# A Simple Method to Estimate the In Situ Performance of Noise Barriers
## 5 Conclusions  
The acoustic performance of traffic noise barriers, regarding sound insulation, is normally evaluated by standardized parameters, such as the single-number rating of airborne sound insulation, \(DL_{R}\), or the single-number sound insulation rating, \(DL_{SI}\). However, the final performance of these noise reduction devices, being also dependent on in situ specificities, is more often characterized by the Insertion Loss frequency-dependent curve, \(IL_{i}\), or the corresponding weighted single-number, \(DL_{IL}\), which has been estimated by different authors. In this work, based on the Huygens-Fresnel-Kirchhoff principle, a simplified model is proposed to obtain the Insertion Loss provided by a noise barrier, assuming that the noise barrier's sound reduction index is known and only a numerical acoustic simulation, with a completely rigid noise barrier, has to be performed. This simplified model is herein verified by comparison with a FDTD numerical simulation method, applied to both traditional and sonic crystal-based noise barriers. Then, the relationship between the two parameters used in the quantification of the acoustic performance of noise barriers, namely, the Insertion Loss (\(IL\)) and the airborne sound insulation (\(DL_{R}\)), was explored. The good agreement between the values obtained by the FDTD model and by the simple model proposed in this paper was shown, but was also interestingly demonstrated that, no matter how much the acoustic insulation of a noise barrier is increased, its final performance, given by the Insertion Loss parameter, reaches a maximum and saturates, being controlled by the diffraction at the top of the noise barrier. In the case of noise barriers based on sonic crystals, very good Insertion Loss results have been observed for different filling factors of the crystal distribution, in comparison to 3D simulations, mainly in the medium and high frequencies ranges. These conclusions have been corroborated with \"overlapping models\" [23, 24], and the similarity of the simple proposed model with the evaluation of the insulation achieved by composite heterogeneous panels has been highlighted, making use of the transmission coefficient of the noise barrier.  
Conceptualization, J.R.; methodology, P.G.-S., L.G. and P.A.-M.; software, J.R.; validation, L.G. and P.A.-M.; formal analysis, P.G.-S.; data curation, P.G.-S.; writing--original draft preparation, J.R.; writing--review and editing, L.G. and P.A.-M.; All authors have read and agreed to the published version of the manuscript.  
This work was supported in part by the grant \"PID2019-109175 GB-C22\" funded by MCIN/AEI/10.13039/501100011033. This work was developed within the scope of the POCI-01-0247-FEDER-033990 (iNBRail) co-funded by FEDER, through the Operational Programme for Competitiveness and Internationalization (POCI), and POCI-01-0247-FEDER-033691 (HLS--Hybrid Log Shield) Projects, funded by FEDER funds through COMPETE 2020. This work was also funded by Base Funding--UIDB/04029/2020--of ISISE (Institute for Sustainability and Innovation in Structural Engineering) funded by national funds through the FCT/MCTES (PIDDAC).  
Not applicable.  
The authors declare no conflict of interest.