Numerical Modeling: An Efficient Tool for Analyzing the Behavior of Constructions - Multiscale Geomechanics: From Soil to Engineering Projects - page 269

274 Multiscale Geomechanics

Given that A is always positive, it is clear that the loading condition ( λ iso > 0 )
requires B − C − ˙ D>0 .Ascan be seen under isothermal condition ( D =0 ), during
a humidification path for which ˙ C>0 ,material will collapse so long as condition
˙ B> C is fulfilled. Otherwise, an unloading is detected and the material swells
elastically.

From a theoretical point of view, the same approach should be used to evaluate
the plastic strains due to changes in temperature or the simultaneous action of the two
phenomena.

It should be noted that thermal stress or a mechanical loading may have the same
effect, which is to make an unsaturated soil contract during a subsequent humidification
[MOD 95].

9.3.7. Multimechanism model

The multimechanism approach involves the superpositioning of several plastic
strain mechanisms, each assigned by its own yield function ( f k ), its own flow rule
Ψ k with its own plastic multiplier ( λ k ). Hardening variables can be specific to each
mechanism ( α k ): e.g. degrees of mobilization of mechanisms ( r k ) or possibly ε n , where
the mechanisms are uncoupled, or be common to several mechanisms ( η ) such as plastic
volumetric strain ( ε v ) in the case of a unique critical density. The hardening variables
may then evolve if a mechanism is not active. The flow rule of each mechanism can be
written as follows:

k = λ k Ψ k

ε p

[9.74]

where the volumetric part of the plastic strains generated by the k mechanism is given
by the dilatancy law:
ε v k = λ k Ψ v k [9.75]

The following relations are also applied:
λ k ≥ 0,f k (σ ,α k ,η)≤0; λ p f k (σ ,r k ,ε v )=0
The rate of change for hardening variables is given by their evolution rule:

λ k L α k

α k = [9.76]

λ k L η k ( in our case: η k = ε v

η k = and L η k =Ψ v k ) [9.77]

with