# Deterioration Model for Corroded Circular Columns
## 6 Summary and Conclusions  
In this work, the prediction method of the ModIMK hysteretic model for corroded circular columns was investigated based on data statistics, and the main summary and conclusions are as follows:  
(1) A database of 35 corroded and uncorroded comparative circular columns was established, and the ModIMK model parameters of all the components in the database were calibrated. The database was collected from published papers, and it was a good reference for the study of various properties of corroded circular RC columns. (2) Empirical equations for _CIDCs_ were established using linear regression. After the ModIMK model parameters of the corroded columns in the uncorroded state were determined and combined with these equations, the ModIMK hysteretic model of the corroded columns was defined. The method's accuracy was demonstrated through hysteretic response analyses of six components. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c} \hline \hline
**Test No.** & \(\gamma_{1}\) & \(\Lambda_{h}\) & \(d\) & \(c\) & \(L\) & \(f_{e}\) & \(\mathbf{d_{l}}\) & \(\rho_{l}\) & \(f_{hy}\) & \(\mathbf{s}\) & \(d_{s}\) & \(\rho_{t}\) & \(f_{hy}\) & \(\Lambda\) & **Asp** & \(\mathbf{v}\) \\ \hline C9-25 & 9.70 & 1.000 & 260 & 30 & 820 & 32.400 & 16.0 & 0.023 & 373.20 & 572.30 & 100.0 & 8.0 & 0.010 & 327.00 & 6.250 & 3.154 & 0.250 \\ C5 & 3.83 & 0.455 & 300 & 30 & 1100 & 30.430 & 16.0 & 0.017 & 355.63 & 538.25 & 75.0 & 8.0 & 0.011 & 230.68 & 4.688 & 3.667 & 0.200 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Properties of the RC components for the extra-database application. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**Test No.** & \multicolumn{6}{c}{**CIDCs of Corroded Columns**} & \multicolumn{6}{c}{**Model Parameters of Corroded Columns**} \\  & **CIDC\_My** & **CIDC\_0y** & **CIDC\_Mc/My** & **CIDC\_0p** & **CIDC\_A** & \(\mathbf{M_{y}}\) & \(\mathbf{\theta_{y}}\) & \(M_{e}\)/\(M_{y}\) & \(\mathbf{\theta_{p}}\) & \(\Lambda\) \\ \hline C9-25 & 0.902 & 0.957 & 0.965 & 0.920 & 0.781 & 64.426 & 0.009 & 1.210 & 0.046 & 2.97 \\ C5 & 0.971 & 0.899 & 0.984 & 1.069 & 0.854 & 76.927 & 0.008 & 1.076 & 0.014 & 1.71 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Predicted model parameters of the components for the extra-database application. Figure 6: Predicted and test results of the components for the extra-database application. (3) This study allowed the ModIMK hysteretic model to be applied to the seismic performance study of structures containing corroded circular RC columns, which could not be performed before. Due to the strength and stiffness deterioration-capturing capability of the ModIMK model, it was able to improve the reliability of the seismic analysis results as compared to other models, thus providing great help in seismic performance studies, seismic fragility studies, and seismic risk assessment of this type of structure. The test data collected in this paper were limited, and the obtained prediction equations still have considerable room for improvement. As the research on corroded circular columns progresses and the relevant test data increase, the model can be revised continuously. Conceptualization, [PERSON] ([PERSON]) and [PERSON] ([PERSON]); methodology, H.L. ; software, H.L. ; validation, H.L., [PERSON] ([PERSON]) and [PERSON] ([PERSON]); formal analysis, H.L. ; investigation, H.L. ; resources, [PERSON] ([PERSON]); data curation, H.L. ; writing--original draft preparation, H.L. ; writing--review and editing, H.L. ; visualization, H.L. ; supervision, [PERSON] ([PERSON]); project administration, [PERSON] ([PERSON]); funding acquisition, [PERSON] ([PERSON]). All authors have read and agreed to the published version of the manuscript. This research was supported by \"National Natural Science Foundation of China (U2239252)\" and \"The National Key Technology R&D Program (2012 BAK15B05-04)\". The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.