|
|
 |
  |
|
    
|
|
Statistical Analysis: Statistical Distributions
In RocPlane, for Probabilistic analysis the program allows users to specify statistical distributions for various input parameters. To define a parameter as a random variable in the Probabilistic Input Data dialog, first toggle the Statistical Distribution for that variable from "None" to one of the six possible choices: normal, uniform, triangular, beta, exponential and lognormal.
Select the Statistical Distribution from the pull-down menu
Once a statistical distribution has been selected, you will then be able to enter the standard deviation and relative minimum and maximum values.
Enter the standard deviation and relative minimum and maximum values
|
|
|
 |
|
Statistical Analysis: Monte Carlo and Latin Hyper Cube Analysis
RocPlane provides two statistical sampling methods - Monte Carlo and Latin Hyper Cube - for the Probabilistic analysis model. Unlike some other software packages, you are not forced to use certain methods. For both methods, you can set the Number of Samples and choose Pseudo-Random sampling.
Simply select the sampling method from the pull-down menu
|
|
|
|
|
Statistical Analysis: Graphical Output of Statistical Data - Histogram Plot and Cumulative Plot
When in Probabilistic mode, detailed statistical results can be viewed with the Plot Histogram, Plot Cumulative and Plot Scatter options in the Statistics menu. There is also a Sampler in the cumulative plot to obtain the coordinates of any point on the curve.
The Statistics drop down menu
The Histogram Plot Dialogue to enter all the required parameters
If the Data Type selected is a results variable calculated in the analysis, a Best Fit Distribution, using the Kolmogorov-Smirnov Goodness of Fit test, can be determined for the variable by selecting the Best Fit checkbox. The histogram below represents the distribution of Safety Factor, for all valid wedges generated by the Monte Carlo sampling of the Input Data. The red bars at the left of the distribution represent wedges with Safety Factor less than 1.0.
Safety Factor Histogram
In addition to the histograms, cumulative distributions (S-cures) of the statistical results can also be generated.
The Cumulative Plot Dialogue to enter all the required parameters
Cumulative safety factor distribution
Notice the vertical dotted line on the plot. This is the sampler, which can be toggled in the right click pop-out menu or the "View" drop-down menu.
|
|
|
|
|
Statistical Analysis: Scatter Plots
Scatter (Shotgun) plots allow the user to examine the relationships between two analysis variables. The Show Regression Line option displays the best-fit straight line through the data. The Correlation Coefficient, alpha and beta values are listed at the bottom of the plot. Alpha and beta represent the y-intercept and the slope, respectively, of the best-fit linear regression line to the scatter plot data.
Select variables to plot on the X and axes
Scatter plot between Safety Factor and Wedge Weight
|
|
|
|
|
Statistical Analysis: Correlation Coefficients
The correlation between two different variables can be shown by plotting a scatter graph of the two parameters with the "Show Regression Line" option selected.
Select the Show Regression Line option to display the best fit straight line through the data
The Correlation Coefficient will be listed at the bottom of the plot. The coefficient can vary between -1 and 1 where numbers close to zero indicate a poor correlation, and numbers close to 1 or -1 indicate a good correlation.
Scatter plot of Safety Factor versus Wedge Weight
|
|
|
|
|
Statistical Analysis: Correlation between cohesion and friction angle
(applies only to statistical model)
It is known as a fact that cohesion and friction angle are related in a general way, such that the materials with low friction angles tend to have high cohesion, and materials with low cohesion tend to have high friction angles. In the Input Data Dialog, the user may define the degree of correlation between cohesion and friction angle, for the failure plane. Note this only applies when Normal or Uniform distributions are defined for both parameters.
Enter correlation coefficient between cohesion and friction angle
It is observed that the correlation coefficient listed at the bottom of a cohesion versus friction angle scatter plot is approximately equal to the value entered in the Input Data dialog.
Scatter plot of friction angle versus cohesion
|
|
|
|
|
Statistical Analysis: Current Picked Wedges
Tiling the Histogram and Wedge views, so that both are visible. If you double-click the left mouse button anywhere on the plot, the nearest corresponding wedge will be displayed in the Wedge view. This feature allows the user to view any wedge generated by the Probabilistic Analysis, corresponding to any point along a histogram distribution.
Safety Factor histogram and wedge view
In addition to the Wedge views, all other applicable views (for example, the InfoViewer) are also updated to display data for the currently "Picked Wedge".
InfoViewer and Safety Factor histogram
|
|
|
|
|
Statistical Analysis: Goodness of Fit test
The goodness of fit test for safety factor and wedge weight distributions can be shown by adding the "Best Fit Distribution" line into the histogram plots.
Selecting the best fit distribution option
Histogram plot and best fit distribution of factor of safety
Histogram plot and best fit distribution of wedge weight
|
|
|
|
|
 |
