Modeling Landslides with a Material Instability Criterion - Multiscale Geomechanics: From Soil to Engineering Projects - page 232

236 Multiscale Geomechanics

2100m

Figure 8.10. Mesh of the Petacciato cut

On the other hand, since we do not know the degree of water transfer during the
regular rainy seasons, we chose to start with null values of water pressure at the bottom
of the site. This pressure is augmented step by step at the boundaries, as shown in
Figure 8.11. The physical time of flow between two steps is high enough for there to
be, at the end of each step, a permanent water flow between the left and right banks of
the soil. The water table slope was chosen arbitrarily in order to be more or less parallel
to the mean slope of the site.

u a = u w =0

waterproof bottom

Figure 8.11. Boundary conditions to impose the water level

Finally, the second-order work has been computed at each integration point for each
computation step. Nevertheless, as the criterion depends only on the sign of d 2 W , the
effective quantity computed is:

d 2 W
dσdε

d 2 W n = [8.31]

d 2 W n is called normalized second-order work and represents the cosine of the angle
between stress rate and strain rate vectors. This quantity decreases continuously when
the second-order work tends to zero. As a consequence, changes of the normalized
second-order work's isovalues with the loading make it possible to follow the evolution
of the weakened zones. Figure 8.12 displays these results for typical water levels. It
can be noted that the first instabilities appear at the surface when the water table level is
at about 75% from the maximum level. We should note that potentially unstable zones