Calculating Ground-Borne Noise From Ground-Borne Vibra-tion A Comparison of Different Approaches

K. Alten1,a, H. Friedla, R. Flescha,b1 Corresponding author: karoline.alten@ait.ac.at, Tel: +43 (0) 50550-6690

a AIT - Austrian Institute of Technology, Osterreichisches Forschungs- und Prufzentrum Arsenal Ges.m.b.H,Giefinggasse 2, 1210 Vienna, Austria

b Dr. Ao. Univ.-Prof. at the Institute for Structural Concrete, Technical University, Graz, Austria

AbstractThis study investigates methods of converting ground-borne vibration levels to ground-borne noise levelsand examines the quality of three currently existing computation techniques. During a preliminary seriesof tests, the computation techniques were examined under controlled conditions, where floor vibrationswere generated in a laboratory at discrete frequencies. A second test series then investigated more realisticcircumstances by monitoring the transient vibrations caused by train pass-bys in a standard residential room,while simultaneous sound metering measured the radiated noise. The concurrence of noise and vibrationis mostly observed in buildings subject to heavy traffic pass-bys where no direct sound from the source isimmitted. A definite correlation between the two has yet to be established, as the multitude of parameterswhich influence emission, transmission and immission of waves e.g. train speed and load, embankment andgeology, demand a more complex approach than the current methods seem to be able to offer.

1 Introduction

Ground-borne vibration is a phenomenon associated with heavy moving loads, such as trains or road traffic,which result in seismic waves that are transmitted through the ground. Along their transmission path, thewaves are subject to geometric spreading, absorption, scattering and other mechanisms which affect ampli-tude and frequency content. Seismic waves are usually called ground-borne vibration, or structure-bornevibration, when they reach buildings in the vicinity of the source and are still sufficiently strong to causeperceivable vibrations. The closer the frequencies of the seismic waves are to the buildings natural fre-quency, the stronger the excitation and hence larger amplitudes will be transmitted through the walls andreach the floors or ceilings. These usually act as amplifiers at the point of immission and can result in clearlynoticeable vibration, usually in the range of 180 Hz.

The occupants perception of ground-borne vibration depends on a persons position, their activity, sensi-tivity, ambient influences, as well as the duration and strength of the vibration. Details can be found in theinternational norm ISO 2631 [1], which evaluates the exposure of human bodies to shock and vibration.More specific information in regard to mechanical vibration solely as a result of rail systems is found inISO 14837-1 [2]. It explains the mechanisms of excitation and the general circumstances of interest, beforeproviding guidance on how measurements in affected rooms should be carried out.

The norm approaches the issue of ground-borne noise, which is a by-product of ground-borne vibration. Ifthe vibration of ceilings, floors or walls is strong enough and excites the surrounding air at frequencies inthe hearing range, the resulting air waves could be audible. This so-called structure-borne noise (usuallyin the range of 16 250 Hz) can pose an additional nuisance to the occupants, and is mostly associated

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with rail systems in tunnels or at-grade situations when rooms face away from the tracks, so that no directairborne noise is perceived. ISO 14837 states that the assessment of ground-borne noise can be carried outin the form of direct measurements using sound level meters or derived from ground-borne vibration. Theadvantage of the latter is that only one type of sensor would be needed. Only monitoring vibration levelsis less maintenance-intensive than also putting up a sound level meter, and could ease evaluation at theend. Calculating noise levels from ground-borne vibration only considers the sound radiated from walls andfloors, while a microphone also records internal sources (clattering, rattling) or possible direct noise from(rail) traffic, which is not part of the ground-borne noise evaluation.

2 Theory

Several approaches exist which try to assess the level of ground-borne noise radiated from vibrating struc-tures. Their underlying principle is an equation which links the sound power level to the structure-bornevibration velocity level. Given that the sound emitted by a source is only due to vibration at its surface,according to [3] the sound power level can be expressed as

LW = LV +(10 lg S

S 0+ 10 lg + 10 lg c

(c)0

)dB (1)

LV . . . vibration velocity level averaged over time and plate area [dB], reference v0 = 5 108 m/sS . . . surface area of the radiating plate [m2], with S 0 as reference surface area [1 m2]. . . radiation efficiency of the plate. . . air density [kg/m3]c. . . speed of sound in air [m/s](c)0. . . characteristic acoustic impedance of air (420 Ns/m3 at 20 C)

The equation to calculate sound pressure levels (averaged over measurement surface and time) from soundpower levels is

LP = LW +(10 lg S

S 0+ 10 lg c

(c)0

)dB (2)

Substituting LW from equation (1) into equation 2 gives an expression for the reverberated sound pressurelevel

LP = LV +

10 lg + 10 lg ( c(c)0)2 dB (3)

The last term in all of the above equations accounts for atmospheric conditions; it is generally below 1 dBand hence often neglected, giving the simplified correlation between radiated sound and vibration of a rigidplate:

LP = LV + (10 lg) dB (4)For an infinite rigid plate the radiation efficiency would be 1, cancelling the last term in equation (4). Inrooms, however, this term could be anywhere between 0 and 20 dB, depending on its reflective properties in standard residential rooms, it typically lies between 6 10 dB [4].

2.1 Existing computation techniques

The following chapters give an outline of the three methods investigated in this study. A few other methodsrelating ground-borne vibrations to ground-borne noise do exist, but these are less prevalent in literature andmostly deal with high-speed and maglev trains, which are scenarios not dealt with herein.

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2.1.1 VIBRA 1-2-3 Computations via a transfer spectrum

VIBRA is a software package for predicting ground-borne vibration and noise developed by ZIEGLERCONSULTANTS ([4] [6], [11] and [15]) in collaboration with Federal Swiss Rail (SBB). The underlyingprinciple is a database of previous measurements which have been statistically analysed to create a regressionmodel. This model can be applied in a two-tier approach (simple and advanced) to predict vibration andnoise. The advanced tier allows a more exact prediction, but requires more input parameters. The modelworks on the basis of 1/3 octave bands, where the process of emission-transmission-immission is representedby transfer spectra (see equation (5)).

S ource( f ) Trans f er I( f ) Trans f er II( f ) Trans f er III( f ) = Noise immission( f ) (5)Source(f) is the emission spectrum at a known distance from the track and at a known train speed; TransferI(f), a spectrum accounting for track type and track position e.g. tunnels, switches, track isolation, as wellas factors for geometrical spreading and material damping. The product at this point corresponds to the freefield spectrum recorded at a specified distance from the track. Transfer II(f) accounts for coupling of thebuilding with the soil as waves pass into the structure, and are transmitted to the floors. Transfer III(f) is aspectrum to convert the vibration immission in the building to structure-borne noise and is investigated inthis study. Its coefficients have the unit Pa/mm/s, and should be applied to the rms velocity value:

p( f ) = ( f ) v( f ) (6)p( f ). . . sound pressure per 1/3 octave band with central frequency (f) [Pa]( f ). . . transfer spectrum coefficients [Pa/mm/s] corresponding to Transfer III(f) in equation (5)v( f ). . . rms vibration velocity per 1/3 octave band with central frequency (f) [mm/s]

ZIEGLER CONSULTANTS acquired numerous measurements to empirically determine the transfer spec-trum for a certain setting ([4] and [7]). The spectrum depends on the given architecture, and is thereforeunique to a certain scenario - comparable settings can employ the same transfer spectrum. Multiplyingthe velocity spectrum with these coefficients is essentially an alternative way of incorporating the radiationefficiency added in equation (4). The coefficients range between values of 0.4 and 1.5.

2.1.2 Guideline ONR 199005

ONR 199005 [8] refers to an Austrian guideline, which is currently the only document that explicitly de-scribes a method for the calculation of ground-borne noise from vibration measurements. At present, noother country seems to have a standardised procedure, despite several mentions of the possibility to computenoise from ground-borne vibration in other national norms e.g. ISO 14837, or the British Standard BS 6472-1:2008 [9], which only deal with it as a parallel effect of vibration, and as such it should simply be noteddown or measured directly where possible.

The official Austrian Standard dealing with traffic-induced vibration, ONORM S 9012 [10], refers to ONR199005 for the calculation process:

Lp(v) = LV +(10 lg S

S 0 10 lg V

V0+ 10 lg T

T0+ 14

)dB (7)

Lp(v). . . Sound pressure level in a room [dB], reference p0 = 2 105 Pa.(Index (v) shows that this is the computed as opposed to the measured sound pressure level Lp)LV . . . vibration velocity level of floor [dB], reference v0 = 5 108 m/sS . . . area of radiating surface [m2], with S 0 as reference surface area [1 m2]V . . . volume of room [m3], with V0 as reference volume [1 m3]

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T . . . reverberation time of room [s], with T0 as reference time [1 s]

This equation assumes the radiation efficiency to be constant across the whole frequency spectrum and to be 1for all radiating surfaces (a premise which would only be true for concrete surfaces). The inherent assumptionof regarding the floor to be the main source of radiated noise holds true for standard constructions, wherefloor motion has considerably larger amplitudes than wall vibrations. Hence this method meets its limitswhen it comes to constructions incorporating large drywalls (light-weight gypsum plaster). These are proneto high-amplitude vibrations and would have to be considered as additional sources. A simplification ofequation (7) may be permitted in the case of plain cuboid rooms, with a volume between 50 70 m3 and alength/width ratio no greater than 2:

Lp(v) = LV + 6dB (8)

ISO 14837 suggests that rooms should be furnished during direct measurements of ground-borne noise, butONR 199005 states that any secondary effects such as clattering of glass or furniture cannot be considered inthe calculation. Another issue which is briefly acknowledged in some of the pertinent norms is the severityof low-frequencies despite A-weighting. Ground-borne noise is a rumbling sound predominately composedof long wavelengths. In order to obtain the subjective hearing response, a function known as A-weightingis used, which attenuates particularly the low-frequency spectrum where human hearing is not so sensitive.When noise is entirely composed of low frequencies, it can appear louder and thus more of a nuisance thannoise of the same level but of a broader spectrum, leading to an underestimation of the subjective responsewhen applying A-weighting.

2.1.3 Linear relationship according to Grutz

Like the ONR method, the linear relationship between vibration and noise proposed by Grutz [11] presentsa frequency-independent approach:

LA,eq = c1 + c2 Lv,A (9)where LA,eq is the A-weighted equivalent sound level of ground-borne noise [dB]; Lv,A the A-weighted vibra-tion velocity level of the floor [dB], and c1 and c2 are constants depending on the type of construction. Thevalues assigned to the two Grutz constants depend on whether the investigated structure has a concrete ortimber floor. Table 1 gives the standard values for parameters c1 and c2, statistically derived from a numberof measurements along rail tracks [11].

c1 c2Concrete floor 15.75 0.60Timber floor 19.88 0.47

Table 1: Standard constants for the Grutz formula

3 Experiment

The aim of this study is to assess the reliability of the above-mentioned calculation methods:1. VIBRAs transfer spectrum2. Austrian Guideline ONR 199005 and3. Grutz formula (linear relationship).In a preliminary test, a vibrating table with unisolated foundations was used to generate a set of discretefrequencies between 8 315 Hz. These vertical vibrations were recorded in an adjacent laboratory, wherea group of accelerometers were set up along with a microphone, so that ground-borne noise and vibrationswere recorded without the effects of direct sound from the shaker. This initial experiment helped to answerthe following questions:

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How critical is the choice of receiver? The results showed that as long as an accelerometer falls intothe valid sensitivity range specified by the national norm, its positioning in the room has a far greatereffect than its technical specifications.

To what extent do room characteristics play a role in the calculation? The measurements were taken ina standard-sized furnished room. Seeing as fairly strong vibrations were generated by the shaker, theroom was exposed to unnaturally high levels of mono-frequency vibration which would not normallyoccur due to train traffic. The resulting acoustic resonance effects are probably the main cause of whythe three calculation methods all underestimated the actually recorded sound levels.

Is an artificial vibration source for such parameter tests representative? Using a static discrete-frequencysource is prone to deliver inaccurate results. Generating a fixed frequency of vibration for several sec-onds excites the room in a way that would not occur during a real train pass-by and leads to standingwaves and resonance effects. Recommendation: If a static source has to be used for simulation, afrequency sweep might mitigate resonance effects by avoiding excitation of a discrete frequency fortoo long.

Following this initial trial, the experiment was transferred to a more realistic setting in a five-storey buildingin Vienna, located directly above a train track. The investigated room was chosen on the ground floor of thestructure (see Fig. 1). An accelerometer of the type Wilcoxon 731A was situated at the centre of the floor,while a smaller sensor of type B&K 4370 was placed on a wall and then the ceiling. A microphone (B&K4891) situated on a tripod above the Wilcoxon accelerometer recorded the sound level throughout the tests.

Figure 1: Left: Detailed plan of the five-storey building. Black circle marks location of accelerometersand microphone in a ground-floor room. Right: Room dimensions (in cm) and position of receivers. M =microphone, W = Wilcoxon, B = B&K 4370.

The tracks under the building carry predominately passenger trains, which run at very short intervals in themorning and afternoon, allowing up to 15 trains to be recorded per hour. The data from all sensors weresampled at 1024 Hz. Accelerometer signals were integrated on acquisition, giving velocity data, whichwas turned into velocity levels in decibel re. v0 = 5 108 m/s and spectrally analysed every 1 second(corresponds to the weighting factor slow) to produce 1/3 octave band spectra. The microphone signal (indecibel re. p0 = 2 105 Pa) was also analysed in 1/3 octave bands.Fig. 2 shows vibration and sound levels recorded during 7 train pass-bys. The time axis increases to theright, with dB levels per second per 1/3 octave band shown as a smooth surface plot. Vibration levels ofthe wall are not displayed here because they were considerably lower than those of the floor and ceiling.

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According to ONR 199005, surfaces vibrating 7 dB less than others can be omitted, thus presuming thewalls contribution to the overall structure-borne noise level is negligible. The negative vibration levelsfound in the low frequency bands are due to A-weighting. The low-frequency noise in the form of jaggedpeaks is an artefact of integration during data acquisition.

(a) Floor vibration, Wilcoxon (b) Ceiling vibrations, B&K 4370

(c) Sound levels in the room, B&K 4891

Figure 2: Surface vibrations during seven train pass-bys (marked by letters A G) recorded with differentsensors.

Fig. 2c illustrates the typical properties of structure-borne noise: Microphone recordings in the low frequencybands show a drastic increase of 10 35 dB compared to ambient levels during a train pass-by. This effectdisappears in the higher frequency bands over 160 Hz, proving that radiated sound is perceived as low-frequency rumbling. Fig. 2b shows that the ceiling has a much higher ambient vibration level than the floorin Fig. 2a. The reason is the rooms suspended ceiling; the sensor was mounted in the centre of one of thepanels. These panels are typically not fixed to the grid and vibrate easily.

4 Calculation results

4.1 VIBRAs transfer spectrum

Fig. 3a and Fig. 3b display the ground-borne noise levels as computed with data from the Wilcoxon andB&K 4370 sensor, respectively, when applying the transfer spectrum method. Ideally, the plots shouldresemble the recorded sound levels shown in Fig. 3c, as this would imply the calculation method successfullyreconstructed the sound levels in the room on the basis of surface vibration. The results show that sound

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levels during events tend to be slightly overestimated by approx. 5 10 dB, while ambient sound levels particularly according to floor vibrations are underestimated (in the worst case, by upto 30 dB). The latterobservation is insignificant regarding the quality of the calculation method, as its aim is to predict soundlevels during an event, not to predict ambient noise.

(a) Calculations using Wilcoxon (floor) data (b) Calculations using B&K 4370 (ceiling) data

(c) Sound levels in the room, B&K 4891

Figure 3: Ground-borne noise levels computed according to the transfer spectrum method using data fromtwo different sensor locations. Events AG in (c) mark train passages.

4.2 Guideline ONR 199005

The parameters for this technique according to equation (4) are the area of the radiating surface S, the volumeof the room V and the reverberation time T. For the investigated room, S and V were 38.5 m2 and 102 m3,respectively, while T was set to 0.5 s, which is assumed to be the average value for a typical furnished room[8]. The calculated total sound level marginally exceeds the microphone levels during a train pass-by andunderestimates it in the ambient state (see Fig. 4b). For comparative purposes, the sum over all frequencybands is also computed for the transfer spectrum method, and displayed in Fig. 4a. On the whole, applyingthe ONR Guideline to data from the floor sensor (Wilcoxon) yielded very accurate results which alwayscame within 2 3 dB of the actual sound levels. Calculations using data from the ceiling sensor (B&K 4370)overrated the sound levels during events by approx. 5 10 dB, due to the inherently larger vibrations of thesuspended ceiling.

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(a) Total structure-borne noise levels according to the transfer spectrum method

(b) Total structure-borne noise levels according to the ONR 199005 method

(c) Total structure-borne noise levels according to Grutzs linear relationship

Figure 4: Ground-borne noise levels according to different sensors and different computation approaches.Events A G indicate the same train pass-bys as in the preceding figures.

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4.3 Grutz formula

Like the ONR procedure, this formula can only calculate the total sound level radiated off a surface i.e. notin terms of 1/3 octave bands, as VIBRAs transfer spectrum. Note that equation 9 computes the equivalentsound level, which is a constant level that would produce the same sound energy over a given period oftime. To simplify the evaluation of results, this period is assumed to be 1 second and thus corresponds to therecording interval. For the investigated setting, the coefficients for concrete floor were used as explained inchapter 2.1.3. Fig. 4c shows the total computed sound levels according to Grutz. One can clearly see thatduring train pass-bys, the calculated levels very closely resemble the values measured with the microphone.The Grutz formula appears very successful at reconstructing the actual sound level during an event, especiallywhen using ceiling vibrations. Even when using floor vibrations, which were slightly lower, the calculatedlevels were only 2 3 dB below the microphone record.

5 Conclusion

The principal idea behind this study was to see if ground-borne noise levels could be reliably calculated fromvibration levels. Assessments of the annoyance caused by rail traffic in the form of vibration and/or noisecould be greatly facilitated if noise can be derived from ground movement without demanding additionalinstruments. This is particularly relevant when it comes to monitoring large numbers of houses as time, staffand available equipment are often limiting factors.

For the investigated setting, the walls contribution to the radiated sound was assumed negligible. However,this is not always applicable, as particularly light-weight walls can act as amplifiers to structure-borne vi-bration and produce significant noise. For reliable predictions, all relevant surfaces should be considered.Great discrepancies are to be expected between vibration levels of adjacent plates on the suspended ceiling depending on whether there are lights, cables or other fixtures in contact with a plate making the sensorpositioning a very critical parameter. Due to the great vibration potential of the loosely fitted plates, theceiling can pose a major sound source, but in rooms where the ceiling is not part of the load-carrying solidstructure, the data may be unreliable, even though the results in our case appear acceptable.

Concerning VIBRAs frequency band method, the procedure worked equally well on both sensors, despitethe high ambient noise of the ceiling. This is because the noise is overpowered by the forced vibrationsduring an event i.e. higher signal-to-noise ratio, such that floor and ceiling vibrations have roughly the sameamplitude. The effect of overestimating sound levels during a train pass-by can be seen almost across theentire spectrum and may be because the coefficients in equation (6) were not ideally fitted to the scenario athand.

The ONR method seems to produce equal or even slightly better results than the transfer spectrum method(in terms of summed sound levels). Seeing as it is much simpler in its application, it may be the choice ofpreference when it comes to calculating structure-borne sound pressure levels.

The most accurate results, though, were achieved using Grutzs linear relationship on ceiling vibration data.The recorded structure-borne sound levels in the room were perfectly reconstructed via this method (seeFigure 4c). However, due to the aforementioned unpredictability of suspended ceiling plates, a fair andcomprehensive comparison between all methods will only be possible with the help of further experimentsand an investigation of a range of different scenarios. That way, it will be possible to make a better assessmentof where and under what conditions each procedure performs best.

References

[1] Austrian Standards Institute, ONORM ISO 2631-1:2007 and -2:2007 Mechanical vibration and shock -Evaluation to human exposure to whole body vibration. Part 1: General requirements - Part 2: Vibration

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in buildings (1 Hz to 80 Hz) (2007)

[2] International Organization for Standardization, 14837-1:2005 Mechanical vibration - Ground-bornenoise and vibration arising from rail systems Part 1: General Guidance, (2005)

[3] Muller, G., Moser, M. (Hrsg.), Taschenbuch der Technischen Akustik, 3. Auflage, Springer (2004)

[4] Dr. Armin Ziegler - ZIEGLER CONSULTANTS, Vibrations et sons solidiens dans la proximite desrails ferroviaires, Ecole Polytechnique Federale de Lausanne (2009)

[5] Kuppelwieser, H., Ziegler, A., A tool for predicting vibration and structure-borne noise immissionscaused by railways, Journal of Sound and Vibration, 193(1), 261-267 (1996)

[6] ZIEGLER CONSULTANTS, Software: VIBRA-1-2-3, URL: http://www.z-c.ch/VIBRA123/vibra123.html, accessed May 2010

[7] Benedikt Tappauf, Erschutterungen bei Eisenbahnstrecken, Diploma Thesis at the Institute for Struc-tural Concrete, Tecnnical University Graz (2008)

[8] Austrian Standards Institute, Guideline ONR 199005 Calculation of the secondary airborne noise levelfrom vibration measurements (2008)

[9] British Standards Institute, BS 6472-1:2008 Guide to evaluation of human exposure to vibration inbuildings. Part 1: Vibration sources other than blasting (2008)

[10] Austrian Standards Institute, ONORM S 9012 Beurteilung der Einwirkung von Schwingungsimmis-sionen des landgebundenen Verkehrs auf den Menschen in Gebauden Schwingungen und sekundarerLuftschall (2009)

[11] Mess- und Prognoseergebnisse, Bahnhof Kaltenkirchen, Schienenverkehrserschtterungen, M.O.Rosenquist (2006)

[12] Harris Miller Miller & Hanson Inc., High-Speed Ground Transportation - Noise and Vibration ImpactAssessment, U.S. Department of Transportation, Federal Railroad Administration, HMMH Report No.293630-4 (2005)

[13] R. A. Hood, R. J. Greer, M. Breslin, P. R. Williams: The Calculation and Assessment of GroundborneVibration Noise and Perceptible Vibration From Trains in Tunnels, Journal of Sound and Vibration193(1), (1996), 215-225

[14] A.B. Nagy, P. Fiala, F. Marki, F. Augusztinovicz, G. Degrande, S. Jacobs, D. Brassenx: Prediction ofinterior noise in buildings generated by underground rail traffic, Journal of Sound and Vibration 293(2006) 680-690

[15] ZIEGLER CONSULTANTS, 10. Symposium fur Bauwerksdynamik und Erschutterungsmessungen,EMPA Duebendorf (Switzerland) (2007)

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