## 2 Materials and Methods
### 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\({}^{3}\) and a total area of 12.12 m\({}^{2}\). 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\" BSVA 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., T\({}_{20}\), is evaluated and used to estimate the T\({}_{60}\), 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 \(T_{1}\) 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 \(\alpha_{s}\).  
The difference between \(T_{1}\) and \(T_{2}\) measurements is used to calculate the variation of the equivalent sound absorption area \(A_{T}\) [m\({}^{2}\)] based on [PERSON]'s theory:  
\[A_{T}=55.3V\bigg{(}\frac{1}{c_{2}T_{2}}\,-\,\frac{1}{c_{1}T_{1}}\bigg{)}-4V(m_ {2}-m_{1}) \tag{1}\]  
where \(T_{1}\) and \(T_{2}\)[s] are the reverberation times of the empty reverberation room and of the reverberation room with the test specimen, respectively; \(V\) [m\({}^{3}\)] is the volume of the empty reverberation room; \(c_{1}\) and \(c_{2}\) [m/s] are the propagation speed of sound in air in the room without and with the sample: \(c_{1}=331+0.6\,t_{1}\), \(t_{1}\) [\({}^{\circ}\)C] is the air temperature; and \(m_{1}\) and \(m_{2}\) [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 \(\alpha_{s}\) is defined as  
\[\alpha_{S}=\frac{A_{T}}{S} \tag{2}\]  
where \(S\) [m\({}^{2}\)] 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].