基于概率的单自由度体系震后残余变形计算

准确预测结构的震后残余变形，对于结构震后性能控制及建立考虑可修复性的抗震设计方法具有重要意义。通过对不同参数的双线性单自由度（SDOF）体系分别在100条标准地震动输入下弹塑性地震反应的统计分析，研究了模型参数和地震动不确定性对SDOF体系残余变形和最大弹塑性变形的影响；建立了双线性SDOF体系震后残余变形的概率计算模型。结果表明：不同地震动输入下SDOF体系的残余变形与最大弹塑性变形之比（dR/dm）存在明显的离散性，且离散程度与结构的刚度比、自振周期、相对屈服荷载系数及峰值地面加速度相关；dR/dm的统计分布规律服从对数正态分布，基于该分布函数建立的计算模型可对给定超越概率条件和地震水平下SDOF体系的震后残余变形进行预测。通过典型算例分析认为，可以采用所建议的模型进行SDOF体系震后残余变形分析及可修复性评估。

Seismic residual deformation analysis of single degree of freedom system based on probability

The accurate estimation of seismic residual deformation is necessary for studying the post-earthquake structural performance and seismic design method including restorability of reinforced concrete (RC) structures. Based on the elasto-plastic time history response analysis of bilinear single degree of freedom (SDOF) systems with various parameters under 100 normalized ground motion records respectively, the influences of model parameters and ground motion uncertainty on seismic residual deformation and maximum elasto-plastic deformation of SDOF systems were studied, and the probabilistic calculation model of seismic residual deformation also was presented. The results indicate that the ratios of residual deformation dR to maximum elasto-plastic deformation dm for SDOF systems under different ground motion inputs presents obvious discreteness, and the dispersion degree is significantly associated with stiffness ratio, natural period, relative yield load coefficient and peak ground acceleration. The statistic distribution of dR/dm can be described well by the lognormal distribution, and the residual deformation of SDOF systems with given probability and seismic levels can be predicted using the proposed model. In addition, a typical example of RC single-column bridge pier is presented to illustrate the methods of seismic residual deformation estimation and restorability assessment of SDOF systems.