## Search Results

If your model includes Seismic Load, then the Seismic Load coefficients can be treated as Random Variables in a Slide2 Probabilistic Analysis.

To do this:

1. Select Statistics > Seismic Load. You will see the Seismic Load Statistics dialog.
2. To define the Horizontal and/or Vertical Seismic Coefficients as Random Variables, select the appropriate checkboxes.
3. Now define the statistical parameters for the selected seismic coefficient(s). Select a Statistical Distribution, and enter a Standard Deviation (if applicable), and Relative Minimum and Maximum Values.
4. The Mean Value(s) are the same as the Seismic Coefficients entered in the Seismic Load dialog. These value(s) can be changed in either dialog, if desired.
5. For more information about the statistical parameters which are used to define Random Variables in Slide2, please see the Random Variables topic.

## Correlation Coefficient

If you are defining BOTH the Horizontal and Vertical Seismic Coefficients as Random Variables, then you may also define a Correlation Coefficient for the two variables.

If a Correlation Coefficient is defined, this means that when the statistical samples are generated for the Horizontal and Vertical Seismic Coefficients, the two variables will be correlated. The value of the Horizontal Coefficient will be related to the value of the Vertical Coefficient and vice versa. If you are running a Probabilistic Analysis with both Horizontal and Vertical Seismic Coefficients, then this may be a reasonable assumption to make.

The degree of correlation will depend on the numerical value of the Correlation Coefficient.

• When NO Correlation Coefficient has been defined, the Horizontal and Vertical Seismic Coefficients are treated as completely independent Random Variables. This is equivalent to a Correlation Coefficient = 0.
• The default Correlation Coefficient of + 0.5 produces a general positive correlation between the two variables, with considerable scatter.
• A Correlation Coefficient = 1 (or -1) will produce an exact straight line relationship between the two variables
The Correlation Coefficient option in the Seismic Load Statistics dialog, will only be enabled under the following conditions:
1. BOTH the Horizontal and Vertical Seismic Coefficients are selected as Random Variables (i.e. the checkboxes are selected for each coefficient).
2. The Correlation Coefficient in Slide2 can only be used in conjunction with the following Statistical Distributions – Normal, Uniform and Lognormal. BOTH the Horizontal and Vertical Seismic Coefficients must use Normal, Uniform or Lognormal distributions, in order for the Correlation option to be enabled. (If other Statistical Distributions are used, then the Correlation Coefficient option will NOT be enabled.)
3. If these conditions are met, then the checkbox for Correlation Coefficient will be enabled in the Seismic Load Statistics dialog.

To apply the Correlation Coefficient, select the checkbox and enter a value. The value of the Correlation Coefficient must be between -1 and +1. The default value is +0.5 .

• a POSITIVE correlation coefficient implies that when one variable INCREASES, the other is likely to INCREASE
• a NEGATIVE correlation coefficient implies that when one variable INCREASES, the other is likely to DECREASE

After a Slide2 Probabilistic Analysis has been run, the actual correlation between the Horizontal and Vertical Seismic Coefficients 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 Seismic Load Statistics dialog. See the Slide2 Interpret Help system for more information about Scatter Plots.

## Sensitivity Analysis

If you are performing a Sensitivity Analysis using the Seismic Coefficient(s), then you must define the Minimum and Maximum values in the Seismic Load Statistics dialog, as described above for a Probabilistic Analysis. The Sensitivity Analysis will be carried out by uniformly varying the Seismic Coefficient(s) between the Minimum and Maximum values, in 50 equal increments.

• If you are performing a Sensitivity Analysis, but you are NOT performing a Probabilistic Analysis, then the Distribution, Standard Deviation and Correlation Coefficient options will be disabled in the Seismic Load Statistics dialog, since they are not applicable for a Sensitivity Analysis.
• If you are performing BOTH a Sensitivity Analysis AND a Probabilistic Analysis, then the Sensitivity Analysis will use the Minimum and Maximum values you have defined for the seismic coefficient(s). It will ignore the parameters which are not relevant to the Sensitivity Analysis (i.e. Distribution, Standard Deviation, Correlation Coefficient, which are only applicable for the Probabilistic Analysis).