## 3 Results
### Methodology for Estimating Alkali Ions in the Concrete Pore Solution
#### 3.1.3 Na+ and K+ Concentrations in the Pore Solution  
An alkali partition procedure was proposed, according to which part of the alkali ions are bound in the hydration products, also called C-S-H gel and AF\({}_{\text{m}}\) phases and the others remain in the pore solution. From the mass balance, the quantity of the alkali cations released from the cement, m\({}_{\text{released}}\), is equal to that which is contained in the pore solution, more solution, plus that which is taken up by the hydration products, m\({}_{\text{taken up}}\) (Equation (7)):  
\[\text{m}_{\text{released}}=\text{m}_{\text{pore solution}}+\text{m}_{\text{ taken up}} \tag{7}\]  
The amount in solution is equal to the alkali concentration, [Na+] or [K+], which is assumed to be uniform, is multiplied by the volume of solution, V. The amount of Na+ or K+ that is taken up by the cement hydration products is assumed to be proportional to the amount of such hydration products, and also proportional to the Na+ or K+ concentration in solution. Therefore, their concentrations in the pore solution and in the hydration products were calculated by using Equations (8) and (9), respectively:  
\[\text{m}_{\text{pore solution}}=\text{[Na+ or K+]}\times\text{V} \tag{8}\]  
\[\text{m}_{\text{taken up}}=\text{b}\times\text{P}\times\text{[Na+ or K+]} \tag{9}\]  
where P is the amount of the hydration product that is able to take up alkali ions, divided by the same amount at complete hydration. Therefore, P is dimensionless. The constant b is named as the \"binding factor\" by [PERSON] [8]. Combining Equations (7)-(9), we obtain Equation (10) and (11).  
\[\text{m}_{\text{released}}=\text{m}_{\text{pore solution}}+\text{m}_{\text{ taken up}}=\text{[Na+ or K+]}\times\text{V}+\text{b}\times\text{P}\times\text{[Na+ or K+]} \tag{10}\]  
\[\text{[Na+ or K+]}=\frac{\text{m}_{\text{released}}}{\text{[V}+\text{(b}\times \text{P)]}} \tag{11}\]  
The \"binding factor\", b, is equal to 31.0 cm\({}^{3}\) for Na+ and 20.0 cm\({}^{3}\) for K+, and it can be defined as an equivalent volume of pore solution. P is the quantity F that is obtained from Equation (5), equal to 0.721 at after 28 days. The volume of the pore solution, V, was calculated in Section 3.1, and it is equal to 24.93 cm\({}^{3}\).  
Finally, the amount in solution is equal to the alkali concentration, [Na+ or K+] at 28 days, which is shown in Table 10.  
[PERSON] and [PERSON] [23] developed a model to estimate the pore solution alkalinity. They found that a reduction in pore solution alkalinity is the key factor for reducing ASR expansion. Also, they reported on the effect of the Ca/Si ratio, and the amount of C-S-H gel on the alkali uptake. The effect  
\begin{table}
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of the coal fly ash on the Portland cement paste is the formation of a higher amount of C-S-H gel, with a lower Ca/Si ratio. On the contrary, granulated blast-furnace slag leads to a higher amount of C-S-H gel, with a similar Ca/Si ratio than the plain Portland cement. Thus, the higher amount of C-S-H gel is, the higher alkali metal ions uptake. However, they can be released from the C-S-H gel in the long-term [23].