Quantitative Seismic Damage Assessment of Resilient Concrete Columns Using Drift Ratio-Based Fractal Dimension

The objective of this paper is to develop assessment models to quantitatively evaluate the seismic damage caused to resilient concrete columns intended for buildings located in strong-earthquake-prone regions such as Japan and China. The proposed damage assessment models are based on the fractal analysis of crack patterns on the surface of damaged concrete columns and expressed in the form of a fractal dimension (FD) versus transient drift ratio relationship. To calibrate the proposed damage assessment models, a total of eighty images of crack patterns for eight concrete columns were utilized. All the columns were reinforced by weakly bonded ultra-high-strength (WBUHS) rebars and tested under reversed cyclic loading. The experimental variables covered the shear span ratio of the column, the concrete strength, the axial load ratio, and the amount of steel in the WBUHS rebars. A box-counting algorithm was adopted to calculate or derive the FD of the crack pattern corresponding to each transient drift ratio. The test results reveal that the FD is an efficient image-based quantitative indicator of seismic damage degree for resilient concrete columns and correlates strongly with the transient drift ratio and is subjected to the influence of the shear span ratio. The influence of the other experimental variables on the derived FDs is, if any, little. Based on the test results, a linear equation was developed to define the relationships between the FD and transient drift ratio, and a multi-linear equation was formulated to relate the transient drift ratio to the residual drift ratio, an important index adopted in current design guidelines to measure the repairability of damaged concrete structures. To further verify the efficiency of the drift ratio-based FD in seismic damage assessment, the correlation between the FD and relative stiffness loss (RSL), an indicator used to measure the overall damage degree of concrete structures, was also examined. The driven FD exhibited very strong correlation with RSL, and an empirical equation was developed to reliably assess the overall seismic damage degree of resilient concrete columns with an FD.