基于分形维数的RC框架地震损伤识别与评估

Fractal Dimension-Based Seismic Damage Identification and Assessment of RC Frames

摘要: 本研究旨在提出一种基于分形维数的钢筋混凝土(RC)框架结构地震损伤识别与评估方法。研究通过ABAQUS软件建立了一个三层单跨的RC框架有限元模型，选取El Centro波、Kobe波和一条人工地震波作为输入。采用盒计数法计算结构在地震作用下位移和加速度响应信号的分形维数(D_B)。研究对比了损伤前后响应信号分形维数的变化，分析了分形维数与地震波中心频率、楼层位置以及结构损伤程度的关联。研究发现，响应信号的分形维数随损伤程度的增加而显著增大，且加速度信号的分形维数对损伤更为敏感。基于此，论文提出了一种新的“分形损伤指数”(FDI)，并给出了与“基本完好”、“轻微损伤”和“中等损伤”三个等级相对应的FDI建议阈值，旨在为结构损伤预警和震后快速评估提供补充性指标。

Abstract: This study aims to propose a seismic damage identification and assessment method for Reinforced Concrete (RC) frame structures based on fractal dimension. A three-story, single-bay finite element model of an RC frame was established using ABAQUS software, with the El Centro wave, Kobe wave, and an artificial seismic wave selected as inputs. The box-counting method was employed to calculate the fractal dimensions (D_B) of displacement and acceleration response signals of the structure under seismic excitation. The study compared the changes in fractal dimensions of the response signals before and after damage and analyzed the correlations between the fractal dimension and the central frequency of the seismic wave, the story level, as well as the degree of structural damage. The results indicate that the fractal dimension of the response signals increases significantly with the degree of damage, and the fractal dimension of the acceleration signal is more sensitive to damage. Based on these findings, a novel “Fractal Damage Index” (FDI) is proposed, along with suggested FDI thresholds corresponding to three damage levels: “Basically Intact”, “Slightly Damaged”, and “Moderately Damaged”. This aims to provide a supplementary indicator for structural damage early warning and rapid post-earthquake assessment.