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Uncertainty of an in situ method for measuring ground acoustic impedance

  • August 2015
  • Conference: 44th Inter-noise congress
  • At: San Francisco
Authors:
David Ecotière at Centre d'Etudes et d'Expertise sur les Risques, l'Environnement, la Mobilité et l'Aménagement
David Ecotière
  • Centre d'Etudes et d'Expertise sur les Risques, l'Environnement, la Mobilité et l'Aménagement
Philippe Glé at Centre d’études et d’expertise sur les risques, l’environnement, la mobilité et l’aménagement
Philippe Glé
Benoit Gauvreau at Université Gustave Eiffel
Benoit Gauvreau
Régis Boittin
Régis Boittin
Régis Boittin
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Abstract and Figures

The ground acoustic impedance is a key parameter for outdoor sound propagation. Laboratory approaches for measuring the impedance of outdoor ground are often less interesting than in situ approaches because these kinds of ground often require non destructive techniques. The chosen in situ method consists in fitting the transfer function between the frequency spectra measured at two different microphones above the ground with a theoretical model. The theoretical model is based on the Rudnick theory together with an impedance model adapted to the ground studied (the Miki model or the Zwicker and Kosten model are used here). The uncertainty of the method has been estimated by organizing an inter laboratory experimental campaign and by estimating the repeatability and the reproducibility according to the ISO 5725. Five independent laboratories have tested five different types of outdoor grounds (synthetic lawn, lawn, grass, slightly compacted soil, asphalt). It is shown that the uncertainty for estimating the flow resistivity of the impedance model is increasing with the flow resistivity value : the relative standard uncertainty for the flow resistivity estimation is smaller than 20% for flow resistivity smaller than 5 000 kNsm-4 but can be much higher for very reflective material.
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Uncertainty of an in situ method for measuring ground acoustic
impedance
David Ecotière
a)
Philippe Glé
b)
Center for Expertise and Engineering on Risks, Urban and Country Planning, Environment and
Mobility (CEREMA), DTer Est, ERA32, 11 rue Jean Mentelin, 67035 Strasbourg Cedex 2,
France.
Benoit Gauvreau
c)
LUNAM Université, French Institute of Science and Technology for Transport, Development
and Networks (IFSTTAR), AME, LAE, CS4, 44344 Bouguenais, France.
Régis Boittin
d)
Center for Expertise and Engineering on Risks, Urban and Country Planning, Environment and
Mobility (CEREMA), DTer Normandie-Centre, 11 rue Laplace CS2912, 41029 Blois, France.
Hubert Lefèvre
e)
Center for Expertise and Engineering on Risks, Urban and Country Planning, Environment and
Mobility (CEREMA), DTer Centre-Est, 8-10, rue Bernard Palissy 63017 Clermond-Ferrand
Cedex 2, France.
David Lunain
f)
Center for Expertise and Engineering on Risks, Urban and Country Planning, Environment and
Mobility (CEREMA), DTer Méditerannée, Pôle d'activités Les Milles, 30 avenue Albert Einstein
CS 70499, 13593 Aix en Provence Cedex 03, France.
a)
email: david.ecotiere@cerema.fr
b)
email: philippe.gle@cerema.fr
c)
email: benoit.gauvreau@ifsttar.fr
d)
email: regis.boittin@cerema.fr
e)
email: hubert.lefevre@cerema.fr
f)
email: david.lunain@cerema.fr
The ground acoustic impedance is a key parameter for outdoor sound propagation.
Laboratory approaches for measuring the impedance of outdoor ground are often less
interesting than in situ approaches because these kinds of ground often require non
destructive techniques. The chosen in situ method consists in fitting the transfer function
between the frequency spectra measured at two different microphones above the ground
with a theoretical model. The theoretical model is based on the Rudnick theory together
with an impedance model adapted to the ground studied (the Miki model or the Zwicker
and Kosten model are used here).
The uncertainty of the method has been estimated by organizing an inter laboratory
experimental campaign and by estimating the repeatability and the reproducibility
according to the ISO 5725. Five independent laboratories have tested five different types of
outdoor grounds (synthetic lawn, lawn, grass, slightly compacted soil, asphalt). It is shown
that the uncertainty for estimating the flow resistivity of the impedance model is increasing
with the flow resistivity value : the relative standard uncertainty for the flow resistivity
estimation is smaller than 20% for flow resistivity smaller than 5 000 kNsm-4 but can be
much higher for very reflective material.
1 INTRODUCTION
The ground acoustic impedance is a key parameter for outdoor sound propagation
1
.
Laboratory approaches for measuring the impedance of outdoor ground are often less interesting
than in situ approaches because these kinds of ground often require non destructive techniques.
We present here the estimation of the uncertainties of an in situ method for measuring the ground
impedance parameters.
2 EXPERIMENTAL ESTIMATION OF THE GROUND IMPEDANCE
PARAMETERS
2.1 Theory
The two microphones method
The in situ method
2,3
consists in fitting the difference of frequency spectra measured at two
different microphones above a ground, with a theoretical one.
Fig. 1 – General confguration of the impedance measurement
Acoustic pressures from a single source are recorded for two positions above the ground (Fig. 1),
which yields to a measured transfer function that can be set under the form:
=∆
2
1
log20 p
p
L
measured
(1)
The identification of the ground impedance parameters consists in computing the theoretical
transfer function
computed
L∆ and to minimize the following difference between these two functions
using the least square method on a given frequency range:
∑
∆−∆=
max
min
2
),(),()(
f
fmeasuredccalculated
ZfLZfLZF (2)
where Z is the acoustic surface impedance.
Propagation model
Ground and atmosphere are supposed homogeneous and separated by a plane boundary. In these
conditions, assuming that atmosphere and ground are two semi-infinite media, Rudnick’s model
4
can be used to describe the sound propagation over this plane. The time dependence
tj
e
ω
−
is
used. Thus, pressure at a position
i
in the atmosphere, resulting from a point source, can be found
using the following relationship:
ri
jkR
i
di
jkR
i
R
e
Q
R
e
p
ridi
+=
(3)
Where
R
di
and
R
ri
are respectively the lengths of the direct and and the reflected paths between
the source and the receiver
i
as described Fig. 1.
Q
i
is the complex reflexion coefficient in
spherical waves corresponding to the reflected path
i
and is related to the complex reflection
coefficient in plane waves
R
pi
by:
)()1(
ipipii
wFRRQ −+= (4)
with:
+
−
=
−
−
=
+=
∫
∞
−
−
−
0
0
0
2
00
²
2/1
cos
cos
²sin
²²
1
²sin)²1( 2
21)( 2/1
ZZ ZZ
R
k
k
Z
Z
RRk
jw
dueejwwF
i
i
pi
i
ipi
ri
i
jw
u
w
ii
i
i
θ
θ
θ
θ
(5)
In these equations, k and Z are respectively the wave number and surface impedance of the
ground while k
0
and Z
0
are the wave number and the characteristic impedance of the air.
θ
i
is the
angle between the incident wave and the normal to the ground.
Impedance model
These acoustical properties of the ground can be predicted by a number of models in the
literature, depending on the various mechanisms of dissipation taken into account and of the
microstructure description. Ground is usually considered motionless
5
, which enables to use the
rigid frame hypothesis, in such a way we can directly describe the ground with an equivalent
fluid model. Two models have been used here, by Miki
6
and Zwikker and Kosten
7
. Surface
impedance can be calculated in these conditions as a function of the characteristic impedance of
the material Zc, its wave number k, and the thickness e of the material:
)coth( jkeZcZ
−
=
(6)
Miki model:
Miki model is a correction of Delany and Bazley
8
empirical model initially developed for fibrous
materials whose porosities are close to 1, in the frequency range delimited by :
00.101.0 <<
σ
f (7)
The following relationships are used to compute the characteristic impedance and the complex
number of the material, as a function of the airflow resistance
σ
expressed in kN.s.m
-4
and the
frequency f :
+
+=
+
+=
−−
−−
618.0618.0
0
632.0632.0
0
41.1181.71
43.85.51
σσ
σσ
f
j
f
kk
f
j
f
ZZc
(8)
Zwikker and Kosten model:
This second model is a more general description of porous materials, on the basis of cylindrical
pores, leading to:
KZc
ρ
=
and
K
k
ρ
ω
=
(9)
With
1
0
1
0
)(
)(
2
1
−
∞
−
−
−
−= jJ
jJ
j
λ
λ
λ
φ
ρα
ρ
and
1
0
1
0
)Pr(
)Pr(
Pr
)1(2
1
−
−
−
−
−
+= jJ
jJ
j
P
K
λ
λ
λ
γ
φ
γ
(10)
σφ
αωρ
λ
30
10
8
∞
=,
J
0
and
J
1
are respectively the Bessel functions of order 0 and 1,
Pr
is the Prandtl
number of air, γ the ratio of the specific heats of the air, and
X
the conjugate number of
X
.
Three parameters are used in this model to describe the material, its open porosity φ, its
resistivity σ (expressed in kN.s.m-4) and its tortuosity
∞
α
.
2.3 Experimental set-up
The method described in Section 2.1 has been applied with a dedicated portable measurement
device presented
Fig. 2
and composed of:
- for the emission:
o a loudspeaker Navsound Fugue 70W,
o a power amplifier Pioneer GM-A3602,
- for the reception:
o Microtechgefell M370 class 1 microphones,
o MMF M32 conditioners,
o a Acoustics Engeneering Triton 2 channels acquisition card.
Fig. 2 – Experimental apparatus (left) and experimental set-up in situ (right)
This device is completely controlled via a laptop with the help of a Scilab program enabling the
execution of the different steps of the measurement:
- calibration of the acquisition card and microphones,
- emission of sound (white noise),
- recording, impulse response calculation and time windowing (10 ms windowing),
- result display and identification.
The performance of the card has thus been evaluated by looping inputs and outputs, and by
calculating the ratio between signals amplitudes as well as time delays for 1000 frequencies
between 10 and 20kHz. The characteristics are presented in Fig. 3. It appears that the difference
in attenuation between the two channels is lower than 0.1dB in this frequency range, and that the
attenuation can be assumed constant in the frequency range of interest for the measurement (100-
2000Hz) since variations are again lower than 0.1dB. Concerning time delays, the card shows a
quite constant evolution as a function of frequency, with delays of about 0.293s. The peaks
visible here are not related to a frequency behaviour but to a random delay in the computer.
Fig. 3 – Characteristics of the acquisition card: ratio between input and output (left) and time
delay (right) as a function of frequency
Finally, the following geometry has been chosen for the experimental setup:
- Source height (hs): 0.6m
- Source-microphones distance (d): 4m
- Microphone heights (hr1, hr2) : 0.06 and 0.6m
3 UNCERTAINTIES ESTIMATION OF THE METHOD
3.1 Round Robin Test
The uncertainties of the method are estimated with the reproducibility and the repeatability
thanks to a round robin test.
In order to get an estimate of the reproducibility, five independent laboratories have been
involved in an experimental campaign on a single site, at the same time, and with the same kind
of material (see section 2.3). The dependence between uncertainties and impedance parameters
have been investigated by testing five different types of outdoor grounds (synthetic lawn, natural
lawn, grass, slightly compacted soil, non porous asphalt : Fig. 4). For each ground, 3 different
close locations have been tested (except for grass : 6 locations). For each location and for each
laboratory, 5 repetitions of the measurement enable to estimate the repeatability of the method.
For each ground, the environmental conditions were considered to be stable enough between sets
of measurements to ensure the stability of the ground properties.
a) Synthetic lawn
b) Natural lawn
c) Grass
d) Compacted ground
e) Non porous asphalt
Fig. 4 – Ground samples
The Miki impedance model has been used for all ground, except for synthetic lawn for which the
Zwikker and Kosten model has been considered. The mean least square procedure of
minimization has been done for frequencies ranges from 100 Hz to 1500 Hz (2000 Hz for
synthetic lawn), excluding the frequency domain centred on the first dip interference +/- 100 Hz.
The tested flow resistivities range from 10 to 10
6
kNsm
-4
(5.10
5
kNsm
-4
for synthetic lawn) and
the tested ground thicknesses range from 5 to 50 mm. For synthetic lawn, the tortuosity has been
set to 1.
Two examples of the measured and of the fitted transfer function are presented on Fig. 5.
Fig. 5 – Example of fitted and measured transfert function for asphalt (left) and for synthetic lawn
(right).
3.1 Results
Although the method provides estimations of both parameters air flow resistivity and ground
thickness (for Miki model), only the uncertainties on the air flow resistivity parameter σ are
presented here.
The reproducibility variance
2
R
s is given by
10:
222 rLR
sss += (11)
where
2
r
s is the repeatability variance and
2
L
s is the interlaboratory variance. Both are calculated
from the round robin test results according to the ISO 5725-2
10
. These two quantities provide the
range of the uncertainties of the method: the repeatability can be interpreted as a minimum value
of the uncertainty as it only includes the random variations that remain when all influence factors
are under control (same apparatus, same operator, same sample) ; whereas the reproducibility
can be interpreted as a maximum value of the uncertainty because it includes not only the
repeatability, but also the variations between laboratories (different apparatus, different operator,
...).
For the five ground tested, the mean air flow resistivity ranges from around 50 kNsm
-4
, for
synthetic lawn, to around 20 000 kNsm
-4
, for asphalt (Fig. 6). We can notice very contrasted
dispersion of the flow resistivity depending on the ground type: the higher is the mean flow
resistivity, the higher is the dispersion. The synthetic lawn ground presents a very narrow
dispersion with quasi constant values, this may be due to the artificial nature of this material that
may probably provide very homogeneous properties of the ground.
Very contrasted values are also observed for reproducibility and repeatability that range from
around 10 to 15 000 kNsm
-4
for reproducibility, and from around 5 to 13 000 kNsm
-4
for
repeatability (Table 1).
Asphalt
Compacted
Lawn
Grass
Synth_lawn
10 50 100 500 5000 50000
Air flow resistivity
kNsm-4
Fig. 6 – Box plot of measured air flow resistivities for the 5 ground tested
Table 1 : Mean, reproducibility and repeatability (kNsm-4) of the air flow resistivity of the 5
ground tested.
Mean
R
s
r
s
L
s
Non porous Asphalt 19 609 15 070 13 065 7 510
Compacted ground 3 519 567 512 245
Natural lawn 1 154 248 217 119
Grass 277 34 34 6
Synthetic lawn 51 7 5 5
The dependence between reproducibility (resp. repeatability) and the air flow resistivity is
plotted on Fig. 7: a remarkable linear behaviour is observed for air flow resistivity smaller than 5
000 kNsm
-4
, whereas uncertainties drastically increase in a non linear manner for high value of
air flow resistivity (asphalt). For air flow resistivity smaller than 5 000 kNsm
-4
, some linear
approximations can be obtained for reproducibility and repeatability (Fig. 8):
1214,0 −=
σ
R
s with
4
0005
−
≤kNsm
σ
(12)
σ
06,0=
r
s with
4
0005
−
≤kNsm
σ
(13)
A statistical linear regression analysis indicates that those linear models are statistically
significant with R-squared >0,99 and p_value<10
-12
.
The linear approximations (12-13) show that the relative uncertainty of the method is lower than
20% (14%) when reproducibility conditions are assumed, whereas it is lower than 6% when
repeatability conditions can be assumed. Those values are low enough to give satisfactory results
in outdoor sound propagation applications. Nevertheless, the method appears to be less efficient
for more reflective surface : relative uncertainty can reach 100% for high values of flow
resistivity, as for asphalt here.
50 200 500 2000 10000
0 5000 10000 15000
Reproducibility
Air flow resistivity (kNsm-4)
sR (kNsm-4)
Asphalt
Compacted
Lawn
Grass
Synth_lawn
50 200 500 2000 10000
0 5000 10000 15000
Repeatability
Air flow resistivity (kNsm-4)
sr (kNsm-4)
Asphalt
Compacted
Lawn
Grass
Synth_lawn
Fig. 7 – Reproducibility (left) and repeatability (right) as a function of the air flow resistivity.
0 1000 2000 3000 4000
0 100 200 300 400 500
Reproducibility
Air flow resistivity (kNsm-4)
sR (kNsm-4)
Asphalt
Compacted
Lawn
Grass
Synth_lawn
sR = 0.14 sigma -12
R2=0.996
0 1000 2000 3000 4000
0 100 200 300 400 500
Repeatability
Air flow resistivity (kNsm-4)
sr (kNsm-4)
Asphalt
Compacted
Lawn
Grass
Synth_lawn
sr = 0.06 sigma
R2=0.99
Fig. 8 – Linear approximation of reproducibility (left) and repeatability (right) for
4
5000
−
≤kNsm
σ
(R2 is the squared regresion coefficient).
The standard deviation of reproducibility
R
s (or repeatability, depending of the measurements
conditions) can finally be used to provide a confidence interval associated with future
measurements obtained with the method:
];[
+−
=
σσ
IC
with
R
sd.
,
±=
+−
σ
. d is the coverage
factor that depends on the confidence level that is chosen and of the shape of the probability
density function of
σ
that is assumed. The value of d=1.95, relative to a normal distribution and
to a 95% confidence interval, is often considered.
4 CONCLUSIONS
A method for estimating ground impedance parameter from in situ measurements has been
presented. The method is based on the fitting of the transfer function of pressures measured and
calculated at 2 microphones above a ground. The uncertainty of the method for the air flow
resistivity estimation has been quantified by organizing an inter laboratory experimental
campaign and by estimating the repeatability and the reproducibility according to the ISO 5725.
The reproducibility (resp. repeatability) gives a relative uncertainty lower than 20% (resp. 6%)
for air flow resistivity smaller than 5 000 kNsm
-4
. For this range, a very satisfactory linear
approximation can be adopted to deduce the uncertainty from the air flow resistivity value. For
very reflective material, the uncertainty (reproducibility or repeatability) is no longer linear and
can reach 100% of the estimated value. The method is therefore more adequate for air flow
resistivity values ranging from 10 to 5 000 kNsm
-4
than for more reflective ground. This
restriction interval corresponds however to many common outdoor ground.
5 ACKNOWLEDGEMENTS
This research was supported by the French Ministry of Sustainable Development and of the
Energy (DGPR, DGITM) under the PLUME project. The authors thank the St Georges sporting
center of Blois for facilitating the conduct of the round robin test.
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models”, J. Acoust. Soc. of Jap., 11(1), (1990).
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10. Standard ISO 5725-2:1994, Accuracy (trueness and precision) of measurement methods and
results - Part 2: Basic method for the determination of repeatability and reproducibility of a
standard measurement method, 1994.
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The influence of the ground and atmosphere on sound generation and propagation from wind turbines creates uncertainty in sound level estimations. Realistic simulations of wind turbine noise thus require quantifying the overall uncertainty on sound pressure levels induced by environmental phenomena. This study proposes a method of uncertainty quantification using a quasi-Monte Carlo method of sampling influential input data (i.e., environmental parameters) to feed an Amiet emission model coupled with a Parabolic Equation propagation model. This method allows for calculation of the probability distribution of the output data (i.e., sound pressure levels). As this stochastic uncertainty quantification method requires a large number of simulations, a metamodel of the global (emission-propagation) wind turbine noise model was built using the kriging interpolation technique to drastically reduce calculation time. When properly employed, the metamodeling technique can quantify statistics and uncertainties in sound pressure levels at locations downwind from wind turbines. This information provides better knowledge of sound pressure variability and will help to better control the quality of wind turbine noise prediction for inhomoge-neous outdoor environments.
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... The ground resistivity 4+ range is defined to cover the acoustic absorption properties of grounds usually encountered in the wind turbine context: the minimum and the maximum value are respectively 50 kN.s.m -4 and 5000 kN.s.m -4 . It should be noted that the ranges of characteristic values of the parameter 4+ for the different ground typologies all have an important dispersion (Attenborough et al., 2006;Carpinello et al., 2004;Embleton et al., 1983;Nicolas and Berry, 1984), with a distribution that is not uniform in a given interval, which reflects the spatial and temporal variability of this parameter as well as the experimental uncertainties (metrological and methodological) related to its measurement (Attal, 2016;Attal et al., 2019;Ecotière et al., 2015). A lognormal distribution is used (Ostashev and Wilson, 2015), whose parameters are empirically adjusted to obtain the predominance of [200; 1000] kN.s.m -4 which are the most frequently encountered values around wind farms Kayser et al., 2018). ...
Calculation of wind turbine noise uncertainty for downwind conditions
Conference Paper
Full-text available
  • May 2021
Wind turbine noise variability is significant for outdoor environments because of the influence of atmospheric conditions and ground properties that are both variable in time and space. Thus, realistic prediction of sound pressure levels involves to estimate the overall uncertainty induced by the most influential environmental phenomena on both acoustic emission and propagation. To do so, this study performs a method of propagation of uncertainty by using a quasi-Monte Carlo sampling of input data (i.e. environmental parameters) in order to feed an Amiet emission model coupled to a PE propagation model, and next to calculate the probability distribution of output data (i.e. sound pressure levels). As stochastic uncertainty propagation requires a high number of simulations, a metamodel of the global model (emission-propagation) for wind turbine noise was built using kriging technique in order to drastically reduce calculation duration. The results provide useful statistics and uncertainties information about sound pressure levels at neighborhood of a wind turbine: this information provide a better knowledge of sound pressure variability and will help to a better control of the quality of wind turbine noise prediction for inhomogeneous outdoor environment.
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... It should be noted that the ranges of characteristic values of the parameter a fr for the different ground typologies have an important dispersion (Attenborough et al., 2006;Carpinello et al., 2004;Embleton et al., 1983;Nicolas and Berry, 1984), with a distribution that is not uniform in a given interval. This reflects the space and time variability of this parameter as well as the experimental uncertainties (metrological and methodological) related to in situ measurement (Attal, 2016;Attal et al., 2019;Ecotière et al., 2015). Thus, a lognormal distribution is used (Ostashev and Wilson, 2015), whose parameters are empirically ad-justed to obtain the predominance of [200;1000] kN·s·m 4 which are the most frequently encountered values around wind farms Kayser et al., 2018). ...
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... kN·s·m ≠4 (voir section 2.3.2). Par ailleurs, les plages de valeurs caractéristiques du paramètre a fr pour les di érentes typologies de sols présentes dans la littérature possèdent toutes une dispersion importante[Embleton et al., 1983;Nicolas et Berry, 1984;Carpinello et al., 2004;Attenborough et al., 2006], avec une distribution qui n'est pas uniforme dans un intervalle donné, traduisant les variabilités spatiale et temporelle de ce paramètre, ainsi que les incertitudes expérimentales (métrologiques et méthodologiques) relatives à sa mesure[Ecotière et al., 2015;Attal, 2016;Attal et al., 2019].L'expérience acquise par l'UMRAE au cours de ses travaux passés concernant le développement d'un matériel de mesure in situ d'absorption acoustique de sols de l'environnement ...
Estimation des incertitudes de modélisation du bruit des éoliennes
Thesis
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  • Nov 2020
Il existe aujourd'hui un enjeu sociétal majeur à étudier l’émission et la propagation du bruit émis par les éoliennes, et notamment de quantifier l'incertitude sur l'estimation des niveaux sonores. En effet, bien que ces niveaux sonores soient relativement faibles en regard de ceux générés par d’autres sources acoustiques de l’environnement (e.g. les transports terrestres), les nuisances sonores d’origine éolienne sont souvent mises en avant comme gêne potentielle. Ainsi, ces travaux de thèse visent à quantifier la dépendance spatiale et fréquentielle des incertitudes rencontrées en acoustique environnementale, et en particulier concernant le bruit des éoliennes. Pour ce faire, un couplage est réalisé entre un modèle d’émission acoustique permettant de prendre en compte les spécificités acoustiques des éoliennes (spectre et directivité), et un modèle de propagation acoustique permettant de prendre en compte les effets de l’atmosphère (thermique et aérodynamique) et les effets de sol (absorption et rugosité) sur la propagation acoustique. Une analyse de sensibilité est ensuite effectuée afin de déterminer les paramètres de l’environnement les plus influents sur la dispersion des niveaux sonores. Suite au développement d’un métamodèle, une analyse d’incertitude est réalisée afin d’estimer la variabilité totale des niveaux sonores. Enfin, la méthode est appliquée à quelques exemples de situations caractéristiques du contexte éolien.
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In Situ Measurements of Soil Physical Properties by Acoustical Techniques
Article
Full-text available
  • May 1990
The feasibility of acoustical techniques for monitoring surface air porosity (total porosity minus volumetric water content), air permeability, and pore structure and the variation of these properties to depths of several centimeters below the surface is demonstrated. Both acoustic reflection and transmission measurements were made in the audio-frequency range. The acoustic-reflection measurements involve analysis of propagation data from a small loudspeaker and two vertically separated microphones. The acoustic-transmission measurement requires a specially designed probe microphone. -from Authors
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Outdoor ground impedance models
Article
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Many models for the acoustical properties of rigid-porous media require knowledge of parameter values that are not available for outdoor ground surfaces. The relationship used between tortuosity and porosity for stacked spheres results in five characteristic impedance models that require not more than two adjustable parameters. These models and hard-backed-layer versions are considered further through numerical fitting of 42 short range level difference spectra measured over various ground surfaces. For all but eight sites, slit-pore, phenomenological and variable porosity models yield lower fitting errors than those given by the widely used one-parameter semi-empirical model. Data for 12 of 26 grassland sites and for three beech wood sites are fitted better by hard-backed-layer models. Parameter values obtained by fitting slit-pore and phenomenological models to data for relatively low flow resistivity grounds, such as forest floors, porous asphalt, and gravel, are consistent with values that have been obtained non-acoustically. Three impedance models yield reasonable fits to a narrow band excess attenuation spectrum measured at short range over railway ballast but, if extended reaction is taken into account, the hard-backed-layer version of the slit-pore model gives the most reasonable parameter values.
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Automatic characterisation of ground surfaces from in situ measurements
Article
Full-text available
The study of long term acoustic performance of road pavements requires to access the evolution of the intrinsic parameters of these surfaces, such as resistivity or tortuosity. In long range sound propagation as well, it is well known that ground absorption is time varying. The understanding of this variation is an important issue. In both application cases, nondestructive measurement methods are required. The present contribution focuses on the 2-parameter model by Delany and Bazley for outdoor surfaces and the 4-parameter one by Hamet-Berengier for porous road pavements. It is shown that for both models the absorption coefficient spectrum obtained by an ISO 13472-1 compliant measurement contains enough data for the automatic identification. For the 2-parameter model the identification is based on a suitable cost function. The complexity of the function is low enough for a resolution by exhaustive search. It turns out that, for a large set of soft ground samples, the cost function is convex. Therefore the resolution can be done quite efficiently by classical gradient descent methods. Regarding the 4-parameter model, although the cost function is no longer convex, the resolution can be performed using a global optimization tool, like an evolutionary algorithm.
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The Propagation of an Acoustic Wave along a Boundary
Article
  • Jan 1947
The sound field of a point source near the boundary of two media cannot be obtained by an acoustic‐ray approach. In fact, such an approach which utilizes the reflection coefficient for plane waves leads to completely contradictory results at grazing incidence. A more rigorous solution is obtained, the procedure followed being exactly similar to that initiated by Sommerfeld to derive the electromagnetic field of a vertical dipole situated near a conducting plane. The results of such an analysis as applied to an acoustic point source are presented. As pointed out by Van Der Pol, the resultant solution may be regarded as that due to the point source and a diffuse image. The discussion of the solution is restricted to cases in which the sound source is at the boundary although it is given for all source heights. The solution shows that when the boundary medium has a high real specific acoustic impedance, non‐zero fields are obtained at all points along the boundary. For bounding media adequately described by simple porosity theory, the acoustic pressure at the boundary is inversely proportional to the square of the distance and the square of the frequency, at reasonably large distances and low frequencies. Also there appears to be decreased phase velocities along the boundary. Some calculations of the sound pressure as a function of height above Quietone show, among other things, the presence of a minimum occurring some distance above the boundary. At large distances from the source there are very large decreases in amplitude as the receiver height is increased in the region above this minimum.
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Ground characterization by short‐range propagation measurements
Article
  • May 1990
In recent years, short‐range measurements of excess attenuation from a point source have been used together with semiempirical formulas for frequency dependence of impedance to enable the acoustical characterization of ground surfaces, including snow, in terms of a single parameter. This has then been advocated as a basis for predicting ground and propagation effects at longer ranges. An alternative method is described for determining acoustical properties of ground surfaces including sands, soils, and snow from iterative least‐squares fitting of the level difference spectrum obtained between a pair of vertically separated microphones within 2 m of a broadband point source. The method is based on a three‐parameter model for the surface normal impedance as a function of frequency, together with well‐established formulations for propagation from a point source above either local or extended reaction surfaces. The three parameters are porosity, effective flow resistivity, and tortuosity. Independent (nonacoustic) measurements of porosity compare tolerably well with the acoustically determined values for soils that are homogeneous to several centimeters depth. For such soils, fitting comparisons reveal the superiority of the three‐parameter impedance model to the single‐parameter semiempirical model. Where there are obvious surface crusts, a double‐layer model based upon a two‐parameter approximation for the characteristic impedance of each layer is found to give better agreement with short‐range propagation measurements than the three‐parameter homogeneous approximation.
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Acoustical Properties of Fibrous Absorbent Materials
Article
Results are presented of an investigation into the acoustical properties of a range of fibrous absorbent materials. Measured values of characteristic impedance and propagation coefficient are shown to normalise as a function of frequency divided by flow-resistance and can be represented by simple power-law functions. Absorption coefficients of thin layers of material over a range of flow-resistance values are also shown. Supplementary data provide a basis for estimating the flow-resistance of a material from its bulk density.
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  • Jan 1949
  • C Zwikker
  • C.-W Kosten
C. Zwikker and C.-W. Kosten, Sound Absorbing Materials, Elsevier, New-York, (1949).