考虑矩震级影响的位移谱阻尼调整系数

Damping Scaling Factor with a Consideration of Influence of Moment Magnitude

基于408条地震地面运动记录统计分析，首先研究了矩震级（ Mw ）对位移谱阻尼调整系数（ DSF ）的影响。结果表明：Mw 对DSF的影响与周期（ T ）和阻尼比（ξ）有关；在T ＞0．6 s的范围内，当ξ＜5％时， DSF随着Mw的增长而增长；当ξ＞5％时， DSF随着Mw的增长而减小。随着T的增长， Mw 对DSF的影响越显著；ξ越远离5％， Mw对DSF的影响越显著。在T ＜0．6 s的范围内， Mw对DSF无显著影响；当Mw ＝5～6时， DSF受T的影响显著；随着Mw的增大，在T ＞～0．6 s范围内， DSF受T的影响逐渐减弱；当Mw ＝7～8时，在T ＞0．6 s范围内，除阻尼比为0．5％和1％的DSF外， DSF基本不随T而变化；DSF相对于ξ存在异方差性。然后提出了只考虑周期和阻尼比影响的DSF回归方程，计算出在指定周期和阻尼比处的残差，根据在长周期处该回归方程的残差随Mw 显直线分布，最后提出了包含线性矩震级项的DSF回归模型并给出了模型的回归系数。该模型的残差随Mw 和相对能量持时（ D5-95）的分布表明：模型能体现Mw对DSF的影响，能间接地体现D 5-95对DSF的影响。模型的标准差能体现DSF相对于ξ的异方差性。

The influence of moment magnitude （ Mw ） on damping scaling factor （ DSF） was firstly investigated based on the statistical analysis of 408 earthquake ground motion records .It is showed that the effect of Mw on DSF depends on period of vibration （ T） and damping ratio （ξ） .The DSF increases as Mw increases for the periods greater than about 0.6 s ifξ＆lt;5%, but it decreases ifξ＆gt;5%.The pattern with Mw is much more sig-nificant as T increases orξdeviates from 5%.Almost no pattern with Mw is seen for the periods less than about 0.6 s.DSF is significantly affected by T when Mw =5~6.The influence of T on DSF becomes less significant with the increase of Mw for the periods greater than about 0.6 s.When Mw =7 ~8 DSF does not basically change with T within the range of periods greater than 0.6 s except DSF corresponding to 0.5% and 1%damping .The heteroscedasticity in the DSF with respect to ξexists.Then DSF regression equation was pro-posed that only depends on T andξand equation residuals was calculated at specified T andξ.Finally accord-ing to the residual plots showing an almost linear relationship with Mw at long periods , the regression model that includes a linear magnitude term was proposed and regression coefficients were tabulated .Residual analysis shows that the proposed model can reflect the influence of Mw on DSF and can indirectly reflect the influence of significant duration （ D5-95 ） on DSF .The standard deviation of the model can reflect heteroscedasticity in the DSF with respect toξ.