# Acoustic Emission Monitoring in Prestressed Concrete:
## 2 Acoustic Emission and Attenuation of Elastic Waves in Concrete Constructions  
Acoustic emission (AE) refers to the phenomenon whereby waves are generated and propagate elastically within a material, such as during the formation of cracks. The dynamic deformations appearing on a structure's surface can be detected via piezoelectric sensors, thereby facilitating the monitoring of material changes and structural integrity. To analyse the underlying phenomena, the measured time-amplitude signals are typically reduced to a few characteristic features in either the time or frequency domain. Notably, these features include the peak amplitude \(A_{\text{peak}}\) and energy \(E\), as highlighted in [19]. The propagation of elastic waves is subject to attenuation effects, which must be considered in the design of measurement campaigns and the evaluation of results. Geometric attenuation, for instance, results in a decrease in the source impulse's energy, as the wavefront expands with increasing distance \(r\). For spherical waves, the sound intensity \(I\) and the sound level \(A\) can be expressed with  
\[I\propto\frac{1}{r^{2}}\quad\text{and}\quad A\propto\frac{1}{r}\quad\text{( spherical waves)} \tag{1}\]  
and for cylindrical waves with  
\[I\propto\frac{1}{r}\quad\text{and}\quad A\propto\frac{1}{\sqrt{r}}\quad\text{( cylindrical waves)} \tag{2}\]  
Considering just the geometric part, the decrease in sound intensity or sound level decreases by 6 dB for spherical waves and 3 dB for cylindrical waves with each doubling of  
Figure 1: Signal sources under investigation: (**a**) wire break artificially induced on girders under laboratory conditions; (**b**) rebound hammer impulses applied longitudinally on the tendons cross-sectional surface; and (**c**) rebound hammer impulses applied orthogonally to the tendons on the concrete surface. distance from the source. In contrast, plane wavefronts remain unaffected by geometric attenuation. Furthermore, along the propagation path, both sound intensity and level are reduced due to scattering, reflection, and absorption. For describing dispersive attenuation, the application of an exponential decay function is appropriate:  
\[I\propto I_{0}e^{-\alpha\cdot r}\quad\text{and}\quad L\propto L_{0}e^{-\alpha \cdot r}, \tag{3}\]  
where \(\alpha\) is the material- and frequency-dependent attenuation coefficient. Due to the heterogeneous composition, the attenuation behaviour of elastic waves in concrete is quite complex. On the mesoscale, the material composition is important, which is why aggregates, pores, and reinforcement have so often been addressed in investigations [20; 21; 22; 23; 24; 25]. Experiments have predominantly been conducted on small-scale specimens to describe the relationship between signal amplitudes and propagation distances, quantified through attenuation coefficients. A pronounced frequency-dependent attenuation of amplitude, correlated with the concrete's composition, has been observed consistently. [PERSON] et al. investigated small cubic concrete specimens with 150 mm edges and found that attenuation increases linearly below 100 kHz, from approximately 10 dB/m at 10 kHz to 200 dB/m at 100 kHz, and then ascends slightly to between 230 and 400 dB/m at 1 MHz [24]. However, this study did not consider the effects of partial reflections at the specimen-transducer interface or diffraction loss. Addressing these factors, [PERSON] et al. demonstrated that both partial reflections and diffraction losses generally lead to an overestimation of attenuation coefficients, particularly highlighting the dominant effect of reflection losses over diffraction [26]. In cement paste, attenuation estimates extended up to 6 MHz, showing an attenuation coefficient of about 140 dB/m at 1 MHz. [PERSON]'s investigations into mortar samples revealed attenuation coefficients in the range of 220-250 dB/m at 1 MHz [27; 28]. Further studies explored the influence of void content on mortar's attenuation coefficient, indicating increases in attenuation with greater void content.