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strength, 0.8 is usually applied. The reliability coefficient
)
is related to current
norms, i.e. accepted probability of failure. For example
)
= 3 is identical to a
probability of
P
f
=
10
-3
. The standard deviation
sdZ
can be found by vectorial
summation, for independent variables
sdXi
]
2
sdZ
=
%
i
[
Z
/
X
i
)
(8.5)
Applying partial safety factors is referred to as a level I approach, i.e. quasi-
probabilistic using characteristic values. More sophisticated methods are the semi-
probabilistic approach (level II) using normal distributions and linearisation (mean
value or design point approach), and the full-distribution approach (level III) using
numerical integration (Monte Carlo approach). In standards and guidebooks more
information can be found. Sophisticated methods are usually applied to define
partial safety factors.
peat
Level III (Monte Carlo)
clay
- shear strength behind the
wall is hardly mobilized
- using level I will give a
conservative design
sand
99 calculations
influence factor values
E clay
= 0.878
clay
= 0.320
sand
= 0.064
clay
= 0.037
peat
= 0.000
E peat
= 0.114
peat
= 0.107
clay
= 0.037
peat
= 0.174
c clay
= 0.079
c peat
= 0.002
(a) mechanical system and relative shear stress (b) influence factors
Figure 8.7 System analysis for mechanical influence factors (Schweckendiek)
Special care is to be taken when applying the level I approach. The suggested
partial safety factors may not be representative in characteristic failure modes,
since locally the development of the mobilised shear strength may be limited. In
that case, the straightforward application of level I approach will result in a
conservative design. This effect can be covered in an adjusted
-factor in formula
(8.4) after employing proper mechanical analysis, see Fig 8.7.
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