## 3 Results and Discussion
### Ultrasonic Tests  
The ultrasonic waves were registered automatically every 2 seconds during push-out testing. All signals acquired by sensor S2 for specimens #1 to #9 are illustrated in Figure 10. Only an initial part of the signal with a length of 0.1 ms was analyzed to reduce the influence of interactions of waves with the compression test kit of the testing machine. The reference signal, i.e., the signal registered at the beginning of the push-out test is marked in black and the last acquired signal is marked in red. For specimens #1-#3, representing the adhesive-type failure (mode I), signals relating to successive states of mechanical degradation are similar and no significant changes in the magnitude or phase can be observed. In the case of push-out specimens #4-#10, for which the cohesive or mixed adhesive-cohesive failure occurred (mode II), experimental waveforms changed considerably during mechanical degradation. Figure 9: Interface slip between steel and concrete for tested push-out specimens (#1–#9). The results of applying the Sprague and Geers metric to all signals registered during the monitoring of the push-out test are presented in Figure 11. For clarity of observation, the load-time curves were provided for each specimen. Additionally, for specimens #4-#7, red dashed lines were drawn at the moment of initiation of the crack in the concrete cube. The S&G metric expresses the difference between the reference signal and the other signals registered during the push-out test. The error measures can range from 0 to 1 or more. The perfect agreement of time histories results in a zero value of the error measures, while the value of unity indicates a difference of 100%. The value of the \(P\)-error is always positive while the value of the \(M\)-error can be positive or negative, depending on whether the monitored signal has higher or lower amplitude than the reference signal. At the beginning of the process, the \(P\)-error fluctuated around the value of about 5% and the \(M\)-error around the value of about 0%. These values resulted from the presence of measuring noise in the subsequently triggered measuring signals. Considering the specimens with the adhesive-type damage (the first row in Figure 11), all error measures are rather constant during the entire push-out test. A slight increase in the \(P\)-error value was observed for specimen #6; however, based on these errors it was not possible to detect incoming damage before the failure. The second group are specimens belonging to failure modes IIa and IIb, for which the separation between the steel plate and concrete was preceded by the cracking of concrete. For specimens #4, #5 and #6, the increase in the \(P\)-error can be observed before the initiation of the diagonal cracks. This increase was quite sudden for specimen #5, but for specimens #4 and #6 it was gradual signaling incoming damage. Moreover, for specimen #6, the \(M\)-error gradually decreased before the initiation of the diagonal cracks. In the case of specimen #7, for which the crack appeared in the middle of the concrete cube, the gradual increase of the \(P\)-error and the decrease in the \(M\)-error can be seen, enabling detection of the micro-crack zones in the concrete long before the appearance of the macro-crack. The last two specimens represented the failure of mode IIc. For the specimen #8, the detection of the cohesive failure was possible based on both the \(M\) and \(P\)-errors. In the case of specimen #9, the gradual increase of the \(P\)-error was observed (similarly as for specimen #2) indicating the increase in the load but not the appearance of the failure. This was because, the failure of specimen #9 was mainly adhesive, with a small area at which the cohesive failure occurred. As a damage indicator, the \(C\)-error is proposed because it contains both the magnitude and phase errors. For each specimen, two horizontal lines were drawn in the plots of the comprehensive error (Figure 11).