Slope Stability Analysis Resources


Essential Reading: 

Chapter 12 - Stabilisation of Rock Slopes

 

Practical Exercise - Geotechnical Slope Stability Analysis: Planar Rock Slope Failure

 

RocPlane Slope Stability Software

RocPlane is an analysis tool for evaluating the possibility of planar sliding failure in rock slopes. A planar wedge can be defined by:

 

  • A sliding plane

  • The slope face

  • The upper ground surface

  • An optional tension crack

In ROCPLANE, the planes defining a wedge can be specified at any angles, which result in a kinematically feasible wedge (ie. a wedge which can slide out of a slope). Almost any 3 or 4 sided wedge can be defined by the slope planes, failure surface and tension crack.

  Planar-Sliding-Stability-Analysis-for-Rock-Slopes

Run the Rocscience RocPlane program from the main menu

Select: File → New

 A wedge model will immediately appear on your screen, as shown in the above figure. Whenever a new file is opened, the default input data will form a valid wedge. The first thing you will notice is the four-view, split screen format of the display, which shows: 

  • TOP

  • FRONT

  • SIDE and

  • PERSPECTIVE

 views of the model. The Top, Front and Side views are orthogonal with respect to each other (ie. viewing angles differ by 90 degrees). Before we proceed, it is very important to note the following:

 

  • Although ROCPLANE displays the model in a 3 dimensional format, the ROCPLANE analysis is strictly a 2-dimensional analysis. The 3D display is for the purpose of improved visualization of the problem geometry.

  • All input data assumes that the problem is uniform in the direction perpendicular to the wedge cross-section. The analysis is performed on a “slice” through the cross-section, of unit width.

  • All analysis results (eg. wedge weight, wedge volume, normal force, resisting force, driving force etc), are therefore stated in terms of force per unit length, volume per unit length, etc.

 

Project Settings

Project Settings allows the user to enter a Project Title, and select a Unit System and Analysis Type.

RocPlane_Modeling1 The Analysis Type can be changed in the Project Settings dialogue

Select: Analysis → Project Settings

 Enter “ROCPLANE Quick Start Tutorial” as the Project

Title. Leave Units = Metric and Analysis Type = Deterministic. Select OK.

 

  • The Project Title appears in the Info Viewer listing, and also on printouts of the wedge view.

  • Units determine the length and force units used in the analysis.

  • Deterministic analysis means that all input data is assumed to be exactly known, and a single safety factor is calculated. Probabilistic analysis allows for uncertainty in input data. This results in a range of safety factors, from which a probability of failure is calculated. This is covered in the next tutorial.

 

Input Data

Now let’s see what input data was used to create this model.

RocPlane_Modeling2 Deterministic Input Data Dialogue

 

Select: Analysis → Input Data

 

The Geometry input data which you see in this dialog is the default input data, which forms a valid default wedge, each time a new file is started. Examine the input data in this dialog. Do not change any values just yet, we will be coming back to this shortly. Before you close the dialog, notice the Safety Factor, Wedge Weight etc information displayed in the lower right corner. The Safety Factor (FS = …) is also displayed in the ROCPLANE toolbar, at the top of the screen. Notice that the wedge weight, normal force etc, are all expressed as “tonnes per metre”. Since the analysis is performed on a slice of unit width, the “per metre” refers to the direction perpendicular to the wedge cross-section, as mentioned earlier.

Select Cancel to close the dialog.

3D Wedge View

The mouse buttons can be used to interactively manipulate the view as follows:

 

  • The Perspective view of the model allows the model to be rotated for viewing at any angle with the LEFT mouse button.

  • The wedge can be moved out of the slope with the RIGHT mouse button (or the mouse wheel) in any of the four views.

 

Rotating The Model

Press and HOLD the LEFT mouse button anywhere in the Perspective view.

Notice that the cursor changes to a “circular arrow” symbol to indicate that you may rotate the model.

Now keep the LEFT mouse button pressed, and move the cursor around.

The model is rotated according to the direction of movement of the cursor.

To exit the rotation mode, release the LEFT mouse button. Notice that the cursor reverts to the normal arrow cursor.

Repeat the above steps to rotate the model for viewing at any angle.

 

Moving The Wedge Out Of The Slope

Press and HOLD the RIGHT mouse button anywhere in ANY of the four views.

Notice that the cursor changes to an “up-down arrow” symbol.

Now, keep the RIGHT mouse button pressed, and move the cursor UP or DOWN.

The wedge will slide UP or DOWN out of the slope.

Note: If your model does NOT have a Tension Crack, then the wedge will slide UP or DOWN along the Failure Plane.

If your model DOES have a Tension Crack, then the wedge will slide DOWN along the Failure Plane, and UP along the Tension Crack Plane.

To exit this mode, release the RIGHT mouse button.

Notice that the cursor reverts to the normal arrow cursor.

TIP – if you have a mouse with a mouse wheel, rotating the mouse wheel will also move the wedge out of the slope. You may find this even more convenient than using the right mouse button.

 

Resetting The Wedge

To reset the wedge in its normal position, click and RELEASE the RIGHT mouse button in any of the four views. The wedge will snap back to its normal position.

 

Resizing The Views

You can change the relative size of the Top / Front / Side / Perspective views in a number of ways:

 

Double-clicking in any view will maximize that view.

Double-clicking again in the maximized view, will restore the four view display.

Alternatively, hover the cursor over the vertical or horizontal dividers between the views, or over the intersection point of the four views.

The cursor will change to a “parallel line” or “four arrow” symbol.

Press and HOLD the LEFT mouse button, and drag to re-size the views.

Maximizing views can also be accomplished with the View → Layout options.

To reset the four views to equal size, select View→ Layout → All Views.

 Double-clicking in any view will maximize that view.

Double-clicking again in the maximized view, will restore the four view display.

 

Zooming

Zooming (from 50% to 800%) is available in the View → Zoom menu, to increase or decrease the displayed size of the model in all four views, simultaneously. Individual views can be zoomed in or out using the Page Up / Page Down keys, the + or – numeric keypad keys, the F4 / F5 function keys, or the Zoom options in the toolbar. The F2 function key is a shortcut to Zoom All. You must first click in the view with any mouse button, to make it the active view, before you can zoom the view.

 

Display options

You may change colours and other viewing options in the Display Options dialog.

Select: View → Display Options.

 

Select new slope, wedge and background colours.

Select Apply in order to view changes.

You can minimize the dialog, by selecting the _ arrow in the upper right corner of the dialog.

To maximize the dialog, select the _ arrow.

Select the Defaults button to restore the original program defaults, and select Close to exit the dialog.

 

2D Wedge View

A 2D view of the wedge model is available, by selecting the 2D View option.

Select: Analysis → 2D View

This will generate a new view, which only displays the 2D wedge model. Remember that the ROCPLANE analysis is a 2D analysis, and that the 3D display is for visualization purposes only.

 

The 2D view can display model lengths and angles, as well as tables of analysis results and input data. Let’s see what display options are available with the 2D view. 

Select: View → Display Options

(Note: Display Options is also available in the right-click menu on the 2D View).

 

Experiment with the 2D display options to see the effects on the display. You must select Apply in order to view the changes. You can select the Defaults button to restore the original program default display options. Select Close when you are done.

 

Zooming

The wedge model in the 2D view can be zoomed in a variety of ways:

 

  • Rotate the mouse wheel to zoom in or out

  • Select the zoom options in the toolbar

  • Use the F2, F4 or F5 function keys

 

Panning

The wedge model in the 2D view can be panned left, right, up or down, using the arrow keys on the keyboard, or by clicking and holding the mouse wheel or middle button of your mouse, and dragging.

 

Changing the input data and re-calculating the Safety Factor

Close the 2D view by selecting the X in the upper right corner of the view. Alternatively, you can return to the 3D view at any time, by selecting the 3D View toolbar button. Now let’s experiment with changing the Input Data and re-calculating a new Safety Factor. This is simply a matter of:

 

Entering the desired Input Data.

Selecting the Apply button

 

For a Deterministic analysis, the Safety Factor is immediately calculated and displayed in the lower right corner of the dialog.

Select: Analysis → Input Data.

Let’s first increase the slope angle.

 Enter a slope angle of 55 degrees.

Select Apply, and a new Safety Factor (1.515) is calculated, as you can see at the bottom right of the Input Data dialog, and in the toolbar.

Minimize the Input Data dialog now, so that you can better view the new wedge (select the _ arrow in the upper right corner of the dialog).

 

More About The Input Data Dialog

Before we proceed, we will discuss some properties of the Input Data dialog. As you may have noticed, the Input Data dialog in ROCPLANE works a little differently than a regular dialog.

 

It is known as a “roll-up” dialog, since it can be “rolled-up” (minimized) or “rolled-down” again, by selecting the _ or _ arrow in the upper right corner of the dialog.

Alternatively, double-clicking the LEFT mouse button on the title bar of the dialog, will also minimize / maximize the dialog.

It can be left up on the screen while performing other tasks. When not needed, it can be “rolled-up” and dragged out of the way (for example, the top of the screen) with the LEFT mouse button.

If multiple files are open, the Input Data dialog will always display the data in the active file.

The Apply button can be used to compute results based on the current Input Data, without closing the dialog.

The F3 function key can be used as a shortcut to display the Input Data dialog.

You may find these properties of the Input Data dialog useful, for example, when performing parametric analysis, or when working with multiple files.

Now maximize the Input Data dialog, by selecting the arrow, or double clicking on the title bar of the dialog.

 

Strength

Change the shear strength of the failure plane.

 

Select the Strength tab of the Input Data dialog. Enter a Cohesion =5. Select Apply.

The Safety Factor drops to 1.258.

Several different shear strength models are available in ROCPLANE

 

Water Pressure

By default, Water Pressure is NOT applied to a ROCPLANE model, and the analysis is therefore applicable to a DRY slope. To include Water Pressure in the analysis:

 

Select the Forces tab in the Input Data dialog.

Select the Water Pressure checkbox.

Various Water Pressure Distribution Models are available, by selecting from the list. This includes:

 

Peak Pressure Mid Height

Peak Pressure at Toe

Peak Pressure at Tension Crack Base

Custom Pressure

 

For this example, we will use the default method (Peak Pressure at Mid-Height).

You may also define a Percent Filled, to define the water level in the slope.

Let’s use the default 100% filled for now.

Select Apply. The Safety Factor decreases to 0.623.

This wedge would therefore be very unstable for these water pressure and shear strength conditions.

Change the Percent Filled to 50. Select Apply.

The Safety Factor increases to 1.099.

Minimize the Input Data dialog (select the _arrow).

Use the right mouse button (click and drag) or the mouse wheel, to slide the wedge all the way out of the slope.

Notice that the water level in the slope is indicated by blue shading.

Since we entered a percent filled = 50 %, notice that the lower half of the failure plane is shaded blue.

Also notice, if you rotate the model in the Perspective view (click and drag the LEFT mouse button), a blue arrow, representing the Water Pressure force is displayed normal to the failure plane, on the underside of the wedge.

Click the right mouse button in any view, to reset the wedge in the slope. Maximize the Input Data dialog.

 

Seismic Force

Now we will include Seismic Force in the analysis.

 

Select the Seismic Force checkbox.

Enter a Seismic Coefficient of 0.2.

Select Apply, and the Safety Factor drops to 0.746.

Notice that an arrow representing the Seismic Force is now displayed on the model.

The Seismic Force applied to the wedge is F = 0.2 * g * m, where g = acceleration due to gravity and m = mass of the wedge (per unit width of the slope cross-section).

Remove the Seismic Force by clearing the Seismic checkbox, and selecting Apply.

 

Tension Crack

Let’s now add a tension crack to the model.

 

Select the Geometry tab in the Input Data dialog.

Select the Tension Crack checkbox. Select Apply.

The Safety Factor is now 0.98. Notice that the wedge now appears quite different.

We used the “Minimum FS Location” option for the Tension Crack.

This means that ROCPLANE will automatically determine the location of the Tension Crack which produces the minimum safety factor.

 

In this case, the minimum safety factor results when the Tension Crack is placed exactly at the crest of the slope, therefore the Upper Slope Face of the wedge is no longer present. The wedge is formed only by the slope, failure plane and tension crack. NOTE – the Minimum FS Location option does NOT necessarily mean that the Tension Crack is placed at the crest of the slope. It is placed at the location which produces the minimum safety factor, which happens to be the crest of the slope in this example.

 

Now let’s use the Specify Location option, which allows the user to specify the location of the tension crack, as measured horizontally from the crest of the slope.

 

Select the Specify Location option for the Tension Crack, and enter the Distance From Crest = 20. Select Apply.

The new safety factor = 1.04.

The Tension Crack is now located 20 meters behind the crest of the slope, as shown in the figure below.

 

Info Viewer

Let’s take a look at the Info Viewer option.

Select: Analysis → Info Viewer

A convenient summary of model and analysis data is displayed in its own view. Scroll down to view all of the information. The Info Viewer text can be copied to the clipboard, saved to a file, or printed, using options available in the File menu, the Edit menu or the rightclick menu.

 

Exporting Images

In ROCPLANE, various options are available for exporting image files.

 

Export Image File

The Export Image File option in the File menu, allows the user to save the current view directly to several image file formats. The current view can also be copied to the Windows clipboard using the Copy option in the toolbar, the Edit menu or the right-click menu. This will place a bitmap image on the clipboard which can be pasted directly into word or image processing applications. TIP- to capture the entire application window to the clipboard, use the Alt-PrintScreen keyboard combination. This is useful if you have multiple tiled views on the screen, or to capture all four views of the 3D wedge view.

 

Black And White Images (Grayscale)

The Grayscale option, available in the toolbar, the View menu or the right-click menu, will automatically convert all views of the current document to Grayscale, suitable for black and white image requirements. This can be useful when sending images to a black and white printer, or for capturing black and white image files. That concludes this “quick start” tutorial. To exit the

program:

Select: File → Exit

 

Probabilistic Analysis

Probabilistic analysis features of ROCPLANE. If you have not already done so, run ROCPLANE by double-clicking on the ROCPLANE icon in your installation folder.  If the ROCPLANE application window is not already maximized, maximize it now, so that the full screen is available for viewing the model. To begin creating a new model:

Select: File → New

A default wedge model will immediately appear on your screen. Whenever a new file is opened, the default input data will form a valid wedge.

 

Project Settings

Project Settings allows the user to enter a Project Title, and select a Unit System and Analysis Type. Let’s switch the Analysis Type to Probabilistic.

Select: Analysis → Project Settings.

Enter “ROCPLANE Probabilistic Tutorial” as the Project Title.

Leave Units = Metric and change the Analysis Type to Probabilistic. Select OK.

 

Note:

  • Analysis Type can also be changed at any time, using the drop-down list box in the ROCPLANE toolbar. This is a convenient shortcut.

  • The Project Title appears in the Info Viewer listing,  and also on printouts of the wedge view.

  • Units determines the length and force units used in the analysis. Analysis Type can be selected from the drop-down list box in the toolbar.

 

Probabilistic Input Data

Select: Analysis → Input Data

 

Defining Random Variables

To define a random variable in ROCPLANE:

 

First select a Statistical Distribution for the variable. (In most cases a Normal distribution will be adequate.)

Enter Standard Deviation, Minimum and Maximum values.

NOTE that the Minimum / Maximum values are specified as RELATIVE distances from the mean, rather than absolute values.

Any variable for which the Statistical Distribution = “None” will be assumed to be “exactly” known, and will not be involved in the statistical sampling.

See the ROCPLANE Help system for information about the properties of the statistical distributions available in ROCPLANE.

For this example, we will define Normal Statistical Distributions for the following variables:

Failure Plane Angle

Failure Plane Cohesion

Failure Plane Friction Angle

 

Failure Plane Angle

Select the Failure Plane tab in the Input Data dialog, and enter the following data for the Angle:

mean = 28

Distribution = Normal

Std. Dev. = 2

Rel. Min. = 5

Rel. Max. = 5

 

Failure Plane Strength

Select the Strength tab and enter the following data for the Failure Plane Cohesion and Friction Angle:

Cohesion (Mean) = 10

Friction Angle (Mean) = 35

For both Cohesion and Friction Angle:

Distribution = Normal

Standard Deviation = 2

Relative Min = Relative Max = 5

 

Water Pressure

Select the Water tab.

Select the Water Pressure Exists checkbox.

We will use all of the default settings:

Peak Pressure – Mid Height

Percent Filled = 100%

Distribution = None.

 

Probabilistic Analysis

To carry out the ROCPLANE Probabilistic Analysis, select Apply or OK in the Input Data dialog.

 

Apply will run the analysis without closing the dialog. OK will run the analysis and close the dialog. The analysis will be run using the parameters you have just entered. Calculation should only take a few seconds. The progress of the calculation is indicated in the status bar.

 

Probability of Failure

The primary result of interest from a Probabilistic Analysis is the Probability of Failure.

This is displayed in the toolbar at the top of the screen.

For this example, if you entered the Input Data correctly, you should obtain a Probability of Failure of 14.5%. (ie. PF = 0.145 means 14.5% Probability of Failure).

Later in this tutorial, we will discuss Random versus Pseudo-Random sampling. By default, Pseudo-Random sampling is in effect, which means that you will always obtain the same results each time you run a Probabilistic Analysis with the same input data. If Pseudo-Random sampling is turned OFF, then different results will be generated each time the analysis is run.

 

Wedge Display

The wedge initially displayed after a Probabilistic Analysis, is based on the mean input values, and is referred to as the Mean Wedge. It will appear exactly the same as one based on Deterministic Input Data with the same orientation as the mean Probabilistic Input Data. Other wedges generated by the Probabilistic Analysis can be displayed, as described in the Viewing Other Wedges section.

 

Histograms

To plot histograms of results after a Probabilistic Analysis:

Select: Statistics → Plot Histogram

Select OK to plot a histogram of Safety Factor.

 

The histogram 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.

 

Mean Safety Factor

Notice the mean, standard deviation, min and max values displayed below the histogram. It should be noted that the mean Safety Factor from a Probabilistic Analysis (ie. the average of all of the Safety Factors generated by the Probabilistic Analysis) is not always the same as the Safety Factor of the Mean Wedge (ie. the Safety Factor of the wedge corresponding to the mean Input Data values). Verify this by switching to the Wedge View. In the title bar of the wedge view, the safety factor of the Mean Wedge is displayed. Compare this value to the Mean safety factor listed at the bottom of the Histogram. These values will in general not be equal. There are various reasons for this:

 

Monte Carlo sampling does not sample your input data distributions “exactly” .

TIP – you can apply a 3D effect to histograms with the 3D Histogram option in the right-click menu.

For a Monte Carlo analysis, the mean Safety Factor is not necessarily the same as the Safety Factor of the Mean Wedge.

Number of samples is small.

If invalid wedges are generated by the probabilistic analysis (eg. invalid geometries), this can also lead to differences between the deterministic safety factor and the probabilistic mean safety factor.

 

NOTE: if you use Latin Hypercube sampling, and a large number of samples eg. (10000), the deterministic and probabilistic mean safety factors should be very nearly equal. This is left as an optional exercise to explore, after completing this tutorial. Switch back to the Histogram view. (TIP – if you select the Window → Tabs option, tabs will appear at the bottom of the application window, allowing you to easily switch between different views)

 

Viewing Other Wedges

Now tile the Histogram and Wedge views, so that both are visible.

Select: Window → Tile Vertically

A useful property of Histograms (and also Scatter Plots) is the following: If you double-click the LEFT mouse button anywhere on the plot, the nearest corresponding wedge will be displayed in the Wedge view. For example:

 

Double-click at any point along the histogram.

Notice that a different wedge is now displayed.

The Safety Factor of this wedge is displayed in the title bar of the Wedge view, and the title bar will indicate that you are viewing a “Picked Wedge” rather than the “Mean Wedge”.

Double-click at various points along the histogram, and notice the different wedges and safety factors displayed in the wedge view.

For example, doubleclick in the “red” Safety Factor region, to view wedges with a Safety Factor < 1.

 

This feature allows the user to view any wedge generated by the Probabilistic Analysis, corresponding to any point along a histogram distribution. In addition to the Wedge View, all other applicable views (for example, the Info Viewer) are also updated to display data for the currently “Picked Wedge”. Note:

 

  • This feature can be used on histograms of any statistical data generated by ROCPLANE, and not just the Safety Factor histogram

  • This feature also works on Scatter plots.

 

Resetting the Mean Wedge

To reset all views so that the Mean Wedge data is displayed:

Select: View → Reset Wedge

This will display the Mean Wedge in the Wedge View, and all other applicable views will also be updated to display the Mean Wedge data.

 

Histograms of Other Data

In addition to Safety Factor, you may also plot histograms of:

 

  • Wedge Weight, Wedge Volume

  • Normal, Driving and Resisting Forces

  • Failure Plane Length, Upper Face Length

  • Any random input variable (ie. any Input Data variable which was assigned a Statistical Distribution)

 

For example:

 

Select: Statistics → Plot Histogram

In the dialog, set the Data Type = Wedge Weight, and select OK.

 

A histogram of the Wedge Weight distribution will be generated. Note that all of the features described above for the Safety Factor histogram, apply to any other Data Type. For example, if you double-click on the Wedge Weight histogram, the nearest corresponding wedge will be displayed in the Wedge View. Let’s generate one more histogram.

 

Select: Statistics → Plot Histogram

This time we will plot one of our Input Data random variables.

Set the Data Type = Failure Plane Angle.

Select the Plot Input Distribution checkbox. Select OK.

 

The histogram shows how the Failure Plane Angle Input Data variable was sampled by the Monte Carlo analysis. The curve superimposed over the histogram is the Normal distribution you defined when you entered the mean, standard deviation, min and max values for Failure Plane Angle in the Input Data dialog.

 

Show Failed Wedges

Let’s demonstrate one more feature of Histogram plots, the Show Failed Wedges option. Right-click on the Histogram and select Show Failed Wedges. The distribution of failed wedges (ie. wedges with Safety Factor < 1) is now highlighted on the Histogram. This option allows the user to see the relationship between wedge failure, and the distribution of any input or output variable. The Show Failed Wedges option allows the user to see the relationship between wedge failure and the distribution of any input or output variable. As we would expect, the failed wedges correspond to larger Failure Plane Angles’

 

Cumulative Distributions (S-curves)

In addition to the histograms, cumulative distributions (S curves) of the statistical results can also be plotted.

Select: Statistics → Plot Cumulative

Select OK.

The cumulative Safety Factor distribution will be generated. (Maximize the view if necessary).

 

Notice the vertical dotted line visible on the plot. This is the Sampler, and allows you to obtain the coordinates of any point on the cumulative distribution curve. • To use the sampler, just SINGLE click the LEFT mouse button anywhere on the plot, and the sampler will jump to that location, and display the results. • Alternatively, press and HOLD the LEFT mouse button on the plot, and you will see the double-arrow icon. Move the mouse left or right, and the sampler will continuously display the values of points along the curve. The display of the Sampler can be turned on or off in the right-click menu or the View menu. A point on a cumulative probability curve, gives the probability that the plotted variable will be less than or equal to the value of the variable at that point. For a cumulative Safety Factor distribution, the cumulative probability at Safety Factor = 1, is equal to the Probability of Failure, the cumulative probability at Safety Factor = 1, is equal to 0.145, which is the Probability of Failure for this example.

 

Scatter Plots

Scatter Plots allow the user to examine the relationships between analysis variables. To generate a Scatter Plot:

 

Select: Statistics → Plot Scatter

In the Scatter Plot dialog, select the variables you would like to plot on the X and Y axes, for example, Safety Factor vs. Wedge Weight.

Select the Show Regression Line option to display the best fit straight line through the data.

Select OK to generate the plot.

 As can be seen  there appears to be very little correlation between Safety Factor and Wedge Weight. However, Safety Factor does generally increase with increasing Wedge Weight. The Correlation Coefficient, listed at the bottom of the plot indicates the degree of correlation between the two variables plotted. The Correlation 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. Note that a negative correlation coefficient simply means that the slope of the best fit linear regression line is negative.

 

Alpha and beta, also listed at the bottom of the plot, represent the y-intercept and slope, respectively, of the best fit linear regression line to the scatter plot data. Note:

  • As demonstrated earlier with Histograms, you may double-click the mouse on a Scatter Plot, to display the data for the nearest wedge on the plot. This is left as an optional exercise for the user to demonstrate.

  • The Show Failed Wedges option, described previously for Histograms, also works on Scatter Plots. For example, right-click and select Show Failed Wedges. All wedges with Safety Factor < 1 are now highlighted in RED on the Scatter Plot.

  • For the special case of Cohesion vs. Friction angle, a user-defined correlation coefficient can be specified in the Input Data dialog. See the Additional Exercises at the end of this tutorial for details.

 

Random vs. Pseudo-Random Sampling

By default in ROCPLANE, Pseudo-Random Sampling is in effect for a Probabilistic analysis. Pseudo-Random Sampling allows the user to obtain reproducible results from a Probabilistic Analysis. Tile the views and we will demonstrate this.

Select: Window → Tile Vertically

The Probabilistic Analysis can be re-run at any time, by selecting the Compute button in the toolbar.

Select: Analysis → Compute

Notice that even though the analysis is re-run, all graphs, and the probability of failure, remain unchanged.

Select Compute again to verify this.

 

Pseudo-Random Sampling means that the SAME "seed" number is always used to generate random numbers for the sampling of the input data distributions. This results in identical sampling of the input data distributions, each time the analysis is run (with the same input parameters). The Probability of Failure, mean Safety Factor, and all other analysis output, will be reproducible. This can be useful for demonstration purposes, the discussion of example problems, etc. The Pseudo-Random Sampling option can be turned off in the Input Data dialog, under the Sampling tab.

Select: Analysis → Input Data

 In the Input Data dialog, select the Sampling tab, and clear the Pseudo-Random Sampling checkbox. Select OK. Now re-select the Compute button, several times. Notice that after each Compute:

 

  • All graphs are updated and display new results,

  • The probability of failure will in general, be different each time the analysis is run (for this example, you should find that the Probability of Failure will vary between about 14 and 18 %)

 

This demonstrates the difference between Random and Pseudo-Random sampling, and also graphically demonstrates the ROCPLANE Monte Carlo analysis. Note that the Wedge view does not change when you recompute, since by default the Mean Wedge is displayed, (ie. the wedge based on the mean Input Data), which is not affected by re-running the analysis.

 

Info Viewer

Let’s examine the Info Viewer listing for a Probabilistic Analysis.

Select: Analysis → Info Viewer

A convenient summary of model and analysis parameters is displayed in its own view. Scroll down to view all of the information. As with the plot views, if you re-compute the analysis, the Info Viewer listing is automatically updated to reflect the latest results.

 

Current Wedge Data

Notice the Current Wedge Data listing in the Info Viewer. By default, the Mean Wedge data is displayed after a Probabilistic analysis. As we pointed out earlier, if you double-click on a Histogram or Scatter plot, the nearest wedge will be displayed in the Wedge View. The Current Wedge Data in the Info Viewer will also be updated, to reflect the data for the “picked” wedge. Let’s demonstrate this.

 

Close (or minimize) all views you may have on the screen, EXCEPT the Info Viewer and the Safety Factor Histogram.

Select the Tile Vertically toolbar button.

If necessary, scroll down in the Info Viewer view, so that the Current Wedge Data is visible.

Double-click at different points on the Safety Factor histogram, and notice that the Current Wedge Data is updated to show the data for the “picked” wedge.

Note: the Mean Wedge Data information is still displayed, above the Picked Wedge data, as can be seen in the following figure.

To reset the Current Wedge Data to the Mean Wedge data:  Select: View → Reset Wedge

 

Additional Exercises: Sampling Method

So far we have used Monte Carlo sampling throughout this tutorial. As an additional exercise, set the Sampling Method to Latin Hypercube, and re-run the analysis.

Select: Analysis → Input Data

 

In the Input Data dialog, select the Sampling tab, and set the Sampling Method to Latin Hypercube. Select the Apply button.

 

Examine the Probability of Failure, and the Safety Factor Histogram. The results should be very similar to the Monte Carlo analysis. The difference is in the sampling of the Input Data random variables. For example, generate a Histogram of Failure Plane Angle.

 

Select: Statistics → Plot Histogram

Set the Data Type = Failure Plane Angle.

Select the Plot Input Distribution checkbox. Select OK.

 Compare the histograms from before

The Latin Hypercube sampling method results in a much smoother sampling of the Input Data distribution, compared to the Monte Carlo method.

 

Correlation Coefficient for Cohesion and Friction Angle

In this tutorial, Cohesion and Friction Angle were treated as completely independent variables. In fact, 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. In the Input Data dialog, the user may define the degree of correlation between Cohesion and Friction Angle, for the Failure Plane. This only applies if:

 

BOTH Cohesion and Friction Angle are defined as random variables (ie. assigned a statistical distribution)

Normal or Uniform distributions are defined (will not work for other distribution types).

As a suggested exercise, try the following:

Define Normal distributions for the Cohesion and Friction Angle.

Select the “Correlation coefficient between cohesion and friction angle” checkbox.

Enter a correlation coefficient. (Initially, use the default value of –0.5.)

Re-run the analysis.

Create a Scatter Plot of Cohesion vs. Friction Angle.

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 (ie –0.5 in this case). Note the appearance of the plot.

Now repeat steps 3 to 6, 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.

 NOTE that the default correlation coefficient of –0.5 is a good typical value to use, if more precise data is not available.

 

Exporting Data to Excel

After generating any graph in ROCPLANE, you can easily export the data to Microsoft Excel with a single mouse click, as follows:

 

Select the Chart in Excel button from the toolbar. (Alternatively, you can right-click on a graph and select Chart in Excel from the popup menu.)

If you have Microsoft Excel on your computer, this will automatically start up the Excel program, export the graph data to Excel, and generate a graph in Excel.

 

Finally, we will note the Export Dataset option in the Statistics menu. This option allows the user to export raw data from a Probabilistic Analysis, to the clipboard, a file, or to Excel, for post-processing. Any or all data generated by the probabilistic analysis, can be simultaneously exported.

 

 

DPG (Version 3, 2011)