# Performance of Low-Height Railway Noise Barriers with Porous Materials
## 3 Experimental Characterisation of Porous Concrete  
In the porous concrete material, granules are usually distributed differently from the what is observed in fibrous materials by following a log-normal pore distribution, resulting in smaller porosity and higher tortuosity. The absorption coefficient of these materials depends on the size of the pores, the porosity, the tortuosity and the thickness of the material sample. Six samples of porous concrete were produced using expanded clay aggregates, with grain size of 0-2 mm. All samples were prepared with 10.1 cm of diameter and thickness of 4, 6 and 8 cm, being these procedure previously presented in [23]. The sample proportions in weight (kg) are presented in Table 1.  
Several approaches can be used to characterise acoustic absorbing materials, such as those described for example in [PERSON] et al. [28], [PERSON] et al. [29] or [PERSON] et al. [30]. Here, an experimental experimental procedure based on the use of an impedance tube was used to characterise the normal incidence acoustic properties of the porous concrete samples. As described in ISO 10534-2 [31], these properties can be obtained from the transfer function between two microphones. To obtain the intrinsic acoustic properties of the porous concrete samples, the Two-Cavity Method proposed by [PERSON] et al. [32] was used. The impedance tube used has a circular cross-section of 10.1 cm diameter, the cut-off frequency being approximately 1600 Hz for the chosen microphone spacing. A white noise signal was used to excite the speaker from the analyser, OR 34 Compact Analyzer, the sound pressure was measured using two microphones B&K Type 4188 1/2'', positioned at 16 cm and 10 cm from the sample surface, and the pressure data were post-processed in Matlab, to obtain both the surface impedance and the sound absorption. A schematic representation of the experimental setup is presented in Figure 6, where the term \(d_{1}\) is the sample thickness, and D is the air cavity thickness. The two-cavity method is based on two measurements of the same sample through the ISO 10534-2 procedure. Each measurement uses a different air cavity depth, D, between the sample and the rigid termination. The complex characteristic impedance, \(\tilde{Z}_{c}\), and the complex wave number, \(\tilde{k}_{c}\), can be determined, respectively, by the following equations,  
\[\tilde{Z}_{c}=\sqrt{\frac{\tilde{Z}_{s1}\tilde{Z}_{s2}\big{(}Z_{1}-Z_{1}^{ \prime}\big{)}-Z_{1}Z_{1}^{\prime}\big{(}\tilde{Z}_{s1}\tilde{Z}_{s2}\big{)}} {\big{(}Z_{1}-Z_{1}^{\prime}\big{)}-\big{(}\tilde{Z}_{s1}\tilde{Z}_{s2}\big{)} }}\,, \tag{1}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Grain Size (mm)** & **Aggregate (\%)** & **Cement (\%)** & **Water (\%)** \\ \hline
0–2 & 43.96 & 37.36 & 18.68 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Materials proportions in weight (kg) of the produced samples. Figure 6: Schematical representation of the experimental two-cavity method (retrieved from [23]). \[\tilde{k}_{c}=\frac{\mathrm{j}}{2\,d_{1}}\ln\left(\frac{\tilde{Z}_{s1}+\tilde{Z}_{c }}{\tilde{Z}_{s1}-\tilde{Z}_{c}}Z_{s2}+\tilde{Z}_{c}\right), \tag{2}\]  
where \(d_{1}\) is the sample thickness, \(\tilde{Z}_{s1}\) is the complex surface impedance measured with the first air cavity depth D, and \(\tilde{Z}_{s2}\) is the complex surface impedance measured with the second air cavity depth D\({}^{\prime}\). \(Z_{1}\) and \(Z_{1}^{\prime}\) denote the acoustic impedance of each air cavity,  
\[Z_{1}=-\mathrm{j}\rho_{0}c_{0}\cot(k_{0}\mathrm{D}), \tag{3}\]  
\[Z_{1}^{\prime}=-\mathrm{j}\rho_{0}c_{0}\cot(k_{0}\mathrm{D}^{\prime}). \tag{4}\]  
The measurements were performed for a rigid termination and an air cavity depth D = 2 cm. This option preserves the method's validity and allows minimising the number of measurements for each sample to determine both its sound absorption coefficient and its intrinsic acoustic properties. Figure 7 shows the porous concrete samples and sound absorption curves between samples with different thicknesses.