# Advanced Joint Combinations Analysis

This tutorial will perform a Probabilistic Analysis on a geometry with four joints. We will first look at the individual combinations. We will then proceed to compute all of the joint combinations at once.

Topics Covered in this Tutorial:

- Probabilistic Joint Combination Analysis
- Analysis of Individual Joint Combinations
- Analysis of All Joint Combinations

Finished Product:

The finished tutorial can be found in the *Tutorial 11 Advanced Joint Combination.weg5* file located in the *Examples > Tutorials* folder in your **UnWedge** installation folder.

## 1.0 Model

If you have not already done so, run the **UnWedge** program by double-clicking on the **UnWedge** icon in your installation folder. Or from the Start Menu, select **Programs** > **Rocscience** > **UnWedge**. If the **UnWedge** application window is not already maximized, maximize it now so that the full screen is available for viewing the model.

For this tutorial we will start by reading in the file *Tutorial 01 Quick Start.weg5*, which you should find in the *Examples > Tutorials* folder in your **UnWedge** installation folder and open.

### 1.1 PROJECT SETTINGS

- Select
**Project Settings**from the toolbar or the**Analysis**menu. - Ensure
**Units = Metric, stress as MPa**. - Change
**Analysis Type = Probabilistic**. - Navigate to the
**Sampling**tab on the left of the dialog. - Change the
**Number of Samples = 1000**. - Ensure the
**Advanced Location Dependent Scaling**box is checked. - Select
**OK**.

### 1.2 INPUT DATA

- Select
**Input Data**from the toolbar or the**Analysis**menu. - Navigate to the
**Joint Orientations**tab. - Select the
**Add**button to add a new joint. - Change
**Joint 4****Dip =****60**and**Dip Direction =****90**. - Change all four joint
**Properties =****smooth joint**as shown. - Navigate to the
**Joint Properties**tab. - Select the
**rough joint**tab on the left of the dialog. - Select the
**Delete**button to delete the**rough joint**.

Only the**smooth joint**should be displayed on the left of the dialog. - Change the
**Joint Structure****Continuity**from**Infinite**to**Persistence**. Keep the default**Persistence = 5 m**. - Select
**OK**.

### 1.3 JOINT PROPERTIES

- Select
**Statistics > Joint Properties**to open the**Joint Properties Statistics**dialog. - Select
**Add**. - Enter the following:
**Property**=**Persistence****Distribution**=**Exponential****Mean**=**5****Rel. Min**=**4****Rel. Max**=**10** - Select
**OK**.

## 2.0 Combination 1: Joints 1,2,3

- Select
**Input Data**from the toolbar or the**Analysis**menu. - Navigate to the
**Joint Orientations**tab. - Note under
**Joint Combination**that we are looking at**Combination 1 of 4**.**Combination 1**uses**Joints 1**,**2**, and**3**. - Select
**Cancel**.

We are now ready to compute.

- Select
**Compute**on the toolbar or the**Analysis**menu. - Switch to the
**Probability View**.

You should see the following:

From the **Sidebar**, we can see that we are currently looking at the **Maximum Support Pressure**. Most of the roof segments have a **Maximum Support Pressure** of **0.032 MPa**.

- Select
**New Window**on the toolbar or the**Window**menu.

The**Probability View**should now be vertically tiled with the**3D Wedge View**. - Click on one of the
**0.032**roof segments in the**Probability View**to see the resulting**3D Wedge View**. - Close the
**3D Wedge View**and maximize the**Probability View**. - Right-click on one of the
**0.032**roof segments (e.g.,**Segment 10**) and select**Plot Histogram**. - Select
**OK**.

You should see the following Histogram:

**NOTE:** Notice that the last column of the histogram is very high. This means there is a high frequency of wedges with a support pressure of approximately 0.031 MPa. The reason for this anomaly is due to the probabilistic range of our persistence variable. In the **Joint Properties** dialog we gave persistence a range between** 1 m** and **15 m**. Whenever the persistence reaches a length such that the resulting wedge is bigger than the tunnel itself, **UnWedge** scales that wedge down to the maximum size for the tunnel.

Now that we have studied the results of the first joint combination, we will go on to look at the second.

Close the Histogram view.

## 3.0 Combination 2: Joints 1,2,4

- Select
**Input Data**from the toolbar or the**Analysis**menu. - Navigate to the
**Joint Orientations**tab.

On the bottom of the dialog, we can see that we are looking at**Combination 1 of 4**total combinations. - Click on the up arrow to go to
**Combination 2**.

This combination takes joints 1, 2, and 4 into account. - Select
**OK**. - Select
**Compute**on the toolbar or the**Analysis**menu. - Switch to the
**Probability View**.

The**Maximum Support Pressure**on the roof now varies between**0.057 MPa**and**0.086 MPa**. - Select
**New Window**on the toolbar.

The **Probability View** should now be vertically tiled with the **3D Wedge View**, as shown.

- Close the
**3D Wedge View**and maximize the**Probability View**. - Right-click on one of the roof segments (e.g.,
**Segment 12**) and select**Plot Histogram**in the popup menu. - Select
**OK**in the dialog.

You should see the following Histogram:

Note that in this combination, unlike the previous one, the **Support Pressure** follows a generally exponential distribution without any extreme anomalies. This is because, in this combination, the maximum persistence is never met so **UnWedge** does not have to scale down a large number of wedges.

We will now go on to look at the third joint combination.

Close the Histogram view.

## 4.0 Combination 3: Joints 1,3,4

- Select
**Input Data**from the toolbar or the**Analysis**menu. - Navigate to the
**Joint Orientations**tab.

Under**Joint Combinations**, we can see that we are looking at**Combination 2 of 4**total combinations. - Click on the up arrow to go to
**Combination 3**. This combination takes**Joints 1**,**3**, and**4**into account. - Select
**OK**. - Select
**Compute**on the toolbar or the**Analysis**menu. - Switch to the
**Probability View**.

The**Maximum Support Pressure**on the roof segments now varies between**0.005 MPa**and**0.021 MPa**. - Select
**New Window**on the toolbar or**Window**menu.

The**Probability View**should now be vertically tiled with the**3D Wedge View**. - Click on one of the
**0.005 MPa**segments to view the resulting wedges.

- Close the
**3D Wedge View**and maximize the**Probability View**. - Right-click on one of the
**0.005 MPa**roof segments (e.g.,**Segment 15**) and select**Plot Histogram**on the popup menu. - Select
**OK**in the dialog.

You should see the following Histogram:

We will now go on to look at the fourth joint combination.

Close the Histogram view.

## 5.0 Combination 4: Joints 2,3,4

- Select
**Input Data**from the toolbar or the**Analysis**menu. - Navigate to the
**Joint Orientations**tab.

Under**Joint Combinations**, we can see that we are looking at**Combination 3 of 4**total combinations. - Click on the up arrow to go to
**Combination 4**. This combination takes**Joints 2**,**3**, and**4**into account. - Select
**OK**. - Select
**Compute**on the toolbar or the**Analysis**menu. - Switch to the
**Probability View**.

The**Maximum Support Pressure**on the roof segments now varies between**0.011 MPa**and**0.024 MPa**. - Select
**New Window**on the toolbar or**Window**menu.

The**Probability View**should now be vertically tiled with the**3D Wedge View**. - Click on one of the
**0.011 MPa**segments (e.g.,**Segment 8**) to view the resulting wedges. - Close the
**3D Wedge View**and maximize the**Probability View**. - Right-click on one of the
**0.011 MPa**roof segments (e.g.,**Segment 8**) and select**Plot Histogram**on the popup menu. - Select
**OK**in the dialog.

You should see the following Histogram:

Close the Histogram view.

## 6.0 All Joint Combinations

We have seen different results from each combination of joints. We will now show how we can look at all four joint combinations at once.

We should note here that the number of samples we entered in the **Project Settings** dialog at the beginning of the tutorial (1000) was the number of samples used for each combination. That is to say, for **Joint Combination 1**, 1000 wedge orientations were computed, and the **Maximum Support Pressure** from all these samples was studied in the **Probability View**. Similarly, for **Joint Combination 2**, 1000 samples were computed, and the **Maximum Support Pressure** from all these samples was studied.

In this section, we will look at all four joint combinations at once. Because there are four different combinations of joints, **UnWedge** will divide the number of samples by four. Therefore, for **Joint Combination 1**, 1000/4 = 250 samples will be computed. Similarly, 250 samples will be computed for **Joint Combination 2**, and so on. For the sake of consistency, and in order to have comparable results, we want 1000 samples to be computed for each joint combination as before. Therefore, we will use a sampling size of 4000.

- Select
**Project Settings**from the toolbar or the**Analysis**menu. - Click on the
**Sampling**tab and change the**Number of Samples =****4000**. - Select
**OK**. - Select
**Input Data**from the toolbar or the**Analysis**menu. - Navigate to the
**Joint Orientations**tab.

Under**Joint Combinations**, we can see that we are looking at**Combination 4**out of the four total combinations. - Select the
**Compute All Joint Combinations (Probabilistic)**checkbox. - Select
**OK**. - Select
**Compute**on the toolbar or the**Analysis**menu. - Switch to the
**Probability View**.

You should see the following:

The **Maximum Support Pressure** on the roof segments now varies between **0.057 MPa** and **0.086 MPa**. Notice that the **0.086 MPa** value is the **Maximum Support Pressure** from **Joint Combination 2**; it is also the maximum of the pressures we saw in the four different joint combinations, for this segment. For the right-most segment, notice that the **0.057 MPa** value is the **Maximum Support Pressure** we saw from all the combinations for this segment. This demonstrates that we are now looking at the **Maximum Support Pressure** from all of the possible joint combinations.

- Right-click on one of the
**0.086 MPa**roof segments (e.g.,**Segment 9**) and select**Plot Histogram**. - Select
**OK**. - Select
**New Window**.

The**Probability View**should now be vertically tiled with the**3D Wedge View**and the Histogram. - Minimize the
**Probability View**and select**Tile Vertically**on the toolbar or**Window**menu.

You should see the following on your screen.

Recall that **Joint Combination 1** gave us a maximum support pressure of **0.032 MPa** for this segment.

Double-click on the Histogram where the **Support Pressure** is about **0.032 MPa**. The resulting **3D Wedge View** is almost identical to the one we saw in the **Joint Combination 1** section of the tutorial. From the **Sidebar** we can see that the exact pressure in the figure is **0.033 MPa**.

Now, double-click on the Histogram where the **Support Pressure** is maximum (**0.086 MPa**). You will notice that the resulting wedges are identical to those we saw in **Joint Combination 2**. Recall the maximum support pressure on this roof segment for **Combination 2** was also **0.086 MPa**.

It will be left as an exercise for the user to examine the wedges resulting from double-clicking on the Histogram on the same pressures seen in **Joint Combination 3** and **4**.

In conclusion, using the **Compute All Joint Combinations (Probabilistic)** checkbox, allows the user to view the results from all possible joint combinations at once.

This concludes the tutorial. You are now ready for the next tutorial, Tutorial 12 - Batch Compute in UnWedge.