Geoscience Reference
In-Depth Information
between these two quantities reduce the correlation parameters to a single one
[BIA 72, CAS 58, SKE 53]. Chapter 5 in this volume provides interesting comparisons
on these correlations for different clays;
2) case of sands: the relative density
D
r
=
e
max
−e
e
max
−e
min
or the density index
I
D
=
1 − D
r
and the grain-size distribution together with the shape of grains are basic
parameters from which correlations are established for sands [BIA 94].
9.4.2.
Directly measurable parameters
9.4.2.1.
Elastic parameters
9.4.2.1.1. Clay
We can use the results of geophysical measurements; however, there are correlations
for the shear modulus of clays that link this parameter to the void ratio (
e
), the state
of overconsolidation (
OCR
) and mean stress (
p
0
). Certain authors suggest using the
plasticity index
I
p
and consistency index (
I
c
=
w
P
−w
w
L
−w
P
). As the void ratio and the
plasticity index in turn are correlated, these two approaches are identical. Seed and
Idriss [SEE 70] connect the shear modulus
G
max
to maximum undrained strength
(
C
u
), which also takes into account the influence of the initial state. A number of
correlations of the literature are shown in Figure 9.7 and Tables 9.3 and 9.4.
The Poisson's ratio varies between 0.2 and 0.3. The elasticity exponent
n
e
varies
between 0.5 and 0.9 for clays.
9.4.2.1.2. Sands
As for clay, correlations based on
p
0
and void ratio
e
are given for sand. Hardin and
co-authors [HAR 63, HAR 68, HAR 78] give the same relationship for low plasticity
clay and Monterrey sand. Exponent
n
e
is about 0.5 for sand. According to Brul, in
unsaturated soils, the shear modulus increases as a function of suction [BRU 80].
However, we can expect that this increase is limited by the maximum capillary stress.
Furthermore, Coronado [COR 05] and co-authors [COR 07] have shown that a unique
relationship can be found between the evolution of the elastic modulus and the
generalized effective stress for different water contents. In the Cam Clay model, a
linear evolution between the void ratio and the logarithm of the mean effective stress
is assumed during an isotropic unloading path (parameters
κ
or swelling index
C
s
),
whereas, in our model, the elastic modulus satisfies a power law. It is only in the
special case where
n
e
=1
that the two laws are equivalent. Although the value
of
n
e
can approach unity for some clays, an exponential increase is not reasonable
for sands.
9.4.2.2.
Plastic compressibility (
β
)
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