Probabilistic Analysis

In a Probabilistic Analysis, you can define statistical distributions for input parameters (e.g. joint orientation, shear strength, water level), to account for uncertainty in the values of input parameters. When the analysis is computed, this results in a safety factor distribution from which a probability of failure (PF) is calculated.

The general procedure for carrying out a Probabilistic Analysis with RocSlope2 is as follows.

1. Select Analysis Type

   Set the Analysis Type to Probabilistic in the Project Settings Statistics tab.

2. Set Sampling Options

   In the Statistics tab, you can choose the Sampling Method, Number of Samples, and Pseudo-Random Numbers options.

3. Define Random Variables
   In order to carry out a Probabilistic Analysis, you must define one or more input parameters (e.g. joint orientation, shear strength) as Random Variables, by assigning Statistical Distributions to the desired variables and entering the required statistical parameters (e.g. mean, standard deviation).
   
Any input parameter which is not assigned a Statistical Distribution is assumed to be exactly known (by the Mean value), and will not be involved in the statistical sampling process.

See the following topics for more information on which input parameters can be defined as Random Variables:


• Slope Property Statistics
• Slope Geometry Statistics
• Joint Property Statistics
• Joint Orientation Statistics
• Point of Force Application Statistics
• Point Load Statistics
  
  
4. Compute:

   The Probabilistic Analysis is automatically computed once the Analysis Type is changed to Probabilistic, and again each time any of the input data is added or modified.

5. View Analysis Results:

   After the analysis is computed, the Results Grid will display a list of each block's result (Factor of Safety, Joint Info, etc.). Probabilistic input and output data can be plotted on Histogram, Scatter, and Cumulative Plots. Data can also be exported for further analysis and processing.

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 Samples - 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 Samples), then the Probability of Sliding = Probability of Failure.