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to the overconsolidated character of London clay samples tested by Skempton. Besides,
for normally consolidated clays, Biarez and Favre [BIA 72] give indicative values of
7 kPa and 1 MPa for vertical effective stresses to reach
w
L
and
w
P
, respectively (see
Figure 9.8(a)).
9.4.2.2.2. Sands
For sands, there is a correlation between the value of
C
c
at the critical state and
void ratios and
e
min
and
e
max
which are themselves connected to the ratio
d
60
/d
10
.
According to Grésillons
et al.
quoted by Saïm [SAI 97], when
D
r
varies from 0 to 1,
σ
0
varies between 100 kPa and 5 MPa (see Figure 9.8(b), and Figure 9.9). The synthesis
carried out by Saïm shows that the value of 5 MPa can possibly be increased to 7 MPa.
Hicher and Rahman [HIC 94] propose a relationship for determining
β
from
e
min
,
e
max
,
U
c
=
d
60
d
30
d
10
and
C
z
=
d
60
.d
10
:
β =2.3(1 + e)
β
norm
I
e
[9.83]
with
I
e
= e
max
− e
min
:
β
norm
= log P
c
max
− log P
c
min
log P
c
max
= −4 log U
c
− 7.5 · e
min
+4.75 · I
e
+7.1±0.3
log P
c
min
= −12 log C
z
− 4.7 · e
max
+9.71 · I
e
+2.2±0.5
Wherever
n
e
=1
,the plastic compressibility modulus
β
of the model is obtained
from the parameters
λ = C
c
/2.3
and the elasticity stiffness
K
∗
, which should be
estimated for the range of considered
p
. We note that assuming a linear relationship
in the plane (
e − log p
) implies a value of
β
which varies with the void ratio:
1+e
0
λ−k
∗
β =
[9.84]
where
k
∗
is the mean slope of the elastic line in the
(e −
log
p
) plane, as defined in
section 9.4.2.2. Because of the higher value of plasticity compressibility with respect to
the elastic one, for an initial approximation,
k
∗
can be neglected before
λ
and
β ≈
1+e
0
λ
can be assumed.
9.4.2.3.
Friction and dilatancy angles (
φ
pp
and
ψ
)
In principle, these two angles are similar (e.g. Cam Clay model) unless experimental
results show otherwise.
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