# A Simple Method to Estimate the In Situ Performance of Noise Barriers
###### Abstract
The final performance is quantified by a parameter known as Insertion Loss [5] (\(IL_{i}\), the subindex \(i\) stands for the particular one third octave band considered) which is nothing more than the difference between the sound pressure levels for the situation before installing (without) the screen and after installing (with) the screen, namely:  
\[IL_{i}=10\log\left(\frac{p_{i\ (without)}}{p_{i\ (with)}}\right)^{2} \tag{3}\]  
To allow the comparison between parameters, let us define a single parameter that quantifies the effect of the screen encompassing the whole frequency range of interest by means of a weighting, analogous to that already indicated when defining \(DL_{R}\) and \(DL_{SI}\), i.e.,:  
\[DL_{IL}=-10\log\left|\frac{\sum_{i=1}^{18}10^{0.1\ L_{i}}10^{-0.1\ L_{i}}}{ \sum_{i=1}^{18}10^{0.1\ L_{i}}}\right|\text{dBA} \tag{4}\]  
where \(L_{i}\) are the values of the normalized traffic noise spectrum, given by the standard EN 1793-3 [3], and \(IL_{i}\) is the insertion loss for the \(i\)-th one third octave band. Many simple formulae and charts to estimate the insertion loss of semi-infinite noise barriers can be found in the literature. The first attempt was published by [PERSON] [6], while [PERSON] [7] presented the best-known work. [PERSON] [7] performed an exhaustive experimental investigation validating his proposal, based on a single parameter, the Fresnel number. Subsequently, other authors proposed different approaches to the problem. Without being exhaustive, it is worth mentioning the works of [PERSON] [8] and [PERSON] and [PERSON] [9,10]. Another simple formula, in good agreement with [PERSON] [7] data, was proposed by [PERSON] [11] that has been included in the ISO 9613-2 [12]. Predictions obtained by these formulae and charts can deviate largely from experimental data in some cases. To solve this problem, numerical methods can be used to estimate the performance of noise barriers. Numerical methods such as the Finite Element Method (FEM), the Boundary Element Method (BEM), the Pseudo Spectral Time Domain (PSTD)method and the Finite Difference Time Domain (FDTD) method have been applied to the study of noise barriers. For convenience the authors have used the later method in this work. Several papers have demonstrated the suitability of this method for the study of sound propagation in the presence of acoustic screens [13; 14; 15; 16]. In any case, both approximate formulas and numerical simulations usually assume a high insulation, so that sound transmission through the barrier is not taken into account. For example, in [12] it is assumed that the surface density is at least 10 kg/m\({}^{2}\), which should ensure an overall insulation above 25 dBA. In this work, a simple model is proposed to obtain the insertion loss value in the case that the insulation of the material with which the screen is constructed allows significant sound transmission thorough the barrier. The remaining part of the paper is organized as follows: first, Section 2 concerns the proposal of the simple model to estimate the insertion loss of a noise barrier; in Section 3 the numerical method used to verify the proposed model is explained; Section 4 is devoted to the comparison between the proposed model and the numerical simulations; finally, the conclusions of the work are presented in Section 5.