MINIMUM
REQUIREMENTS

• Windows XP or later, 32 or 64 bit
• Intel Pentium 4
• 256 MB memory (RAM)

SUGGESTED REQUIREMENTS

• Windows 7, 64 bit
• Dual or Quad Core Processor
• 4 GB memory (RAM)

 

Phase² 8.0 offers probabilistic analysis using the point estimate method. With this method random variable distributions are represented by two point estimates at plus / minus one standard deviation from the mean. The analysis is computed for all possible combinations of point estimates, from which statistical results are computed (e.g. mean and standard deviation of output variables). The point estimate method allows you to carry out a probabilistic finite element analysis with minimal input and computation effort.

Principle of point estimate method assuming two random variables

 

 

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Probabilistic Analysis: Project Settings

The Phase² probabilistic analysis uses the Rosenblueth point estimate method. To enable probabilistic analysis select the Probabilistic Analysis checkbox in the Project Settings dialog. You can then define random variables (material properties, joint properties, field stress) using the options in the Statistics menu.

Statistics option in Project Settings dialog

 

 

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Probabilistic Analysis: Random Variables

For a Phase² probabilistic analysis you must define one or more input random variables (e.g. material strength, modulus, etc). You can define material properties, joint properties and field stress as random variables. Only the mean and standard deviation need to be defined, the statistical distribution of each variable is assumed to be normal.

In the Material Property Statistics dialog you can define elastic and strength parameters as random variables (e.g. cohesion and friction angle, young’s modulus).

Material property statistics dialog

 

 

 

In the Joint Property Statistics dialog you can define joint strength and elastic parameters as random variables (e.g. cohesion, friction angle, normal and shear stiffness).

 

Joint property statistics dialog

 

 

In the Field Stress Statistics dialog you can define field stress parameters as random variables (e.g. Sigma 1, Sigma 3).

Field stress statistics dialog

 

You can define any combination of random variables. A typical analysis might use 2 to 5 variables. More than about 10 variables is not recommended as the number of analyses required is exponential with the number of variables. See Tutorial 31 for an introduction to probabilistic analysis with Phase².

 

 

 

 

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Probabilistic Analysis: Statistical Contours

The results of the probabilistic analysis can be displayed as contours of mean, standard deviation or coefficient of variation of any output variable.

 

Contours of Sigma 1(Mean)

Contours of Sigma 1 (Standard Deviation)

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Probabilistic Analysis: Error Plot

The Error Plot option allows you to plot the mean and standard deviation of data along any material query after a Probabilistic Analysis. The central curve plots the mean data values along the query and the height of the vertical bars indicate plus / minus one standard deviation from the mean values.

 

 

 

 

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Probabilistic Analysis: Yield Zones

The Show Yield Zones option highlights all yielded finite elements after a probabilistic analysis (i.e. if an element failed during any run of the probabilistic analysis it will be highlighted). The shading of the elements indicates the probability of failure of the elements.

Display of yielded elements with Show Yield Zones

 

 

 

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Probabilistic Analysis: Slope Stability

You can carry out probabilistic slope stability analysis by running SSR analysis together with probabilistic analysis as described in Tutorial 32. A probability of failure will be calculated which can be compared with results from Slide.

Probabilistic SSR slope stability analysis results