## Materials and Methods
### Dynamic Elastic Modulus Measurements with Resonance Frequency Tests  
As shown in Figure 2, the three to four longitudinal and transverse resonance frequencies of the concrete cylinders were measured based on ASTM C215-14 [6]. A steel ball hammer with a diameter \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{3}{*}{**ID**} & \multirow{3}{*}{\
\begin{tabular}{c} **Cement** \\ **Type** \\ \end{tabular} } & \multirow{3}{*}{**W/B**} & \multirow{3}{*}{**S/A**} & \multirow{3}{*}{**W**} & \multirow{3}{*}{**C**} & \multirow{3}{*}{**S**} & \multirow{3}{*}{**G**} & \multicolumn{3}{c}{
\begin{tabular}{c} **Unit Quantity (kg/m\({}^{3}\))** \\ **Mineral Admixture** \\ \end{tabular} } & \multicolumn{3}{c}{**Chemical Admixture**} \\ \cline{5-12}  & & & & & & & & & **FA** & **GBFS** & **AE** & **SP** \\  & & & & & & & & **(Binder\%)** & **(Binder\%)** \\ \hline Mix1 (20 MPa) & \multirow{2}{*}{Type I} & 0.45 & 0.46 & 259 & 121 & 777 & 934 & 58 & 69 & 0.9 & - \\ \hline Mix2 (40 MPa) & 0.35 & 0.47 & 308 & 166 & 761 & 886 & 81 & 85 & - & 1 \\ \hline \hline \end{tabular}  
* \({}^{1}\)SCMs: Supplementary cementitious materials, W: water, C: cement, S: sand, G: crushed cobblestone, FA: fly ash, SC: slag cement, AE: air-entraining agent, SP: superplasticizer, GBPS: granulated blast furnace slag.  
\end{table} 
Table 1: Proportions of the concrete mixture groups \({}^{1}\). Figure 1: Experimental setup for static destructive test. of 10 mm was used to generate stress waves in the concrete cylinder. This hammer was suitable for generating very low to 20 kHz frequency signals. An accelerometer (PCB 353B16, PCB, Depew, NY, USA) with a resonance frequency of approximately 70 kHz was used to measure the dynamic response of the concrete cylinders. The time signals measured with the accelerometer were stabilized by a signal conditioner (PCB 482C16, PCB, Depew, NY, USA) and were digitized with 1 MHz sampling through an oscilloscope (NI-PXIe 6366). The time signals were transformed into the frequency domain by a fast Fourier transform algorithm. Figure 3 shows typical spectral amplitudes of the concrete cylinders at 4, 7, 14, and 28 days in the Mix 2 cylinder. The resonance frequency appears as a large amplitude in the amplitude spectrum. The most dominant frequency was considered as the basic resonance frequency of the longitudinal \(f_{LT}\) and transverse \(f_{TR}\) modes, with four resonance frequencies in the LT mode and three resonance frequencies in the TR mode. The first of these frequency values was used to calculate the Ed of the LT and TR modes, using Equations (1) and (2) from ASTM C215-14. \[ASTM.LT =\alpha_{LT}mf_{LT}^{2}(Pa) \tag{1}\] \[ASTM.TR =\alpha_{TR}mf_{TR}^{2}(Pa) \tag{2}\]  
In the above, _ASTM.LT_ and _ASTM.TR_ are the \(Ed\) values calculated with \(f_{LT}\) and \(f_{TR}\), respectively, as the first resonance frequencies. \(\alpha_{LT}\) has a constant value with regard to the dimensions of the specimen (=\(5.093\times(L/d^{2})\)), where d is the diameter and L is the length. \(\alpha_{TR}\) has a constant value with  
Figure 3: Resonance frequency by curing ages according to ASTM resonance test. (**a**) frequencies of longitudinal mode, (**b**) frequencies of transverse mode. Figure 2: Resonance frequency test setup. (**a**) longitudinal mode and (**b**) transverse mode. regard to [PERSON]'s ratio and the size of the cylinders (=1.6067 \(\times\) (\(L^{3}T/d^{4}\))). \(T\) is a correction factor corresponding to the Poisson's ratio, and m is the mass of the cylinders in kg [6]. In addition, as in the method of predicting the dynamic elastic modulus (\(Ed\)) with two frequencies as proposed by [PERSON] et al., the dynamic Poisson's ratio was obtained through Equation (3), and the Ed was predicted through Equation (4).