Acoustic Assessment of Multiscale Porous Lime-Cement Mortars

Noise pollution is an issue of high concern in urban environments and current standards and regulations trend to increase acoustic insulation requirements concerning airborne noise control. The design and development of novel building materials with enhanced acoustic performance is an efficient solution to mitigate this problem. Their application as renders and plasters can improve the acoustic conditions of existing and brand-new buildings. This paper reports the acoustic performance of eleven multiscale porous lime-cement mortars (MP-LCM) with two types of fibers (cellulose and polypropylene), gap-graded sand, and three lightweight aggregates (expanded clay, perlite, and vermiculite). Gap-graded sand was replaced by 25 and 50% of lightweight aggregates. A volume of 1.5% and 3% of cellulose fibers were added. The experimental study involved a physical characterization of properties related to mortar porous microstructure, such as apparent density, open porosity accessible to water, capillarity absorption, and water vapor permeability. Mechanical properties, such as Young’s modulus, compressibility modulus, and Poisson’s ratio were evaluated with ultrasonic pulse transmission tests. Acoustic properties, such as acoustic absorption coefficient and global index of airborne noise transmission, were measured using reduced-scale laboratory tests. The influence of mortar composition and the effects of mass, homogeneity, and stiffness on acoustic properties was assessed. Mortars with lower density, lower vapor permeability, larger open porosity, and higher Young’s and compressibility modulus showed an increase in sound insulation. The incorporation of lightweight aggregates increased sound insulation by up to 38% compared to the gap-graded sand reference mixture. Fibers slightly improved sound insulation, although a small fraction of cellulose fibers can quadruplicate noise absorption. The roughness of the exposed surface also affected sound transmission loss. A semi-quantitative multiscale model for acoustic performance, considering paste thickness, active void size, and connectivity of paste pores as key parameters, was proposed. It was observed that MP-LCM with enhanced sound insulation, slightly reduced sound absorption.


Introduction
Airborne noise is a significant issue in urban environments that has been associated with urban pollution and health problems [1]. To tackle these problems, new building and urban regulations have upgraded the requirements to reduce noise production and improve acoustic insulation [2]. Most of the existing buildings do not meet those requirements due to their low acoustic performance and must be refurbished in due course to reduce noise and improve urban health.
Noise reduction in buildings refers both to the effect on the urban environment and inside buildings. In the first case, sound absorption of coating materials, which depends on surface continuity and material open porosity connectivity, can reduce sound reflection and therefore urban acoustic pressure [3,4]. Sound transmission from outside to the interior of the buildings depends on sound insulation, which is related to mass, homogeneity, stiffness, and material continuity of the building enclosure [5].

1.
Discussing the effect of gap-graded aggregates, lightweight aggregates, and fibers on airborne noise absorption and acoustic insulation of porous lime-cement mortars.

2.
Considering the influence of physical and mechanical parameters over sound insulation performance of multiscale porous lime-cement mortars. 3.
Analyzing the relationship between sound absorption and sound insulation parameters of multiscale porous lime-cement mortars.

4.
Describing a multiscale semi-quantitative model for the acoustic performance of porous lime-cement mortars.

Experimental Program
Eleven lime-cement mortar mixtures were evaluated, studying physical properties related to the material's porous structure, mechanical properties measured by ultrasonic pulse transmission, and noise absorption and insulation properties.

Materials
The components used for the mortar compositions were: • A binder mixture of an aerial lime type CL-90 S, designated according to the European standard UNE-EN 459-1 [23], and a white cement type BL-II/B-L 32,5 N, designated according to the European standard UNE-EN 197-1 [24] and the Spanish standard UNE 80,305 [25]. • Two types of siliceous sand: a continuous particle size distribution of 0-4 mm (CGA) and a gap-graded particle size distribution of 2-3 mm (GGA), characterized by the lack of particles under 2 mm.  Table 1 summarizes the eleven lime-cement mortar compositions used in this study. The proportion in volume lime to cement to aggregate remained 1:1:6 for all mortars. The amount of water was fixed in each case to achieve a plastic consistency [26]. It can be pointed out that no polymeric plasticizer was used. Two reference mortars with continuousgraded (REF) and gap-graded (REFC) natural siliceous aggregates were designed. Three lightweight aggregates were used to replace 25 and 50% of natural aggregate, resulting in five new mortar compositions (only 25% of replacement was considered for expanded clay). Cellulose fiber and PP fiber were added to the gap-graded reference and the mixture with 25% of perlite, resulting in four new mixtures. Table 1. Components in kg for a batch of 1 m 3 of multiscale porous lime-cement mortars (adapted from [6]). REF  REFC  CF15  CF30  A25  P50  P25  P25CF30 P25PPF  V50  V25   Cement  214  214  214  214  214  214  214  214  214  214  214  Lime  68  68  68  68  68  68  68  68  68  68  68  Cellulose fibers  - (2-3)  -1502  1502  1502  1127  751  1127  1127  1127  751  1127  Expanded clay  ----82 -

Physical Properties Characterization
Physical characterization of the porous structure of the mortar samples was performed to measure apparent density (D AP ), open porosity accessible to water (P O ), capillary water absorption (C), and water vapor permeability (P V ), according to the European standards UNE-EN 1015-10, UNE-EN 1015-18, and UNE-EN 1015-19, respectively [27][28][29]. Table 2 presents the physical parameters experimentally measured on mortar samples, which have been previously correlated [6]. Table 2. Physical properties related to mortar microstructure (adapted from [6,30]

Mechanical Characterization
Ultrasonic pulse velocity transmission of 250 kHz compressive (p-) and shear (s-) waves were used to calculate Young (E) and compressibility (K) moduli and Poisson's ratio (ν), according to the methods described elsewhere [30]. Table 3 records the experimental results obtained to characterize elastic stiffness and compressibility parameters.

Acoustic Characterization
Two parameters were used to characterize the acoustic performance of mortars. Noise reduction coefficient (α NRC ) was calculated using an impedance tube test ( Figure 1) on samples of 96 ± 2 mm diameter and 40 ± 2 mm thickness (UNE-EN ISO 10534-2 [31]) and frequencies ranging from 50 to 1600 Hz [6]. mortar sample (M) placed on a 150 × 150 mm 2 gap. The perimeter of the sample was conveniently insulated to avoid acoustic bridges and edge noise. A 100 dBA pink noise sound source (A) was placed in the emitting compartment and the acoustic pressure was measured in thirds of an octave with three sound-level meters (S) placed inside both compartments and outside the acoustic chamber, according to the European standard UNE-EN ISO 10140-4 [33]).  A background noise of 50 dBA was recorded at the external sound-level meter and 40 dBA inside the closed acoustic chamber. Each mortar sample was measured every 15 s for 60 s on both sides: one corresponding to the side manufactured on the outer side of Noise insulation was experimentally evaluated with the sound reduction index (R A ) measured in a reduced scale acoustic chamber [12,32] on 220 × 240 mm 2 mortar samples with a thickness of 24 ± 2 mm ( Figure 2). The acoustic chamber ( Figure 3) consisted of two compartments acoustically insulated (Emitting-E and Receiving-R) separated with a mortar sample (M) placed on a 150 × 150 mm 2 gap. The perimeter of the sample was conveniently insulated to avoid acoustic bridges and edge noise. A 100 dBA pink noise sound source (A) was placed in the emitting compartment and the acoustic pressure was measured in thirds of an octave with three sound-level meters (S) placed inside both compartments and outside the acoustic chamber, according to the European standard UNE-EN ISO 10140-4 [33]).
Two parameters were used to characterize the acoustic performance of mortars. Noise reduction coefficient (αNRC) was calculated using an impedance tube test ( Figure 1) on samples of 96 ± 2 mm diameter and 40 ± 2 mm thickness (UNE-EN ISO 10534-2 [31]) and frequencies ranging from 50 to 1600 Hz [6].
Noise insulation was experimentally evaluated with the sound reduction index (RA) measured in a reduced scale acoustic chamber [12,32] on 220 × 240 mm 2 mortar samples with a thickness of 24 ± 2 mm ( Figure 2). The acoustic chamber ( Figure 3) consisted of two compartments acoustically insulated (Emitting -E-and Receiving -R) separated with a mortar sample (M) placed on a 150 × 150 mm 2 gap. The perimeter of the sample was conveniently insulated to avoid acoustic bridges and edge noise. A 100 dBA pink noise sound source (A) was placed in the emitting compartment and the acoustic pressure was measured in thirds of an octave with three sound-level meters (S) placed inside both compartments and outside the acoustic chamber, according to the European standard UNE-EN ISO 10140-4 [33]).  A background noise of 50 dBA was recorded at the external sound-level meter and 40 dBA inside the closed acoustic chamber. Each mortar sample was measured every 15 s for 60 s on both sides: one corresponding to the side manufactured on the outer side of A background noise of 50 dBA was recorded at the external sound-level meter and 40 dBA inside the closed acoustic chamber. Each mortar sample was measured every 15 s for 60 s on both sides: one corresponding to the side manufactured on the outer side of the mold, designated rough side (RG), and the other casted against the mold, denominated smooth side (SM). Acoustic pressure in dBA was measured for each frequency range between 100-5000 Hz, comparing measurements with and without mortar samples, as described in Figure 3. These experimental values were used to calculate the sound reduction index for each frequency range, and consequently calculate the global sound level inside the emitted (L Ex ) and received (L Rx ) compartments in dBA and the experimental values of critic frequency (ƒc) of the acoustic range ( Figure 3). the mold, designated rough side (RG), and the other casted against the mold, denominated smooth side (SM). Acoustic pressure in dBA was measured for each frequency range between 100-5000 Hz, comparing measurements with and without mortar samples, as described in Figure 3. These experimental values were used to calculate the sound reduction index for each frequency range, and consequently calculate the global sound level inside the emitted (LEx) and received (LRx) compartments in dBA and the experimental values of critic frequency (ƒc) of the acoustic range ( Figure 3).  The acoustic insulation was assessed according to the European standard UNE-EN ISO 717-1 [34] and Equations (1)-(3), where R A is the acoustic insulation or global sound reduction index in dBA of the mortar sample, R A-C is the index estimated in dBA according to the acoustic mass law and f c-c is the critic frequency in Hz calculated considering apparent density (D AP ) in kg/m 3 , Young's modulus € in N/mm 2 , Poisson's ratio coefficient (ν), and sample thickness (d) in m. Table 4 summarizes the experimental values of the acoustic parameters related to sound absorption (α NRC ) and acoustic insulation (R A-SM , R A-RG , and R A-C ). Mortars REF, P50, V50, V25, and P25CF30 showed low α NRC values (0.037 ± 0.002). On the other hand, REFC, CF15, and A25 reached α NRC values above 0.1. The different behavior can be related to the porous structure of lightweight aggregates and the net of voids among the gap-graded aggregate particles [6]. Table 4. Acoustic properties of multiscale porous lime-cement mortars (adapted from [6]). Acoustic insulation calculated according to Equation (2) (R A-C ), considering the physical and mechanical properties of the mortars, was very similar for all the mixtures as expected, due to the larger influence of mass in Equation (2) and the slight differences of D AP . Calculated R A-C values reached 31 ± 2 dBA, 4-15 dBA larger than those measured in the laboratory (R A-SM and R A-RG ).

Parameters
The spectral frequency analysis showed the largest absorption values for 300 Hz and a decrease can be observed between 600 and 1000 Hz, followed by an increase until 1600 Hz. Acoustic reduction showed a maximum at 250 Hz and a second peak at 1600 Hz, with a critic frequency (f c ) around 500 Hz. However, the critic frequency calculated according to Equation (3) (f c-c ) would be between 860 and 1460 Hz, and the thirds of the octave that showed closer values were 800, 1000, and 1250 Hz.

Discussion: Acoustic Assessment of Multiscale Porous Lime-Cement Mortars
The effect of gap-graded aggregates (GGA), lightweight aggregates (LA), and fibers (F) on the acoustic properties of a multiscale porous lime-cement mortar (MP-LCM) is discussed. According to the literature [5], three groups of sound insulation parameters were considered: mass (D AP ), homogeneity (P O and P V ), and stiffness (E, K, and ν). The acoustic properties of multiscale porous lime-cement mortars (MP-LCM) are then discussed. The relationship between airborne noise absorption (α NRC ) and acoustic insulation (R A ) is also analyzed. Finally, a model for the acoustic performance of MP-LCM is proposed. When mixtures with lightweight aggregates (A25, P25, and V25) were considered, a change in acoustic properties regarding REFC was measured. Expanded clay (A25) slightly increased noise absorption up to 0.113, whereas perlite and vermiculite (P25 and V25) exhibited lower values than REFC. On the other hand, lightweight aggregates enhanced the acoustic insulation of the rough face. Only perlite (P25) showed better acoustic insulation performance of the smooth face, reaching the largest R A-SM value (25 dBA). The proportion of LA (perlite and vermiculite) hardly influenced airborne noise absorption. Regarding acoustic insulation of MP-LCM, double LA volume slightly varied the R A values, except for the rough face of V50. That is, vermiculite showed the maximum value of R A-RG (25.70 dBA).

Effect of MP-LCM Composition on Acoustic Properties
Cellulose fibers (CF) also modified the acoustic properties of MP-LCM. Sound absorption highly depended on the proportion of cellulose fibers, producing CF15 the maximum value of sound absorption (0.127). However, a larger number of fibers (CF30) did not enlarge the noise absorption coefficient (α NRC ) of MP-LCM [8]. It was observed that cellulose fibers and the volumetric fraction of CF did not significantly change the acoustic insulation. CF15 did not improve REFC values, whereas CF30 only increased R A-RG by 1 dBA. CF30 only achieved an extra 2 dBA of acoustic insulation regarding CF15.
The mortar mixture with perlite lightweight aggregate (P25) was combined with two types of short fibers: cellulose fibers (P25CF30) and polypropylene fibers (P25PPF). In these mixtures, the type of fibers modified the noise absorption differently: P25PPF increased the α NRC value, whereas P25CF30 reduced it. On the other hand and regarding acoustic insulation, mortars with both types of fibers presented lower R A values than P25, especially the rough side of P25CF30, which corresponded to the minimum R A measured value.

Assessment of Airborne Sound Reduction
According to the acoustic mass law (Equation (2)), sound insulation can be related to superficial weight (R A-C ). The calculated and the experimental acoustic insulation (R A ) are compared in Figure 4. It can be observed that the laboratory measurements were lower than the calculated sound reduction indices because the superficial weight was very similar for all the multiscale porous lime-cement mortars (MP-LCM). Therefore, the effectiveness of MP-LCM to reduce noise transmission must also depend on other parameters [5]. The influence of mass (D AP ), homogeneity (P O and P V ), and stiffness (E, K, and ν) on the acoustic insulation performance of MP-LCM was analyzed.    Apparent density was measured by filling with water the net of voids among the gapgraded aggregate particles and disregarding part of the volume of the sample. Therefore, changes in mass (D AP ) on MP-LCM were not sufficient to achieve an improvement in acoustic insulation.

Homogeneity and Sound Insulation Performance
According to experimental results, acoustic insulation (R A ) and open porosity (P O ) were directly related (Figure 6a) when the smooth and rough sides were compared. The use of GGA produced accessible voids, turning the mortars into pervious materials [11]. Large voids degrade the acoustic insulation performance because of sound diffraction [5,10]. However, the open porosity of MP-LCM increased due to paste fines content that filled the large voids of GGA and refined the mesopores network [6,8]. On the other hand, acoustic insulation and water vapor permeability (PV) showed an inverse relationship (Figure 6b). Water vapor permeability increased due to the increase in small pore size and a better-connected pore network. Consequently, it can be said that extra acoustic insulation was achieved by reducing water vapor permeability and increasing the open porosity of MP-LCM.

Elastic Stiffness, Compressibility, and Airborne Noise Transmission
Some relations between sound insulation (RA) and mechanical parameters calculated However, the open porosity of MP-LCM increased due to paste fines content that filled the large voids of GGA and refined the mesopores network [6,8]. On the other hand, acoustic insulation and water vapor permeability (P V ) showed an inverse relationship (Figure 6b). Water vapor permeability increased due to the increase in small pore size and a better-connected pore network. Consequently, it can be said that extra acoustic insulation was achieved by reducing water vapor permeability and increasing the open porosity of MP-LCM.

Elastic Stiffness, Compressibility, and Airborne Noise Transmission
Some relations between sound insulation (R A ) and mechanical parameters calculated from ultrasonic pulse velocity (E, K, and ν) were identified:

•
The global sound reduction indices (R A ) decrease when Young's (E) and compressibility (K) moduli increased, in both types of surfaces (Figure 7). That is, larger stiffness and compressibility meant a reduction in the acoustic insulation performance of MP-LCM.
• Airborne noise transmission (R A ) and Poisson's ratio (ν) were inversely proportional ( Figure 8). Accordingly, it can be said that more compressible MP-LCM enhances acoustic insulation of the smooth side (R A-SM ) and the rough side (R A-RG ). However, the open porosity of MP-LCM increased due to paste fines content that filled the large voids of GGA and refined the mesopores network [6,8]. On the other hand, acoustic insulation and water vapor permeability (PV) showed an inverse relationship (Figure 6b). Water vapor permeability increased due to the increase in small pore size and a better-connected pore network. Consequently, it can be said that extra acoustic insulation was achieved by reducing water vapor permeability and increasing the open porosity of MP-LCM.

Elastic Stiffness, Compressibility, and Airborne Noise Transmission
Some relations between sound insulation (RA) and mechanical parameters calculated from ultrasonic pulse velocity (E, K, and ν) were identified: • The global sound reduction indices (RA) decrease when Young's (E) and compressibility (K) moduli increased, in both types of surfaces (Figure 7). That is, larger stiffness and compressibility meant a reduction in the acoustic insulation performance of MP-LCM.   Figure 9 plots acoustic insulation (R A ) against airborne noise absorption (α NRC ). Larger noise absorption of MP-LCM was observed to slightly reduce sound insulation. Previously, selecting aggregate grading (GGA) enhanced the noise reduction coefficient due to a reduced open porosity and optimal void size [6,8]. Nevertheless, increasing open porosity improved the acoustic insulation of MP-LCM (Figure 6a). Accordingly, a compromise between noise insulation and absorption must be searched. This study demonstrated that MP-LCM can be designed to achieve acoustic insulation in a range from 18 to 24 dBA and a noise absorption above 0.10.  Figure 10 presents a multiscale semi-quantitative model for acoustic performance, following the basic model for pervious lime-cement-based mortars described elsewhere [8]. At the macroscale, three phases were identified: a lime-cement shell (PS), spherical monotonic size aggregates (A SMS ), and a continuous void network (CVN). Lime-cement shell thickness (d PS ) and active void size (VAS) were associated, as active void size varied inversely to paste shell thickness [8]. At the paste shell microscale, a multiphase matrix was considered (cement gel, lime crystals, fines, fibers, and air). Paste thickness and type of microscale phases depended on the component type and volume of paste [6,8]. following the basic model for pervious lime-cement-based mortars described elsewhere [8]. At the macroscale, three phases were identified: a lime-cement shell (PS), spherical monotonic size aggregates (ASMS), and a continuous void network (CVN). Lime-cement shell thickness (dPS) and active void size (VAS) were associated, as active void size varied inversely to paste shell thickness [8]. At the paste shell microscale, a multiphase matrix was considered (cement gel, lime crystals, fines, fibers, and air). Paste thickness and type of microscale phases depended on the component type and volume of paste [6,8]. Sound absorption varied due to the relation between the active void size and the paste shell thickness [8]. Reducing the size of the voids meant decreasing the noise absorption coefficient (αNRC), as other authors have reported that creating open porosity in concrete improved sound absorption due to the internal friction within the void walls, airflow resistivity, and tortuosity [10,19].

Multiscale Porous Lime-Cement Mortars: A Model for Acoustic Performance
The effect of lightweight aggregates (LA), such as perlite and vermiculite, on the paste shell thickness must also be discussed. LA increased the paste volume due to the filler effect of the large amount of LA dust produced by the fracture of LA particles [6] that thickened the shell and reduced the active void size, decreasing αNRC [8]. Sound absorption barely changed when the amount of LA was doubled, as the void network was already clogged.
On the other hand, expanded clay absorbed more noise since its particles were not broken and therefore the volume of paste was lower [6] and the paste shell thinner. Cellulose fibers also thickened the paste shell, although the amount of fiber was affected differently. A greater amount of fiber may lead to agglomerations, which further increase the paste shell thickness [8]. In addition, when perlite and fibers were combined, different behaviors were observed depending on the fiber type and the volumetric fraction added. A larger number of cellulose fibers implied a thicker paste shell and lesser sized void, producing one of the lowest noise reduction coefficients.
According to the experimental results (Figure 9), the acoustic insulation performance of MP-LCM (RA) improved when sound absorption (αNRC) decreased. Therefore, sound insulation in MP-LCM will enhance when paste thickness increase. In addition, the paste shell is characterized by pore connectivity (CPP), fines, and/or fiber content. The pore connectivity of the paste is related to the water vapor permeability and some authors have correlated water vapor permeability, air permeability, and acoustic performance [9]. Perlite and vermiculite improved acoustic insulation as they reduced CPP. Although expanded clay (A) reduced CPP, it did not improve acoustic insulation due to the porous structure of the aggregate and larger particle size than perlite and vermiculite [6]. That means greater inertia to vibrate and less acoustic energy dissipation [10,12]. The different aggregate intra-particle pores affected the acoustical behavior [9]. Combining LA with Sound absorption varied due to the relation between the active void size and the paste shell thickness [8]. Reducing the size of the voids meant decreasing the noise absorption coefficient (α NRC ), as other authors have reported that creating open porosity in concrete improved sound absorption due to the internal friction within the void walls, airflow resistivity, and tortuosity [10,19].
The effect of lightweight aggregates (LA), such as perlite and vermiculite, on the paste shell thickness must also be discussed. LA increased the paste volume due to the filler effect of the large amount of LA dust produced by the fracture of LA particles [6] that thickened the shell and reduced the active void size, decreasing α NRC [8]. Sound absorption barely changed when the amount of LA was doubled, as the void network was already clogged.
On the other hand, expanded clay absorbed more noise since its particles were not broken and therefore the volume of paste was lower [6] and the paste shell thinner. Cellulose fibers also thickened the paste shell, although the amount of fiber was affected differently. A greater amount of fiber may lead to agglomerations, which further increase the paste shell thickness [8]. In addition, when perlite and fibers were combined, different behaviors were observed depending on the fiber type and the volumetric fraction added. A larger number of cellulose fibers implied a thicker paste shell and lesser sized void, producing one of the lowest noise reduction coefficients.
According to the experimental results (Figure 9), the acoustic insulation performance of MP-LCM (R A ) improved when sound absorption (α NRC ) decreased. Therefore, sound insulation in MP-LCM will enhance when paste thickness increase. In addition, the paste shell is characterized by pore connectivity (CPP), fines, and/or fiber content. The pore connectivity of the paste is related to the water vapor permeability and some authors have correlated water vapor permeability, air permeability, and acoustic performance [9]. Perlite and vermiculite improved acoustic insulation as they reduced CPP. Although expanded clay (A) reduced CPP, it did not improve acoustic insulation due to the porous structure of the aggregate and larger particle size than perlite and vermiculite [6]. That means greater inertia to vibrate and less acoustic energy dissipation [10,12]. The different aggregate intra-particle pores affected the acoustical behavior [9]. Combining LA with fibers meant a lower acoustic insulation performance, as fibers increased pore connectivity, especially cellulose fibers.

Conclusions
This paper presents an experimental study to evaluate the effect of gap-graded aggregates (GGA), lightweight aggregates (LA), and fibers (F) on the acoustic performance of multiscale porous lime-cement mortars (MP-LCM). The experimental program comprised measuring physical and mechanical properties and assessing airborne noise absorption and acoustic insulation. Mass, homogeneity, and stiffness were correlated to the global index of