Environmental Engineering Reference
In-Depth Information
1
0.1
0.01
0.001
0.5
0.6
0.7
0.8
0.9
1.0
1.1
y
=1/FS
Figure 7.13
CCDF plot from Subset Simulation.
Y
= 1/
FS
(i.e.,
P
(
Y
>
y
) vs.
y
) from Subset Simulation. The failure probability can also be
directly obtained from the plot.
7.7.2 hypothesis test results
With a large number of failure samples generated from Subset Simulation, hypothesis testing
is performed for the James Bay Dike design scenario for identifying the important uncertain
parameters. Using the 1134 failure samples generated from Subset Simulation, the μ
f
values
for ϕ
Fill
, γ
Fill
,
T
cr
,
S
uM
,
S
uL
, and
D
Till
are calculated. This can be achieved using an Excel built-
in function “AVERAGE (),” which uses 1134 failure samples as input. Then, hypothesis tests
T
cr
to about 93 for undrained shear strength of the lacustrine clay
S
uL
. The decreasing order
of the
Z
H
absolute values is
S
uL
,
D
Till
, γ
Fill
,
S
uM
, ϕ
Fill
, and
T
cr
. This implies that the uncertain
parameter
S
uL
has the most significant effect on the slope failure probability, while the uncer-
tainty on
T
cr
only has minimal influence on the failure probability.
7.7.3 bayesian analysis results
Since
S
uL
is identified as the most important uncertain parameter from hypothesis tests,
Bayesian analysis is performed to quantify the variation of
P
(
F
) as the
S
uL
value changes.
Table 7.8
Summary of hypothesis test results for the James Bay Dike design example
Uncertain parameter
T
cr
S
uM
S
uL
D
Till
ϕ
Fill
γ
Fill
30.00
20.00
4.00
34.50
31.20
18.50
Unconditional mean
μ
1.79
1.10
0.48
3.95
6.31
1.00
Standard deviation
σ
Failure sample mean
μ
f
29.12
20.85
3.89
31.87
13.76
19.84
Absolute value of
Z
H
16.52
26.05
7.49
22.43
93.08
45.28
Ranking
5
3
6
4
1
2
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