Geoscience Reference
In-Depth Information
Travasarou (2007) simplified seismic displacement method. The earth fill is 30m high
and has a side slope of 2H:1V with a shape similar to that shown in Figure 14.4a. The
embankment is located on a rock site at a rupture-distance of 12km from a
M
w
=
2
strike-slipfault.Asimplifieddeterministicanalysisisperformedtoevaluatethepotential
movement of adeep slidethrough the base of the earth embankment.
7
.
The average shear wave velocity of the earth fill was estimated to be 300m/s. For
the case of base sliding at the maximum height of this trapezoidal-shaped potential
sliding mass, the best estimate of its initial fundamental period is
T
s
=
/
=
4
H
V
s
(
)(
)/(
/
)
≈
.
4
30m
300m
s
0
4s. The degraded period of the sliding mass is estimated to
be 0.6s (i.e., 1
6s). The yield coefficient for a deep failure surface
wasestimatedtobe0.14fromapseudostaticslopestabilityanalysesperformedwithtotal
stress undrained shear strength properties of
c
.
5
T
s
=
1
.
5
(
0
.
4s
)
=
0
.
20
◦
for the compacted
=
10kPa and
φ
=
earth fill.
The best estimate of the spectral acceleration at the degraded period of the sliding mass
can be computed as the mean of the median predictions from multiple attenuation rela-
tionships. Using Abrahamson and Silva (1997) and Sadigh et al. (1997) for the rock site
condition for a strike-slip fault with
M
w
=
7
.
2 and
R
=
12km,
S
a
(
0
.
6
s
)
=
0
.
44
g
and
0
52
g
, respectively. Thus, the design value of
S
a
at the degraded period of sliding mass
is0
.
48
g
, itsinitialfundamental period is 0.4s,and
k
y
is0.14.
The probability of“zero” displacement occurring iscomputed using Eq. (14.4) as
.
P
(
D
=
“0”
)
=
1
−
(
−
1
.
76
−
3
.
22ln
(
0
.
14
)
−
0
.
484
(
0
.
4
)
ln
(
0
.
14
)
+
3
.
52ln
(
0
.
48
))
=
0
.
01
(14.8)
There is only a 1% probability of negligible displacements (i.e.,
1cm) occurring for
this event. Hence, it is likely that non-negligible displacements will occur. The 16% and
84%exceedancevaluesofseismicdisplacementcanbeestimatedusingEq.(14.5)assum-
ingthatthesevaluesareapproximatelyhalfanddoublethemedianestimate,respectively.
The median seismicdisplacement iscalculated using
<
2
(
)
=−
.
−
.
(
.
)
−
.
(
.
)
)
ln
D
1
10
2
83ln
0
14
0
333
(
ln
0
14
2
+
0
.
566ln
(
0
.
14
)
ln
(
0
.
48
)
+
3
.
04ln
(
0
.
48
)
−
0
.
244
(
ln
(
0
.
48
))
+
1
.
50
(
0
.
4
)
+
0
.
278
(
7
.
2
−
7
)
=
2
.
29
.
(14.9)
The median estimated displacement is
D
10cm, and the
16%to84%exceedancedisplacementrangeis5to20cm.Thus,theseismicdisplacement
due to deviatoric deformation is estimated to be between 5 and 20cm for the design
earthquake scenario. The direction of this displacement should be oriented parallel to
the direction of slope movement, which will be largely horizontal for this case. For the
total crest displacement of the embankment, a procedure such as Tokimatsu and Seed
(1987) would be required to estimate the vertical settlement due to cyclic volumetric
compression of thecompacted earth fill.
=
exp
(
ln
(
D
))
=
exp
(
2
.
29
)
≈
