## 4 Strength Properties
### Principal Component Analysis of UCS in Stabilized Soil  
PCA is a multivariate statistical technique widely used for dimensionality reduction, data illustration, and identifying patterns or relationships within complex datasets. Figure 15a-c represent scree plots, which display the eigenvalues associated with each PC of UCS for cementitious materials at different curing ages (7, 14, and 28 days). The first principal component demonstrates dominant explanatory power, accounting for 58.8% of the total variance in both 7-day and 14-day specimens, with a slight increase to 61.1% at 28 days of curing. The second principal component contributes substantially less variance,  
Figure 14: Showing resistance to strength loss for different cement contents (0–8%) across various lime percentages (0–30%). maintaining 33.3% across 7-day and 14-day periods before showing minimal change at the 28-day interval. The third principal component exhibits diminishing importance over time, decreasing from 7.9% at both 7 and 14 days to 5.6% at 28 days. The cumulative variance patterns show remarkable stability, with the first two components explaining 92.1% of total variance for 7-day and 14-day specimens, increasing marginally to 94.4% at 28 days, ultimately reaching 100% when all three components are considered. The elbow criterion clearly indicates that two principal components provide optimal dimensionality reduction, as evidenced by the sharp inflection point between the second and third components across all curing periods. This consistency suggests that the underlying variance structure of UCS data remains relatively stable throughout the curing process, with the first two principal components capturing the vast majority of meaningful variation in the lime-cement stabilized clay soil system, while the extended curing time to 28 days shows only marginal improvements in the concentration of variance within the primary components. The PCA biplots in Figure 16 reveal systematic changes in mixture composition-strength relationships across curing periods, with distinct clustering patterns based on cement and lime contents. At 7 days (Figure 16a), samples demonstrate clear separation along Principal Component 1, where higher cement contents (6% and 8%) occupy the positive PC1 space (0.5 to 2.0) while lower cement contents (0%, 2%, 4%) cluster in the negative range (\(-2.0\) to \(-0.5\)). The lime content gradient (0-30%) shows that samples  
Figure 15: Scree plot illustrating eigenvalues versus principal components for UCS data, depicting variance distribution: (**a**). A 7-day curing time. (**b**). A 14-day curing time. (**c**). A 28-day curing time. with 20-30% lime achieve PC2 values exceeding 1.0, particularly in high cement groups. The 14-day analysis (Figure 16b) maintains similar clustering but exhibits increased PC2 dispersion (\(-1.5\) to 2.0), with high cement samples continuing to dominate positive PC1 space and lime effects becoming more pronounced at 25-30% contents achieving PC2 values above 1.5. By 28 days (Figure 16c), the distribution becomes more dispersed with PC1 spanning from \(-2.0\) to 3.0 and PC2 ranging from \(-2.0\) to 2.5, indicating complex long-term interaction patterns. Throughout all curing periods, cement content serves as the primary discriminating factor in PC1, while lime content increasingly influences the secondary component over time, with the most significant effects observed in samples containing \(\geq\)6% cement combined with \(>\)20% lime content. Furthermore, integrating variables such as admixture dosages and UCS values at different curing ages provides a comprehensive understanding of observed trends and relationships. This integration with PCA results facilitates the development of predictive models and empirical relationships for optimizing mixture designs and achieving desired performance targets.