## 3 Results
### Methodology for Estimating Alkali Ions in the Concrete Pore Solution
Table 5 gives the fractional distribution of the total non-sulfate Na\({}_{2}\)O and K\({}_{2}\)O that are assumed to occur in the main clinker phases, which have been considered in this work. The contents of Na\({}_{2}\)O and K\({}_{2}\)O in each of the major phases were then calculated (Table 6) by using the fractional distribution that was proposed by [PERSON], and given in Table 5.  
Table 6 shows the total non-reactive alkalis that are calculated by subtracting the measured total alkalis content from the measured water-soluble alkalis, as well as the assumed distribution to occur in the main clinker phases. [PERSON] and [PERSON] [19] proposed an empirical formula (Equation (5)) to express the rates of reaction of alite, belite, aluminate, and ferrite. In this function, F is the fraction of the major clinker phases reacted at time T, in days, and k\({}_{1}\), k\({}_{2}\), and k\({}_{3}\) are constants, as shown in Table 7.  
\[\text{F}=1-\exp\left[-\text{k}_{2}(\text{T}-\text{k}_{3})^{k1}\right] \tag{5}\] \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Na\({}_{2}\)O and K\({}_{2}\)O Fractions in Each Phase**} & **0.44** & **0.29** & **0.17** & **0.41** & **0.36** & **0.27** & **0.03** & **0.03** \\ \hline \multirow{3}{*}{**CEMENT**} & **Calculated Non-Soluble** & \multirow{3}{*}{**C\({}_{3}\)S (\%)**} & \multirow{3}{*}{**C\({}_{2}\)S (\%)**} & \multirow{3}{*}{**C\({}_{3}\)A (\%)**} & \multirow{3}{*}{**C\({}_{4}\)AF (\%)**} \\  & **Alkalis (\%)** & & & & & & & \\ \cline{2-2} \cline{6-10}  & **Na\({}_{2}\)O** & **K\({}_{2}\)O** & & & & & & \\ \hline CEM 1 52.5 R & 0.10 & 0.02 & 0.04 & 0.01 & 0.02 & 0.01 & 0.03 & 0.01 & 0.00 & 0.00 \\ CEM 1 52.5 R (white) & 0.03 & 0.03 & 0.01 & 0.01 & 0.01 & 0.01 & 0.01 & 0.01 & 0.00 & 0.00 \\ CEM 14 2.5 R-SR 3 & 0.23 & 0.04 & 0.10 & 0.01 & 0.04 & 0.02 & 0.08 & 0.01 & 0.01 & 0.00 \\ CEM 1 52.5 R-SR 5 & 0.19 & 0.01 & 0.08 & 0.00 & 0.03 & 0.00 & 0.07 & 0.00 & 0.01 & 0.00 \\ CEM 14 2.5 R & 0.13 & 0.01 & 0.06 & 0.00 & 0.02 & 0.00 & 0.05 & 0.00 & 0.00 & 0.00 \\ CEM 1 52.5 R (low-alkali) & 0.08 & 0.01 & 0.04 & 0.00 & 0.01 & 0.00 & 0.03 & 0.00 & 0.00 & 0.00 \\ \hline Average (\%) & 0.13 & 0.02 & 0.06 & 0.01 & 0.02 & 0.01 & 0.05 & 0.01 & 0.00 & 0.00 \\ Maximum (\%) & 0.23 & 0.04 & 0.10 & 0.01 & 0.04 & 0.02 & 0.08 & 0.01 & 0.01 & 0.00 \\ Minimum (\%) & 0.03 & 0.01 & 0.01 & 0.00 & 0.01 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 \\ \hline [PERSON]’s proposal (\%) & & & & 0.17 & 0.14 & 0.27 & 0.79 & 1.05 & 0.97 & 0.06 & 0.07 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Total non-soluble alkalis and fractions of Na\({}_{2}\)O and K\({}_{2}\)O bounded in the main clinker phases. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Non-Sulfate Alkalis Fraction** & **Alite** & **Belite** & **Aluminate** & **Ferrite** \\ \hline Non-sulfate Na\({}_{2}\)O fraction & 0.44 & 0.17 & 0.36 & 0.03 \\ Non-sulfate K\({}_{2}\)O fraction & 0.29 & 0.41 & 0.27 & 0.03 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Fractional distribution of the total non-sulfate Na\({}_{2}\)O and K\({}_{2}\)O that are assumed to occur in the main clinker phases [8]. Equation (5) was then used in the present work to obtain the fractions that were reacted for each clinker phase, C\({}_{3}\)S, C\({}_{2}\)S, C\({}_{3}\)A, and C\({}_{4}\)AF, bound water, and Ca in C-S-H and AF\({}_{\rm m}\) phases, at time T (in days) replacing the set of constants that are given in Table 7. Figure 1 illustrates the fractions reacted for the C\({}_{3}\)S, C\({}_{2}\)S, C\({}_{3}\)A, and C\({}_{4}\)AF clinker phases, bound water, and Ca uptake in the C-S-H and AF\({}_{\rm m}\) phases over time, as calculated with Equation (5). Then, the fractions reacted for each clinker phase at 28 days was multiplied by the weight of Na\({}_{2}\)O or K\({}_{2}\)O in the phase, to obtain the weight of Na\({}_{2}\)O or K\({}_{2}\)O that was released, respectively. Table 8 presents the results obtained.