# Probability of Failure

The definition of **Probability of Failure** in **RocPlane** is:

PF = Number of Failed Wedges / Number of Samples

where:

Number of Failed Wedges = number of wedges with safety factor < 1

Number of Samples = number of samples specified in the Input Data dialog

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.

## 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**RocPlane**, 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**RocPlane**, or which cannot be removed from the slope.

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

The **Probability of Sliding** is listed in the Info Viewer.

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** 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

## Previous Definition of Probability of Failure

It is important to note that the definition of **Probability of Failure** and **Probability of Sliding**, described above, was introduced in **RocPlane** version 2.040. In earlier versions of the program (version 2.038 and earlier), the Probability of Failure which was reported, was in fact the Probability of Sliding (as defined above).

That is, in **RocPlane** version 2.038 and earlier:

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

The definition of Probability of Failure was revised to the current definition, because the earlier version (where Probability of Sliding was reported as the Probability of Failure), had a tendency to overestimate the Probability of Failure in some cases, which could lead to overly conservative slope designs.