## 4 \({}^{29}\)Si MAS NMR Analysis
### Calculation of Conversion Fraction based on \({}^{29}\)Si MAS NMR Results  
The conversion fraction of pozzolanic material used in this study was calculated based on the \({}^{29}\)Si MAS NMR results shown in Section 4.1. The total number of silicate tetrahedra, \(\Sigma\)Q, in the concrete powder sample for NMR can be obtained from  
\[\sum_{\text{Q}}=\bigg{[}w_{Cemem}\bigg{(}\frac{p_{\text{C3S}}}{\psi_{\text{C3S }}}+\frac{p_{\text{C2S}}}{\psi_{\text{C2S}}}\bigg{)}+w_{Puzzolan}\frac{p_{s}}{ \psi_{s}}+f_{s}w_{Sand}\frac{p_{s}}{\psi_{s}}\bigg{]}N_{A} \tag{2}\]  
where \(N_{A}\) is Avogadro's constant and \(\psi_{\text{C3S}}\), \(\psi_{\text{C2S}}\), and \(\psi_{S}\) are the molecular weights of C\({}_{3}\)S, C\({}_{2}\)S, and S, respectively. These values are assumed as \(\psi_{\text{C3S}}\) = 0.228 kg/mol, \(\psi_{\text{C2S}}\) = 0.172 kg/mol, and \(\psi_{S}\) = 0.06 kg/mol [11]. \(p\) and \(w\) are the weight fraction and the weight of subscribed components in the OPC, pozzolans, and sand, respectively. \(f_{s}\) is the fraction of sand included in the NMR experiments. It should be noted that the amount of sand included in the concrete sample is not equal to that of the concrete mixture. In Equation (2), the third term represents the Q\({}^{3}\) and Q\({}^{4}\) of the natural sand in the concrete sample for the NMR analysis. Thus, the total number of silicate tetrahedra in the sand, \(\Sigma\)Q\({}_{3A,Sand}\), can be obtained from  
\[\sum_{\text{Q3, 4, {Sand}}}=\bigg{[}f_{s}w_{Sand}\frac{p_{s}}{\psi_{s}}\bigg{]}N _{A}. \tag{3}\]  
Similarly, the total number of silicate tetrahedrons in the pozzolans, \(\Sigma\)Q\({}_{4,Puzzolans}\), can be calculated as  
\[\sum_{\text{Q4, {Puzzolans}}}=\bigg{[}w_{Puzzolans}\frac{p_{s}}{\psi_{S}} \bigg{]}N_{A}. \tag{4}\]  
To calculate the conversion fraction of the pozzolans, the Q\({}^{3}\) and Q\({}^{4}\) of the natural sand must first be evaluated. Then, the effect of the sand included in the NMR test can be eliminated. In this study, 80% of the SiO\({}_{2}\) in the natural sand was considered and the fraction of sand included in NMR experiments, \(f_{s}\), was calculated as followings:  
\[\sum_{\text{Q}}=470\bigg{(}\frac{0.54}{0.228}+\frac{0.21}{0.172}\bigg{)}+452 \frac{0.8}{0.06}f_{s}=1687+6027f_{s}\text{ from Equation }(2) \tag{5a}\] \[\sum_{\text{Q3, 4, {Sand}}}=452\frac{0.8}{0.06}f_{s}=6027f_{s}\text{ from Equation }(3)\] (5b) \[\text{Q}^{3}+\text{Q}^{4}=55.7\%\text{ from NMR results for OPC}\] (5c) \[\frac{6027f_{s}}{1687+6027f_{s}}=0.557,\ f_{s}=35.2\% \tag{5d}\]  
As presented in Equation (5), the total number of silicate tetrahedrons, \(\Sigma\)Q, in the concrete powder sample can be obtained by applying Equation (2) with the chemical composition of the cement (Table 1) and mixture design properties (Table 3) that were used in this study. Then, the fraction of sand included \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Label** & **Q\({}^{0}\)** & **Q\({}^{1}\)** & **Q\({}^{2}\)** & **Q\({}^{3}\)** & **Q\({}^{4}\)** \\ \hline OPC & 0.182 & 0.104 & 0.157 & 0.437 & 0.120 \\ OPC C & 0.173 & 0.076 & 0.147 & 0.466 & 0.138 \\ FA15 & 0.164 & 0.088 & 0.148 & 0.481 & 0.119 \\ FA15 C & 0.098 & 0.053 & 0.129 & 0.527 & 0.192 \\ SF35 & 0.203 & 0.104 & 0.155 & 0.398 & 0.141 \\ SF35 C & 0.182 & 0.086 & 0.169 & 0.455 & 0.109 \\ NS20 & 0.218 & 0.096 & 0.147 & 0.448 & 0.091 \\ NS20 C & 0.182 & 0.087 & 0.161 & 0.469 & 0.101 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Deconvoluted Intensities of Q\({}^{n}\). in the NMR experiments, \(f_{s}\), can be calculated with Equation (3), using the NMR results shown in Table 4. From these results, \(f_{s}\) was calculated as 35.2%. By assuming the calculated \(f_{s}\) of the OPC was the same as the \(f_{s}\) of the specimens with pozzolanic materials (FA15, SF25, and NS20), the conversion fractions of the pozzolans were calculated for the FA15, SF35, and NS20 specimens. The detailed calculation procedure for the FA15 specimen is shown in Equation (6).