Modeling Landslides with a Material Instability Criterion - Multiscale Geomechanics: From Soil to Engineering Projects - page 228

232 Multiscale Geomechanics

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Figure 8.7. Mohr-Coulomb, Drücker-Prager and Van-Eekelen limit surfaces
in the deviatoric plane with ϕ c = ϕ e =19 ◦

ϕ c and ϕ e are the friction angles in compression and extension, respectively. B p and B c
are two hardening constants permitting the evolution of this hardening to be calibrated.
Finally, ε eq is the total Von Mises plastic strain obtained during the loading. The non-
associated feature is described with a plastic potential defined in the same manner as the
loading surface, but using the dilatancy angle instead of the friction angle. Evolution
of ψ is given, assuming that

ϕ − ψ = cte cte ∈ R [8.19]

all along the loading.

The Petacciato landslide was probably triggered by the heavy rainfalls which
preceded the event. For this additional reason, we used a model which allowed the
main characteristics of unsaturated soils to be described. This behavior is governed
by the equation of the transfer of flow water within unsaturated soils. This equation is
formulated with the generalized Darcy law and the mass balance equation:

v = −k(S r ) ∇(h) [8.20]

with k the permeability depending on the saturation degree S r and h the hydraulic head
defined as follows:

p
ρg +z

h = [8.21]

Furthermore,ifwehypothesizethatthewaterisincompressible,thebalanceequation
for the water mass could be written as

div (v)=− ∂θ