## 2 Experimental Test
### Test Method  
The density and compressive strength of pastes were measured using 50 \(\times\) 50 \(\times\) 50 mm\({}^{3}\) cubes according to ASTM C138 [40] and ASTM C109 [41], respectively. The flexural strength test was conducted on 40 \(\times\) 40 \(\times\) 160 mm\({}^{3}\) beams following ASTM C348 guidelines [42]. To predict the compressive strength over time, the hyperbolic model was used [43; 44; 45; 46; 47]. This model was effective in determining the initial rate (IRCS) and ultimate value (UCS) of the compressive strength. The hyperbolic function, which was solved using MATLAB software R2024, is represented as follows:  
\[C_{s}=\frac{t}{\frac{1}{\lambda}+\frac{t}{B}}\]  
where  
\[C_{s} =\text{ compressive strength value (MPa)}\] \[t =\text{ curing age (days)}\] \[A =\text{ initial rate of compressive strength (IRCS) (MPa/day)}\] \[B =\text{ ultimate compressive strength (UCS) values (MPa)}\]  
For the _TWA_ test, 100 \(\times\) 100 \(\times\) 100 mm\({}^{3}\) cubes were used following ASTM C1585 specifications [48]. The process included several steps. First, the specimens were cast, demolded, and then cured in the water at a controlled temperature of 24 \({}^{\circ}\)C until the testing date. During testing, the specimens were removed from the water and dried in an oven  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline
**Oxide** & **SiO2** & **Al2O3** & **Fe2O3** & **CaO** & **MgO** & **SO3** & **K2O** & **Na2O** & **LOI** & **Other** \\ \hline OWA & 24.73 & 3.41 & 3.83 & 36.13 & 2.81 & 0.03 & 9.56 & 1.42 & 14.7 & 3.38 \\ \hline Cement & 18.53 & 3.93 & 3.06 & 61.78 & 1.74 & 2.92 & 0.47 & 0.18 & 6.3 & 1.09 \\ \hline \end{tabular}
\end{table}
Table 1: Chemical composition of OWA and cement.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Paste Code** & **Cement** & **OWA** & **W/C Ratio** \\ \hline
0\% OWA & 1 & 0 & 0.45 \\ \hline
5\% OWA & 0.95 & 0.05 & 0.45 \\ \hline
10\% OWA & 0.9 & 0.1 & 0.45 \\ \hline
15\% OWA & 0.85 & 0.15 & 0.45 \\ \hline
20\% OWA & 0.8 & 0.2 & 0.45 \\ \hline \end{tabular}
\end{table}
Table 2: Mix proportions of paste.  
at 80 \({}^{\circ}\)C for 48 h until a constant weight was achieved, denoted as the dry weight (A). The specimens were then immersed in water for five minutes, removed, and their weight was recorded as the initial weight (B). This process was repeated at intervals of 10, 20, 60, 120, and 450 min. The percentage of total water absorption was calculated as per the following formula:  
\[TWA=\frac{B-A}{A}\times 100\]  
Regarding the _CWA_ evaluation, 100 \(\times\) 100 \(\times\) 100 mm\({}^{3}\) cubes were tested adhering to ASTM C1585 guidelines [48]. These cubes underwent the same curing process as previously performed and were subsequently dried. Upon removal from the oven, the cubes were sealed on four sides at a distance of 3 to 5 mm from the bottom surface, as depicted in Figure 3. The weight of the specimens was reported as \(W_{1}\), representing the dry weight. After one min of submersion, the cubes were taken out, wiped, and weighed as \(W_{2}\). This procedure was repeated at 3, 5, 10, 30, 60, 120, and 140 min and one, two, and three days. Using the obtained results, the CWA at each reading was determined as follows:  
\[CWA=\frac{W_{2}-W_{1}}{A\cdot d}\]  
where  
\[\begin{array}{llll}W_{2}-W_{1}&=&\text{Cumulative water absorption (kg)}\\ A&=&\text{Surface area of the cube through which water penetrates (m${}^{2}$)}\\ d&=&\text{Density of water (kg/m${}^{3}$)}\end{array}\]