确定土层自由场地震动的二维简化模型
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摘要
为了研究均匀土层自由场地震动的二维简化模型,首先利用弹性波动理论,得到土介质的二维波动方程,采用分离变量法来求解该方程,根据土层上下界面的边界条件确定土层竖向振动的特征频率和振型;根据波沿水平方向向无穷远处传播的衰减特性确定波沿水平方向衰减系数,得到土层自由场自由振动的相对位移的解析解。然后,采用振型叠加法求解强迫振动情况下的波动方程,得出二维情况下均匀土层在地震作用下沿水平方向相对位移的解析解。通过上述计算,得到了土层自由场地震动的二维简化模型。通过具体算例,分别对研究的二维简化模型与一维剪切梁模型进行了比较。比较结果表明,地下土层水平维度对于均匀土层自由场地震动反应的影响很小。
The simplified 2-D model for determination of free field seismic motion of uniform soil strata was studied.Firstly,the two-dimensional wave equation of the soil was obtained with the theory of elastic wave.The method of separation of variables was used to solve the equation.The natural frequencies and mode shapes of vertical vibration of soil were determined by using the boundary conditions of the upper and lower soil interface.According to the wave attenuation properties of wave propagation to infinity,the wave attenuation coefficient along the horizontal direction was determined,and the relative displacement analytical solution of free vibration was obtained.Then the forced vibration equation was solved by using the mode superposition method.As a result,the analytical solution of the horizontal relative soil displacement was obtained.Through the above calculations,the simplified 2-D model for determination of free field seismic motion of soil strata was obtained.Finally,the 2-D model was compared with the 1-D shear beam model,and the results show that the horizontal dimension has little effect on the seismic response of the soil.
The simplified 2-D model for determination of free field seismic motion of uniform soil strata was studied.Firstly,the two-dimensional wave equation of the soil was obtained with the theory of elastic wave.The method of separation of variables was used to solve the equation.The natural frequencies and mode shapes of vertical vibration of soil were determined by using the boundary conditions of the upper and lower soil interface.According to the wave attenuation properties of wave propagation to infinity,the wave attenuation coefficient along the horizontal direction was determined,and the relative displacement analytical solution of free vibration was obtained.Then the forced vibration equation was solved by using the mode superposition method.As a result,the analytical solution of the horizontal relative soil displacement was obtained.Through the above calculations,the simplified 2-D model for determination of free field seismic motion of soil strata was obtained.Finally,the 2-D model was compared with the 1-D shear beam model,and the results show that the horizontal dimension has little effect on the seismic response of the soil.
引文
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[2]齐文浩,薄景山,张忠利.土层地震反应分析的研究现状[J].世界地震工程,2010,26(增刊1):368-372.QI Wenhao,BO Jingshan,ZHANG Zhongli.Research status on studies of soil layer seimic response analysis[J].World Earthquake Engineering,2010,26(sup1):368-372.(in Chinese).
[3]黄义,王春玲,曹彩芹.成层地基一维土层对地震的随机反应分析[J].世界地震工程,2004,20(1):126-132.HUANG Yi,WANG Chunling,CAO Caiqin.Random response analysis of stratified foundations to earthquakes[J].World Earthquake Engineering,2004,20(1):126-132.(in Chinese).
[4]王美霞,杨顶辉,宋国杰.二维SH波方程的半解析解及其数值模拟[J].地球物理学报,2012,55(1):914-924.WANG Meixia,YANG Dinghui,SONG Guojie.Semianalytical solutions and numerical simulations of 2D SH wave equation[J].Chinese Journal of Geophysics,2012,55(1):914-924.(in Chinese).
[5]刘晶波,王艳.成层介质中平面内自由波场的一维化时域算法[J].工程力学,2007,24(7):16-22.LIU Jingbo,WANG Yan.A 1Dtime-domain method for in-plane wave motion of free field in layered media[J].Engineering Mechanics,2007,24(7):16-22.(in Chinese).
[6]DAVIS C A.Lateral seismic pressures for design of rigid underground lifeline structures[C]//Proceedings of the 6th U.S.Conference on Lifeline Earthquake Engineering.California:American Society of Civil Engineers(ASCE),2003:1001-1010.
[7]胡聿贤.地震工程学[M].2版.北京:地震出版社,2006.
[8]张克绪,谢君斐.土动力学[M].北京:地震出版社,1989.
[9]杨桂通.弹性力学[M].北京:高等教育出版社,1998.
[10]刘晶波,杜修力.结构动力学[M].北京:机械工业出版社,2005.
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