Environmental Engineering Reference
In-Depth Information
Because the parameter values are varied randomly, two @Risk™ runs with the same
number of calculations will usually result in slightly different values of the factor of
safet y.
The retaining wall example was completed using @Risk™ for a total of 20,000 iterations.
The calculated probability of failure is the mean value of the output cell formulated in step
5. The mean value is equal to 0.024 or 2.4% probability of failure.
The Monte Carlo analysis procedure was used to calculate probabilities of failure against
sliding through the clay and bearing capacity failure in the clay beneath the retaining wall.
The standard deviation of the undrained shear strength of the clay is estimated to be 24 kN/m
2
.
The calculated probability of failure for sliding in the clay is 2.5%. The calculated probability
of failure for bearing capacity in the clay is 2.4%.
3.7.1 accuracy of calculations
Because the accuracy with which values of
P
f
can be computed is governed primarily
by the accuracy with which the values of the parameters and their standard deviations
can be estimated, it is clear that computed values of
P
f
should not be considered to be
highly precise. Variations in the values of
P
f
by a factor of two or three due to reasonable
changes in parameter values are to be expected. This degree of precision (or imprecision)
should be kept in mind when considering the acceptability of the results of probability
calculations.
The effect of the number of iterations used in @Risk™ is illustrated by
Figure 3.17.
To
verify the accuracy of the calculated value of failure probability, it is useful to run several
3.3
3.1
P
(
f
) sliding on granular surface
P
(
f
) sliding on clay surface
P
(
f
) bearing capacity failure
2.9
2.7
2.5
2.3
2.1
1.9
1.7
0
20000
40000
60000 80000
Number of iterations
100000
120000
140000
160000
Figure 3.17
Probability of failure for several Monte Carlo simulations of retaining wall stability.
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