# Shear Strength and Durability of Expansive Soil Treated with Recycled Gypsum and Rice Husk Ash
## 3 Results and Discussion
### Expansion Index

Table 17: Expansion index and collapse index of cycle two samples with varying curing days. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Curing Period (Days)** & **Expansion Index** & **Collapse Index** & **Classification** \\ \hline
7 & 0 & 0.06\% & No Collapsibility \\
14 & 0 & 0.43\% & No Collapsibility \\
21 & 0 & 1.04\% & Low Collapsibility \\
28 & 0 & 0.18\% & No Collapsibility \\
35 & 0 & 4.14\% & Collapsibility \\ \hline \hline \end{tabular}
\end{table} 
Table 18: Expansion index and collapse of index of cycle three samples with varying curing days. With small \(p\)-values of only 0.00014 for \(\mathrm{x_{1}}\) and \(\mathrm{x_{1}}^{2}\), the number of curing days is considered statistically significant in the resulting unconfined compression strength values. However, higher \(p\)-values were obtained for the number of cycles (\(\mathrm{x_{2}}\)) and the combined effect of the curing period and cycles (\(\mathrm{x_{1}}\)\(\times\)\(\mathrm{z}\)), indicating that its effect on the UCS is statistically insignificant. The equation of the surface regression suggests a quadratic fit for the response of the unconfined compression strength to the combined effects of curing days and the number of cycles. The relationship between the three variables is given in Equation (13), with an adjusted R\({}^{2}\) of 0.6039, which signifies a medium correlation. \[y=32.2259-1.4818x_{1}+0.0254{x_{1}}^{2}+3.2080x_{2}-0.4565{x_{2}}^{2}-0.0280x_{ 1}x_{2} \tag{13}\]  
Figure 9 illustrates the fitted surface regression of the unconfined compression strength values across varying curing days and number of cycles. The \(x\)-axis represents the curing days, the \(y\)-axis represents the number of cycles, and the \(z\)-axis represents the strength values. The variation of the surface along the \(x\)-axis resembled the shape of a parabola, with the peak situated in the early stages of the curing period, as shown by the dark red surface. The critical point is located along the 30-day curing period, represented by the dark green surface. Variations along the \(y\)-axis are minimal, as suggested by the similarity in the color of the contour across different numbers of cycles. Despite the medium correlation exhibited by the prediction model, the surface regression curve equation is still viable in determining the UCS of the soil using both the number of cycles and curing days in the absence of any available data. Since soil is subjected to infinite wet-dry cycles, it is also helpful to determine a critical number of cycles that will result in total strength loss. Considering the variation along the number of cycles, a quadratic curve is generated to visualize the anticipated loss of strength, as shown in Figure 10. The curve trend suggests a total loss of strength after eight cycles as UCS reached \begin{table}
\begin{tabular}{c c c} \hline \hline
**Variables** & **Coefficients** & \(p\)**-Value** \\ \hline \(c\) & 32.33586 & 7.45 \(\times\) 10\({}^{-6}\) \\ \(x_{1}\) & \(-1.48181\) & 0.00136 \\ \({x_{1}}^{2}\) & 0.025434 & 0.001397 \\ \(x_{2}\) & 3.208004 & 0.558037 \\ \({x_{2}}^{2}\) & \(-0.45647\) & 0.724482 \\ \(x_{1}\)\(\times\)\(\mathrm{z}\) & \(-0.02801\) & 0.71079 \\ \hline \hline \end{tabular} where: \(c\) = intercept, \(x_{1}\) = curing days, and \(x_{2}\) = cycles.  
\end{table} 
Table 20: Surface regression parameters for the treated samples. Figure 9: Fitted regression surface curve of UCS versus the number of cycles and curing days. a value of only 0.39 kPa. It must be noted that the developed response surface model is only applicable to the treated expansive soil in this study and will need further verification for other types of soil or additives.