Geoscience Reference
In-Depth Information
Additionally, often a range of expected seismic displacements is desired. The proposed
methodologycanbeusedtocalculatetheprobabilityoftheseismicdisplacementexceed-
ingaselectedthresholdofdisplacement
foraspecifiedearthquakescenarioandslope
properties. For example, consider a potential sliding mass with an initial fundamental
period
T
s
,yieldcoefficient
k
y
,andanearthquakescenariothatproducesaspectralaccel-
eration of
S
a
(
(
d
)
1
.
5
T
s
)
. The probability of the seismic displacement
(
D
)
exceeding a spec-
ified displacement threshold
(
d
)
is
(
>
)
=[
−
(
=
)
]·
(
>
|
>
)
P
D
d
1
P
D
“0”
P
D
d
D
“0”
(14.6)
The term
P
may
be computed assumingthat theestimated displacements are lognormally distributedas
(
D
=
“0”
)
is computed using Eq. (14.4). The term
P
(
D
>
d
|
D
>
“0”
)
ln
d
ln
d
−
P
(
D
>
d
|
D
>
“0”
)
=
1
−
P
(
D
≤
d
|
D
>
“0”
)
=
1
−
(14.7)
σ
(
d
where ln
)
is computed using Eq. (14.5) and
σ
=
0
.
66.
The trends in the Bray and Travasarou (2007) seismic displacement model are shown in
Figures 14.13 and 14.14. For the
M
w
=
7 earthquake at a distance of 10km scenario
(i.e., Figures 14.13a,b), the importance of yield coefficient is clear. As yield coefficient
increases, the probability of “zero” seismic displacement increases and the median esti-
mateofnonzerodisplacementdecreasessharply.Thefundamentalperiodofthepotential
sliding mass is also important, with values of
T
s
from 0.2 to 0.4s leading to a higher
likelihood of seismic displacement. For a
M
w
=
.
7
5 earthquake at different levels of
500
1
500
Magnitude 7
Soil Site
Magnitude 7
Soil Site
Magnitude 7.5
T
s
= 0.3 s
0.8
100
100
0.6
0.4
10
10
0.2
0.05
1
0
0
1
0.5
1
1.5
2
0
0.5
1
1.5
2
0
0.1
0.2
0.3
0.4
(a)
Fundamental Period (s)
(b)
Fundamental Period (s)
(c)
Yield Coefficient
Fig. 14.13. Trends fromthe Bray and Travasarou (2007) model: (a) probability of
negligible displacements and (b)median displacement estimate for a
M
w
=
7strike-slip
earthquake at a distance of 10km, and (c)seismicdisplacement as afunction of yield
coefficient for several intensitiesof ground motion
(
M
w
=
7
.
5
)
for asliding block with
T
s
=
0
.
3s
