指数函数模量成层地基上变截面坝的随机地震反应分析

Random Earthquake Response of the Varied Section Dam on the Layered Foundation with Exponential Function Shear Modulus

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。

Abstract:

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 .