Geoscience Reference
In-Depth Information
An examination of Figures 5.19a and 5.20a reveals a difference in the
C
c
(Biarez's approach) and
C
*
c
(Burland's approach) slopes, particularly between
σ
'
v
= 100 and
σ
'
v
= 1,000, when the liquid limit is high (
w
L
=100% to 160%). On the
other hand, for the lower
w
L
,
C
c
and
C
*
c
are similar, and fit well the experimental
data given by Burland for different values of
w
L
(see Figure 5.20a).
5.9.2.
Comparison of models and mixed model
5.9.2.1.
Plotting Biarez's model in Burland's space (I
v
- log
σ
'
v
)
According to correlation [5.7] we have:
ee
I
ee
−
=
P
=
0.46 3 log '
−
σ
[5.30]
L
v
−
L
P
Using [5.27] and [5.30] to express Biarez's model as a function of
I
v
, we obtain
the NCRS equation [5.31] in Burland's space:
*
100
−
ee
−
ee
−
P
I
=
1.38
−
−
0.46
log '
σ
[5.31]
L
P
L
P
V
C
*
C
*
C
*
According to Biarez, hence [5.2]
P
e
= and
*
1000
L
e
=, equation [5.31]
*
6,5
becomes:
ee
*
−
*
=
6,5
1000
1.38 0.46 log '
−
σ
−
1
.
[5.32]
V
C
*
Considering a linear variation between
Δ
e
and log '
v
Δ
σ
, we obtain:
e e
log100 log1,000 log6.5 log1,000
*
−
*
*
−
*
100
1000
=
6.5
1000
[5.33]
−
−
Thus, Biarez's model given by relation [5.32] becomes:
=−
2 log '
σ
.
[5.34]
V
Equation [5.34] is a straight line in the (
I
v
-
log
σ
'
v
) plane, passing through two
specific points (
I
v
= 0,
σ
'
v
= 100 kPa) and (
I
v
= -1,
σ
'
v
= 1,000 kPa), represented by
the NCRS line in Figure 5.21a. A representation of both the NCRS line and the ICL
in Burland's plane shows that the two curves converge at a vertical stress range
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