Evaluating Seismic Stability of Embankment Dams - Multiscale Geomechanics: From Soil to Engineering Projects - page 353

displacement amplitude in order to estimate the impact of a safety factor smaller
than 1. This is the objective of the approaches presented here.
Newmark's approach was the first to calculate the displacement of an unstable
mass when the factor of safety was smaller than 1 or K > Kc . Γ mean (t) is the
acceleration applied by the seismic loading to the soil mass studied at time t :
− if Γ mean (t) > K c g , the sliding is calculated by integrating the acceleration
Γ mean (t) − K c g ;
− if Γ mean (t) < K c g , there is no irreversible movement (see Figure 10.5).
Figure 10.5. Example of an accelerogram k MOY (A), of Kc (B), and of integrated displacement
(C) compared to measured displacement (C), after Ambraseys
There are a lot of applications of this approach that distinguish themselves by the
hypotheses on the accelerograph, the studied mass and the method for evaluating
Γ mean (t) . If we assume the absence of liquefaction, we can calculate the irreversible
deformations within the geo-structure by comparing K c g to the maximum
acceleration of the sliding mass K max g (max(Γ mean (t) ) at any time t of the
accelerograph duration.
Ambraseys et al. [AMB 67] calculated K max as a function of the natural period of
the geo-structure T 0 and the geometry of the unstable zone. They have applied the El
Centro seismic loading on a triangular mass at the vertical distance y = n.h from the
crest, having a natural period T 0 and a damping factor ξ. To determine the