一种平稳地震地面运动的改进金井清谱模型

A MODIFIED KANAI-TAJIMI SPECTRAL MODEL FOR THE STATIONARY EARTHQUAKE INDUCED GROUND MOTION PROCESS

该文提出了一种描述平稳地震地面运动过程随机特性的功率谱密度函数模型。假定基岩地震动为某种过滤白谱过程,通过两个特定频率参数控制该过滤白谱的低频和高频含量,从而实现对基岩地震动物理特性的模拟。利用金井清滤波器对基岩过滤白谱进行过滤,得到地震地面加速度的谱密度模型。通过数学推导解释了该模型的物理机制,选择汶川地震强震观测数据拟合模型中的相关参数,给出了汶川地震场地相应的模型参数建议取值。该文模型在物理机制上可以认为是金井清谱模型的改进方案,但修正了金井清谱模型在零频处奇异的缺陷。

The model of a power spectral density function is developed for the stationary stochastic process presenting the earthquake ground motion. First, the acceleration of motion on the rock is assumed to be a random process with characteristic of filtered Gaussian white noise, in which the spectral amplitudes are reduced during both the lower frequency extent and the higher frequency extent by two frequency control parameters. Thus the physical properties of the rock motion are simulated and the energy of the motion is finite. Then the overlaying soil is represented to be a linear single-degree-of-freedom system, and the power spectral density function of the ground acceleration is solved by the random dynamic analysis procedure for the SDOF system, excited by the motion of the rock. Furthermore, the physical mechanism of the modeling presented is explained, and the instrumented data of the strong ground motion received from the 2008 Wenchuan earthquake are employed to fit the parameters in the model for the illustration to the reasonable values of the modeling parameters. It may be considered that the stationary model presented is a modified Kanai-Tajimi spectrum because of the use of the Kanai filter, but eliminates the singular point in zero frequency existed in the Kanai-Tajimi spectrum.