Probability of Failure

The definition of Probability of Failure in RocSlope2 is:

PF = Number of Failed Blocks / Number of Blocks Generated

where:

• Number of Failed Blocks= number of valid blocks with safety factor < Design Factor of Safety.

• Number of Blocks Generated = total number of blocks formed from the Deterministic run of each realization of the random input variables.

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

Probability of Sliding

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

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

where:

Number of Valid Blocks = Number of Blocks Generated - Number of Invalid Blocks

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

The generation of a valid or invalid block 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 block geometries.

• A valid block is a kinematically feasible block, which conforms to the block plane definitions used in RocSlope2, and which can be removed from the slope.
• An invalid block is a block which does not conform to the block plane definitions used in RocSlope2, or which cannot be removed from the slope.
• An invalid block 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 block).

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

The Probability of Sliding is listed in the Report Generator, or you can calculate the value from the values in the Results Grid (i.e. Number of Failed / Number of Valid).

If the statistical sampling of orientations does not produce any Invalid Blocks (i.e. Number of Valid = Number of Blocks Generated), then the Probability of Sliding = Probability of Failure.

The Probability of Failure can also be written as:

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

= (Number Valid / Number of Blocks Generated) x (Number Failed / Number Valid)

= Number Failed / Number of Blocks Generated