（1 大连理工大学土木工程学院， 大连 116024; 2 大连理工大学海岸和近海工程国家重点实验室, 大连 116024)

［摘要］为合理反映钢筋混凝土结构的损伤演化规律，研究了单自由度体系基于损伤模型的损伤曲线及演化方程。引入Logistic曲线，并采用增量动力分析方法，以Ghobarah刚度退化损伤模型和修正Park-Ang损伤模型为基础，确定了Logistic方程的参数。由此得到了基于损伤模型的Logistic损伤演化方程的计算方法。该方程可描述结构从无损状态发展到损伤加速阶段、损伤恒速阶段、损伤减速阶段至收敛到损伤临界值的全过程。为验证该方程，以实际算例分析了一钢筋混凝土柱在22条地震波增量动力分析下的损伤演化曲线。结果表明：虽然在不同地震波下结构的损伤演化曲线存在一定的离散性，但所表现出的损伤演化规律相同；基于Ghobarah刚度退化损伤模型和修正Park-Ang损伤模型的Logistic损伤演化曲线，能够描述该钢筋混凝土柱不同阶段的损伤发展状态。

［关键词］Logistic曲线； 单自由度； 损伤演化； 损伤模型； 增量动力分析； Pushover分析； 地震动

中图分类号：TU352-1文献标识码：A文章编号：1002-848X(2018)02-0027-06

Damage evolution rule of single degree of freedom system based on damage model

Guo Xiang1, He Zheng1,2

(1 Department of Civil Engineering, Dalian University of Technology, Dalian 116024, China; 2 State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China)

Abstract:In order to reflect the damage evolution rule of reinforced concrete structures, the damage curve and damage evolution equation of the single degree of freedom system were studied based on the damage models. The Logistic curve was introduced and the incremental dynamic analysis (IDA) was used to gain the reasonable damage curve and the parameters of the Logistic equation based on the Ghobarah stiffness-degraded damage model and the modified Park-Ang damage model. The obtained Logistic evolution can well describe the 5 stages of damage including zero-damage stage, damage acceleration stage, damage constant velocity stage, damage deceleration stage and stage of damage converged to critical value. To verify the proposed equation, IDA with 22 ground motion records were conducted on a reinforced concrete column. Results show that although the damage evolution curves diverge from each other under different seismic waves, the tendency and evolution law are the same. And the Logistic equation based on the Ghobarah stiffness-degraded damage model and the modified Park-Ang damage model can  well reflect the damage development tendency of the reinforced concrete column in different stages.

Keywords:Logistic curve; single degree of freedom; damage evolution; damage model; incremental dynamic analysis; Pushover analysis; earthquake motion

*国家自然科学基金项目（91315301, 51261120376）。

通讯作者：何政，博士，教授，Email：hezheng@dlut.edu.cn。