Numerical Modeling: An Efficient Tool for Analyzing the Behavior of Constructions - Multiscale Geomechanics: From Soil to Engineering Projects - page 251

formulation which is only a generalization of the Cam Clay model. This comes down
to writing the model for an axisymmetrical triaxial test.

The main features of the simplified model are essentially those stated in the previous
section. In what follows, we will describe how these aspects are formulated under the
theory of incremental plasticity:
1) We write the constitutive law in terms of Terzaghi's effective stresses [TER 67]
in the case of saturated soils. We will see in section 9.3.5, the generalization of the
effective stress concept in unsaturated soils and its role in describing the behavior of
partially saturated soils.
2) Using the incremental theory of plasticity:
a) we assume that the strain rate (or increment) can be decomposed into an
elastic part ε e and a plastic part ε p :

ε = ε e + ε p [9.1]

b) the stress tensor rate depends on the rate of elastic strains:

σ = λ ε v I +2µε e [9.2]

or:

p

= K · ε v

[9.3]

e

µ · ε s = [9.4]

where λ , µ = G , K , E and ν are elasticity parameters, so that:

νE
(1 + ν)(1 − 2ν)

λ = [9.5]

E
2(1 + ν)

µ = G = [9.6]

E
3(1 − 2ν)

K =

[9.7]

3) The role played by the confinement is multiple:
a) in the elastic range, the results obtained by applying the Hertz theory to
assemblies of spherical beads under elastic isotropic loading can be generalized and
applied to granular materials [BIA 94]. This theory, which takes into account the
increase of the contact surface during loading, results in a non-linear relationship
between stresses and strain given by a stiffness modulus of the form:

E = α(p ) n

[9.8]