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D-G EO S TABILITY, User Manual
20.4.5
Stochastic water level model
The Bishop probabilistic random field model determines the probability of failure given a safety
factor. It can do so for differing external water levels. The external water levels provide a basis
for a stochastic description of the water level. The model incorporates the uncertainty in the
external water level by the execution of the following steps.
D-G EO S TABILITY determines the conditional probability of failure for different user-specified
external water levels and their associated hydraulic fields.
D-G EO S TABILITY combines the resulting relationship between the reliability index and
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the external water level, using linear interpolation, with a Gumbel assumption for the
water level distribution. This is in order to find the integrated probability of failure that is
shown in the report. D-G EO S TABILITY applies a FOSM procedure for this purpose.
Figure 20.2: Linear interpolation between the conditional reliability index β and the external water level h
Equation 20.23 shows the exceeding probability for the design level, according to the Gumbel
distribution. This distribution is determined by the Gumbel parameters B and ugumbel .
2.3
P (h > hdesign ) = 1 − exp − exp −
(hdesign − ugumbel )
B
(20.23)
Parameter B is the decimate height; the increase of the external water level that reduces the
exceeding probability with a factor 10.
D-G EO S TABILITY determines the parameter ugumbel from the input values of B , the design
level hdesign and the allowed exceeding frequency at the design level.
20.4.6
Stochastic model factor
It is possible to model all remaining uncertainty on the 2D calculation model, the loads and the
geometry via the global model factor. This factor represents the required safety factor Frequired
by a mean value and a standard deviation.
The default D-G EO S TABILITY values are safe values, obtained from Dutch research on water
retaining structures.
Experience with these safe values indicates that the model factor will generally dominate the
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