Reliability-based design - Risk and Reliability in Geotechnical Engineering - page 361

20

10

-0.6 m

0

70

90 110 130 150 170 190

-10

-20

1.5

1

δ = 1000

0.5 100

50

0

70 10

5

-0.5 110 150 190

-1

2

-1.5

1

x -coordinates (m)

-2

Figure 9.8 Design point index of clay unit weight as a function of horizontal autocorrelation distance δ in
meter.

built-in constrained optimization program. It reflects sensitivity and the underlying statisti-
cal assumptions from case to case in a way that the specified partial factors cannot.
At higher values of autocorrelation distance δ, the correlation coefficients approach 1.0;
the design point indices of γ of the 24 slices approach a common value, as shown by the
nearly horizontal line in Figure 9.8 for δ = 1000 m. The design point indices of c u —deined as
( c ui * − μ cui )/σ cui —of the 24 slices also approach a uniform common value when δ = 1000 m;
however, the individual design point values of c u differ from slice to slice because the mean,
μ cui , and standard deviation, σ cui , vary from slice to slice.
The implications of not considering seabed erosion versus treating seabed as random (to
account for uncertain depth of erosion) were discussed in Low et al. (2007).
The results of reliability analysis are only as good as the statistical input and reliability
method used (e.g., FORM or SORM), in the same way that the results of deterministic analy-
sis are only as good as the deterministic input and method used (e.g., Spencer method or other
methods). A reliability analysis requires additional statistical input information that is not
required in a deterministic factor-of-safety approach, but results in richer information pertain-
ing to the performance function and the design point that is missed in a deterministic analysis.
The FORM reliability approach reflects the underlying analytical formulations and statis-
tical assumptions and is able to locate the most probable combination of parametric values
that would cause failure and the corresponding reliability index, without relying on rigid
partial factors.

9.6 SYSteM ForM relIabIlItY analYSIS oF a SoIl SloPe
WIth tWo equallY lIkelY FaIlure MoDeS

A slope in two clayey soil layers was analyzed in Ching et al. (2009) using MCS and IS
methods. The same two-layered slope was analyzed in Low et al. (2011), using system reli-
ability bounds for multiple failure modes. It was shown that when two (rather than one)