## 2 Predictive Equations and Machine Learning Models
### Training of the Machine Learning Models  
The datasets used to train the machine learning (ML) models include both synthetic and real data points. Due to the differences in the availability of data points for strain and stress prediction, different datasets were used as the base dataset for the generation of synthetic data points. The base dataset for the confined compressive strength model consists of 225 data points whereas the base dataset for the ultimate strain prediction consists of 159 data points. The datasets contain information about the unconfined concrete strength (\(f_{\rm co}\)), diameter of the circular column being tested (d), height of the column (L), ultimate tensile strength of the AFRP material (\(f_{\rm f}\)), elastic modulus of the AFRP (\(E_{\rm f}\)), and the thickness of the AFRP jacket (\(t_{\rm f}\)) as input variables. The confined compressive strength (\(f_{\rm cc}\)) and the ultimate strain of confined concrete (\(\epsilon_{\rm cu}\)) are the output variables predicted by the ML models. Figure 1 shows the Pearson correlation between all the input features and the compressive strength of the confined concrete (\(f_{\rm cc}\)). The Pearson correlation values between the variables are shown inside the boxes in the upper right triangle of the correlation diagram. Equation (1) illustrates the calculation of the Pearson correlation values (\(r_{\rm xy}\)), where x and y denote two variables. An \(r_{\rm xy}\) value close to \(1\) denotes strong linear proportionality between two variables, whereas an \(r_{\rm xy}\) value close to \(-1\) denotes strong inverse proportionality between two variables. In the upper right triangular part of the diagram, the number of stars denotes the strength of correlation between two variables. The frequency distribution histogram of each variable is shown in the diagonal of the diagram. The lower left triangular part of the correlation diagram displays the bivariate scatter plots of the variables with regression lines. According to Figure 1, the strongest correlation in the dataset between any two variables can be observed between the confined compressive strength of concrete (\(f_{\rm cc}\)) and the unconfined compressive strength of concrete (\(f_{\rm co}\)), with an \(r_{\rm xy}\) value of 0.24. The second strongest correlation is between the AFRP elastic modulus (\(E_{\rm f}\)) and the ultimate tensile \begin{table}
\begin{tabular}{c c} \hline
**Model** & **Reference** \\ \hline \(f_{\rm cc}=f_{\rm co}+6.4\frac{f_{\rm cc}}{D}\) & [PERSON] et al. [21] \\ \(f_{\rm cc}=f_{\rm co}\left(\frac{\left(1+5.54\frac{g_{\rm cc}}{D_{\rm cc}} \right)}{\sqrt{1+\frac{16D}{30}\left(1-1.45\frac{g_{\rm cc}}{D_{\rm cc}} \right)}}\right)\) & [PERSON] and [PERSON] [22] \\ \(f_{\rm cc}=f_{\rm co}\left(1+1.2\left(\frac{2\frac{2\rm f_{\rm cc}}{D_{\rm cc }}\right)}{\frac{125}{D_{\rm cc}}\left(\frac{2\rm f_{\rm cc}}{D_{\rm cc}} \right)}^{0.37}\right)\) & [PERSON] and [PERSON] [23] \\ \(f_{\rm cc}=f_{\rm co}+6.2\frac{f_{\rm cc}}{D}\) & [PERSON] et al. [24] \\ \hline \end{tabular}
\end{table} 
Table 1: Equations for the predictions of the compressive strength \(f_{\rm cc}\). \begin{table}
\begin{tabular}{c c} \hline
**Model** & **Reference** \\ \hline \(\epsilon_{\rm cu}=\epsilon_{\rm co}\left(1+19\frac{f_{\rm cc}}{D_{\rm cc}} \right)\) & [PERSON] et al. [21] \\ \(\epsilon_{\rm cu}=\epsilon_{\rm co}+0.152\frac{f_{\rm cc}}{D_{\rm cc}}\) & [PERSON] et al. [24] \\ \hline \end{tabular}
\end{table} 
Table 2: Equations for the predictions of the ultimate strain \(\epsilon_{\rm cu}\). strength of AFRP (\(\rm f_{f}\)). On the other hand, there is a relatively strong inverse proportionality between the AFRP elastic modulus (\(\rm E_{f}\)) and the total thickness of the AFRP jacket (\(\rm t_{f}\)).