# Correlation of Plastic Strain Energy and Acoustic Emission Energy in Reinforced Concrete Structures
## 3 Seismic Loading  
### RC Slab  
A prototype one-story, one-bay structure (2.8 m high and 4.8 m long) consisting of an RC slab supported on four box-type steel columns was designed following current Spanish codes NCSE-02 and EHE-08. From this prototype structure, the corresponding test model was derived by applying the similarity laws described in [15]. The depth of the slab was 125 mm. It was reinforced with steel meshes: one on the top made with 6 mm diameter bars spaced 100 mm, and another on the bottom consisting of 10 mm diameter bars spaced 75 mm. The average yield stress of the reinforcing steel was 467 MPa, and the average concrete strength was 23.5 MPa. The model was tested with a uniaxial MTS \(3\times 3\) m\({}^{2}\) shaking table as shown in Figure 15.  
The acceleration record used for the tests reproduced the North-South (NS) component of the 1980 Campano-Lucano earthquake recorded at Calitri (Italy). Two series of seismic simulations were applied to the test model. The same accelerogram was used in all simulations, the scaling factor of the peak accelerations (PA) being the only difference (Figure 16). Displacements, strains and accelerations were acquired simultaneously during each seismic simulation.  
Eight VS30-V AE sensors were placed on the specimen at the eight positions indicated in Figure 15. AE signal acquisition was carried out using a sampling period of 1.6 \(\upmu\)s, 45 dB\({}_{\text{AE}}\) as the detection threshold and amplifiers of 34 dB\({}_{\text{AE}}\). An AE signal discrimination procedure was applied to prevent  
Figure 15: RC slab with AE sensors (S1 to S8) on the shaking table. (**a**) Elevation. (**b**) Plan (bottom view). Distances in mm.  
spurious and friction sources using guard sensors and an RMS filter [18]. The accumulated AE MARSE energy, \(E^{AE}\), was calculated for the first-hit of the events constructed with the eight channels [15]. As an example, Figure 17 shows \(E^{AE}\) with dashed lines for simulations D1 (before the sliding point of the reinforcement steel inside the concrete) and D2 (after sliding point). In this figure, the overall plastic strain energy \(W_{P}\) dissipated is superimposed by solid lines. Both \(E^{AE}\) and \(W_{P}\) were normalized by their values at the end of each simulation. As seen in Figure 17, for simulation D1, the two energy curves are very well correlated. However, in simulation D2, this correlation is not maintained, the accumulated AE energy being consistently lower than the cumulative strain energy.  
Figure 16: (a) Acceleration of Campano-Lucano earthquake scaled at 100% (Simulation D1); (b) Seismic simulations (name and Peak Acceleration (PA)).  
Figure 17: Accumulated AE energy (dashed line) and accumulated plastic strain energy (solid line) obtained for the RC slab. Both were normalized at the end of each simulation.  
Figure 18 represents the final values of both energies obtained in each simulation, normalized by their respective values \(E_{0}^{AE}\) and \(W_{P,0}\) at the onset of the sliding point of the steel reinforcement, timed at \(t_{0}\). At that moment, the steel columns also began to yield. The AE threshold used (45 dB\({}_{\text{AE}}\)) during acquisition could not record the very low amplitude AE proceeding from the plastic strain of steel. This fact justifies the very good correlation between \(E^{AE}\) and \(W_{P}\) up to \(t_{0}\) and the deviation of the two energies after this point, again in very good agreement with Equations (1) and (2).