## 4 Results and Discussions
### Pattern Recognition of AE Data  
The AE signals were classified according to the agglomerative hierarchical algorithm as explained in Section 3.1. Dendrograms resulting from the analysis are presented in Figure 7. Dashed red lines in the subfigures indicate the desired height of links for clustering. The results of the pattern recognition show three clusters for each reactive specimen (both confined and unconfined). The clusters of confined specimens are indicated by Cluster-1, Cluster-2, and Cluster-3. Accordingly, the clusters of the unconfined specimen are labeled Cluster-4, Cluster-5, and Cluster-6. The horizontal axis in Figure 7 gives the data labels, which show either labels of the original data sets (signal number) or the label number of the clusters that resulted from merging the original data. The height of each link shows the distance between the two objects. Each link between two objects is shown by an upside-down U-shaped line in the figure. The data is shown in terms of the first three principal components (PC) to visualize the distribution of clusters with respect to each other in Figure 8. Although some signals in the cluster 5 and 6 were not ideally separated, in general, the clusters indicate a reasonable separation in the PC space (Figure 8). The reason for an overlap between clusters 5 and 6 is that some signals in cluster 5 have a similar energy contribution in a specific frequency range to some signals in cluster 6. As seen in Figure 9b, clusters 5 and 6 have similar average energy contribution between 250 to 300 kHz. Figure 7: Clustering dendrograms. (**a**) Confined specimen; (**b**) Unconfined specimen. The average energy of signals in terms of frequency ranges is shown in Figure 9 for the reactive specimens. These values, as previously mentioned, were calculated using the FFT amplitude spectrum. Afterward, the calculated values were normalized by the total energy of the signal. The average values for each cluster were then calculated. The energy shift to the higher frequency components for the unconfined specimen is apparent when viewed alongside the confined specimen. The clusters in each specimen can be separated based on the frequency content. In the confined specimen, the low-frequency cluster (Cluster-1) has approximately 69% of its energy in a frequency range of 0-100 kHz. The medium-frequency cluster (Cluster-2) has 42% of its energy concentrated in a  
Figure 8: Clusters in principle component dimensions. **(a)** Confined specimen; **(b)** Unconfined specimen. Figure 9: Average normalized signal energy in frequency domain. **(a)** Confined specimen; **(b)** Unconfined specimen. frequency range of 50-150, while the high-frequency cluster (Cluster-3) has 51% of its energy between 150-300 kHz. In the unconfined specimen, the low-frequency cluster (Cluster-4) has 62% of its energy in a frequency range of 0-150 kHz and the medium-frequency cluster (Cluster-5) has 49% of its signal energy in the frequency range of 150-300 kHz. The high-frequency cluster (Cluster-6) has 54% of its signal energy concentrated between the frequencies of 300-450 kHz. The Cluster-3 and Cluster-5 share similar frequency content. More signal features for the clusters are illustrated in Figure 10. The average feature values for each cluster were normalized by the maximum feature values for each cluster. In the confined specimen, Cluster-1 initiated at a higher concrete age (data was analyzed through a concrete age of 195 days) than clusters with higher frequencies (Cluster-2 and Cluster-3). The average amplitude of the signals in Cluster-3 (the highest frequency) is higher than the other signals. Average signal strength for Cluster-1 is lower than the values for Cluster-2 and Cluster-3, and duration is higher for the cluster with the lowest frequency content, for example, Cluster-1. A clear correlation is present between the frequency content of the signal clusters and the rise angle values (rise time over amplitude ratio) as has been observed by other researchers [31; 32].