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q/p'
pp
M
q/p'
pp
M
q/p'
ic
M
1.2
1.2
0.7
pente = 1
η = 0.71
pic
1.0
1.0
0.6
0.8
0.5
0.8
Cc = 0.53
0.4
0.6
0.6
Cc = 0.22
a
0.3
m = 0.645
b
c
0.4
0.4
0.2
0.2
0.2
0.1
ε1
0.0
0.0
0.0
0.0 0.5
1.0
1.5
2.0
2.5
p'/p'
pp
0
5
10 15 20 25 30
0.0 . 2 . 4 . 6 . 8 . 0
p'/p'
ic
DU/sig'
30
q/p'
0
M
I
D
0.8
2.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.6
1.5
0.4
d
0.2
e
f
1.0
0.0
-0.2
0.5
-0.4
ε
1
p'/p'
0
p'
-0.6
0.0
0.0
0.5
1.0
1.5
2.0
0.01
0.10
1.00
10.00
0
5
10 15 20 25 30
Mekkaoui FRNDF6
Figure 5.15.
Reference behavior for undrained sands
5.7.2.
Perfect plasticity normalization of the curves in the (q -
ε
1
) plane and pore
pressure variation
All the undrained loading paths in the (q - ε
1
) plane tend towards the horizontal
asymptote
Mp'
pp
. A normalization with
Mp'
pp
(Figure 5.15a) keeps the intermediate
peak that characterizes the sands with a small theoretical overconsolidation (“loose”
behavior). We associate the (q - ε
1
) plane with the (
q
/
Mp'
pp
-
p'
/
Mp'
pp
) plane, where
all the curves tend towards the bissectrice. The (Δ
U
/σ'
30
- ε
1
) plane in Figure 5.15d
permits the control of cavitation
1
(
the test curves were cut when cavitation
appeared
, according to Biarez's criteria [MEK 02]).
5.7.3.
Initial stress p'
0
normalization in the (q - p) plane
All the paths in the
q/Mp'
0
-
p'/p'
0
plane start from the point with coordinates
(1 - 0) and tend towards the first bissectrice (see Figure 5.15e).
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