Tutorial 04 Joint Combinations[1] Unwedge

Joint Combinations Tutorial 4-1

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

Import DXF Joint Combinations Combination Analyzer Required Support Pressure Design Factor of Safety Adding support pressure Passive / Active support force

Unwedge v.3.0 Tutorial Manual


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



Input Data Now lets 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.



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.



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.



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.



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.



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 drop-list. 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.



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.



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.

If the safety factor of a wedge is already greater than the Design Factor of Safety, then the Required Support Pressure is zero.

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.



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:

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.

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.

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.



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:

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.

All other Factor of Safety values (representing the most critical wedge for each joint combination) are GREATER THAN the Design Factor of Safety.

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.




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:

Required Support Pressure is calculated assuming a Passive force application.

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.

Joint Combinations TutorialModelInput DataManual Selection of Joint Combinations

Combination AnalyzerRequired Support PressurePassive or Active Support Force Application

Documents

Tutorial 04 Joint Combinations[1] Unwedge