## 4 Results and Discussion
### Relationship between Initial Chord and Compressive Strength  
In the concrete cylinder in this study, materials similar to crushed cobblestone and granulated blast furnace slag (GBFS) were used, and Equation (17) (proposed by [PERSON]) was used for comparison with the theoretical strength curve; _k1_ is the aggregate, and _k2_ is the correction coefficient of the SCMs [35]. According to Table 13, 0.95 for both _k1_ and _k2_ was used. Such concrete has the advantage of slow strength development at an early age but demonstrates significant progress for long-term strength.  
\[E_{c}=k_{1}k_{2}33500(f_{c}/60)^{1/3}(\omega_{c}/2400)^{2}(\text{MPa}) \tag{17}\]  
Figure 16 shows the relationship between the static elastic modulus (_Ec_) (_Ec_ predicted from _Ei_, actual _Ec_) and compressive strength (_fc_). The theoretical strength curve of the Noguchi equation and trend of the measured _Ec_ and _fc_ data are suitable, and close to the line. Therefore, the _Ec_ and _fc_ are well-measured, and the values of _Ec_ and _fc_ are within a reasonable range. The results were the same for the _Ec_ values predicted using the initial chord elastic modulus (_Ei_). Thus, it was confirmed that there is a high correlation (with intensity) when predicting the correct _Ec_ using the _Ei_.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Lithological Type of Coarse Aggregate** & **k1** & **Type of Addition** & **k2** \\ \hline Crushed limestone, calcined bauxite & 1.20 &
\begin{tabular}{c} Silica fume, ground-granulated \\ blast-furnace slag, fly ash fume \\ \end{tabular} & 0.95 \\ \hline Crushed quartzitic aggregate, crushed anddesite, crushed basalt, crushed clay slate, crushed cobblestone & 0.95 & Fly ash & 1.10 \\ \hline Coarse aggregate, other than above & 1.00 & Addition other than above & 1.00 \\ \hline \hline \end{tabular}
\end{table}
Table 13: Practical values of correction factor _k1_ and _k2_.  
Figure 16: Relationship between _Ec_ (measured _Ec_ and predicted _Ec_) and _fc_.  
In this study, to confirm the accurate prediction and applicability of actual initial chord elastic modulus (_Ei_) values, the _Ei_ was compared with the dynamic elastic modulus (_Ed_) of three theoretical equations, using a resonance frequency test. In addition, the relationship among the predicted _Ei_ and static elastic modulus (_Ec_) values and the compressive strength (_fc_) was analyzed. It was found that the _Ei_ is more correlated with the _Ec_ than the _Ed_, confirming the need for accurate _Ei_ prediction. In addition, it was confirmed that the correlation between the frequencies collected by the resonance frequency test according to the ASTM method (but not the fracture test) and the _Ei_ and _Ec_ was high, and that the _Ei_ and _Ec_ could be predicted using the resonance frequency. As a result of predicting the Ei using ML (ensemble, ANN), multiple linear regression (MLR), and correction factor methods from the collected frequency, it was possible to overcome the nonlinear behavior of concrete in the range of the initial _Ec_. Thus, the prediction error was smaller than when using the MLR or correction factor methods. The predicted _Ei_ showed a higher correlation with the _Ec_ and fc than the _Ed_ and was able to identify the applicability of the _Ei_.