自振特性分析[J].地震工程与工程振动,1986,6(4):21~35.Xiong Jianguo,Xu Yiyan.Analysis of natural vibration characteristics of horizontally-layered soil sites[J].Chinese Earthquake Engineering and Structure Dynamics,1986,6(4):21~35.(in Chinese)
[7]栾茂田,金崇磐,林皋.非均质地基振动特性及地震反应分析[J].大连理工大学学报,1992,32(1):81~87.Luan Maotian,Jin Chongpan,Lin Gao.Vibration behavior and seismic response of vertically non-homogeneous soil deposites[J].Journal of Dalian University of Technology,1992,32(1):81~87.(in Chinese)
[8]高玉峰,金建新,谢康和,王朝晖.成层地基一维土层地震反应解析解[J].岩土工程学报,1999,21(4):498~500.Gao Yufeng,Jin Jianxin,Xie Kanghe,Wang Zhaohui.General solution to the soil seismic response on stratified foundations[J].Chinese Journal of Geotechnical Engineering,1999,21(4):498~500.(in Chinese)
[9]王竹溪,郭敦仁.特殊函数概论[M].北京:科学出版社,1979.Wang Zhuxi,Guo Dunren.Introduction to special functions[M].Beijing:Science Press,1979.(in Chinese)
[10]奚定平.贝塞尔函数[M].北京:高等教育出版社;柏林:施普林格出版社,1998.Xi Dingping.Bessel functions[M].Beijing:China Higher Education Press;Berlin:Springer-Verlag,1998.(in Chinese)
[2]Wolf J P.土-结构动力相互作用[M].吴世明译.北京:地震出版社,1989.Wolf J P.Dynamic soil-structure interaction[M].Wu Shiming.Beijing:Seismic Press,1989.(in Chinese)
[3]Davis R.Effects of weathering on site response[J].Earthquake Engineering and Structure Dynamics,1995,24(2):301~309.
[4]Zhao J X.Estimating modal parameters for a simple soft-soil site having a linear distribution of shear wave velocity with depth[J].Earthquake Engineering and Structure Dynamics,1996,25(2):163~178.
[5]Zhao J X.Modal analysis of soft-soil sites including radiation damping[J].Earthquake Engineering and Structure Dynamics,1997,26(1):93~113.
[6]熊建国,许贻燕.分层土自振特性分析[J].地震工程与工程振动,1986,6(4):21~35.Xiong Jianguo,Xu Yiyan.Analysis of natural vibration characteristics of horizontally-layered soil sites[J].Chinese Earthquake Engineering and Structure Dynamics,1986,6(4):21~35.(in Chinese)
[7]栾茂田,金崇磐,林皋.非均质地基振动特性及地震反应分析[J].大连理工大学学报,1992,32(1):81~87.Luan Maotian,Jin Chongpan,Lin Gao.Vibration behavior and seismic response of vertically non-homogeneous soil deposites[J].Journal of Dalian University of Technology,1992,32(1):81~87.(in Chinese)
[8]高玉峰,金建新,谢康和,王朝晖.成层地基一维土层地震反应解析解[J].岩土工程学报,1999,21(4):498~500.Gao Yufeng,Jin Jianxin,Xie Kanghe,Wang Zhaohui.General solution to the soil seismic response on stratified foundations[J].Chinese Journal of Geotechnical Engineering,1999,21(4):498~500.(in Chinese)
[9]王竹溪,郭敦仁.特殊函数概论[M].北京:科学出版社,1979.Wang Zhuxi,Guo Dunren.Introduction to special functions[M].Beijing:Science Press,1979.(in Chinese)
[10]奚定平.贝塞尔函数[M].北京:高等教育出版社;柏林:施普林格出版社,1998.Xi Dingping.Bessel functions[M].Beijing:China Higher Education Press;Berlin:Springer-Verlag,1998.(in Chinese)
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