## 3 Results and Discussion
### Atterberg Limits  
The variations of PI with fly ash content are presented in Figure 10. As seen in this figure, the LL of the original soil was the highest (45%) followed by the mixture with 40% fly ash (36%), the mixture with 50% fly ash (35%), and the mixture with 60% fly ash (24%). The PL also followed a similar pattern, except for the mixture with 50% fly ash. The explanation for the decrease in the PL could be attributable to the fact that the multivalent cations (Ca\({}^{2+}\), Fe\({}^{3+}\), and Al\({}^{3+}\)) provided by the fly ash work by displacing monovalent cations (Mg\({}^{2+}\) > Ca\({}^{2+}\) >Na\({}^{+}\) > K\({}^{+}\)), so the abundance of multivalent cations changes the soil particles' electrical charge that makes the soil particles attracted to each other. The electrical attraction of soil particles aids the flocculation and is attributed to the change in soil nature (granular nature after flocculation and agglomeration) and results in reducing soil plasticity. As seen in Figure 10, both the mixture with 40% fly ash content and the original soil showed the highest PI (12%), followed by the mixture with 50% fly ash (10%) and the mixture with 60% fly ash (5%). [PERSON] [18] pointed out that the swell potential of soil is related to soil activity. The higher the soil activity value, the greater the soil swell potential. Similarly, the soil activity is also related to the PI value. The higher the PI value, the greater the soil swell potential. As stated above, when part of the clay in untreated soil was replaced by fly ash, the PI value of treated soil decreased. This decrease leads to a reduction in volumetric swelling in treated soil, which coincided with [PERSON]'s finding. Furthermore, [PERSON] et al. [19] and [PERSON] [20] proposed and used a relationship between percent swelling (S) and PI value, \(S~{}=~{}2.16\times 10^{-3}(PI)^{2.44}\). Thus, volumetric swelling of the fly ash-treated soil would decrease as the PI values decrease. The PI values of fly ash-treated soil in this study were smaller than that of untreated soil (Figure 10) and PI values decreased with increased fly ash content, except for 40% fly ash content, which lead to a more pronounced reduction in volumetric swelling. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Curing Period**} & \multicolumn{2}{c}{**Fitted**} & \multirow{2}{*}{**drying/dx = 0**} & \multirow{2}{*}{**d\({}^{2}\)y/dx\({}^{2}\)**} & \multirow{2}{*}{**R\({}^{2}\)**} & \multirow{2}{*}{**RMSE**} & \multirow{2}{*}{**MAE**} & \multicolumn{2}{c}{**x = Optimum**} & \multicolumn{1}{c}{**y = Max**} \\  & **Polynomial Equation** & & & & & & **Fly Ash** & **UCS** \\  & **(y = f(x))** & & & & & & **Content (\%)** & **(kPa)** \\ \hline \multirow{2}{*}{0 day} & As shown in & \multirow{2}{*}{\begin{tabular}{} \end{tabular} } & \(-0.3878\)\(+\) & \multirow{2}{*}{\(-0.3878\)} & \multirow{2}{*}{0.9995} & \multirow{2}{*}{209.80} & \multirow{2}{*}{195.96} & \multirow{2}{*}{35} & \multirow{2}{*}{331} \\  & Figure 9 & 13.496 & & & & & & & \\ \hline \multirow{2}{*}{2 days} & As shown in & \multirow{2}{*}{\begin{tabular}{} \end{tabular} } & \(-1.3532\)\(+\) & \multirow{2}{*}{\(-1.3532\)} & \multirow{2}{*}{0.4500} & \multirow{2}{*}{1262.18} & \multirow{2}{*}{1206.72} & \multirow{2}{*}{33} & \multirow{2}{*}{1639} \\  & Figure 9 & 41.467 & \(=\) & & & & & & \\ \hline \multirow{2}{*}{8 days} & As shown in & \multirow{2}{*}{\
\begin{tabular}{} \end{tabular} } & \(-2.0978\)\(+\) & \multirow{2}{*}{\(-2.097\)} & \multirow{2}{*}{0.7682} & \multirow{2}{*}{1308.69} & \multirow{2}{*}{1246.79} & \multirow{2}{*}{32} & \multirow{2}{*}{2036} \\  & Figure 9 & 66.802 & \(=\) & & & & & & \\ \hline \multirow{2}{*}{28 days} & As shown in & \multirow{2}{*}{
\begin{tabular}{} \end{tabular} } & \(-1.4068\)\(+\) & \multirow{2}{*}{\(-1.4068\)} & \multirow{2}{*}{\(0.6415\)} & \multirow{2}{*}{1201.19} & \multirow{2}{*}{1150.92} & \multirow{2}{*}{46} & \multirow{2}{*}{1623} \\  & Figure 9 & 47.954 & \(=\) & & & & & \\ \hline \hline \end{tabular}
\end{table}