Geoscience Reference
In-Depth Information
with
-
p
: the mean effective stress estimated from relations [9.54] or [9.62], depending
on whether the gas phase is discontinuous or continuous, respectively:
p
= p − (p
w
− p
a
)
if
p
w
− p
a
>p
sat
p
= p − π
c
if
p
w
− p
a
≤ p
sat
where
p
sat
is the pressure at which the meniscus forms or disappears in the soil.
It represents the limit between the saturated and unsaturated behavior. It may have
different values, under drainage and imbibition paths: (
p
sat
= p
desat
if
p
w
− p
a
< 0
)
or imbibition (
p
sat
= p
resat
if
p
w
− p
a
> 0
);
-
p
ns
c
= p
c
0
exp(βε
v
)+(π
c
)
:the critical pressure for unsaturated behavior
which is a function of the plastic volumetric strain
ε
v
, plastic compressibility
β
,
critical pressure at initial state
p
c
0
and of
(π
c
)
, which is a function of capillary
stress controlling the extension of elasticity of the unsaturated soil;
-
d
is the parameter measuring the distance between the critical state line and the
isotropic normally consolidation (virgin) state in (
e − ln p
) plane for a saturated soil.
Note: The influence of temperature on the behavior is governed by this parameter
which can evolve with temperature [LAL 95, MOD 97]. As the isotropic consolidation
line moves to the right side of the perfect plasticity (critical state) when the temperature
(
T
) increases, the following relation can be considered for
d
:
d(T)=d
0
exp
−βς(T)
where
ς
represents the variation of the void ratio with temperature.
Thedeviatoricmechanismsremainunchangedexceptthatamodifiedcriticalpressure
is introduced:
f
k
= q
k
− p
k
· r
k
· (1 − b ln
p
p
ns
c
) · sin φ
pp
[9.68]
Therefore, the variation of the friction angle due to the nonsaturation is taken into
account by
p
n
c
, which couples the two types of mechanisms. As mentioned earlier, the
isotropic mechanism is assumed to be associated as well as the deviatoric mechanisms
for their deviatoric part. For the volumetric strain associated with these mechanisms,
the same dilatancy rule has been used. The coupling between mechanisms is done by
p
n
c
and leads to expansion or narrowing of the isotropic and deviatoric yield surfaces.
During a thermal loading, if the stress point remains on the yield surface, as the mean
effective stress is not modified, this coupling leads to increasing deviatoric strength and
thermal hardening, which is even more pronounced for unsaturated soil. Assuming that
the friction angle varies with temperature, this effect can be counterbalanced. The laws
Search WWH ::
Custom Search