Reliability-based design - Risk and Reliability in Geotechnical Engineering - page 353

X* m N σ N Mean StDev nx Correlation matrix R

Lognormal
Lognormal
Lognormal
Lognormal

C
ϕ
Q h / m
Q v / m

15
25
300
1100

3
2.5
45
110

15.21
20.76
412.6
1185

14.7
24.52
276.5
1091

3.013
2.071
61.55
118.2

0.17
-1.81
2.21
0.794

1 -0.5

1
0
0

0
0
1
0.5

0
0
0.5
1

-0.5
0
0

B
4.51

L
25

D
1.8

γ e B B ¢ e L L ¢ q q u (X*)

21 0.871 2.769 0 25 427.9 427.92

c a P o Ω

12.17 37.8 19.203 N q

N c
N g

6.906
15.58
5.995

S q
1.025
d q

S c
1.029

S γ
0.982
d γ
1

i q
0.643

i c
0.582

i γ
0.4065

PerFunc d c

1.16

β
3.00
Array formula for β

1.126

0.00

=SQRT(MMULT (TRANSPOSE(nx), MMULT(MINVERSE(crmatrix),nx)))

Q v (kN/m)

Q h (kN/m)

2.5 m

D = 1.8 m

c , ϕ, γ

B

Figure 9.3 Determining foundation width B , for a reliability index β of 3.0.

9.2.1 rbD compared with eC7 or lrFD design, and
complementary roles of rbD to eC7 and lrFD design
In the geotechnical design based on EC7, the characteristic values of resistance parameters
are divided by partial factors to obtain the design values, while the characteristic values of
action (load) parameters are multiplied by partial factors to obtain the design values. The
resistance thus diminished is required to be greater or equal to the amplified actions (load-
ings), Figure 9.4 , which also summarizes the three design approaches DA1, DA2, and DA3.
The DA2 is akin in principle to the LRFD of North America. With respect to the character-
istic value, Clause 2.4.5.2(2)P EN 1997-1 defines it as being “selected as a cautious estimate
of the value affecting the occurrence of the limit state,” and Clause 2.4.5.2(10) of EC7 states
that statistical methods may be used when selecting characteristic values of geotechnical
parameters, but they are not mandatory.
One may note the following similarities and differences between an RBD and that based
on EC7 and LRFD, in the context of the RBD of Figure 9.3 :

i. The x * column denotes the point where the four-dimensional equivalent dispersion
ellipsoid touches the LSS. It is the most probable failure combination of the parameters.