Joint Combinations Tutorial
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Joint Combinations Tutorial
It is inherent in the Unwedge analysis, that wedges can only be formed
by the intersection of 3 joint orientations. Unwedge does NOT consider
more than 3 joint planes simultaneously in the analysis.
However, if your input data includes more than 3 possible joint
orientations, the Joint Combinations option allows you to select and
analyze different combinations of 3 joints. The selection of combinations
can be done manually, or the Combination Analyzer can be used to
help you automatically determine which are the most critical
combinations of joints to analyze.
Topics Covered
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Import DXF
Joint Combinations
Combination Analyzer
Required Support Pressure
Design Factor of Safety
Adding support pressure
Passive / Active support force
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Model
Select Project Settings from the toolbar or the Analysis menu.
Select: Analysis → Project Settings
In the Project Settings dialog, make sure that the units are Metric, stress
as tonnes/m2. Select OK.
For this tutorial we will start by reading in a DXF file which contains the
coordinates of the opening section boundary.
Select: File → Import → Import DXF
Navigate to the Examples > Tutorials folder in your Unwedge installation
folder and open the Tutorial 04 tunnel boundary.dxf file.
The model should appear as follows.
Figure 1: Tunnel boundary for joint combinations tutorial.
Switch to the 3D Wedge View.
Select: View → Select View → 3D Wedge View
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Input Data
Now let’s define the tunnel and joint properties in the Input Data dialog.
Select: Analysis → Input Data
1. Select the General tab in the Input Data dialog. Enter Tunnel
Trend = 60, Plunge = 0.
2. Note the Design Factor of Safety (= 1.5 by default). We will be
discussing this later in the tutorial.
3. Select the Joint Orientations tab in the Input Data dialog.
4. By default, 3 joint orientations are already defined. We will keep
the 3 default orientations, and add two more joints for a total of
five.
5. Select the Add button twice in the Input Data dialog. This will
create two new rows in the data entry grid, in which you can
define the orientation of two additional joints.
6. Enter Dip = 65 and Dip Direction = 0 for Joint 4.
7. Enter Dip = 30 and Dip Direction = 135 for Joint 5. The dialog
should look as follows.
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TIP: you can also import plane orientations from a Dips file, by selecting
the Import button in the Input Data dialog. Dips is a program for the
graphical and statistical analysis of orientation data using spherical
projection techniques. See the Rocscience website for details.
8. Select the Joint Properties tab in the Input Data dialog.
9. Enter Phi = 35 and Cohesion = 0 for the default joint property
type (Joint Properties 1).
10. Now go back to the Joint Orientations tab. Note that “Joint
Properties 1” is assigned to all 5 joints (i.e. all joints will be
assumed to have the same strength properties for this example).
11. Notice the Joint Combinations option in the Input Data dialog.
Since we have more than 3 joint orientations defined, the Joint
Combinations option allows you to select which combination of 3
joints will be used for the Unwedge analysis.
Figure 2: Joint combinations option in Input Data dialog.
You can manually cycle through all possible combinations of 3 joints by
clicking on the Combination control. Or you can automatically analyze
all possible joint combinations with the Combination Analyzer option.
We will demonstrate both options.
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Manual Selection of Joint Combinations
You can manually cycle through all possible combinations of 3 joints by
clicking on the Combination control. Each time you click on the up /
down arrow buttons, a new joint combination will be selected. Since we
have 5 possible joints, this results in 10 possible combinations of 3
different joints.
1. Click on the “up” arrow of the Combination control.
2. Each time you click, a different combination of 3 joints is selected,
as indicated by the Joint Combinations selection, and also in the
stereonet at the right of the dialog.
3. The currently selected joint orientations (great circles) will be
highlighted in colour on the stereonet. Joint orientations which
are currently NOT used will be displayed in grey on the
stereonet.
Figure 3: Selected joint orientations highlighted on stereonet.
TIP: the display of unused joints on the stereonet can be turned on/off in
the Display Options dialog, under the General tab, by selecting the Show
Unused Joints on Stereonet checkbox.
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Figure 4: Wedges produced by joint combination 1,3,5.
4. Drag the Input Data dialog over to the side of the screen, so that
you can see the full 3D Wedge view.
5. Now click through all 10 joint combinations, and observe the
different wedges which are formed. A great variety of different
sizes and shapes of wedges can be formed from the 10 joint
combinations. Note: the displayed length of the tunnel
automatically changes according to the size and orientation of the
wedges which are formed.
6. The current analysis results (safety factor, wedge weight etc) are
displayed in the Wedge Information panel in the Sidebar, each
time you select a different joint combination.
The manual selection and analysis of joint combinations is of limited
practical usefulness if you have more than 4 or 5 joint orientations.
Therefore we will now demonstrate the Combination Analyzer option
which automates the process of analyzing multiple joint combinations.
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Combination Analyzer
The Joint Combination Analyzer allows you to automatically carry
out the Unwedge analysis on all possible combinations of 3 joints, if your
input data includes more than 3 possible joint planes.
A summary of analysis results can then be viewed, which allows you to
quickly determine which combination of 3 joints is the most critical (i.e.
you can sort results according to maximum required support pressure,
safety factor, wedge weight etc).
To use the Joint Combination Analyzer:
1. Select the Combination Analyzer button in the Input Data
dialog (or you can select Combination Analyzer from the
Analysis menu).
2. You will see the Combination Analyzer dialog.
3. Select the Compute Combinations button in the Combination
Analyzer dialog to compute the Unwedge analysis for all possible
combinations of 3 joints.
4. A summary of results will be displayed in the dialog. The results
can be sorted according to Required Support Pressure, Factor of
Safety, Wedge Volume, etc, by selecting the desired parameters
from the two drop-list boxes at the top of the dialog. NOTE: we
will discuss the significance of Required Support Pressure in the
next section.
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5. The first list box (Sort By) is the primary sorting criterion. The
parameter in the second list box (Then By) is used as a secondary
sorting criterion if identical results are encountered in the
primary sorting. Select Required Support Pressure in the first
list box, and Wedge Volume in the second list box. You should
see the following results.
6. Results are always sorted from “most critical” to “least critical”.
For example, the first joint combination in the list will always
represent the highest support pressure, the largest wedge volume
or weight, the lowest safety factor, etc, according to the primary
sorting criterion.
7. You can also filter the results with the Wedge Selection droplist. You can choose Perimeter Wedges, End Wedges, All Wedges,
or any individual wedge (e.g. Roof Wedge). NOTE: when the
Wedge Selection represents multiple wedges (e.g. Perimeter
Wedges), the displayed results represent the most critical wedge
for each joint combination.
8. Experiment with the sorting and wedge selection parameters,
and observe the listing of results. When you are finished, reset
the sorting parameters to Required Support Pressure and
Wedge Volume, and Wedge Selection to Perimeter Wedges.
9. Based on these sorting criteria, the most critical wedge is
produced by Joint Combination 2,3,4, with a required Support
Pressure = 8.15 tonnes/m2 and a Wedge Volume = 174 m3.
10. Click on Combination 2,3,4 at the top of the results list. Make
sure the checkbox at the bottom of the dialog is selected (“Use
selected combination when dialog is closed”). Select OK in the
dialog. The wedges for Joint Combination 2,3,4 will now be
displayed in the 3D Wedge View.
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11. Select the Filter List button in the sidebar. In the Wedge
Information Filter dialog, select the Defaults button, and then
select the checkboxes for Wedge Volume and Support Pressure.
Select OK.
12. Look at the results for the Upper Right Wedge (wedge #7) in the
Wedge Information panel. This is the most critical wedge
determined by the Combination Analyzer. Notice the Support
Pressure (8.15 tonnes/m2) and Wedge Volume (174 m3)
correspond to the results computed in the Combination Analyzer
dialog. Notice that the Support Pressure for all other wedges is
less than the required support pressure for wedge #7.
Figure 5: Wedges produced by the most critical joint combination 2,3,4 determined
by Combination Analyzer.
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Required Support Pressure
The Required Support Pressure is the uniform support pressure
applied normal to the excavation boundary, which would be required to
achieve the Design Factor of Safety for a particular wedge.
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If the safety factor of a wedge is already greater than the Design
Factor of Safety, then the Required Support Pressure is zero.
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The Design Factor of Safety is entered in the Input Data dialog
under the General tab. For this tutorial we are using the default
value of Design Factor of Safety = 1.5.
We will now verify the relationship between the Required Support
Pressure calculated by Unwedge, and the Design Factor of Safety, by
applying a support pressure to the excavation boundary.
Switch to the Perimeter Support Design View.
Select: View → Select View → Perimeter Support
Before we add the support pressure, notice that the current safety factor
of the Upper Right Wedge is 0.327, as displayed in the Wedge
Information panel in the sidebar.
Select the Add Pressure option from the Support menu.
Select: Support → Add Pressure
You will see the Add Pressure dialog. Enter a Pressure = 8.15 tonnes/m2.
Select the checkbox “Apply around the whole opening section”. Leave the
Force Application method = Passive. Select OK.
Because we selected the checkbox to “Apply around the whole opening
section”, the support pressure will be automatically applied to the entire
perimeter of the opening section. Your screen should look as follows.
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Figure 6: Support pressure applied to entire perimeter of opening section.
The support pressure is applied as a UNIFORM pressure, normal to each
line segment of the opening section boundary.
Now observe the results in the Wedge Information panel:
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The Factor of Safety for the Upper Right Wedge = 1.500, which is
equal to the Design Factor of Safety. Because we applied the
required support pressure calculated for the unsupported wedge,
the actual factor of safety is now equal to the Design Factor of
Safety.
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The Required Support Pressure for the Upper Right Wedge is
now zero, since no further support pressure is required to achieve
the Design Factor of Safety.
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Because we applied the support pressure to the entire opening
section boundary, the factor of safety for all other wedges is
greater than the Design Factor of Safety. In general, if you apply
the required support pressure for the most critical wedge, all
other wedges will have a factor of safety GREATER THAN the
Design Factor of Safety.
The Required Support Pressure can be used as a starting point for the
design of the actual support system (e.g. bolts and shotcrete). For
example, it can help you to estimate bolt capacity, length and pattern
spacing. In any case, it will take some trial and error to design the actual
support system to achieve the Design Factor of Safety for all wedges.
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Now we will demonstrate that, by applying the Required Support
Pressure for the most critical joint combination, the Factor of Safety for
all wedges produced by all joint combinations is greater than the Design
Factor of Safety. Return to the Combination Analyzer.
Select: Analysis → Combination Analyzer
The results of the Combination Analyzer are not saved after you close the
dialog, so we have to re-compute. Select the Compute Combinations
button in the Combination Analyzer dialog.
Now select Factor of Safety as the primary sorting criterion, and
Required Support Pressure as the secondary sorting criterion, as
shown below.
NOTE:
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The lowest factor of safety = 1.500 (i.e. the Design Factor of
Safety), for the most critical wedge of joint combination 2,3,4.
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All other Factor of Safety values (representing the most critical
wedge for each joint combination) are GREATER THAN the
Design Factor of Safety.
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In all cases, the Required Support Pressure is now zero.
This demonstrates that by applying the Required Support Pressure for
the most critical joint combination, all wedges for all joint combinations
will have a Factor of Safety greater than (or equal to) the Design Factor
of Safety.
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Passive or Active Support Force Application
Finally, remember that we applied the support pressure as a Passive
force (in the Add Pressure dialog). Passive force application means that
the support force acts to increase the resisting forces which stabilize the
wedge. Note:
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Required Support Pressure is calculated assuming a Passive force
application.
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Bolts or shotcrete in Unwedge are always implemented as a
passive support force.
It is also possible to apply an Active support pressure (by selecting Force
Application = Active in the Add Pressure dialog). Active force application
means that the support force acts to decrease the driving forces on the
wedge.
In general, Passive support will always give a lower Factor of Safety
than Active support, and will therefore result in a more conservative
estimate of support design requirements. For more information about
Passive or Active force application, see the Theory section of the Unwedge
help system.
That concludes this tutorial on the analysis of joint combinations with
Unwedge.
Unwedge v.3.0
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