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where
S
i
and
p
i
represent the degree of saturation and the pressure of phase
i
(
w
: water,
a
: air), respectively. Generally, this first approach is amended by the introduction of
an additional factor, the function of
S
w
called the Skempton coefficient [SKE 61], and
obtained experimentally, so that:
σ
f
= B(S
w
)p
w
I
[9.59]
Again, it is common to improve this approach by introducing experimental
coefficients. The coefficient most frequently used is that of Bishop [BIS 54]:
σ
f
= p
a
I − χ(S
w
)P
c
I
[9.60]
where
P
c
= p
a
−p
w
is the suction. The simplest formulation of Bishop's coefficient is
χ(S
w
)=S
w
[9.61]
Experiencehasshownthatparameter
χ
dependsonthestresspathandsoilproperties.
Currently, models of increasing complexity can reproduce the behavior of
unsaturated soils. These models take into account different aspects of observed behavior
and can be used over a long period of the structure's lifetime, if not all of it. We can
divide the research on the mechanical behavior of unsaturated soils into three parts: that
of the definition of effective stress, of volume change and the collapse phenomenon,
and finally, of shear strength.
Historically, the first time non-saturation in the behavior of a structure was
considered was through the work of Duncan and Chang [CHA 77], who calculated
the behavior of a dam without explicitly taking into account the air pressure or the
degree of saturation as an additional unknown variable. Under these circumstances,
the modeling is done assuming a saturated or pseudo-saturated material, taking into
account implicitly the reduction of the volume of air. Even though, unlike elastoplastic
models, the non-linear model of Duncan and Chang does not take into account the
generation of pore pressure by shear, this gap is overcome for clay by the fact that its
volumetric compressibility depends mainly on the isotropic stress [POU 95]. The error
regarding the pore pressure and the safety factor seems to be less than
10%
in the case of
clay; for sandy clay, it can be more. Ghaboussi and Kim [GHA 82] have validated this
approach of variable compressibility of water by using an elastoplastic model which
gives a good agreement for pressures and displacements during the construction of the
Quedradona dam. These saturated or pseudo-saturated models are justified under two
conditions:
- the clay is wet enough, which means that it is compacted on the wet side, so
that the fluid is considered to be continuous and the principle of effective stress is
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