Environmental Engineering Reference
In-Depth Information
The family of curves in Figure 11.1 and the associated Table 11.1 with the four levels
of engineering reflect the generally accepted concept that—“A larger factor of safety does
not necessarily imply a smaller risk, because its effect can be negated by the presence of
larger uncertainties in the design environment” (Kulhawy and Phoon, 1996; D'Andrea and
Sangrey, 1982; Tavares and Serafim, 1983; Christian et al., 1994). The curves in Figure 11.1
provide a practical grouping related to the standard deviation of the safety factors calculated
with four different levels of engineering.
Figure 11.1 shows data from over 75 projects spanning over four decades used to develop
the relationships. The projects included zoned and homogeneous earth dams, tailings dams,
natural and cut slopes, and some earth-retaining structures. The probability of failure deter-
minations reflect quantified expert judgment as explained by Silva et al. (2008).
Figure 11.2 presents a correlation between FS and annual probability of failure (APF)
similar to that in Figure 11.1, but applicable to safety with respect to internal erosion. The
factor of safety against internal erosion, FS ie , is computed as
i
FS
=
(11.1)
ie
i
cr
where
i is the gradient acting at point of interest
i cr is the critical gradient, or gradient required to initiate transport of soil particles in the
soil at the point of interest
The critical gradient can be estimated in the laboratory as described by Southworth
(1980) or Schmertmann (2000).*
10 -8
10 -7
I
10 -6
II
10 -5
10 -4
III
10 -3
10 -2
IV
10 -1
1 0
1
2
3
4
5
6
7
8
9
10
Factor of safety
Figure 11.2 p(f) for internal erosion.
* i cr in Equation 11.1 corresponds to Schmertmann's i p .
 
 
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