Environmental Engineering Reference
In-Depth Information
Since the position of the failure surface that is potentially the most critical is not
known
a priori
,
computation involves proceeding by iteration, and varying the
position of the surface considered. Such algorithms are now offered in a standard
way in computer programs.
3.3.4.
Finite-elements method
All the above-mentioned methods of slices run up against the problem of the
distribution of stresses in the mass. The remedy lies in the introduction of relations
that make deformations operate, in particular through elastoplastic laws and the
resolution of the boundary-valued problem by finite elements (see Figure 3.9, or the
example in [FRA 08]).
In this case, Mohr-Coulomb's law is often selected for the plasticity criterion,
and to the two material constants
c'
and
φ'
we add those of elasticity,
E
and
v.
Two algorithms are often used to evaluate the overall stability of the slope. In the
first case, gravity
g
is gradually increased by multiplying it by a factor
F
, starting
from unity. In the second case, strength parameters (
c'
and
tg φ'
) are gradually
decreased by dividing them by a factor
F
, starting from unity. The overall safety
corresponds to the maximum value of
F
leading to the divergence of the solution.
For the moment these methods are relatively seldom used in practice for slope
stability analysis; one of the reasons for this is that the safety factors obtained with
the finite-element method do not necessary correspond to those given by the proven
methods of slices. However, finite-element models present major benefits because
they enable:
- deformations to be taken into account (progressive failure, post-peak behavior,
determination of warning thresholds, etc.);
- better constitutive modeling of the different layers;
- the possibility of incorporating hydro-mechanical couplings;
- geometries and boundary conditions of great complexity;
- the possibility of making calculations in three dimensions (these effects are
often far from negligible in reality);
- identification of the failure mechanism without
a priori
setting
a potential
failure surface geometry.
