# Correlation of Plastic Strain Energy and Acoustic Emission Energy in Reinforced Concrete Structures
## 2 Cyclic Loading  
### RC Beams  
Firstly, a 100 \(\times\) 100 \(\times\) 1000 mm\({}^{3}\) RC beam (Figure 1) was built and subjected to three-point bending tests [13]. Concrete compressive strength was 25 MPa. Reinforcement consisted of four longitudinal bars of 4 mm thickness and 76 \(\times\) 76 mm\({}^{2}\) square stirrups. Reinforcement steel yield strength was 500 MPa. Applied force, \(Q\), and the corresponding vertical displacement, \(\delta\), were measured with a load cell and a displacement transducer. AE signals were acquired with ten channels of AMSY-5 equipment using ten VS30-V sensors (Vallen Systeme, Icking, Germany) with an almost flat bandwidth response in low frequency (25-100 kHz). Sampling frequency was set at 5 MHz, and the number of samples per signal was 4096. The threshold used was 35.1 dB\({}_{\text{AE}}\). Sensors S9 and S10 were configured as guard sensors to eliminate noise generated by friction at the supports. After recording, only signals passing the guard sensors and a filter based on the Root Mean Square (RMS) (explained in more detail in [13]) were taken into account during the analysis. Figure 1: Undamaged Reinforced Concrete (RC) beam and ten Acoustic Emission (AE) sensors. S1 and S2 on face C; S3 and S4 on face B; S5 and S6 on face A; S7 and S8 on face D. Distances in mm. The bending test was carried out by applying a history of incremental load cycles controlled by force (Figure 2). Each cycle comprises three branches: loading, holding load and unloading, which are represented in Figure 2 by sets of three consecutive segments separated by a segment of null load. Final failure occurred at \(Q=30.72\) kN. Figure 3 shows the load-displacement and load-curvature diagrams. Residual plastic deformations are clearly observed from the initial cycles, indicating that damage took place even in the earlier cycles. This damage likewise results in a degradation of stiffness (Figure 4). This figure shows that for cycles 1, 2 and 3, the variation of stiffness between the loading and unloading branches was not significant. However, from cycle 4 onward, this variation becomes more noticeable. Thus, from Figures 3 and 4 it follows that the reinforcement steel began to plastify during cycle 4. The stiffness degradation became more pronounced as the load increased from cycle 5 on  
Accumulated AE MARSE energy, \(E^{AE}\), was calculated for the first hit of the events constructed with sensors S1-S8 [13] (Figure 5). In this figure, the plastic strain energy \(W_{P}\) dissipated by the specimen is also included. Both \(E^{AE}\) and \(W_{P}\) were normalized by their respective values \(E^{AE}_{0}\) and \(W_{P,0}\) at the onset of yielding in the steel reinforcement, referred to hereafter as \(t_{0}\). \(W_{P}\) was obtained by integrating the load-displacement curve (\(Q\)-\(\delta\)). \(W_{P}\) is the sum of the energy dissipated by the concrete, \(W_{PC}\), and the energy dissipated by the steel, \(W_{PS}\), as  
\[ \begin{array}{c}W_{P}=W_{Pc}\;\;if\;\;t<t_{0}\\ W_{P}=W_{Pc}+W_{Ps}\;\;if\;\;t\geqslant t_{0}.\end{array}  \tag{1}\]  
AE energy is also a double contribution of concrete and steel. However, with the AE threshold used (35.1 dB) during acquisition, the very low amplitude AE proceeding from the plastic strain of steel cannot be recorded, _i.e._,  
\[E^{AE}=E^{AE}_{c}+E^{AE}_{s}\cong E^{AE}_{c}. \tag{2}\]  
As observed in Figure 5, before the yielding point, a very good correlation exists between \(E^{AE}/E^{AE}_{0}\) and \(W_{P}/W_{P,0}\). However, after this point, \(E^{AE}\) is always lower than \(W_{P}\). Moreover, the decreasing of AE energy--and thus its separation from the plastic strain energy--is in good agreement with the results reported in [21], _i.e._, AE energy decreases as the energy absorbed by the reinforcement through plastic deformations increases. This result also supports the increase of the \(b\)-value at the onset of yielding in the steel reinforcement [13]. In sum, it is held that  
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