# Random Numbers

Sequences of random numbers are utilized in *Slide2* to generate random slip surfaces and random input data samples for a Probabilistic Analysis. The generation of random numbers in *Slide2* is controlled by the **Random Numbers** option in the Project Settings dialog.

The **Random Numbers** option is applicable to the following analysis options:

- The random generation of slip surfaces, for the following search methods:
- Slope Search (circular surfaces)
- Block Search (non-circular surfaces)
- Path Search (non-circular surfaces)

- The random generation of input data samples for a Probabilistic Analysis.

If you are using one of the slip surface search methods listed above, OR you are performing a Probabilistic Analysis, then the **Random Numbers** option will affect the analysis, as described below.

If you are NOT using one of the slip surface search methods listed above, AND you are NOT performing a Probabilistic Analysis, then the Random Numbers option will have NO effect on the analysis results.

For information about how random number generation is used for slip surface generation or probabilistic sample generation, see the following topics: Block Search, Path Search, Slope Search, or Probabilistic Analysis.

## Random Number Generation

A sequence of random numbers, is generated by specifying a "seed" value, and entering this seed value into a "random number generator". For a given seed value, and a given random number generator, the SAME sequence of random numbers will always be generated. A different seed, or a different generator, will produce a different sequence of random numbers.

There are two options for specifying the seed value â€“ **Pseudo Random** or **Random**.

## Pseudo-Random (Constant Seed Value)

**Pseudo-Random** analysis means that the ANALYSIS RESULTS WILL ALWAYS BE IDENTICAL, each time the analysis is run. This is because the same "seed" is used in each case, to generate the same sequence of random numbers, which is then used to generate the slip surfaces and / or probabilistic samples.

For example, if the Pseudo Random option is selected, this means that *Slide2* will always generate EXACTLY the same slip surfaces, and EXACTLY the same probabilistic samples, each time the analysis is run. This means that ALL ANALYSIS RESULTS (e.g. safety factors, probabilities of failure) will be identical, each time the analysis is re-computed.

The purpose of the Pseudo Random option, is to allow you to obtain reproducible analysis results, even though random numbers are used to generate some of the program input data (e.g. slip surfaces and / or probabilistic samples). The Pseudo Random option is useful, because for the purposes of generating reports, presentations and demonstrations, it is often necessary to be able to present and discuss a known set of results.

By default, if the Pseudo Random option is selected, *Slide2* 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 also specify their own seed value, by selecting the **Specify Seed** checkbox.

## Pseudo-Random + Specify Seed (Constant Seed Value)

The **Specify Seed** option allows you to specify your own seed value, rather than using the program default seed value. To do this, select the **Specify Seed** checkbox, and enter any number.

If you specify your own seed value, then the analysis will still be Pseudo Random. That is, 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).

## Random (Variable Seed)

To simulate a true random analysis, you can select the **Random** option. If you select the Random option, *Slide2* 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 slip surfaces will be generated, and / or different probabilistic samples will be generated, and you may obtain different global minimum slip surfaces, safety factors and probabilities of failure.

The Random 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 **Random** option, and you would like to be able to reproduce the results, then you must do the following:

- In the Report Generator listing in the
*Slide2*Interpret program, the ACTUAL VALUE of the random number seed generated by*Slide2*, will be listed. - Copy this number from the Report Generator listing.
- Go back to the
*Slide2*Model program, select Pseudo Random > Specify Seed in Project Settings, and enter the value of the random seed that you have copied from*Slide2*Interpret. - If you re-run the analysis, you will find that you can reproduce the results that were generated by the Random option, as long as you use the
**Specify Seed**option with the same seed value which was generated by the Random option.

## Random Number Generator

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. There are two random number generators available in *Slide2*.

Park Miller v.3

A minimal random number generator developed by Park and Miller (1983), which can generate an almost unlimited sequence of distinct random numbers (approximately 2 ^ 31).

Rand

**Rand** is a commonly used random number generator, which can generate a maximum of 32,768 distinct numbers.

Practically speaking, it will make little or no difference to the *Slide2* analysis results, which random number generator is chosen. Both methods generate uniformly distributed sequences of random numbers on the interval of 0 to 1. However, if a very large number of samples is being generated (for example, 10,000 or more), you should be aware that the **Rand** generator will eventually start "repeating" the same values, and this may bias the results somewhat. In general, the Park Miller v.3 method is preferred, due to the nearly unlimited sequence of distinct random numbers which is generated.

Further information about random number generators and statistical distributions can be found in Saucier (2000) .