The use of numerical models on service equipment noise prediction in heavyweight and lightweight timber buildings

Abstract

In modern constructions, service equipment is the most used and complex technology. Air and liquid flow inside piping or conduit provides conditioning, well-being and comfort within buildings. Nevertheless, fluid movements inject both structure-borne and airborne noise, causing annoyance on people living inside edifices. In order to avoid this issue, the model provided by ISO 12354-5 standard could be used. Unfortunately, the standard describes very well the process in order to calculate the resulting noise caused by air flow service equipment, but it does not offer clear definitions of parameters related to waste water installations. As a consequence, very few researches and studies are available at present because of the difficulty on initial data set and on interpretation of requested parameters. In this article, the ISO 12354-5 method for waste water pipe source is critically analysed, modified and then applied to real case studies. Considerations on coupling terms are proposed, discussed and used in the standard equations, calculating the theoretical values and providing possible solutions for all missing data; results demonstrate how the suggested modified models matched very well measurements outcomes.

Keywords

Building services acoustic waste water ISO 12354-5 lightweight buildings numerical models resilient materials sound power level structure-borne power coupling term flanking transmission

Introduction

Service equipment is a frequent noise source in buildings.^1,2 As a matter of fact, air and water motion causes sound waves propagating through building structures. Sound level prediction due to service equipment could be modelled using ISO 12354-5 methods.³

Noise from air equipment (heating, ventilation, and air conditioning (HVAC)) is widely studied and well described in the literature. Sharland⁴ described methods for noise reduction on pipes, silencers and so on. Beranek and Vér⁵ proposed empiric equations to predict source airborne sound and its possible attenuation.

On the other hand, concerning waste water flushing system prediction models, only a single international study is available at the moment. Even in their recent review, Mak and Wang⁶ did not report waste⁷ water noise topic.

Villot⁸ described the application of the ISO 12354-5 standard to some cases. Other studies on the same standard focus on different issues; these reseach report interlaboratory tests, performed in order to understand the repeatability of structure-borne sound determination, using substitution method⁹ or ‘two-stage’ method;¹⁰ Schevenels et al.¹¹ focus their research on the injected structure-borne sound determination, whether Gerretsen¹² depicted some aspects on the predictions of this parameter caused by house-hold equipment. Santoni and Fausti¹³ studied the structure-borne sound using field measurements.

Kornadt et al.¹⁴ highlighted that data related to sources for structure-borne sound are missing at the moment. Vogel et al.¹⁵ described a two-stage method in order to determine the sound power level value L_w, but, in their sources list, the waste water installation is missing. Therefore, in years, researchers try to handle with the structure-borne sound from small¹⁶ to large¹⁷ equipment. Even Seoane et al.¹⁸ do not include building service equipment in their work. Weber and Mohr¹⁹ described the possible complications or laboratory measurements.

This lack of researches on ISO 12354-5 waste water noise prediction is related to several issues:

Complexity of the proposed models.

Difficulty to find initial input data.

Source directivity is often indeterminable.

Lack of precise indication on how input data are to be used and applied to real cases.

Absence of unique interpretation of described parameters.

Source is often close to reflecting partitions. Fro this reason, the diffuse-field approach has to be used very carefully.

Therefore, the aims of this study are (1) to critically analyse the ISO 12354-5 methods for waste water pipe source, (2) to modify and adapt them in order to obtain reliable results and then (3) to apply them to real case studies.

The first section presents the complex calculation method contained in the standard. The second section describes all the bullets point and provides an interpretation of possible solutions. In the last section, the proposed calculation is applied to real case studies and compared with field measurements.

Materials and method

The models contained in the standard are described and a critic in-depth analysis is provided. It includes a step-by-step description, unrolling all phases and providing possible solutions for missing data.

The waste water source is related with two different noise natures:

Airborne;

Vibration.

Both of them are caused by flushed waste water and come from pipes; nevertheless, for model purposes, they are separated, because the propagation paths as well as the transmission modalities are different.

The former (airborne) is generated inside the pipe. A part of it propagates within the conduit and exits where the pipe ends. The other portion comes out of the pipe walls and spreads through the building (see Figure 1).

Figure 1.

Airborne propagation paths.

This noise is caused by the impact of the flushed water against the pipe. The induced vibration finds a solid propagation path along both the conduit walls and the building partitions (Figure 2).

Figure 2.

Vibrations propagation paths.

The general expression of the sound pressure level at receiver due to service equipment is the result of the sum of the following parameters

L_{n} = 10 \cdot \log (\sum 10^{\frac{L_{n, d}}{10}} + \sum 10^{\frac{L_{n, a}}{10}} + \sum 10^{\frac{L_{n, s}}{10}}) (dB)

(1)

where L_n is the total normalized sound pressure level due to the source(s) (dB); L_n,d is the sound pressure level due to the sound transmission through the pipe (dB); L_n,a is the sound pressure level due to airborne sound transmission through the building structure (dB) and L_n,s is the sound pressure level due to structure-borne sound transmission through the building structure (dB).

If more than one pipe is included in the room, the total normalized sound pressure level and its included parameters will be the result of the sum of multiple contributions. In the standard, equation (1) is valid both for air conduits and for waste water pipe. For this reason, it has to be adapted case by case.

The sound pressure level due to the transmission through the pipe L_n,d is related to the airborne noise connected to waste water movement. Therefore, its influence could be neglected since the waste water does not flow into receivers’ room.

The sound pressure level due to airborne sound transmission through the building structure L_n,a is constituted of different components such as sound power level of the source L_w, flanking transmission R_ij, sound transmission to element in the source room D_s and two adaptation terms. The first one derives from laboratory tests according to EN 14366 standard,²⁰ the second from ISO 12354-1 standard²¹ and the third is expressed as follows (equation (2))

D_{s} = 10 \log (\frac{Q^{'}}{4 π r^{2}} + \frac{e^{- \frac{A_{s}}{S_{t}}}}{A_{s}}) \cdot S_{i} (dB)

(2)

where Q′ is the source directivity, r is the average distance from source to element (m), A_s is the equivalent absorption area in the source room, S_t is the total area of boundaries of the source room (m²) and S_i is the area of the single element.

The sound pressure level L_n,s due to structure-borne sound transmission through the building structure is constituted of different components such as the characteristic structure-borne sound power level of the source L_ws,c, the coupling term for the source of the supporting building element D_c, the adjustment term from structure-borne to airborne excitation for supporting building element D_sa, the flanking transmission R_ij and two adaptation terms.

The first one is derived from the laboratory test according to EN 14366 standard, the second is related to the mobility of the supporting element, the third refers to sound radiation and critical frequency and it could be expressed using ISO 12354-1 model.

Discussion and analysis of the theoretical expression

The complexity of presented model lies in the plural nature of the noise. For this reason, it is very difficult for a designer, technician or researcher to understand every single phase. In Figure 3, a scheme of the presented steps is depicted.

Figure 3.

Scheme of the studied parameters or steps.

The first step consists in the analysis of EN 14366 laboratory results from pipe producers. These certificates have to be deeply analysed because very often they include the structure-borne sound insulating support. This fact do change the former input data (Figure 4). The A configuration refers to the laboratory test of airborne noise of a waste water pipe fastened with rigid support. The B one reports a conduit secured using sound insulating support.

Figure 4.

Airborne laboratory results for different configurations: A with rigid support and B with sound insulating support.

It is evident how the two configurations provide very different final values. Therefore, the equations have to offer adaptation terms in order to calculate final values. At present, no relation is provided.

Furthermore, in order to calculate D_s parameter, the directivity of the source as well as the average distance from source to element is required. As Villot previously highlighted,⁸ it is almost impossible to determine the directivity of a waste water pipe without assuming approximations. The distance from the element is often very short. In the case of a waste water pipe inserted into a wall, the distance is almost 0 and the D_s ratio tends to an infinite value. Even using small distance (i.e. one or two centimetres), final values do not result reliable.

The D_s parameter has to be calculated on every propagation path. Nevertheless, if the calculation is performed for the other elements of the buildings, it can be seen that results are negligible, because both distance and propagation path tend to minimum values. As a matter of fact, the A_s parameter increases a lot and the r (power by 2) parameter will increase as well. This leads to final negligible values and so, at the end, only the direct D_s could be used.

The R_ij evaluation could be easily performed using ISO 12354-1 models. On the other hand, this standard was intended to operate on heavyweight homogeneous partitions,^22–24 while the use in lightweight or double leaf structures is compromised. As it could be understood from equation (3), the K_ij terms are based on the mass ratio between the walls composing the junctions

\begin{array}{l} K_{13} = 5, 7 + 14.1 \cdot M + 5.7 \cdot M^{2} \\ K_{12} = 5, 7 + 5.7 \cdot M^{2} \\ M = \frac{{m^{'}}_{i \neg}}{{m^{'}}_{i}} \end{array}

(3)

where ${m^{'}}_{i \neg}$ is the mass per unit area of the element in the transmission path ij (kg/m²) and ${m^{'}}_{i}$ is the mass per unit area of the other perpendicular element composing the junction (kg/m²)

As seen before, in timber buildings, many technologies are possible;^24–27 the most used and studied is the one composed by particle or gypsum board on top on wooden glulam beams, with screw attaching the boards to the beams. Concerning this type, no mass ratio could effectively be computed.²⁸ In timber buildings, the subjective response related to service equipment is of paramount importance.^25,29,30

In the next step, the EN 14366 laboratory results for structure-borne sound are analysed. As before, these certificates have to be analysed because very often they include the structure-borne sound insulating support. This fact changes the former input data as shown in Figure 5. The A configuration refers to a waste water pipe fastened with rigid support. The B one reports a conduit secured using vibration insulating support.

Figure 5.

Structure-borne laboratory results for different configurations: A with rigid support and B with sound insulating support.

Here, the effect of the vibration insulating support is evident but the A type values could not be used as input data for equation (1) because they do not represent the real structure-borne sound power level.

Furthermore, for B configuration, when the elastic support is not present, the D_c influence depends on the mobility of the system. This effect is related to the elasticity of the support. The ISO 12354-5 standard proposes the following equation (4) in order to analytically solve the composed system

D_{c} = - 10 \log Re {Y_{i}} - 30 (dB)

(4)

Y_{i} \approx \frac{f_{c}}{150, 000 \cdot t} (m / N s)

where Y_i is the mobility of the system (m/N s) and f_c is the critical frequency (Hz). This could be calculated using ISO 12354-5 as reported in equation (5)

f_{c} = \frac{c_{0}}{1.8 \cdot c_{L} \cdot t} (Hz)

(5)

where t is the element thickness (m), c₀ is the sound speed in air (m/s) and c_L is the longitudinal velocity inside the propagating material (m/s). The longitudinal velocity is expressed using the following equation

c_{L} = \sqrt{\frac{E}{ρ}} (m / s)

(6)

where E is Young’s modulus (Pa) and ρ is the density of the element (kg/m³).

The typical resilient materials used as vibration insulators are, for example, expanded rubber, expanded polyethilen (PE) (see Figure 6).

Figure 6.

Typical vibrant insulator application: (a) expanded PE and (b) resilient ring.

Young’s modulus values of these materials are very difficult to find. Moreover, often the resilient rings have not regular shapes since they present ‘wave’ or ‘point’ features (see Figure 7). The final performance of the linear materials is not equal to the shaped one.

Figure 7.

Vibration insulators presentig shaped morphology.^31,32

This could be overcome using the literature³³ or standard³⁴ models where equation (7) is reported

E = s^{'} . d

(7)

where s′ is the dynamic stiffness^35–37 of the resilient layer (Mn/m³) and d is its thickness (m).

The calculation of the sound power levels L_w and L_wsc derives from EN 14366 results according to equations (8) and (9)

L_{w} = L_{a} + 10 \cdot \log \frac{A_{ref}}{4} = L_{a} + 4 (dB)

(8)

L_{wsc} = L_{sc} + 8 \cdot \log f + 23.5 (dB)

(9)

L_w has no frequency expression so it is not possible to perform frequency domain calculations as for L_wsc.

Finally, another issue is related to terminology. Since the available methods were studied both for air and for water service equipment, lexicon is unfortunately ambiguous. As an example, the word ‘element’ is used in almost every description. Nevertheless, this is a very general subject and it does not identify a precise and unique object or case. Even if in the ‘air’ case, the ‘elements’ are easily identified; on the other hand, in the ‘water’ instance, some specifications could be very useful.

As an example, the D_s term (equation (2)) is described as the sound transmission to element in the source room. In the case of a pipe included in a wall or in a shaft, both in heavyweight or in lightweight construction, source room and receiving room coincide. Therefore, the ‘element’ is not a definite identification. In the same way, the average distance r from source to element is difficult to understand, because the ‘element’ is not clearly identified.

Real case studies

In this section, the models discussed before are applied to possible real cases both in heavyweight and in lightweight timber constructions in order to compare and analyse if the methods are applicable to both technologies. Then, for the latter ones, an evaluation using field measurements is provided.

Case 1 – heavyweight structures – pipe within a wall

This analysis focuses on a waste water installation embedded in a wall which separate different superimposed apartments.

The conduit has a 5 mm expanded PE layer all around it and it lays within a 25 cm hollow bricks walls (see Figure 8). As a consequence, only a thin mortar layer divides the pipe from the receiving room.

Figure 8.

Case 1 scheme: pipe embedded in a wall.

The flanking walls are realized with 8 cm hollow bricks and the dividing floors were realized using beam and pot technology.³⁸ The noise source is in apartment A when a 2 L/s water flow is released (flushing cistern) on the upper floor. The prediction is performed in apartment B.

In order to acquire the input data, a certificate according to EN 14366 standard is required.³⁹ Considering the topic discussed above, some approximation have to be assumed. In Tables 1 and 2, a summary of 500 Hz 1/3 octave band calculated results are reported.

Table 1.

Calculations and considerations concerning airborne sound pressure level.

– Sound power level L_w	Using EN 14366 results and equation (1), the sound power level results L_w500 Hz = 38.4 dB(A)
– Direct transmission D_s	No distance from source to element is present, then D_s = 0
– Flanking transmissions R_{ij, ref}	– Dividing wall (d): m′ = 287 kg/m² R_w500 Hz = 52 dB S = 8.1 m² – Mortar covering layer (D): m′ = 110 kg/m² R_w500 Hz = 24.3 dB – Flanking walls (1, 2): m′ = 136 kg/m² R_w500 Hz = 44 dB S = 8.1 m² – Upper floor (3): m′ = 458 kg/m² R_w500 Hz = 54.3 dB S = 9 m² – lower floor (4): m′ = 458 kg/m² R_w500 Hz = 54.3 dB S = 9 m² Though, final values results: ➢ R_{Dd 500 Hz} = 26.5 dB ➢ R_{1d 500 Hz} = 59.2 dB ➢ R_{2d 500 Hz} = 59.2 dB ➢ R_{3d 500 Hz} = 63.8 dB ➢ R_{4d 500 Hz} = 63.8 dB

Table 2.

Calculations and considerations concerning structure-borne sound pressure level.

– Structure-borne sound power level L_wsc	Using EN 14366 results and equation (1), the sound power level results L_{wsc, 500 Hz} = 51.7 dB(A)
– Coupling term D_c	In the laboratory certificate, the test conditions are described. It is reported that the pipe was fastened using a vibration insulating support. Though, it is not possible to compute the mobility using equations (4)–(7), beacause final values are already affected by its decoupling influence. Here, it could be assumed that the insulating results are equal both using expanded PE and insulating support(s), then D_c = 0
– Flanking transmissions R_{ij, ref}	– Dividing wall (Dd): m′ = 285 kg/m² R_w500 Hz = 52 dB S = 8.1 m² – Flanking walls (1, 2): m′ = 136 kg/m² R_w500 Hz = 44 dB S = 8.1 m² – Upper floor (3): m′ = 458 kg/m² R_w500 Hz = 54.3 dB S = 9 m² – Lower floor (4): m′ = 458 kg/m² R_w500 Hz = 54.3 dB S = 9 m² Though, final values results: ➢ R_{Dd 500 Hz} = 52 dB ➢ R_{1d 500 Hz} = 40 dB ➢ R_{2d 500 Hz} = 40 dB ➢ R_{3d 500 Hz} = 61.5 dB ➢ R_{4d 500 Hz} = 61.5 dB
– Adjustment term D_sa	The pipe excites the dividing wall (c_L,D = 3500 m/s, t = 25 cm) and this transmits the vibrations to the flanking vertical partitions (c_L1,2 = 2600 m/s, t = 12 cm) and horizontal ones (c_L3,4 = 3500 m/s, t = 24 cm): ➢ D_{sa D} = –32.6 dB(A) ➢ D_{sa 1,2} = –26.2 dB(A) ➢ D_{sa 3,4} = –35.7 dB(A)

Using Table 1 assumptions, it can be concluded that the final airborne sound pressure level results L_{na, A,500 Hz} = 8.8 dB(A). Using Table 2 assumptions, it can be concluded that the final structure-borne sound pressure level results L_{n, s,500 Hz} = 38.4 dB(A).

The final sound pressure level results L_{n, A,500 Hz} = 38.4 dB(A). The final frequency level values are reported in Table 3.

Table 3.

Final results for case 1.

Hz	125	250	500	1000	2000	4000	L_A (dB(A))
L_{na, A}	8.6	5.6	8.8	10.9	9.6	8.2	16.7
L_{ns, A}	33.0	39.4	38.4	38.4	35.6	39.1	45.6
L_{n, A}	33.1	39.4	38.4	38.4	35.6	39.1	45.6

Case 2 – heavyweight structures – pipe within insulated shaft

This analysis takes into account a waste water installation inserted in a shaft filled with fibrous material and fastened on a wall separating two different apartments using vibration insulator support (Figure 9). Flanking transmissions are the same of case 1. The noise source is inside the shaft and the prediction is provided in the same dwelling as before when a 2 L/s water flow is released (flushing cistern).

Figure 9.

Case 2 scheme: pipe within insulated shaft.

In order to acquire the input data, a certificate according to EN 14366 standard is required.³⁹ Considering the topic discussed above, some approximation have to be done. In Tables 4 and 5, a summary of 500 Hz 1/3 octave band calculated results are reported.

Table 4.

Calculations and considerations concerning airborne sound pressure level.

– Sound power level L_w	Using EN 14366 results and equation (1), the sound power level results: L_w500 Hz = 38.4 dB(A)
– Direct transmission D_s	– Assuming that the pipe is a cylindrical source, the directivity results: Q′ = 1, – average distance: r = 15 cm, – shaft total area: S_t = 2.43 m², – equivalent absorption area: A_s = 2.19 m², ➢ D_s = 13.9 dB
– Air propagation paths R_{ij, ref}	– Shaft walls (Dd): m′ = 136 kg/m² R_w500 Hz = 44 dB S = 2.43 m² – Dividing wall (1, 2): m′ = 285 kg/m² R_w500 Hz = 52 dB S = 8.1 m² – Upper floor (3, 4, 5): m′ = 458 kg/m² R_w500 Hz = 54.3 dB S = 9 m² – Lower floor (6, 7, 8): m′ = 458 kg/m² R_w500 Hz = 54.3 dB S = 9 m² Though, final values results: ➢ R_{Dd 500 Hz} = 44 dB ➢ R_{1d 500 Hz} = 49.1 dB ➢ R_{2d 500 Hz} = 49.1 dB ➢ R_{3d 500 Hz} = 60.7 dB _➢R_{4d 500 Hz} = 60.7 dB ➢ R_{5d 500 Hz} = 60.7 dB ➢ R_{6d 500 Hz} = 60.7 dB ➢ R_{7d 500 Hz} = 60.7 dB ➢ R_{8d 500 Hz} = 60.7 dB

Table 5.

Calculations and considerations concerning structure-borne sound pressure level.

– Structure-borne sound power level L_wsc	Using EN 14366 results and equation (1), the sound power level results: L_{wsc 500 Hz} = 51.7 dB(A)
– Coupling term D_c	In the laboratory certificate, the test is described. It is reported that the pipe was fastened using a vibration insulating support. Though, it is not possible to compute the mobility using equations (4)–(7), because final values are already affected by its decoupling influence. Here, it could be assumed that the insulating results are equal both using expanded PE and insulating support(s), then D_c = 0
– Adjustment term D_sa	As for D_c term, it is not possible to compute the parameter, since the pipe is never in solid contact with partitions, then D_sa = 0
– Flanking transmissions R_{ij, ref}	– Dividing wall (Dd): m′ = 285 kg/m² R_w500 Hz = 52 dB S = 8.1 m² – Shaft walls (1, 2): m′ = 136 kg/m² R_w500 Hz = 44 dB S = 2.43 m² – Upper floor (3): m′ = 458 kg/m² R_w500 Hz = 54.3 dB S = 9 m² – Lower floor (4): m′ = 458 kg/m² R_w500 Hz = 54.3 dB S = 9 m² Though, final values results: ➢ R_{Dd 500 Hz} = 52 dB ➢ R_{1d 500 Hz} = 49.1 dB ➢ R_{2d 500 Hz} = 49.1 dB ➢ R_{3d 500 Hz} = 65.2 dB ➢ R_{4d 500 Hz} = 65.2 dB

Using Table 4 assumptions, it can be concluded that the final airborne sound pressure level results L_{na, A,500 Hz} = 11.3 dB(A). Using Table 5 assumptions, it can be concluded that the final structure-borne sound pressure level results L_{ns, A,500 Hz} = 13.3 dB(A).

The final sound pressure level results L_{n, A,500 Hz} = 15.4 dB(A). The final frequency level is reported in Table 6.

Table 6.

Final results for case 2.

	125 Hz	250 Hz	500 Hz	1000 Hz	2000 Hz	4000 Hz	LA (dB(A))
L_{na, A}	8.0	7.3	11.3	14.6	13.4	16.6	20.8
L_{ns, A}	18.7	20.2	13.3	7.8	−0.9	−1.6	23.2
L_{n, A}	19.0	20.4	15.4	15.4	13.6	16.7	25.1

Case 3 – lightweight structures – pipe within a wall

This analysis takes into account a waste water installation inserted in a precast lightweight wooden panel and fastened on a dividing wall separating two different apartments using vibration insulator support (Figure 10). The noise source is in apartment A whereas the prediction is provided for apartment B when a 2 L/s water flow is released (flushing cistern). The dividing wall is constituted of six gypsum layers coupled with fibrous panels, as described in Figure 10. Dividing floors are constructed using glulam^40,41 technology coupled with a suspended ceilings. Flanking walls are realized using timber frame structures closed with gypsum boards.

Figure 10.

Case 3 scheme – pipe within a wall.

In order to acquire the input data, a certificate according to EN 14366 standard is required.³⁸ As above, some approximation has to be done. In Tables 7 and 8, a summary of 500 Hz 1/3 octave band is reported.

Table 7.

Calculations and considerations concerning airborne sound pressure level.

– Sound power level L_w	Using EN 14366 results and equation (1), the sound power level results: L_w500 Hz = 38.4 dB(A)
– Direct transmission D_s	No distance from source to element is present, then D_s = 0
– Flanking transmissions R_{ij, ref}	– Dividing wall (d): m′ = 160 kg/m² R_w500 Hz = 54.8 dB S = 8.1 m² – Flanking wall (1): m′ = 140 kg/m² R_w500 Hz = 56.3 dB S = 8.1 m² – Flanking wall (2): m′ = 101 kg/m² R_w500 Hz = 28 dB S = 8.1 m² – Upper floor (3): m′ = 180 kg/m² R_w500 Hz = 56.3 dB S = 9 m² – Lower floor (4): m′ = 180 kg/m² R_w500 Hz = 56.3 dB S = 9 m² Though, final values results: ➢ R_{Dd 500 Hz} = 54.8 dB ➢ R_{1d 500 Hz} = 65.7 dB ➢ R_{2d 500 Hz} = 51.8 dB ➢ R_{3d 500 Hz} = 63.7 dB ➢ R_{4d 500 Hz} = 63.7 dB

Table 8.

Calculations and considerations concerning structure-borne sound pressure level.

– Structure-borne sound power level L_wsc	Using EN 14366 results and equation (1), the sound power level results L_{wsc, 500 Hz} = 51.7 dB(A)
– Coupling term D_c	In the laboratory certificate, the test is described. It is reported that the pipe was fastened using a vibration insulating support. Though, it is not possible to compute the mobility using equations (4)–(7), because final values are already affected by its decoupling influence, then D_c = 0
– Flanking transmissions R_{ij, ref}	See Table 7
– Adjustment term D_sa	The pipe excites the dividing wall. Nevertheless, this is constituted of many different impedance layers. The hollow space damping effect does not permit a solid transmission and as a matter of fact, it is the most vibration insulator Though, c_{L, D} = 100 m/s, t = 60 cm ➢ D_{sa D} = –18.6 dB(A)

Using Table 7 assumptions, it can be concluded that the final airborne sound pressure level does not result influent for final prediction, since the final value results negative. Using Table 8 assumptions, it can be concluded that the final structure-borne sound pressure level results L_{n, s,500 Hz} = 17.8 dB(A).

The final sound pressure level results L_{n, A,500 Hz} = 17.8 dB(A). The final frequency level is reported in Table 9.

Table 9.

Final results for case 3.

Frequency [Hz]	125	250	500	1000	2000	4000	L_A (dB(A))
L_{na, A}	−	−	−	−	−	−	−
L_{ns, A}	16.8	18.3	17.8	19.2	13.5	17.5	25.3
L_{n, A}	16.8	18.3	17.8	19.2	13.5	17.5	25.3

Case 4 – lightweight structures – pipe within a shaft

This analysis takes into account a waste water installation inserted in an insulated shaft (0.30 × 0.30 × 2.7 m) lying in a corner of the room (see Figure 11). Flanking structures are similar to case 4.

Figure 11.

Case 4 scheme – pipe within insulated shaft.

The noise source is inside the apartment as well as the receiver. Therefore, the prediction was considered using an internal receiver, when a 2 L/s water flow is released (flushing cistern).

In order to acquire the input data, a certificate according to EN 14366 standard is required.³⁹ Considering the topic discussed above, some approximation have to be done. In Tables 10 and 11, a summary of 500 Hz 1/3 octave band is reported.

Table 10.

Calculations and considerations concerning airborne sound pressure level.

– Sound power level L_w	Using EN 14366 results and equation (1), the sound power level results: L_w500 Hz = 38.4 dB(A)
– Direct transmission D_s	– Assuming that the pipe is a cylindrical source, the directivity results: Q′ = 1, – average distance: r = 15 cm, – shaft total area: S_t = 1.62 m², – equivalent absorption area: A_s = 1.46 m², D_s = 9.4 dB
– Flanking transmissions R_{ij, ref}	– Shaft walls (Dd): m′ = 35 kg/m² R_w500 Hz = 29 dB S = 1.62 m² – Supporting wall (1): m′ = 140 kg/m² R_w500 Hz = 54.8 dB S = 8.1 m² – Corner wall (2): m′ = 160 kg/m² R_w500 Hz = 56.3 dB S = 8.1 m² – Upper floor (3): m′ = 180 kg/m² R_w500 Hz = 54.8 dB S = 9 m² – Lower floor (4): m′ = 180 kg/m² R_w500 Hz = 54.8 S = 9 m² Though, final values results: ➢ R_{Dd 500 Hz} = 29 dB ➢ R_{1d 500 Hz} = 44.9 dB ➢ R_{2d 500 Hz} = 45.2 dB ➢ R_{3d 500 Hz} = 65.5 dB ➢ R_{4d 500 Hz} = 63.7 dB

Table 11.

Calculations and considerations concerning structure-borne sound pressure level.

– Structure-borne sound power level L_wsc	Using EN 14366 results and equation (1), the sound power level results L_{wsc, 500 Hz} = 51.7 dB(A)
– Coupling term D_c	In the laboratory certificate, the test is described. It is reported that the pipe was fastened using a vibration insulating support. Though, it is not possible to compute the mobility using equations (4)–(7), because final values are already affected by its decoupling influence
– Flanking transmissions R_{ij, ref}	See Table 10
– Adjustment term D_sa	As for D_c term, it is not possible to compute the parameter, since the pipe is never in solid contact with partitions

Using Table 10 assumptions, it can be concluded that the final airborne sound pressure level results L_{na, A,500 Hz} = 23 dB(A). Using Table 11 assumptions, it can be concluded that the final structure-borne sound pressure level results L_{n, s,500 Hz} = 16.9 dB(A).

The final sound pressure level results L_{n, A,500 Hz} = 23.9 dB(A). The final frequency level is reported in Table 12.

Table 12.

Final results for case 4.

Frequency [Hz]	125	250	500	1000	2000	4000	L_A (dB(A))
L_{n, A}	32.7	28.5	23.9	19.4	23.8	28.4	35.8

Comparison with in situ measurements

In situ measurements were carried out in order to understand whether the considerations described in previous paragraphs may be acceptable or are just theoretical assumption with no real implications.

For the heavyweight case, only case 2 was worthy to be investigated. For lightweight cases (similar to case study 3 and 4, see Figure 12) on field tests were performed. All tests were carried out according to ISO 16032,⁴² when buildings were concluded.

Figure 12.

Realization of waste water pipe inside a lightweight construction.

Results are summarized in Table 13, Figures 13 –15, providing a final value of L_a = 24.8 dB(A), L_a = 25.2 dB(A) and L_a = 35.3 dB(A), confirming that the assumptions related to coupling terms D_c, D_sa and D_s are robust, reliable and correct.

Figure 13.

Sound pressure level of case 2 measurement according to ISO 16032.

Figure 14.

Sound pressure level of case 3 measurement according to ISO 16032.

Figure 15.

Sound pressure level of case 4 measurement according to ISO 16032.

Table 13.

In situ results according to ISO 16032 for cases 2–4.

	Corner average value L_ASmax (dB(A))	Centre average value L_ASmax (dB(A))	Adjustment term k
Case 2	32.0	30.8	6.8
Case 3	29.1	26.2	2.15
Case 4	36.8	36.8	1.56

Conclusion

Numerical models were used in order to predict the final sound pressure level in buildings due to waste water sources. ISO 12354-5 methods were analysed and modified in order to fit real case studies. Many issues were studied and some solutions were proposed. Application on coupling term D_c was critically discussed and analysed, when laboratory measurements are performed using insulating support. Final choice was to consider this parameter negligible since its effect is already computed in EN 14366 methodology tests even if supports will not perfectly stop all vibrations. The influence of D_s parameter was demonstrated to be insignificant when the pipe is enclosed within wall, since on the other hand the average distance to the element r forces this term to an infinite value. In situ measurements were used to verify and confirm the above considerations, showing a very good agreement with the modified models. Furthermore, the research highlighted how every adjustment terms have to be deeply investigated every time the method is applied and how unfortunately there is no general rule to be followed.

In the end, this study demonstrated how the ISO 12354-5 methods have to be modified and adapted in order to be used in lightweight and heavyweight buildings. All described considerations highlighted how models proposed by ISO 12354-5 standard are too general and how they need modifications and integration in order to compute and forecast final reliable results.

Footnotes

Acknowledgements

M.C. and F.B. collected, elaborated and described all the reported data. M.C. and F.B. performed in situ measurements. P.F. and C.S. overviewed the research. M.C. wrote the paper.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship and/or publication of this article.

ORCID iD

Marco Caniato

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