# Acoustic Emission and Modal Frequency Variation in Concrete Specimens under Four-Point Bending
## 5 Discussion  
The aim of the present study was to analyze both AE signals and modal frequency variations during the loading and damage of pre-notched concrete beams. The specimens were tested in the four-point bending configuration by an MTS universal machine. The tests were conducted by controlling the axial displacement of the hydraulic jack and continued up to complete failure. As a comment on the general trend of the conducted tests, the load-displacement curves revealed an elasto-softening behavior of the specimens, with multiple snap-back instabilities in the post-peak branch. In two cases, a globally unstable behavior was registered in the softening branch; this character is reflected by the acoustic emission energy analysis. We also remark that piezoelectric pickups typical of music technology, recently adopted by some of the authors to extract modal parameters of slender metallic elements in the lab [8; 9; 10], were successfully used here, as long as the natural frequencies of stubby concrete specimens are extracted. The main remarks, related to the results of the present study, can be summarized as follows. AE energy and natural bending frequencies were used as two independent parameters to monitor the same damage process. It was found that the natural bending frequencies decrease as the cumulated AE energy increases. In fact, both these kinds of parameters can be used as damage indicators: the former is correlated to the energy emitted by the material during crack formation and propagation, while the latter is correlated to the loss in global stiffness due to the cross-section reduction provoked by crack propagation. First acoustic emissions were registered even before the peak load, while no sensible variations in the natural frequencies were observed. After the peak load, as was expected, AEs increased up to final failure, while the natural frequencies progressively decreased as the vertical displacement was increased. The obtained trends suggest that a certain amount of AE energy (which, however, is not a constant) must be emitted by the specimen before initial/new decreases in the natural frequencies can be observed. Lastly, linear finite element models of the unloaded specimen, where the notch depth was varied, were used to look for a first correlation between the frequency reduction and the crack propagation (simplifying the actual phenomenon). Such a correlation is of interest to acquire information about the cross-section integrity, and therefore to evaluate its resisting capacity. However, the former issue was addressed here only partially (a deeper investigation would have required performing more sophisticated nonlinear analyses), whereas the latter was not addressed at all, it being beyond the scope of the present study. On the other hand, much literature on the evaluation of crack location and depth based on measured natural frequencies (and modes) exists (e.g., see [43; 44; 45; 46; 47; 48; 49; 50; 51; 52]). Figure 11: (**a**) Numerical (FEM) fundamental vibration mode and frequency of the unloaded beam for increasing notch depth (\(\xi=a/h\)) and (**b**) approximate evaluation of crack advancement based on measured and calculated (FEM) fundamental frequencies. This work represents a first attempt to correlate AE signals produced by material damage with variations in the natural vibration frequencies of a cracking element. Such a combination between the AE and the DI techniques could have significant implications in structural monitoring. More precisely, the AE signal analysis can effectively be used as damage precursor, detector, and identifier; the analysis of the variation in modal properties can more conveniently be adopted to catch information about the global rigidity of the structure and, eventually, to evaluate its damage level and safety by inverse procedures. The main steps of a possible combined monitoring of a complex structure can be resumed as follows:  
1.