成层场地由基岩反应谱直接计算地表反应谱的等效线性化方法

以太平洋地震工程中心NGA强震数据库为基础,同时收集并分析处理了2008年汶川地震和2011年日本太平洋冲地震的强震记录。通过对近4000个水平地震记录的分析,获得了水平地震动峰值速度(PGV)与阻尼比5%的最大拟速度谱值的简便统计关系式,并与已有研究进行对比验证了该公式的适用性。为了将该公式应用到场地地震反应分析中,用该关系式对近场强震记录进行了回归分析并验证了其适用性。对于水平成层场地,利用笔者提出的PGV与最大拟速度谱的关系式以及速度与应变的近似关系,可由该层的反应谱计算其等效应变,从而可按照等效线性化方法的原理求得传递函数。以加速度反应谱与功率谱密度函数之间的相互转换关系为基础,以功率谱为载体,假定输入地震动为平稳随机过程,根据随机振动理论可由传递函数和输入功率谱算得各层的反应谱。对实际工程场地和竖向钻孔场地的分析表明,该方法有较好的计算精度和适用性。

Calculation of free field response spectrum from bed rock response spectrum directly for horizontally-layered site using equivalent linear method

A stable relationship between the peak ground velocity (PGV) and the 5%-damped maximum pseudo-spectral velocity (maxPSV) is presented based on analysis of horizontal records of PEER NGA project as well as those strong motion records of Wenchuan M8.0 Earthquake (2008) and the M9.0 Earthquake near the East Coast of Honshu, Japan. The validity and the applicability of this relationship are inspected using near-source records. This relationship is validated by comparison with the former work. A new approach to calculate the free field response spectrum directly from the bed rock response spectrum at a horizontal layered site is presented using the following iterative procedure firstly, using the standard equivalent linear method model and the assumed strain level at the center of each layer, the transfer functions are determined for a unit input specified at the bed rock. Secondly, treating the earthquake motions as a stationary stochastic process with power spectral density (PSD) function which is converted from the bed rock response spectrum, the PSD functions of every layer are calculated by the transfer functions. Finally, the equivalent strain of every layer, which is used to get a new shear modulus and damping to determine new transfer function, is obtained by converting the PSD functions to response spectra, evaluating the PGV from the results, and calculating strain using the relationship between the shear strain and the particle velocity of homogeneous medium. The applicability and the validity of the proposed approach are demonstrated by comparing the results with those of other methods for the same project site, as well as with the response spectra of the down-hole array records in Japan.