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diagnose an illness that can lead to near death early enough. In other words, each
numerical model has to demonstrate its ability to reproduce the failure of real geo-
structures. This exercise offers the opportunity to control the values of the instability
criteria.
The phase of model validation showed that the number of cycles or the value of
the extremum could be affected by the resolution scheme. To detect a change in the
loading direction would require a capacity to accurately differentiate an effective
change from a numerical change due to an oscillatory convergence after a real
extremum. Tests showed that this detection was not very effective, which leads to
the calculation of a number of cycles depending on the numerical choices during the
model integration. An improved version for the determination of the number of
cycles was developed [BAG 08]. Concerning the justification, the seismic behavior
of the San Fernando Dam was retained as modeling case. The interesting feature of
this site was that it had been subjected to several earthquakes and was very well
documented. In 1952, an earthquake with PGA = 0.12 g did not produce any
damage, whereas one in 1971 led to the failure of the upstream facing of the lower
embankment, but not the one of the upper embankment.
10.6.7.1. Instability criteria
In the analysis carried out by the numerical model, the consequences of an
earthquake are estimated during and after the seismic loading in terms of strains,
irreversible displacements and the occurrence of liquefaction. The comparison with
in situ observations allows us to evaluate and then generalize the criteria of seismic
instability and failure to embankment and rockfill dams.
10.6.7.2. Shear strains
The evaluation in terms of strain amplitude is based on the analysis of the second
invariant of the strain tensor. This term allows us to determine the position of the
localized shear bands within the geo-structure. The interpretation is based on the
visualization of the possible kinematics of failure or of zones of significant shearing.
The EDF practice consists of connecting:
− a liquefied zone to a zone with shear strain greater than 5%, generalizing
Seed's criterion to the whole earth structure obtained from laboratory experiments;
− a generalized failure to a concentration of strains greater than 5% across the
whole dam from upstream to downstream.
It is essential to be able to visualize the shear zones in order to estimate the
spreading, localization and concentration of these zones. The risk of failure becomes
significant when these zones connect the upstream and downstream sides of the dam
without discontinuity, mobilizing a large volume of soil.
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