Civil Engineering Reference
In-Depth Information
1.60e-3
1.40e-3
1.20e-3
1.00e-3
8.00e-4
6.00e-4
frequency = 2.4 kHz
phase velocity = 67.9 m/s
4.00e-4
2.00e-4
0.00
0.00
0.02
0.04
0.06
0.08
0.10
0.12
(a)
distance (m)
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00
0.04
0.06
0.08
0.10
0.12
0.14
0.16
(b)
distance (m)
Figure 8.4
Results at 2.4 kHz: (a) time of flight, (b) attenuation (Allard
et al
. 2002).
Reprinted with permission from Allard, J. F., Jansens, G., Vermeir, G. & Lauriks, W.
Frame-borne surface wave in air-saturated porous media.
J. Acoust. Soc. Amer.
111
,
690 - 696. Copyright 2002. Acoustical Society of America.
In Figure 8.2 a contribution of both frame-borne waves appears before the Rayleigh
wave with a much smaller amplitude. This contribution is not detectable with the current
measurement set-ups.
8.4
Layer of finite thickness - modified Rayleigh wave
The amplitude of the Rayleigh wave is noticeable in the layer up to a distance from the
surface equal to twice the Biot shear wavelength. The coefficients
r
ij
for the material
given in Table 8.1 are negligible for large thicknesses, but their moduli increase when
the thickness decreases, and the location of the Rayleigh poles is modified because the
coefficients
M
i,j
depend on the thickness via the coefficients
r
ij
. The location of the
