**Investigation of Acoustic Properties on Wideband Sound-Absorber Composed of Hollow Perforated Spherical Structure with Extended Tubes and Porous Materials**

### **Dengke Li 1,2,\*, Zhongcheng Jiang 2, Lin Li 3, Xiaobo Liu 2, Xianfeng Wang <sup>2</sup> and Mu He <sup>4</sup>**


Received: 4 November 2020; Accepted: 11 December 2020; Published: 16 December 2020

**Abstract:** Traditional porous media such as melamine foam absorb sound due to their three-dimensional porous struts. However, the acoustic properties at low frequencies are greatly related to its thickness. In this paper, a novel type of thin and lightweight sound absorber composed of melamine foam and hollow perforated spherical structure with extended tubes (HPSET) is introduced to enhance the sound absorption performance at low frequencies. A theoretical model for the normal absorption coefficient of the HPSET with melamine foam is established. Good agreements are observed between the simulated and the experimental results. Compared with the virgin melamine foam, the proposed absorber can greatly improve the low-frequency sound absorption and retain the mid- to high-frequency sound absorption, while the thickness of the proposed absorber is less than 1/28 of the wavelength.

**Keywords:** hollow perforated spherical structure with extended tubes; low frequency sound absorption; melamine foam; wideband sound absorber

#### **1. Introduction**

Melamine foams are porous materials widely used in the transport and civil engineering industries for their remarkable properties of sound absorption and special abilities to withstand extreme environments (such as heat insulation, fire protection and environmental protection). At present, the research on this type of foam material has produced a series of papers, and the manufacturing process is protected by a large family of patents [1,2]. However, in practical noise applications, such as rail locomotive vehicles, the internal noise of the vehicle is mainly dominant in the low-frequency noise of 100–1000 Hz. If a single layer of melamine foam is used to absorb the low frequency noise inside the cab, the foam materials usually require a relatively large space and material thickness [3]. Many researches focused on the optimization of the pore size of porous foams, since the sound energy dissipation mechanism of porous materials originates from the visco-thermal dissipation of micropores. Perrot [4] studied the sound absorption properties of the open-cell foam metal structure based on the Kelvin structure. He pointed out that the pore size directly determines the flow resistivity of the material. When the pore size is small, the flow resistivity of the material increases, and the sound

wave is not easy to enter the material; when the pore structure is large, the flow resistivity is very small, and the large-size micropores cannot provide sufficient damping for the incident sound waves. Later, Trinhet et al. [5] studied the sound absorption of polyurethane foam with membrane in the pore network, and their results show that decreasing the openness of the membrane could enhance sound absorption performances of the material in low frequency ranges. Park et al. [6,7] built a multiscale numerical model to optimize the sound absorption properties of PU foams, they found that the acoustic damping at low frequencies could be improved with an optimum mean cell size and cell openness.

Optimization of the geometrical parameters of the porous structure could improve the sound absorption of the porous foams to some extent; however, their first sound absorption peak frequency is still determined by its quarter wavelength resonance frequency. In recent years, much attention has been paid on developing meta-acoustic materials to enhance the low frequency absorbing performance. Kidner and Fuller experimentally investigated the use of heterogeneous (HG) acoustic materials to improve low frequency insertion loss of blankets [8]. An active-passive method, which, based on FOAM-PVDF structure, was also introduced by Fuller to enhance the transmission loss of foam materials [9]. Fuller and his colleagues further [10] used meta-materials that are composed of small masses and poro-elastic media to improve the sound absorption of the porous materials at low frequencies. Based on numerical analyses of the finite element method, Groby et al. [11,12] conducted several studies on periodic inclusions embedded in the porous layer to improve the sound absorption bandwidth. However, their effective sound absorption bandwidth of the composite absorber still lies in the mid-or high-frequency range (>1000 Hz).

Relying on the multi-layer resonance system, the sound absorption bandwidth of porous media could be significantly broadened by using the perforated plates. Lin [13] studied the structure of the sound-absorbing material behind the micro-perforated plate, and their results revealed that, when the sound-absorbing material occupied the entire cavity, the combined structure had a broader sound absorption band. Li et al. [14] studied theoretically and experimentally the sound absorption coefficient of sound-absorbing materials combined with micro-perforated plates by using the transfer matrix method. They analyzed influences of different placement of sound-absorbing materials on the sound absorptive performance for the composite absorber, and proposed a wideband sound-absorbing configuration in which the sound-absorbing material was placed in front of the micro-perforated plate. However, the composite absorber still requires a large installation space.

More recent work has laid foundations of improving the low frequency sound absorption performance by using extended tube resonators [15–19]. Li et al. [16–18] presented a kind of multiple extended tube resonators to enhance the low frequency range from 100 to 1600 Hz in a constrained space of 100 mm. In order to further improve the low frequency sound absorption of a thin layer melamine foam below 500 Hz, a new type of resonant absorber comprised of hollow perforated spherical structure with extended tubes is introduced in the present work. Hence we theoretically and experimentally investigated the low sound absorption performance of the combined absorber, and found that the coupling between the Helmholtz resonance and the quarter wavelength resonance shows a great potential to ameliorate sound absorptive performance of a traditional porous foam at low- and mid- frequencies. Meanwhile, the sound absorption in low frequency range could be greatly enhanced by tuning the tube parameters. Our proposed sound absorber reaches the same sound absorption performance of PPETs-PSAM [17,18], while it is more practical in noise control application since this device is simply made of a thin and lightweight hollow perforated spherical structure, and could be easily combined with porous foams. In what follows, we firstly conduct a theoretical analysis of the performance of combined absorber in Section 2, and then focus on parametric studies in Section 3. Section 4 is aimed at experimental verifications by impedance tube. Finally, Section 5 draws some conclusions.

#### **2. Theoretical Analyses**

#### *2.1. Impedance Model of Melamine Foam*

Following the well-known JCAL model proposed by Johnson et al. [20] and Lafarge et al. [21], the equivalent density ρ*eq*(ω) and modulus *Keq*(ω) of the porous fluid are

$$\rho\_{\text{eq}}(\omega) = \frac{\alpha\_{\text{os}}\rho\_0}{\Phi} \left[ 1 - j \frac{\sigma \Phi}{\omega \rho\_0 \alpha\_{\text{os}}} \sqrt{1 + j \frac{4 \alpha\_{\text{os}}^2 \eta \rho\_0 \alpha \nu}{\sigma^2 \Lambda^2 \phi^2}} \right] \tag{1}$$

*Keq*(ω) = <sup>γ</sup>*P*0/<sup>φ</sup> γ − (γ − 1) <sup>1</sup> <sup>−</sup> *<sup>j</sup>* <sup>φ</sup><sup>η</sup> *k*0 *Npr*ρ0ω 1 + *j* 4*k*<sup>0</sup> 2*Npr*ρ0ω ηΛ<sup>2</sup> φ<sup>2</sup> <sup>−</sup><sup>1</sup> (2)

where ω is the angular frequency, ρ<sup>0</sup> is the density of the air, η is the viscosity of the air, σ is the airflow resistivity, *P*<sup>0</sup> is the mean ambient pressure, φ is the porosity of the material considered, *Npr* is the Prandtl number of the air, and γ = *Cp*/*Cv* is the specific heat ratio, in which *Cp* and *Cv* are the specific heat capacities at constant pressure and at constant volume respectively. The JCAL model involves six characteristic parameters: the static viscous permeability *k*0, the porosity φ, the tortuosity α∞, the viscous characteristic length Λ, the static thermal permeability *k*<sup>0</sup> and the thermal characteristic length Λ'.

According to formula (1) and formula (2), the wave number *ks* and characteristic impedance *Zs* of the equivalent fluid medium is

$$Z\_s(\omega) = \sqrt{\rho\_{\text{eq}}(\omega) \mathcal{K}\_{\text{eq}}(\omega)}, \text{ and} \tag{3}$$

$$k\_{\rm s}(\omega) = \omega \sqrt{\rho\_{\rm eq}(\omega) / K\_{\rm eq}(\omega)} \tag{4}$$

For the melamine foam with a thickness of *H,* the surface impedance at *x* = *H* of the sample backed by a rigid wall (see Figure 1) is given by

$$Z\_{PM}(\omega) = \frac{-jZ\_s(\omega)\cot(k\_s(\omega)H)}{\Phi} \tag{5}$$

**Figure 1.** Illustration of HPSET and melamine foam installed at an impedance tube. The thickness of the foam is *H*, and the inner diameter of the HPSET is 2*R*. The diameters and the maximum length of the extended tubes are *d*<sup>0</sup> and *t*. All extended tubes inlets are shaped to follow the sphere curvature. The cross-sectional areas of HPSET and impedance tube are *S* and *S*0.

In this paper, an experimental characterization approach, which requires direct measurements of φ and *k*<sup>0</sup> and an impedance tube technique [22–24], is adopted to characterize the transport parameters of melamine foam [25,26]. Parameters of the melamine foam are listed in Table 1. The porosity φ is measured by a porosimeter, the air-flow resistivity σ is directly measured by resistivimeter, and the remaining four transport parameters (α∞, Λ, Λ , *k*<sup>0</sup> ) are determined by the inverse characterization techniques using a three-microphone impedance tube [24]. We use a commercially available software RokCell (v3.0, MATELYS, Lyon, France) [27] to automatically obtain the estimations of the parameters.

**Table 1.** Parameters of the melamine foam.


#### *2.2. Impedance Model of the Hollow Perforated Spherical Structure with Extended Tubes (HPSET)*

Figure 1 illustrates the placement of the HPSET and melamine foam in an impedance tube. According to the well-known Maa model [28,29], the acoustic impedance of a single extended tube can be expressed as

$$Z = \frac{\Delta P}{\overline{u}} = j\omega\rho\_0(t + 0.85d\_0) \left[ 1 - \frac{2}{\mathbf{x}\sqrt{-j}} \frac{J\_1(\mathbf{x}\sqrt{-j})}{J\alpha(\mathbf{x}\sqrt{-j})} \right]^{-1} + \frac{\sqrt{2\omega\rho\_0\eta}}{4} \tag{6}$$

where *x* = *d*<sup>0</sup> ωρ0/(4η) is the ratio between the perforation radius and the viscous boundary layer thickness inside the tube of the perforations (also named "perforation constant"), *d*<sup>0</sup> is the inner diameter of the extended tubes, *t* is the maximum length of the tubes, η is the viscosity of the air, <sup>ω</sup> denotes the angular frequency, *<sup>j</sup>* <sup>=</sup> <sup>√</sup> −1 represents the imaginary unit, ρ<sup>0</sup> is the mass density of the air, and *J*0, *J*<sup>1</sup> are Bessel's functions of zero and first order.

The normalized impedance of the spherical resonating cavity is *ZD* <sup>=</sup> <sup>−</sup>*<sup>j</sup>* cot ω *c* (*V*−*Vtubes*) *S* , then the normalized impedance of HPSET absorber is given as

$$Z\_{\rm HPSET} = \frac{Z}{\varphi\_{p}\rho\_{0}c} + Z\_{D} = r\_{p} + j\omega\nu\_{p} - j\cot\left(\frac{\omega}{c}\frac{(V - V\_{\rm fus})}{S}\right) \tag{7}$$

with

$$r\_p = \frac{32\eta t}{q\_p \rho\_0 c d\_0^2} \left( \left( 1 + \frac{x^2}{32} \right)^{1/2} + \frac{\sqrt{2} x d\_0}{64t} \right) \tag{8}$$

$$
\omega m\_p = \frac{\omega t}{q \rho c} \left( 1 + \left( 9 + \frac{\mathbf{x}^2}{2} \right)^{-1/2} + 0.85 \frac{d\_0}{t} \right) \tag{9}
$$

where ρ0*c* denotes the characteristic impedance of the air, *c* is the sound speed in the air (m/s), φ*<sup>p</sup>* = *NA*0/*S* corresponds to the perforation ratio of the HPSET (*N* denotes the number of extended tubes, *A*<sup>0</sup> = π*d*<sup>0</sup> 2/4 denotes to the inner cross-sectional area of the extended tubes, *S* = π*R*<sup>2</sup> is the cross-sectional area of the HPSET. *d*<sup>0</sup> is the inner diameter of the extension tubes and *R* is the inner radius of the HPSET). *V* = 4π*R*3/3 and *Vtubes* = π*tNd*<sup>0</sup> 2/4 are the volume of the perforated ball and the extended tubes, respectively.

#### *2.3. Normal Incidence Sound Absorption of HPSET with a Melamine Foam*

Considering the sound waves impinges vertically on the composite absorber as illustrated in Figure 1. As the HPSET is embedded within the melamine foam, the equivalent impedance is the parallel of the HPSET and the melamine. Based on the impedance transfer formula [30], the specific acoustic impedance of the melamine foam at the surface of the composite absorber can be calculated as

$$Z\_{PM}' = \frac{Z\_{PM}(\omega) + j\rho\_0 c \tan(k\_i(\omega)(R - H))}{\rho\_0 c + jZ\_{PM}(\omega)\tan(k\_i(\omega)(R - H))} \tag{10}$$

Then, the characteristic impedance of the composed absorber is given as

$$Z' = \left(\frac{1 - q\rho\_b}{Z'\_{\rm PM}} + \frac{q\rho\_b}{Z\_{\rm HPSET}}\right) \tag{11}$$

where ϕ*<sup>b</sup>* = *S*/*S*0, and *S*<sup>0</sup> denotes the cross-sectional area of the impedance tube, *S* denotes the cross-sectional area of the HPEST. The normal incidence sound absorption coefficient of HPSET combined with melamine foam installed at an impedance tube is calculated as

$$\alpha = \frac{4\text{Real}(Z')}{\left(1 + \text{Real}(Z')^2\right) + \text{Imag}(Z')^2} \tag{12}$$

#### **3. Simulation Results and Discussion**

#### *3.1. Analytical Study of Normal Incidence Sound Absorption Coe*ffi*cient of the HPSET with a Melamine Foam*

Figure 2 illustrates the analytical results of the normal incidence sound absorption coefficient of the HPSET with a melamine foam obtained from Equation (12), in which the sound absorption of HPSET and a single layer melamine foam are also shown for a comparison. In the following simulations, the inner diameter of the HPSET is 2*R* = 65 mm, the number of perforations is *N* = 2, the diameters and lengths of the extended tubes are *d*<sup>0</sup> = 4.9 mm and *t* = 10 mm, respectively. The Helmholtz resonance absorption peak of the HPSET is found at 380 Hz and the anti-resonance frequency of this combined absorber is observed at 500 Hz, while the quarter wavelength resonance frequency of the porous material is around 1500 Hz. It is shown in Figure 2a that the sound absorption of the composite absorber is superior to the single layer melamine foam and HPSET. It is clear that the sound absorption of a single layer porous foam is less than 0.5 below 500 Hz. While the composite absorber reaches a wideband sound absorption (greater than 0.5) in the frequency range from 350 Hz to 2000 Hz, hence combination of HPSET with melamine foam could greatly enhance the low frequency sound absorptive performance of the melamine foam.

It is revealed from Figure 2b that the relative resistance of single layer melamine foam and HPSET are less than 1, which is less than the combined absorber in the frequency range from 360 Hz to 2000 Hz. Hence, the present absorber could improve the acoustic resistance and enhance the sound absorption. Meanwhile, the relative acoustic reactance of this combination is nearly zero at the resonance frequency of 380 Hz and 1500 Hz, which ensures the wideband absorptive performance of the proposed absorber. The low frequency sound absorptive performance could be further enhanced by combining multiple HPSETs with different resonance frequency.

#### *3.2. Parametric Study of the Sound Absorption Coe*ffi*cient of HPSET with a Melamine Foam*

Since the sound absorption of HPSET-Melamine foam absorber is influenced by many parameters, we take the same analytical process and investigate the main parameters in this section. The resistivity of the melamine foam is a key factor which dominates the sound absorption. It is demonstrated in Figure 3a that the resistivity of the melamine foam will greatly influence sound absorption both at the anti-resonance frequency and the quarter wavelength resonance frequency. When increasing the resistivity of the melamine foam, the sound absorption at the anti-resonance frequency is enhanced, while the sound absorption at the quarter wavelength resonance frequency is firstly increased and then decreased. The absorption peak at Helmholtz resonance frequency decreases slightly with the

increase in resistivity. Hence, a reasonable resistivity is required to match the specific resistance of the incident sound waves for the composite absorber.

**Figure 2.** Analytical results of normal incidence sound absorption of HPSET with melamine foam. (**a**) Normal incidence sound absorption coefficient; (**b**) Characteristic acoustic resistance and reactance.

Figure 3b demonstrates the variation of the diameter of extended tubes on the overall sound absorption of the present absorber. The tube diameter is a critical factor which controls the sound absorption performance of the sound absorption of HPSET. When the tube diameter is too large, the relative resistance is less than 1, and the sound absorption is decreased. On the opposite, a small-diameter will induce overlarge acoustic resistance which will also decrease the sound absorption.

As illustrated in Figure 3c,d, the low frequency sound absorption peak of the combined absorber is greatly shifted to lower frequencies by decreasing the tube number or increasing the tube length, while the high sound absorption peak remains the same. It is noted that the low frequency sound absorption of the HPSET is due to the increase in mass reactance, and the resonance frequency could be tuned via optimizing the tube parameters.

**Figure 3.** Comparison of the normal incidence sound absorption of composite absorber with different parameters. (**a**) The resistivity of melamine foam; (**b**) The diameter of extended tubes; (**c**) The length of extended tubes; (**d**) The number of extended tubes.

#### **4. Experimental Validation**

The normal-incidence sound absorption coefficient of the HPSET with melamine foam is measured by an impedance tube (B&K 4206, see Figure 4) based on the transfer function method. The measurements are manipulated according to the ISO 10534-2 standard [31], and the experiment set up is shown in Figure 4. The distance between the two microphones is 50 mm and the measured frequency range is from 0 to 1600 Hz. The inner diameter of the impedance tube is 100 mm. The room temperature is 17.5 ◦C, the atmosphere pressure is 1.01 <sup>×</sup> 10<sup>5</sup> Pa, and the relative humidity is 66.4%. The hollow perforated spherical structure used in the experiments is made of plastic, and the extended tubes are made of copper. Parameters for the HPSETs are shown in Table 2. Thickness of hollow perforated spherical structure and extended tubes is 0.5 mm. The thickness of the foam is 50 mm, and the average densities of the HPSET with foam are 47.1 kg/m3.

**Table 2.** Parameters of the tested samples of HPSETs.


Figure 5 shows the comparison of the experimental result and the calculation result for the sound absorption coefficient of the melamine foam. The calculation result uses the inverse characterization techniques described in Section 2.1 (inversion method-based parameters are listed in Table 1). It is shown that the calculation result is highly consistent with the actual experimental result, which verifies the reliability of this inversion characterization method.

**Figure 5.** Sound absorption coefficient of the melamine foam. The red solid line and blue dashed line represent the calculated results by inversion method and directly measured results, respectively.

The measured and calculated sound absorption coefficient curves of HPSET with melamine foam are shown in Figure 6. Good agreement is observed between the measurement and calculation. The HPSET combined with a porous foam in a limited thickness of 65 mm reaches a good sound absorption property in the frequency range from 200 to 1600 Hz. The thickness of the porous material is only 1/28 of the sound wavelength, which realizes the purpose of controlling the large wavelength with thin layer materials.

**Figure 6.** Sound absorption coefficient of the composite absorber for (**a**) HPSET1 and (**b**) HPSET2 (see Table 2). Red solid line: calculation by inversion method; Blue dashed line: direct measurement.

#### **5. Conclusions**

A thin and lightweight sound absorber is presented to improve the acoustic properties at low frequencies of melamine foams. The absorption performance of the compound absorber is validated experimentally by using an impedance tube, and the measured results are consistent with the calculation results. Our research implies that the tube diameter and the resistivity are critical factors controlling the absorption performance. When decreasing the tube number or increasing the tube length, the resonance frequency is greatly shifted to lower frequencies. Both theoretical and measured results show that the HPSET combined with a melamine foam can keep good sound absorptive performance in the frequency range from 200–1600 Hz in a limited thickness. Compared with conventional absorbers, the proposed absorber is practical in noise control applications such as in domains of rail vehicles, aircrafts cabin and automobiles.

**Author Contributions:** Conceptualization, L.L.; Methodology, D.L.; Software, M.H.; Formal Analysis, L.L. and Z.J.; Investigation, D.L. and M.H.; Data Curation, X.L. and X.W.; Writing—Original Draft Preparation, D.L.; Writing—Review and Editing, M.H. and Z.J.; Visualization, L.L. and D.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** The first author would like to acknowledge the support from the project of China Postdoctoral Science Foundation (Grant No. 256069).

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


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### *Article* **Development of a Panel Membrane Resonant Absorber**

**Yaw-Shyan Tsay \*, Jui-Yen Lin and Faxin Ma**

Department of Architecture, National Cheng Kung University, Tainan 701, Taiwan; N78031132@mail.ncku.edu.tw (J.-Y.L.); N76073031@mail.ncku.edu.tw (F.M.) **\*** Correspondence: tsayys@mail.ncku.edu.tw; Tel.: +886-6-2757575 (ext. 54155)

**Abstract:** The bass ratio describes the relationship between the reverberation energy in the low frequency region and that of the middle frequency. An appropriate bass ratio can create a warm sound; however, too much bass can influence speech clarity (C50) and work efficiency and can even cause listeners to feel tired or exhausted. Using perforated plate resonance theory and membrane resonance theory, this research developed the panel membrane resonant absorber (PMRA), which not only provides an outstanding continuous absorption spectrum in the broadband range of 100–800 Hz but also presents an aesthetic appearance at a low cost. We divided this study into two parts: (1) PMRA development and experiment and (2) field application and measurement to confirm the sound absorption performance of the PMRA. In part 1, PMRA was developed by combining different materials and thicknesses of the air cavity. In the field study of part 2, the PMRA with the appropriate sound-absorbing curve was installed in a small auditorium, where we conducted field measurements for reverberation time (RT) and speech clarity (C50). According to the experimental results, the PMRA had great absorption performance at a low frequency. In the field validation, the PMRA was found to effectively decrease the low-frequency RT while also maintaining the RT of middle-high frequency. The C50 of the auditorium was also improved.

**Keywords:** speech clarity; bass ratio; sound absorption; reverberation time

**1. Introduction**

At the beginning of the 20th century, Sabine proposed the famous reverberation time (RT) theory, which brought room acoustics into the scientific realm. However, many acousticians have proposed different methods to inspect the pros and cons of room acoustics. Knudsen and Harris [1] believe that a RT below 500 Hz used in the field of music should be higher than the middle frequency. Ehmer [2] experimented with 250 Hz and found that when the masking sound is 20 dB, the 250 Hz threshold of the same frequency is increased by about 10 dB, the masking sound is 80 dB, and the 250 Hz test signal threshold is raised by about 50 dB. Beranek [3] proposed the bass ratio (BR) indicator and believed that in the acoustic design of a hall, the RT for low frequencies (125–250 Hz) should be increased by 20% compared to intermediate frequencies (500–1000 Hz), suggesting that a concert hall could be even up to 50%, which can make the sound warm and brilliant. Therefore, while low frequency is of considerable importance in a space, too much low-frequency energy will have the opposite effect. Fuchs and Zha [4] proposed that both language and music have non-negligible energy in the low frequency, which may generate standing waves in space, indirectly strengthen the low-frequency sound field energy, and shield the middle and high frequencies that are extremely important for clarity, thus affecting speech clarity (C50).

Furthermore, in addition to the feedback on the physical level of the low-frequency sound, the psychological impact is also an important factor. Vasudevan and Gordon [5] found that low-frequency noise mainly occurs in indoor environments, while Leventhall [6] considered the low-frequency noise band to be 10–200 Hz and pointed out that LAeq underestimated low-frequency noise most of the time. Alimohammadi et al. [7] found

**Citation:** Tsay, Y.-S.; Lin, J.-Y.; Ma, F. Development of a Panel Membrane Resonant Absorber. *Appl. Sci.* **2021**, *11*, 1893. https://doi.org/10.3390/ app11041893

Academic Editor: Edoardo Piana

Received: 6 January 2021 Accepted: 17 February 2021 Published: 21 February 2021

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**Copyright:** © 2021 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/).

that low-frequency noise caused users to feel annoyed, whereas Waye and Rylander [8] proposed that the low-frequency noise of ventilation equipment was prone to higher levels of psychosocial symptoms, sleep disturbance, and headaches for people who are annoyed. Caniato [9] found that underestimating the interference caused by LAeq can affect sleep conditions, and Falourd et al. [10] found that low-frequency background noise causes reduced speech intelligibility and users feel stressed and fatigued. Abbasi et al. [11] conducted a noise test with 35 young males aged 20 to 30 years old and found that noise between 65 dB and 75 dB obviously caused psychological fatigue, increased heart rate, and reduced working memory. Therefore, in order to reduce the likelihood of generated low-frequency sound, some researchers have proposed the sound absorption method.

Common sound absorption systems on the market, such as Helmholtz resonance, perforated panel resonance (PPR), micro-perforated panel (MPP), and membranous vibration (MV), each have sound absorption characteristics at a different frequency. Helmholtz resonance is for mid-low frequency, but the frequency band is narrow. PPR is also for midlow frequency but is wider than that of Helmholtz. The MPP has better sound absorption performance than PPR, but the manufacturing cost is higher. MV is the only one that can facilitate artistic creation with sound absorption ability at mid-low frequency. Since this research is focused on low frequency, we adopted the PPR and MV systems. As a result, in this paper, we took advantage of the sound absorption characteristics of PPR and MV to reach better performance at a low frequency.

A bass trap is normally used to solve the problem of acoustics at a low frequency. Some people will create a bass trap by themselves since they are expensive and enormous, but such DIY products are without measurements to confirm the sound absorption performance. Therefore, this research designed an absorbent material for low frequency (125 and 250 Hz). Common methods for improving sound absorption on building walls include installation of curtains, wood panels, porous cotton materials with perforated panels, and sandwich structure. Considering price, porous cotton materials with perforated panels have been commonly adopted in interior renovations but have not shown outstanding sound absorption performance at low frequency. Cudina et al. [ ˇ 12] designed a sound absorber by hanging a painting to reduce the RT and found that canvas without an oil color layer and different air layer behind had a low performance of sound absorption coefficient at low frequency. The result showed the sound absorption coefficients at 125 and 250 Hz were under 0.1. Considering the influence of sound absorption performance via canvas surface tension, Zainulabidin et al. [13] found that surface tension has no significant effect on sound absorption properties.

Traditional absorbers such as porous materials necessitate a thick absorbing material when working at a low-frequency range [14]. Hybrid materials have been proposed for broadband of low-frequency absorption with a thinner structure. Zhao et al. [15] proposed a double porosity material (DPM) that combined the micro-pore from the porous layer and the meso-pore made by the labyrinthine channel to absorb low-frequency sound. Dupont et al. [16] proposed a multi-pancake material that connected perforated materials to provide a collection of periodically spaced materials as resonant absorbers of low frequency. Liu et al. [17] proposed a perforated composite Helmholtz resonator (PCHR) that combined separating plates with a Helmholtz resonator and provided a continuous absorption spectrum in the broadband range of 450–1360 Hz. Furthermore, Zhu et al. [18] combined periodic acoustic metamaterial resonators (AMRs) with a porous layer and provided a broadband absorption of the audible sound wave at the low frequency of 180–550 Hz. Tang et al. [19] proposed a perforated honeycomb-corrugation hybrid (PHCH) model that combined a lightweight sandwich panel with a perforated honeycomb-corrugation core, providing outstanding sound absorption over a broadband low-frequency range. However, most of these hybrid materials are still in the research and development stage, their prices are relatively high, and they have not yet been verified in the field.

In general, historical buildings are usually decorated with smooth, hard, and highreflex skin materials, such as glass, concrete, and wood, which result in long RT. On the

other hand, according to Taiwan's Cultural Assets Protection Law, decoration can only be carried out after being approved regarding its configuration, shape, color, and style, thus placing restrictions on decoration. As described above, sound absorption performance has to be improved at low frequency. Therefore, for this paper, we designed public art with two sound absorption systems in order to study panel membrane resonant absorber (PMRA) sound absorption performance at low frequency.

The theory of sound absorption of PPR combined with sound absorption of MV was adopted in this research. The former has better sound absorption performance at middle frequency, while the latter has better performance at low frequencies. Therefore, the specimens, including different combinations that consisted of expanded metal mesh (EMM) and canvas, were tested to develop the PMRA with better absorption performance. This study had two parts—PMRA development and field verification. First, the PMRA was developed with different combinations of EMM and canvas; then, the sound absorption performances of the materials and PMRA were tested using ISO 354 [20]. Last, the PMRA with the best performance at 125 Hz was installed in a historic building, and its performance in the field was measured and verified. The field verification was focused on room acoustics of long RT at low frequency.

#### **2. PMRA Development and Prototyping**

#### *2.1. Specimens*

The development process of the PMRA included two stages. In stage 1, the sound absorption performances of single materials (EMM and canvas, as shown in Figure 1) with different air cavities were measured. Then, in stage 2, different air thicknesses in the PMRA composed of EMM and canvas were measured. The size of each PMRA was 1.8 × 1.2 m. The thickness and density of EMM were 1.2 mm and 2.25 kg/m3, respectively, while the density of the canvas was 0.36 kg/m3. Group A consisted of a 10 cm high wooden frame, canvas covered the surface and fixed the periphery as a membrane structure, and EMM was installed inside as a resonator, which was collocated at different heights to study sound absorption performance. Group B used a 20 cm high wooden frame and the same installation method as Group A. The detailed information of the materials and specimens are provided in Tables 1 and 2, and Figures 2–5.

(**a**) Expanded metal mesh (**b**) Canvas

#### **Figure 1.** Materials.

**Table 1.** Detailed thickness of stage 1 specimens.



**Table 2.** Detailed thickness of stage 2 specimens.

(**b**) Specimen of EMM

**Figure 5.** Group B section in stage 2, as Table 2.

#### *2.2. Experiments*

In this study, the sound absorption efficiency was measured using the reverberation room, which conforms with the ISO/IEC 17025 [21] testing and calibration laboratory operation regulations, and the methodology of measurement suite is in accordance with ISO 354:2003 [22]. The reverberation room is an unshaped hexahedron. The volume of the reverberation room is 171.3 m3, its surface area is 184.3 m2, and its floor area is 32.8 m2. The laboratory adopts a floating structure to reduce the outside interference on the experiment. As described above, the single PMRA was 2.16 m2 (1.8 m × 1.2 m), and the total area of the test specimen was 4.32 m2 (1.8 m × 2.4 m), which was placed on the center of the floor. Figure 6 shows the reverberation room environment, and the receive point and calculation of the sound absorption coefficient are shown in Equation (1).

$$a\_s = 55.3 \times V \left(\frac{1}{c\_2 T\_2} - \frac{1}{c\_1 T\_1}\right) - 4V(m\_2 - m\_1) \tag{1}$$

where *V* is the volume of the empty reverberation room (m3); *c* is the propagation speed of sound in air (m/s); *T*<sup>1</sup> is the reverberation time of the empty reverberation room (s); *T*<sup>2</sup> is the reverberation time of the reverberation room after the test specimen has been introduced (s); and *m*1, *m*<sup>2</sup> is the power attenuation coefficient (m<sup>−</sup>1).

**Figure 6.** Reverberation room of National Cheng Kung University Architectural Acoustics Lab.

#### **3. Measurement Results of PMRA**

Figures 7 and 8 demonstrate the results of the first stage. By increasing the air layer behind the expanded metal mesh, we found that the absorption frequency band became wider, and the resonance frequency moved to low frequency. The surface density of the canvas was small. Although the low frequency was slightly improved by increasing the air layer behind it, the sound absorption efficiency was relatively weak throughout the entire frequency band. Due to the limitation of the materials' surface density, changing the air layer had a greater impact on the low frequency of absorption efficiency with the expanded metal mesh than with the canvas.

**Figure 7.** The sound absorption coefficient of expanded metal mesh (EMM) with single-layer structure in stage 1.

**Figure 8.** The sound absorption coefficient of canvas with single-layer structure in stage 1.

The results of the second stage are shown in Figures 9 and 10. In Group A, the soundabsorbing performance significantly increased at a frequency range from 125 to 250 Hz via increased air space behind EMM, that is, at 125 Hz, it increased from 0.14 to 0.33, and at 250 Hz from 0.53 to 0.75. Although the sound absorption coefficient at low frequency increased, it was still lower than 0.6 when under 250 Hz.

**Figure 9.** The sound absorption coefficient of Group A in stage 2 (specimen height 10 cm). A1: canvas with 5.8 cm air-layer + EMM with 3 cm air-layer; A2: canvas with 3.8 cm air-layer + EMM with 5 cm air-layer; A3: canvas with 1.3 cm air-layer + EMM with 7.5 cm air-layer; A4: canvas with 0 cm air-layer + EMM with 10 cm air-layer.

In Group B, the air space was increased to 20 cm, and the overall sound absorption performance was significantly improved at low frequencies compared to Group A. Therefore, the sound absorption coefficient rose above 0.4; at 250 Hz, it increased from 0.48 to 0.91, at 125 Hz, from 0.35 to 0.80. B4 sound absorption performance not only performed better than the other specimens in Group B at 100 Hz and 125 Hz, but also at medium and high frequencies.

As shown above, in Group A, as the air layer increased, the sound absorption coefficient of each frequency band improved. The sound absorption coefficients of A2 to A4 at 250–500 Hz were all above 0.6. However, the objects of this study were 125 and 250 Hz. Therefore, in Group B, we increased the air layer to 20 cm and found that the sound absorption coefficient moved to low frequency. B4 performed well at 125 Hz, and the 250 Hz sound absorption coefficient was 0.76. Therefore, this study chose B4 as the specimen for subsequent development.

**Figure 10.** The sound absorption coefficient of Group B in stage 2 (specimen height 20 cm). B1: canvas with 15.8 cm air-layer + EMM with 3 cm air-layer. B2: canvas with 8.8 cm air-layer + EMM with 10 cm air-layer. B3: canvas with 3.8 cm air-layer + EMM with 15 cm air-layer. B4: canvas with 0 cm air-layer + EMM with 20 cm air-layer.

#### **4. Field Validation of PMRA**

#### *4.1. The Historic Building*

In this study, we adopted Ge-Chi Hall of National Cheng Kung University as the object of field verification. Ge-Chi Hall has a historical and cultural background and is a typical small auditorium, as shown in Figure 11. The building is approximately 220 m2, with a volume of 1600 m3, and a total interior surface area of 1060 m2. The overall wall was made of cement, the first floor was made of wood and cement, and the second floor was made of wood without fixed seats. The first floor was for the auditorium, while the second floor was for the media. As described, these materials were all smooth surface materials, which causes a long RT. However, Ge-Chi Hall is primarily used for ceremonial activities, including musical performances, speeches, dinner parties, and evening parties. As a result, we targeted the RT and C50 in this study, especially at low frequency.

**Figure 11.** Ge-Chi Hall environment and section diagram.

#### *4.2. Acoustic Index*

This study refers to the bass ratio by Beranek [3], which is identified as the ratio of RT between 125 Hz, 250 Hz, and middle frequency (500 Hz and 1000 Hz), as shown in Equation (2). Beranek classified the ratio of RT into four levels, as shown in Table 3.

$$\begin{aligned} \text{Ratio of RT} &= \begin{cases} \begin{array}{c} T\_{125}/T\_{mid} \\ T\_{250}/T\_{mid} \end{array} \\\\ T\_{mid} &= (T\_{500} + T\_{1000})/2 \end{aligned} \tag{2} \end{aligned} \tag{2}$$

where *T*<sup>125</sup> is the reverberation time of 125 Hz (s), *T*<sup>250</sup> is the reverberation time of 250 Hz (s), and *T*mid is the reverberation time of 500 and 1000 Hz (s).

**Table 3.** Ratio of reverberation time (RT) at low frequency (Beranek, 1962).


According to ISO 3382-1 [22], the C50 is the ratio of early-to-late arriving sound energy ratio, and it can be calculated through Equation (3). When C50 > 0, the early sound energy dominates the sound field and satisfies basic speech intelligibility. In general, the C50 have a high relation with RT—the lower the RT, the better the C50.

However, the target in this paper is to compare the RT and C50 at a low frequency in Ge-Chi Hall with and without PMRA. RT is valued by BR, and we observed how much C50 increased.

$$C\_{50} = 10 \lg \frac{\int\_0^{50} p^2(t) d\_t}{\int\_{50}^{\infty} p^2(t) d\_t} dB \tag{3}$$

where C50 is the early-to-late index, and *p*(*t*) is the instantaneous sound pressure of the impulse response measured at the measurement point.

#### *4.3. Field Measurement*

The measurement environment had air conditioning, NC was 35, temperature was 26 °C, and relative humidity was 55%. In this study, the sound source was an omnidirectional loudspeaker via B&K Dirac software that output MLS digital signals and analysis after a 1/2 free-field microphone received the sound power, as shown in Figure 12. In Figure 13, the sound source is shown set on the stage, and all receive points are evenly distributed on the first floor (P1–P5) and second floor (P6–P7); the measured data were the total average.

**Figure 12.** System of the field measurement.

Figure 14 shows the RT results of Ge-Chi Hall without PMRA. At 125, 250, 500, and 1000 Hz, the RT values were 1.74, 1.53, 1.31, and 1.21 s, respectively. According to the RT ratio proposed by Beranek [3], 500 and 1000 Hz of RT were substituted into Equation (2) for the field measured, and the calculation revealed that the 125 and 250 Hz RT of the space

should be between 1.19 and 1.60 s, and 1.22 and 1.43 s, respectively. The comparison result shows that 125 and 500 Hz need to be reduced by at least 0.14 s and 0.1 s, respectively, to fall within an appropriate RT.

**Figure 13.** Sound source and measurement points.

**Figure 14.** RT of Ge-Chi Hall without panel membrane resonant absorber (PMRA).

#### *4.4. Installation of PMRA*

As described herein, for the field verification, we conducted a two-phase measurement of current situation investigation and improvement investigation, followed by the position measurement of RT and C50. After improvement, the survey installed PMRA on both sides of the front and back walls of the auditorium on the first floor, as well as on both sides of

the back and the walls on both sides of the media booth on the second floor. The PMRA was based on type B4 for field verification implementation. The following two sizes were used: 180 (L) × 125 (W) × 20 cm (H) with seven pieces and 120 (L) × 90 (W) × 20 cm (H) with two pieces. The installation position is shown in Figure 15.

**Figure 15.** PMRA setting position.

#### *4.5. Field Performance of PMRA*

Figure 16 shows the RT of Ge-Chi Hall with PMRA. The RT results were 1.55, 1.40, 1.28, and 1.16 s at 125, 250, 500, and 1000 Hz, respectively. The 500 Hz and 1000 Hz of RT in the measured field were substituted into Equation (2), which indicated that 125 Hz and 250 Hz should be between 1.16 and 1.47 s, and 1.19 and 1.37 s, respectively. Therefore, the PMRA effectively reduced the RT at low frequency, which was within a suitable RT range at both 125 and 250 Hz. Overall, by minimizing the high-frequency sound absorption as much as possible in this study, we found that PMRA can effectively reduce the RT at 125 and 500 Hz; thus, the result was consistent with the purpose of this research.

**Figure 16.** RT of Ge-Chi Hall with PMRA.

As shown in Figure 17, the C50 of Ge-Chi Hall without PMRA were −4.26, −2.41, and −2.23 dB at 125, 250, and 500 Hz, respectively. After PMRA was installed, the C50 was −2.19, −0.73, and −1.35 dB, reflecting increases of 2.07, 1.68, and 0.98 dB, respectively. Therefore, PMRA can effectively increase C50 performance at 125, 250, and 500 Hz. However, whether PMRA was installed or not, we observed no significant effect at 1000 Hz to 8000 Hz.

**Figure 17.** A comparison of C50 with or without PMRA at each band.

Figure 18 shows the comparison of the C50 with and without the PMRA at 500 Hz. Due to the PMRA installed point, speculated P1 had a long distance with PMRA, and P2 was close to outside noise. Therefore, C50 had an increased limitation, while the others were significantly increased.

**Figure 18.** A comparison of C50 with or without PMRA at 500 Hz.

#### **5. Conclusions**

In this paper, we developed a PMRA prototype set with different structure combinations and used laboratory measurements to confirm the basic sound-absorbing characteristics of PMRA, choose a better sample on the basis of the research results, apply it to the actual field, and then study the low-frequency improvement of building acoustics.

The laboratory measurement was separated into two stages. In the first stage, we studied the sound absorption performance of the surface materials. The second stage was to study the membrane structure with single-layer EMM and to design a composite plate mold resonance sound absorber, which we used to explore each group's sound absorption characteristics of different materials and air space. We ultimately found that B4 had a better sound absorption performance than others at low frequency (125 Hz), and thus we chose and installed B4 in field validation.

For the difference between PMRA being installed in Ge-Chi Hall or not, the RT was reduced by 0.19 s at 125 Hz and 0.13 at 250 Hz, while C50 increased by 2.07 and 1.68 at 125 and 250 Hz, respectively. The overall results show that PMRA not only effectively reduced low frequency and increased C50, but also was both practical and aesthetic as a sound absorber.

**Author Contributions:** Conceptualization, Y.-S.T.; Formal analysis, Y.-S.T.; Investigation, J.-Y.L.; Project administration, Y.-S.T.; Resources, Y.-S.T.; Supervision, Y.-S.T.; Writing—original draft, F.M.; Writing—review & editing, J.-Y.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** Ministry of Science and Technology, Taiwan: MOST 109-2622-E-006-032.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


**Hasina Begum \* and Kirill V. Horoshenkov**

Department of Mechanical Engineering, The University of Sheffield, Sheffield S1 3JD, UK; k.horoshenkov@sheffield.ac.uk

**\*** Correspondence: hbegum3@sheffield.ac.uk; Tel.: +44-75-2157-0011

**Abstract:** It is known that aerogel impregnated fibrous blankets offer high acoustic absorption and thermal insulation performance. These materials are becoming very popular in various industrial and building applications. Although the reasons for the high thermal insulation performance of these materials are well understood, it is still largely unclear what controls their acoustic performance. Additionally, only a small number of publications to date report on the acoustical properties of fibrous blankets impregnated with powder aerogels. There is a lack of studies that attempt to explain the measured absorption properties with a valid mathematical model. This paper contributes to this knowledge gap through a simulation that predicts the measured complex acoustic reflection coefficient of aerogel blankets with different filling ratios. It is shown that the acoustic performance of a fibrous blanket impregnated with aerogel is generally controlled by the effective pore size and porosity of the composite structure. It is shown that there is a need for refinement of a classical Biot-type model to take into account the sorption and pressure diffusion effects, which become important with the increased filling ratio.

**Keywords:** acoustics; aerogels; modeling; fiber; porous materials

#### **1. Introduction**

There is a global need to reduce the use of fossil fuels and the release of greenhouse gases. Currently, 40% of energy consumption in Europe comes solely from the building sector [1], which is a major source of greenhouse gases. Due to this high level of energy consumption, the European council has introduced a 27% energy efficiency target for 2030 [2]. This has led to industries sourcing better energy-saving products for the market, with thermal insulation being the most effective way to reduce the energy consumption and loss. Achieving such a significant energy efficacy requires the development and upscaling of new commercial products based on aerogels.

One popular emerging thermal insulation product is aerogel blankets. Aerogel blankets consist of a silica aerogel embedded in a reinforcing fibrous matrix, which allows the brittle aerogel to become a flexible, durable solid used for buildings [3] and pipelines. The silica aerogel can undergo a surface modification process (typically hydrophobization) to enhance surface life stability [4], thus reducing the aerogel's susceptibility to moisture and rapid spoilage [5]. Silica aerogels themselves have porosity values as high as 98%, densities as low as 0.05–0.5 g/cm3, surface areas in the range of 300–1000 m2/g [6] and thermal conductivity values as low as 0.02 W/mK [7]. Application of aerogels on their own are limited due to their fragility and low mechanical modulus. Using them as composites in the form of aerogel blankets removes their fragility, as the aerogel grains are now incorporated within a fibrous matrix such as fiberglass or rockwool, giving them impeccable mechanical strength and a breadth of flexibility in terms of product development [8].

Conventional porous materials, such as nonwovens and polymer foams [9], can also prevent the reflection of sound incident waves to provide a high sound absorption performance [6,10] that is a highly desired property. Nonwovens in particular are ideal for

**Citation:** Begum, H.; Horoshenkov, K.V. Acoustical Properties of Fiberglass Blankets Impregnated with Silica Aerogel. *Appl. Sci.* **2021**, *11*, 4593. https://doi.org/10.3390/ app11104593

Academic Editor: Edoardo Piana

Received: 23 April 2021 Accepted: 14 May 2021 Published: 18 May 2021 Corrected: 10 March 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 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/).

sound absorption due to their large surface area and high porosity, which offers increased frictional losses between sound waves and the fibrous matrix, leading to their good sound absorption performance [11].

Monolithic silica aerogels alone have unusual viscoelastic properties and have been used in the form of clamped plates to become the main source of intrinsic losses allowing them to exhibit subwavelength resonances for high sound absorption [12,13]. However, these materials are highly fragile. Utilizing them as aerogel powder into a fibrous, flexible matrix results in a multi-functional system that can fulfill a range of practical needs in many industry and domestic applications. Their fused nanoparticles in particular result in extremely low elastic stiffness, which provides a relatively low acoustic impedance and exceptionally low flexural wave speed, making it ideal for use as a subwavelength flexural element for controlling airborne sound [14]. Super-insulative acoustic absorbing materials such as aerogel blankets can be tailored and combined with other products to widen their applications and to provide lighter, thinner and more economical products.

It is known that the acoustic properties of aerogels alone are greatly influenced by the interstitial gas type, pore structure and aerogel density [15,16], and more recently the pioneering efforts to embed granular aerogels into a reinforced fibrous network [3] have shown promising acoustical behavior. The combination of the density and granular size of aerogel [17] and fiber reinforcement and decreased pore size greatly influences the sound absorption [18]. Motahari et al. [19] investigated the aging time of silica aerogels in cotton nonwoven mats on the sound absorption performance. They found that the presence of low density (0.088 g/cm3) silica aerogel at different molar ratios of the precursors MeOH/TEOS used and the low aging time enhanced the sound absorption coefficient in the low frequency range of 250 to 2500 Hz. Furthermore, Eskandari et al. [20] investigated the acoustical behavior of synthesized silica aerogels mixed into UPVC blankets of different weight ratios. They found that neat UPVC only had a maximum sound absorption of 17% at a frequency of 1800 Hz; however, when silica aerogel was applied at 0.5, 1.5 and 3 weight %, the maximum sound absorption of UPVC increased to 24, 28 and 43%, respectively, therefore highlighting that acoustical properties were greatly increased upon the addition of silica aerogel. A more extensive review of acoustical properties of aerogels can be found in reference [4].

However, there is a general lack of understanding regarding what leads to the observed acoustical properties of granular aerogels embedded into fibrous mats. A majority of previous works have not attempted to apply any valid theoretical models to predict key acoustical properties of these systems to explain the measured data. There are limited data on the effect of the filling ratio on the acoustical properties of aerogel impregnated fibrous blankets. Additionally, despite some previous efforts (e.g., [6,9]), there is a limited understanding on the ability of some prediction models to explain the general acoustical behavior of these materials. There was no discussion on the values of the non-acoustical parameters that the authors of references [6,9] had to use in the prediction models they chose in their works to simulate the measured absorption coefficient data.

Our work aims to address this gap via a careful characterization of the acoustical behavior of granular silica aerogels impregnated into fiberglass mats. The acoustical properties of five samples of aerogel blankets with varying concentrations of aerogel powder (at micrometric particle sizes) at filling ratios of 0, 25, 50, 75 and 100% were measured and predicted using a mathematical model. This work helps to better understand the relation between their micro-structure and measured acoustical performance.

The structure of this paper is as follows. Section 2 highlights the various techniques used to characterize the chemical and physical material properties of aerogel blankets. Section 3 looks at the experimental acoustical data derived from the analysis of these materials. Section 4 attempts to explain these data with a mathematical model to understand what intrinsic properties of aerogel blankets make them acoustically absorbing.

#### **2. Materials and Methods**

#### *2.1. Materials Preparation*

As specified in the patent [21], sodium silicate diluent was prepared using distilled water to achieve 3 to 10 weight % of SiO2 and stirred with hexamethydisilazane (HDMS) whilst slowly adding nitric acid (HNO3) to allow gelation to occur. The silylated hydrogel and co-precursor were gradually immersed in n-hexane for a one-step solvent exchange and sodium ion removal. Water present in the hydrogels is detached due to surface modification of the organic groups (–CH3)3 in HDMS. The hydrogel from which water was removed was then dried at ambient pressure and pulverized to form a superhydrophobic synthetic silica aerogel powder [22] with the particle diameter in the range of 1–20 μm impregnated into a fiberglass blanket at different weight % of 25, 50, 75 and 100 powder to blanket at a later manufacturing process. This is a standard process [23]. The fiber diameter in the blanket was 10 microns and its density was approximately 73 kg/m3. It is a standard commercial E-glass fiber needle mat produced by Lih Feng Jiing Enterprise Co Ltd (Tainan City, Taiwan) [23]. The impregnated fiberglass blankets were then cut to a 10 mm diameter size using a hand-held hole saw that had smooth blade edges to ensure a perfect fit into the impedance tube when tested for acoustical properties.

#### *2.2. Materials Characterization*

Microstructural observations such as particle distribution of the silica aerogels within fiberglass mats were performed using scanning electron microscopy (SEM). Images were obtained with a FEI Nova NanoSEM 230 instrument (FEI, Hillsboro, OR, USA) at an accelerating voltage of 10 kV and a minimum working distance of 5 mm. The silica aerogels were fixed on the sample holder using a carbon pad and subsequently coated with 15–20 nm of platinum for SEM analysis.

The acoustical properties of aerogel blankets were measured in a 10 mm impedance tube that was custom made by Materiacustica [24]. This 2-microphone tube setup was developed to test small material specimens in accordance with the standard ISO 10534-2:2001 [25]. This setup enabled us to measure the normalized surface acoustic impedance, complex reflection coefficient and sound absorption coefficient of a hardbacked porous layer in the frequency range of 300–3000 Hz. The spacing between the two microphones was 30 mm, which is usual for this frequency range as recommended in the standard [25]. The thickness of the samples used in the acoustic experiments was between 7 and 11 mm, which is a typical thickness of a commercial product [23,26]. Figure 1 illustrates a typical specimen of fiberglass blanket impregnated with aerogel that was used in the acoustic experiments. Figure 2 shows a photograph and jigsaw drawing of the vertically standing impedance tube.

**Figure 1.** 10 mm diameter of fiberglass blanket samples cut for fitting into the impedance tube.

**Figure 2.** 2-Microphone impedance tube setup to measure the surface impedance of a porous layer [25].

#### **3. Modeling of the Acoustical Properties of Fibrous and Granular Media**

Basic modeling of the acoustical properties of this kind of material requires a mathematical model that takes into account the classical visco-thermal effects in the voids' between the fibers and loose granules of powder. However, a fibrous blanket impregnated with aerogel is a more complicated void structure that has at least three scales of porosity. The fiberglass blanket itself consist of 10 μm interlaced fibers that form a porous structure with sub-millimeter size pores of approximately 0.1 mm. The aerogel particles are around 20 μm in size and contain nano-pores of 20 nm in size.

There are several models that exist that can predict the acoustical properties of classical fibrous media [27]. In this work we attempt to use the model proposed by Horoshenkov et al. [28], which is based on the following three parameters: (i) the median pore size, *s*; (ii) porosity, *φ*; and (iii) the standard deviation in pore size, *σs*. This reduced number of parameters allows easier inversion of key morphological characteristics of porous media from acoustical data. This model predicts the dynamic density, *<sup>ρ</sup>*, and complex compressibility, *C*, of air in the material pores. These quantities are given by the analytical equations, which are presented in reference [28]. The MATLAB code to predict these quantities can be found in reference [29].

The normalized surface impedance of a hard-backed layer of porous material that is typically measured in the impedance tube is:

$$Z\_s = -jZ\_c \cot(k\_c d) / \rho\_0 c\_0 \tag{1}$$

where *<sup>j</sup>* <sup>=</sup> √−1, *<sup>d</sup>* is the sample thickness, *<sup>ρ</sup>*<sup>0</sup> is the ambient density of air, *<sup>c</sup>*<sup>0</sup> is the sound speed in air,

$$Z\_{\mathfrak{c}} = \sqrt{\frac{\widetilde{\rho}}{\widetilde{\mathbb{C}}}} \tag{2}$$

is the characteristic impedance and

$$k\_c = \omega \sqrt{\hat{\rho}\hat{\mathbf{C}}} \tag{3}$$

is the wavenumber in the porous material. Here, *ω* is the angular frequency of sound. In this work, we use the complex reflection coefficient data

$$R = \frac{Z\_{\mathfrak{s}} - 1}{Z\_{\mathfrak{s}} + 1} \tag{4}$$

to fit the model. The work presented in reference [30] shows that the complex reflection coefficient is a reliable quantity to determine the effective values of the three non-acoustical parameters in the model [28] through the parameter inversion. This is the complex acoustical quantity that is measured directly using the standard impedance tube method [25]. The real and imaginary parts of this quantity are bounded between −1 and +1, which makes them attractive to use in the parameter inversion process. The complex reflection coefficient can also be used to predict the acoustic absorption coefficient

$$\mathfrak{a} = 1 - \left| \mathbb{R} \right|^2 \tag{5}$$

which is a usual measure of the ability of the porous layer to absorb sound.

#### **4. Results and Discussion**

*4.1. Microstructural Analysis*

Figures 3–7 present SEM images of the fiberglass blankets with a progressive increase in the aerogel powder filing ratio from 0 to 100%. These images can be used to identify the aerogel particle distribution in fiberglass blankets and the structure of the fiber network. The SEM magnification scale in each of these images changes between 40, 100 and 500 microns to provide a better view inside into the microstructure. We note that SEM image analysis is sensitive to the loading of samples on to the carbon stub; a large amount deposited will affect the coating and this may fracture the image surfaces. Furthermore, there may be sampling bias causing the contrast/brightness settings to be adjusted and this may also affect the results.

Figure 3 clearly shows that there is little to no aerogel powder present in virgin fiberglass. It also shows that the spacing between individual fibers is in the order of 100 s of microns and that these randomly oriented fibers form a complicated network. The addition of a relatively small (25%) amount of aerogel powder does not significantly affect the inter-fiber space (see Figure 4). For this case, aerogel particles mainly attach themselves to the fibers (see Figure 4a) causing an apparent increase in the fiber diameter (see Figure 4). In the case of the samples with 50 and 75% concentrations (Figures 5 and 6, respectively), a similar effect can be visually observed, but the apparent increase in the fiber diameter is more significant whereas the size of the inter-fibrous space is clearly reduced. In the ultimate case, when the aerogel filling ratio in the fibrous sample is 100% (see Figure 7), a considerable proportion of the inter-fibrous space is occupied with aerogel powder so that the effective pore size appears to be significantly reduced visually.

**Figure 3.** SEM images taken at different magnifications (3000× (**a**), 800× (**b**) and 200× (**c**)) showing the fiberglass blanket without any aerogel.

**Figure 4.** SEM images taken at different magnifications (3000× (**a**), 800× (**b**) and 200× (**c**)) showing the fiberglass blanket structure with an aerogel filling ratio of 25%.

**Figure 5.** SEM images taken at different magnifications (3000× (**a**), 800× (**b**) and 200× (**c**)) showing the fiberglass blanket structure with an aerogel filling ratio of 50%.

**Figure 6.** SEM images taken at different magnifications (3000× (**a**), 800× (**b**) and 200× (**c**)) showing the fiberglass blanket structure with an aerogel filling ratio of 75%.

**Figure 7.** SEM images taken at different magnifications (3000× (**a**), 800× (**b**) and 200× (**c**)) showing the fiberglass blanket structure with an aerogel filling ratio of 100%.

#### *4.2. Acoustical Properties*

The acoustical properties were measured at the University of Sheffield in a 10 mm impedance tube [25]. Five specimens were cut from different areas on a sample of each type of fibrous blanket and their properties were measured. The repeatability of each measurement was found within ±2.9% for the absorption coefficient and ±5.8% for the reflection coefficient. Figure 8 shows a comparison between the measured absorption coefficients for the five samples. Figure 9 presents a comparison between the measured and predicted real and imaginary parts of the complex reflection coefficients for these five materials.

**Figure 8.** An example of the measured sound absorption coefficient of a 8–9 mm thick hard-backed layer of the five fibrous blankets with a progressive increase in the aerogel filling ratio.

**Figure 9.** Examples of the measured (marker) and predicted (solid lines) complex reflection coefficient data for fiberglass blanket without any aerogel (**top**), 50% aerogel impregnated blanket (**middle**) and 100% aerogel impregnated blanket (**bottom**).

The results presented in Figure 8 suggest that there is a progressive increase in the absorption coefficient as the aerogel impregnation increases from 0 to 50%. When the aerogel filling ratio reaches 75% this increase becomes less pronounced. Increasing the filling ratio beyond 75% reduces the absorption coefficient significantly. This reduction makes sense because it is likely associated with a densely packed inter-fibrous space, which becomes almost full with aerogel (see Figures 6 and 7), causing a considerable reduction in the pore size (see Table 1) in a relatively thin material layer. For the filling ratios of 75% and above the characteristic impedance (see Figure 9) and attenuation of sound in a layer with such small pores becomes very high, limiting the value of the absorption coefficient [27]. The absorption coefficient of this relatively thin fibrous blanket with 50–75% filling ratios is still relatively high (30–70%) particularly above 1000 Hz (see references [4,13]). This level of absorption has a practical value in applications related to engineering noise control.

**Table 1.** Values of the non-acoustical parameters inverted from fitting the model [28] to the measured complex reflection coefficient data for the five types of fiberglass blankets.


An obvious question here is: *What happens to the fiberglass pore properties when the percentage of aerogel powder impregnating the blanket increases?* In order to answer this question we attempted to fit the mathematical model [28] to the complex acoustic reflection coefficient data measured in the impedance tube. We used the optimization procedure described in reference [30] to invert the three parameters of the best fit. This procedure has been used extensively by many researchers (see [27] for a review of parameter inversion methods). Figure 9 shows three examples of this fit for fiberglass blankets with aerogel filling ratios of 0, 50 and 100%.

Table 1 presents a summary of the mean values of the three non-acoustical parameters in the adopted theoretical model [28], which were inverted from its fit to the measured data for the five filling ratios. This table also provides the porosity values calculated from the material density data, mean layer thickness measured directly and root mean square error (RMS) calculated between the predicted and measured reflection coefficient spectra. The superscript (*i*), which appears with a non-acoustic parameter in this table, means that the values of this parameter were inverted rather than measured directly.

The results shown in Figure 9 and the parameter values listed in Table 1 suggest that the model generally provides a very close fit to the data (an RMS error better than 2.5%), particularly when the filling ratio is equal to or below 50%. The agreement between the predicted and measured reflection coefficient spectra reduces slightly with the increased filling ratio. The inverted value of the median pore size (Table 1) decreases progressively from 99.4 to 20.5 μm as the filling ratio increases from 0 to 75%. This makes physical sense, as the SEM images in Figures 3–7 illustrate this. This range of pore sizes is also consistent with that measured non-acoustically for similar materials [6]. When the filling ratio increases, the inter-fiber pores are progressively replaced with much smaller intergrain pores. The transport (inner) pores in the grains of aerogel do not seem to contribute significantly to the measured acoustical properties. This is reflected in a consistently underpredicted porosity value, *φ*(*i*). The progressive change in the inverted porosity value make sense for the filling ratios between 0 and 50%, dropping from 99.4 to 92.9%,

respectively. These values match the measured porosity values within 3%. When the filling ratio increases to 100%, the inverted porosity of *φ*(*i*) = 50.5% is significantly below the measured porosity of *φ* = 93.6%. Additionally, the median pore size inverted for this type of blanket is not realistic. This suggests that the physical behavior of the blanket layer with 100% filling ratio is no longer captured accurately by the model. As the proportion of aerogel powder in the material approaches 100%, the sorption and thermal diffusion effects are likely to become much more important [31]. These effects are not captured by the adopted model [28], which only accounts for the classical visco-thermal and inertia effects.

#### **5. Conclusions**

This work is a systematic study of the acoustical properties of fibrous blankets that are impregnated with an aerogel powder. The level of impregnation (filling ratio) has been progressively changed from 0 to 100% with respect to the material weight. The complex acoustic reflection coefficient of these materials was measured in the frequency range of 300–3000 Hz using a standard impedance tube setup [25]. These data were used to invert the three parameters of the theoretical model [28] via the best fit method [30]. It was found that the adopted model can predict the reflection coefficient spectrum relatively accurately with the RMS error being below 4%. The absorption coefficient of these relatively thin (8–9 mm thick) fibrous blankets with 50–75% filling ratios is relatively high (30–50%), particularly above 1000 Hz. This level of absorption has a practical value in applications related to engineering noise control.

The results of the parameter inversion obtained with the adopted model suggest that the impregnation of fibrous blanket with an aerogel powder results in a progressive reduction in the effective pore size. For the filling ratios in the range of 0–50% there is also a small but progressive reduction in the inverted porosity, which is within 3% of that measured directly. The absorption coefficient increases progressively with the increased filling ratio, reaching its maximum when the filling ratio is between 50% and 75%. This decrease in the effective pore size results in an increased acoustic attenuation and better coupling, which are important to maximize the acoustic absorption for such a thin porous layer. Increasing the filling ratio beyond 75% results in a significant drop in the absorption. This drop is associated with a considerable drop in the porosity value (*φ* = 0.505) and substantial increase in the pore size (*s* = 83 μm) inverted for the filling ratio of 100%. The discrepancy between the model and data for this filling ratio increases. As the proportion of aerogel powder in the material approaches 100%, the open porosity does not drop significantly, i.e., the proportion of the open interconnected pores remains relatively constant. However, the sorption and thermal diffusion effects in the inner pores in the aerogel grains become much more important [31]. These pores have nanometer scales [6], which is much smaller than the values of *s* inverted with the model [28] (see Table 1). The effects that occur in nanometer pores cannot be captured by the adopted model [28], which only accounts for the classical visco-thermal and inertia effects in pores that are much larger than the mean free path (68 nm in air at ambient pressure and temperature).

This work suggests that in order to predict the acoustic behavior of fibrous blankets with high aerogel filling ratios there is a clear need to refine the model [28] to include the sorption and pressure diffusion effects. The adopted model does require unrealistic values of the median pore size and porosity to achieve a good fit. This model can be refined by including in it the work by Venegas and Umnova [31]. In this way the dynamic compressibilities of the air filling the inter-fiber pores and in the nanoscale pores in the aerogel grains can be combined to account for all of the physical effects that contribute to the observed acoustical behavior.

**Author Contributions:** Conceptualization, H.B. and K.V.H.; methodology, H.B.; software, K.V.H.; validation, formal analysis, H.B.; investigation, H.B.; resources, H.B.; data curation, H.B.; writing—original draft preparation, H.B.; writing—review and editing, K.V.H.; visualization, H.B.; supervision, K.V.H.; project administration, K.V.H.; funding acquisition, K.V.H. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was partly funded by the EPSRC-sponsored Centre for Doctoral Training in Polymers, Soft Matter and Colloids, grant number EP/L016281/1, and industry sponsors—Armacell.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data are available online (see ref. [29]).

**Acknowledgments:** The authors would like to thank the EPSRC-sponsored Centre for Doctoral Training in Polymers, Soft Matter and Colloids at The University of Sheffield for their financial support of this work. We would also like to thank our industry partner Armacell and Mark Swift and Pavel Holub for their continued support throughout this research study. We extend our thanks to Shanyu Zhao at the Swiss Federal Laboratories for Materials Science and Technology for allowing us to use their electron microscopy center for high magnification SEM image analysis.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.

#### **References**


## *Article* **More Than Just Concrete: Acoustically Efficient Porous Concrete with Different Aggregate Shape and Gradation**

**Louena Shtrepi 1,\*, Arianna Astolfi 1, Elena Badino 1, Giovanni Volpatti <sup>2</sup> and Davide Zampini <sup>3</sup>**


#### **Featured Application: The use of acoustically efficient porous concrete with weighted absorption coefficients (***αw***) in the range of 0.30 to 0.75 for noise control in outdoor and indoor applications.**

**Abstract:** The interest in the use of resistant acoustic materials has put further attention on the use of porous concrete in the building industry. This work investigates the acoustic properties of four different mix designs of porous concrete obtained with two types of aggregates, that is, normal weight and lightweight aggregates. The assessment of the sound-absorbing performances has been conducted in the small-scale reverberation room (SSRR) at Politecnico di Torino (Italy), in agreement with the procedure indicated in the ISO 354 Standard. For each concrete type, three panel thicknesses, i.e., 20 mm, 40 mm, and 60 mm, were tested. Moreover, different mounting conditions were investigated, considering the combination of single panels in multiple layers, adding an air gap between the panel and the backing, and inserting a layer of rock wool in the air gap itself. The results show weighted absorption coefficients (*αw*) in the range of 0.30 to 0.75 depending on the thickness and mounting conditions. These encouraging values make these materials useful for efficient practical applications in indoor and outdoor environments.

**Keywords:** acoustics; acoustic measurements; sound absorption coefficient; cement-based materials; building materials; pervious concrete; acoustic concrete

#### **1. Introduction**

The implementation of noise control strategies in outdoor environments is a challenging task for several professionals, and an increasing number of studies highlight the importance of the architectural design on urban noise mitigation in canyon streets [1,2] squares [3] and inner yards [4]. A detailed overview of the acoustic strategies used for the building envelope design in order to improve the urban acoustic environment is given in [5]. These studies have pointed out the need for sound-absorbing and -scattering materials suitable for outdoor environments. Moreover, several indoor spaces such as airports, train stations, schools, etc. are characterized by requirements similar to those of outdoor spaces regarding highly durable and resistant acoustic materials. Therefore, this work aims to investigate the sound absorbing properties of porous concrete of different mix designs, thicknesses and mounting conditions, as this material results suitable for outdoor and indoor applications. Compared to other porous sound absorbers, porous concrete has the capability to withstand the atmospheric elements, and therefore it is suitable for applications in outdoor and indoor environments when resistance, low deformability, and high durability are required.

**Citation:** Shtrepi, L.; Astolfi, A.; Badino, E.; Volpatti, G.; Zampini, D. More Than Just Concrete: Acoustically Efficient Porous Concrete with Different Aggregate Shape and Gradation. *Appl. Sci.* **2021**, *11*, 4835. https://doi.org/10.3390/ app11114835

Academic Editors: Edoardo Piana, Paolo Bonfiglio and Monika Rychtarikova

Received: 27 April 2021 Accepted: 21 May 2021 Published: 25 May 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 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/).

Porous absorbers are the most widespread type of sound absorbers. According to their microstructure, porous absorbers can be further classified into granular, cellular, and fibrous [6,7]. The most fundamental properties of porous materials influencing their sound absorbing properties are flow resistivity and porosity and second, pore shape factor and tortuosity [7].

Conventional concrete is generally characterized by poor sound-absorbing properties, as the prevailing phenomena occurring are sound reflections. In general, normal concrete has an absorption coefficient value of 0.05–0.10 [8]. However, porous concrete has the capability to work as a porous sound-absorbing material as it is characterized by high porosity, i.e., open pore structure on its surface and an interconnected network of pores. It is also known as pervious, gap-graded, permeable, or enhanced porosity concrete [9] and is currently widely used in urban environments as paving material to support environmentally sustainable rainwater management [10]. It has been also exploited for its acoustic absorbing properties in traffic noise barriers and railway noise reduction [11–13]. Pervious concrete mainly consists of normal Portland cement, coarse aggregates (aggregate dimension greater than 5 mm), and water, which generate a void content that generally ranges from 15% to 35% [10,14–16]. Pervious concrete acoustic panels belong to the class of granular sound absorbers with pores created by the presence solid aggregates which are bonded together by a cementitious binder. The key factor to allow sound absorption to occur is the accurate definition of the quantity of binder to ensure that there is enough binder to keep the aggregate together without clogging the pore network and still allow for an appropriate resistance for its use and handling. Overall, the sound-absorbing properties of granular materials tend to be uneven in frequency and to be characterized by peaks [17].

Different strategies have been proposed with the intent to improve the sound absorbing properties, i.e., with the aim to enhance the rate and the evenness of the sound absorption provided by altering the microstructural properties of the pervious concrete. Note that these strategies applied to the mix design aim to vary the fundamental properties, i.e., flow resistivity, porosity, pore shape factor, and tortuosity, which control the absorbing performance. Indeed, the sound absorption properties of porous concrete are strictly related to the void ratio of the concrete. Therefore, it is important to adequately control the void ratio and aggregate type, which influence tortuosity and flow resistivity [18], pore size, and pore aperture size, which are used to control porosity [8]. A higher void ratio leads to higher and wider peak values in acoustic absorption coefficients, resulting in a shift of the peak of the coefficient towards the higher frequencies [12,19,20].

The effect on sound absorption of the aggregate size and different aggregate types by blending or combining them in multiple layers has been studied in [11,13,21,22]. Aggregate size can be used to control the pore dimensions, as the median pore size increases for increasing aggregate size [19,21]. With respect to aggregate size, it has been observed that most previous studies endorse the use of aggregate with dimensions in the range 1 to 10 mm [11,21,22], as smaller aggregates would clog the pores, thus reducing porosity, and bigger ones, despite increasing the pore volume, would reduce the tortuosity of the pore network. When considering the use of different aggregate types such as lightweight and normal-weight aggregates, the study in [22] suggests that lightweight aggregates can absorb cement paste from micropores on the surface of the aggregates. As a result, for an equal absolute volume ratio of aggregates, smaller size lightweight aggregates result in slightly higher sound absorbing performance, as they have a larger total surface area compared to bigger ones, and therefore the cement paste covering the aggregates can be better absorbed when smaller aggregates are used and result in higher void ratio values with respect to normal weight aggregates [22]. Other studies have investigated the use of different materials as aggregates, such as crumb rubber, cenospheres, and recycled aggregates [12,13,23–25]. The possibility of blending aggregates with different size in the concrete matrix has been studied in [19,21], highlighting that, as a general rule, aggregate size should be selected in order to ensure that smaller aggregates do not enter the pores created by the bigger ones. Porous concretes with blends of aggregates of different materials

have been tested in [11], where expanded perlite aggregates were replaced by different percentages of slag, evidencing a nonlinear impact on the sound absorption performance of the panels. Concrete samples featuring aggregates of different dimensions or material have been combined into layers in [11,13,22], evidencing the coupling two layers of concrete with the external one featuring aggregates with lower bulk densities or bigger pores sizes compared to the back layer lead to increased sound absorbing performances.

Slight differences in sound absorption have been reported regarding the shape of the aggregates; for instance, this was shown in [22], i.e., which has compared round shape (lightweight) and irregular shape (normal weight) aggregates with similar gradation.

Moreover, as for all the acoustic porous materials, the thickness of the porous layer also results as important for the acoustic absorption coefficient spectra. The principal maximum peak of the absorption coefficient is displaced to lower frequencies when the thickness increases [13,18,21]. However, there is a threshold regarding the thickness of granular materials above which the absorption does not increase further [7]. Table A1 (Appendix A) briefly summarizes the details and the main findings of previous research investigating the effects of design factors on the sound absorption coefficient of porous concrete. The studies which analyzed different aggregate size, material and shape, and on panel thickness have been clustered evidencing if and the extent to which such variable was found to have an influence on the sound absorbing properties of the panels.

Recent reviews on the strategies that have been proposed to enhance the sound absorbing performances of concrete have been presented in [17,26]. However, these reviews highlight the fact that further research is required to provide larger datasets to refine and produce better estimation of the sound absorption of concrete materials.

Therefore, the following study aims to provide further experimental data on the investigation of some design guidelines for sound absorbing concrete emerging from the past research regarding the aggregate shape and size. The present study investigates, through a systematic research approach, the effects of concrete mix design (four different conditions), sample thickness (three different conditions), and mounting conditions (three different conditions) on the absorption properties of porous concrete tested in a small-scale reverberation room (SSRR). Therefore, the main aim of this study is to define the sample configuration that could lead to an increase of the sound absorption properties of concrete panels. More than 30 different combinations of the aforementioned variables have been considered. Note that besides providing a useful database of measured data in addition to previous research, this work presents novel configurations, that is, mounting conditions with an air gap and combination in multiple layers with other porous materials. To the authors' knowledge, this has not been studied in previous literature.

This work aims to increase awareness on the porous concrete properties among several professionals such as architect, designers, acousticians, policy-makers, etc. that deal with noise control strategies in outdoor and indoor environments.

#### **2. Materials and Methods**

The research has been organized through the following steps:


#### *2.1. Tested Concretes*

Information regarding the porous concrete types, identified with the letters A, B, C, and D, are summarized in Table 1. The following parameters are reported: aggregate size (according to EN 933-2:2020 [27]), aggregate particle density (according to EN 1097-6:2013 [28]), void ratio (according to ASTM C1754/C1754M [29]), flexural strength

(according to EN 12390-5:2019 [30]), previous concrete density (according to ASTM C1754/ C1754M [29]), and water permeability (according to ASTM D2434-19 [31]). Two different types of aggregates have been used in the mix design: normal weight and lightweight. The normal weight aggregates have been used in concrete type A and have an irregular shape with an average dimension of 4–8 mm, while the lightweight aggregates have an almost perfect round shape, i.e., spherical, with different dimensions ranging between 4 and 8 mm, 2 and 4 mm, and 0.5 and 1 mm for concretes B, C, and D, respectively.

**Table 1.** Four mix design of porous concrete characteristics with respect to: aggregate size, aggregate particle density, void ratio, flexural strength, previous concrete density, and water permeability.


Details of the aggregate shape can be visualized in Figure 1.

**Figure 1.** Sample (**A**): crushed normal weight aggregates 4–8 mm; Sample (**B**): round lightweight aggregates 4–8 mm; Sample (**C**): round lightweight aggregates 2–4 mm; Sample (**D**): round lightweight aggregates 0.5–1 mm.

Concrete A differs significantly from the other three regarding the concrete density value, which is strongly affected by the higher values of the aggregate particle density. The four concretes present a similar void ratio. However, while this parameter is constant for concretes A, B, and C, it decreases for concrete type D, which features smaller aggregates. It can also be noticed that there is a decrease in the flexural strength for lower densities and smaller aggregate dimensions.

For each concrete, three different sample types have been manufactured with three different thicknesses, i.e., 20 mm, 40 mm, and 60 mm (Figure 1); for each of them, three samples have been produced. The panels are square-shaped in plan with a side dimension of 60 cm. Three different mounting conditions were tested for the samples with a thicknesses of 20 and 40 mm, that is, coupling different samples in multiple layers (Figure 2), adding a 50 mm air gap between the sample and the room floor (Figure 3), and adding a layer of fibrous material (rock wool) in the air gap itself (Figure 4). The identification codes of the samples and mounting conditions have been summarized in Table 2. The coupling of different samples in multiple layers has been performed only within the same concrete in order to compare their performance with single layers of the same thickness and investigate any anisotropy at the back surface of each layer. The multiple layer configuration is obtained by superimposing one panel to the other, with no joint or glue connecting them. This mounting solution could be practically useful when modular solutions are explored and would limit the need for different formwork thicknesses. The introduction of a rock wool layer in the air gap has been tested with sample D of 20 mm thickness only as it resulted in the highest sound absorption performances compared to the 20 mm samples of A, B, and C concretes. In this case, two thicknesses of the rock wool layer—30 and 50 mm—have been introduced in the air gap.

**Figure 2.** Multiple layers of 20 + 20 mm and 20 + 40 mm. Sample (**A**): crushed normal weight aggregates 4–8 mm; Sample (**B**): round lightweight aggregates 4–8 mm; Sample (**C**): round lightweight aggregates 2–4 mm; Sample (**D**): round lightweight aggregates 0.5–1 mm.

**Figure 3.** Mounting on 50 mm air gap. Sample (**A**): crushed normal weight aggregates 4–8 mm; Sample (**B**): round lightweight aggregates 4–8 mm; Sample (**C**): round lightweight aggregates 2–4 mm; Sample (**D**): round lightweight aggregates 0.5–1 mm.

**Figure 4.** (**a**) 30 mm and (**b**) 50 mm rock wool filling 50 mm air gap. (**c**) Sample D of 20 mm over one of the two conditions.

**Table 2.** Summary of the tested samples and configurations of the porous concrete. Single layers have been tested in configurations of multiple layers, with air gap and with rock wool in the airgap (+tested and −untested configurations of single layers).


The assessment of the sound absorbing performances has been conducted in the smallscale reverberation room (SSRR) of Politecnico di Torino (Italy), following the procedure indicated in the ISO 354 Standard [32]. The reliability of the measurement was tested with respect to reproducibility and repeatability, by repeating the measures three times on three different samples of the same typology and considering their arithmetic mean to describe the performances of each type. The sound absorbing properties are expressed as 1/3 octave

band sound absorption coefficients (*α*) and also as weighted sound absorption coefficients (*αw*) for an easier comparison.

#### *2.2. Sound Absorption Coefficient Measurements*

The small-scale reverberation room (Figures 1–4) is installed in the Applied Acoustics laboratory at DENERG (Department of Energy, Politecnico di Torino, Torino, Italy). The room has been primarily built for random-incidence scattering coefficient measurements according to ISO 17497-1 [33], but it is also suitable for measurement of sound absorption coefficient according to ISO 354 [32,34]. It is an oblique angled room with pairs of non-parallel walls with a volume of 2.86 m<sup>3</sup> and a total area of 12.12 m2. A more detailed description of the room construction has been provided in Shtrepi and Prato [35].

The measurement procedure consists in using the integrated impulse response method [32] for simultaneous measurements on six different microphone positions in two conditions, i.e., with and without the sample inside the room. The measurement chain consists of six 1/4" BSWA Tech MPA451 microphones and ICP104 (BSWA Technology Co., Ltd., Beijing, China), two ITA High-Frequency Dodecahedron Loudspeakers with their specific ITA power amplifiers (ITA-RWTH, Aachen, Germany), and a sound card Roland Octa-Capture UA-1010 (Roland Corporation, Shizuoka, Japan). This setup allows to perform 12 measurements, which refer to the minimum number required by ISO 354:2003 [32]. The software used for the measurements, i.e., sound generation, recording, and signal processing, is MATLAB combined with the functions of the ITA-Toolbox (an opensource toolbox by RWTH-Aachen, Aachen, Germany) [36].

For each of the 12 measurements the reverberation time relative to a 20 dB decay, i.e., T20, is evaluated and used to estimate the T60, i.e., the reverberation time occurring for a 60 dB decay, as done in the full-scale reverberation room (FSRR) data processing. The data are spatially averaged with the ensemble averaging method in order to obtain the reverberation times *T*<sup>1</sup> and *T*2, which are obtained without and with the sample inside the room, respectively. Equations (1) and (2) are applied to estimate the random-incidence absorption coefficient *αs*.

The difference between *T*<sup>1</sup> and *T*<sup>2</sup> measurements is used to calculate the variation of the equivalent sound absorption area *AT* [m2] based on Sabine's theory:

$$A\_T = 55.3V \left(\frac{1}{c\_2 T\_2} - \frac{1}{c\_1 T\_1}\right) - 4V(m\_2 - m\_1) \tag{1}$$

where *T*<sup>1</sup> and *T*<sup>2</sup> [s] are the reverberation times of the empty reverberation room and of the reverberation room with the test specimen, respectively; *V* [m3] is the volume of the empty reverberation room; *c*<sup>1</sup> and *c*<sup>2</sup> [m/s] are the propagation speed of sound in air in the room without and with the sample: *c*<sup>1</sup> = 331 + 0.6 *t*1, *t*<sup>1</sup> [ ◦C] is the air temperature; and *m*<sup>1</sup> and *m*<sup>2</sup> [m−1] is the power attenuation coefficient of the climatic conditions in the reverberation room without and with the sample (calculated according to ISO 9613-1 [37]).

The random-incidence absorption coefficient *α<sup>s</sup>* is defined as

$$
\alpha\_S = \frac{A\_T}{S} \tag{2}
$$

where *S* [m2] is the area covered by the test sample. Note that the edge area is included in the calculations of *S* considering the four concretes as isotropic materials [38].

#### **3. Results**

The results of the measured sound absorption coefficients are reported in the graphs in Figures 5, 7 and 8 and discussed in separate sections, based on the tested conditions, i.e., thickness and mounting method for each concrete type (A–D). Figures 5, 7 and 8 present an immediate reading of the design factors considered within the sample typology to evidence improvements/deterioration given the mix design. Furthermore, the figures in Appendix B

compare the results of considered panel samples (A–D) for a given design factor, in order to help the reader with a more immediate understanding of the differences between samples (A–D). In the end, more general conclusions are drawn to compare the performances of the different sample types. Moreover, the single index for weighted sound absorption (*αw*) in SSRR measurements has been estimated and used for comparisons.

#### *3.1. Effect of Sample Thickness and Concrete Type*

Figure 5 shows the graphs of the four samples (A–D) for three different thicknesses of the single layers. Overall, the absorption spectra of panels A are uneven, and tend to provide poor absorption (<0.25) at frequencies lower than 630 Hz, while at higher frequencies, the sound absorption coefficients ranges between 0.40 and 0.70 for panels with either 40 mm or 60 mm thicknesses. The 20 mm thick panel features an absorption peak at 3150 Hz, which reaches the value of 0.90 and provides a poor absorption (<0.25) at frequencies lower than 2000 Hz. The 40 and 60 mm panels present a higher absorption coefficient with respect to the 20 mm panels in the 500–2000 Hz frequency range.

**Figure 5.** Comparison of the absorption coefficients for samples (**A**–**D**) with different thicknesses obtained from multiple layer combinations (20, 40, 20 + 20, 60, and 20 + 40 mm). Sample (**A**): crushed normal weight aggregates 4–8 mm; Sample (**B**): round lightweight aggregates 4–8 mm; Sample (**C**): round lightweight aggregates 2–4 mm; Sample (**D**): round lightweight aggregates 0.5–1 mm.

The absorption spectra of samples B are uneven and tend to provide poor absorption (<0.25) at frequencies lower than 630 Hz for panels with either 40 mm or 60 mm thicknesses, while at higher frequencies the absorption coefficient ranges between 0.20 and 0.60. The 20 mm thick panel features an absorption peak at 2500 Hz of about 0.60 and provides poor absorption (<0.25) at frequencies lower than 1600 Hz. This might be due to the curing process of the 40 mm sample, which might have led to lower porosity of these samples.

The absorption spectra of panels C are also slightly uneven and tend to provide poor absorption (<0.25) at frequencies lower than 630 Hz for panels with either 40 mm or 60 mm thicknesses, while at higher frequencies, the absorption ranges between 0.40 and 0.80. The 20 mm thick panel features an absorption peak around 4000 Hz, achieving a value of 0.90 and provides poor absorption (<0.25) at frequencies lower than 1600 Hz. The absorption coefficient for this thickness becomes lower than 0.25 at frequencies below 2000 Hz. The 60 mm sample reaches significant high values of absorption coefficient (>0.40) at 800 Hz, while the 40 mm panel at 1250 Hz.

The absorption spectra of panel D are more even than the other three typologies, and tend to provide significant absorption (>0.40) at frequencies higher than 630 Hz for panels with either 40 mm or 60 mm thicknesses, where the sound absorption ranges between 0.40 and 1. The 20 mm thick panel feature an absorption peak between 2500 Hz and 4000 Hz, achieving a value of 1.20; the peak is broader than those featured by 20 mm thick panels of types A–C. Values higher than 1 may occur in the measurements with finite sample size for materials with high absorption properties [39,40]. The 20 mm sample of panel D achieves significant absorption (>0.40) above 1000 Hz, while for panels A–C, this occurred above 2500 Hz, 2000 Hz, and 3150 Hz, respectively. The sound absorbing performances of thicker panels are extended towards the lower frequencies, in the range below 1600 Hz. Indeed, for the thicker panels (40 mm and 60 mm), the significant absorption range is extended in a similar way down to 630 Hz.

#### *3.2. Effect of Sample Mounting in Multiple Layers*

The graphs in Figure 5 show the absorption coefficients of the four sample types both in the single layer and multiple layer configurations with panel thicknesses of 20, 40, and 60 mm, for an easier comparison. Sample A graph shows that the sound-absorbing performances achieved when coupling two panels of 20 mm thick are comparable to those achieved by a single panel with a thickness of 40 mm. A similar trend is observed comparing the 60 mm thick panel with the combination of 20 + 40 mm thick panels. However, there are some differences occurring above 1250 Hz. It can be observed that above 2500 Hz both the 20 + 20 mm and the 20 + 40 mm combination show lower values of sound absorption compared to the 40 and the 60 mm single layers samples, respectively. It can be noticed that the multiple layer 20 + 40 mm of sample A outperforms the 60 mm sample only at the 800 Hz peak and in the frequency range 1250 to 2500 Hz.

Sample B graph shows that the sound absorbing performances achieved when coupling two panels 20 mm thick are comparable to those achieved by a single panel with a thickness of 40 mm. However, the combination 20 + 20 outperforms the 40 mm single layer panel in the range of 1000 to 2000 Hz. By contrast, the performances of the 60 mm thick panel are higher than those of 20 + 40 mm thick panels combined for frequencies higher than 1600 Hz. The multiple layer 20 + 40 outperforms the 60 mm sample in the range 630–1250 Hz.

The results of Sample C show that the sound absorbing performances achieved when coupling two panels that are 20 mm thick are slightly lower than those achieved by a single panel with a thickness of 40 mm, particularly for frequencies range 800–2000 Hz and above 3150 Hz. The performances of the 60 mm thick panel are comparable with those achieved by the combination of 20 + 40 mm thick panels. However, the multiple layer 20 + 40 outperforms the 60 mm sample in the range 1250–2500 Hz.

Sample D results show that the sound absorbing performances achieved when coupling two panels 20 mm thick are comparable to those achieved by a single panel with a thickness of 40 mm. A similar trend is observed comparing the performances achieved by a 60 mm thick panel with that of the combination of 20 + 40 mm thick panels. This might be due to the high and uniform porosity obtained for all the samples of type D compared to the other panel types, as seen in Figure 6. In these cases, further care should be put in the treatment of the mix design and its curing in samples A, B, and C, as heavier aggregates might sediment and result in nonuniform distribution of the pores within the panel and its front/back surfaces.

**Figure 6.** Back surface for Sample (**A**): crushed normal weight aggregates 4–8 mm; Sample (**B**): round lightweight aggregates 4–8 mm; Sample (**C**): round lightweight aggregates 2–4 mm; Sample (**D**): round lightweight aggregates 0.5–1 mm.

#### *3.3. Effect of Sample Mounting with an Air Gap*

The graphs in Figure 7 show the four sample types (A–D) mounted with an air gap of 50 mm between the panel and the rigid backing, i.e., the SSRR floor. The graph of Sample A shows that the performance is enhanced at the lower frequencies when an air gap is left between the panel of 20 mm and the backing, while the sound absorption at high frequencies decreases. The maximum peak is shifted at lower frequencies, i.e., at ~630 Hz, with an absorption coefficient of ~0.60. The 40 mm layer seems to be less affected by the presence of the air gap and the maximum peaks remain unvaried in frequency for this thickness. However, a slight decrease is reported at high frequencies and an increase of about 0.10 is observed at the peak value corresponding to 1250 Hz.

**Figure 7.** Comparison of the absorption coefficients for samples (**A**–**D**) of different thicknesses (20 and 40 mm) mounted with an air gap of 50 mm. Sample (**A**): crushed aggregates 4–8 mm; Sample (**B**): round lightweight aggregates 4–8 mm; Sample (**C**): round lightweight aggregates 2–4 mm; Sample (**D**): round lightweight aggregates 0.5–1 mm.

Sample B shows different trends for the 20 mm and 40 mm layers. However, when an air gap is left between the panels and the backing, the performance is enhanced at the lower frequencies for the 20 mm and 40 mm layers. The high frequency sound absorption decreases for the 20 mm layer when the air gap is added, while the maximum peak is shifted at lower frequencies, i.e., at ~630 Hz, with an absorption coefficient of ~0.60. The 40 mm layer seems to be less affected by the presence of the air gap at high frequencies above 2000 Hz. Conversely, the air gap seems to decrease the absorption over the 630 to 2000 Hz range for the 40 mm layer. A peak value appears at the frequency of 200 Hz with a value of about 0.55 of the absorption coefficients.

Sample C shows a decrease of the absorption coefficient at high frequencies for both 20 mm and 40 mm layers when an air gap is left between the panels and the backing. For the 20 mm panel, this is significant above 2500 Hz, while for the 40 mm panel, it is more evident in the 1000 to 2500 Hz range. The performances are slightly enhanced at the lower frequencies in the range 315 to 800 Hz for the 20 mm sample and in the range 315 to 2500 Hz for the 40 mm sample, with the maximum peaks that are shifted at 630 Hz and 800 Hz, respectively.

The sound-absorbing performances of sample D show a decrease at high frequencies when an air gap is left between the panels and the backing above 1600 Hz and above 800 Hz for the 20 mm and 40 mm panels, respectively. Nevertheless, the sound absorption coefficients in those ranges result above 0.55. The performances are enhanced at the lower frequencies, where several peaks appear around 250 Hz, 400 Hz, and 800 Hz. The absorption coefficient increases for both thicknesses in the 160 to 630 Hz range when the air gap is added, showing a very similar trend for both 20 mm and 40 mm panels.

#### Effect of Sample Mounting with an Air Gap Filled with Porous Material

The previous sections showed that sample D presents the highest sound absorption coefficients extended over the broader range of frequencies. In order to further improve the performance of the combination of panel D with an air gap, another strategy has been used considering the air gap filled with porous material. The introduction of a rock wool layer in the air gap has been tested with the sample of 20 mm thickness only. Two thicknesses of the rock wool layer, that is, 30 and 50 mm, have been introduced in the air gap. Recall that the air gap considered here is of 50 mm. Therefore, the first layer of rock wool (30 mm) allowed to have a 20 mm air gap left between the concrete sample and the rock wool layer, while the 50 mm rock wool allowed to test a fully filled air gap.

Figure 8 shows that the with the insertion of 30 mm and 50 mm rock wool in the air gap the sound absorption coefficients have very similar trends above 630 Hz. Generally, the combination of an air gap with a porous material (e.g., rock wool) is shown to improve the acoustic performance down to 250 Hz. A peak value at 800 Hz is further increased when the air gap is filled with rock wool compared to the empty condition. Furthermore, a significant improvement is obtained in the 250 to 800 Hz frequency range reaching values of sound absorption coefficients of 0.60–0.90.

**Figure 8.** Sample D single layer of 20 mm combined with an air gap of 50 mm filled with a rock wool layer of 30 and 50 mm.

#### *3.4. Single Number Acoustic Index α<sup>w</sup>*

Based on the above results, the weighted sound absorption coefficients *α<sup>w</sup>* derived from the SSRR measurements were calculated. These single indices are useful for an immediate and practical comparison of the performance of different conditions. The higher the *α<sup>w</sup>* values, the better the material capability in sound absorption. Their values normally range from 0 to 1, with 1 meaning 100% sound absorption.

The weighted sound absorption coefficient *α<sup>w</sup>* is derived from practical sound absorption coefficients, *α<sup>p</sup>* which is calculated as an average of the one-third octave sound absorption coefficients within the octave in accordance with ISO 11,654 [41]. Weighted sound absorption coefficient *α<sup>w</sup>* can be obtained with the reference curve (*α*<sup>250</sup> = 0.8; *α*<sup>500</sup> = 1; *α*<sup>1000</sup> = 1; *α*<sup>2000</sup> = 1; *α*<sup>4000</sup> = 0.9), which is shifted in steps of 0.05 towards the *α<sup>p</sup>* values until the sum of unfavorable deviations is less or equal to 0.10. The unfavorable deviations occur when the measured value is lower than the value of the reference curve. Finally, the weighted sound absorption coefficient is the value of the adjusted reference curve at 500 Hz.

Table 3 shows that there are a few differences among the single indices within each concrete data. It is evident from these values that the highest performance is obtained for panel type D. The *α<sup>w</sup>* values for the single layer of type D samples become significant (>0.40) for a thickness of 60 mm. The single layers of 20 mm and 40 mm present an improvement of the *α<sup>w</sup>* values when they are mounted with an air gap behind (*α<sup>w</sup>* = 0.50). This mounting condition performance is further improved when the air gap is filled with a porous material. It can be noticed that when the entire gap is filled with rock wool (50 mm), the highest *α<sup>w</sup>* is obtained. A significant improvement due to the air gap is also obtained for sample C, while a slight improvement is reported for sample A. Conversely, depending on the sample thicknesses, sample B values of *α<sup>w</sup>* are either not affected or reduced when the air gap is added at the back of the 20 mm and 40 mm thick layers, respectively.

**Table 3.** Comparison of single acoustic indices related to the weighted absorption coefficient (*αw*) for the four concrete types (A–D).


#### **4. Discussion**

Given the results herein, a few aspects can be highlighted with respect to previous findings presented in Section 1 and Appendix A. The sound-absorbing properties of the panels under examination (i.e., A–D) were generally found to be extended towards the lower frequencies with increasing thicknesses of the panels (i.e., 20 mm, 40 mm, or 60 mm). The result is coherent with the findings of previous studies, such as in [13,18,21]. However, panel B exhibits an unexpected behavior, as while the sound absorbing properties of the thicker panels are higher at lower frequencies compared to the 20 mm sample, as it can be seen in the 500 to 1600 Hz frequency range, the 20 mm thick sample outperforms the 40 mm thick one in the range of 1600 to 4000 Hz. Moreover, no peak shift towards the lower frequencies is reported for the 60 mm thick panel compared to the 40 mm thick one, as both present an absorption peak at 800 Hz. These two aspects may suggest that the superficial and inner porosity of panels B are not uniform among the different thicknesses. Moreover, it can be argued that for this typology that the thickness threshold is ~40 mm, i.e., no further increase of the absorption coefficient below 800 Hz is obtained with the thickness increase from 40 to 60 mm [7]. Sample D outperforms the other typologies and confirms that its superficial and inner structures are made of many small and uniformly distributed pores and apertures connected with each other and with the outer surface [11].

When comparing samples with round lightweight aggregates, i.e., B–D, it can be observed that there is a decrease in the sound absorption when the aggregate size increases from 0.5–1 mm (sample D) to 4–8 mm (sample B). This is due to an increase in the median pore size when increasing aggregate size as shown in [21], which would reduce the tortuosity of the pore network, thus resulting in lower absorption values. Indeed, sample D has a lower water permeability (Table 1), which is inversely correlated to tortuosity [42]. Moreover, note that sample A with crushed normal weight aggregates results in higher values of the absorption coefficient when compared to sample B, which has similar void ratio (25%) and aggregate dimensions (4–8 mm) to sample A, but features different aggregate shapes and densities, i.e., round lightweight aggregates. This might be due to a higher tortuosity enabled by internal pores with varied size connected to the surface, which is coherent with the aspects highlighted in [11]. This kind of difference was not observed in previous studies, that is, the work in [22], where only slight differences between round-shape (lightweight) and irregular shape (normal weight) aggregates with the same gradation were found.

When considering panels composed of two layers, the presented results have highlighted some discrepancies between the sound absorbing performances of multilayered panels and those of a single layer panel of the same thickness in case of panel samples A–C. Conversely, samples D in the multilayered and single layer solution of equal thickness exhibit similar performances. This behavior may be linked to the different degrees of uniformity in the pore distribution of the different panel samples. In samples D, both sides of the panel present a uniform distribution of the pores apertures and the measurement results also suggest a higher connection of the internal pores to the surface as highlighted in [11]. Differently, for samples A–C, the closed pores presented in the back side of the panels (Figure 6) may not allow full activation of the absorption of the second layer. This highlights that the sound absorption performances of such sample may be improved if greater attention is paid during the treatment of the mix design and its curing in samples.

By comparing the sound absorbing performances of the different panel types measured mounted with an air gap of 50 mm, it emerges that the panel type D outperforms the other typologies. It presents a more uniform frequency-dependent sound absorption, a broader frequency range of high values of absorption coefficient, and absorption coefficients higher than those of other panel typologies. The performances of panels type C are slightly better than those of panels A and B. The worst performance is presented by panel type B, which is generally associated with the lower sound absorbing coefficient throughout the spectrum. This might be due to the effect of regular and bigger aggregates, which lead to reduced tortuosity of the pore network [21]. However, the behavior of samples A, B and C does not change much with the air gap, suggesting that the sound is at least partly blocked by the sample. Indeed, as it was highlighted also for the multilayer investigation, for the other three typologies the back sides of the panels (Figure 6) present a higher number of closed pores, which do not allow to fully activate the absorption due to the combination with the air gap.

Generally, when considering the additional layer of air gap, note that the performance of the 20 mm sample behaves as a layer of microperforated panel mounted with an air gap, i.e., presenting a clear sound absorption coefficient peak at low frequencies with poor values at higher frequencies [7]. This similarity is more evident for samples A and B, which are expected to have pore networks with lower tortuosity due to the greater dimension of the aggregates (4–8 mm) as presented in [21]. The 40 mm sample shows a similar behavior, which can resemble that of a multilayer microperforated panel (MPP) [43]. In this case, the thickness of the panel allows for a higher tortuosity of the pore network, which still allows for some absorption at higher frequencies. Indeed, the microperforated panel sound

absorption model presented by Maa [44,45] has been used in several studies to describe the acoustic behavior of concrete.

By partially or completely filling the air gap at the back of the 20 mm thick sample D with rock wool as porous material within the air gap, the sound absorbing performances were reported to improve down to 250 Hz. This is because the air resonance in the air gap and porous material layer is further damped by the porous material layer. This is coherent with the findings related to MPPs [43] and highlights the improvements on absorption with broader bandwidth and lower frequencies efficiency. These solutions' results are appropriate for several outdoor applications dealing with railway noise and traffic noise reductions and feature a spectrum of interest in the range of 125 to 4000 Hz [46]. Moreover, the investigated mounting systems could be integrated with structural multilayer building facades [47,48].

Note that it was observed that although sample D results with the highest performance in terms of evenness and rate, it presents poor performances related to wear resistance compared to the other types, which may hamper their application in actual scenarios if no facings or other protective solutions are used. Another option is to use panels of type B and C, which, when coupled in layers of 20 + 40 mm, reach sound-absorbing performances close to those of the same configuration of panels type D for frequencies higher than 800 Hz. Alternatively, a systematic investigation may be useful to detect the thresholds values of the concrete parameters (e.g., paste volume) in order to obtain acceptable mechanical properties and still preserve highly efficient acoustical properties.

The study highlights the necessity to develop a higher number of experimental investigations by controlling the variables of the mix design in more systematic way. This approach has been possible to follow only through model applications as in [45].

#### **5. Conclusions**

The present study has been carried out in order to characterize the sound absorbing performances of a set of porous concrete panels varying in concrete mix design (A–D), thickness and mounting method. The measurements have been conducted in the 1:5 scale reverberation room of the Politecnico di Torino, in accordance with the ISO 354-1:2003 standard. The sound absorbing performances of the different panels have been described as 1/3 octave band and as weighted sound absorption coefficient *αw*. The following conclusions have been drawn.


(v) The frequency dependent absorption coefficient and the weighted absorption coefficient *α<sup>w</sup>* comparisons showed that, depending on the mounting method, the performance of the concrete samples with aggregate dimensions of 0.5–1 mm, i.e., panel D, can be further improved. The *α<sup>w</sup>* reaches values 0.50 and 0.75 for the condition with an empty air gap of 50 mm and air gap completely filled with a rock wool layer, respectively. These values are comparable to those of most used conventional porous materials.

Note that the mix design mechanical properties remain a crucial aspect that need to be considered when the applicability of such materials is discussed. It was observed that the material with higher acoustic performance (round lightweight aggregate of 0.5–1 mm) presents poor performances related to wear resistance, which makes the application of such panels in actual scenario impractical. Therefore, we endorse further testing in the attempt to find the most performing solution balancing sound absorption with wear resistance performances. Alternatively, when wear resistance is required, it is possible to use panels of type B and C, which, when coupled in layers of 20 + 40 mm, reach sound-absorbing performances close to those of the same configuration of panels type D for frequencies higher than 800 Hz.

Further research could be conducted along this line of research to explore other mix design and mounting method strategies to hopefully increase awareness about the potential benefits of the application of sound absorbing porous concrete in the frame of the architectural and urban design strategies. Such research may include (1) acoustic absorption of materials with blended aggregates of different dimensions, weights and shapes, (2) acoustic absorption for alternative mounting methods, (3) acoustic absorption modeling of porous concrete of single layers and multilayer structure, and (4) possible applications in case studies for outdoor and indoor environments.

**Author Contributions:** Conceptualization, L.S., A.A., G.V., and D.Z.; methodology, L.S. and A.A.; formal analysis, L.S. and E.B.; investigation, L.S. and E.B.; resources, G.V. and D.Z.; data curation, L.S. and E.B.; writing—original draft preparation, L.S. and E.B.; writing—review and editing, L.S., A.A., E.B., and G.V.; visualization, L.S. and E.B.; supervision, L.S. and A.A.; project administration, L.S., A.A., and G.V.; funding acquisition, A.A. and L.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** The work has been funded by CEMEX Innovation Holding AG.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** The authors are grateful to Marta Bivanti and Giuseppe Vannelli for their contribution to the small-scale reverberation room measurements. They would like to thank the colleagues of CEMEX Innovation Holding AG who helped in manufacturing the samples.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **Appendix A**

Summary of the main findings of past studies on the effect on sound absorption of aggregate size.

(LS); aggregate (aggr.); sound absorption (*α*). **Mix Design Variable Effect [Refs] Details Method Main Findings** Aggregate size Influence [11] 0–2 mm/ 1–5 mm/1–3 mm Single sized 1–3 mm and 1–5 mm aggr. result in higher *<sup>α</sup>* Influence [19,21] 2.36–4.75 mm/ 4.75–9.5 mm/ 9.5–12 mm Single sized Concrete with 2.36–4.75 mm and 4.75–9.5 mm aggr. provide higher *α* than that with 9.5–12 mm aggr. Blended The effect of blending aggr. on *α* varies depending on the aggr. size. Best performance with blends of 2.36–4.75 mm and 4.75–9.5 mm aggr. Limited influence [22] 4–8 mm/8–12 mm/ 12–19 mm Single sized Slight increase in *<sup>α</sup>* for smaller aggr. (4–8 mm) compared to bigger ones Influence [12,13] >5 mm/ 1.25–5 mm/ <1.25 mm Single sized Concrete with aggr. dimensions >5 mm feature higher *α* than alternatives with smaller aggr. Layered Three-layered solutions with the aggr. dimensions (from exterior layer) of >5 mm/1.25–5 mm/ <1.25 mm result in the higher *α* No influence [22] 8–13 mm/ 13–19 mm Layered The variation of aggr. dimensions in the back layer does not affect the *α* Aggregate material Influence [11] Expanded perlite/slag/ clay ceramsite Single type Expanded perlite aggr. provides the highest *<sup>α</sup>* with respect to slag and clay ceramsite Expanded perlite/slag % replacement The *<sup>α</sup>* decrease with the relative increase in content of slag over expanded perlite aggr. Layered The combination of 8 cm slag (lower layer) and 12 cm expanded perlite (upper layer) is the most performing one among those considered Influence [22] LW + NW aggr./only LW aggr. Layered Layered solution with LW aggr. in the exterior layer and NW aggr. in the back layer outperform single layer with LW aggr. Limited influence [22] NW/LW aggr. Single type A slight increase in *α* is reported for crushed NW aggr. in comparison to rounded LW ones with similar sizes. The results do not seem consistent when varying the thickness of the concrete panel Influence [13] Bottom ash vs. normal aggr. Single type Bottom ash concrete results in higher or comparable *α* than a typical porous concrete sample Influence [23] Crumb rubber/fine normal aggr. % replacement Replacing fine aggr. with crumb rubber ones increase *α*, for increasing percentages of replacement (up to 20%) Influence [24] Bottom ash/recycled/ LS aggr. % replacement The replacement of LS aggr. with bottom ash and recycled aggr. result in higher *α*; the 2 nd peak shifts towards the higher frequencies for higher percentages of replacement No influence [20] Recycled aggr./ LS aggr. % replacement With equal target void ratio, the effect of replacing LS aggr. with recycled ones had very slight influence Influence [25] Cenosphere The increase of volume fraction of cenospheres

**Table A1.** Summary of the main findings of past studies on the effect on sound absorption of aggregate size, dimensions and type, and panel thickness. Abbreviations used in the table body: lightweight (LW); normal weight (NW); limestone

result in increased *α* from 0 to 20 to 40%; further increases result in lower performance

addition Single type


**Table A1.** *Cont.*

#### **Appendix B**

Graphs supplemental to the results provided as a direct comparison between different concrete typologies regarding thickness variation, multilayer combination, and mounting condition over an airgap.

**Figure A1.** Comparison of the absorption coefficients for samples A–D with different thicknesses. Sample A: crushed normal weight aggregates 4–8 mm; Sample B: round lightweight aggregates 4–8 mm; Sample C: round lightweight aggregates 2–4 mm; Sample D: round lightweight aggregates 0.5–1 mm.

**Figure A2.** Comparison of the absorption coefficients for samples A–D with different thicknesses obtained from multiple layer combinations (20 + 20 and 20 + 40 mm). Sample A: crushed normal weight aggregates 4–8 mm; Sample B: round lightweight aggregates 4–8 mm; Sample C: round lightweight aggregates 2–4 mm; Sample D: round lightweight aggregates 0.5–1 mm.

**Figure A3.** Comparison of the absorption coefficients for samples A–D with different thicknesses (20 and 40 mm) mounted over an airgap of 50 mm. Sample A: crushed normal weight aggregates 4–8 mm; Sample B: round lightweight aggregates 4–8 mm; Sample C: round lightweight aggregates 2–4 mm; Sample D: round lightweight aggregates 0.5–1 mm.

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