指数函数模量成层地基上变截面坝的随机地震反应分析
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摘要
利用剪切梁理论推导出了指数函数剪切模量成层地基上变截面坝的自振频率方程及任意阶振型函数的解析表达式,在此基础上用振型叠加原理分别给出了地基和变截面坝的地震反应解析表达式。利用随机振动理论,并基于基岩输入地震加速度的功率谱密度函数(白噪声谱和过滤白噪声谱),研究了地基和变截面坝对地震的随机动力响应问题。数值计算表明:①在白噪声谱的情况下,土层和变截面坝的最大期望反应均有别于过滤白噪声谱时的相应值;②平稳输入与输出时地基和变截面坝的最大期望反应与平稳输入非平稳输出的相应值很接近;③平稳输入过高地估计了土层和变截面坝的随机响应。
The formulas for computing natural frequencies and the modes of varied section dam on layered foundation with exponential function shear modulu are derived according to shear beam theory.Furthermore,the seismic responses of the dam and the layered foundation are calculated using mode-superposition scheme.Dynamic responses of the dams and the layered foundations to earthquake are studied by the theory of random vibration,in which two cases of power spectral intensity function for earthquake acceleration inputing at base rock are considered: the white noise spectrum and the filter white noise spectrum.The numerical calculation results show that: ① In the case that the power spectral density of the earthquake acceleration inputing at base rock is the white noise spectrum,the maximum expected responses of the layered foundation and the dam are different from the case of the filter white noise spectrum.② In stationary importing and exporting,the maximum expected responses of the dam and the foundation are as same as that in the case of stationary importing and no stationary exporting.③ In both case of the earthquake acceleration inputing at base rock and the stationary random response process,the random responses of the foundation and the dam are over-estimated.
The formulas for computing natural frequencies and the modes of varied section dam on layered foundation with exponential function shear modulu are derived according to shear beam theory.Furthermore,the seismic responses of the dam and the layered foundation are calculated using mode-superposition scheme.Dynamic responses of the dams and the layered foundations to earthquake are studied by the theory of random vibration,in which two cases of power spectral intensity function for earthquake acceleration inputing at base rock are considered: the white noise spectrum and the filter white noise spectrum.The numerical calculation results show that: ① In the case that the power spectral density of the earthquake acceleration inputing at base rock is the white noise spectrum,the maximum expected responses of the layered foundation and the dam are different from the case of the filter white noise spectrum.② In stationary importing and exporting,the maximum expected responses of the dam and the foundation are as same as that in the case of stationary importing and no stationary exporting.③ In both case of the earthquake acceleration inputing at base rock and the stationary random response process,the random responses of the foundation and the dam are over-estimated.
引文
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[4]Ikuo Towhata.Seismic Wave Propagation in Elastic Soil withContinuous Variation of Shear Modulus in the Vertical Direc-tion[J].Soil and Foundation,1996,36(1):61-72.
[5]王春玲,黄义,张为民.指数函数剪切模量的成层土地震反应解析解[J].长安大学学报(自然科学版),2003,23(4):15-17.
[6]Lin Jiahao.A Fast CQC Algorithm of PSD Matrices for Ran-dom Seismic Responses[J].Computer&Structures,1992,44(3),683-687.
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[8]王春玲,黄义.指数函数剪切模量土层的地震随机反应[J].岩土力学,2003,24(6):892-895.
[9]林家浩.剪切梁随机地震响应的李兹法[J].应用力学学报,1994,11(3):107-110.
[10]孔宪京,韩国城,张天明.土石坝与地基地震反应分析的波动-剪切梁法[J].大连理工大学学报,1994,34(2):173-179.
[11]刘平,李琪.基底隔震建筑的剪切梁动力模型[J].工程力学,1998,15(3):90-97.
[2]J P Wolf.Dynamic Soil-Structure Interaction[M].[S.l.]:Prentice-Hall,1985.
[3]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.
[4]Ikuo Towhata.Seismic Wave Propagation in Elastic Soil withContinuous Variation of Shear Modulus in the Vertical Direc-tion[J].Soil and Foundation,1996,36(1):61-72.
[5]王春玲,黄义,张为民.指数函数剪切模量的成层土地震反应解析解[J].长安大学学报(自然科学版),2003,23(4):15-17.
[6]Lin Jiahao.A Fast CQC Algorithm of PSD Matrices for Ran-dom Seismic Responses[J].Computer&Structures,1992,44(3),683-687.
[7]曾心传,秦小军.土层对地震的随机反应分析[J].地震工程与工程振动,1998,18(3):27-38.
[8]王春玲,黄义.指数函数剪切模量土层的地震随机反应[J].岩土力学,2003,24(6):892-895.
[9]林家浩.剪切梁随机地震响应的李兹法[J].应用力学学报,1994,11(3):107-110.
[10]孔宪京,韩国城,张天明.土石坝与地基地震反应分析的波动-剪切梁法[J].大连理工大学学报,1994,34(2):173-179.
[11]刘平,李琪.基底隔震建筑的剪切梁动力模型[J].工程力学,1998,15(3):90-97.
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