## 3 Results
### Normalization of the Strength and Stiffness of the Materials
The ANOVA results for the XG-PPF mixtures (Tables A5 and A10) indicate that PPF, XG, and compaction density significantly influence the treated soil's strength (q\({}_{\rm u}\)) and stiffness (G\({}_{\rm o}\)) (\(p\) < 0.001). Interactions between factors were not significant, except for a slight trend in Go for the PPF \(\times\)XG interaction (\(p\) = 0.090). This suggests a predominantly additive behavior. The models explain over 68% of the observed variability. Interestingly, in the Go analysis for GG-based blends (Table A8), the interaction between GG and cement was statistically significant (\(p\) < 0.001), suggesting that this residue interacts differently with cement compared to CLW and GY. This could be attributed to GG's granular morphology and pozzolanic potential, which may influence matrix continuity and stiffness development when combined with cement under high compaction conditions. In contrast, CLW- and GY-based blends showed no significant interaction terms with cement, highlighting a more predictable and homogeneous response. In addition, the progression of qu values across increasing compaction densities supports the known influence of dry unit weight on mechanical performance. For example, in cement-CLW blends, UCS values rose from 345-370 kPa at 1.70 g/cm\({}^{3}\) to over 650 kPa at 1.80 g/cm\({}^{3}\) for the same binder dosage. Similarly, XG-PPF blends consistently showed higher strength and stiffness than their XG-only counterparts, suggesting that PPF improves internal friction and fiber-matrix bonding, even though its effect could not be isolated \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Mix**} & \multicolumn{2}{c}{**Normalization Index (\(\
abla\))**} & \multicolumn{2}{c}{**For Normalization**} \\ \cline{2-5}  & \(\boldsymbol{q_{u-n}}\) & \(\boldsymbol{G_{o-n}}\) & \(\boldsymbol{q_{u}(\text{kPa})}\) & \(\boldsymbol{G_{o}(\text{MPa})}\) \\ \hline Soil–cement–15\%CLW & \(n/(B_{iv})^{0.28}=30\) & \(n/(B_{iv})^{0.28}=30\) & 975.04 & 4692.11 \\ Soil–cement–30\%CLW & \(n/(B_{iv})^{0.28}=30\) & \(n/(B_{iv})^{0.28}=30\) & 1122.56 & 5426.83 \\ Soil–cement–10\%GG & \(n/(B_{iv})^{0.28}=30\) & \(n/(B_{iv})^{0.28}=30\) & 1320.01 & 5300.33 \\ Soil–cement–20\%GG & \(n/(B_{iv})^{0.28}=30\) & \(n/(B_{iv})^{0.28}=30\) & 1553.16 & 6515.44 \\ Soil–cement–10\%GY & \(n/(B_{iv})^{0.28}=30\) & \(n/(B_{iv})^{0.28}=30\) & 1516.83 & 4523.20 \\ Soil–cement–20\%GY & \(n/(B_{iv})^{0.28}=30\) & \(n/(B_{iv})^{0.28}=30\) & 1832.77 & 5471.41 \\ Soil–XG & \(n/(C_{iv})^{0.02}=30\) & \(n/(C_{iv})^{0.02}=30\) & 2165.62 & 4118.58 \\ Soil–XG-PPF & \(n/(C_{iv})^{0.03}=30\) & \(n/(C_{iv})^{0.03}=30\) & 2034.72 & 4345.75 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Normalization data. statistically. These observations align with previous findings that show improved post-peak behavior and energy absorption in biopolymer-fiber systems. Taken together, the ANOVA models and experimental trends suggest that while cement remains the dominant factor governing strength and stiffness development, sustainable additives such as construction residues, XG, and PPF can play a strategic role in optimizing mechanical behavior. The lack of significance in several interaction terms, such as residue \(\times\)\(\gamma\)d or XG \(\times\)\(\gamma\)d, may be attributed to the predominantly independent effects of each variable on the mechanical behavior of the soil. This suggests that, within the tested ranges, the influence of compaction density and binder content acts in an additive manner rather than modifying each other's effects. In practical terms, this behavior simplifies the mix design process, as improvements in strength or stiffness can be achieved by adjusting individual factors without requiring complex synergistic tuning. However, it also highlights the need for further investigation under broader ranges or different environmental conditions, where non-linear or synergistic effects could become more pronounced.