Geoscience Reference
In-Depth Information
b) the effect of confinement on the strength of soils is double. Its effect is
manifested both at the level of perfect plasticity and intermediate behavior. This role is
mainly due to the friction characteristics of the granular media and is reflected by the
fact that the behavior of soils at perfect plasticity is governed by the Coulomb criterion.
The yield surface has the following form:
f(q,p
,α)=q−η(α)·p
≤0
[9.14]
where
η
is the mobilized shear (
q/p
). It reaches its final value
M
at perfect plasticity
where
6sin φ
pp
3 − sin φ
pp
M=
[9.15]
In this equation,
α
denotes the set of hardening variables due to shear and
volume change that we will specify later.
4) To introduce the influence of strain hardening in shear, it is assumed that the
plastic shear strain
p
-since the last load reversal for cyclic conditions-controls the
mobilized strength:
η(r)=r·M
[9.16]
n
p
+
p
a +
p
r(
p
)=
ela
+
− r
ela
[9.17]
here
<a>
+
=(a+ |a|)/2
.
The first parameter of strain hardening (
r
) that we call the degree of mobilization
of plastic shear is introduced here. It moves between its initial value (
r
ela
), which sets
the size of the domain where shear does not introduce strain hardening (which may be
called the elastic deviatoric or shear field), to unity at perfect plasticity. Very often, a
hyperbolic evolution (
n
p
=1
)ischosen similarly to the hyperbolic curves observed
for stress-strain (the hyperbolic law of Duncan is based on this observation). This
hardening can be adjusted according to experimental results. Parameter
a
, which is
one of the key parameters of the model, controls the evolution of this strain hardening.
5) The role of density is introduced by use of a Cam Clay type relation:
η(
p
,ε
v
)=r(
p
)·F(p
,p
c
(ε
v
)) · M
[9.18]
p
p
c
(ε
v
)
F(p
,p
c
(ε
v
)) = 1 − b · ln
[9.19]
with
p
c
(ε
v
)=p
0
exp(βε
v
)
[9.20]
where
p
c
0
is the initial critical pressure corresponding to the initial void ratio,
β
is
the plastic compressibility introducing the influence of densification or unpacking of
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