# Correlation of Plastic Strain Energy and Acoustic Emission Energy in Reinforced Concrete Structures
## 3 Seismic Loading
### RC Frame  
A prototype RC building was designed following the current Spanish seismic code NCSE-02, assuming that it was located in Granada (Spain), the most earthquake-prone region in all of Spain. From this prototype, and by applying scale factors, the test model displayed in Figure 19 was projected and constructed [14; 19; 20]. Basically, the test specimen consisted of four RC columns connected by RC beams (Figure 19). Figure 19: RC frame with AE sensors (S1 to S20). (**a**) Plan (bottom view); (**b**) Elevation. Figure 18: Accumulated AE energy (black square) and accumulated plastic strain energy (red triangle). RC slab. AE signals were acquired with twenty VS30-V AE sensors (Figure 19), recording the waveform with a sampling frequency of 2.5 MHz and a detection threshold of 50 dB\({}_{\text{AE}}\) and preamplifiers of 34 dB\({}_{\text{AE}}\). In addition, the steel reinforcement was instrumented with 192 strain gauges and 10 uniaxial accelerometers, and nine displacement transducers were installed on the RC specimen in order to measure the in-plane translations and the inter-story drifts in the direction of the seismic loading. The RC frame was subjected to the same earthquake pattern as the RC slab. In this case, five seismic uniaxial tests were consecutively applied to the specimen with steadily increasing values of _PA_, _i.e._, 50%, 50%; 100%; 200% and 300%. Figure 20 shows the corresponding accelerograms. A local damage study in the C3 and C4 beam-column connections was based on the AE energy generated at the zones around these connections, which are, in fact, the most critical points of the specimen. For interior connection C4, the sensors S2, S6, S9 and S10 were configured to construct the AE events, and the rest were considered as guard sensors. Likewise, for the exterior column-beam connection C3, only the sensors S3, S7 and S8 were configured to construct the AE events, the rest being considered as guards [19]. The Morlet Continuous Wavelet Transform (CWT) was applied in order to reconstruct AE signals using only scales 18 to 20, which correspond to the 45-64 kHz frequency band, tentatively assigned to the concrete cracking [16; 17]. The accumulated AE MMSE energy, \(E^{AE}\), was calculated for the reconstructed AE signals corresponding to the first-hit of events. Results are shown in Figure 21 along with the overall plastic strain energy (\(W_{P}\)) dissipated by the specimen [13; 14]. Both \(E^{AE}\) and \(W_{P}\) were normalized by their respective values \(E^{AE}_{0}\) and \(W_{P,0}\) at the onset of yielding of the steel reinforcement. Figure 21 reflects the same result as in previous tests, namely a very good correlation between \(E^{AE}\) and \(W_{P}\) until \(t_{0}\), and a divergence of the energies after this point, in very good agreement with Equations (1) and (2). It is worth noting that, besides the good correlation between \(E^{AE}_{0}\) and \(W_{P,0}\), it is consistently observed that the development of cracks in concrete reduces the fundamental frequency of vibration of the specimen and increments the fraction of damping [14; 25; 26]. The reduction of the fundamental frequency is due to the decrease of stiffness. The increase of damping is associated with the energy dissipated through friction between the planes of fracture after cracking. Moreover, the accumulated damage (in terms of plastic strain energy) always increases monotonically over time, and the rate of this increase tends to augment with the amplitude of the applied load. This satisfactory correlation is consistent with the results of other researchers [27; 28; 29; 30]. Since in the specimens subjected to seismic loading, the forces were applied dynamically in successive seismic simulations, only macroscopic cracks were observed at the end of each one. These cracks were evident after the first seismic simulation.