Geoscience Reference
In-Depth Information
10.6.6.
Modelimplementation
The model has been implemented in FLAC 2D (Fast Lagrangian Analysis of
Continua), version 3.40. It is based on the finite difference method and has been
developed in order to analyze coupled hydromechanical problems. The code has
three advantages: it is easy to use, easy to implement constitutive models, and
possible to calculate in large strains. However, the numerical resolution for cyclic
loading requires us to distinguish between applied loads and numerical cycles used
to guarantee the calculus convergence. Indeed, the material cyclic contractancy is
taken into account at the end of each half-cycle, which requires the reactualization of
the effective stress state and of the mechanical properties in Ramberg-Osgood's
formulation. In the 1D case, the notion of the cycle is clear: a cycle corresponds to
the maximum strain amplitude. For a 2D analysis, the strain tensor has three
independent components, and for a 3D case, the seismic loading is even more
complex. A half-cycle is determined by detecting the maximum values in the strain
space. The change in the loading direction is defined by a negative value of the
variable corresponding to the projection of the actual strain state on the strain state at
the end of the last cycle. This variable can be expressed by the scalar product of the
actual strain vector and of the reference unit vector, written in 2D as:
d
=
(
) (
c p
ε- ε . ε - ε
) (
c p c p
ε - ε . ε - ε
− ε
,
ε
c
,
ε
cp
: strain vectors
(
ε
11
- ε
22;
2ε
12
of the actual state, of the last change
(index
c
) and of the penultimate change (index
cp
) of loading direction, respectively.
− (ε − ε
c
) corresponds to the strain evolution during the actual cycle since the last
direction change.
− (ε
c
− ε
cp
) corresponds to the reference vector of the last half-cycle.
Once the extremum in memory has been confirmed as correct, the number of
half-cycles is reactualized and the volumetric strain of the actual half-cycle is
injected as the soil response to the loading.
10.6.7.
ModelqualificationinthecaseoftheSanFernandodamfailure
Every design method has to be numerically validated and physically justified.
This procedure is called qualification. A numerical model applied to a dam can be
compared to a doctor examining a patient. Whereas anybody is capable of
diagnosing a state of good health, only a competent practitioner can correctly
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