Civil Engineering Reference
In-Depth Information
of Biot waves exist, the two frame-borne waves which are similar to the waves which
propagate in the frame in vacuum, and the air-borne wave which is similar to the wave
which propagates in the air saturating a rigid frame. Due to the different interactions
between frame and air, both kinds of waves simultaneously propagate in the frame and
in air, but the air-borne wave mainly propagates in air. For anisotropic porous media with
the frame much heavier than the air, the Biot waves are of the same kind. More precisely,
two waves polarized in the meridian plane are frame-borne waves and the third wave
is an air-borne wave similar to that which propagates in a rigid framed porous medium
which is described in Section (10.5.3). The wave polarized in a direction perpendicular
to the meridian plane is the third frame-borne wave. Another consequence of the partial
decoupling is shown in Section (10.8): the phase speeds of the Rayleigh waves for a
usual glass wool are very close to the phase speeds for the frame in vacuum.
10.4.5 Illustration
A representation of the slowness as a function of the real angle
θ
between the direction
of propagation and the axis of symmetry
Z
is given in Figures 10.1 and 10.2 for waves
polarized in the meridian plane, and in Figure 10.3 for waves polarized perpendicular to the
meridian plane. The porous medium is described by the parameters of Table 10.1. Similar
parameters can describe a glass wool. The Lafarge model (Equation 5.35) is used for the
bulk modulus and the Johnson
et al
. model (Equation 5.36) for the effective densities. The
frequency is 0.5 kHz. Both slowness components
q
and 1/
c
are related to the slowness
s
and the real angle
θ
by
s
sin
θ
=
1
/c
(10.53)
s
cos
θ
=
q
(10.54)
0.03
0.025
0.02
0.015
Pseudo shear wave
0.01
Pseudo compressional frame borne wave
0.005
Air borne wave
0
0
0.5
1
1.5
2
2.5
3
θ
(radian)
Figure 10.1
Re
s
as a function of
θ
for the waves polarized in the meridian plane.
