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The Sampling options in the CPillar Project Settings dialog allow you to choose:

  • Sampling Method
  • Number of Samples

for a Probabilistic Analysis in CPillar.

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 CPillar:

  • Monte Carlo
  • Latin Hypercube
NOTE: For both sampling methods, a constant seed value is used to generate sequences of random numbers to generate the sample values. This is referred to as pseudo-random sampling, which allows you to obtain reproducible results for a Probabilistic Analysis.

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 behavior in geotechnical engineering.

Monte Carlo Sampling of Normal Distribution
Monte Carlo sampling of Normal distribution (1000 samples)

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)].

Latin Hypercube Sampling of Normal Distribution (
Latin Hypercube sampling of Normal distribution (1000 samples)

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 data random variable (e.g. Pillar Length) will be generated, according to the Sampling Method and statistical distribution for each random variable. The analysis will then be run 1000 times, 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.

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