非线性成层地基下基岩平稳地震动输入

采用二次反演计算基岩的平稳地震动输入。首先根据《建筑抗震设计规范》（GB 50011—2001）的地震影响系数曲线，利用加速度峰值等效原则迭代计算得到地面加速度平稳功率谱密度；然后通过等价线性化法计算地基各土层的剪切模量和阻尼比，将地面加速度平稳功率谱密度作为地面边界上的虚拟稳态输入，运用半无限长剪切梁上的一维波动方程，通过非线性迭代分析求得非线性分层地基下基岩的加速度平稳功率谱密度。该方法可为缺乏地面或基岩地震加速度记录资料的地区的堤坝等大型上部结构及隧道、管道等建筑物的随机地震响应分析提供较为可靠准确的基岩地震动输入，并可得到地基中不同深度的加速度、剪应变等动力响应的稳态峰值期望值，为应用随机理论进行工程抗震计算提供了依据。

Study on stationary earthquake motion input at bedrock under nonlinear layered soils

Stationary earthquake motion input at bedrock is evaluated by a two-step inversion method.Firstly,the stationary power spectral density(PSD) of acceleration at the ground level is obtained by an iterative approach of equivalence of peak acceleration according to the response spectrum in the Chinese seismic code(GB 50011-2001).Secondly,after the stiffness and damping ratio of each soil layer were calculated by the equivalent linearization technique,the stationary PSD of acceleration at the ground level was applied as the pseudo stationary inputs.By the use of the one-dimensional wave propagation function on the semi-finite shear beam,the stationary earthquake motion at bedrock under nonlinear layered ground was evaluated iteratively.It provides relatively reliable and accurate earthquake motion inputs at the bedrock for the stochastic seismic analysis of dams,tunnels and pipelines at regions for which few acceleration observation data at the ground level or bedrock are obtained,and it can also estimate the stationary dynamic response such as peak acceleration and peak shear strain under the ground as a primarily reference value for further dynamic analysis.The results show that the method is practical.