Civil Engineering Reference
In-Depth Information
and
q
0
=
4
.
4
×
10
−
8
m
2
. The predicted bulk modulus is different for both permeabilities,
the transition frequencies where Im
K
has a maximum are located at very different
frequencies. Measurements of the bulk modulus have been performed at low frequencies
with the measurement set-up described in Section (5.2.2). The porous medium was a
foam with porosity, tortuosity, viscous and thermal dimensions, close to those used for
the predictions. The measured bulk modulus in Lafarge
et al
. (1997) was close to the
one predicted with the lowest permeability,
q
0
=
10
−
8
m
2
.
1
.
3
×
5.5.6 Prediction of the surface impedance
In Figure 5.8 the surface impedance at normal incidence is given by Equation (4.137),
Z
s
jZ
c
/(φ
tan
kl)
. All the parameters have been measured with nonacoustical meth-
ods, except the thermal static permeability
q
0
,
and the parameter
b
of the Pride
et al
. model
which have been chosen to adjust the predicted impedance to the measured impedance.
=−
8
6
4
2
0
0
500
1000
1500
2000
2500
3000
f (Hz)
60
40
20
0
−
20
0
500
1000
1500
2000
2500
3000
f (Hz)
Figure 5.8
The
surface
impedance
of
a
layer
of
sand
of
thickness
l
=
3
cm.
Prediction
of
effective
density
from
Equation
(5.32)
with
the
parame-
10
−
10
m
2
,φ
ters
q
0
=
1
.
23
×
=
0
.
37
,
=
31
µ
m
,α
∞
=
1
.
37
,b
=
0
.
6, prediction of bulk
modulus with Equation (5.35),
=
10
−
10
m
2
(Tizianel
et al
.,
1999). Reprinted with permission from Tizianel, J., Allard, J. F., Castagnede, B.,
Ayrault, C., Henry, M. & Gedeon, A. Transport parameters and sound propagation in
an air-saturated sand.
J. Appl. Phys.
86
, 5829 - 5833. Copyright 1999, American Institute
of Physics.
m, and
q
0
=
90
µ
5
×
