Environmental Engineering Reference
In-Depth Information
4
3
2
1
0
1
2
3
4
5
-1
-2
-3
-4
-5
Limiting ultimate settlement
s
cf
£ 1.94
5%
s
cf
£ 3.56
95%
1.0
0.9
0.8
0.7
Mean
s
cf
= 2.68 m
MC
From β
indices
= Φ(β)
0.6
0.5
0.4
0.3
0.2
0.1
0
1
2
3
4
5
Ultimate settlement
s
cf
(m)
Figure 9.22
Reliability indices for different limiting ultimate settlements, and comparison of CDF based on
β
indices with CDF from Monte Carlo simulations.
As shown in
Figure 9.22
,
the CDF based on 19 values of β indices is practically indistin-
//www.palisade.com
)
. For the assumed statistical input and correlation structure, the 90%
confidence interval of the ultimate consolidation settlement is (1.94, 3.56 m). The measured
ultimate settlement shown in
Figure 9.18
is within this interval. Other confidence intervals
can also be read from
Figure 9.22
.
Considerations such as this should be much more useful
in the design stage than a deterministic analysis that yields a single ultimate settlement value
with no indication at all of the effect of uncertainties (parametric, modeling, and others) on
the predicted ultimate settlement.
Figures 9.23
and
9.24
show the CDF curves obtained from reliability indices
(
Equations
CDF curves from 5000 realizations of MCS.
It is of interest to note that the ni
i
values of
c
v
and
c
h
in cells AE30:AE31 of the lower
Figure 9.21
are practically zero. The implied insensitivities of the ultimate consolidation
settlement to the coefficients of consolidation (
c
v
and
c
h
) are theoretically consistent (ulti-
mate settlement not a function of rate parameters
c
v
and
c
h
) and are automatically revealed
in a reliability analysis. In contrast, reliability analysis with respect to the limiting degree of
consolidation at
t
= 1 year and settlement remaining at
t
= 1 year will show nonzero values
for the
n
i
values of the coefficients of consolidation
c
v
and
c
h
, both parameters having an
effect on the rate of consolidation.
Search WWH ::
Custom Search