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# Probability of Failure

The definition of Probability of Failure in UnWedge is:

PF = Number of Failed Wedges / Number of Samples,

for each segment.

Where:

This definition of the Probability of Failure is considered representative of the overall probability of wedge failure for a given set of probabilistic input data.

NOTE: The default value of Design Factor of Safety = 1, however this value can be changed in the Project Settings dialog.

Probability of Sliding

Another measure of probabilistic failure for wedges is the Probability of Sliding. This is defined as:

Probability of Sliding = Number of Failed Wedges / Number of Valid Wedges

Where:

Number of Valid Wedges = Number of Samples - Number of Invalid Wedges

The Probability of Sliding is the probability that a kinematically valid wedge will fail (slide).

The generation of Valid or Invalid wedges is related to the random sampling of orientation distributions (joint, slope or tension crack). Depending on your geometry input, it is possible for the random sampling of the input data to generate invalid wedge geometries.

• A Valid Wedge is a kinematically feasible wedge, which conforms to the wedge plane definitions used in UnWedge, and which can be removed from the slope.
• An Invalid Wedge is a wedge which does NOT conform to the wedge plane definitions used in UnWedge, or which cannot be removed from the slope.
• An Invalid Wedge can also be defined by the settings in the Failure Mode Filter dialog (e.g., if you exclude certain failure modes then these become invalid wedges).

The Number of Valid Wedges is also equal to the Number of Failed Wedges + Number of Stable Wedges.

You can calculate the Probability of Sliding from the Probabilistic Analysis summary in the Sidebar (i.e., Number of Failed / Number of Valid).

If the statistical sampling of orientations does NOT produce any Invalid Wedges (i.e., Number of Valid = Number of Samples), then the Probability of Sliding = Probability of Failure.

Note that the Probability of Failure for each segment can also be written as:

Probability of Failure = (Probability of Kinematically Valid Wedges) x (Probability of Sliding)

= (Number Valid/Number Samples) x (Number Failed/Number Valid)

= Number Failed / Number Samples