*4.2. 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.

(b)

**Figure 7.** Clustering dendrograms. (**a**) Confined specimen; (**b**) Unconfined specimen.

**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.

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

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.

**Figure 10.** Normalized signal features. (**a**) Confined specimen; (**b**) Unconfined specimen.

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]. The higher the frequency components are in a signal, the lower rise angle value the signal possesses. In the unconfined specimen, Cluster-5 and Cluster-6 exhibit higher hit rates at the higher concrete age compared to Cluster-4, and the average amplitude of signals for the clusters with higher frequency components is slightly higher than for signals in Cluster-4. However, the average duration for the signals in the cluster with the low-frequency components (Cluster-4) is much longer than the duration for Cluster-5 and Cluster-6.

In Figure 11, the variation of cumulative signal strength in terms of the age of the concrete for each cluster is presented. The cumulative signal strengths were normalized by the maximum value for each specimen. In the confined specimen, the signals with the highest frequency components (Cluster-3) have dominant CSS from the early age. However, the CSS of Cluster-2 is very close to the CSS of Cluster-3 up to the concrete age of 150 days. After 150 days, the CSS rate for Cluster-3 increases, while the CSS rate of Cluster-2 continues with approximately the same rate. The signals in cluster Cluster-1 have negligible signal strength compared to Cluster-2 and Cluster-3 and initiate primarily after 120 days. In the unconfined specimen, the AE energy is primarily attributed to cluster Cluster-4 up to approximately 150 days. After 150 days, the clusters with the higher frequency components (Cluster-5 and Cluster-6) become prominent in terms of AE energy release.

**Figure 11.** Normalized cumulative signal strength. (**a**) Confined specimen; (**b**) Unconfined specimen.

The distribution of total AE signal strength for the classified clusters and sensors at different ages of the concrete (66, 150, 195 days) are illustrated in Figure 12. These distributions are referred to as signal strength contribution factors (SSCF). The 66th day and 195th day were selected to illustrate the trend of data at the beginning and end of the evaluated time window. The 150th day was selected because in both reactive specimens there was an obvious change in the rate of CSS of the clusters with high-frequency components in comparison to the lower frequency components. The figures on the left show results of the confined specimen and the figures to the right show data from the unconfined specimen.

**Figure 12.** Distribution of total AE signal strength in terms of clusters and sensors. (**a**) Confined specimen at age of 66 days; (**b**) Unconfined specimen at age of 66 days; (**c**) Confined specimen at age of 150 days; (**d**) Unconfined specimen at age of 150 days; (**e**) Confined specimen at age of 195 days; (**f**) Unconfined specimen at age of 195 days.

In the confined specimen, most of the energy contribution is related to Cluster-2 (energy concentration in 50–150 kHz) and Cluster-3 (energy concentration in 150–300 kHz). The SSCF for Cluster-3 is increases with time, particularly after 150 days. Most of the AE energy for Cluster-3 is concentrated in sensor 3 (mid-thickness of the specimen) after 100 days. Cluster-2 and Cluster-3 both have prominent AE energy at sensor 2 before the 66th day. Then the highest AE energy portion moves to sensor 3, whereas SSCF of Cluster-2 is much lower than Cluster-3, especially after 150 days. The SSCF for cluster Cluster-1 is negligible compared to other clusters. In the unconfined specimen, the highest SSCF is for cluster Cluster-4 (energy concentration between 0–150 kHz) at sensor 4 (attached to top reinforcement) at 66 days. However, this energy contribution decreases with time, and the SSCF of the clusters with high-frequency components (Cluster-5 and Cluster-6) increases with time. There is no obvious energy concentration in the sensor located at mid-thickness of the specimen (sensor 6), which

is different from what is observed in the confined specimen. In both specimens, the SSCF declines in low-frequency signals and increases in high-frequency signals with time. This trend in signal frequency from low to high in the confined specimen is not pronounced before 150 days. The SSCF for cluster Cluster-3 is slightly greater than the Cluster-2 at 150 days. The signal frequency trend initiates primarily after 150 days in this specimen. On the other hand, in the unconfined specimen, the frequency content evolution of AE signals is obvious from an earlier stage of ASR reaction (66 days) and is more significant after 150 days.

The confined specimen has a higher extensional strain along the Z direction than the unconfined specimen (approximately 42% more at 195 days). This expansion leads to tension concentration through the thickness of the confined specimen. Since there is no confinement through the specimen thickness it is susceptible to crack formation. In the unconfined specimen, the expansion strain is more evenly distributed between the X-Y plane and the thickness. Therefore, the tension is more uniformly distributed in the entire specimen in comparison to the confined specimen. This is also observable from the AE data, where sensor 3, located at the mid-height of the confined specimen, has a larger SSCF than the unconfined specimen (e.g., 65% for the confined specimen versus 35% for the unconfined specimen at 195 days).

As mentioned previously, the frequency of AE signals progresses from low to high as the concrete ages. This may be attributable to the formation of cracking through the coarse aggregate due to ASR progression. The crack formation inside the aggregate is expected to have higher frequency components than the cement matrix and interfacial transition zone (ITZ) as mentioned by Farnam et al. [17]. The transition from low-frequency signals to the high-frequency signals in the confined specimen initiated later than for the unconfined specimen (after 150 days). However, there are different contradictory hypotheses relating to formation of cracks in concrete due to ASR [33]. For instance, osmotic pressure theory was proposed by Hanson to describe the mechanism of expansion [34]. In this theory, the cement paste surrounding to reactive aggregates acts as a semi-permeable membrane, which water solution can pass inside the region around the reactive aggregates, but alkali-silica ions are enclosed in the reactive regions. This causes osmotic pressure and alkali-silica gel swells and exerts pressure to the cement paste. This pressure leads to crack formation in the cement paste [34]. McGowan and Vivian also proposed a similar theory as osmotic theory, which transforming a solid alkali-silica layer on a reactive aggregate to a gel by absorbing moisture from the pore solution was explained as a main reason of cracking in the cement paste due to ASR [35]. Bazant and Steffens suggested that the cracking is caused in the cement paste and interfacial transition zone due to accumulation of alkali-silica gel in the interfacial transition zone and resulting gel pressure [36]. On the other hand, Dron and Brivot assumed that crack formation occurred far away from reactive aggregates due to diffusing dissolved silica away from aggregate into the pores in the cement paste [37]. Some researchers observed that ASR gel initially forms inside a reactive aggregate and causes the pressure and crack formation inside the aggregate and surrounding cement paste [12,38–41]. Ponce and Batic [42] related the cracking pattern of concrete due to ASR to the types of reactive aggregate. ASR cracks start to form inside aggregate or in the cement matrix depending on the aggregate type [42].

In the confined specimen, the CSS rate of Cluster-3 (energy concentration 150–300 kHz), started to increase at the age of 150 days. In the unconfined specimen, the CSS rate for the cluster with the higher frequency components also increases around that time. 150 days is close to the inflection point of the volumetric strain curve, after which point expansion rates decrease. In addition, the first visible cracks were observed at the age of 150 days on the sides of the unconfined specimen, but no cracks were visible on the top surface of the unconfined specimen. Cracks could not be traced in the confined specimen on the sides due to the steel confinement frame. From the above observations, 150 days is a significant time period for ASR in the specimens, which generally agrees with trends in the AE data.
