Civil Engineering Reference
In-Depth Information
Using the symbols
G
3
Pa
=
3
HG
2
Pb
=
3
G
2
I
Pd
=
6
GHI
+
H
3
Pe
=
3
GI
2
3
GH
2
Pc
=
+
(10.B.5)
+
3
H
2
I
=
3
HI
2
Pf
I
3
Pg
=
q
P
can be written
q
P
=
q
z
Pc
q
z
Pd
q
z
Pe
q
z
Pf
q
z
Pg
Pa
+
q
z
Pb
+
+
+
+
+
(10.B.6)
The parameters
T
1
,T
2
,T
3
are now given by
T
12
q
P
T
1
=
T
11
+
(10.B.7)
T
22
q
P
+
T
23
q
P
T
2
=
T
21
+
(10.B.8)
T
32
q
P
+
T
33
q
P
+
T
34
q
P
T
3
=
T
31
+
(10.B.9)
The slowness component
q
z
satisfies the following equation
A
6
q
z
+
A
5
q
z
+
A
4
q
z
+
A
3
q
z
+
A
2
q
z
+
A
1
q
z
+
A
0
=
0
(10.B.10)
where
A
6
=
T
0
+
T
12
I
+
T
23
N
+
T
34
Pg
(10.B.11)
A
5
=
T
12
H
+
T
23
M
+
T
34
Pf
(10.B.12)
A
4
=
T
11
+
T
22
I
+
T
33
N
+
T
12
G
+
T
23
L
+
T
34
Pe
(10.B.13)
A
3
=
T
22
H
+
T
33
M
+
T
23
K
+
T
34
Pd
(10.B.14)
A
2
=
T
21
+
T
32
I
+
T
22
G
+
T
33
L
+
T
23
J
+
T
34
Pc
(10.B.15)
A
1
=
T
32
H
+
T
33
K
+
T
34
Pb
(10.B.16)
A
0
=
T
1
+
T
32
G
+
T
33
J
+
T
34
Pa
(10.B.17)
References
Biot, M. A. (1962) Generalized theory of acoustic propagation in porous dissipative media.
J. Acoust. Soc. Amer
.
34
, 1254 - 1264.
Castagnede, B., Aknine, A., Melon, M. and Depollier, C. (1998) Ultrasonic characterization of the
anisotropic behavior of air-saturated porous materials.
Ultrasonics
36
, 323 -343.
Cheng, A. H. D. (1997) Material coefficients of anisotropic poroelasticity.
Int. J. Rock Mech. Min.
Sci
.
34
, 199 -205.
