Evaluating Seismic Stability of Embankment Dams - Multiscale Geomechanics: From Soil to Engineering Projects - page 348

determine the connection of these two indexes with the epicentral distance on one
hand, and the nature of the foundation soil, on the other.
10.4.4.3. Semi-empirical method
This method is used to generate strong seismic loads of level 2 and considers that
there is a scale effect between local slides and the overall movement. The final
loading is reconstituted from the summation of the local shocks using Green
functions [HAR 78]. The fault is decomposed into several elements. Local slides are
synchronized to the fault displacement by a probabilistic approach [BOO 83]. The
application domain of this approach is limited to high frequencies.
10.4.4.4. Theoretical method
This method consists of calculating the transmission of the energy and the
motion of the fault through a 3D mesh or a horizontal multilayer model [BOU 81].
However, the frequency content in the high-frequency domain depends very much
on the path followed; the lack of geological knowledge of this path leads to an
inaccuracy of the frequencies determined that are higher than 1 Hz.
10.4.4.5. Hybrid method
The method consists of adding the results obtained by the semi-empirical method
in the high-frequency domain and the results obtained by the theoretical approach in
the low-frequency domain.
10.4.4.6. Probabilistic method
This method benefits from a high amount of accumulated data from various
seismic recordings. The US Geological Survey publishes maps of the spectral
acceleration for a given probability and a given frequency. Therefore, it is possible
to determine spectrums of a given probability, i.e. spectrums of pseudo-accelerations
having the same probability of being exceeded for each frequency. By comparing
the probabilistic and deterministic spectrums, we can estimate the return period of
the latter. The probabilistic spectrum is obtained by combining three uncertain
events [ATK 97; TOR 97]:
− the activation of each source;
− the activation of each magnitude given by a law of the type log N = A - bM ,
with N being the number of earthquakes of magnitude equal or smaller than M ;
− the activation of each distance by an attenuation law.
All these approaches have to be improved by knowing the effect of the
mechanism of fault failure: the type of failure, the energy released, the length, etc.