# Experimental Analysis and Simulation of a Porous Absorbing Layer for Noise Barriers
###### Abstract
As suggested in ISO 10534-2 [17], using an impedance tube to evaluate the sound absorption coefficient with normal incidence is a low-cost and simple approach that yields relevant information. However, it has certain drawbacks because different sound incidence angles are typically present in real-world situations. The values for the material's surface impedance are also provided by this approach, though. The method suggested by ISO 354 [18] may be used to experimentally estimate the sample's sound absorption coefficient under diffuse field conditions. This experimental methodology is more onerous than the previous one, but presents the benefit of considering different sound incidence angles and uses a larger sample, which is a scenario closer to real application. Theoretical methods have been proposed by some authors in order to derive values of sound absorption in diffuse field conditions based on values determined with normal incidence approaches [19]. The transition from the sound absorption coefficient with normal incidence, obtained using an impedance tube, to the diffuse field coefficient can be made with London's equations [6; 19]. In these conditions, the medium has to be considered infinite and the propagation inside the medium is locally reactive. To describe the absorbing behavior of the porous materials under study, fluid-equivalent models, taking into account the complex bulk modulus and fluid-equivalent density, have been proposed [20; 21; 22; 23; 24]. Works related to the sound-absorption properties of granular materials have been developed by [PERSON] and [PERSON] [25], showing some expected values of the macroscopic parameters for materials incorporating expanded clay. [PERSON] et al. [26] and [PERSON] et al. [27] also presented works with granular materials for sound absorption purposes. These are of particular interest, revealing some estimated values of the relevant properties for expanded clay-based materials. Porous concrete, like most porous materials,is composed of pores of varying shapes and sizes. Although variation in the shape of the pores is less important, the statistical parameters of the pore size distribution can have a considerable effect on the acoustic properties of the porous media [28]. Based on these previous studies, it becomes possible to predict the behavior of porous materials through theoretical and numerical models [22; 28; 29]. In this study, the Horoshenkov-Swift [20] model has been used, since it is quite adequate to model granular materials. In that model, the porous materials are represented as equivalent fluids [23]. Four parameters--air-flow resistivity, tortuosity, open porosity, and the standard deviation of the pore size--are used in this model to describe how the porous material behaves in terms of sound absorption. Aside from modeling the acoustic behavior of the surface material of the barriers, it is of utmost importance to assess the global behavior of the acoustic barrier, in particular in what concerns the reduction in the environmental noise it provides for protected receivers. This topic has been addressed by numerous authors, using different methods. Indeed, engineering calculation methods, such as those proposed in the CNOSOS-EU methodology or in the ISO 9613-2 [30] can be used to estimate the insertion loss provided by specific noise barrier solutions, also taking into account the environmental setting in which it is implemented. More advanced methods, based on the use of numerical methods that solve the wave equation in the time or frequency domains, can also be used to have a more detailed and theoretically accurate view of the effect of these devices. Several works make use of advanced numerical methods, such as the Boundary Element Method (BEM), including some reference works, such as [31], and many publications by the co-authors of the present paper [32; 33; 34].