## 3 Results and Discussions
### Elastic Modulus
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Mix ID**} & \multicolumn{2}{c}{**Compressive**} & \multicolumn{5}{c}{**Elastic Modulus, \(E_{c}\) (GPa)**} \\ \cline{2-10}  & \multicolumn{2}{c}{**Strength,\(f_{cm}\) (MPa)**} & \multirow{2}{*}{**Test**} & \multirow{2}{*}{**[PERSON] \& [PERSON]**} & \multirow{2}{*}{**[PERSON]**} & **[PERSON] \&** & **Test/[PERSON] \&** & **Test/[PERSON]** & **Test/[PERSON] \& [PERSON]** \\ \hline A1-S10 & 20.0 & 15.4 & 14.2 & 18.8 & 15.7 & 1.08 & 0.82 & 0.98 \\ A2-S20 & 40.0 & 21.8 & 17.9 & 26.7 & 22.2 & 1.22 & 0.82 & 0.98 \\ A3-S30 & 54.0 & 26.6 & 19.8 & 31.2 & 25.8 & 1.35 & 0.85 & 1.03 \\ A4-S50 & 65.0 & 30.3 & 21.0 & 34.8 & 28.3 & 1.44 & 0.87 & 1.07 \\ B1-S20 & 48.0 & 24.1 & 19.0 & 29.4 & 24.3 & 1.27 & 0.82 & 0.99 \\ B2-S30 & 63.0 & 30.1 & 20.8 & 33.8 & 27.9 & 1.45 & 0.89 & 1.08 \\ B3-S20 & 53.0 & 27.8 & 19.6 & 30.9 & 25.6 & 1.42 & 0.90 & 1.09 \\ B4-S30 & 69.0 & 31.2 & 21.4 & 35.5 & 29.2 & 1.46 & 0.88 & 1.07 \\ C1-S10 & 26.0 & 19.0 & 15.5 & 21.3 & 17.9 & 1.22 & 0.89 & 1.06 \\ C2-S20 & 46.0 & 24.8 & 18.7 & 28.4 & 23.8 & 1.32 & 0.87 & 1.04 \\ C3-S30 & 59.0 & 29.0 & 20.4 & 32.2 & 27.0 & 1.42 & 0.90 & 1.08 \\ C4-S50 & 69.0 & 30.9 & 21.4 & 35.1 & 29.2 & 1.44 & 0.88 & 1.06 \\ D1-S20 & 46.0 & 22.1 & 18.7 & 28.8 & 23.8 & 1.18 & 0.77 & 0.93 \\ D2-S30 & 63.0 & 27.2 & 20.8 & 33.8 & 27.9 & 1.31 & 0.80 & 0.98 \\ D3-S20 & 37.0 & 20.6 & 17.4 & 26.0 & 21.4 & 1.18 & 0.79 & 0.96 \\ D4-S30 & 49.0 & 24.2 & 19.1 & 30.2 & 24.6 & 1.26 & 0.80 & 0.98 \\ E1-S10 & 17.0 & 14.5 & 13.5 & 17.0 & 14.5 & 1.07 & 0.85 & 1.00 \\ E2-S20 & 36.0 & 20.4 & 17.3 & 24.9 & 21.1 & 1.18 & 0.82 & 0.97 \\ E3-S30 & 51.0 & 24.6 & 19.4 & 29.7 & 25.1 & 1.27 & 0.83 & 0.98 \\ E4-S50 & 63.0 & 29.8 & 20.8 & 33.2 & 27.9 & 1.43 & 0.90 & 1.07 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: The predicted and test values of elastic modulus. The elastic modulus of FS-GPC mixes was predicted by the empirical relationships suggested by different studies. According to ACI 318-14, the static modulus of normal density (1500-2500 kg/m\({}^{3}\)) OPC concrete can be estimated by the following equation (Equation (12)):  
\[E_{c}\ =0.043\times\rho^{1.5}\times\sqrt{f_{c}^{\prime}} \tag{12}\]  
Another relationship (Equation (13)) suggested by CEB-FIP Model Code 90 (1993) for static modulus of normal density concrete is given by:  
\[Ec=0.85\times 2.15\times 10^{4}\times\left(\frac{f_{c}^{\prime}}{10}\right)^{0.33} \tag{13}\]  
Figure 17: The compressive strength variations of groups A and C mixes with alkaline activator content. Figure 18: The influence of mix design variables on elastic modulus of FS-GPC mix specimens at the age of 28 days. where \(E_{c}=\) elastic modulus of concrete (MPa), \(\rho=\) density of concrete \(\left(\text{kg/m}^{3}\right)\), and \(f_{c}^{\prime}=\) characteristic compressive strength (MPa). [PERSON] et al. (2011) proposed Equation (14) based on their test results to calculate the elastic modulus of FA based geopolymer concrete mixes cured at elevated temperature [47]. \[E_{c}=2707\times\sqrt{f_{c}}+5300 \tag{14}\]  
where, \(E_{c}\) is the elastic modulus of concrete (MPa) and \(f_{c}\) is the compressive strength of concrete at the age of 3 days. The heat cured geopolymer concrete achieved compressive strength close to the ultimate strength during the initial curing period. However, the ambient cured geopolymer concrete develops strength gradually over time. Therefore, the strength after 28 days of curing has been used to calculate the elastic modulus in the present study. [PERSON] and [PERSON] (2013) analyzed the data obtained from their experimental study on ambient cured FS-GPC specimens and proposed the Equation (15) to estimate the elastic modulus [30]. \[Ec=5300\times\left(f_{c}\right)^{\frac{3}{3}} \tag{15}\]  
[PERSON] and [PERSON] (2017) also suggested a relationship (Equation (16)) based on their experimental results to predict the elastic modulus of ambient cured blended low calcium FA based GPC mixes [48].