# A Simple Method to Estimate the In Situ Performance of Noise Barriers
## 4 Model Validation
### Application to Traditional Noise Barriers  
Initially, the application of the simple model to traditional barriers is considered. For brevity, only the results for a 3 m-high acoustic screen, with the measurement microphones placed at a height of 1.5 m and a distance to the screen of 4 m, will be shown. To simulate the 3D conditions, the results obtained for larger distances are averaged, as described by [19; 20], in order to correctly simulate an incoherent line source based on several two-dimensional coherent line source simulations. The results of the numerical simulations carried out are illustrated in Figure 4, for the case of the model shown in Figure 2 (conventional noise barrier). For clarity, Figure 4 includes only four representative values of the noise barrier's sound reduction index, R (6, 12, 18 dB and the perfectly rigid and reflective case, R = \(\infty\)), with constant values of \(R\) assigned to all one third octave bands. In Figure 4, the results of the IL index as a function of the frequency, for different values of noise reduction, \(R\), are shown, considering for each case the same value of \(R_{i}\) for all the analysed frequencies. The first thing that can be seen is the good agreement between the values obtained by means of the \"modified FDTD\" model and by the simple model proposed in this paper (Equation (5)). The agreement is not so good in the low frequency range where the assumption of incoherence is less likely to be adequate. However, the most interesting conclusion is the smaller difference values of insertion loss, \(IL\), when compared with the corresponding \(R\) values, for the less insulating noise barriers. This result is logical, taking into account that the parameter \(IL\) not only considers the transmitted wave but also the diffracted wave, which considerably reduces the performance of the noise barrier, mainly for the higher ins  
Figure 3: Schematic representation of the locations of the particle velocities and acoustic pressures grid nodes near the noise barrier in the modified FDTD simulation model, for the simulation of sound transmission through the noise barrier. an infinite value of \(R\) is considered, the \(IL\) index is maximized, reaching a value around 20 dB for higher frequencies. This means that, no matter how much the acoustic insulation of a noise barrier is increased (thus decreasing the transmission through them) their final performance, given by \(IL\), reaches a maximum and saturates. This trend is more clearly seen in Figure 5, where the relationship between the global \(IL\) (\(DL_{IL}\)) and \(DL_{R}\) indexes is represented. In this figure, the dashed line represents the global insulation of the noise barrier, given by \(DL_{R}\) index (when diffraction at the top of the noise barrier is not taken into account). The continuous line indicates the variation in the global \(IL\) index with the increase in the acoustic insulation (\(DL_{R}\)). Again, one can see that the saturation in the global acoustic performance of the noise barrier is around 15 dB, although the \(DL_{R}\) value still increases. That means that the final performance of the noise barrier should be estimated with the global \(IL\) index and not the acoustic insulation (\(DL_{R}\)). For better comparison of the results, the numerical values and the absolute differences are provided in Table 1. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{\(\mathbf{DL_{R}}\)} & \multirow{2}{*}{\(\mathbf{DL_{IL}}\) (\(\mathbf{dBA}\)) FDTD} & \multirow{2}{*}{\(\mathbf{DL_{IL}}\) (\(\mathbf{dBA}\)) Simplified Proposed} & \multirow{2}{*}{\(\mathbf{Absolute Difference}\) (\(\mathbf{dBA}\))} \\ \cline{1-1}  & & **Simulation** & **Model (Equation 5)** & \\ \hline
6.0 & 5.9 & 5.6 & 0.3 \\ \hline
12.0 & 11.0 & 10.5 & 0.5 \\ \hline
18.0 & 14.3 & 13.8 & 0.6 \\ \hline
24.0 & 15.7 & 15.2 & 0.4 \\ \hline
30.0 & 16.0 & 15.7 & 0.3 \\ \hline
35.0 & 16.0 & 15.8 & 0.2 \\ \hline \hline \end{tabular}
\end{table}