## 5 Principal Component Regression Analysis
### Causality Analysis Using Principal Component Regression (PCR)  
PCR analysis reveals the temporal evolution of soil property influences unconfined compressive strength development during stabilization curing (Figure 20). The analysis identifies two primary components: PC1 representing compressibility-related factors (void ratio, porosity, compression index) and PC2 encompassing stiffness-related properties (compressibility modulus, pre-consolidation stress). Both components exhibit negative coefficients, confirming inverse relationships with UCS where parameter reductions correlate \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Principal Component** & **Regression Coefficient** & **Variance Contribution (\%)** & **Sensitivity Ranking** \\ \hline PC1 (soil compressibility) & 0.72 & 46\% & High Sensitivity \\ \hline PC2 (modulus vs. pre-consolidation stress) & 0.51 & 20\% & Moderate Sensitivity \\ \hline PC3 (pre-consolidation stress) & \(-\)0.32 & 15\% & Low Sensitivity \\ \hline PC4 (porosity and compression index) & 0.18 & 12\% & Minor Impact \\ \hline PC5 (void ratio and compression index) & \(-\)0.08 & 7\% & Negligible Impact \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Principal component analysis of soil parameters. with strength increases. PC1 demonstrates intensifying influence across the curing timeline, with coefficients strengthening from \(-\)76.84 at 7 days to \(-\)139.96 at 14 days and \(-\)170.70 at 28 days. This progressive enhancement indicates that compressibility-related parameters become increasingly dominant UCS determinants as curing advances. The trend aligns with fundamental stabilization theory, where continued lime and cement hydration progressively modifies soil structure through pozzolanic reactions that systematically reduce porosity and void ratio. Conversely, PC2 exhibits variable temporal behavior, with coefficients changing from \(-\)39.7 at 7 days to \(-\)86.84 at 14 days before recovering to 21.24 at 28 days. This pattern indicates that stiffness-related properties contribute less significantly to strength development, particularly during extended curing periods, becoming progressively overshadowed by compressibility factors. The divergent PC1 and PC2 trajectories underscore complex soil stabilization dynamics, where structural improvements through reduced porosity and increased densification emerge as predominant strength-driving mechanisms. This temporal evolution provides guidance for optimizing stabilization practices by emphasizing techniques that enhance compressibility-related properties. Model performance metrics demonstrate progressive improvement with extended curing. The coefficient of determination increases from 68.7% at 7 days to 83.0% at 28 days, while cross-validation RMSE decreases from 11.2 kPa to 7.8 kPa, indicating that soil-stabilizer relationships become increasingly deterministic and reliable as curing advances. Throughout all temporal stages, PC1 maintains statistical significance as the predominant UCS predictor (\(p<0.001\)), establishing compressibility parameters as invariant strength determinants regardless of curing duration (Table 4). The principal component regression (PCR) causality analysis, which identifies the temporal evolution of soil property influences on unconfined compressive strength (UCS) during curing, demonstrates both alignment and contrast with alternative methodologies in geotechnical literature. The PCR results reveal a dominant role for compressibility-related parameters (PC1: \(\beta=-\)170.70 at 28 days) over stiffness-related properties (PC2: \(\beta=\) 21.24 at 28 days), with PC1's influence intensifying over curing time. This aligns with studies  
Figure 20: Influence of PC1 and PC2 on UCS changes over curing periods of 7, 14, and 28 days. employing multivariate adaptive regression splines (MARS) [69], which similarly prioritize porosity and void ratio in UCS prediction.