Statistics
The Statistics tab in the Project Settings dialog allows users to define the analysis type, sampling settings, and random number generation method.
To access the Statistics settings:
- Select Home > Analysis > Project Settings
- The Project Settings dialog will open. Select Statistics
from the left menu to edit the settings.
The Analysis Type can be selected in the Statistics tab within the Project Settings dialog. The analysis options are:
- Deterministic
- Probabilistic
Deterministic Analysis
In a Deterministic Analysis, it is assumed that all input parameters are "exactly" known (e.g. wedge plane orientations, shear strength, etc.). RocSlope2 computes the factor of safety (FS) for a single wedge. See the Deterministic Analysis topic for more information.
Probabilistic Analysis
In a Probabilistic Analysis, statistical information can be entered to account for uncertainty in joint orientation, shear strength and other parameters. This results in a safety factor distribution from which a probability of failure (PF) is calculated. See the Probabilistic Analysis topic for more information.
Sampling
The Sampling options allow you to choose:
- Sampling Method
- Number of Samples
Sampling Method
The Sampling Method determines how the statistical input distributions for the random variables you have defined for a Probabilistic Analysis will be sampled. Two Sampling Methods are available in RocSlope2:
- Monte Carlo
- Latin Hypercube
Monte Carlo Method
The Monte Carlo sampling technique uses random numbers to sample from the input data probability distributions. Monte Carlo techniques are commonly applied to a wide variety of problems involving random behaviour in geotechnical engineering.
Latin Hypercube Method
The Latin Hypercube sampling technique gives comparable results to the Monte Carlo technique, but with fewer samples [Iman et. al. (1980), Startzman et. al. (1985)]. The method is based upon "stratified" sampling with random selection within each stratum. This results in a smoother sampling of the probability distributions. Typically, an analysis using 1000 samples obtained by the Latin Hypercube technique will produce comparable results to an analysis of 5000 samples using the Monte Carlo method. [Hoek et. al. (1995)].
Number of Samples
The Number of Samples which will be generated for each Random Variable for a Probabilistic Analysis. For example, if Number of Samples = 1000, then 1000 values of each input random variable (e.g. Friction Angle of Joint Property 1) will be generated, according to the Sampling Method and statistical distribution for each random variable. The analysis will then be run 1000 times for each valid block in each Analysis Method (Wedge, Planar, and Toppling), and a safety factor calculated for each set of input data samples. This results in a distribution of safety factors, from which the Probability of Failure (PF) is calculated from total number of analyses run for each Analysis Method.
Pseudo-Random Number Generation
At the heart of the random number generation process, is a mathematical algorithm (the random number "generator"), which actually generates the sequences of random numbers. RocSlope2 uses the Rand number generation method. Rand is a commonly used random number generator, which can generate a maximum of 32,768 distinct numbers. If a very large number of samples is being generated (for example, 10,000 or more), the user should be aware that the Rand generator will eventually start "repeating" the same values, and this may bias the results somewhat.
Further information about random number generators and statistical distributions can be found in Saucier (2000).
The pseudo-random number generation settings contain the following options:
- Constant Seed Value
- Specify Seed (optional)
- Variable Seed Based on Time
Pseudo-Random sampling allows you to obtain reproducible results from an analysis. If the Constant Seed Value option is selected, this means that the same "seed" number is always used to generate random numbers for the sampling of the input data distributions. This results in an identical sampling of the input data distributions, each time the analysis is run (with the same input parameters). The Probability of Failure, mean Safety Factor, and all other analysis output, will be reproducible. This can be useful for demonstration purposes, the discussion of example problems, etc.
Constant Seed Value
By default, if the Constant Seed Value option is selected, RocSlope2 will always use the same "seed" value, to generate the same sequence of random numbers (this value is hard coded into the program). However, the user may specify their own seed value by selecting the Specify Seed check box.
Specify Seed
The Specify Seed option simply allows the user to specify their own value of seed, rather than using the program's default seed value. To do this, select the Specify Seed check box, and enter any number.
If the user specifies their own seed, then the analysis will still be Pseudo Random (i.e. if you re-run the analysis, you will always get exactly the same results). However, the results will not be the same as the results using the default seed value.
Each different value of seed will produce different results. However, for any given constant seed value, you will always get the same results (i.e. safety factor, probability of failure, and all other analysis results).
Variable Seed Based on Time
To simulate a true random analysis, you can select Variable Seed Based on Time. RocSlope2 will automatically generate a new seed value (based on the current time on your computer), each time you run an analysis.
This means that the analysis results will be different each time that you re-run the analysis. Different probabilistic input samples will be generated, and the Probability of Failure, mean Safety Factor, and all other analysis output, may vary with each run.
This option allows you to study the effect of re-running the analysis, using different random numbers (and therefore different input data) each time.
How to Reproduce a Random Analysis
If you have run an analysis with the Variable Seed Based on Time option, and you would like to be able to reproduce the results, then you must do the following:
- Select Home > Information > Report Generator
- In Report Generator, the actual value of the random number seed generated by RocSlope2 will be listed.
- Copy this number from the Report Generator listing.
- Select Home > Analysis > Project Settings > Statistics
- Select the Constant Seed Value option and check off Specify Seed. Enter the value of the random seed that you have copied from the Report Generator.
- If you re-run the analysis, you will find that you can reproduce the results that were generated by the Variable Seed Based on Time option.