# Correlation of Plastic Strain Energy and Acoustic Emission Energy in Reinforced Concrete Structures
## 4 Conclusions  
The Acoustic Emission (AE) technique was used to assess damage in several reinforced concrete (RC) elements and structures subjected to different types of loading. Simple beams, beam-column subassemblages, flat-slab structures supported on steel columns, and RC frame structures were tested. The RC elements and structures were subjected to static cyclic loads and randomly applied dynamic loadings. During each test, the AE was recorded by several low-frequency sensors. In addition, forces, accelerations and displacements were measured with load cells, accelerometers and displacement transducers. Analysis of the AE signals served to calculate the AE MARSE energy accumulated throughout the test. By integrating the load-displacement curves, the energy dissipated through plastic deformations was calculated. Plastic strain energy is commonly recognized as a good indicator of damage; and it was found that there is a good correlation between the AE MARSE energy calculated with the AE measurements and the cumulative damage on the concrete measured in terms of plastic strain energy. Such a correlation points to the utility of AE signals for developing damage indices based on AE MARSE energy, as they are capable of assessing the damage in RC structures subjected to different types of loadings. An example of the damage index based on the correlation of the strain and acoustic energies is the Sentry function, proposed in [31], in terms of the logarithmic ratio of both energies. The reason why AE MARSE energy can be utilized for the establishment of damage indices in reinforced concrete (RC) elements is that the failure of RC structural elements is typically due to the degradation (damage) of concrete, not of the reinforcing steel. That is, what typically limits the ultimate capacity of a RC element is the amount of plastic strain energy accumulated in the concrete, not in the reinforcing steel. It is also worth noting that, in a real experiment or in a real structure, calculating the damage index in terms of AE MARSE energy requires an estimation of the final value of the AE MARSE energy (_i.e._, the value associated with failure). Past research [15; 32] ascertained that this estimation can be made on the basis of the information collected from previous experiments and the volume of concrete of the specimen or of the real structure. A change in specimen size does not have appreciable effects on damage patterns, but the volume \(V\) of damaged concrete affects the number of AE events as well as the AE MARSE energy; simple relationships that relate AE MARSE energy with \(V\) have been proposed [33; 34; 35; 36].  
This research received financial support from the local government of Spain, Consejeria de Innovacion, Ciencia y Tecnologia, projects P07-TEP-02610 and PE12-TEP-02429, from the Spanish National Plan for Scientific Research, Development and Technological Innovation (projects BIA 2005-00591 and DPI 2006-02970),  
Figure 21: Accumulated AE energy (dashed line) and accumulated plastic strain energy (solid line). RC frame.  
and from the Formacion del Profesorado Universitario (FPU) Program of Spain's Ministry of Education, Culture and Sports (AP2010-2880). All authors contributed to the work presented in this paper, and to the writing of the final manuscript. [PERSON] and [PERSON] were responsible for the Acoustic Emission and the analysis of the data. [PERSON] and A.B-C. provided discussion on the testing procedure and the results, and were responsible for the mechanical testing and AE monitoring. The authors declare no conflict of interest.  
The following abbreviations are used in this manuscript:  
AE Acoustic Emission  
RC Reinforced Concrete