## 3 Results and Analyses
### RA-AF Analysis Results  
The K-means analysis results of AE signal features presented in the preceding subsection reveal limitations in cluster separation efficacy. Specifically, inter-cluster data overlap persists across certain feature dimensions, despite prior dimensionality reduction retaining four principal components. This residual multidimensionality likely impedes cluster distinction, as further dimension reduction proves challenging, consequently compromising classification performance. To further investigate the AE signature evolution during eccentric compressive loading, an integrated clustering approach combining Gaussian mixture models (GMMs) and a K-means algorithms was implemented on RA-AF values. The probability density cloud map of RA-AF calculated by GMM is illustrated in Figure 12, and the dashed boundary surrounds the principal data cluster, comprising 95% of the total dataset. The K-means-clustered RA-AF data are presented in Figure 13. In these figures, Geometric markers differentiate fracture types: squares (tensile cracks) and circles (shear cracks). Chromatic coding represents cluster assignments, with point transparency indicating classification confidence (\(\alpha=0.2\) for low-confidence predictions confidence level < 0.8) in mixed cracks. Lower transparency signifies high confidence (confidence level > 0.8). The results demonstrate that mixed cracks dominated throughout the failure process, followed by tensile cracks, with shear cracks exhibiting the smallest proportion. As depicted in Figures 14 and 15, the spatiotemporal evolution of RA-AF characteristics under varying loading conditions was quantified through probability density contour maps and distribution matrices. During initial loading, both specimens exhibited predominant AE signal generation from Cluster 1, with minor contributions from Clusters 2 and 3. C-1 demonstrated higher AE counts with increased shear cracking prevalence, contrasting with C-2's lower AE event frequency. Probability density maps revealed AE event concentration in high-AF and low-RA regions, indicating tensile crack dominance. Minor populations displayed high-RA and low-AF signatures (shear precursors), correlating with cement matrix microcracking and aggregate-cement interfacial slip. Phase II witnessed increased AE events in both specimens while maintaining Cluster 1 predominance. A leftward shift in the probability density centroid was seen in C-1, while migration toward shear-characteristic zones was observed in C-2. This phase marked the micro-to-macro crack transition with intensified interfacial transition zone (ITZ) degradation and aggregate slippage. Phase III showed progressive AE intensification in C-2 but attenuation in C-1. Density distributions reflected increased tensile and mixed-mode fracturing in both specimens. This mechanical response indicates reduced elastic energy release through established fracture pathways during major crack propagation. During post-failure displacement control, AE signals further increased with altered cluster distribution. Probability density maps demonstrated significant RA-AF signature migration toward predominantly mixed-mode and shear cracking. This behavior is attributed to reinforcement yielding, concrete crack widening, and compressive crushing mechanisms. \begin{table}
\begin{tabular}{c c c c} \hline  & & **Energy (Kp)** & **Amplitude (dB)** \\ \hline \multirow{4}{*}{C-1} & Cluster 1 & 0.031–125.174, mean = 0.8 & 45.3–60.8, mean = 49.5 \\  & Cluster 2 & 0.329–566.5, mean = 16.2 & 46.1–82, mean = 58.2 \\  & Cluster 3 & 0.246–701.9, mean = 65 & 46.3–78.5, mean = 59 \\  & Cluster 4 & 980–3140.5, mean = 1568.4 & 74–83.7, mean = 79.9 \\ \hline \multirow{4}{*}{C-2} & Cluster 1 & 0.031–125.174, mean = 0.8 & 45.3–60.8, mean = 49.5 \\  & Cluster 2 & 0.329–566.5, mean = 16.2 & 46.1–82, mean = 58.2 \\ \cline{1-1}  & Cluster 3 & 0.246–701.9, mean = 65 & 46.3–78.5, mean = 59 \\ \cline{1-1}  & Cluster 4 & 980–3140.5, mean = 1568.4 & 74–83.7, mean = 79.9 \\ \hline \end{tabular}
\end{table}