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−
h
is the height of the dam; and
−
Vs
is the velocity of the shear waves crossing the dam from bottom to top.
The maximum value of the displacement is given as function of
K
max
,
Kc
and
V
,
where:
−
Kc
is determined by the pseudo-static approach;
−
V
is the maximum displacement rate at the base of the dam; two methods of
determination are possible:
- maximum velocity of the accelerograph at the base (in cm.s
-1
);
- V
=
PGA/(2;n
0
)=4 x PGA x P
with
n
0
being the mean number of times the
accelerograph passes through zero and
P
the fundamental frequency of the
earthquake.
Figure 10.7 was obtained from the calculations of the displacements induced by
three earthquakes of various magnitudes for dam heights between 50 and 65 m. The
authors think that the displacements calculated for
Kc/K
max
< 0.2 are unreliable.
However, a comparison between calculated and measured displacements on Chilean
dams have shown that Ambraseys' method gave better results than the Makdisi and
Seed's method [MAK 78]. The latter contains three steps:
− the first step consists of calculating the modulus and the damping ratio of the
dam;
− the second step consists of defining the maximum acceleration at the crest;
− the third step consists of defining the maximum acceleration of the circular
sliding surface at the depth
y
;
K
max
is determined by using the abacus in Figure 10.6.
The displacement
U
is given by the abacus in Figure 10.8. For various earthquake
magnitudes, the ratio
U
(in seconds) is function of
Kc/K
max
.
k
×
0
T
×
g
max
10.5.6.
Analysisoftheliquefactionrisk
The analysis of the risk of liquefaction is based on the evaluation of the
resistance of the foundation and embankment by penetrometer testing. The
in situ
resistance is too scattered to be determined by laboratory testing. Youd has
organized a workshop in order to establish norms for the prediction of
in situ
liquefaction. The general report of this colloquium remains the state of the art
[YOU 01].
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