Geoscience Reference
In-Depth Information
Z = R - S
(8.1)
where
R
is the structural resistance (design) and
S
denotes the effect of actions
(loading excitations or solicitation). If
Z
< 0 the construction fails.
Z
= 0 is the limit
state. The ratio
R/S
can be related to an overall safety factor
0
(the old-fashioned
way). The resistance
R
depends on various structural elements
X
i
and the effect of
loading
S
can be composed of different components
Y
j
. For a specific model
approach the method of partial safety factors may express the reliability, as follows
R
(…,
X
i
/
i
,…) /
S
(…,
Y
j
j
,…) >
m
(8.2)
m
is a resistance factor
related to model factors (design methods for
Z
). The design approach, which can be
adopted, includes either calculations, prescriptive measures, experimental models
or the observational method (see Eurocode 7). In applying (8.2) one may choose to
lower strength through
where
i
is a material factor,
j
is a loading factor, and
i
(the Resistance Factor Approach) or to increase loads
through
j
(the Load Factor Approach).
Considering normal distributions of
X
i
and
Y
j
, one may use the 5% or 95%
confidence level with
X
i
=
i
(1 - 1.64
V
i
)
and
Y
j
=
j
(1 +1.64
V
j
)
(8.3)
where
sd
the respective standard deviation.
V
follows from observations, educated guesses or
specific codes (see recommendations of the JCSS: Joint Commitee on Structural
Safety). Typical values for
V
are given in Table 8.1.
is the respective mean value,
V
the variation coefficient
(V=
sd
/
)
and
TABLE 8.1 TYPICAL VALUES FOR THE VARIATION COEFFICIENT
recommended V value if
tests results are limited
soil property
range of typical V values
0.01 - 0.10
0.0
weight
compressibility
m
v
0.20 - 0.70
0.40
undrained shear strength
c
u
0.20 - 0.40
0.30
cohesion
c
0.30 - 0.50
0.40
friction tan
0.05 - 0.15
0.10
When applying the method of partial safety factors, one needs sufficient soil
investigation in order to obtain the statistical values
sd
of each characteristic
parameter. The interpretation of tests is important; one may choose an average, a
global or a local value, related to the situation. The partial safety factor
and
i
is based
on statistical analysis, according to
i
=
1/(1
-
)
V
i
) with
i
=
(
Z
/
X
i
)
sdXi
/
sdZ
(8.4)
i
i
expresses a weighted
contribution, i.e. the relative importance of the considered parameter to the overall
reliability. For dominant loading aspects,
Here,
i
is a relative standard deviation. The factor
= 0.7 is adopted and for dominant
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