Flanking transmission of airborne sound involving wooden and stone elements in historical buildings

Abstract

Historical old buildings bring together a whole set of unique characteristics with substantial influence on the acoustic behaviour, especially concerning the junctions between light and heavy elements, as is the case with wooden floors and stone masonry walls. The lack of information about the acoustic characteristics of wooden structures leads to the use of theoretical prediction methods, which do not accurately represent real conditions. The wooden floor’s complex design hampers the study of its acoustical behaviour. This difficulty becomes greater when the analysis targets the structural systems instead of the single elements. Consequently, the need of a deeper knowledge about the characteristics which influence the acoustic behaviour of these junctions leads to the research on the acoustic component associated with the flanking transmission paths of airborne sound – vibration reduction index (K_ij). Structural reverberation times (T_s) for both elements were acquired in order to feature the in situ real condition. ISO 10848-1 standard procedure was followed for both measurements. In situ flanking transmission measurements between wooden structural floors and stone masonry walls will allow their comparison with theoretical prediction methods, as defined by the EN 12354-1 standard method. Results show a great deviation between in situ measurements of the vibration reduction index (K_ij) and the obtained results for the same index through theoretical models.

Keywords

Flanking transmission of airborne sound vibration reduction index historic building retrofit building acoustic

Introduction

A growing concern with the retrofit of historical buildings has emerged in the historical centre of Portuguese cities. Historical building retrofit leads to the reuse and recycling of materials and structural systems. The structural elements’ design is representative of another time in Portuguese construction when the elements’ acoustic behaviour was not taken into account. Therefore, bringing these structural systems back to use became arduous once acoustical comfort became a priority. This study intends to further the contribution to the knowledge of the acoustical behaviour in the structural systems of historical buildings.

Portuguese historical buildings were built mainly with stone masonry and wooden elements. Stone masonry was used primarily for structural elements, such as resistant walls. The remaining elements, such as floors, were built with wooden structures. The object of this study is the junction between the wooden and stone elements. Airborne sound insulation analysis was achieved in a previous paper focused on the variation between site and laboratory measurements for wooden floors.¹ Site and laboratory measurement results vary because of the flanking transmissions, which exist on site measurements. The intention of this study is to characterize the influence of the flanking transmission for airborne sound paths, through the vibration reduction index, and compare with theoretical results. Structure-borne transmission for airborne sound paths is one of the characteristics that interfere in the elements’ global sound insulation. Vibration reduction index (K_ij) and structural reverberation time (T_s) of the elements are both obtained through site measurements in accordance with ISO 10848-1² procedures.

EN 12354-1³ theoretical prediction models for structure-borne transmission cannot accurately describe the structural systems’ acoustical behaviour, especially for this kind of light and heavy junctions between non-homogeneous structural elements.

Some studies have been developed regarding structure-borne transmission. Hopkins⁴ analyses the vibration reduction index for masonry walls junctions obtained by laboratory measurements and theoretical models. Another study was performed for cross-laminated timber building systems regarding the flanking transmission between a floor-wall junction.⁵ On both cases, the suitability of theoretical EN 12354 models for flanking transmissions is analysed.

This study intended to contribute to the flanking transmission analysis for the case of Portuguese historical structural systems (floor-wall/light-heavy junction).

Characterization of buildings’ solutions under study

The building addressed in this article is located at Porto’s historical centre and the solutions applied are characteristic of the houses built between the 19th century and the early 20th century. The building elements under study are the interior floors and the stone masonry walls. The floor’s design is based on a wooden structural solution. The wooden floors consist of main beams arranged parallel to each other. These beams sit on resistant walls, the parting walls and their junction is performed by means of bolted plates directly on the wall or by means of a belt wooden beam, which distributed the loads onto the resilient walls. For flooring, the use of wooden floorboards was the most common solution. The ceilings were performed by placing a lining consisting of lath nailed to wooden planks which were also nailed to the main beams. The lining of ceilings was performed with mortar and stucco finish. The ornamentation of ceilings in prime areas such as living rooms and hallways through perimeter frames, and sometimes in the centre of the compartment, was frequent (Figure 1). The parting walls are resistant walls and are mostly composed by stone masonry, with thicknesses that can reach the 80-cm mark in some cases. The final coating of these walls is made with mortar, stucco and wallpaper finish.^6,7

Figure 1.

(a) Ceiling of the floor under study, (b) reception room and (c) emission room.

Figure 1 shows the building elements addressed in this article, and Figure 2 shows the wooden floor and the stone masonry wall scheme.

Figure 2.

(a) Wooden traditional floor scheme – 1: wooden floorboards; 2: wooden structural beams; 3: wooden planking; 4: wooden lath; and 5: gypsum mortar. (b) Stone masonry wall scheme – 1: stone masonry and 2: gypsum mortar.

Figure 2 describes the wooden floor and the stone masonry wall structural system under study. Figure 3 shows the measurements location, between the first and the second floor, in the building under study.

Figure 3.

(a) Building floor plans and (b) building section cut.

Experimental conditions and measurement methods

Junctions and sound transmission paths

The historical buildings addressed in this study usually exhibit two kinds of junctions between the stone masonry walls and the wooden floors. The beams are commonly supported by the stone masonry walls in the smaller span’s direction, as is the present case. These beams sat on the walls by means of a belt wooden beam (Figure 4(a)), which distributed the loads onto the stone masonry walls. In this sort of junction, it is possible to identify three possible transmission paths along the stone masonry parting wall and the wooden floor (PW-F junction). In the second kind of junction, which usually occurs in the largest span’s direction, the beam connects to the stone masonry wall (Figure 4(b)). In this junction, it is possible to identify three possible transmission paths among the stone masonry façade wall and the wooden floor (F-F junction). Figure 4 presents the two cases addressed in this study and on both images we can observe the vibration reduction indexes (K_ij) paths.

Figure 4.

(a) Flanking transmission paths for the stone masonry parting wall and the wooden floor junction (PW-F junction). (b) Flanking transmission paths for the stone masonry facade wall and the wooden floor junction (F-F junction).

Site measurement of the vibration reduction index with structure-borne excitation

The measurement of the flanking transmission was accomplished in accordance with ISO 10848-1 standards. The flanking transmission by coupled elements and junctions was obtained by the vibration reduction index (K_ij) quantification. For lightweight types of elements like timber and wooden floors on beams, the vibration reduction index is obtained by the following equation²

K_{i j} = \bar{D_{v, i j}} + 10 l g \frac{l_{i j}}{\sqrt{a_{i} a_{j}}} dB

where $\bar{D_{v, i j}}$ is the direction average-level difference and is obtained by the vibrations measurements with structure-borne excitation. $\bar{D_{v, i j}}$ is obtained from the mean value of the velocity level differences $D_{v, i j}$ and $D_{v, j i}$ , and each velocity level difference is obtained by exciting the structure at several points, and by measuring the surface’s average velocity level for both elements i and j. A transient excitation provided by the impact of a hammer was used for creating the vibration on the source element.

The equivalent absorption length $a_{i}$ of an element i, expressed in metres, is the length of a fictional totally absorbing junction of the element i when the critical frequency is assumed to be 1000 Hz, giving the same losses as the total losses of the element i in a given situation. The equivalent absorption length is given by the following equation²

a_{i} = \frac{2, 2 π^{2} S_{i}}{T_{s, i} c_{0} \sqrt{\frac{f}{f_{r e f}}}}

where $T_{s, i}$ is the structural reverberation time of the element i and $S_{i}$ is the surface area of the element i.

Figure 5 shows the site measurement procedures, the transducer positions on the parting wall element and the transducer receiving positions on the wooden floor element. For each element (source and receiving plate) was measured nine transducers positions for three excitation positions. Each pair of transducers was measured simultaneously and separately.

Figure 5.

(a) Vibration transducer positions on the element i for the PW-F junction. (b) Vibration transducer positions on the element j for the PW-F junction. (c) Vibration transducer and sensor signal conditioner. (d) Vibration transducer positions on the element i for the F-F junction. (e) Vibration transducer positions on the element j for the F-F junction. (f) Signal analyser software.

Table 1 shows the equipment’s specifications used in this article.

Table 1.

Equipment’s specifications.

Specifications	Vibration transducer	Sensor signal conditioner
Brand	PCB Piezotronics	PCB Piezotronics
Sensitivity	106.2 mV/g	–
Voltage gain	–	1:100
Frequency range	5–10,000 Hz	0.15–50,000 Hz
Weight	2 g	0.3 kg

Tables 2 and 3 show the tested elements’ different characteristics found in the building under study.

Table 2.

Wooden floor layers’ characteristics.

Layer	Thickness (mm)	Density (kg/m³)
Floorboard (pine)	20–30	480
Beams (pine)	200–250	480
Planking (pine)	30	480
Lath (pine)	30	480
Gypsum mortar	20	1000
Gypsum mortar	10	1000

Table 3.

Masonry wall layers’ characteristics.

Layer	Thickness (mm)	Density (kg/m³)
Stone masonry	400–500	900
Gypsum mortar	20–25	1000

Table 4 shows the surface area of each element under study.

Table 4.

Surface area for the elements under study.

Element	Surface area (m²)
Stone masonry parting wall	12.77
Stone masonry façade wall	6.24
Wooden floor	17.08

Determination of structural reverberation time

Structural reverberation time is obtained by point excitations and measurements of the velocity or acceleration at different transducer positions. ISO 10848-1 gives guidance on the number and location of excitation and response positions. The structural reverberation time of the test element is determined by the energetic averaging of the individual decay curves (Figure 6).²

Figure 6.

(a) Vibration transducer positions on the wooden floor element. (b) Vibration transducer positions on the stone masonry wall element.

Theoretical model calculation

Vibration reduction index

The vibration reduction index, K_ij, can be deduced depending on the types of junctions and on the mass per unit area of the elements connected at the junction in accordance with the EN 12354-1 standards. For a rigid T-junction the vibration reduction index, K_ij, can be obtained for each path by the following expressions³

\begin{array}{l} K_{11} = 5.7 + 14.1 M + 5.7 M^{2} (dB) \\ K_{12} = 5.7 + 5.7 M^{2} (dB) \\ K_{21} = 5.7 + 15.7 M^{2} (dB) \end{array}

For a junction of lightweight double leaf wall and homogeneous elements, the vibration reduction index, K_ij, can be obtained for each path by the following expressions³

\begin{array}{l} K_{11} = 3.0 - 14.1 M + 5.7 M^{2} (dB) \\ K_{12} = 10 + 10 | M | + 3.3 l g \frac{f}{f_{k}} (dB) \end{array}

where M is the mass ratio between the mass per unit area of the element i in the transmission path ij and the mass per unit area of the other perpendicular element making the junction. So M is defined as follows: $M = l g (m_{i} / m_{j})$ .

Results and discussion of results

Structural reverberation time

Structural reverberation times on both stone masonry wall and wooden floor element were obtained through site measurements with the objective of characterizing the in situ situation. Figure 7 represents some of the structural reverberation time decay curves for the stone masonry parting wall and for the wooden floor. The energetic averaging of the individual decay curves obtained for the stone masonry parting wall was $\bar{T_{s}} = 0, 042 s$ .

Figure 7.

Graphic representation of the reverberation time decay curves for the stone masonry parting wall.

The energetic averaging of the individual decay curves obtained for the wooden floor as shown in Figure 8 was $\bar{T_{s}} = 0, 197 s$ .

Figure 8.

Graphic representation of the reverberation time decay curves for the wooden floor.

As expected, the structural reverberation time for the wooden floor structure was higher (approximately five times greater) once the many elements that constitute the floor structure are less rigid and have a less rigid junction between each other than the stone masonry wall. The theoretical value for structural reverberation time for the wooden pine elements is 0.73 s, approximately four times greater than the experimental result. The theoretical value for structural reverberation time for the stone masonry wall elements fluctuates from 0.29 to 1.17 s, seven times and 27 times greater than the experimental result.

Experimental vibration reduction index

Tables 5 –7 contain the obtained direction-averaged velocity level difference $(\bar{D_{v, i j}})$ for the PW-F junction.

Table 5.

Direction-averaged velocity level difference between elements i and j (K₁₁) for the PW-F junction.

f (Hz)	100	125	160	200	250	315	400	500	630
D_v,ij (dB)	16.81	13.93	12.98	13.42	8.30	9.84	2.12	4.73	12.91
D_v,ji (dB)	7,48	5.13	9.56	10.15	16.05	10.94	10.10	12.36	18.00
$\bar{D_{v, i j}}$ (dB)	12.15	9.53	11.27	11.79	12.18	10.39	6.11	8.55	15.46
f (Hz)	800	1000	1250	1600	2000	2500	3150	4000	5000
D_v,ij (dB)	16.00	22.14	23.23	30.42	34.65	31.03	25.45	24.19	23.89
D_v,ji (dB)	22.24	24.45	23.19	29.53	27.51	28.63	30.68	30.44	23.71
$\bar{D_{v, i j}}$ (dB)	19.12	23.30	23.21	29.97	31.08	29.83	28.07	27.31	23.80

Table 6.

Direction-averaged velocity level difference between elements i and j (K₁₂) for the PW-F junction.

f (Hz)	100	125	160	200	250	315	400	500	630
D_v,ij (dB)	7.07	9.10	7.95	13.45	10.30	10.80	6.67	10.73	18.47
D_v,ji (dB)	36.68	35.76	40.87	30.36	26.16	19.09	27.77	38.87	47.24
$\bar{D_{v, i j}}$ (dB)	21.87	22.43	24.41	21.90	18.23	14.95	17.22	24.80	32.86
f (Hz)	800	1000	1250	1600	2000	2500	3150	4000	5000
D_v,ij (dB)	17.25	24.01	22.75	29.73	32.02	28.09	23.12	20.58	20.48
D_v,ji (dB)	48.02	48.69	55.18	58.68	49.69	50.41	48.45	51.01	53.75
$\bar{D_{v, i j}}$ (dB)	32.63	36.35	38.96	44.20	40.86	39.25	35.78	35.79	37.12

Table 7.

Direction-averaged velocity level difference between elements i and j (K₂₁) for the PW-F junction.

f (Hz)	100	125	160	200	250	315	400	500	630
D_v,ij (dB)	33.95	35.15	35.11	35.75	27.81	34.56	37.59	36.80	32.45
D_v,ji (dB)	6.93	4.86	7.21	8.06	9.42	7.40	6.09	5.55	5.38
$\bar{D_{v, i j}}$ (dB)	20.44	20.00	21.16	21.91	18.62	20.98	21.84	21.17	18.91
f (Hz)	800	1000	1250	1600	2000	2500	3150	4000	5000
D_v,ij (dB)	44.02	44.68	47.31	52.30	56.52	53.55	54.04	51.64	48.66
D_v,ji (dB)	13.34	25.34	28.51	31.63	26.03	25.69	30.34	30.67	21.73
$\bar{D_{v, i j}}$ (dB)	28.68	35.01	37.91	41.96	41.28	39.62	42.19	41.15	35.20

Tables 8 –10 contain the obtained direction-averaged velocity level difference $(\bar{D_{v, i j}})$ for the F-F junction.

Table 8.

Direction-averaged velocity level difference between elements i and j (K₁₁) for the F-F junction.

f (Hz)	100	125	160	200	250	315	400	500	630
D_v,ij (dB)	5.62	6.11	17.80	17.38	9.29	17.97	11.09	12.79	16.13
D_v,ji (dB)	15.73	15.51	27.51	27.85	29.06	25.13	19.85	24.45	29.95
$\bar{D_{v, i j}}$ (dB)	10.67	10.81	22.66	22.62	19.18	21.55	15.47	18.62	23.04
f (Hz)	800	1000	1250	1600	2000	2500	3150	4000	5000
D_v,ij (dB)	23.84	27.19	25.19	23.08	10.32	9.98	12.10	9.54	6.79
D_v,ji (dB)	32.12	32.25	31.78	43.72	43.15	42.96	41.99	39.33	33.03
$\bar{D_{v, i j}}$ (dB)	27.98	29.72	28.49	33.40	26.74	26.47	27.05	24.43	19.91

Table 9.

Direction-averaged velocity level difference between elements i and j (K₁₂) for the F-F junction.

f (Hz)	100	125	160	200	250	315	400	500	630
D_v,ij (dB)	4.22	4.21	14.46	13.62	10.14	16.99	19.06	21.96	20.73
D_v,ji (dB)	54.57	53.42	52.04	49.62	58.57	60.57	57.16	48.01	44.14
$\bar{D_{v, i j}}$ (dB)	29.40	28.81	33.25	31.62	34.36	38.78	38.11	34.99	32.43
f (Hz)	800	1000	1250	1600	2000	2500	3150	4000	5000
D_v,ij (dB)	33.61	39.31	37.34	32.29	14.81	13.18	16.64	12.10	6.82
D_v,ji (dB)	42.42	42.56	37.89	37.75	32.69	31.32	31.39	31.29	27.25
$\bar{D_{v, i j}}$ (dB)	38.01	40.94	37.62	35.02	23.75	22.25	24.01	21.70	17.04

Table 10.

Direction-averaged velocity level difference between elements i and j (K₂₁) for the F-F junction.

f (Hz)	100	125	160	200	250	315	400	500	630
D_v,ij (dB)	38.25	42.33	50.23	52.17	41.81	47.06	45.00	51.32	47.67
D_v,ji (dB)	19.10	14.67	21.27	20.29	27.12	27.70	18.97	23.72	29.57
$\bar{D_{v, i j}}$ (dB)	28.67	28.50	35.75	36.23	34.47	37.38	31.98	37.52	38.62
f (Hz)	800	1000	1250	1600	2000	2500	3150	4000	5000
D_v,ij (dB)	54.54	50.45	46.29	45.77	51.58	49.11	50.90	49.27	45.79
D_v,ji (dB)	31.82	25.85	31.38	43.14	42.60	42.21	40.69	38.07	32.45
$\bar{D_{v, i j}}$ (dB)	43.18	38.15	38.84	44.45	47.09	45.66	45.80	43.67	39.12

Figures 9 and 10 show the obtained results for the vibration reduction index (K_ij) for the PW-F junction and for the F-F junction.

Figure 9.

One-third-octave-band vibration reduction index values for the PW-F junction. Single number rating of the vibration reduction index $\bar{K_{i j}}$ for each path.

Figure 10.

One-third-octave-band vibration reduction index values for the F-F junction. Single number rating of the vibration reduction index $\bar{K_{i j}}$ for each path.

The loss by structure-borne transmission for the path K₁₁ is higher (16.8 dB) for the F-F junction than for the PW-F junction (5.15 dB). The F-F junction design explains the transmission loss’ higher value. In the PW-F junction, the parting wall is connected to the wooden floor structure (see Figure 4(a)) and no further elements are installed in the parting wall structure. In the F-F junction, the façade wall is a continuous structure in the building and contains elements like balconies and windows, and the wooden floor structure is supported by the resistant parting wall and is only adjacent to the façade wall (see Figure 4(b)). Hence in the case of the F-F junction, the loss by structure-borne transmission can become greater once the continuity of the stone masonry wall structure is ensured, which is not the case for the PW-F junction. Also, the windows and balconies in the façade are one of the reasons for the higher vibration reduction index because the decrease of the surface area of the element (S_i and S_j) contributes to the decrease of the equivalent absorption length (a_i and a_j), increasing the vibration reduction index for the K₁₁ path.

For the K₁₂ path, structure-borne transmission loss is higher for the F-F junction. For the K₁₂ path, the existing connection for the PW-F junction between the wooden floor and the parting wall contributes to a smaller structure-borne transmission loss. The junction design allows a structure-borne energy dissipation through the embedded beams onto the parting wall. For the F-F junction, the design hampers the structure-borne energy dissipation causing the increase of the vibration reduction index.

The same mechanism explains the results for the K₂₁ path. The increase in stiffness on the junctions among elements is propitious to the structure-borne transmission losses.

Theoretical and experimental results

Table 11 gathers the experimental and theoretical vibration reduction indexes obtained.

Table 11.

Experimental vibration reduction index and theoretical reduction index.

	Experimental vibration reduction index, $\bar{K_{i j}}$ (dB)	Theoretical reduction index for a rigid T-junction, $K_{i j}$ (dB)	Theoretical reduction index for a lightweight-homogeneous element junction, $K_{i j}$ (dB)
PW-F junction, $\bar{K_{11}}$	5.15	1.1	9.25
PW-F junction, $\bar{K_{12}}$	20.44	6.5	–
PW-F junction, $\bar{K_{21}}$	17.67	6.5	13.84
F-F junction, $\bar{K_{11}}$	16.80	1.1	9.25
F-F junction, $\bar{K_{12}}$	31.92	6.5	–
F-F junction, $\bar{K_{21}}$	32.40	6.5	13.84

The results show that theoretical values obtained from EN 12354-1 standards are not suitable to describe the vibration reduction indexes for this kind of historic buildings. Two theoretical models were tested for the rigid T-junction and for the lightweight-homogeneous element junction. The obtained results for the rigid T-junction cannot describe the structure-borne transmission losses behaviour, so this theoretical model does not apply for this type of junctions. For the PW-F junction, the results obtained for the lightweight-homogeneous element junction approach the experimental values, even though the theoretical model does not predict the K₁₂ path for this kind of junction and in the experimental situation, the values are not negligible. Both theoretical models cannot describe the structure-borne transmission losses behaviour for the F-F junction.

Conclusion

This article aims to contribute to the retrofitting actions by deepening the knowledge on the acoustical behaviour of historical buildings. This deeper knowledge allows for the re-use of. Historical buildings are built by outdated construction methods and the only way to really understand their real acoustical behaviour is by testing the site situation. In this way, it will be tangible to study and to comprehend the solutions’ acoustical behaviour. Investigating the acoustic parameters by site measurements may be a way to contribute to the historical buildings solutions retrofit.

This study provided in-depth knowledge on the losses by structure-born transmission for the historical buildings’ junctions. Theoretical models are inadequate for this type of historical structures. EN 12354-1 models are suitable for homogeneous elements which is not the case study. Vibration reduction indexes are not negligible for the historical buildings and are one of the parameters that interfere with the overall sound insulation.

In the present case, the use of a transient excitation, provided by the impact of a hammer, raised some issues regarding the excitation of the heaviest element. So, it will also be important to quantify the vibration reduction indexes with a stationary excitation to comprehend which of the two methods is more appropriate for this type of structural elements.

Further study may be necessary to replicate the experimental site measurements as well as in other similar construction historical buildings. Thus, it will be feasible to characterize the structure-borne transmission losses for the same type of junctions between structural elements. A further examination could provide a confirmation of the present results for the light/heavy kind of junctions analysed in the present paper.

Footnotes

Acknowledgements

The authors thank the MSc student José Dias for the help on the site measurements, Houselab for providing the building and technical conditions for site measurements and VIBEST for providing the equipments.

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

Dóris Queirós

References

Queirós

Rodrigues

Pereira

Historical building acoustical retrofit: an experimental examination of traditional wooden floors. Build Acoust 2016; 23: 181–191.

ISO 10848-1:2006. Acoustics: laboratory measurement of the flanking transmission of airborne and impact sound between adjoining rooms: part 1: frame document.

EN 12354-1:2000. Building acoustics: estimation of acoustic performance of buildings from the performance of elements: part 1: airborne sound insulation between rooms.

Hopkins

Measurement of the vibration reduction index, K_ij on free-standing masonry wall constructions. Build Acoust 1999; 6(3): 235–257.

Schoenwald

Zeitler

Sabourin

et al . Sound insulation performance of cross laminated timber building systems. In: INTER-NOISE and NOISE-CON congress and conference proceedings, Innsbruck, 15–18 September 2013. Reston, VA: Institute of Noise Control Engineering.

Teixeira

JJL

. Porto bourgeois house construction system description between centuries XVII and XIX. Pedagogical aptitude and scientific capacity Proofs. Porto: Faculty of Architecture, University of Porto, 2004.

Fernandes Rocha

Calejo Rodrigues

. Maintenance as a guarantee for roofing performance in buildings with heritage value. Buildings 2016; 6(2): 15.