Combination Analysis Tutorial 3-1 Combination Analysis Tutorial It is inherent in the Swedge analysis (when the Block Shape = Wedge), that tetrahedral wedges can only be formed by the intersection of 2 joint orientations with an optional tension crack. Swedge does NOT consider more than 2 joint planes simultaneously in the analysis, for tetrahedral wedges. However, if your input data includes more than 2 possible joint orientations, the Combinations analysis type allows you to analyze all possible combinations of 2 joints. The joint orientation data can be entered or copied directly into Swedge or imported from a Dips file. You may define a single set of orientation data or two sets. If two sets are defined, then the two sets can have different strength properties, and all possible combinations (using one joint from each set), will be analyzed. Topics Covered in this Tutorial Project Settings Combinations Analysis Type Limiting Wedge Size Barton-Bandis Strength Scatter Plot Persistence Scaling Stereonet Bolts
Combination Analysis Tutorial 3-2 In this tutorial we ll look at the analysis of a dataset containing 356 joint orientations. Given 356 measurements of joint orientation, stored inside a Dips data file, we ll look at how to determine all the possible combinations of wedges that could be formed by the 356 joints. We ll look at the practical issues of determining the minimum factor of safety wedge and the use of slope dimensions and persistence information to get a better idea of the distribution of wedge size and safety factor. Finally, we ll determine the bolt force required to guarantee a minimum factor of safety for all combinations. Model Select Project Settings from the toolbar or the Analysis menu. Select: Analysis Project Settings 1. Select the General tab in the Input Data dialog. Select the Combinations Analysis Type. 2. Select Metric, stress as MPa for Units. 3. Press the OK button to exit the Project Settings dialog. Input Data Now let s define the slope and joint properties in the Input Data dialog. Select: Analysis Input Data 1. Select the Slope tab in the Input Data dialog. Enter Dip = 65, Dip Direction = 180, and Height=20m for the Slope. 2. Enter Dip = 0, Dip Direction = 180 for the Upper Face. Since the Dip Direction of the Upper Face is the same as the Slope Face, you could also check the Use Slope Dip Direction checkbox. 3. Select the Joints tab in the Input Data dialog.
Combination Analysis Tutorial 3-3 4. Press the Import From Dips button. Navigate to the Examples > Tutorials folder in your Swedge installation folder and open the Tutorial 03 Combinations.dip file. In the Dips Data Import Options dialog that comes up, keep the defaults and press the OK button. Dips is an industry standard Rocscience program for the plotting of joint orientation data on a stereonet. The above data file contains 356 joint measurements that were entered and saved using Dips. You can also cut and paste orientation data directly from Microsoft Excel, or any other spreadsheet program, if you do not have Dips. You may also manually define the joint sets by typing the data into the grid. 5. Change the Joint Shear Strength Model to Barton Bandis. Enter JRC=7, JCS=50 MPa, and Phir=25 degrees. 6. Press the OK button to save your changes, compute the combinations, and exit the Input Data dialog. Analysis Results After closing the Input Data dialog, computation of all the possible combinations of the 356 joint planes will occur. Figure 1 illustrates the results of this computation. Some of the notable results are: The results of the combination analysis are in the wedge information panel. The results for the wedge with the minimum factor of safety are displayed. The total number of combinations is 63190. The total number of combinations when running one joint set will be n(n-1)/2, where n is the total number of joints (356 in this case). Since not all combinations produce a wedge, the number of valid combinations is displayed. Of these valid wedges, the number of combinations that produce a wedge that is unstable/failed (factor of safety less than 1.0), and the number of combinations that produce a stable wedge (factor of safety greater than or equal to 1.0) are displayed. The wedge combination with the minimum factor of safety, 0.656, is the wedge formed by joints with dip/dip directions 55/204 and 60/178. The wedge weight for this wedge is 16.76 MN.
Combination Analysis Tutorial 3-4 Figure 1: Analysis results for combinations tutorial. Now let s plot the distribution of wedge weight versus safety factor for all the combinations. Select: Statistics Plot Scatter In the Scatter Plot parameters dialog, make sure the X Axis Dataset is set to Safety Factor and the Y Axis Dataset is set to Wedge Weight. Press OK. The following figure shows the distribution of factor of safety versus wedge weight.
Combination Analysis Tutorial 3-5 Figure 2: Scatter plot of factor of safety versus wedge weight. It s obvious from the above figure that some of the combinations produce huge wedges. To see the wedge corresponding to any of the data points in the graph, you simply have to double-click on the data point. Double-Click on the most upper right data point, this is the point with a factor of safety of 100 and a wedge weight around 344 thousand MN. Change to the wedge view using the Analysis > Wedge View menu option, the Wedge View toolbar button, or the wedge view tab at the bottom of the program window. Note the following: As seen in figure 3, the wedge with the maximum weight has a persistence and maximum trace length of over 15 kilometers. Clearly there is no chance that this wedge could exist with joint plane continuity of this magnitude. This size of wedge with a weight of over 344 thousand MN is clearly not possible and some mechanism should exist for limiting the size of wedges that are formed.
Combination Analysis Tutorial 3-6 Figure 3: Wedge with maximum weight. Limiting Wedge Size In the current analysis we ve seen that wedges produced by certain combinations can result in wedges with unrealistic size and extent. Swedge provides a number of methods for limiting the size of wedges that are formed in an analysis. Select: Analysis Input Data 1. Select the Slope tab in the Input Data dialog. 2. Check the Slope Length option and define a Length=30m. The slope length is in the same direction as the strike of the slope. Defining a slope length is just one method you have of limiting the size of the wedges that are formed.
Combination Analysis Tutorial 3-7 3. Check the Bench Width option and define a Width=10m. The bench width, or upper face width, is the extent of the upper face measured perpendicular to the slope crest. This distance is measured in the horizontal plane, NOT in the plane of the upper face if it is dipping at an angle > 0. 4. Check the Minimum Wedge Size option and use 0.001 MN. This option is useful for filtering out very small insignificant sliver shaped wedges that may be formed. 5. Press the OK button to save your changes, compute the combinations, and exit the Input Data dialog. Analysis Results Limited Wedge Size When the program uses options such as slope length and bench width to limit the wedge size, wedges which exceed these limits are scaled down so that they fit the slope dimensions. The wedges are NOT removed from the analysis and set as invalid; they are simply resized so that they fit the dimensions of the slope. In this way, the program always tries to determine a wedge for a given set of joint orientations. Note the following: The minimum factor of safety wedge is completely different. If you look at Figure 1 and the maximum trace length of the unlimited minimum factor of safety wedge, you ll see that it exceeds 70m. This is considerably larger than the slope length of 30m and bench width of 10m used to limit the wedge size. As a result, the unlimited wedge is scaled down in size which has the effect of lowering its weight and increasing its factor of safety. The number of valid, invalid and failed wedges has changed, but not by much. Even with the scaling of wedges that exceed the slope dimensions, some wedges can not be scaled to fit inside the slope.
Combination Analysis Tutorial 3-8 Figure 4: Limited wedge size. Now let s revisit the scatter plot. Click on the Scatter Plot tab at the bottom of the Swedge window. Notice that there are no longer the huge wedges that existed in Figure 2. Figure 5: Scatter plot of factor of safety versus wedge weight (limited wedge size).
Combination Analysis Tutorial 3-9 Limiting Wedge Size Using Joint Persistence Not only can you limit the size of the wedge based on slope dimensions, but you can also use joint persistence (the maximum length of a joint inplane) or trace length information to limit the size of the wedges. Select: Analysis Scale Wedge 1. Check on the checkboxes for both the persistence of joint 1 and joint 2. 2. Enter a value of 10m for the persistence of both joint 1 and joint 2. This will result in wedges where the maximum persistence of either joint plane does not exceed 10m 3. Press OK to run the analysis and exit the Scale Wedge dialog. Analysis Results Limited Wedge using Persistence Tile the wedge view and the scatter plot using the Window > Tile Horizontally menu option. Double-click in the perspective view of the wedge to expand it. You will quickly notice that the using persistence has the following effect: The factor of safety has once again increased to 0.8 The weight of the wedges has decreased considerably. The size of the minimum factor of safety wedge is no longer the maximum size wedge that can fit in the slope. It does not extend the full height, length or width of the slope. It has been scaled down to meet the persistence condition. In the wedge information panel you will see that the maximum persistence is 10m, the value you set in the Scale Wedge dialog. Try double-clicking on a few data points in the scatter plot. You will notice that the persistence values for each of these wedges do not exceed the 10m you defined as the maximum persistence in the Scale Wedge dialog. Use the View > Show Min FS Wedge menu option to once again show the wedge with the minimum factor of safety.
Combination Analysis Tutorial 3-10 Figure 6: Scaled wedge size using persistence To get an idea of the relative distribution of failed to stable combinations, we can plot a histogram of Factor of Safety. Select: Statistics Plot Histogram Leave the Data Type as Safety Factor and press the OK button. A histogram of Safety Factor is displayed.
Combination Analysis Tutorial 3-11 Notice the red bar at the left of the plot which represents the unstable wedges with a factor of safety less than 1.0. Also notice the bar at the far right side of the plot. This bar represents all the wedges with a factor of safety greater than or equal to 100. Swedge truncates the factor of safety at 100 so that all wedges with a factor of safety greater than 100 are given a factor of safety of 100. Now lets change the chart properties to look at a distribution of factor of safety between 0 and 20. 1. Right-click inside the histogram chart view.
Combination Analysis Tutorial 3-12 2. In the context menu that appears, select the Chart Properties option. 3. In the Axes section, set the Horizontal Minimum to 0 and the Horizontal Maximum to 20. The histogram is updated as you make each change. 4. Press Close to close the Chart Properties dialog.
Combination Analysis Tutorial 3-13 Note: Double-clicking in the histogram view will pick the wedge with a safety factor closest to the safety factor at which the mouse lies when you double-click. Stereonet Another tool for visualizing the results of the Combination analysis is the Stereonet view. In the stereonet view, you can plot all the poles of the 356 joint planes. You can also plot all the valid lines of intersections (23448 in this tutorial). You also have the option to highlight the poles and lines of intersection that represent unstable wedges. Select: Analysis Stereonet By default, all the 356 poles are drawn along with the great circles representing the slope, upper face, and the currently set joint 1 and joint 2 that is used to plot the 3D wedge view (the minimum factor of safety wedge). Now lets plot the line of intersections and the failed wedges. Right-click and notice that the Show Intersections and Show Failed options are selected by default. Turn off the Show Planes menu option by selecting it. These options are also available in the View > Stereonet menu.
Combination Analysis Tutorial 3-14 Figure 7: Stereonet view of combination analysis results.
Combination Analysis Tutorial 3-15 Support Another issue is the addition of support to guarantee that all possible wedge combinations will have a factor of safety above some value. For example, we ll look at what bolt force is required to ensure that no wedge has a factor of safety less than 1.2. We ll assume that the bolt is horizontal and trending to the north (directly into the slope face). Select: Analysis Wedge View Select: Support Add Bolt 1. Move the cursor in the perspective wedge view so that it s over the wedge on the slope face. The cursor will change from to when the cursor is over the wedge. Press the left mouse button. 2. In the Bolt Properties dialog, change the plunge of the bolt to 0 degrees. By default the bolt has a capacity of 0.2 MN. Notice with a capacity of 0.2 MN, the bolt increases the factor of safety from 0.8 to over 55. Press OK. A computation of all the wedge combinations will occur. Each wedge will include a 0.2 MN bolt force with a trend/plunge of 0/0. After computation, you will notice that the minimum factor of safety wedge has once again changed and that the minimum factor of safety is 1.6.
Combination Analysis Tutorial 3-16 3. To determine the bolt capacity that will yield a minimum factor of safety of 1.2 choose the Support > Edit Bolt menu option. Move the mouse such that the pick box overlies a portion of the bolt that you just added. The cursor will change color when it is over the bolt. Press the left mouse button to pick the bolt. 4. In the Bolt Properties dialog, select the Factor of Safety option and enter 1.2 for the factor of safety. Press Apply. The minimum factor of safety wedge requires a bolt capacity of 0.09 MN to increase its factor of safety to 1.2. Press OK. After computation of all the combinations, the minimum factor of safety wedge now has a factor of safety of 1.2. Thus a 0.09 MN bolt with a trend of 0/0 will ensure all wedge combinations will have a factor of safety of at least 1.2. Verify this by looking at the scatter plot. You should also note that you may have to use edit bolt a number of times to iterate to a point where the minimum factor of safety wedge is your design factor of safety. This is because different bolt forces can change the minimum factor of safety wedge. This concludes the Combination Analysis tutorial.