# Performance of Low-Height Railway Noise Barriers with Porous Materials
## 5 Methodology  
The following section describes the methodology used for the design of a low-height acoustic barrier for use in a railway environment. It presents the steps required to define the properties of the boundaries under analysis, the location of the receptors for a better evaluation of the acoustic performance of the solutions, the definition of the barrier geometry and the incorporation of porous material in order to increase its effectiveness. Figure 10 presents a schematic diagram of the steps developed in each section until the final result. The application of the 2D BEM model makes it possible to analyse how the presence of barriers next to the railway affects the propagation of sound waves. The adequate discretisation of the boundaries involved in the calculation is an essential step in the application of the numerical method. Figure 11 shows as an example the boundaries considered in the calculation, highlighting for a simple geometry the barrier description, represented by the midpoints of each boundary element. At this stage it is necessary to define the boundary conditions of the elements that are part of the acoustic medium only, which allows us to calculate the system of equations. Except for the porous material, which was defined by the coupling of the external and internal BEM, the other boundaries in contact with the acoustic medium have prescribed boundary conditions. For the vehicle and part of the acoustic barrier, a purely reflective condition was defined, meaning that the particle velocity along these boundaries is null. However, for the track (indicated in the figure as red dots), an impedance condition was prescribed, which allows the ballast acoustic absorption coefficient to be considered. Information gathered from Metro do Porto, SA, enabled the modelling of the elements that are part of the railway context, thus being as close as possible to the real scenario. Figure 11: Boundaries to be described and the respective mesh of boundary elements. Figure 10: Schematic representation of the methodology and results. This information allowed to set the distance between the track and the barrier, based on safety requirements related to track works. Considering this information, the distance between the external rail of the track and barrier was set at 1.225 m. To allow a better performance of the system, a curved barrier was subsequently defined in such a way that the reflection of the incident waves took place in the normal direction to its surface, thus sending more energy back to the origin and taking advantage of the sound-absorbing characteristics of the track. For that purpose, the time domain propagation of an acoustic wave was analysed, in order to better understand the shape of the incident wave front reaching the barrier, and trying to match the inner shape of the barrier to the shape of this wave. Figure 12a presents the time domain simulation of the acoustic wave at the location where the barrier is to be placed, also representing a curved low-height noise barrier with the inner face coinciding with the wave front. The final geometry of the barrier is shown in Figure 12b. In addition to the considerations described above, it was also necessary to take into account the absorption capacity of the ballast, since the development of the work presented here is based on the premise of an integrated barrier solution. Thus, the development of the barrier geometry sought to take advantage of the acoustic absorption properties of the railway track (ballast). Taking into account the results presented by [PERSON] [38] for the acoustic absorption coefficient for a 17 cm ballast layer, the surface impedance was calculated by Equation (14). Figure 13 shows the absorption curve for the diffuse field and the corresponding calculated surface impedance approximation for the calculated frequency range.