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# Correlation Coefficient

If you are performing a Probabilistic analysis with RocPlane and you are using the Mohr-Coulomb strength criterion for the Failure Plane, you can define a Correlation Coefficient between cohesion and friction angle in the Strength tab of the Probabilistic Input Data dialog.

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. This option allows the user to define the correlation between these two variables.

The Correlation Coefficient option is enabled only under the following conditions:

1. Strength Model = Mohr-Coulomb.
2. Random Variables = Parameters.
3. BOTH Cohesion and Friction Angle are defined as random variables (i.e., assigned a Statistical Distribution).
4. Statistical Distribution = Normal/Uniform/Lognormal/Exponential/Gamma (will not work for other distribution types).

NOTE: When the check box is NOT selected (the default), Cohesion and Friction Angle are treated as completely independent variables.

By default, when the check box is NOT selected, Cohesion and Friction Angle are treated as completely independent variables.

To see the effect of the Correlation Coefficient:

1. Create a file with probabilistic input data.
2. Use Normal or Uniform distributions for Cohesion and Friction Angle.
3. Select the Correlation coefficient between cohesion and friction angle check box Strength tab of the Probabilistic Input Data dialog.
4. Enter a correlation coefficient. (Initially, use the default value of –0.5.)
5. Run the probabilistic analysis.
6. Create a Scatter Plot of Cohesion vs. Friction Angle.
7. Note the correlation coefficient listed at the bottom of the Scatter Plot. It should be approximately equal to the value entered in the Input Data dialog. (It will not in general be exactly equal to the user-defined correlation coefficient since the results are still based on random sampling of the input data distributions).
8. Note the appearance of the plots (i.e., the degree of scatter between the two variables).
9. Repeat steps 4 to 8, using correlation coefficients of -0.6 to -1.0, in 0.1 increments. Observe the effect on the Scatter Plot. Notice that, when the correlation coefficient is equal to –1, the Scatter Plot results in a straight line.