# Experimental Analysis and Simulation of a Porous Absorbing Layer for Noise Barriers
## 2 Materials and Methods
### Experimental Methods
#### 2.2.1 Macroscopic Parameters  
To make use of theoretical material models that allow simulating the acoustic behavior of granular porous materials, it becomes necessary to experimentally obtain a number of macroscopic parameters that characterize the porous material itself. For the purpose of this work, the required parameters were the porosity, the tortuosity, the airflow resistivity, and the standard deviation of the average pore size of the porous concrete samples.  
The porosity of the test specimens was determined, after drying the samples to constant mass (at \(70\pm 5\)\({}^{\circ}\)C), by weighing the test specimens on a hydrostatic balance and immediately after removing the excess water with a damp cloth. Porosity was determined experimentally using the water-saturation method (based on [38]) and this parameter is given by:  
\[\phi=V_{f}/V_{t} \tag{1}\]  
in which: \(V_{f}=\left(M_{\text{sat}}-M_{dry}\right)/\rho_{\text{water}}\) is the void volume of the porous concrete sample, and \(V_{t}\) is the sample total volume.  
For the determination of the samples' tortuosity, a laboratory experiment, based on the electrical conductivity of the sample and described in the work developed by [PERSON] and [PERSON] [39] (see Figure 5a), was implemented and used. In this technique, the test specimen is mounted in a PVC tube that is closed by two electrodes. Next, the tube is filled with a conductive liquid (in this study, salty water) and a power supply generates an electric field between the two electrodes at the ends. Electrical potential differences in the water and sample make it possible to determine the tortuosity of the porous concrete sample.  
Following this methodology, tortuosity is then given by the following expression:  
\[\alpha_{\infty}=\phi\frac{\sigma_{a}}{\sigma_{f}} \tag{2}\]  
where: \(\phi\) is the sample porosity; \(\sigma_{a}\) is the electrical resistivity of the sample saturated with the fluid, and \(\sigma_{f}\) is the electrical resistivity of the fluid.  
Using the method described in ISO 9053-2 [40], the airflow resistance and airflow resistivity of the porous concrete samples were determined. This procedure is based on the alternating airflow method, a condition of paramount relevance to ascertain the  
Figure 4: Porous concrete sample tested in the reverberant room. (**a**) Specim with approximate area of 10 m\({}^{2}\), (**b**) surface sample detail, and (**c**) sample detail in cross-sectional view, with porous concrete layer over a concrete structural layer.  
alternating component of the pressure in the test volume. The following equation defines the airflow resistivity:  
\[\sigma=\frac{R_{s}}{d} \tag{3}\]  
with \(R_{s}\) being the specific airflow resistance, of the test specimen, in Pa-s/m, and \(d\) being the thickness of the test specimen in the direction of flow (in m). Figure 5b shows the experimental apparatus used.  
The only parameter that has not been obtained by means of laboratory measurements was the standard deviation of the average pore size, \(\sigma_{p}\). Indeed, this is not a simple parameter to estimate in the laboratory, and the authors opted to adopt average values based on the work of [PERSON] et al. [36].