-
Probabilistic Analysis Tutorial 2-1
Swedge v.6.0 Tutorial Manual
Probabilistic Analysis Tutorial
This tutorial will familiarize the user with the Probabilistic
Analysis features of Swedge.
In a Probabilistic Analysis, you can define statistical
distributions for input parameters (e.g. joint orientation, shear
strength, water level), to account for uncertainty in their values.
When the analysis is computed, this results in a distribution of
safety factors, from which a probability of failure (PF) is
calculated.
The finished product of this tutorial can be found in the
Tutorial 02 Probabilistic.swd file, located in the Examples >
Tutorials folder in your Swedge installation folder.
Topics Covered in this Tutorial
Project Settings Random Variables Fisher Distribution Tension
Crack Mean Wedge Picked Wedges Histograms Scatter Plots Stereonet
View Show Failed Wedges
-
Probabilistic Analysis Tutorial 2-2
Swedge v.6.0 Tutorial Manual
Failure Mode Filter Design Factor of Safety
If you have not already done so, run the Swedge program by
double-clicking on the Swedge icon in your installation folder. Or
from the Start menu, select Programs Rocscience Swedge 5.0
Swedge.
If the Swedge application window is not already maximized,
maximize it now, so that the full screen is available for viewing
the model.
When the Swedge program is started, a default model is
automatically created, allowing you to begin defining your model
immediately. If you do NOT see a wedge model on your screen:
Select: File New
Whenever a new file is created, the default input data will form
a valid wedge.
Project Settings
The Project Settings option allows you to configure the main
analysis parameters for your model (i.e. Analysis Type, Units,
Sampling Method etc). Select Project Settings from the toolbar or
the Analysis menu. Keep the Block Shape as Wedge.
Select: Analysis Project Settings
You will see the Project Settings dialog.
Analysis Type By default a Deterministic Analysis is selected
for a new file. Select the General tab in the Project Settings
dialog, and change the Analysis Type to Probabilistic.
-
Probabilistic Analysis Tutorial 2-3
Swedge v.6.0 Tutorial Manual
Units For this tutorial we will be using Metric units, so make
sure the Metric, stress as MPa option is selected for Units.
Sampling and Random Numbers Select the Sampling tab in the
Project Settings dialog. The Sampling Method determines how the
statistical distributions for the random input variables will be
sampled. The default Sampling Method = Latin Hypercube, and the
default Number of Samples = 10,000. See the Swedge help topics for
more information about the sampling options.
Select the Random Numbers tab. Note that Pseudo-Random sampling
is in effect by default. This allows you to obtain reproducible
results for a probabilistic analysis, by using the same seed value
to generate random numbers. We will discuss Pseudo-Random versus
Random sampling later in this tutorial.
Also note the Design Factor of Safety option. This option is
used in probabilistic and combination analyses for determining both
the probability of failure and the number of failed wedges in
graphs. The probability of failure is now P(FS < Design FS).
For this tutorial, well keep the default value of 1.
-
Probabilistic Analysis Tutorial 2-4
Swedge v.6.0 Tutorial Manual
Do not make any changes to these settings, we will use the
defaults.
Project Summary Select the Project Summary tab in the Project
Settings dialog.
Enter Swedge Probabilistic Analysis Tutorial as the Project
Title.
NOTE: the Project Summary information can be displayed on
printouts of analysis results, using the Page Setup option in the
File menu and defining a Header and/or Footer.
Select OK to close the Project Settings dialog.
-
Probabilistic Analysis Tutorial 2-5
Swedge v.6.0 Tutorial Manual
Probabilistic Input Data
Select Input Data from the Analysis menu or the toolbar.
Select: Analysis Input Data
For a Probabilistic analysis, the Input Data dialog is organized
under several tabs as shown below.
To carry out a Probabilistic Analysis with Swedge, at least one
input parameter must be defined as a random variable. To define a
random variable, select a statistical distribution (e.g. Normal,
Lognormal, Fisher, etc) for the variable, and enter appropriate
statistical parameters for the distribution (e.g. standard
deviation, min and max values).
For more information about statistical input see the Swedge help
system.
For this example, we will be defining the following input
parameters as random variables:
Joint 1 orientation Joint 1 shear strength Joint 2 orientation
Joint 2 shear strength Tension Crack orientation
-
Probabilistic Analysis Tutorial 2-6
Swedge v.6.0 Tutorial Manual
All other model input parameters will be assumed to be exactly
known (i.e. Statistical Distribution = None) and will not be
involved in the statistical sampling.
Slope Select the Slope tab in the Input Data dialog. We will
assume that the orientation of the slope plane is constant for the
probabilistic analysis, so we will not enter statistical data (i.e.
Statistical Distribution = None).
Use the default orientation values (Dip = 65, Dip Direction =
185) and Unit Weight = 0.026.
Enter a Slope Height = 20 meters.
Select the Length checkbox and enter a Slope Length = 60 meters
(see note below).
Slope Length
NOTE: for a Probabilistic analysis, it is usually a good idea to
define a Slope Length. This will limit the size of wedges according
to this dimension. If you leave the slope length undefined, then,
depending on your joint orientation distributions, very large
wedges can be generated parallel to the slope, which may give
unrealistic or misleading analysis results.
Upper Face Select the Upper Face tab in the Input Data dialog.
We will assume that the orientation of the upper face is constant
for the probabilistic analysis, so we will not enter statistical
data (i.e. Statistical Distribution = None).
Use the default orientation values (Dip = 12, Dip Direction =
185).
Select the Bench Analysis checkbox and enter a Bench Width = 15
meters (see note below).
Bench Width
NOTE: for a Probabilistic analysis, it is usually a good idea to
define a Bench Width. This will limit the size of wedges according
to this dimension. If you leave the Bench Width undefined, then,
depending on your joint orientation distributions, very large
wedges can be generated perpendicular to the slope, which may give
unrealistic or misleading analysis results.
Joint 1 Orientation Select the Joint 1 tab in the Input Data
dialog.
-
Probabilistic Analysis Tutorial 2-7
Swedge v.6.0 Tutorial Manual
Note that there are TWO methods of defining the variability of
joint orientation in an Swedge Probabilistic analysis:
Orientation Definition Method = Dip / Dip Direction
Orientation Definition Method = Fisher Distribution
With the Dip / Dip Direction method, the Dip and Dip Direction
are treated as independent random variables (i.e. you can define
different statistical distributions for Dip and Dip Direction).
The Fisher Distribution method generates a symmetric,
3-dimensional distribution of orientations around the mean plane
orientation. Only a single standard deviation is required. In
general, a Fisher Distribution is recommended for generating random
joint plane orientations, because it provides more predictable
orientation distributions, and lessens the chance of input data
errors.
For more information about the Orientation Definition Method see
the Swedge Help system.
We will use the Fisher Distribution option. Select Orientation
Definition Method = Fisher Distribution. Enter Mean Dip = 45, Mean
Dip Direction = 105, and Standard Deviation = 7.
-
Probabilistic Analysis Tutorial 2-8
Swedge v.6.0 Tutorial Manual
Joint 2 Orientation Select the Joint 2 tab in the Input Data
dialog.
Select Orientation Definition Method = Fisher Distribution.
Enter Mean Dip = 70, Mean Dip Direction = 235, and Standard
Deviation = 7.
-
Probabilistic Analysis Tutorial 2-9
Swedge v.6.0 Tutorial Manual
Joint 1 Strength Select the Strength 1 tab in the Input Data
dialog.
Note that there are TWO methods of defining the statistical
variability of joint shear strength in an Swedge Probabilistic
analysis:
Random Variables = Parameters
Random Variables = Strength
With the Parameters method, the individual strength criterion
parameters (e.g. cohesion and friction angle) can each be assigned
a statistical distribution.
With the Strength method, the shear strength variability is
defined with respect to the mean strength envelope. This method has
the advantage of only requiring a single parameter (coefficient of
variation) to define the shear strength variability.
For more information about the probabilistic joint shear
strength options in Swedge, see the Swedge Help system.
Select Random Variables = Strength.
Select Statistical Distribution = Lognormal.
Enter Coefficient of Variation = 0.25, Cohesion = 0.02, Phi =
20.
-
Probabilistic Analysis Tutorial 2-10
Swedge v.6.0 Tutorial Manual
NOTE:
The Coefficient of Variation is defined as the Standard
Deviation (of the shear strength) divided by the Mean (shear
strength).
Only Lognormal (and Gamma) distributions are allowed for
defining shear strength as a random variable, because Lognormal and
Gamma distributions are only defined for positive values. This
ensures that the randomly generated values of shear strength will
always be positive (negative shear strength has no physical meaning
in Swedge).
Joint 2 Strength Select the Strength 2 tab in the Input Data
dialog.
Select Random Variables = Strength.
Select Statistical Distribution = Lognormal.
Enter Coefficient of Variation = 0.25, Cohesion = 0, Phi =
30.
-
Probabilistic Analysis Tutorial 2-11
Swedge v.6.0 Tutorial Manual
-
Probabilistic Analysis Tutorial 2-12
Swedge v.6.0 Tutorial Manual
Tension Crack Lets include a Tension Crack for this model, and
define the orientation as a random variable.
1. Select the Tension Crack tab in the Input Data dialog.
2. Select the Tension Crack Exists checkbox.
3. Select Orientation Definition Method = Fisher
Distribution.
4. Enter Mean Dip = 70, Mean Dip Direction = 165, and Standard
Deviation = 7.
5. For the Tension Crack Location, select the Use Bench Width to
Maximize option.
NOTE: the Use Bench Width to Maximize option will automatically
locate the Tension Crack to create the maximum possible wedge size
for the specified Bench Width. A Tension Crack will NOT be included
if it decreases the wedge size.
-
Probabilistic Analysis Tutorial 2-13
Swedge v.6.0 Tutorial Manual
Compute
Select OK in the Input Data dialog to Compute the Swedge
Probabilistic analysis.
Using the Latin Hypercube sampling method, Swedge will generate
10,000 random input data samples for each random variable, using
the specified statistical distributions, and compute the safety
factor for 10,000 possible wedges.
The calculation should only take a few seconds. The progress of
the calculation is indicated in the status bar.
TIP: you can also select the Apply button in the Input Data
dialog to Compute the analysis without closing the dialog. This
allows you to easily test different input parameters and re-compute
the results.
Probabilistic Analysis Results
The primary result of interest from a Probabilistic analysis is
the Probability of Failure. This is the first result reported in
the Sidebar Information Panel under Probabilistic Analysis.
For this example, if you entered the Input Data correctly, you
should obtain a Probability of Failure (PF) of about 9% (PF =
0.0884).
Sidebar Information Panel A summary of analysis results is
displayed in the Sidebar information panel at the right of the
screen.
-
Probabilistic Analysis Tutorial 2-14
Swedge v.6.0 Tutorial Manual
Notice that the Probability of Failure is equal to the Number of
Failed Wedges (i.e. safety factor < 1), divided by the Number of
Samples (entered in the Project Settings dialog) = 884 / 10000.
NOTE: for a discussion of the Probability of Failure see the
Swedge help system.
-
Probabilistic Analysis Tutorial 2-15
Swedge v.6.0 Tutorial Manual
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 data.
The safety factor of the Mean Wedge = 1.366 as shown in the
Sidebar.
Figure 1: Mean Wedge display
Note that the Tension Crack for the Mean Wedge is located to
create the maximum wedge size for the given bench width. Remember
that the Use Bench Width to Maximize option is in effect for the
Tension Crack.
You can also view the wedge with the Minimum safety factor
generated by the Probabilistic analysis. Right-click in the Wedge
View and select Show Min FS Wedge from the popup menu. The minimum
safety factor wedge will be displayed, and the Sidebar now displays
analysis information for the Min FS Wedge (Safety Factor =
0.544).
To restore the Mean Wedge display and information, right-click
in the Wedge View and select Show Mean FS Wedge.
-
Probabilistic Analysis Tutorial 2-16
Swedge v.6.0 Tutorial Manual
Histograms To plot histograms of results after a Probabilistic
Analysis, select Plot Histogram from the toolbar or the Statistics
menu:
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 random sampling of the Input Data. The red bars at
the left of the distribution represent wedges with Safety Factor
less than 1.0.
Right-click on the histogram and select 3D Histogram from the
popup menu. This will display the histogram bars in 3D.
-
Probabilistic Analysis Tutorial 2-17
Swedge v.6.0 Tutorial Manual
Figure 2: Safety Factor histogram.
Mean Safety Factor
At the bottom of the histogram plot, notice the mean, standard
deviation, min and max values.
Note that the mean Safety Factor from a Probabilistic Analysis
(i.e. the average of all of the Safety Factors generated by the
Probabilistic Analysis) will in general, be slightly different from
the Safety Factor of the Mean Wedge (i.e. the Safety Factor of the
wedge corresponding to the mean Input Data values).
In this case:
From the histogram, the mean safety factor = 1.424.
In the Sidebar, the safety factor of the Mean Wedge = 1.366.
Theoretically, for an infinite number of samples, these two
values should be equal. However due to the random nature of the
statistical sampling, the two values will usually be slightly
different, for a typical probabilistic analysis with a finite
number of samples.
-
Probabilistic Analysis Tutorial 2-18
Swedge v.6.0 Tutorial Manual
Selecting Random Wedges
Now tile the Histogram and Wedge views, so that both are
visible.
Select: Window Tile Vertically
Figure 3: Safety Factor histogram and wedge view.
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, and results for the wedge will be displayed in the
Sidebar.
For example:
1. Double-click at any point along the histogram.
2. Notice that a different wedge is now displayed.
3. In the Sidebar, the analysis results are updated to display
results for the wedge that you are viewing, which is referred to as
a Picked Wedge.
4. Double-click at various points along the histogram, and
notice the different wedges and analysis results which are
displayed. For example, double-click in the red Safety Factor
region, to view wedges with a Safety Factor < 1.
-
Probabilistic Analysis Tutorial 2-19
Swedge v.6.0 Tutorial Manual
This feature allows you to view any wedge generated by the
Probabilistic Analysis, corresponding to any point on a histogram
or scatter plot.
In addition to the Wedge View, all other applicable views (for
example, the Info Viewer and the Stereonet View) 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 Swedge, and not just the Safety Factor histogram
this feature also works on Scatter plots.
Right-click in the wedge view and select Show Mean FS Wedge from
the popup menu, to reset the mean wedge display.
Histograms of Other Data
In addition to Safety Factor, you can also plot histograms
of:
other random output variables (e.g. wedge weight, normal stress
on joint planes, driving force etc),
random input variables (i.e. any input data variable which was
assigned a statistical distribution).
For example:
Select: Statistics Plot Histogram
In the dialog, select Data Type = Wedge Weight, select the Best
Fit Distribution checkbox, and select OK. A histogram of the wedge
weight and the best-fit distribution to the data will be
displayed.
In this case the Best Fit distribution is a Normal distribution,
with parameters listed at the bottom of the plot. The Best Fit
distribution can be displayed for analysis output variables.
The features described above for the Safety Factor histogram,
also apply to other Data Types. For example, if you double-click on
the Wedge Weight histogram, the nearest corresponding wedge will be
displayed in the Wedge View.
Close the Wedge Weight histogram view, and the Safety Factor
histogram view, by selecting the X in the upper right corner of
each view.
Right-click in the wedge view and select Show Mean FS Wedge from
the popup menu, to reset the mean wedge display.
-
Probabilistic Analysis Tutorial 2-20
Swedge v.6.0 Tutorial Manual
Now lets generate a histogram of an input random variable.
Select: Statistics Plot Histogram
Select Data Type = Dip of Joint 1.
NOTE: for input random variables, the Input Distribution can be
displayed on histograms. However, because the orientation of Joint
1 was generated using a Fisher Distribution, which is
3-dimensional, the Input Distribution cannot be displayed on the
histogram, which is a 2-dimensional plot of only one component
(Dip) of the Joint 1 orientation.
Show Failed Wedges
Lets demonstrate one more feature of Histogram plots, the Show
Failed Wedges option. By default, this option is selected, and the
distribution of failed wedges (i.e. wedges with Safety Factor <
1) is highlighted on the Histogram. The Show Failed Wedges option
allows you to see the relationship between wedge failure, and the
distribution of any input or output variable.
In this case, there is not a strong correlation between wedge
failure and Joint 1 dip angle. However, there appears to be some
bias towards failure at higher dip angles, as might be
expected.
Figure 4: Joint 1 Dip Angle failed wedge distribution is also
displayed.
-
Probabilistic Analysis Tutorial 2-21
Swedge v.6.0 Tutorial Manual
Scatter Plots Scatter plots allow you to examine the
relationship between any two 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, lets plot the normal
stress versus shear strength for one of the joint planes. Select
the Show Regression Line option to display the best fit straight
line through the data.
Select OK to generate the plot.
From the failed wedge data, it can be readily seen that wedge
failure corresponds to low values of normal stress and shear
strength, as we would expect.
Since we used the Mohr-Coulomb strength criterion, the best fit
linear regression line for the Scatter plot corresponds
(approximately) to the mean strength envelope. We can verify this
from the parameters listed at the bottom of the plot.
The alpha value (0.02029) represents the y-intercept of the
linear regression line on the Scatter plot. For Joint 1, recall
that we defined the cohesion = 0.02 MPa. For the Mohr-Coulomb
criterion, cohesion is the y-intercept of the strength
envelope.
The beta value (0.362) represents the slope of the linear
regression line. For the Mohr-Coulomb criterion, the slope of the
strength envelope is equal to tan(phi). For Joint 1 we defined phi
= 20 degrees. Arctan(0.362) = 19.9.
-
Probabilistic Analysis Tutorial 2-22
Swedge v.6.0 Tutorial Manual
Figure 5: Normal stress versus shear strength for Joint 1.
Also note the Correlation Coefficient, listed at the bottom of
the plot, which 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.
The Correlation Coefficient is related to the Coefficient of
Variation which we defined for the shear strength of Joint 1. To
demonstrate this:
1. Select Input Data and select the Strength 1 tab.
2. Enter Coefficient of Variation = 0.1 and select Apply in the
dialog to re-compute the analysis.
3. Notice that the scatter of data around the mean strength
envelope is much narrower, and the Correlation Coefficient has
increased to 0.899.
4. Enter Coefficient of Variation = 0.01 and select Apply.
5. The scatter of data is very narrow, and the Coefficient of
Variation = 0.999.
6. To restore the original strength data, re-enter Coefficient
of Variation = 0.25 and select OK.
-
Probabilistic Analysis Tutorial 2-23
Swedge v.6.0 Tutorial Manual
Stereonet View The Stereonet View in Swedge displays a
stereographic projection of the wedge planes (great circles) and
corresponding poles. For a Probabilistic analysis, the stereonet
can display the poles of all randomly generated plane orientations,
and the joint intersections. Orientations corresponding to failed
wedges can be highlighted.
Select: Analysis Stereonet
Right-click on the Stereonet View and make sure that the Show
Planes, Show All Poles, Show Intersections and Show Failed options
are all selected. Your screen should look like the following
figure.
Figure 6: Stereonet view showing random poles, intersections and
failed data.
Notice the three sets of data (poles) corresponding to Joint 1,
Joint 2 and the Tension Crack orientations. The set of data in the
lower half of the plot are the joint intersections. The poles and
intersections corresponding to failed wedges are highlighted in
red.
-
Probabilistic Analysis Tutorial 2-24
Swedge v.6.0 Tutorial Manual
Compute (Random Sampling) So far in this tutorial we have used
the default Pseudo-Random sampling option. Pseudo-Random sampling
allows you to obtain reproducible results for a Probabilistic
analysis, by using the same seed value to generate random numbers.
This is why you can obtain the exact values shown in this
tutorial.
We will now demonstrate how different outcomes can result from a
Probabilistic analysis, by allowing a variable seed value to
generate the random input data samples.
Before we start, lets arrange the views as follows:
1. Select the Tile option from the toolbar or the Window menu,
to tile all of the open views.
2. If you have followed the instructions in this tutorial, you
should have four views open as shown in the following figure (Wedge
View, Stereonet View, Joint 1 Dip Histogram, and Scatter Plot).
Note that you will need to decrease the font size of the scatter
plot title and footer, as well as the font size of the histogram
footer, in order for them to fit in the reduced window. Right-click
in the chart window and select Chart Properties. In the Fonts
section, click on Title Font and Footer Font and change the font
size in the dialog that appears.
Figure 7: Tiled views of probabilistic analysis results.
-
Probabilistic Analysis Tutorial 2-25
Swedge v.6.0 Tutorial Manual
If your screen does not look similar to the above figure (e.g.
you have additional views open), then close all views except for
the four noted above, and re-tile the views.
Now go to the Project Settings dialog.
Select: Analysis Project Settings
1. Select the Random Numbers tab, and change the Random Number
Generation method from Pseudo-Random to Random. The Random option
will use a different seed value to generate random numbers, each
time you re-run the Probabilistic analysis. This will result in
different sampling of your input random variables, and different
analysis results (e.g. Probability of Failure) each time you
re-compute.
2. Select the Sampling tab in the Project Settings dialog, and
decrease number of samples from 10,000 to 1000. (This will make the
change in results easier to see on the plots).
3. Select OK in the Project Settings dialog.
4. Select the Compute option from the toolbar.
-
Probabilistic Analysis Tutorial 2-26
Swedge v.6.0 Tutorial Manual
5. Notice that the Histogram plot, Scatter plot, Stereonet view,
and Probability of Failure, are updated with new results.
6. Select Compute repeatedly, and observe how the plots and the
probability of failure are updated each time the analysis is
re-run.
7. Note that the Wedge view does not change when you re-compute,
since by default the Mean Wedge is displayed, (i.e. the wedge based
on the mean Input Data), which is not affected by re-running the
analysis.
8. For this example, if you re-run the analysis several times,
you will find that the Probability of Failure will vary between
about 7 and 11%.
Selecting Random Wedges We will again demonstrate the ability to
pick random wedges by double-clicking on either Histograms or
Scatter plots, and we will also note the effect on the Stereonet
view.
Double-click on the Histogram or Scatter plots repeatedly and
observe the following:
1. The Sidebar displays results for the Picked Wedge (i.e. the
wedge which corresponds to the data location at which you clicked
on the plot).
2. The Wedge View is updated to display the Picked Wedge.
3. The great circles on the Stereonet are updated to display the
planes representing the Picked Wedge.
-
Probabilistic Analysis Tutorial 2-27
Swedge v.6.0 Tutorial Manual
Figure 8: New random sampling, 1000 samples, picked wedge.
-
Probabilistic Analysis Tutorial 2-28
Swedge v.6.0 Tutorial Manual
Filtering by Sliding Mode We will now look at one of the new
features in Swedge 6.0, the ability to filter wedges by sliding
mode. This option is available in both probabilistic and
combination analyses.
Select: Analysis Failure Mode Filter
Click on the Apply failure mode filter checkbox to activate the
filter options. By default all the filters are selected. De-select
the failure modes that you do not want included in the presented
results.
In this tutorial, we will de-select only the Allow sliding on
both joint #1 and joint #2 filter.
Click OK, and the filter will be applied. In this example,
applying the filter produces a No Wedges are Formed message. This
means that all of the wedges generated in this probabilistic
analysis fail by sliding along both joint #1 and joint #2. We can
confirm this by exporting the results to excel and looking at the
failure modes for each wedge.
To export the analysis results, select Statistics > Export
Dataset. Click on Excel, and the analysis results will open in
Excel. Navigate to the Failure Mode column (the last column) and
notice that for each wedge, the failure mode is Sliding on joints
1&2.
That concludes the Swedge Probabilistic Analysis Tutorial.
Probabilistic Analysis TutorialProject SettingsAnalysis
TypeUnitsSampling and Random NumbersProject Summary
Probabilistic Input DataSlopeSlope Length
Upper FaceBench Width
Joint 1 OrientationJoint 2 OrientationJoint 1 StrengthJoint 2
StrengthTension Crack
ComputeProbabilistic Analysis ResultsSidebar Information
PanelWedge DisplayHistogramsMean Safety FactorSelecting Random
WedgesHistograms of Other DataShow Failed Wedges
Scatter PlotsStereonet ViewCompute (Random Sampling)Selecting
Random WedgesFiltering by Sliding Mode