Performance of Low-Height Railway Noise Barriers with Porous Materials

  Citation: Lázaro, J.; Pereira, M.; Costa, P.A.; Godinho, L. Performance of Low-Height Railway Noise Barriers with Porous Materials. Appl. Sci. 2022,12, 2960. https://doi.org/ 10.3390/app12062960 Academic Editor: Massimo Garai Received: 4 February 2022 Accepted: 3 March 2022 Published: 14 March 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). applied sciences Article Performance of Low-Height Railway Noise Barriers with Porous Materials João Lázaro 1,*,† , Matheus Pereira 1,† , Pedro Alves Costa 1,† and Luís Godinho 2,† 1CONSTRUCT, Faculty of Engineering (FEUP), University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal; [email protected] (M.P.); [email protected] (P.A.C.) 2ISISE, Department of Civil Engineering, University of Coimbra, Pólo II, Rua Luís Reis Santos, 3030-788 Coimbra, Portugal; [email protected] *Correspondence: jlazar[email protected] † These authors contributed equally to this work. Abstract: Rail transport is the most sustainable transportation mode, with the lowest energy consumption and carbon footprint. However, the noise induced by railway traffic in urban regions is a significant drawback and several reports point out the risks and the amount of people suffering from direct exposure to railway noise. One of the most used mitigation measures for railway noise is the implementation of noise barriers. Although they offer a significant reduction in noise levels, their height makes people feel enclosed. Therefore, in the case of railway infrastructure, the solution to the problem may lie in the use of barriers with a lower height placed close to the railway track. As the noise-forming mechanisms are mainly located at the track level, placing the barrier in a position close to the track allows mitigating rail noise without causing the problems identified above for the population in the vicinity. The purpose of this paper is to illustrate the development of a barrier solution to be used in a railway context through numerical modelling with the Boundary Element Method (BEM). The solutions developed were placed close to the track and have a low height. The geometry was defined so as to direct the energy back to the track to take advantage of the acoustic properties of the ballast. The addition of a porous granular material on the inner face of the barrier allows the control of reflections between the vehicle body and the barrier, increasing its acoustic efficiency. Finally, considering the most efficient solution, the insertion loss in a network of receivers located 10 m away from the track is analysed in order to study the noise reduction levels in a place where human receivers are usually located. Keywords: railway noise; low height noise barriers; acoustic efficiency; noise mitigation 1. Introduction Railway transport is the most sustainable mode of transport, with the lowest energy consumption and carbon footprint compared to any other mode of transport. However, a report by the European Environment Agency (EEA) [ 1 ] from 2019 on this subject states that at the European level, rail noise is the second most dominant source, with an estimated 22 million people exposed to at least 55 dB during the day and night periods. On the same subject, however, with a different time horizon, the report by the European Environment Agency [ 2 ], whose aim is to project scenarios for the decade 2020 to 2030, states that the situation of the population’s exposure to environmental noise level in Europe will worsen in practically all areas responsible for current exposure levels. The projections suggest that in 10 years more than one million people will be exposed to excessive rail noise, both in urban centres and outside these agglomerations. In light of the above, a report of the World Health Organisation (WHO) Regional Office for Europe [ 3 ] is presented. This document highlights the effects of noise and incorporates a number of indications for certain policies that must be implemented in order to ensure health and well-being for people living with the most diverse forms of environmental noise. The WHO working group state Appl. Sci. 2022,12, 2960. https://doi.org/10.3390/app12062960 https://www.mdpi.com/journal/applsci Appl. Sci. 2022,12, 2960 2 of 18 that, for the daytime period, noise levels should be below 54 dB, and for the night-time period, they should not exceed 44 dB. Finally, it stresses that interventions to reduce noise levels and to comply with the limits indicated should focus on interventions at the track level, the improvement of rolling stock and the implementation of small noise barriers. Rail noise mitigation measures can be applied in three different locations and according to the environment and the level of noise pressure reduction that one wants to achieve [ 4 ]. Usually, the most widely deployed solutions are those that act at the level of the propagation path or at the level of the receivers. In places where housing density is high, the solutions that act on the path of propagation are more advantageous in economic terms [ 4 ]. Acoustic barriers are usually artificial and solid elements made of different types of material and placed in different positions, depending on the place to be protected. This noise mitigation solution has been widely adopted in the context of road noise mitigation, and there are several methods for designing these solutions. Acoustic barriers can have different operating principles depending on the material they are made of; i.e., they can work by reflecting acoustic waves and/or absorbing them. In general, the barriers are vertical elements between 3 m and 4 m high positioned along the road or railway. However, despite the inherent benefits of reducing noise and improving the quality of life of the population living nearby, this type of solution faces the reluctance of the populations living near the railway infrastructure. This situation is related to the size of the barrier, affecting the field of vision, causing a sense of imprisonment, loss of natural light or affecting air circulation. From another perspective, for those who travel on trains, complaints are also registered for similar reasons [ 5 – 7 ]. In order to tackle some of the negative points identified for the higher acoustic barriers, namely, being obstacles to one’s field of vision, the natural evolution of thinking has led to the creation of solutions whose working principle is similar to the one intended to be applied in the work presented in this document. The inherent advantage of low-height solutions is related to the positioning of this element. As the mechanisms of noise generation are mostly at the level of the rail [ 8 ], the placement of the barrier in a position close to the track allows the propagation of sound waves to be interrupted close to the source. The reduced height of these elements thus allows this positioning close to the source without constituting an obstacle to the field of vision of passengers and passers-by. Bearing this in mind, several authors have worked on this issue in order to develop a solution to mitigate the noise levels associated with rail traffic. The studies from the literature present solutions for the design of the barriers and for a more effective numerical modelling. Koussa [ 9 ] studied, both numerically and experimentally, the use of gabion walls as a form of mitigation. The results indicate that this solution can achieve up to 8 dB(A) of insertion loss. Jilibois [ 10 ] presents a full-scale model of an L-shaped barrier built with wooden panels and inside with absorbent fibrous material. Tests carried out by the experimental author revealed an attenuation of 10 dB(A). Nieuwenhuizen [ 11 ] showed that the Dutch calculation scheme for conventional barriers is reasonably applicable for low-height solutions. Finally, Kasess [ 12 ] proposes corrective functions that allow one to efficiently calculate complex geometries using BEM, in order to apply more complex geometries in noise mapping programs. To control the reflections between the car body and the noise barrier, an absorptive treatment is required. Fibers and foams are commonly used in passive noise control; however, for external applications, these materials require protection against environmental agents and structural reinforcement. Because of these requirements, the interest in sound absorptive solutions, such as porous concrete, made using consolidated lightweight and sustainable granular materials have increased over recent decades [ 13 – 21 ]. The investigation of the fluid-equivalent representation of porous concrete made with expanded clay has been shown to be relevant in the scientific community. Carbajo et al. [22] studied perforated concrete and highlighted the higher durability and the excellent strength-to-weight ratio of this solution. Pereira et al. [ 23 ] studied the influence of the water–cement ratio, the expanded clay grain size, and the sample thickness in the sound absorption behaviour, while Zolanvari [ 24 ] studied the fluid-equivalent representation of porous concrete using different aggregates. Appl. Sci. 2022,12, 2960 3 of 18 The modelling of the railway scenario has, for the reasons given, an important role to play in forecasting and creating measures to mitigate rail traffic-induced noise. The Boundary Element Method (BEM) is widely used to solve acoustic problems [ 7 , 25 ], and can be an excellent option to model the effect of mitigation measures. The versatility of this numerical method allows the creation of simply reflective acoustic barriers and/or the inclusion of porous material which acts as a sound absorption element, allowing the improvement of the performance on the barrier, mitigating the energy reflected between the vehicle and the barrier. In this article, the BEM will be used to solve an external acoustic problem, essentially to test the geometry of the barriers. In addition, a BEM formulation considering multiple material regions is implemented to allow the modelling of the effect of possible absorptive materials coupled to the noise barrier. Using this model, it becomes possible to model the absorptive materials using equivalent fluid theories, leading to a realistic representation of such media. To assess the capacity of the barrier, the insertion loss was used, i.e., the difference between the scenario with and without the barrier. Using the insertion loss allows the barrier to be assessed as a noise control measure placed in a location with specific characteristics. In this way, the IL calculation presents the actual losses over a wide range of frequencies, for any set of receivers, regardless of the scenario to be evaluated and mainly regardless of the type of material and geometry of the prototype. This paper’s structure is as follows: Section 2shows the experimental railway noise characterisation. Section 3presents the experimental procedure used to characterise porous concrete samples, allowing the fluid-equivalent theory representation. Section 4 presents the numerical formulation of the BEM used to model the described problem. Section 5presents the strategy used to define the barrier’s geometry and the parametric study of different noise barrier configurations. Then, Section 6shows the sound pressure levels predicted around the noise barrier, in the presence of the train, and the insertion loss results. Finally, Section 7summarises the main conclusions of this work. 2. Railway Noise Characterisation Noise induced by rail traffic has several sources with different characteristics. Despite the various components of railway noise, the noise generated by the wheel-rail interaction plays the most important role in noise generation. The variable that most conditions the sound pressure levels and the origin of the noise is the running speed of the vehicles as illustrated in Figure 1, where the main noise sources are defined according to the train speed. 10 20 50 100 200 300 400 Speed [km/h] 70 80 90 100 110 120 130 Sound Pressure Level [db(A)] Traction noise Rolling noise Aerodynamic noise Total Figure 1. Evolution of the contribution of the different sources according to the speed of circulation (adapted from [26]). The complete study of the railway noise problem involves examining several dimensions, namely generation, propagation and reception. Therefore, the definition of measures Appl. Sci. 2022,12, 2960 4 of 18 aimed at its mitigation requires a clear understanding of these dimensions. Consequently, it can be concluded that only the characterisation of noise in different types of scenarios, with different running speeds, vehicle types, track types and urban meshes allows a clearer view of the noise levels involved and especially which variations are associated with the different traffic conditions mentioned above. In this context, the main objective of the experimental characterisation is to clarify the noise levels associated with the traffic under analysis. The systematisation of maximum noise levels, as well as the frequency content involved, relating them to specific conditions, makes it possible to better define mitigation measures to deal with the noise content identified. In this work, a characterisation campaign has been performed, in which the acquisition of the signal was made using four microphones Behringer type ECM 8000, connected to a Focusrite Sclarett 4Pre USB for the signal acquisition, as is shown in Figure 2. Postprocessing of the data was performed in Matlab using the ITA-Toolbox functions [ 27 ]. Figure 2. Experimental setup for the acoustic signal acquisition; ( 1 ) Behringer ECM 8000 microphone, (2) computer, (3) Focusrite Sclarett 4Pre USB acquisition unit. The placement of the microphones was defined to allow acquiring the noise in the closest possible place to the source, and at successively larger distances from the source, thus allowing to study in a complete way the propagation of the sound waves. Figure 3shows the setup used for the measurement, with the distance between microphones and position relative to the track. Figure 4shows photos taken at the measurement site, in scenarios with and without vehicle, respectively. As can be seen from the illustrations, the microphone called M1 is very close to the source, while the others, M2, M3 and M4, occupy a relative position in accordance with places where pedestrians circulate. Before each measurement campaign, verification was performed making use of a BK 4231 microphone calibrator. Since some of the microphones are positioned close to the railway, some influence of potential air-flow generated by the train passage will inevitably be included in the registered responses. However, the registered acoustic signals are still relevant to better understand the acoustic responses at positions close to the railway, since sound pressure levels at such positions greatly helps to define effective mitigation measures to tackle the exposure of pedestrians and sensible receivers. Figure 3. Experimental setup configuration. Appl. Sci. 2022,12, 2960 5 of 18 (a) Appl. Sci. 2022,1, 0 5 of 19 (a) (b) Figure 4. Photographs of the in situ experimental characterisation. ( a ) Photograph of the microphones on site. (b) Photograph of the measurement setup in the presence of the vehicle. The sound pressure levels (SPL) collected in a ballast track context in each of the four available microphones are shown below, in Figure 5. From the experimental characterisation it was possible to collect data from numerous passages with different running speeds. In order to summarise the data collected, the noise levels corresponding to the two recorded speed (respectively, 84 km/h and 78 km/h) recorded are presented. The data are presented in one-third octave bands and it is intended to highlight from among the various receivers the most significant spectral content that will serve as a basis for the numerical simulations explained in the previous sections. 20 40 60 100 200 400 1k 2k 4k 6k 10k 20k Frequency [Hz] 0 10 20 30 40 50 60 70 80 90 100 Sound Pressure Level [dBA] Microphone 1 (M1) V=84km/h V=72km/h (a) 20 40 60 100 200 400 1k 2k 4k 6k 10k 20k Frequency [Hz] 0 10 20 30 40 50 60 70 80 90 100 Sound Pressure Level [dBA] Microphone 2 (M2) V=84km/h V=72km/h (b) 20 40 60 100 200 400 1k 2k 4k 6k 10k 20k Frequency [Hz] 0 10 20 30 40 50 60 70 80 90 100 Sound Pressure Level [dBA] Microphone 3 (M3) V=84km/h V=72km/h (c) 20 40 60 100 200 400 1k 2k 4k 6k 10k 20k Frequency [Hz] 0 10 20 30 40 50 60 70 80 90 100 Sound Pressure Level [dBA] Microphone 4 (M4) V=84km/h V=72km/h (d) Figure 5. Records of measured sound pressure levels; in blue a vehicle operating at 84 km/h; in yellow a vehicle operating at 72 km/h. ( a ) First microphone; ( b ) Second microphone; ( c ) Third microphone; (d) Fourth microphone. Sound pressure levels (SPL), presented in Figure 5are filtered to take into account the response of the human ear, and thus are presented in dB(A). By analysing the onethird octave bands presented, it is concluded that the most prevalent frequency content responsible for the highest noise levels is between 200 Hz and 4000 Hz, i.e. the frequency interval between the two discontinuous black lines in each of the third octave bands. This information has been the basis for the numerical modelling presented later in this paper, (b) Figure 4. Photographs of the in situ experimental characterisation. ( a ) Photograph of the microphones on site. (b) Photograph of the measurement setup in the presence of the vehicle. The sound pressure levels (SPL) collected in a ballast track context in each of the four available microphones are shown below, in Figure 5. From the experimental characterisation it was possible to collect data from numerous passages with different running speeds. In order to summarise the data collected, the noise levels corresponding to the two recorded speed (respectively, 84 km/h and 78 km/h) recorded are presented. The data are presented in one-third octave bands and it is intended to highlight from among the various receivers the most significant spectral content that will serve as a basis for the numerical simulations explained in the previous sections. 20 40 60 100 200 400 1k 2k 4k 6k 10k 20k Frequency [Hz] 0 10 20 30 40 50 60 70 80 90 100 Sound Pressure Level [dBA] Microphone 1 (M1) V=84km/h V=72km/h (a) 20 40 60 100 200 400 1k 2k 4k 6k 10k 20k Frequency [Hz] 0 10 20 30 40 50 60 70 80 90 100 Sound Pressure Level [dBA] Microphone 2 (M2) V=84km/h V=72km/h (b) 20 40 60 100 200 400 1k 2k 4k 6k 10k 20k Frequency [Hz] 0 10 20 30 40 50 60 70 80 90 100 Sound Pressure Level [dBA] Microphone 3 (M3) V=84km/h V=72km/h (c) 20 40 60 100 200 400 1k 2k 4k 6k 10k 20k Frequency [Hz] 0 10 20 30 40 50 60 70 80 90 100 Sound Pressure Level [dBA] Microphone 4 (M4) V=84km/h V=72km/h (d) Figure 5. Records of measured sound pressure levels; in blue a vehicle operating at 84 km/h; in yellow a vehicle operating at 72 km/h. ( a ) First microphone; ( b ) Second microphone; ( c ) Third microphone; (d) Fourth microphone. Sound pressure levels (SPL), presented in Figure 5are filtered to take into account the response of the human ear, and thus are presented in dB(A). By analysing the onethird octave bands presented, it is concluded that the most prevalent frequency content responsible for the highest noise levels is between 200 Hz and 4000 Hz, i.e., the frequency interval between the two discontinuous black lines in each of the third octave bands. This information has been the basis for the numerical modelling presented later in this paper, Appl. Sci. 2022,12, 2960 6 of 18 allowing the definition of the frequency range and content that needs to be mitigated by the noise barrier. 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. Table 1. Materials proportions in weight (kg) of the produced samples. Grain Size (mm) Aggregate (%) Cement (%) Water (%) 0–2 43.96 37.36 18.68 Several approaches can be used to characterise acoustic absorbing materials, such as those described for example in Ciaburro et al. [ 28 ], Arenas et al. [ 29 ] or del Rey 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 Utsuno 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 00 , 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 d1 is the sample thickness, and D is the air cavity thickness. Figure 6. Schematical representation of the experimental two-cavity method (retrieved from [23]). 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, ˜ Zc , and the complex wave number, ˜ kc , can be determined, respectively, by the following equations, ˜ Zc=s˜ Zs1˜ Zs2Z1−Z0 1−Z1Z0 1˜ Zs1˜ Zs2 Z1−Z0 1−˜ Zs1˜ Zs2, (1) Appl. Sci. 2022,12, 2960 7 of 18 ˜ kc=j 2d1 ln˜ Zs1+˜ Zc ˜ Zs1−˜ Zc ˜ Zs2+˜ Zc, (2) where d1 is the sample thickness, ˜ Zs1 is the complex surface impedance measured with the first air cavity depth D, and ˜ Zs2 is the complex surface impedance measured with the second air cavity depth D 0 . Z1 and Z0 1 denote the acoustic impedance of each air cavity, Z1=−jρ0c0cot(k0D), (3) Z0 1=−jρ0c0cotk0D0. (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 7shows the porous concrete samples and sound absorption curves between samples with different thicknesses. Each curve corresponds to the average between the two samples of same thickness, respectively, 4, 6 and 8 cm. It was observed that the increase in the thickness produces a shift in the sound absorption coefficient curve towards low frequencies. (a) (b) Figure 7. Sound absorption behaviour of porous concrete. ( a ) Porous concrete built samples. ( b ) Average of the sound absorption coefficient for three different thicknesses: 4, 6, and 8 cm. (retrieved from [23]). To predict the acoustic behaviour of porous concrete with different thicknesses and to represent these materials as the fluid-equivalent theory, the Horoshenkov and Swift model was used [33]. This model was derived assuming rigid frame granular media with a log-normal pore size distribution to predict the the characteristic impedance, ˜ Zc , and the wave number, ˜ kc , of porous concrete samples. It considers four macroscopic parameters to determine the acoustic behaviour: air flow resistivity, σ , open porosity, φ , tortuosity, τ , and the standard deviation of the pore size, σp. The inverse technique was performed using a genetic algorithm in which the objective function was based on the quadratic sum of errors between the analytical and experimental data, along a frequency range with n f discrete frequency values, OF(ω) = n f ∑ i=1αana −αexp, (5) where αana is the absorption coefficient obtained from the Horoshenkov and Swift model [ 33 ], and αexp is the experimental absorption coefficient. These four macroscopic parameters were previously obtained in [ 23 ], and are presented in Table 2. The open Appl. Sci. 2022,12, 2960 8 of 18 porosity was the only macroscopic parameter experimentally determined, using the water saturation method. Table 2. Macrospic parameters obtained for the porous concrete studied samples. Airflow Resistivity σ [Ns/m4]Open Porosity φ[-] Tortuosity α∞[-] Standard Deviation of the Pore Size σp [-] 3896.06 0.46 1.89 0.25 Figure 8shows a comparison between the complex properties using the presented macroscopic parameters and those experimentally obtained through the two-cavity method for a sample with 4 cm. As observed in [ 34 ], an excellent agreement can be observed between the experimental data and the semi-phenomenological prediction, allowing us to represent and predict the porous concrete behaviour for different samples thicknesses and geometries. 200 400 600 800 1k 1.2k 1.4k 1.6k Frequency [Hz] - 1000 - 500 0 500 1000 1500 2000 Characteristic impedance [Pa.s/m] Real Two-Cavity Method Imag. Two-Cavity Method Real Horoshenkov-Swift Model Imag. Horoshenkov-Swift Model (a) 200 400 600 800 1k 1.2k 1.4k 1.6k Frequency [Hz] - 20 0 20 40 60 80 Wavenumber [rad/m] Real Two-Cavity Method Imag. Two-Cavity Method Real Horoshenkov-Swift Model Imag. Horoshenkov-Swift Model (b) Figure 8. Comparison between the experimental characterisation and the semi-phenomenological representation n. (a) Characteristic impedance, ˜ Zc. (b) Wave number, ˜ kc(retrieved from [34]). 4. Numerical Modelling The Boundary Element Method, BEM, was used to model the acoustic problem since it allows analysing complex geometries without the need to describe the whole propagation medium, and allows us to solve problems with both infinite or limited domains [6]. In the frequency domain, the problem is governed by the Helmholtz equation, ∇2p+k2p=δ(r1−r0). (6) where pis the acoustic pressure and k is the wave number. The development of Equation (6) yields Equation (7), which allows the acoustic problem to be solved by integration along the defined boundaries. Thus, solving Equation (7) can be defined as approximating the solutions for each boundary element j. N ∑ j=1 v(x,~ n)ZΓiρωG(x,x0)dΓj+ N ∑ j=1 p(x)ZΓH(x,x0,~ n)dΓj+cpp(x0)=pinc x0,xf(7) Usually, the matrix formulation is used as the preferred means to carry out the Boundary Element Method [35,36], Cp−Hp=iρ0ωGv+pinc. (8) Appl. Sci. 2022,12, 2960 9 of 18 where pand vare the acoustic quantities to be calculated—the pressure and velocity of particles according to the surface—and pinc is the acoustic pressure in the free field due to a source located on the domain. The G and H matrices are fully populated matrices. Finally, Cis a diagonal array whose values depend on the collocation point. It is common to add the matrix Cand H, writing the previous equation in its most simplified form, Hp=iρ0ωGv+pinc. (9) The formulation presented up to this point only allows the study of the interaction of the boundaries with a single external medium, in this case, the acoustic medium. In order to represent the porous materials that are to be placed on the barrier and that will be studied in this document, it is necessary to extend the method to include the simulation of porous materials as fluid-equivalents. In other words, it is necessary to simulate more than one propagation medium, with different properties. Therefore, it is necessary to define each of the media and ensure that in the interfaces between them there is coupling between the pressures and normal velocity. The systematisation of this problem involves the definition of the equations presented in Equation (7) for each propagation domain and the boundaries valid for both the external, Ωexterior and internal domain, Ωi, as illustrated in Figure 9. Figure 9. Representation of the coupled interior/exterior problem. The coupling between domains is achieved by ensuring equilibrium and continuity conditions at the shared boundaries of the domains [37]. pΩext =pΩint (10) 1 iωρΩext ∂pΩext ∂n=−1 iωρΩn ∂pΩint ∂n(11) The calculation process involves solving a system of equations taking into account the equations defined for the two mediums under consideration (Equation (7)). The system of equations can be expressed as (iωρΩext GΩext {˜ v}+HΩext {ˆ p}={¯ pinc},f or air −iω˜ ρΩjGΩj{¯ v}+HΩj{¯ p}=0, f or porous material (12) Once the acoustic variables at the defined boundaries are known, the acoustic pressure at the external receivers is equal to the sum of the incident acoustic pressure and the acoustic pressure resulting from the interaction of the boundaries with the acoustic medium, as shown in Equation (13). pT=pinc +pS(13) Appl. Sci. 2022,12, 2960 16 of 18 Figure 20. Insertion loss maps for the curved noise barrier with absorptive layer for frequencies 315 Hz, 400 Hz, 500 Hz, 630 Hz, 800 Hz and 1000 Hz ( a – f ), with the presence of the receivers (black dots) used to calculate mean IL (Figure 18). Figure 21. Insertion loss maps for the curved noise barrier with absorptive layer for frequencies 1250 Hz, 1600 Hz, 2000 Hz, 2500 Hz, 3150 Hz and 4000 Hz ( a – f ), with the presence of the receivers (black dots) used to calculate mean IL (Figure 18). 7. Conclusions This paper presents the development of a low-height acoustic barrier to be used close to the noise source in a railway environment. The development of the solution is composed by two distinct phases, namely the optimisation of the barrier geometry and the integration of a porous material in order to increase the acoustic performance of the solution. Taking advantage of sound pressure level records acquired in the railway environment in the metropolitan area of Porto, it was possible to define the most important frequency content and thus design a solution whose performance was superior in that frequency range. The numerical modelling and study of the various solutions were carried out by applying a BEM formulation with multiple regions, simulating the porous material as an equivalent fluid and thus incorporating its acoustic absorption properties. The parametric study presents the methodology for sizing the curved barrier. Through the simulation of a sound wave, the inner face of the barrier was constructed so that it coincides with the shape of the incident wave front coming from the source. Thus, the reflection normal to the propagation direction is favoured and, as such, more energy is sent in the direction of the noise source and the railway. In this way, an integrated solution was built taking Appl. Sci. 2022,12, 2960 17 of 18 advantage of the acoustic absorption capacity of the track to absorb the energy sent back. In a complementary manner, a porous concrete layer was added, which on the one hand has a good acoustic absorption capacity and on the other hand guarantees the durability required for solutions used outdoors. The main purpose of the porous material is to absorb part of the energy arising from the reflections between the barrier and the vehicle, ensuring that the energy that is not sent back to the track can be sent in the direction of the external receivers. The results presented show the clear improvement achieved by using porous material as a means of absorbing part of the energy in detriment of purely reflective solutions. The curved solution with porous material presents an IL in the defined receivers higher than 10 dB in all the calculated frequency range; for some frequencies the IL value is even higher than 15 dB, with the maximum registered in the frequency 3150 Hz where the IL value is higher than 25 dB. In this way, the presented solution appears to be an useful element for the reduction in train-induced noise, guaranteeing an effective mitigation. In addition, due to its low-height, this solution does not represent a visual obstacle, as is usual for noise barriers, but it still effectively reduces noise levels at the receivers of interest. Author Contributions: Conceptualisation, J.L., M.P., P.A.C. and L.G.; methodology, J.L., M.P., P.A.C. and L.G.; software, J.L., M.P. and L.G.; validation, J.L., M.P., P.A.C. and L.G.; formal analysis, J.L., M.P., P.A.C. and L.G.; investigation, J.L. and M.P.; resources, J.L., M.P., P.A.C. and L.G.; data curation, J.L. and M.P.; writing—original draft preparation, J.L. and M.P.; writing—review and editing, P.A.C. and L.G.; visualisation, J.L., M.P., P.A.C. and L.G.; supervision, P.A.C. and L.G.; project administration, P.A.C. and L.G.; funding acquisition, J.L., P.A.C. and L.G. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by Base Funding—UIDB/04708/2020 and Programmatic Funding—UIDP/04708/2020 of the CONSTRUCT—Instituto de I&D em Estruturas e Construções— funded by national funds through the FCT/MCTES (PIDDAC); Base Funding—UIDB/04029/2020— of ISISE (Institute for Sustainability and Innovation in Structural Engineering) funded by national funds through the FCT/MCTES (PIDDAC); Project POCI-01-0247-FEDER-033990 funded by FEDER funds through COMPETE2020—Programa Operacional Competitividade e Internacionalização (POCI); National funds (PIDDAC) through FCT/MCTES; Individual Grant: SFRH/BD/148367/2019. Conflicts of Interest: The authors declare no conflict of interest. References 1. EEA (European Environment Agency). Environmental Noise in Europe—2020; Technical Report; EEA (European Environment Agency): Copenhagen, Denmark, 2020; ISBN 9789294802057. 2. Blanes, N.; Marin, A.; Ramos, U.M.J. 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