Tutorial 03 Combination Analysis

7/30/2019 Tutorial 03 Combination Analysis

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Combination Analysis Tutorial 3-1

Combination Analysis Tutorial

It is inherent in the Swedge analysis, that 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.

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 aredefined, 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

Swedge v.5.0 Tutorial Manual


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In this tutorial well look at the analysis of a dataset containing 356 joint

orientations. Given 356 measurements of joint orientation, stored inside

a Dips data file, well look at how to determine all the possible

combinations of wedges that could be formed by the 356 joints. Well 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,well 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 Project Settings dialog. Select the

Combinations Analysis Type.

2. Select Metric Units.

3. Press the OK button to exit the Project Settings dialog.

Input Data

Now lets 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.



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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 plottingof 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=5000 tonnes/m2, 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 willbe 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 1676 tonnes.



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Figure 1: Analysis results for combinations tutorial.

Now lets 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.



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Figure 2: Scatter plot of factor of safety versus wedge weight.

Its 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 34 million tonnes.

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 apersistence 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 34 million tonnes is

clearly not possible and some mechanism should exist for limiting

the size of wedges that are formed.



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Figure 3: Wedge with maximum weight.

Limiting Wedge Size

In the current analysis weve 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.



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3. Check the Bench Width Analysis 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 the default 0.1

tonnes. 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, youll 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.



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Figure 4: Limited wedge size.

Now lets 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).



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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 in-

plane) 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 extendthe 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.



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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.

Notice the red bar at the left of the plot which represents the unstablewedges 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.



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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.

2. In the context menu that appears, select the Chart Properties

option.

3. In the Axes Range, set the horizontal range from 0 to 20.

4. Press OK to close the Chart Properties dialog, the histogram will

be updated with the new range.

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.



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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 ofintersection 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 select the Show Intersections menu option. Right-click again and

select the Show Failed menu option. Right-click again and turn off the

Show Planes menu option by selecting it. These options are also availablein the View > Stereonet menu.

Figure 7: Stereonet view of combination analysis results.



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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, well look at what bolt force is required to ensure that nowedge has a factor of safety less than 1.2. Well assume that the bolt is

horizontal and trending to the north (directly into the slope face).

Select: AnalysisWedge View

Select: Support Add Bolt

1. Move the cursor in the perspective wedge view so that its 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 0degrees. By default the bolt has a capacity of 20 tonnes. Notice

with a capacity of 20 tonnes, 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 20 tonne 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

3. To determine the bolt capacity that will yield a minimum factor of

safety of 1.2 choose the Support > Edit Bolt menu option. Movethe 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.



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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 9

tonnes to increase its factor of safety to 1.2. Press OK.

After computation of all the combinations, the minimum factor ofsafety wedge now has a factor of safety of 1.2. Thus a 9 tonne 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.

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Tutorial 03 Combination Analysis