土层时域分析中黏滞阻尼形式的比较

Comparative study of viscous damping formulation in time-domain site response analysis

时域分析中采用粘滞阻尼反映小应变条件下土的阻尼特性,瑞雷阻尼则是常用的黏滞阻尼形式。本文基于有限差分方法,构建一组数值计算模型,以实际地震记录作为输入,以不同的土层条件作为分析对象,采用加速度、位移和反应谱指标评价了瑞雷阻尼形式对土层地震反应的影响,并将不同阻尼形式下的计算结果与响嘡台阵真实记录进行了对比分析。计算结果表明:阻尼形式对加速度反应和反应谱的影响显著,对位移反应影响有限,但位移幅值沿土层高度的变化规律较复杂;不同阻尼形式时反应谱短周期段的谱值差别明显,而对反应谱长周期段谱值影响有限;高频地震动激励,深软土层中不同阻尼形式的计算结果离散性大;在确定阻尼形式时要综和考虑土层特征和地震动频谱特性,只考虑土层卓越频率的阻尼形式会低估土层地震反应。对于长周期地震动输入,本文建议目标频率取土层第3阶频率,对于高频地震动,目标频率可取为反应谱峰值对应频率。

This paper revisits the effect of damping matrices on site response analysis in time-domain based on Fi- nite difference method（FDM）. Numerical models are developed to simulate the wave propagation through an elastic medium after considering soil thickness H, shear velocity Vs and spectral characteristics of input motions. A full Rayleigh damping matix is adopted and the low frequency is selected as the fundamental site frequency, the high frequency （ optimal frequency） is determined by five methods. In order to compare the results of different methods with actual records, the equivalent linearization method and time-domain with five damping formulations on the seismic response of soil layers in Xiang-tang Array are also presented. Analyzes reveal that damping models have significant influence on acceleration and spectral acceleration, but ground displacement response limited. The max- imum absolute displacement distribution on soil depth is much more complex than acceleration in different models. The spectral acceleration value difference is large in short period, while has little influence on long period. The re-suhs of different models are discrete in large soil thickness and low shear velocity when input high frequency mo- tions. The site frequency and frequency characteristics of input motions should be considered to establish damping matrix. For long period input motions, the site 3rdfrequency can be selected as optimal frequency, and the predomi- nant frequency of motions should be used in high frequency input motions. Seismic response of the site is underesti- mated when only the site fundamental frequency is adopted, especially in deep soft site.