基于Copula函数的渡槽结构地震动易损性分析

Analysis of Seismic Fragility of Aqueduct Structure Based on Copula Function

在结构易损性分析中,由于构件之间的地震需求存在相关性,直接建立渡槽系统中基本构件的联合概率分布函数较为困难,为此引入二维Copula函数对构件地震需求之间的相关结构进行描述,简化联合分布函数的建模过程。首先,对某输水渡槽中的一跨进行时程分析,以地面峰值加速度为自变量,以排架的位移延性比和橡胶支座的变形大小为损伤指标,考虑地震动和结构参数的不确定性,建立排架、橡胶支座的易损性曲线;其次,通过Copula函数建立渡槽系统的易损性曲线;最后,通过1阶界限法得到渡槽系统易损性的上、下界。计算结果表明,基于Copula函数计算得到的失效概率均位于1阶界限法的上、下界之间。研究结果有助于简化渡槽系统易损性曲线的建模过程,为研究渡槽构件地震需求之间的相关性提供新思路和方法。

It is hard to directly establish the joint probability distribution function of the basic components in the aqueduct system because of the correlation of seismic demand among components in structural vulnerability analysis.A new method for analyzing the vulnerability of the aqueduct structure is proposed.A two-dimensional Copula function is introduced to describe the related structures of component seismic demands and simplify the modeling process of the joint distribution function.First,the vulnerability curves of a bent and rubber bearing are created based on the analysis of time history on a cross of an aqueduct.The independent variable is the peak ground acceleration,and the damage index is the displacement ductility ratio of bent and the deformation of rubber bearing.The uncertainty of ground motion and structural parameters is considered.Second,the vulnerability curve of the aqueduct system is established using the Copula function.Finally,the upper and lower bounds of the aqueduct system vulnerability are obtained by the first-order boundary method.The results show that the failure probability calculated based on the Copula function is between the upper and lower bounds of the first-order boundary method.The results help to simplify the modeling process of the aqueduct system vulnerability curve,and at the same time,providing a new way to study the correlation between seismic demand of aqueduct components.