# Deterioration Model for Corroded Circular Columns
## 2 Database
### Explanations of the Database  
(1) The corrosion rates of the longitudinal reinforcement in columns 15, 17, and 19 were not provided in [PERSON] et al. [19]. Therefore, they were estimated according to the change in the longitudinal reinforcement elongation rate and the change in the chloride ion \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Physical Significance** & **Parameter** & **Physical Significance** \\ \hline \multirow{3}{*}{_c_} & Thickness of concrete & \multirow{3}{*}{_s_} & Stirrup spacing, mm \\  & cover, mm & & \\ \cline{3-3} \(d\) & Diameter of circular & \(v\) & Axial load ratio \\  & column, mm & & \\ \cline{3-3}  & Longitudinal & & Corrosion rate of \\ \cline{3-3} \(d_{l}\) & reinforcement & \(Y_{l}\) & longitudinal \\  & diameter, mm & & reinforcement \\  & & & Ratio of stirrup \\ \cline{3-3} \(d_{s}\) & Stirrup diameter, mm & \(\lambda\) & spacing to \\ \cline{3-3}  & & & longitudinal bar \\ \cline{3-3}  & Compressive strength & & \\ \cline{3-3} \(f_{c}\) & of concrete, based on & & \\ \cline{3-3}  & Standard cylinder & \(\lambda_{h}\) & Corrosion height ratio \\  & test, MPa & & \\ \cline{3-3}  & Ultimate strength of & & \\ \cline{3-3} \(f_{ls}\) & longitudinal & \(\lambda_{sp}\) & Shear span ratio \\  & reinforcement & & \\ \cline{3-3} \(f_{ly}\) & Yield strength of & & \\ \cline{3-3} \(f_{ty}\) & longitudinal & \(\rho_{l}\) & Longitudinal \\  & reinforcement, MPa & & reinforcement ratio \\ \cline{3-3} \(f_{ty}\) & Yield strength of & & \\ \cline{3-3} \(f_{ty}\) & stirrup, MPa & & \\ \cline{3-3} \(L\) & Shear span, mm & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Design and corrosion parameters of columns and their physical significance. \begin{table}
\begin{tabular}{c c} \hline \hline
**Design and Corrosion Parameters** & **Range of Values** \\ \hline \(Y_{I}\) (\%) & 3.82–15.3 \\ \(\lambda_{h}\) & 0.25–1.0 \\ \(D\) (mm) & 240–500 \\ \(f_{c}\) (MPa) & 30.43–44.3 \\ \(v\) & 0–0.41 \\ \(\lambda_{sp}\) & 3.15–7.5 \\ \(f_{ly}\) (MPa) & 355.63–596.4 \\ \(f_{ty}\) (MPa) & 230.68–454 \\ \(\rho_{l}\) & 0.015–0.0563 \\ \(\rho_{t}\) & 0.0022–0.0167 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Ranges of important design and corrosion parameters. content of the surrounding concrete [27; 28], and the average of the estimated values of the two methods was taken. (2) In the case where the corrosion rate is not very high, the displacements of the two types of circular columns, which have the same corrosion rate in the plastic hinge area at the bottom and different corrosion rates in the part above the plastic hinge, are very close to each other in the small deformation stage under horizontal force [27]; while in the large deformation stage, the displacements of the column are mainly determined by the plastic hinge region [11]. Consequently, when various sections of the column exhibit varying corrosion rates, the corrosion rate of the column can be represented by the corrosion rate observed in the plastic hinge zone. (3) The hysteretic curves obtained from the tests are represented in the form of horizontal shear versus horizontal displacement. However, in this work, these curves were converted to be described in terms of the bending moment and chord rotation, and the influence of the \(P-\Delta\) effect was considered during the conversion process [29]. (4) The type of static cyclic test configuration in this collection was cantilever [29]. (5) The columns failing in the shear failure mode were not collected in this paper because most of the corroded columns were not highly corroded, and most of them were in the flexural or flexural shear failure modes. (6) The corrosion rate of the longitudinal reinforcement was used to represent the degree of corrosion in the column.