Mohr-Coulomb Correlation

It is known that Cohesion and Friction Angle are related in a general way, such that materials with low friction angles tend to have high cohesion, and materials with low cohesion tend to have high friction angles. The Correlation option in the Material Statistics dialog, allows you to define a Correlation Coefficient between Cohesion and Friction angle for any material with a Mohr-Coulomb strength type.

If a Correlation Coefficient is defined, this means that when the statistical samples are generated for Cohesion and Friction Angle, the two variables will be correlated. The value of Cohesion will be related to the value of Friction Angle, and vice versa. This simulates the relationship between Cohesion and Friction Angle which exists in real materials.

By default, when no correlation has been defined, Cohesion and Friction Angle are treated as completely independent variables. To define a Correlation Coefficient for Cohesion and Friction Angle:

  1. Select the Correlation button in the Material Statistics dialog.

  2. You will see the Mohr-Coulomb Correlation Coefficient dialog. For EACH material that you would like to define a Correlation Coefficient, select the Apply checkbox, and enter a Correlation Coefficient.

  3. The allowable value of the Correlation Coefficient is – 1 to 1.

  4. The default correlation coefficient of –0.5 is a good typical value to use, for the correlation between Cohesion and Friction Angle, if more precise data is not available. A negative Correlation Coefficient simply means that as one variable decreases, the other variable is likely to increase (which is the case for Cohesion and Friction Angle).

  5. The Correlation Coefficient for Cohesion and Friction Angle in Slide, is only applicable if ALL of the following conditions are met (for a given material):

If ALL of these conditions are met, then the Correlation Coefficient for Cohesion and Friction Angle will be applicable, and will be used in the Slide analysis. In order to see which materials are applicable, select the Show Applicable Materials only checkbox in the Mohr-Coulomb Correlation Coefficients dialog. This will hide all non-applicable materials, and only display the materials for which the above conditions have been met.

  1. When you have specified the desired Correlation Coefficients for the desired materials, select OK and you will be returned to the Material Statistics dialog.

After a Slide Probabilistic Analysis has been run, the actual correlation between Cohesion and Friction Angle can be observed by viewing a Scatter Plot of the two variables. The actual Correlation Coefficient (listed on the Scatter Plot), should be close to the value you have specified in the Mohr-Coulomb Correlation Coefficients dialog. See the Slide Interpret help for more information about Scatter Plots.

Advanced Correlation

To correlate random variables other than Mohr-Coulomb cohesion and friction angle, you must use the Advanced Correlation option. This is available by selecting the Advanced Correlation button in the Mohr-Coulomb Correlation dialog.

Statistical Distributions which can be correlated

The following table indicates the allowable combinations of statistical distributions for which Mohr-Coulomb cohesion and friction angle can be correlated, using the Mohr-Coulomb Correlation Coefficients dialog.

 

Normal

Uniform

Triangular

Beta

Exponential

Lognormal

Gamma

Normal

 

 

 

 

 

 

 

Uniform

 

 

 

 

 

 

 

Triangular

 

 

 

 

x

x

x

Beta

 

 

 

 

x

 

x

Exponential

 

 

x

x

 

 

 

Lognormal

 

 

x

 

 

 

 

Gamma

 

 

x

x

 

 

 

NOTE: if you use the Advanced Correlation option then you may define correlation between any distribution types.