Reliability-based design - Risk and Reliability in Geotechnical Engineering - page 367

Figure 9.12c shows the curves of reliability index β = 3 as a function of the thickness t
and external diameter d of the tubular pile, for the deflection performance criterion and
pile-bending failure mode. The configuration at location a (i.e., 32 mm annular wall thick-
ness and external diameter 1.42 m) yields a reliability index of 3 with respect to both the
deflection and the bending moment modes. Configurations along line ac will have a reli-
ability index of 3 for the bending moment mode, and >3 for the deflection mode, whereas
configurations along line ab mean a reliability index of 3 for the deflection mode, and >3 for
the bending moment mode.

9.8 ForM DeSIgn oF an anChoreD Sheet PIle Wall

The Microsoft Excel constrained optimization approach for RBD of the anchored sheet
pile wall in Figure 9.13 was presented in Low (2006). Another example was presented in
Low (2005). Given the uncertainties and correlation structure in Figure 9.13 , one wishes
to find the required total wall height H so as to achieve a reliability index of 3.0 against
rotational failure about point “ A. ” The solution ( Figure 9.13 ) indicates that a total height
of 12.15 m would give a reliability index β of 3.0 against rotational failure. With this wall
height, the mean-value point is safe against rotational failure, but failure occurs when the
mean values descend/ascend to the values indicated under the x * column. These x * values

crmatrix (Correlation matrix)

x* Mean StDev nx γ γ sat q s ϕ′ δ z

γ
γ sat

γ

Normal
Normal
Normal

16.204
18.443
10.276

17
20
10

0.85
1
2

-0.93632
-1.55725
0.13807

1 0.5 0 0.5 0 0

γ sat 0.5 1 0 0.5 0 0

00 1 0 0 0

q s q s

Normal
Normal

33.514
17.292

38
19

2
1

-2.24307
-1.70765

0.5 0.5 0 1 0.8 0

ϕ′ ϕ′

δ
z

δ 00 0 0.8 1 0

z

Normal 2.9632 2.4 0.3 1.87735 00 0 0 0 1

Surcharge q s

Boxed cells contain
equations

d ∗ = H - 6.4 - z ∗

d ∗

1.5 m T

K a K ah K p K ph H PerFn

A

0.3 0.249 5.904 5.637 12.15 2.79 0.00

6.4 m

γ, ϕ′, δ

Forces Lever arm Moments
(kN/m)

β

3.00

(m) (kN-m/m)

2

Water table

1 -31.1 4.575
2 -82.8 2.767
3 -149 7.775
4 -35.6 8.733
5189.2 9.72

-142
-229
-1156
-311
1839

1

z

γ sat

Dredge level

3

For a given H, the embedment depth
d is random due to random z which
implies uncertain dredge level

d

5

4

Figure 9.13 Design total wall height for a reliability index of 3.0 against rotational failure. Dredge level and
hence z and d are random variables.