Environmental Engineering Reference
In-Depth Information
Table 3.8 Monte Carlo simulation of sliding on
a granular surface, sliding on a clay
surface, and bearing capacity with
changes in the standard deviation
Normal Distribution 10,000 Iterations
P(f) bearing
capacity (%)
σ su
500
2.08
600
3.80
700
5.62
800
7.70
P(f) Sliding on
clay (%)
σ su
500
2.33
600
4.18
700
6.13
800
8.34
P(f) Sliding on
granular (%)
σ tan δ
0.05
2.58
0.06
3.65
0.07
4.93
0.08
6.59
simulations using different numbers of iterations. Considering that any reliability analysis is
most highly dependent on the choice of the standard deviations of the variables; variations
in the probability of failure like those shown in Figure 3.17 are not significant.
The influence of standard deviation is shown in Table 3.8. The probabilities of failure for
all three failure modes were calculated with the values of standard deviations increased by
20%, 40%, and 60%. These increases in the standard deviation values increased the calcu-
lated probabilities of failure by as much as a factor of 3.7.
Although the Monte Carlo method can only be applied to computer analyses, it provides
a useful standard of comparison for other methods because it does not involve assumptions
that the factor of safety is normally or lognormally distributed.
3.8 haSoFer lInD MethoD
Filz and Navin (2006) found that the Hasofer Lind (1974) method is more accurate than
the simpler Taylor Series or PEMs of reliability analyses, discussed subsequently. While
the Taylor Series or the PEMs require an assumption on the distribution of the factor of
safety, the Hasofer Lind method requires an assumption on the distributions of the vari-
ables involved in the analysis. This is considered more accurate because the distribution
of the safety factor is difficult to predict and thus subject to wider variations (Baecher and
Christian 2003). The Hasofer Lind method is used less than the Taylor Series or the PEMs
because it requires more calculations, and in its original formulation required closed-form
equations (Filz and Navin 2006). The Simplified Hasofer Lind method of reliability analysis
 
Search WWH ::




Custom Search