Manual Phase 2 Completo

Quick Start Tutorial

1-1

Quick Start Tutorial 10 MPa

20 MPa 30 °

0 , 15

-5 , 10

5 , 10

-5 , 0

5,0

external boundary expansion factor = 3

This “quick start” tutorial will demonstrate some of the basic features of Phase2 using the simple model shown above. You will see how quickly and easily a model can be created and analyzed with Phase2. The finished product of this tutorial can be found in the Tutorial 01 Quick Start.fez file, located in the Examples > Tutorials folder in your Phase2 installation folder.

Model If you have not already done so, run the Phase2 Model program by double-clicking on the Phase2 icon in your installation folder. Or from the Start menu, select Programs → Rocscience → Phase2 7.0 → Phase2. If the Phase2 application window is not already maximized, maximize it now, so that the full screen is available for viewing the model. Note that when the Phase2 Model program is started, a new blank document is already opened, allowing you to begin creating a model immediately.

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Project Settings The Project Settings dialog is used to configure the main analysis parameters for your Phase2 model. Although we do not need to customize the Project Settings for this tutorial, let’s take a look at the dialog.

Select: Analysis → Project Settings

Since we will be using Metric (MPa) units for this tutorial, you should make sure that the Units option is set to Metric, stress as MPa, under the General tab. This determines the units of length, force, stress and unit weight used in the analysis. NOTE: Phase2 remembers the most recently selected Units in Project Settings, and uses this as the setting for all new documents. Select the Stages tab, and note that we will be analyzing a single stage model. (Multi-stage modeling is covered in the next tutorial). Select the Project Summary tab and enter Quick Start Tutorial as the Project Title. Do not change any other settings in the dialog. Select OK.

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Entering Boundaries First create the excavation as follows:

Select: Boundaries → Add Excavation Enter the following coordinates in the prompt line at the bottom right of the screen. Note: press Enter at the end of each line, to enter each coordinate pair, or single letter text command (e.g. “a” for arc). Enter vertex [t=table,i=circle,esc=cancel]: -5 10 Enter vertex [t=table,a=arc,i=circle,u=undo,esc=cancel]: -5 0 Enter vertex [...]: 5 0 Enter vertex [...]: 5 10 Enter vertex [...]: a You will see the Arc Options dialog. Select the 3 Points on Arc option, Number of Segments = 20. Select OK. Enter second arc point [u=undo,esc=cancel]: 0 15 Enter third arc point [u=undo,esc=cancel]: c

By entering “c” at the last prompt, the arc closes on the first point of the excavation. Note that arcs in Phase2 are actually made up of a series of straight line segments. The Arc option and many other useful shortcuts are also available in the right-click menu. Select Zoom All (or press the F2 function key) to zoom the excavation to the center of the view. Now we will create the external boundary. In Phase2, the external boundary may be automatically generated, or user-defined. We will use one of the ‘automatic’ options.

Select: Boundaries → Add External You will see the Create External Boundary dialog. We will use the default settings of Boundary Type = Box and Expansion Factor = 3, so just select OK, and the external boundary will be automatically created.

The boundaries for this example have now been entered.

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Meshing The next step is to generate the finite element mesh. In Phase2, meshing is a simple two-step process. First you must Discretize the boundaries, and then the Mesh can be generated. You can also configure various Mesh Setup parameters before generating the mesh. We will do this first, although default parameters are in effect if you do not use the Mesh Setup option.

Select: Mesh → Mesh Setup

9 Enter: Mesh Type = Graded Elem. Type = 3 Noded Tri. Gradation Factor = 0.1 9 # Excavation Nodes = 60

Enter the # of Excavation Nodes = 60, and select OK. Now discretize the boundaries.

Select: Mesh → Discretize The discretization of the boundaries, indicated by red crosses, will form the framework for the finite element mesh. Notice the summary of discretization shown in the status bar, indicating the actual number of discretizations for each boundary type. Discretizations: Excavation=59 External=49

Note that the number of excavation discretizations is 59, but we entered 60 in the Mesh Setup dialog. Don’t worry, this is normal. Due to the nature of the discretization process, the actual number will not always be the same as the number you entered. If you are not happy with a given discretization, it can always be customized using a variety of custom discretization options (see the Phase2 help topics for more information). Now generate the finite element mesh, by selecting the Mesh option from the toolbar or the Mesh menu.

Select: Mesh → Mesh

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The finite element mesh is generated, with no further intervention by the user. When finished, the status bar will indicate the number of elements and nodes in the mesh: ELEMENTS = 764 NODES = 436

If you have followed the steps correctly so far, you should get the same number of nodes and elements as indicated above. TIP: you can Discretize and Mesh in one step, by selecting the Discretize and Mesh option.

Boundary Conditions For this tutorial, no boundary conditions need to be specified by the user. The default boundary condition will therefore be in effect, which is a fixed (i.e. zero displacement) condition for the external boundary.

Field Stress Field Stress determines the initial in-situ stress conditions, prior to excavation. In Phase2 you can define either a Constant field stress or a Gravity field stress. For this tutorial we will use a Constant field stress.

Select: Loading → Field Stress

9 Enter: Fld. Str. Type = Constant 9 Sigma 1 = 20 Sigma 3 = 10 Sigma Z = 10 9 Angle = 30

Enter Sigma 1 = 20, Angle = 30, and select OK. Notice that the small “stress block” in the upper right corner of the view indicates the relative magnitude and orientation of the field stress you entered. Note the definition of the Constant Field Stress Angle in Phase2 – the Angle is the counter-clockwise angle between the Sigma 1 direction and the horizontal axis.

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Properties We will now define the properties of the rock mass.

Select: Properties → Define Materials With the first tab selected, enter the following properties:

9 Enter: 9 Name = rock mass Init.El.Ld.=Fld Stress Only Material Type = Isotropic Young’s Modulus = 20000 9 Poisson’s Ratio = 0.2 Failure Crit. = Mohr Coul. Material Type = Elastic Tens. Strength = 0 Fric. Angle (peak) = 35 9 Cohesion (peak) = 12

Enter Name = rock mass, Poisson’s ratio = 0.2 and cohesion = 12 MPa, and select OK. Since you entered properties with the first (Material 1) tab selected, you do not have to Assign these properties to the model. Phase2 automatically assigns the Material 1 properties for you. If you define properties with the Material 2, Material 3, Material 4 etc. tabs (e.g. for a multiple material model), then you will have to use the Assign option to assign these properties. We will deal with assigning properties in Tutorial 2.

Excavating We have one last thing to do to complete our simple model. Although we do not have to assign material properties, we do have to use the Assign Properties option, in order to excavate the material from within the excavation boundary. This is easily done with a few mouse clicks.

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Select: Properties → Assign Properties You will see the Assign Properties dialog, shown in the margin. 1. Use the mouse to select the Excavate button at the bottom of the Assign Properties dialog. 2. A small cross-hair icon ( + ) will appear at the end of the cursor. Place the cross-hair anywhere within the excavation boundary, and click the left mouse button. 3. The elements within the excavation boundary will disappear, indicating that the region within the boundary is now “excavated”. 4. That is all that is required. Select the X button at the upper right corner of the Assign dialog (or press Escape twice, once to exit the “excavate” mode, and once to close the dialog). The Assign dialog will be closed, and the excavation will be complete. We are now finished with the modeling, the model should appear as shown below.

Figure 1-1: Finished model – Phase2 Quick Start Tutorial TIP: assigning can also be done using a right-click shortcut (right-click in the desired area and the popup menu will have an Assign Material submenu).

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Compute Before you analyze your model, save it as a file called quick.fez. (Phase2 files have an .fez filename extension.)

Select: File → Save Use the Save As dialog to save the file. You are now ready to run the analysis.

Select: Analysis → Compute The Phase2 Compute engine will proceed in running the analysis. When completed, you will be ready to view the results in Interpret.

Interpret To view the results of the analysis:

Select: Analysis → Interpret This will start the Phase2 Interpret program.

Principal Stress By default, after a Phase2 stress analysis, you will always see a contour plot of the major principal stress Sigma 1, when a file is opened in Interpret. This is shown in the figure below.

Figure 1-2: Contours of Major Principal Stress

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Notice the effect of the field stress orientation (30 degrees from horizontal) on the Sigma 1 contours. Now let’s zoom in to get a closer look at the stress contours around the excavation. An easy shortcut to zoom in to your excavation(s), is to use the Zoom Excavation option.

Select: View → Zoom → Zoom Excavation Notice the high stresses at the upper left and lower right of the excavation. The maximum Sigma 1 is at the sharp corner at the lower right.

Stress Trajectories Now toggle the display of principal stress trajectories on, by selecting the Stress Trajectories toolbar button. The principal stress trajectories are shown as small cross icons where the long axis of the cross is oriented in the direction of the major in-plane principal stress (Sigma 1) and the short axis is the direction of the minor in-plane principal stress (Sigma 3).

Figure 1-3: Display of principal stress trajectories Toggle off the display of stress trajectories by re-selecting the Stress Trajectories toolbar button. (Stress Trajectories can also be turned on or off in the Display Options dialog.)

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Creating a Query We can graph the stress on the boundary or at any other location in the rock mass using the Query option. A Query allows you to view and plot analysis results based on the current contour data. (Queries are discussed in more detail in later tutorials). 1. Right-click on the excavation boundary and select Query Boundary from the popup menu. 2. Select OK in the dialog and a Query will be created for the boundary (you will see data values displayed along the boundary). 3. Right-click again on the excavation boundary, and select Graph Data from the popup menu. 4. Select Create Plot in the dialog, and you should see the following graph.

Figure 1-4: Principal stress on excavation boundary The maximum stresses on the graph correspond to the maximum stresses on the Sigma 1 contour plot. Close the query graph. Right click on the excavation boundary and select the Queried Values option, to turn off the display of the query values along the boundary. If you see the number 1 displayed on the boundary, this is the query ID number, which can also be turned on or off in the right-click menu.

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Strength Factor Let’s now look at the Strength Factor contours. Select Strength Factor from the data list in the toolbar.

Select: Select Zoom All (or the F2 function key) to view the entire model.

Select: View → Zoom → Zoom All Let’s change the number of contour intervals, so that we get even numbered intervals.

Select: View → Contour Options In the Contour Options dialog, select the Custom Range option and enter the Number (of contour intervals) = 7, and select Done. (Note: Contour Options is also available in the default right-click menu).

Figure 1-5: Strength Factor Contours. Notice that the minimum strength factor contour interval is between 1 and 2. Therefore, based on this elastic analysis, no failure is to be expected for this model. Let’s verify this with the Query option. Right-click on the excavation boundary (which still has the query applied), and select Graph Data from the popup menu. You should see the following graph.

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Figure 1-6: Strength Factor around excavation boundary. As can be seen from the graph, the Strength Factor at the boundary is greater than 1 at all points (although it is close to 1 at two locations, which correspond to the high stress regions shown in Figure 1-4). Because the strength factor is greater than 1 throughout the model, no additional information would be gained from a plastic analysis of this model (i.e. if you defined the rock mass material type as plastic, the analysis results would be the same). Close the Strength Factor graph. Right click on the excavation boundary and select Delete Query to remove the query from the model.

Displacements Let’s look at the displacements. Select Total Displacement from the data list in the toolbar.

Select: The total displacement contours will be plotted, and the status bar will indicate the maximum displacement for the entire model (about 11 mm). Maximum Total Displacement = 0.01155 m

Now select Zoom Excavation again.

Select: View → Zoom → Zoom Excavation As can be seen from the contours, the maximum displacement is occurring at the excavation walls. Now let’s display the deformation vectors and the deformed boundaries.

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Select the Deformed Boundaries and Deformation Vectors buttons in the toolbar. The deformed shape of the excavation boundaries is graphically illustrated by the use of these options. The deformation is magnified by a scale factor, which can be user-defined in the Display Options dialog. This is left as an optional exercise. In the figure below, the maximum deformation was set to 8 mm, as displayed on the screen.

Many of the Display Options are also available in the toolbar.

Figure 1-7: Total displacement contours, with deformation vectors and deformed boundaries displayed. Toggle off the deformation vectors and deformed boundaries by reselecting the corresponding buttons in the toolbar. Contour Options is available in the right-click menu.

Now we will change the number of contour intervals, and add some contour labels. Right-click the mouse and select Contour Options. In the Contour Options dialog, change the Number (of contour intervals) to 6. Select Done.

Contour Labels Now let’s add some labels to the contours, to identify the values represented by each contour boundary.

Select: Tools → Add Tool → Label Contour

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A cross-hair cursor will appear on the screen. Click the left mouse button anywhere on or near a contour boundary, and a contour label will be placed at that point. The following figure illustrates what the display might look like after you have added some contour labels to the model. When you have added all of the labels that you wish, press the Esc key or right-click and select Cancel.

Figure 1-8: Contour labels added to displacement contour plot. NOTE: the number of decimal places and number format used for the contour labels, can be customized in the Legend Options dialog. This is available in the View menu or by right-clicking on the Legend. The style (font size etc) used for the Contour Labels can be customized by doubleclicking on a Contour Label.

Data Tips A useful feature of Phase2 are the popup Data Tips which allows the user to obtain model and analysis information, by simply placing the mouse cursor over any model entity or location on the screen. To enable Data Tips, click on the box on the Status Bar (at the bottom of the Phase2 application window), which says Data Tips. When you click on this box, it will toggle through 4 different Data Tip modes (including Off mode). Click on this box until it displays Data Tips Max.

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Now move the mouse cursor over the model, and you will see that the material properties of the rock mass are displayed when the cursor is placed anywhere within the material. Place the cursor over the Stress Block in the upper right corner of the screen, and the Field Stress parameters will be displayed. Click on the Data Tips box in the Status Bar, until it displays Data Tips Query. This mode allows you to obtain exact interpolated values of data at any point on the contour plots. Move the mouse around the contour plot, and notice that the exact value of the currently contoured variable is displayed, as well as the exact location coordinates.

Click on the Status Bar and toggle Data Tips Off. Data Tips can also display a variety of other information, including support properties etc. The user is encouraged to experiment with this option in later tutorials. Data Tips can also be toggled using the Data Tips sub-menu in the View menu.

Info Viewer The Info Viewer option in the Analysis menu or the toolbar, displays a summary of Phase2 input parameters and analysis results, in its own view.

Select: Analysis → Info Viewer

Figure 1-9: Phase2 Info Viewer listing.

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The Info Viewer information can be copied to the clipboard using the Copy option in the toolbar or the Edit menu, or by right-clicking in the view and selecting Copy. From the clipboard, the information can be pasted into word processing programs for report writing. The Info Viewer can also be saved to an html or text file, using the Save option in the right-click menu or the File menu. Close the Info Viewer view, by selecting the X in the upper right corner of the view.

Drawing Tools In the Tools menu or the toolbar, a wide variety of drawing tools are available for customizing views. We will briefly demonstrate some of these options. First, let’s delete the contour labels we added previously.

Select: Tools → Delete Tools Right-click the mouse and select Delete All from the popup menu. Select OK in the dialog which appears, and all contour labels will be deleted. Now press F2 to Zoom All. Let’s add an arrow to the view. Select the Arrow option from the toolbar or the Tools menu.

Select: Tools → Add Tool → Arrow Click the mouse at two points on the screen, to add an arrow pointing anywhere within the rock mass. Now let’s add some text.

Select: Tools → Add Tool → Text Box Click the mouse at a point near the tail of the arrow. You will see the Add Text dialog. The Add Text dialog allows you to type any text and add it to the screen. The Auto-Text option can be used to annotate the model with pre-formatted input and output data. For example: 1. In the Add Text dialog, select the Material Properties “+” box (NOT the checkbox). Then select the Material: rock mass “+” box. Then select the Material: rock mass checkbox. 2. Now select the Insert Auto-text button. The Material Properties for the rock mass will be added to the editing area at the left of the Add Text dialog.

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3. Now select OK. The text is added to the view, and your screen should look similar to Figure 1-10.

Figure 1-10: Auto-text and arrow added to view. TIP: after adding a drawing tool, you can easily change the position, size or formatting style, by clicking on the tool with the mouse. This is described in the next section. Many other drawing tools are available in Phase2, including options which allow you to add dimensioning, dynamic text, calculate areas of polygons, etc. The user is encouraged to experiment with the many different capabilities of the Drawing Tools in Phase2.

Editing Drawing Tools We will now describe the following properties of all drawing tools added through the Tools menu options: Right-click If you right-click the mouse on a drawing tool, you will see a popup menu, which makes available various editing options. For example: •

right-click on the arrow. Delete, Format and Copy options are available in the popup menu.

•

right-click on the text box. Various options are available, including Delete, Format and Edit Text.

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Single-click If you single-click the left mouse button on a drawing tool, this will “select” the tool, and you will see the “control points” highlighted on the tool. While in this mode: •

You can click and drag the control points, to re-size the tool.

•

If you hover the mouse over any part of the drawing tool, but NOT on a control point, you will see the four-way arrow cursor, allowing you to click and drag the entire drawing tool to a new location.

•

You can delete the tool by pressing Delete on the keyboard.

•

You can create a copy of the tool by pressing Ctrl-C on the keyboard, or by selecting Copy from the toolbar or the Edit menu.

Double-click If you double-click the mouse on a drawing tool, you will see the Format Tool dialog. The Format Tool dialog allows you to customize styles, colours etc. Only the options applicable to the clicked-on tool, will be enabled in the Format Tool dialog. (Note: this is the same Format option available when you right-click on a tool). It is left as an optional exercise, for the user to experiment with the various editing options that are available for each Tools option.

Saving Drawing Tools To save drawing tools, select the Save option from the toolbar or the File menu. This will save all drawing tools, so that next time you open the file, the tools will re-appear on the view. If you close a file in Interpret, you will automatically be prompted to save the drawing Tools, if you have not already saved them.

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Exporting Images In Phase2, various options are available for exporting image files.

Export Image File The Export Image option in the File menu or the right-click menu, allows you to save the current view directly to one of four image file formats: •

JPEG (*.jpg)

•

Windows Bitmap (*.bmp)

•

Windows Enhanced Metafile (*.emf)

•

Windows Metafile (*.wmf)

Copy to Clipboard The current view can also be copied to the Windows clipboard using the Copy option in the toolbar or the Edit menu. This will place a bitmap image on the clipboard which can be pasted directly into word or image processing applications.

Black and White Images (Grayscale) The Grayscale option, available in the toolbar or the View menu, will automatically convert the current view to Grayscale, suitable for black and white image requirements. This can be useful when sending images to a black and white printer, or for capturing black and white image files. That concludes this ‘quick start’ tutorial. To exit the Interpret program:

Select: File → Exit

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Materials & Staging Tutorial ROCKMASS

15 , 80

Access drifts

ORE

20 MPa

30 MPa

35 , 80

Stope

0 , 20

20 ,20

This tutorial will demonstrate the use of multiple materials and staging in Phase2, using material and stage boundaries. The model represents a longhole stope in an orebody which has different properties than the surrounding rock mass. The model will consist of a total of four stages – the stope will be excavated in the first three stages, and will be backfilled in the fourth stage. Support (cables) will also be installed from the access drifts to the hangingwall. Support installation is covered in more detail in the Phase2 Support tutorial. The finished product of this tutorial can be found in the Tutorial 02 Materials and Staging.fez file, located in the Examples > Tutorials folder in your Phase2 installation folder.

Model If you have not already done so, run the Phase2 Model program by double-clicking on the Phase2 icon in your installation folder. Or from the Start menu, select Programs → Rocscience → Phase2 7.0 → Phase2.

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Project Settings Whenever we are creating a staged model, the first thing we should always remember to do is define the number of stages in Project Settings, since this affects subsequent modeling options.

Select: Analysis → Project Settings First select the General tab and make sure that the Units option is set to Metric, stress as MPa. This determines the units of length, force, stress and unit weight used in the analysis. Select the Stages tab. Set the Number of Stages = 4, to create a total of four stages. Change the name of the fourth stage to backfill, as shown below.

Select the Project Summary tab and enter Materials and Staging Tutorial as the Project Title. Do not change any other settings in the dialog. Select OK.

Entering Boundaries Next we will define the stope and the three access drifts using Excavation boundaries.

Select: Boundaries → Add Excavation Enter Enter Enter Enter Enter Enter

vertex vertex vertex vertex vertex vertex

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[t=table,i=circle,esc=cancel]: 35 80 [...]: 15 80 [...]: 10 60 [...]: 5 40 [...]: 0 20 [...]: 20 20

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Enter vertex [...]: 25 40 Enter vertex [...]: 30 60 Enter vertex [...,c=close,esc=cancel]: c

Press F2 to Zoom All, to center the excavation in the view.

Select: Boundaries → Add Excavation Enter Enter Enter Enter Enter

vertex vertex vertex vertex vertex

[t=table,i=circle,esc=cancel]: 0 80 [...]: -2.5 80 [...]: -2.5 77.5 [...]: 0 77.5 [...,c=close,esc=cancel]: c

Select: Boundaries → Add Excavation Enter Enter Enter Enter Enter

vertex vertex vertex vertex vertex

[t=table,i=circle,esc=cancel]: -5 60 [...]: -7.5 60 [...]: -7.5 57.5 [...]: -5 57.5 [...,c=close,esc=cancel]: c

Select: Boundaries → Add Excavation Enter Enter Enter Enter Enter

vertex vertex vertex vertex vertex

[t=table,i=circle,esc=cancel]: -10 40 [...]: -12.5 40 [...]: -12.5 37.5 [...]: -10 37.5 [...,c=close,esc=cancel]: c

Now let’s add the two stage boundaries so that the stope can be excavated in three stages. Stage boundaries can be used within excavations, for defining intermediate excavation boundaries.

Select: Boundaries → Add Stage Before we start, right-click the mouse and make sure the Snap option is enabled, so that we can snap the stage boundary vertices to the existing excavation vertices. Enter vertex click on the Enter vertex vertex at 30 Enter vertex select Done

[t=table,i=circle,esc=cancel]: use the mouse to excavation vertex at 10 60 [...]: use the mouse to click on the excavation 60 [...,enter=done,esc=cancel]: right-click and

Notice that when you are in Snap mode, if you hover the cursor over a vertex, the cursor changes to a circle, to indicate that you will snap exactly to a vertex, when you click the mouse.

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Select: Boundaries → Add Stage Enter vertex click on the Enter vertex vertex at 25 Enter vertex select Done

[t=table,i=circle,esc=cancel]: use the mouse to excavation vertex at 5 40 [...]: use the mouse to click on the excavation 40 [...,enter=done,esc=cancel]: right-click and

Since we planned ahead and added extra vertices to the stope where the stage boundaries would be, all we had to do was snap to these vertices to add the stage boundaries. If the stage boundary vertices were not there, we could have still added the stage boundaries using the automatic boundary intersection capability of Phase2, which would automatically add the required vertices. This is demonstrated below with the material boundaries. Next, let’s add the external boundary.

Select: Boundaries → Add External

We will use the default settings of Boundary Type and Expansion Factor so just select OK, and the external boundary will be automatically created. We will now add the material boundaries, which will define the rest of the orebody outside of the excavation.

Select: Boundaries → Add Material You should still be in Snap mode. Enter click Enter Enter

vertex on the vertex vertex

[t=table,i=circle,esc=cancel]: use the mouse to excavation vertex at 15 80 [...]: enter the point 55 240 in the prompt line [...,enter=done,esc=cancel]: press Enter

Select: Boundaries → Add Material Enter click Enter Enter

vertex on the vertex vertex

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Select: Boundaries → Add Material Enter click Enter Enter

vertex on the vertex vertex

[t=table,i=circle,esc=cancel]: use the mouse to excavation vertex at 0 20 [...]: enter the point -40 -140 in the prompt line [...,enter=done,esc=cancel]: press Enter

Select: Boundaries → Add Material Enter click Enter Enter

vertex on the vertex vertex

[t=table,i=circle,esc=cancel]: use the mouse to excavation vertex at 20 20 [...]: enter the point –20 -140 in the prompt line [...,enter=done,esc=cancel]: press Enter

You have just added four material boundaries, representing a continuation of the orebody above and below the excavation. Note the following important point: The second point you entered for each of the four material boundaries was actually slightly outside of the external boundary. Phase2 automatically intersected these lines with the external boundary, and added new vertices. This capability of Phase2 is called ‘automatic boundary intersection’, and is useful whenever exact intersection points are not known, or whenever new boundaries cross existing boundaries where vertices were not previously defined. Since we knew the slope of the material boundaries but not the exact intersection with the external boundary, we just picked a point outside of the external boundary and Phase2 calculated the exact intersection. We are finished defining the boundaries for this model, so let’s move on to the meshing.

Meshing For this model, we will use the default Mesh Setup parameters. Since we do not need to customize the discretization of the boundaries, we will use the Discretize and Mesh shortcut, which automatically discretizes the boundaries and generates the mesh with a single mouse click.

Select: Mesh → Discretize & Mesh The mesh will be generated and the status bar will show the total number of elements and nodes in the mesh. ELEMENTS = 2206 NODES = 1144

The mesh appears satisfactory, so we will proceed with the modeling. (NOTE: the mesh quality can always be inspected with the Show Mesh Quality option in the Mesh menu. This is left as an optional exercise to explore after completing this tutorial, and is described in the Phase2 Help system).

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Boundary Conditions For this tutorial, no boundary conditions need to be specified by the user. The default boundary condition will therefore be in effect, which is a fixed (i.e. zero displacement) condition for the external boundary.

Support

Read in the bolt coordinates from a DXF file.

We will support the hangingwall of the stope with cable bolts installed from the access drifts. To save some time, we will import the bolt geometry from a DXF file, since support installation (pattern bolting and liners) is covered in more detail in the Phase2 Support Tutorial.

Select: File → Import → Import DXF

In the DXF Options dialog, select only the Bolts checkbox and select Import. You will now see an Open file dialog. Open the Tutorial 02 Bolts.dxf file which you should find in the Examples > Tutorials folder of your Phase2 installation folder. Twelve cables (thick blue lines) should now be installed from the access drifts to the hangingwall. Normally, these bolts would be installed using the Add Bolt option, but that is left as an optional exercise to experiment with after completing this tutorial. To get a better look at the bolts:

Select: View → Zoom → Zoom Excavation When finished, press F2 to Zoom All.

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Field Stress For this tutorial we will use a constant field stress. A constant field stress is a reasonable assumption when excavations are relatively deep (i.e. not near the ground surface). For surface or near surface excavations, gravity field stress is more appropriate, this is covered in later tutorials.

Select: Loading → Field Stress

9 Enter: Fld. Str. Type = Constant 9 Sigma 1 = 30 9 Sigma 3 = 20 9 Sigma Z = 20 Angle = 0

In the Field Stress dialog, enter a constant field stress of Sigma 1 = 30 MPa and Sigma 3 = Sigma Z = 20. Leave the Angle = 0 degrees. Select OK. Notice that the stress block indicates the relative magnitude and direction of the in-plane principal stresses you entered. The angle in this case is zero, so Sigma 1 is horizontal.

Properties This is where most of the ‘action’ will be in this tutorial, as far as the modeling is concerned. First we will define the material properties (rockmass, ore, and backfill) and the bolt properties, and then we will assign these properties and the staging sequence to the various elements of our model.

Define Material Properties Select: Properties → Define Materials With the first tab selected at the top of the Define Material Properties dialog, enter the rock mass properties.

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9 Enter: 9 Name = rock mass Init.El.Ld.=Fld Stress Only Material Type = Isotropic 9 Young’s Modulus = 64000 9 Poisson’s Ratio = 0.25 9 Failure Crit. = GHB 9 Material Type = Plastic 9 Comp. Strength = 110 9 mb (peak) = 10 9 s (peak) = 0.05 9 a (peak) = 0.5 9 Dilation = 2.5 9 mb (residual) = 10 9 s (residual) = 0.02 9 a (residual) = 0.5

Select the second tab and enter the ore properties, and select the third tab and enter the backfill properties. Select OK when you are finished.

9Enter: 9 Name = ore Init.El.Ld.=Fld Stress Only Material Type = Isotropic 9 Young’s Modulus = 35000 9 Poisson’s Ratio = 0.25 9 Failure Crit. = GHB 9 Material Type = Plastic 9 Comp. Strength = 54 9 mb (peak) = 2 9 s (peak) = 0.02 9 a (peak) = 0.5 Dilation = 0 9 mb (residual) = 2 9 s (residual) = 0.01 9 a (residual) = 0.5

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9 Enter: 9 Name = backfill 9 Init.El.Ld.=Body Force Only 9 Unit Weight = 0.023 Material Type = Isotropic 9 Young’s Modulus = 2000 9 Poisson’s Ratio = 0.025 9 Failure Crit. = GHB 9 Material Type = Plastic 9 Comp. Strength = 7.5 9 m (peak) = 6 9 s (peak) = 1 9 a (peak) = 0.5 9 Dilation = 1.5 9 m (residual) = 6 9 s (residual) = 1 9 a (residual) = 0.5

Notice the properties we gave to the ore and the backfill. The orebody has a significantly lower stiffness and strength than the rockmass. The backfill has very low stiffness and strength. In addition, the ‘Initial Element Loading’ for the backfill was toggled to ‘Body Force Only’ – the field stress component of initial element loading for a backfill material should always be zero. ‘Body Force Only’ implies that the initial element loading is due to self-weight only. The unit weight of a material must be defined when the initial element loading includes body force. We are finished defining the material properties. Select OK to close the Define Material Properties dialog, and we will now define the bolt properties.

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Define Bolt Properties Select: Properties → Define Bolts

9 Enter: 9 Name = cables 9 Bolt Type = Plain Strd Cbl Borehole Diameter = 48 Cable Diameter = 19 Cable Modulus = 200000 Cable Peak = 0.1 Water/Cement Ratio = 0.35 9 Out-of-Plane Spacing = 2 Attached Face Plates = 9

Enter the bolt properties with the first tab selected and select OK. If you zoom in to the access drifts, you will notice that face plates are now displayed at the upper end of each cable. For more information about the Plain Strand Cable model see the Phase2 Help system and references. Select F2 to Zoom All. You have now defined all the necessary material and bolt properties. We will now proceed to the final part of our modeling, the assigning of the properties and staging sequence.

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Assigning Properties Select: Properties → Assign Properties The Assign Properties dialog allows us to assign the properties we defined to the various elements of our model. In conjunction with the Stage Tabs at the bottom left of the view, it also allows us to assign the staging sequence of the excavations and support. •

In the first stage, we will assign the ore properties, and also excavate the bottom section of the stope, and the three access drifts.

•

In the second stage we excavate the middle section of the stope.

•

In the third stage we excavate the top section of the stope.

•

In the fourth stage, we backfill the entire stope.

Assign Materials 1. Make sure the Stage 1 tab is selected (at the bottom left of the view). 2. Make sure the Materials option is selected at the top of the Assign dialog. 3. Select the “ore” button in the Assign dialog. (Notice that the material names are the names you entered when you defined the three materials – i.e. rock mass, ore and backfill).

Stage 1 – material assignment and excavation of bottom section of stope and access drifts

4. Click the left mouse button in the orebody zones above and below the excavation, as well as the two upper sections of the stope. Notice that these elements are now filled with the colour representing the ‘ore’ property assignment. 5. Select the “Excavate” button in the Assign dialog. 6. Place the cursor in the bottom section of the stope and click the left mouse button. Notice that the elements in this zone disappear, indicating that they are ‘excavated’. NOTE: since we defined the “rock mass” properties using the first tab in the Define Materials dialog, the “rock mass” properties do not need to be assigned by the user. The properties of the first material in the Define Materials dialog, are always automatically assigned to all elements of the model. Therefore the rock mass, on either side of the orebody, is already assigned the correct properties, and it is not necessary for the user to assign properties. Since the access drifts are so small, we’ll have to zoom in so we can accurately select them for excavating.

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Select: View → Zoom → Zoom Excavation Now press the F5 function key twice, to zoom in a bit closer. F5 is equivalent to using the Zoom In option. You can also rotate the mouse wheel to zoom in or out. Again, notice the faceplates which appear at the ends of the cable bolts, at the access drifts we want to excavate. 7. You should still be in “Excavate” mode (if not, select the “Excavate” button in the Assign dialog.)

Stage 2 – excavation of mid-section of stope.

8. Place the cursor in each of the three access drifts, and left click to excavate them. 9. Select the Stage 2 tab. 10. Place the cursor in the middle section of the stope and click the left mouse button, and the elements will disappear.

Stage 3 – excavation of top-section of stope.

11. Select the Stage 3 tab. 12. Place the cursor in the top section of the stope and click the left mouse button, and the elements will disappear.

Stage 4 – backfill of entire stope.

13. Select the Stage 4 tab. 14. Select the “backfill” button in the Assign dialog. 15. Click in each of the three sections of the stope, and the elements will reappear, with the colour representing the ‘backfill’ property assignment. 16. You are now finished assigning materials. As an optional step, select each Stage Tab, starting at Stage 1, and verify that the excavation staging and material property assignment is correct. Assign Bolts

The bolts must now be installed in the correct sequence.

Since we defined our bolt properties with the first bolt property tab selected in the Define Bolt Properties dialog, we don’t have to assign properties (since they are automatically assigned), but we do have to assign the staging sequence of the bolt installation. 1. At the top of the Assign dialog, select the Bolts option from the drop down combo box. 2. Select the Stage 2 tab. 3. Select the “Install” button in the Assign dialog.

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4. Use the mouse to select the middle 4 set of bolts. Right click and select Done Selection. 5. Select the Stage 3 tab. 6. Use the mouse to select the top 4 set of bolts. Right click and select Done Selection. That is all that is required, the bolts should now be installed at the correct stages. Verify your input – when bolts are NOT installed at a given stage, they are displayed in a lighter shade of colour. 7. Select the Stage 1 tab. Only the lower set of four bolts should be installed. 8. Select the Stage 2 tab. Both the lower and middle sets of bolts should be installed. 9. Select the Stage 3 tab. All 12 bolts should now be installed. So we see that the effect of Step 4 above, was to install the middle set of bolts at Stage 2 (and all subsequent stages). The effect of Step 6 was to install the top set of bolts at Stage 3 (and all subsequent stages). Close the Assign dialog, and press F2 to Zoom All. You have now completed the modeling phase of the analysis, the model should appear as in the following figure.

Figure 2-1: Finished model – Phase2 Material & Staging Tutorial

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Compute Before you analyze your model, save it as a file called matstg.fez.

Select: File → Save Use the Save As dialog to save the file. You are now ready to run the analysis.

Select: Analysis → Compute The Phase2 Compute engine will proceed in running the analysis. Since we are using Plastic materials and bolts, the analysis may take a bit of time, depending on the speed of your computer. When completed, you will be ready to view the results in Interpret.

Interpret To view the results of the analysis:

Select: Analysis → Interpret This will start the Phase2 Interpret program.

Viewing Stages By default, you will always see the Stage 1 results when a multi-stage model is opened in Interpret. Viewing results at different stages in Phase2 is simply a matter of selecting the desired stage tab at the lower left of the view.

Sigma 1 Let’s first zoom in.

Select: View → Zoom → Zoom Excavation You are now viewing the Sigma 1 Stage 1 results. Select the Stage 2, 3 and 4 tabs and observe the changing stress distribution. TIP: you can also use the Page Up / Page Down keys to change the viewing stage. Toggle on the principal stress trajectories, using the button provided in the toolbar. Again select the stage tabs 1 to 4, and observe the stress flow around the excavation.

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If you want to compare results at different stages on the same screen, it can easily be done as follows. 1. Select Window→New Window TWICE, to create two new views of the model. 2. Select the Tile Vertically button in the toolbar, to tile the three views vertically. 3. Select Zoom Excavation in each view. 4. Select the Stage 1 tab in the left view, the Stage 2 tab in the middle view, and the Stage 3 tab in the right view. 5. Display the stress trajectories in each view. 6. Hide the legend in the right and middle views (use View → Legend Options, or right-click on a Legend and select Hide Legend). 7. Right-click in any view and select Contour Options. Click in each view, and select Auto-Range (all stages), to ensure that the same contour range is used for all stages. Close the Contour Options dialog. Your screen should appear as shown below.

Figure 2-2: Sigma 1 contours, stages 1, 2 and 3. Principal stress trajectories are displayed.

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Strength Factor While we have the three views displayed, let’s look at the Strength Factor contours. 1. Display the Strength Factor in each view. 2. Toggle Stress Trajectories OFF, and Yielded Elements ON, using the Display toolbar buttons, in each view. Observe the development of strength factor and yielding around the excavation. Note that: •

The orebody has different strength factor contours than the surrounding rockmass, since we assigned it weaker strength parameters than the rockmass.

•

Most of the yielding is in the back and floor of the stope (i.e. in the orebody), although there is some yielding in the rockmass as well.

Let’s view the model full screen again. Maximize one of the views (it doesn’t matter which one). Re-display the legend if necessary (View → Legend Options), and select the Stage 3 tab, if necessary. Zoom in to get a closer look at the yielded elements in the stope back.

Select: View → Zoom → Zoom Window Enter first window point[esc=quit]: 0 100 Enter second window point[esc=quit]: 50 60

You will see that there are actually two symbols used for the yielded element markers – failure in shear is indicated by an × marker, and failure in tension is indicated by a { marker. This is indicated in the Legend. If tensile failure is accompanied by shear failure, the symbols overlap. Display the mesh by selecting the Elements button in the toolbar. Note that each Yielded Element symbol corresponds to a single finite element, as you can see in Figure 2-3.

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Figure 2-3: Strength Factor contours and yielded elements, Stage 3. As an optional step, use the arrow keys (up / down / left / right), to pan the model around the view. View the contours and yielded elements around the entire excavation. You can also pan by holding down the mouse wheel and moving the mouse. Toggle off the Mesh and select Zoom All. Select the Stage tabs 1 to 4, and observe the strength factor contours on the whole model. Toggle off the Yielded Elements.

Displacement Now look at the total displacements.

Select: Total Displacement Select the Stage 1 tab. The maximum total displacement for Stage 1 is about 16 mm, as indicated in the status bar. Maximum Total Displacement = 0.0158 m

Select the Stage 2 tab. Maximum Total Displacement = 0.0216 m

Select the Stage 3 tab. Maximum Total Displacement = 0.0302 m

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Select the Stage 4 tab. Maximum Total Displacement = 0.0303 m

The Stage 3 and Stage 4 maximum displacements are almost identical. Thus far we have not discussed the Stage 4 results. This is discussed in the next section. Zoom in again.

Select: View → Zoom → Zoom Excavation Right-click the mouse and select Display Options. In the Display Options dialog, select the Stress tab, toggle on Deform Boundaries, enter a Scale Factor of 100, and select Done. Select the Stage tabs 1 to 4 again, and observe the displacement contours with the deformed boundaries displayed. The deformed boundaries graphically illustrate the inward movement of the excavation boundaries. It is also interesting to observe the shifting of the access drifts towards the hangingwall – if you did not notice this, select the Stage tabs 1 to 3 and observe the displaced outlines of the access drifts. Note: the Deform Boundaries option is also available in the toolbar. However, if you want to customize the scale factor (as we did here, with a scale factor = 100), you will have to use the Display Options dialog.

Figure 2-4: Total displacement contours, third stage. Deformed Boundary option toggled ON, Scale Factor = 100

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To prepare for the last part of the tutorial, let’s close two of the views we created. First tile the views with the Tile option in the toolbar. Then close two of the views. Then maximize the remaining view, and select Zoom Excavation, if necessary. Turn off the Deformed Boundaries display by selecting the Deformed Boundaries toolbar button.

Stage 4 Remember that in the fourth stage of this model we backfilled the entire stope with a material having representative backfill properties. Except for this, nothing else was changed. Practically speaking, the backfill has no effect on the results for this model, compared to the third stage results. It is left as an exercise for the user to verify that the contour plots in the third and fourth stage are essentially identical. •

The purpose of the backfill in this tutorial was to demonstrate how it could be modeled. A practical use of backfill modeling would be a staged model with several excavations that were excavated and then backfilled in sequence. In this case, the stiffness of the backfill would serve to limit displacements in the backfilled excavations. However, that is beyond the scope of this tutorial, and is left for the user to demonstrate for themselves.

•

One final note – remember we specified the Initial Element Loading for the backfill material as Body Force Only. This effectively gives the backfill an active force resisting the excavation deformation, in addition to the passive material stiffness. However, compared to the field stress in this model, this body force is negligible and its effects on the model are minimal. If we were dealing with a surface excavation and gravity field stress, then the body force loading would be more significant. (If we had specified the Initial Element Loading as ‘None’, then only the backfill stiffness would resist deformation.) See the Phase2 Help system for more information about Initial Element Loading.

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Bolts Now let’s see what’s going on with our bolts. They don’t seem to have any obvious effect on the stress or strength contours, so let’s see what other information we can gather, using the Graph Bolt Data option. First, select the Stage 3 tab.

Select: Graph → Graph Bolt Data Pick bolts to graph[enter=done,*=all, esc=quit]: use the mouse to select the lower set of 4 bolts

When the four bolts are selected (they are highlighted by a dotted line when selected), right-click the mouse and select Graph Selected, and you will see the following dialog:

In the Graph Bolt Data dialog, select the ‘Lines on graph same color as bolt’ option. Select Create Plot, and a graph of Axial Force for the selected bolts will be generated. Now repeat the above procedure for the middle and the top sets of four bolts, to generate two more graphs. Let’s tile the graphs we have created, so that we can view them all on one screen.

Select: Window → Tile Vertically

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On each graph you will notice a legend, with a bolt number and a stage number. On the model, you will notice numbers on each bolt. The bolt numbers on the model correspond to the bolt numbers on the graphs, allowing you to identify the bolts.

Graph ranges and titles can be changed with the Chart Properties option in the right-click menu or the Chart menu.

Figure 2-5: Axial force in cables vs. distance along each cable. Furthermore, the numbers also identify the end of each bolt and therefore the end of each curve. The start of each curve therefore represents the end with the face plate, at the access drifts. An important point to remember when you are installing bolts with face plates between two excavations – the first point of each bolt must be the end with the face plate. You must remember this when you create the bolt geometry using the Add Bolt option or DXF import. Also notice on the plots that the peak capacity of the bolts (0.1 MN) is indicated by a horizontal line. The force in all bolts is well below this line, indicating that there is no yielding in the bolts. Let’s verify that there is no yielding in the bolts. Left-click in the model view, and select the Yielded Bolts button from the toolbar. No yielded bolt elements

As we expected, no bolts have yielded (if there were yielded bolts, the yielded sections would be highlighted with a different colour).

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While we are looking at bolt data, let’s illustrate one more feature, the ability to plot data from multiple stages on a single graph. First, maximize the model view (if you are still looking at the tiled view of all the graphs).

Select: Graph → Graph Bolt Data Pick bolts to graph[enter=done,*=all, esc=quit]: select bolt #4 (the fourth bolt from the bottom of the model).

Right-click the mouse and select Graph Selected as before, except this time select the first three stages to plot, using the checkboxes.

In the Graph Bolt Data dialog, select Stages 1, 2 and 3 to plot. Select Create Plot, and the Axial Force at stages 1, 2 and 3 for the selected bolt will be plotted.

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Figure 2-6: Axial force in Bolt 4 at Stages 1, 2 and 3. In this case, the axial force in the bolt increases from stage 1 to stage 2, and does not change significantly from stage 2 to stage 3. To summarize the bolt data interpretation, it is always important to look at the effect of the excavation on the bolts, and not just the bolts on the excavation. In many cases, the bolts will have little effect on the contour plots (stress, strength, displacement), but will nonetheless be taking a substantial load. Unless the bolts are installed in a zone of yielding with large displacements (see the Phase2 Support Tutorial) this will often be the case. Examining the load in the bolts allows you to design bolt support by varying bolt parameters (diameter, etc) to obtain optimal stress in the bolt system. Close the Axial Force plot.

Differential Results In the Interpret portion of this tutorial, we always used a Reference Stage = 0. Differential results between any two stages can be viewed by setting the Reference Stage > 0 in the Stage Settings dialog. For example:

Select: Data → Stage Settings

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Set the Reference Stage to 1 and select OK. Notice that the Stage Tabs now allow you to view results relative to the reference stage you just entered. We will not explore differential results further in this tutorial, but the user is encouraged to explore this on their own. See the Phase2 Help system for information about how to interpret differential results.

Log File and Load Step Plot Before we conclude this tutorial, let’s examine the Log File which is created during a Phase2 stress analysis, and the Load Step plot.

Select: Analysis → Log File A summary of the number of load steps at each stage, and the number of iterations and final tolerance at each load step, is displayed in its own view. Scroll down to view all of the information. After a plastic analysis, it is a good idea to check the log file to make sure that the solution converged within the specified tolerance. For this example, the final calculated tolerance is less than 0.001 for each load step, indicating convergence within our specified tolerance. The tolerance, number of load steps, and maximum number of iterations, can all be user specified in the Project Settings dialog when you create the model. Close the log file view. Now view the Load Step Plot, which graphically illustrates the data in the Log File.

Select: Analysis → Load Step Plot

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Figure 2-7: Load Step plot for stress analysis. The Load Step Plot plots the maximum displacement at each load step, for each stage. That concludes the ‘Materials and Staging’ tutorial.

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Support Tutorial – Step 1 12 MPa

8 MPa

-35°

external boundary expansion factor = 3

In this first step of the Support tutorial, the above model will be created and analyzed without support. Both an elastic and a plastic analysis will be carried out. Support (bolts and shotcrete) will be added in Step 2 of the Support Tutorial. If you wish to skip the model process, the finished product of Step 1 of the Support Tutorial (with plastic material parameters) can be found in the Tutorial 03 Support1.fez data file located in the Examples > Tutorials folder in your Phase2 installation folder.

Model This model represents a horseshoe shaped tunnel of about 5 metre span, to be excavated in heavily jointed rock. The rock is described as blocky/seamy, of poor quality, and will require support to prevent collapse. If you have not already done so, run the Phase2 Model program by double-clicking on the Phase2 icon in your installation folder. Or from the Start menu, select Programs → Rocscience → Phase2 6.0 → Phase2.

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Entering Boundaries

Read in the tunnel coordinates from a DXF file.

For this example, the coordinates defining the tunnel cross-section have already been saved in DXF format, because of the large number of vertices which were used to accurately define the cross-section. Therefore you will not enter coordinates manually as in previous tutorials, but simply read in the DXF file containing the excavation geometry.

Select: File → Import → Import DXF

In the DXF Options dialog, select only the Excavations checkbox, and select Import. You will then see an Open file dialog. Open the Tutorial 03 Tunnel.dxf file which you should find in the Examples > Tutorials folder in your Phase2 installation folder. You should see the excavation displayed on the screen. Now add the external boundary.

Select: Boundaries → Add External

We will use the default parameters, so just select OK to automatically create a BOX external boundary with an expansion factor of 3. This completes the entry of boundaries for this example, so we will proceed to the meshing.

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Meshing For this model, we will use the default Mesh Setup parameters. Since we do not need to customize the discretization of the boundaries, we will use the Discretize and Mesh shortcut, which automatically discretizes the boundaries and generates the mesh with a single mouse click.

Select: Mesh → Discretize & Mesh The mesh will be generated and the status bar will show the total number of elements and nodes in the mesh. Elements: 1902

Nodes: 990

Boundary Conditions For this tutorial, no boundary conditions need to be specified by the user. The default boundary condition will therefore be in effect, which is a fixed (i.e. zero displacement) condition for the external boundary.

Field Stress For this tutorial we will use a constant field stress.

Select: Loading → Field Stress

9 Enter: Fld. Str. Type = Constant 9 Sigma 1 = 12 9 Sigma 3 = 8 Sigma Z = 10 9 Angle = –35

In the Field Stress dialog enter Sigma 1 = 12 MPa, Sigma 3 = 8, Sigma Z = 10, and enter an Angle of –35 degrees (note the minus sign!) Notice that the stress block indicates the relative magnitude and direction of the in-plane principal stresses you entered. Note that the angle you entered is the counter-clockwise angle of Sigma 1 from the horizontal axis. A negative counter-clockwise angle is equivalent to a positive clockwise angle (+35 degrees in this case), as can be seen from the stress block.

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Properties For the initial analysis, we will be defining the rock mass as elastic.

Select: Properties → Define Materials

9 Enter: 9 Name = phyllite Init.El.Ld.=Fld Stress Only Material Type = Isotropic 9 Young’s Modulus = 1120 9 Poisson’s Ratio = 0.3 9 Failure Crit. = GHB Material Type = Elastic 9 Comp. Strength = 50 9 mb (peak) = 0.43 9 s (peak) = 0.00006 9 a (peak) = 0.5

With the first tab selected in the Define Material Properties dialog, enter the above properties. Since we defined the properties with the first material tab selected, we do not have to assign them to the model. Phase2 automatically assigns the properties of the first material, to all finite elements of the rock mass. (Property assignment is covered in detail in the Materials and Staging tutorial). However, we still have to excavate the elements inside the excavation boundary. This can be done with the Assign Properties dialog.

Select: Properties → Assign Properties 1. Select the Excavate button in the Assign dialog. 2. Click the mouse inside the excavation (tunnel) boundary. The elements will disappear, indicating that the tunnel is “excavated”. 3. Now close the Assign dialog. TIP: excavation and material assignment can also be done using the right-click shortcut.

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We are finished with the modeling and can run the analysis. Your model should appear as shown in the following figure.

Figure 3-1: Finished model – Phase2 Support Tutorial (Step 1).

Compute Before you analyze your model, save it as a file called support1.fez.

Select: File → Save Use the Save As dialog to save the file. You are now ready to run the analysis.

Select: Analysis → Compute The Phase2 Compute engine will proceed in running the analysis. When completed, you will be ready to view the results in Interpret.

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Interpret Start the Phase2 Interpret program:

Select: Analysis → Interpret Let’s first view the strength factor contours. Select Strength Factor from the toolbar data list.

Support Tutorial Elastic Analysis

Figure 3-2: Strength Factor Contours, after elastic analysis. Strength factor represents the ratio of available rock mass strength to induced stress, at a given point. You will immediately notice the large zone of overstress surrounding the tunnel. All of the rock contained within the contour marked 1, has a strength factor (based on the elastic analysis results) less than 1, and will fail if left unsupported. (Note: in the Contour Options dialog, you will have to change the number of contour intervals to 7, and the contour Mode to Lines, to obtain the above figure. See the “Note about the Support tutorial figures” at the end of this section). If you added contour labels, delete them now using Tools → Delete All Tools. Now let’s view the displacements.

Select: Notice the maximum displacement displayed in the status bar. Maximum Total Displacement = 0.03723 m

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Zoom in, and toggle the displacement vectors on.

Select: View → Zoom → Zoom Excavation Select: View → Display Options In the Display Options dialog, toggle Deformation Vectors on, enter a Scale Factor of 10, and select Done.

Figure 3-3: Displacement contours and vectors around excavation (elastic analysis). The elastic displacements show an inward displacement of the tunnel walls, as well as a significant floor heave. Now that we have determined, from the elastic analysis, that the region of overstress is significant, we will move on to the plastic analysis of this problem.

Note about the Support Tutorial figures •

The contour plots in the Support tutorial were generated using the Black Lines Auto-Format option in the Contour Options dialog, and customizing the Number of Intervals to a suitable number (e.g. 7 or 8).

•

Contour labels are added using the Label Contour option, and deleted using the Delete Tools or Delete All Tools options.

•

The display of the Legend was toggled off in the Support Tutorial figures.

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Model From Interpret, switch back to the Phase2 Model program:

Select: Analysis → Model We will now define the rock mass to be plastic, and re-run the analysis.

Select: Properties → Define Materials

9 Enter: Name = phyllite Init.El.Ld.=Fld Stress Only Material Type = Isotropic Young’s Modulus = 1120 Poisson’s Ratio = 0.3 Failure Crit. = GHB 9 Material Type = Plastic Comp. Strength = 50 mb (peak) = 0.43 s (peak) = 0.00006 a (peak) = 0.5 Dilation = 0 9 mb (residual) = 0.43 9 s (residual) = 0.00006 9 a (residual) = 0.5

Toggle the Material Type to Plastic, and enter residual mb, s and a parameters equal to the peak parameters. This defines the material as ideally elastic-plastic (i.e. no strength drop once yield is reached). Select OK. We are now ready to re-run the analysis.

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Compute Before you analyze your model, let’s save this as a new file called support2.fez. (Make sure you select Save As and not Save, or you will overwrite the support1.fez file).

Select: File → Save As Save the file as support2.fez.

Select: Analysis → Compute The Phase2 Compute engine will proceed in running the analysis. When completed, you will be ready to view the results in Interpret.

Interpret From Model, switch back to Interpret.

Select: Analysis → Interpret Let’s view the strength factor contours.

Select: Notice the much larger extent of the region encompassed by the contour of strength factor = 2 (compared with Figure 3-2). Also notice that there is no region of strength factor < 1. Since your material is now plastic, the strength factor cannot go below one – when failure (yielding) occurs, the strength factor is by definition equal to one. It is only in an elastic analysis that the strength factor can go below one, as a hypothetical measure of overstress. To view the ‘failure zone’ in a plastic material, toggle the display of yielded elements on, by selecting the Yielded Elements button in the toolbar. The number of yielded elements will be displayed in the status bar. 583 Yielded finite elements

Zoom in using the zoom method of your choice (suggestion: rotate the mouse wheel forward). Observe the zone of plastic yielding (× = shear failure, { = tensile failure) around the excavation. Notice that the yielded zone corresponds roughly with the zone of strength factor < 1 from the elastic analysis (Figure 3-2), with additional propagation beyond this limit, as would be expected from a plastic analysis.

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Support Tutorial Plastic Analysis

Figure 3-4: Strength factor contours and yielded elements, after plastic analysis of unsupported excavation. Toggle the display of yielded elements off, by re-selecting the Yielded Elements button in the toolbar. Let’s look at the plastic displacements.

Select: Note the maximum displacement indicated in the status bar. Maximum Total Displacement = 0.0961 m

This is nearly three times the maximum displacement from the elastic analysis. Toggle the deformation vectors on.

Select: View → Display Options In the Display Options dialog, toggle Deformation Vectors on, enter a Scale Factor of 10, and select Done. Let’s zoom in.

Select: View → Zoom → Zoom Excavation You should see the following figure. Since we used the same scale factor for the deformation vectors, we can make a direct visual comparison between Figure 3-5 and Figure 3-3.

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Figure 3-5: Displacement contours and vectors around excavation (plastic analysis). From the deformation vectors, it can be seen that the overall maximum displacement (0.096m), is occurring in the floor of the tunnel. You are now finished the first step in the “Support Tutorial”. It’s about time we added some support! Continue on to Step 2 of this tutorial.

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Support Tutorial – Step 2 12 MPa

8 MPa

-35°

external boundary expansion factor = 3

In the first step of the Support tutorial, we analyzed the above model without support, using both elastic and plastic material parameters. We will now proceed to analyze the same model after adding: 1. Bolts only 2. Bolts and shotcrete 3. Bolts and shotcrete in conjunction with load splitting. The finished product of this tutorial (with bolts and shotcrete, but before the load splitting) can be found in the Tutorial 03 Support2.fez data file in the Examples > Tutorials folder of your Phase2 installation folder.

Model If you have been following this tutorial from Step 1, then just continue on. If you quit the program after doing Step 1, and wish to continue now, start the Phase2 Model program, and open the support2.fez file you created in Step 1.

Select: File → Open Open the support2.fez file.

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Adding Pattern Bolts Let’s now add some bolts to this model. We will be installing a radial array of 5 meter long pattern bolts, on a 1 x 1 meter grid spacing. Before adding our bolt pattern, let’s zoom in on the excavation, so that we can accurately select the starting and ending points of the bolt pattern.

Select: View → Zoom → Zoom Excavation Select: Support → Add Bolt Pattern

9 Enter: 9 Bolt Length = 5 9 In-Plane Spacing = 1 Apply Ptn. To = Excavation 9 Pattern Type = Radial

Since you are entering a Radial bolt pattern, you will then be prompted: Enter drilling point [esc=cancel]: 100 100

This is the point from which the radial pattern will be generated. Use the keyboard to enter the exact point (100 , 100) as indicated in the prompt above. You can use the mouse to graphically enter the point, but it is best to use the keyboard when an exact point is desired. Next you will be prompted to enter starting and ending vertices for the pattern. Because of the poor quality of the rock and extensive yielding all around the tunnel, we will bolt the entire circumference of the tunnel, including the floor. We can do this as follows: 1. You will be prompted to “Pick starting vertex”. You can start at any vertex, but we will start at the uppermost vertex at the midpoint of the tunnel roof. Use the cursor to select this vertex, located at about 100.0, 102.3. 2. Now sweep the cursor around the excavation boundary. As you move the cursor, you will see the radial bolt pattern displayed. Since we are bolting around the entire tunnel, you can create the pattern in a clockwise or counter-clockwise direction, it doesn’t matter.

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3. You will be prompted to “Pick ending vertex”. When you see the complete bolt pattern around the tunnel, click again on the same vertex as in Step 1. 4. When the end vertex has been entered, the radial bolt pattern will be generated and added to the model, and you will exit the Add Bolt Pattern option. If you make a mistake and the bolt pattern is not correct, then just select Undo and repeat the above steps to add the bolt pattern. Now use Zoom All to bring everything back into view. A shortcut to zoom all is to press the F2 function key.

Bolt Properties Now that the bolt geometry is defined, let’s define the bolt properties. The bolt properties we enter will correspond to fully grouted, untensioned steel dowels, with a maximum load capacity of 20 tonnes (0.2 MN).

Select: Properties → Define Bolts

9 Enter: 9 Name = grouted 9 Bolt Type = Fully Bonded 9 Bolt Diameter = 25 Bolt Modulus = 200000 9 Peak Capacity = 0.2 9 Residual Capacity = 0.2 Pre-Tensioning = 0 Out-of-Plane Spacing = 1

Enter the bolt properties with the first tab selected.

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Since you entered the bolt properties with the first tab selected, you do not have to Assign these properties to the bolts – Phase2 will automatically assign the properties for you. We are now ready to re-run the analysis.

Compute Before you analyze your model, let’s save this as a new file called support3.fez. (Make sure you select Save As and not Save, or you will overwrite the support2.fez file).

Select: File → Save As Save the file as support3.fez.

Select: Analysis → Compute The Phase2 Compute engine will proceed in running the analysis. When completed, you will be ready to view the results in Interpret.

Interpret From Model, switch back to Interpret.

Select: Analysis → Interpret Let’s see the effect of the bolts on the strength factor contours.

Select: The extent of the region encompassed by the contour of strength factor = 2 is noticeably reduced, compared with Figure 3-4. Toggle the display of yielded elements on by selecting the Yielded Elements button in the toolbar. The number of yielded elements will be displayed in the status bar. 547 Yielded finite elements

The yielded zone, based on the extent and location of the yielded elements, is not discernibly different from the unsupported yield zone shown in Figure 3-4. However, the number of yielded finite elements decreased from 583 (unsupported) to 547 (supported).

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Support Tutorial Plastic Analysis + Bolts

Figure 3-6: Strength factor contours and yielded elements, for excavation with pattern bolt support only. Let’s check for yielding in the bolts. Select the Yielded Bolts button in the Display toolbar. The yielded bolt elements will be highlighted in red, and the number of yielded elements will be displayed in the status bar. 237 Yielded bolt elements

Almost all of the bolts have yielded, as shown by the bolt sections highlighted by a yellow dotted line. This indicates tensile failure of a bolt element. Remember that “bolt elements”, for fully bonded bolts, are defined by the intersections of bolts with the finite elements. (Bolt elements can be displayed with the Display Options dialog. This is left as an optional step.) Recall that when we defined the bolt properties, we entered a residual bolt capacity equal to the peak bolt capacity. Therefore, even though the bolts have reached their yield capacity, they still provide support. Finally, let’s look at the effect of the bolts on the displacement.

Select: The maximum displacement indicated in the status bar is now: Maximum Total Displacement = 0.080 m

Compared to the unsupported excavation, the displacements have been slightly reduced, but not by much. (Maximum unsupported displacement = .0961 m). We’ll have to add shotcrete to really support this tunnel.

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Model From Interpret, switch back to Model.

Select: Analysis → Model

Now we add the liner support.

Note: the finished product of the modeling section of this tutorial, with bolts and shotcrete, but before the load splitting, can be found in the tutorial3b.fez data file located in the Examples folder in your Phase2 installation folder, if you wish to skip the model process.

Adding a Liner We will now line the tunnel with shotcrete. First let’s zoom in so that we can see what we are doing.

Select: View → Zoom → Zoom Excavation Select: Support → Add Liner 1. You will see the Add Liner dialog. Just select OK.

2. Click and hold the left mouse button, and drag a selection window which encloses the entire excavation. Release the left mouse button. Notice that all excavation line segments are selected. 3. Right-click the mouse and select Done Selection, or just press the Enter key. The entire tunnel will now be lined, as indicated by the thick blue line segments around the excavation boundary. Anytime you want to line multiple adjacent boundary segments, it is always best to use a selection window, to ensure all desired segments are selected.

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Liner Properties Now define the liner properties. The properties we enter will correspond to a 200 mm thick layer of steel fibre reinforced shotcrete.

Select: Properties → Define Liners

9 Enter: 9 Name = shotcrete 9 Thickness = 0.2 9 Beam = Timoshenko 9 Young’s Modulus = 3000 9 Poisson’s Ratio = 0.25 9 Material Type = Plastic Comp. Str. (peak) = 35 Comp. Str. (res) = 5 Tens. Str. (peak) = 5 Tens. Str. (res) = 0

Enter the liner properties with the first tab selected. Since you entered the liner properties with the first tab selected, you do not have to Assign these properties to the liner – Phase2 will automatically assign the properties for you. We are now ready to re-run the analysis.

Compute Before you analyze your model, let’s save this as a new file called support4.fez. (Make sure you select Save As and not Save, or you will overwrite the support3.fez file).

Select: File → Save As Save the file as support4.fez.

Select: Analysis → Compute The Phase2 Compute engine will proceed in running the analysis. When completed, you will be ready to view the results in Interpret.

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Interpret From Model, switch back to Interpret.

Select: Analysis → Interpret Now let’s see how the addition of the shotcrete liner affected the strength factor and yielding.

Select: The extent of the region encompassed by the contour of strength factor = 2 is now considerably reduced compared with Figures 3-4 and 3-6. Let’s do a direct comparison of the three files on the same screen, as described below. 1. If you have been following the Support tutorial from the beginning, then you should have four files open in Interpret — support1, support2, support3 and support4. If this is the case, then CLOSE the support1 file, and leave the other three open. 2. If you have been closing files as you went along, then re-open the support2 and support3 files. 3. Now tile the three views (use the Tile Vertically button in the toolbar). 4. Display the Strength Factor in each view. 5. Select Zoom Excavation in each view (use the F6 key). 6. Select Zoom Out approximately 5 or 6 times, in each view (use the F4 key). 7. Display the yielded elements in each view. 8. If the legends are displayed, toggle them off (you can right-click on a Legend and select Hide Legend). 9. Your screen should appear as below.

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Strength Factor Unsupported (left) Bolts only (middle) Bolts + Shotcrete (right)

Figure 3-7: Strength factor contours and yielded elements, for support2, support3 and support4 files. Note: if the order of the three views is not as shown in the above figure, then click consecutively in the support4, support3 and support2 views, and re-tile the view. Observe the effect of support on the strength factor contours, and the yielded element zone. It can be seen that the pattern bolting alone did not have much effect, but the application of a shotcrete liner, in conjunction with the pattern bolting, has been effective in reducing failure around the tunnel. The number of yielded finite elements for each model is summarized below (the number of yielded elements is displayed in the status bar whenever the yielded elements are displayed): FILE Support1 (elastic analysis)

# of yielded finite elements 0

Support2 (plastic, no support)

583

Support3 (bolts only)

547

Support4 (bolts + shotcrete)

367

Now maximize the view of the support4 file, so that we can view it full screen again. Toggle the display of yielded elements off, by re-selecting the Yielded Elements button in the toolbar.

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Let’s check for yielding in the bolts. Select the Yielded Bolts button in the toolbar. Again, most of the bolts have yielded, as shown by the bolt sections highlighted in yellow. The status bar indicates the total number of yielded bolt elements. 205 Yielded bolt elements

The number of yielded bolt elements was decreased from 237 to 205 by the presence of the liner. Toggle off the display of yielded bolt elements by re-selecting the Yielded Bolts button in the toolbar. We can look at yielding in the liner in the same manner as yielding in the bolts is displayed. Select the Yielded Liners button in the Display toolbar. The status bar will indicate: 27 Yielded liner elements

Zoom in so that you can see the yielded liner elements.

Select: View → Zoom → Zoom Excavation The yielded liner elements, highlighted in red, are concentrated at the upper right, lower left, and floor of the tunnel. Toggle the yielded liner elements off by re-selecting the Yielded Liners button in the toolbar. Finally, let’s look at the displacements after adding the liner.

Select: The maximum total displacement indicated in the status bar is now: Maximum Total Displacement = 0.0539 m

The combination of bolts and shotcrete has reduced the maximum displacement to about half of the unsupported value (0.096 m). Toggle the deformation vectors on.

Select: View → Display Options In the Display Options dialog, toggle Deformation Vectors on, enter a Scale Factor of 10, and select Done. As can be seen from the contours and the displacement vectors, the maximum displacement is still occurring in the floor of the tunnel. This suggests the casting of a thicker concrete slab on the tunnel floor, however, we will not be exploring this further in this tutorial. You may want to experiment with changing the thickness of the liner on the floor of the tunnel (to say, 300 mm), after completing the rest of this tutorial.

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It is left as an optional exercise to display the Total Displacement contours and Deformation Vectors for the support2, support3 and support4 files, to obtain the figure below.

Figure 3-8: Total displacement contours and vectors for support2, support3 and support4 files. Hints: 1. Tile and zoom the views as described earlier for the strength factor contours. 2. When displaying the deformation vectors for each view, use a Scale Factor of 10 (in the Display Options dialog). 3. In Contour Options, select Custom Range, enter a Range of 0 to 0.12, and Number of Intervals equal to 6, for each view. (The outermost contour shown in Figure 3-8 should then be the 0.02 meter total displacement contour).

Show Values We will now demonstrate another very useful feature of Phase2, the Show Values option, which allows the user to display analysis results for bolts, liners and joints, graphically or numerically, directly on the model. If you are viewing the results for multiple files, first maximize the view of the support4 file. Press F6 to Zoom Excavation. Then select Show Values from the toolbar or the Analysis menu.

Select: Analysis → Show Values → Show Values

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In the Show Values dialog, select the Liners checkbox, and Axial Force. Select other options in the dialog, as shown above. Select OK. You should now see graphical “bars” representing the axial force in each liner element, displayed directly on the model, as shown in Figure 3-9. The Minimum and Maximum values of Axial Force are also displayed.

Figure 3-9: Axial force in liner displayed with Show Values option. Note – the following additional steps were used to obtain the figure above: 1. In Contour Options, set the contour Mode to Off.

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2. In Legend Options, turn the Legend Off. 3. In Display Options, turn Off Excavation boundaries and Bolts. It is left as an optional exercise for the user to experiment with the many different display possibilities which are possible with the Show Values option. NOTE: the Show Values options are also accessible through the rightclick menu. If you right-click on a liner, bolt or joint, the popup menu will provide a Show Values sub-menu, with direct access to all of the data and display options which are applicable. As the final step in the Support tutorial, we will examine one more feature of Phase2, called “load splitting”, using this same example.

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Model If you are viewing multiple files in Interpret, make sure the support4 view is selected, before you switch back to Model.

Select: Analysis → Model

Load Splitting

Now we introduce the load splitting option.

The previous analyses in Step 2 of this tutorial (i.e. pattern bolt support only, and combined pattern bolt/shotcrete support), implicitly assume that the support is installed immediately after excavation, and that no displacement takes place prior to the installation of support. Of course this is not realistic, and a certain amount of deformation will always occur before the support can be installed. The Load Split option in Phase2 allows the user to “split” the field stress induced load, between any stages of the model, rather than applying the entire field stress load in the first stage. Load splitting can therefore be used to simulate the delayed installation of support. In this simple example, it will be done as follows: 1. A staged model is required in order to enable Load Splitting, therefore we will first set the Number of Stages = 2 in Project Settings. 2. Using the Load Splitting option, the Load Split will be defined as 30% in Stage 1 and 70% in Stage 2. 3. The support (bolts and liner) will then be installed in Stage 2, rather than Stage 1. Effectively, this allows some deformation to take place in Stage 1 (before support is installed), and then the support installed in Stage 2 can respond to the remainder of the field stress induced load. The first step towards including load splitting in a model, is to set the Number of Stages in Project Settings.

Select: Analysis → Project Settings

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9 Enter: Project Name = (optional) 9 Number of Stages = 2 Analysis = Plane strain Max. # of iterations = 500 Tolerance = 0.001 # Load Steps = Auto Solver Type = Gauss. Elim. 9 Units = Metric (MPa)

Set the Number of Stages = 2 and select OK. Now we can enter the Load Split information.

Select: Loading → Load Split

In the Load Split dialog, select the Enable Load Split checkbox, and then enter Split Factor = 0.3 for Stage 1 and Split Factor = 0.7 for Stage 2. Select OK. The 0.3 / 0.7 load split assumes that 30 % of the field stress induced load has been relieved by displacement of the excavation boundaries before the support is installed. These load split factors, can be estimated from a plot such as Figure 6-5 in the Phase2 Axisymmetry Tutorial, based on how close the support can be installed to the advancing face of the tunnel.

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Installing the Support Now we have to install the support (bolts and liner) in Stage 2, and we will be finished with the modeling.

Select: Properties → Assign Properties To install the support at Stage 2: 1. Make sure the Stage 2 tab is selected (at the bottom left of the view). 2. In the Assign dialog, select Bolts from the list at the top of the dialog, and then select the Install button. 3. Press F2 to Zoom All (if the model is not fully zoomed). 4. Use the mouse to click and drag a selection window which encloses all of the bolts in the model. 5. The bolts should now be selected. Right-click the mouse and select Done Selection, or press Enter. The bolts are now installed in Stage 2. 6. Now select Liners from the list in the Assign dialog, and select the Install button. 7. Press F6 to Zoom Excavation. 8. Use the mouse to click and drag a window which encloses the entire excavation. All of the liner elements on the excavation boundary should now be selected. 9. Right-click the mouse and select Done Selection, or press Enter. The entire liner is now installed in Stage 2. 10. Close the Assign dialog by selecting the X in the dialog, or press Escape twice (once to exit the Install mode, and once to close the dialog). Now verify the staging of the support. Select the Stage 1 tab. The bolts and liner should appear in a light blue colour, indicating that they are NOT INSTALLED in Stage 1. Select the Stage 2 tab. The bolts and liner should appear in the dark blue colour, indicating that they are installed in Stage 2. Now we will re-run the analysis.

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Compute Before you analyze your model, let’s save this as a new file called support5.fez. (Make sure you select Save As and not Save, or you will overwrite the support4.fez file).

Select: File → Save As Save the file as support5.fez.

Select: Analysis → Compute The Phase2 Compute engine will proceed in running the analysis. When completed, you will be ready to view the results in Interpret.

Interpret From Model, switch back to Interpret.

Select: Analysis → Interpret We will now see what effect the load splitting had on the results of the analysis. Select the Stage 2 tab, since we want to view the final stage results, after the installation of the support. Let’s first look at the strength factor.

Select: Toggle the display of yielded elements on by selecting the Yielded Elements button in the toolbar. The number of yielded elements is now: 413 Yielded finite elements

This compares with 367 yielded finite elements before the load split. It is left to the user to verify that the strength factor contours and yielded zone are essentially the same as prior to the load split. This is not surprising, as we did not expect the load split to have much effect on the strength factor. Toggle the display of yielded elements off, by re-selecting the Yielded Elements button. Of more interest is the state of yielding in the bolts. Select the Yielded Bolts button in the Display toolbar. The status bar now indicates: 161 Yielded bolt elements

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The number of yielded bolt elements is substantially reduced as a result of the load split, from 205 before the load split, to 161. This is the primary result of interest from the load splitting analysis. Similarly, check the yielding in the liner, by selecting the Yielded Liner option in the toolbar. You should see that the number of yielded liner elements is only 4, compared to 27 before the load split. The load split has almost completely eliminated yielding in the liner. Toggle the display of yielded bolts and liners off, by re-selecting the Yielded Bolts and Yielded Liners options. Let’s check the displacements.

Select: The maximum displacement shown in the status bar is now: Maximum Total Displacement = 0.0529 m

This is almost identical to the maximum displacement before the load split, of .0538 m. It is left to the user to verify that the displacement contours and deformation vectors are essentially the same as prior to the load split. In summary, it should be emphasized that the primary effect of the load splitting, for this example, was to decrease the yielding in the bolts and liner, and thus improve the modeling of support. By allowing some unsupported deformation to take place in the first stage, we have traded off some increased yield of the rock mass, for decreased yield in the support. Let’s look at one more thing. Select the Stage 1 tab, and check the first stage displacements.

Select: The maximum displacement indicated in the status bar is: Maximum Total Displacement = 0.0149 m

Compare this with the maximum displacement after the final (second) stage, which was 0.0529. Based on these numbers only, the proportion of the displacement taking place in the first stage is .0149 / .0529 = about 28%. This is roughly in agreement with our load split of 30 / 70. Better agreement than this should not be expected, since our analysis is plastic, and we are only comparing a single number. It is only mentioned to further illustrate the significance of using the load split option in Phase2.

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Additional Exercise One final exercise in the Support Tutorial will be left to the user to complete, if so desired. Thus far we did not discuss the nature of the bolts we installed, however, based on the modulus of 200,000 MPa we can infer that we have been using solid steel dowels. Let’s change the bolt modulus to 75,000 MPa , as an estimated stiffness of a seven strand steel cable. Re-run the analysis, with this one change, keeping all other model parameters the same (as in the load split example). You should find that the strength factor and displacement results are nearly identical as compared to the results using the 200,000 MPa bolts. The big difference is that bolt yielding has been greatly reduced, as summarized in the following table.

Bolt Modulus

Maximum Displacement

Number of Yielded Bolt Elements

200,000 MPa

0.0529 m

161

75,000 MPa

0.0536 m

75

The conclusion that could be suggested, is that solid steel dowels may be too stiff for this very weak and highly stressed rock mass. The high stiffness of the reinforcement is not compatible with the large plastic strains which occur near the excavation boundary and which result in overstressing of the dowel/grout bond. The less stiff cables provide an almost identical support load (in terms of the extent to which the plastic zone is restricted and the deformations are limited) to the grouted dowels, but the cable/grout bond is not overstressed to nearly the same extent as for the dowels.

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Surface Excavation Tutorial 0.2 MPa

4.5 , 4

-10 , 4

6.5 , 4

15 , 4

γh -1 , 0

1,0 4.5 , -1

-10 , -8

6.5 , -1

Kγh

15 , -8

This tutorial illustrates how to model a simple surface excavation, consisting of a trench located near a circular tunnel, and a distributed load directly above the tunnel. The gravity field stress option will be used, and the analysis will be staged, by excavating the tunnel in the first stage, the trench in the second, and adding the load in the third stage. If you wish to skip the model process, the finished product of this tutorial can be found in the Tutorial 04 Surface Excavation.fez data file located in the Examples > Tutorials folder in your Phase2 installation folder.

Model If you have not already done so, run the Phase2 Model program by double-clicking on the Phase2 icon in your installation folder. Or from the Start menu, select Programs → Rocscience → Phase2 6.0 → Phase2.

Project Settings Whenever we are creating a staged model, the first thing we should always do is set the Number of Stages in Project Settings.

Select: Analysis → Project Settings In the Project Settings dialog, enter Number of Stages = 3, and select OK.

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Entering Boundaries First enter the external boundary. A surface excavation will always require a user-defined external boundary. NOTE: •

If you select the Add External option before any excavation boundaries have been entered, then you can immediately begin entering coordinates.

•

If you select the Add External option after defining excavation boundaries, then you will have to select the User Defined option in the Add External boundary dialog, in order to enter coordinates.

Select: Boundaries → Add External Enter Enter Enter Enter Enter Enter Enter

vertex[t=table,i=circle,esc=cancel]: 15 4 vertex[...]: 1 4 vertex[...]: -1 4 vertex[...]: -10 4 vertex[...]: -10 -8 vertex[...]: 15 -8 vertex[...,c=close,esc=cancel]: c

Press F2 to Zoom All. Now enter the circular tunnel.

Select: Boundaries → Add Excavation 1. Right-click the mouse and select the Circle option from the popup menu. You will see the following dialog.

2. Select the Center and radius option, enter Number of Segments = 60 and select OK. 3. You will be prompted to enter the circle center. Enter 0,0 in the prompt line, and the circular excavation will be created.

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Now enter the rectangular trench.

Select: Boundaries → Add Excavation Enter Enter Enter Enter Enter

vertex[t=table,i=circle,esc=cancel]: 4.5 4 vertex[...]: 4.5 -1 vertex[...]: 6.5 -1 vertex[...]: 6.5 4 vertex[...,c=close,esc=cancel]: c

Meshing Before we create the mesh, we will first configure the # of Excavation Nodes in Mesh Setup, so that we get a finer mesh around the excavations.

Select: Mesh → Setup

9 Enter: Mesh Type = Graded Elem. Type = 3 Noded Tri. Gradation Factor = 0.1 9 # Excavation Nodes = 100

Enter Number of Excavation Nodes = 100 and select OK.

Select: Mesh → Discretize The model is discretized, and the status bar will indicate the actual number of discretizations created. Discretizations: Excavation=130, External=75

NOTE: •

The number of excavation discretizations is 130, but we entered 100 in the Mesh Setup dialog. Depending on your excavation geometry, the discretization algorithm will not always give you exactly the #Excavation Nodes you entered in Mesh Setup.

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Notice that Phase2 automatically grades the discretization on the external boundary, according to the distance from excavation boundaries. The discretization on the ground surface is finer near the top of the trench, and is gradually graded more coarsely towards the left and right edges of the model. The discretization along the left, right and bottom edges of the external boundary, is much coarser than along the top edge near the excavations.

Now let’s generate the mesh.

Mesh Select the Mesh option from the toolbar or the Mesh menu, and the mesh will be generated, based on the discretization you just created.

Select: Mesh → Mesh The status bar will indicate the total number of elements and nodes in the mesh. ELEMENTS = 1747 NODES = 912

Note that the automatically graded discretization along the ground surface helps to create a smooth transition between the fine mesh at the top of the trench, and the rest of the ground surface.

Boundary Conditions By default, when the mesh is generated, all nodes on the external boundary are given a fixed, zero displacement boundary condition. This is indicated by the triangular “pin” symbols which you can see at each node of the external boundary. Since this is a surface excavation model, we must specify that the ground surface is a free surface. This is done using the Free option in the Displacements menu.

Select: Displacements → Free Select boundary segments to free [enter=done, esc=cancel]: Use the mouse to select the five segments representing the ground surface. When finished, right-click and select Done Selection, or press Enter.

The triangular pin symbols should now be gone from the ground surface indicating that it is free to move without restraint.

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Figure 4-1: Displacement boundary conditions on external boundary. Let’s now specify the left and right edges of the external boundary as fixed in the X direction only (i.e. free to move in the Y direction) and the lower edge as fixed in the Y direction only (i.e. free to move in the X direction).

Select: Displacements → Restrain X Select boundary segments to restrain in the X direction [enter=done,esc=cancel]: Use the mouse to select the left and right edges of the external boundary. Right-click and select Done Selection, or press Enter.

Select: Displacements → Restrain Y Select boundary segments to restrain in the Y direction [enter=done,esc=cancel]: Use the mouse to select the bottom edge of the external boundary. Right-click and select Done Selection, or press Enter.

Now we have some tidying up to do – the nodes at the bottom corners have rollers, and they should be pinned.

Select: Displacements → Restrain X,Y 1. Right-click the mouse and select Pick by Boundary Nodes from the popup menu. This will change the mode of restraint application from boundary segments to boundary nodes. 2. Select the lower left (-10 , -8) and lower right (15, -8) vertices of the external boundary. 3. Right-click and select Done Selection. Triangular pin symbols now replace the roller symbols at these vertices.

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This brings us to an important point – after applying restraints to boundary segments, you should always check that nodes at the ends of segments have the correct conditions applied. TIP: you can also apply restraints directly by right-clicking on segments or nodes and selecting a restraint option from the popup menu.

Adding a Distributed Load Now let’s add a uniform distributed load to the ground surface segment above the tunnel.

Select: Loading → Distributed Loads → Add Uniform Load

In the Add Distributed Load dialog, enter a Magnitude = 0.2 MN/m2. Select the Stage Load checkbox, and select the Stage Factors button. In the Stage Factors dialog enter Factor = 0 for Stage 1 and Stage 2, and Factor = 1 for Stage 3. Select OK in both dialogs.

Because of the Factors we have defined, the load will only be applied in the third stage of the analysis, and will not exist in the first or second stages. Factor = 1 means the magnitude will be the same as entered in the Add Distributed Load dialog. Factor = 0 means no load will be applied at that stage. Other values of Factor can be used to increase or decrease the magnitude of a load at any stage of a model. Now select the external boundary line segments to be loaded:

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Select boundary segments [enter=done,esc=cancel] : use the mouse to select the external boundary line segment directly above the circular tunnel. Right-click and select Done Selection, or press Enter.

Viewing the Load To view the load, select the Stage 3 tab. Since we only applied the load in Stage 3, it is only visible in Stage 3. For display purposes, the size of the load arrows can be scaled by the user in the Display Options dialog. This is left as an optional exercise. Since we are not finished modeling, select the Stage 1 tab again.

Distributed load added to model.

Field Stress For most problems involving a ground surface, we will want to use a gravity stress field.

Select: Loading → Field Stress

9 Enter: 9 Fld. Str. Type = Gravity 9 Ground Surf. Elev. = 4 9 Unit Wt. Overburden = .02 9 Str.Ratio (in-plane) = 0.5 9 Str.Ratio(out-of-plane) =0.5 Locked-in (in-plane) = 0 Locked-in (out-of-plane) = 0

Enter the above parameters and select OK. Note:

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•

The Ground Surface Elevation is indicated by a horizontal dotted line, and corresponds to the y-coordinate of the top surface of the external boundary (4 meters). The display of this line can be toggled on or off at any time in the View menu.

•

For a gravity field stress, the stress block reflects the in-plane horizontal/vertical stress ratio, which in this case is 0.5.

•

The Unit Weight of Overburden indicates that our material is a soil, rather than rock.

Properties Select: Properties → Define Materials

9 Enter: 9 Name = till In.El.Ld.=Fld Str & Bdy For. 9 Unit Weight = 0.02 Material Type = Isotropic 9 Young’s Modulus = 50 9 Poisson’s Ratio = 0.25 Failure Crit. = Mohr Coul. Material Type = Elastic Tens. Strength = 0 9 Fric. Angle (peak) = 38 9 Cohesion (peak) = 0.01

With the first tab selected in the Define Material Properties dialog, enter the above properties. Note the following: •

the Unit Weight of the material is the same as the Unit Weight of Overburden entered in the Field Stress dialog.

•

The modulus and strength values we entered are those of a till with high frictional strength.

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For gravity field stress, the default setting for ‘Initial Element Loading’ (in the Define Material Properties dialog) is ‘Field Stress and Body Force’. Because we are dealing with a surface excavation and a gravitational stress field, the body force component of loading on each element is significant. (For a Constant stress field, the body force component is usually not considered, and the default ‘Initial Element Loading’ is ‘Field Stress Only’).

Since we defined the properties with the first material tab selected, we do not have to assign them to the model. By default, Phase2 automatically assigns the properties of the first material to all finite elements. We do however, have to assign the staging of the excavations.

Select: Properties → Assign Properties We will excavate the tunnel in Stage 1, and the trench in Stage 2, as follows: 1. Make sure the Stage 1 tab is selected (at the bottom left of the view). 2. Select the “Excavate” button in the Assign dialog. 3. Click the left mouse button inside the circular tunnel. The elements in the tunnel will disappear, indicating that the tunnel is ‘excavated’. 4. Select the Stage 2 tab. 5. Click the left mouse button inside the rectangular trench. The elements in the trench will disappear, indicating that it is ‘excavated’. That’s all that is required. Close the Assign dialog by selecting the X in the upper right corner of the dialog. As an optional step, it’s always a good idea to verify the assignments by selecting each Stage tab in turn and inspecting the model. •

Select Stage 1 – only the tunnel should be excavated.

•

Select Stage 2 – both the trench and tunnel should be excavated.

•

Select Stage 3 – the distributed load should now appear above the circular tunnel.

You can use the Stage tabs at any time to view the stages of your model, and verify material assignments, and excavation and support sequencing. We have now completed the modeling, your finished model should appear as shown below.

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Figure 4-2: Finished model – Phase2 Surface Excavation Tutorial.

Compute Before you analyze your model, save it as a file called surface1.fez.

Select: File → Save Use the Save As dialog to save the file. You are now ready to run the analysis.

Select: Analysis → Compute The Phase2 Compute engine will proceed in running the analysis. When completed, you will be ready to view the results in Interpret.

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Interpret To view the results of the analysis:

Select: Analysis → Interpret This will start the Phase2 Interpret program.

Sigma 1 You are now viewing the Sigma 1 contours for Stage 1. Toggle the principal stress trajectories on by selecting the Stress Trajectories button in the toolbar. As you can see, the gravitational stress field results in horizontal Sigma 1 contours, except where the contours are perturbed by the excavation. Overall, the major principal stress is vertical as can be seen by the ‘long’ axis of the stress trajectories – remember our horizontal / vertical stress ratio was 0.5 (in-plane and out-of-plane). Now view the stress contours for Stage 2 and then Stage 3, by selecting the stage tabs at the lower left of the view.

Figure 4-3: Sigma 1 contours and principal stress trajectories. Gravitational field stress is in effect. Toggle the display of stress trajectories off by re-selecting the Stress Trajectories toolbar button.

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Let’s explore how we might view results for multiple stages on the same screen. The following procedure is just an example of how this could be done. 1. Select Window → New Window. When comparing contours of the same data (e.g. Sigma 1) at different stages, always check that the ranges are the same. If not, use Contour Options to set the desired range.

2. Select Window → Tile Horizontally. 3. Select the Stage 1 tab on the upper view and the Stage 2 tab on the lower view, and compare the contours. 4. Select the Stage 3 tab on the lower view, and compare the Stage 1 vs. Stage 3 contours. 5. Select the Stage 2 tab in the upper view, and compare the Stage 2 vs. Stage 3 contours.

Strength Factor Now close one of the two views, and maximize the remaining view. Press F2 to Zoom All. Change the data type to Strength Factor, and change the number of Contour intervals to 7 in the Contour Options dialog. Based on the Strength Factor contours at Stage 3, it is evident that this excavation would collapse without support. Keeping in mind that our analysis was elastic, notice the regions of failure around the tunnel, and between the trench and the tunnel (i.e. contours with strength factor < 1 in orange, and tension zones in red).

Figure 4-4: Strength factor contours at Stage 3, indicating collapse of material around excavations.

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Displacement Now let’s look at displacements.

Select: View the displacement contours at each stage, by selecting the stage tabs. Observe the maximum displacement, displayed in the status bar, and where it is occurring on the model. The Stage 1 maximum displacement, about 3 mm, is occurring at the bottom of the tunnel. The Stage 2 maximum displacement about 4.5 mm, is occurring at the left side of the trench. The Stage 3 maximum displacement, about 17 mm, is underneath the distributed load. Now let’s turn off the display of the contours, and view the deformed shape of the boundaries and mesh, magnified by a factor of 100. Toggling contours Off is useful when you wish to hide the contours and view other information, for example stress trajectories, deformation vectors or deformed boundaries.

1. Right-click the mouse and select Contour Options. 2. In the Contour Options dialog, set the Mode to Off, and select Done. 3. Right-click the mouse and select Display Options. 4. In the Display Options dialog, select Deform Mesh and Deform Boundaries, and enter a Scale Factor of 100. Select Done. 5. Select Zoom Excavation (in the toolbar, or press F6). 6. Select the Stage 1 tab.

Figure 4-5a: Deformed mesh and boundaries, stage 1. Displacements magnified by 100.

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Notice the flattened shape of the circular tunnel, and the subsidence of the ground surface above the tunnel. If you look carefully, you will notice that the bottom of the tunnel has displaced slightly more than the top. This is due to the gravity stress field, which of course increases with depth. 7. Select the Stage 2 tab.

Figure 4-5b: Deformed mesh and boundaries, stage 2. Displacements magnified by 100. The deformation of the trench boundaries is clearly visible. Notice that the excavation of the trench has shifted the displacement of the tunnel towards the right. 8. Select the Stage 3 tab. The displacements are now dominated by the effect of the load. The maximum displacement is directly beneath the load. The overall displacement of the tunnel has been shifted downward, and the bottom of the tunnel is now almost in its original position.

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Figure 4-5c: Deformed mesh and boundaries, stage 3. Displacements magnified by 100. Let’s “animate” the results. First, set the timing of the animation.

Select: Data → Stage Settings In the Stage Settings dialog, set the Minimum Animation Time to 2 seconds. Select OK. Now select the Animate Tabs option.

Select: Data → Animate Tabs The stage tabs are now automatically selected for you, giving you an animated display of results at each stage. To exit the animation mode, press Escape. Before we move on: •

Display the contours again. Right-click the mouse and select Contour Options. Set the Mode to Filled and select Done.

•

Also turn off the display of the Mesh and Deformed Boundaries, by selecting the corresponding buttons in the toolbar.

•

If you are not already zoomed in, press F6 to Zoom Excavation.

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Query Data Phase2 allows the user to query data anywhere in the material, to obtain values interpolated from the contour plots. These values can be displayed directly on the model, or graphed. A query can be a single point, a line segment, or any arbitrary polyline. The following steps will illustrate how to: •

Create a query, and show the values on the model

•

Graph the query with data from multiple stages on the same plot

•

Edit the query

Creating a Query To create a query:

Select: Query → Add Material Query 1. It will be handy to use the Snap option in this case, so right-click the mouse and select Snap. 2. When you are in Snap mode, if the cursor is near a model vertex, a circle will appear around the vertex, indicating that if you click the mouse, you will “snap” exactly to the location of the vertex. 3. Use the mouse to select the vertex at (4.5 , 4) i.e., the upper left corner of the trench. 4. Use the mouse to select the vertex at (4.5 , -1) i.e., the lower left corner of the trench. 5. Right-click the mouse and select Done. You will see the following dialog:

Choose the options shown above, and select OK.

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6. You should now see 10 values along the left edge of the trench, since we entered 10 locations in the Specify Query locations dialog. (If you are not zoomed in, select Zoom Excavation to get a better view). 7. The values correspond to the stage and the data type you are viewing. Select the stage tabs, and observe the change in the values. 8. Select different data types (e.g., Sigma 1, Strength Factor), and observe the change in values. Number of Decimal Places Displayed The number of decimal places used to display the query values, can be customized by the user in the Legend Options dialog. 1. If you changed data types as suggested above, switch back to viewing Total Displacement, at Stage 2. 2. If the Legend is currently displayed, right-click on the Legend and select Legend Options. 3. (If the Legend is NOT currently displayed, then select Legend Options from the View menu, and select the Show Legend checkbox in the Legend Options dialog.) 4. In the Legend Options dialog, select Number Format = Decimal, and use the mouse to change the number of decimal places (click on the up or down arrows). Notice that as the number of decimal places is changed, the display of values on the query, and also the interval values in the Legend, is immediately updated. 5. Set the number of decimal places to 4, and select OK in the Legend Options dialog. NOTE: the number of decimal places can be independently specified for each data type, and Phase2 will “remember” this information, so you do not have to reset the number of decimal places each time you use the program.

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Graphing a Query A short cut for graphing data for a single query, is to right-click on the query and select Graph Data. 1. Right click on the query (i.e., anywhere along the left edge of the trench), and select Graph Data from the popup menu. 2. You will see the Graph Query Data dialog.

3. Select the Stages to Plot checkboxes for Stage 2 and Stage 3. Select the Create Plot button, and a graph of Total Displacement along the query, for both Stage 2 and Stage 3, will be generated.

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Figure 4-6: Trench wall displacement, before and after adding surface load. This graph shows the “before” and “after” effect of the distributed load on the displacement of the trench wall. The upper curve represents the Stage 3 results, and the lower curve represents the Stage 2 results. The maximum difference is about 3 mm, at about 3.3 meters below the ground surface. Note that each curve on the graph has 10 points. This is because when we created the query, we only specified 10 locations at which to generate values, in the Specify Query Locations dialog. We can change the number of points to obtain a smoother graph. Close the graph, and we will edit the query and generate a new graph.

Editing a Query To edit the query: 1. Right click on the query, and select Edit Locations from the popup menu. 2. You will see the Specify Query Locations dialog again. This time enter 50 as the number of locations. Also, toggle off the “Display queried values” checkbox. Select OK. 3. Notice the values are no longer displayed on the model. Since we are now querying at 50 locations, the numbers would not be readable without zooming in, so we decided to toggle them off.

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4. Now repeat the steps outlined in the previous section (Graphing a Query) to obtain a new, smoother graph with 50 points on each displacement curve. Axis ranges and titles can be modified by rightclicking on the graph and selecting Chart Properties.

Finally, note that the axis ranges and titles can be modified by rightclicking on the graph and selecting Chart Properties. That is left as an optional exercise for the user to complete. Close the view of the graph by selecting the X in the upper right corner of the view. That concludes this tutorial, further exercises based on this model are suggested below.

Additional Exercises Single Stage Model Although this tutorial model was set up as a three stage analysis, it could also have been set up as a single stage model. The staging was done for purposes of illustration, and to allow us to see the intermediate stage results. As an exercise, re-do this problem as a single stage model. Hints: •

you do not have to explicitly define the trench as an excavation, it can be defined implicitly by the external boundary, as illustrated below.

•

in the Mesh Setup option, use #Excavation Nodes = 60, since the only ‘excavation’ in this model (according to the Phase2 boundary definitions) is the circular tunnel, which has 60 segments. After you Discretize, you will have to do some Custom discretizing of the trench boundaries and adjacent segments, to obtain a mesh similar to the one shown below.

Figure 4-7: Surface excavation model, single stage version.

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When you run the analysis, the results should be virtually identical to the third stage results presented in this tutorial, since the analysis in both cases is elastic. If we were doing a plastic analysis, this would not necessarily be the case.

Adding a Liner As another exercise, add a liner to the entire circular tunnel boundary, and re-run the analysis. Use the default liner properties (i.e. an elastic liner, 0.1 m thickness, modulus = 30000 Mpa). For details about adding liners to excavations, see the Support Tutorial, Step 2, in this manual. When you look at the analysis results, notice that the zone of tension around the tunnel is reduced in the Strength Factor contour plot, and also the displacements are reduced. (You can add the liner to the single stage model described above, or you can add it to the staged model, in which case you can experiment with installing the liner at different stages).

External Boundary Distance from Excavations If you go back and examine the contour plots (Sigma 1, Strength Factor, Displacement) in this tutorial, you will see that the external boundary is influencing the contours somewhat, at the left, right and bottom edges of the boundary. For example, the Sigma 1 contours at the lower edge of the external boundary should be horizontal for a gravity stress field, but they are not. This tells us that the external boundary is too close to the excavations, and is actually restricting movement. Re-do the staged analysis with a larger external boundary. For example, in the following figure, the left, right and bottom edges are located at x = –20, x = 25, and y = –18, respectively.

Figure 4-8: Modified external boundary for surface excavation tutorial.

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You will find that: •

The Sigma 1 contours become horizontal at a certain distance below the excavations, which is appropriate for a gravity stress field.

•

The maximum displacements are greater at each stage, as indicated in the table below. ORIGINAL BOUNDARY

EXTENDED BOUNDARY

Stage 1

.0030

.0035

Stage 2

.0045

.0062

Stage 3

.0169

.0184

Table 4-1: Maximum displacement (m) at each stage, for original and extended external boundaries. In general, the extended boundary is far enough away to better simulate ‘infinite’ conditions, and should no longer influence the results near the excavations.

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Joint Tutorial 10 MPa 10 MPa

- 27.5 , 3.5 - 2.5 , 0

2.5 , 0

27.5 , 3.5

external boundary expansion factor = 5

This tutorial involves a circular opening of 2.5 meter radius, to be excavated close to a horizontal plane of weakness (joint), located 3.5 meters above the center of the circular opening. For this analysis, the rock mass is assumed to be elastic, but the joint will be allowed to slip, illustrating the effect of a plane of weakness on the elastic stress distribution near an opening. (This example is based on the one presented on pg. 193 of Brady and Brown, Rock Mechanics for Underground Mining, 1985 – consult this reference for further information.) The finished product of this tutorial can be found in the Tutorial 05 Joint.fez file located in the Examples > Tutorial folder in your Phase2 installation folder.

Model If you have not already done so, start the Phase2 Model program by selecting Programs → Rocscience → Phase2 6.0 → Phase2 from the Start menu.

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Entering Boundaries First create the circular excavation as follows:

Select: Boundaries → Add Excavation 1. Right-click the mouse and select the Circle option from the popup menu. You will see the Circle Options dialog.

2. Select the Center and radius option, and enter a radius of 2.5. Enter Number of segments = 32 and select OK. 3. You will be prompted to enter the circle center. Enter 0,0 in the prompt line, and the circular excavation will be created. Now add the external boundary.

Select: Boundaries → Add External

9 Enter: Boundary Type = Box 9 Expansion Factor = 5

Enter an Expansion Factor of 5, and select OK, and the external boundary will be automatically created. Now add the joint to the model.

Select: Boundaries → Add Joint You will see the Add Joint dialog, which allows you to select a Joint property type, end condition and installation stage. We will use the default selections, so just select OK.

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NOTE: see the Phase2 Help system for a discussion of the Joint End Condition option.

Now enter the following coordinates defining the joint. Enter vertex [t=table,i=circle,esc=cancel]: -30 3.5 Enter vertex [...]: 30 3.5 Enter vertex [...,enter=done,esc=cancel]: press Enter

The joint is now added to the model. Note that the “closed” Joint End Condition is indicated by an icon of a circle with a triangle inside, at both ends of the joint. Phase2 automatically intersects boundaries and adds vertices when required.

Note that the two points defining the joint were actually entered just outside of the external boundary, and Phase2 automatically intersected the boundaries and added new vertices. This capability of Phase2 is very useful, for example when: •

the user does not know the exact intersection of two lines, the automatic intersection capability of Phase2 saves the user the trouble of having to calculate such intersections, or when

•

new vertices are required at known locations, they can be created automatically (rather than manually with the Add Vertices option).

Note: you could have entered (-27.5, 3.5) and (27.5,3.5) at the above prompts (i.e. points “exactly” on the external boundary) and achieved the same result. However, to be on the safe side, we entered points slightly beyond the boundary, to ensure intersection between the newly entered joint boundary, and the existing external boundary.

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All boundaries have now been entered, so we can go ahead and mesh the model.

Meshing We will now proceed to generate the finite element mesh. First let’s customize the Number of Excavation nodes in Mesh Setup.

Select: Mesh → Mesh Setup

In the Mesh Setup dialog, enter Number of Excavation Nodes = 64. Select OK. Now discretize the boundaries.

Select: Mesh → Discretize This will automatically discretize all of the model boundaries. The discretization forms the framework for the finite element mesh. Notice the summary of discretization shown in the status bar, indicating the number of discretizations for each boundary type. Discretizations: Excavation=64, External=112, Joint=75

Note that the # of excavation discretizations = 64, which is exactly what we entered in the Mesh Setup dialog, and is twice the number of line segments entered for the circular excavation. Therefore each line segment of the excavation will have two finite elements on it when the mesh is generated. Now select the Mesh option from the toolbar or the Mesh menu, to generate the finite element mesh.

Select: Mesh → Mesh The finite element mesh is generated, with no further intervention by the user. When finished, the status bar will indicate the number of elements and nodes in the mesh.

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ELEMENTS = 3256 NODES = 1759

If you have followed the steps correctly so far, you should get the same number of nodes and elements as indicated above.

Boundary Conditions For this tutorial, no boundary conditions need to be specified by the user, therefore the default boundary condition will be in effect, which is a fixed (i.e. zero displacement) condition for the external boundary.

Field Stress We will be using the default field stress for this model, which is a constant hydrostatic stress field with Sigma 1 = Sigma 3 = Sigma Z = 10 MPa. Therefore you do not have to enter any field stress parameters, the values we want are already in effect.

Properties The properties of the rock mass and the joint must now be entered.

Select: Properties → Define Materials

9 Enter: 9 Name = rock mass Init.El.Ld.=Fld Stress Only Material Type = Isotropic Young’s Modulus = 20000 9 Poisson’s Ratio = 0.25 Failure Crit. = Mohr Coul. Material Type = Elastic Tens. Strength = 0 Fric. Angle (peak) = 35 Cohesion (peak) = 10.5

With the first tab selected in the Define Material Properties dialog, enter the above properties (only a Poisson’s ratio of 0.25 needs to be entered, all other properties should be at the correct values). Select OK.

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You have just defined the rock mass properties, now do the same for the joint properties.

Select: Properties → Define Joints

9 Enter: Name = Joint 1 Normal Stiffness = 250000 Shear Stiffness = 100000 9 Slip Criterion = Mohr Coul. Tensile Strength = 0 Cohesion = 0 9 Friction Angle = 20 9 Initial Joint Def. = … (off)

With the first tab selected in the Define Joint Properties dialog, enter the above properties. Note – turn OFF Initial Joint Deformation, by clearing the checkbox. You have now defined all the required properties for the model. Since you entered both the rock mass and the joint properties with the first tab selected in the Define Properties dialogs, you do not have to Assign these properties to your model. Phase2 automatically assigns the Material 1 and Joint 1 properties for you. However, we still have to use the Assign Properties option to excavate the material within the circular excavation.

Right-click shortcut for Assigning Assignment of properties and excavation can be easily done with a rightclick shortcut, which we will now demonstrate. 1. Right-click the mouse within the circular excavation. 2. In the popup menu, go to the Assign Materials sub-menu, and select the Excavate option. That’s it, the excavation has been excavated in two quick steps, using the right-click shortcut.

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TIP: when you have a lot of property assignments and excavating to do (e.g. for complex multi-stage models), it is easier to use the Assign Properties dialog to carry out assignments. However, when you only need to make one or two property or excavation assignments, or modifications to existing assignments, the right-click shortcut is very convenient and often faster to use. You have now completed the modeling for this tutorial, your model should appear as shown below.

Figure 5-1: Finished model – Phase2 Joint Tutorial

Compute Before you analyze your model, save it as a file called joint.fez.

Select: File → Save Use the Save As dialog to save the file. You are now ready to run the analysis.

Select: Analysis → Compute The Phase2 Compute engine will proceed in running the analysis. When completed, you will be ready to view the results in Interpret.

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Interpret To view the results of the analysis:

Select: Analysis → Interpret This will start the Phase2 Interpret program. First let’s zoom in so that we can get a better look at what’s going on near the excavation.

Select: View → Zoom → Zoom Excavation That zooms us in a bit too close, so select the Zoom Out button on the Zoom toolbar 3 times, to zoom back out a bit (or press the F4 key three times).

Select: View → Zoom → Zoom Out (Note: we could have used Zoom Window to achieve the same result. The advantage of the above procedure, is that it gives us an exactly reproducible view of the model each time we use it.) Observe the effect of the joint on the Sigma 1 contours. Notice the discontinuity of the contours above and below the joint. The effect of the joint is to deflect and concentrate stress in the region between the excavation and the joint. Now view the strength factor contours.

Select: Notice the discontinuity of the strength factor contours above and below the joint. Now view the Total Displacement contours.

Select: The discontinuity of the displacement contours is not apparent. However, if you experiment with different contour options (e.g. try the Filled (with Lines) mode, the discontinuity of the displacement contours can be seen. This is left as an optional exercise. TIP: the appearance of contour plots, and your interpretation of them, can change significantly if you use different Contour Options. The contour style, range, and number of intervals, can all affect your interpretation of the data.

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Joint Yielding Now let’s check for yielding of the joint. Select the Yielded Joints button in the toolbar. The yielded joint elements are highlighted in red on the model, and the number of yielded elements is displayed in the status bar: 16 Yielded joint elements

Two separate zones of yielding in the joint can be seen, to the right and left of the excavation. View the Strength Factor and Sigma 1 contours, and notice that the region of joint slip corresponds to the region of contour discontinuity, above and below the joint.

Figure 5-2: Yielded joint elements above excavation. Remember that the joint is allowed to slip because when we defined the joint properties, we used the Mohr-Coulomb slip criterion, with a friction angle of 20 degrees. Let’s quickly verify that there are 16 yielded joint elements. Right-click the mouse and select Display Options. In the Display Options dialog, select Discretizations and select Done. You can now count the yielded joint elements, and there are in fact 16 (8 in the left yielded region, and 8 in the right). Toggle off the display of Discretizations in the Display options dialog.

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Graphing Joint Data Graphs of normal stress, shear stress, normal displacement and shear displacement can be easily obtained for joints, using the Graph Joint Data option.

Select: Graph → Graph Joint Data Since there is only one joint in the model, it is automatically selected, and you will see the Graph Joint Data dialog:

The Graph Joint Data option is also available if you right-click on a joint.

Just select Create Plot, to generate a plot of Normal Stress along the length of the joint.

Figure 5-3: Normal stress along joint.

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As expected, there is a sharp drop in normal stress where the joint passes over the excavation. Notice the number 1 at the end of the curve. If you switch back to the model view, you will also see a number 1 on the joint. This serves two purposes: 1) if there are multiple joints in your model, this number serves as an ID number and 2) it identifies which end of the joint corresponds to the end of the curve. For this example, it does not matter, since the joint and model are symmetric. If the model were not symmetric, then the location of the ID number would be important. Now repeat the above procedure, to create a graph of shear stress along the joint (in the Graph Joint Data dialog, select the Data to Plot as Shear Stress, and select Create Plot.)

Figure 5-4: Shear stress along joint. Notice the reversal of the shear stress direction over the excavation. It is this sense of slip which produces the inward displacement of rock on the underside of the plane of weakness. It is left as an optional exercise, to create graphs of normal displacement and shear displacement for the joint, and verify that the shape of the graphs correspond to the normal and shear stress plots. (Normal and shear displacement for joints refers to the relative movement of nodes on opposite sides of the joint).

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Additional Exercise Critical Friction Angle for Slip Calculations in Brady & Brown indicate that if the angle of friction for the plane of weakness exceeds about 24°, no slip is predicted on the plane, and the elastic stress distribution can be maintained. As an exercise, run the analysis using angles of friction for the joint of 20 to 24 degrees, and then use the Yielded Joints option (as described above), to check the slip on the joint. You should find the results below:

Angle of friction for joint

Number of yielded joint elements

20°

16

21°

12

22°

8

23°

4

24°

0

Table 5-1: Effect of joint friction angle on joint slip. The results above confirm that the critical angle for joint slip in this example, is around 24 degrees.

Reference for Tutorial 5 Brady, B.H.G. and Brown, E.T., Rock Mechanics for Underground Mining, George Allen & Unwin, London, 1985, pp193-194.

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Axisymmetry Tutorial 0 , 18

28 , 18 10 MPa

0 , 12 10 MPa 0,6

0,0

4,0

x=0 (axis of symmetry)

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4 , –24

12 , –24

20 , –24

28 , –24

This tutorial will illustrate the axisymmetric modeling option of Phase2. Axisymmetric modeling allows you to analyze a 3-D excavation which is rotationally symmetric about an axis. The input is 2-dimensional, but the analysis results apply to the 3-dimensional problem. An Axisymmetric model in Phase2 is typically used to analyze the end of a circular (or nearly circular) tunnel. The model we will be analyzing, shown above, represents the end of a cylindrical tunnel of 4 meter radius. The finished product of this tutorial can be found in the Tutorial 06 Axisymmetric.fez file located in the Examples > Tutorials folder in your Phase2 installation folder. A few representations of simple axisymmetric models are shown below.

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x=0

a) sphere

b) cylinder

x=0

x=0

c) ‘open’ cylinder

d) infinite cylinder

Figure 6-1: Simple axisymmetric models. For a), b) and c), the left edge of each boundary is coincident with the X = 0 (vertical) axis. For d), the boundary is displaced from the X = 0 axis, therefore modeling an infinite circular tunnel. NOTE: •

Only an external boundary is necessary to define an axisymmetric model – the excavation is implicitly defined by the shape and location (relative to the x=0 axis) of the external boundary. Appropriate boundary conditions must also be applied to complete the modeling.

•

The axis of rotation is always the X = 0 (vertical) axis. Your model must always be mapped to fit this convention, regardless of the actual orientation of the excavation. Because of the symmetry, only “half” of the problem needs to be defined.

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So, to visualize an axisymmetric excavation, just imagine the shape formed by rotating the external boundary about the x=0 axis. Note that Figure 6-1 is for illustration, and that actually the boundaries should be extended relative to the excavations (in Figures 6-1a and 6-1b) to ensure that the fixed boundary conditions do not affect the results around the excavation. Figure 6-1d can actually be defined by a narrow horizontal strip, since the problem is effectively one-dimensional (i.e. results will only vary along a line perpendicular to the tunnel), and is in fact equivalent to a circular excavation in a plane strain analysis. There are various restrictions on the use of axisymmetric modeling in Phase2, for example: •

the field stress must be axisymmetric i.e., aligned in the axial and radial directions.

•

cannot be used with BOLTS (however LINERS are permitted)

•

cannot be used with JOINTS

•

all materials must have ISOTROPIC elastic properties

In this tutorial, we will look at results not only around the end of the tunnel, but also along its length, where the conditions are effectively plane strain. We will later verify these results by comparing with a plane strain analysis.

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Model Start the Phase2 Model program.

Project Settings When you are creating an axisymmetric model, the first thing you should always do is set the Analysis Type to Axisymmetric in the Project Settings dialog.

Select: Analysis → Project Settings

9 Enter: Project Name = (optional) Number of Stages = 1 9 Analysis = Axisymmetric Max. # of iterations = 500 Tolerance = 0.001 # Load Steps = Auto Solver Type = Gauss. Elim. 9 Units = Metric (MPa)

In the Project Settings dialog, toggle the Analysis Type to Axisymmetric, and select OK.

Entering Boundaries Since only an external boundary is required to define an axisymmetric problem in Phase2, proceed directly to the Add External option (rather than the usual procedure of first adding excavations).

Select: Boundaries → Add External Enter the following coordinates at the prompts: Enter Enter Enter Enter Enter Enter Enter Enter

vertex vertex vertex vertex vertex vertex vertex vertex

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Enter vertex [...]: 20 -24 Enter vertex [...]: 28 -24 Enter vertex [...,c=close,esc=cancel]: c

Select Zoom All (or press F2) to zoom the model to the center of the view. This is the only boundary required for the problem, so we can proceed to the meshing.

Meshing As usual, we will discretize and mesh the model. However, let’s first take a look at the Mesh Setup option.

Select: Mesh → Setup

9 Enter: Mesh Type = Graded Elem. Type = 3 Noded Tri. # External Nodes = 60

Notice that the Mesh Setup dialog normally asks you for the # Excavation Nodes. However, for models which have no explicitly defined Excavation boundaries (such as this one), the # External Boundary Nodes is entered instead. Also, the Gradation Factor is not applicable when there are no Excavation boundaries defined. Select OK or Cancel, since we are using the default parameters. Now let’s discretize the external boundary.

Select: Mesh → Discretize The status bar will indicate the actual number of discretizations created on the external boundary. Discretizations: External=64

Note that this is a fairly coarse discretization. The boundary segments which are part of, or adjacent to, the excavation, will require a finer discretization. We can do this with the Custom Discretize option.

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Custom Discretization Select: Mesh → Custom Discretize Select Segments to Discretize [enter=done,esc=cancel]: use the mouse to select the long edge of the tunnel ie. the long vertical segment at the lower left of the external boundary. Right-click and select Done Selection, or just press Enter.

In the Custom Discretize dialog, enter 60 as the number of discretizations, and select OK. The length of the tunnel is now discretized into 60 elements. Now follow this same procedure to apply custom discretizations as indicated in the margin figure. Note: •

you can select more than one line segment at a time, if they require the same number of discretizations (for example, the segments with 6 and 12 discretizations, in this case).

•

the segments which are not marked in the margin figure, are to be left at their original discretizations.

CUSTOM DISCRETIZATION

Mesh Now select the Mesh option from the toolbar or the Mesh menu, and the mesh will be generated, based on the discretization you just created.

Select: Mesh → Mesh The status bar will indicate the total number of elements and nodes in the mesh. ELEMENTS = 1225 NODES = 685

At this point, we will make the following observation – you may have wondered, when we created the external boundary, why we added the extra vertices on the upper left vertical segment and lower right horizontal segment of the boundary, since these boundaries could have been defined by single segments. As you can now see, the extra segments allowed us to custom discretize the boundaries, in order to get a smooth transition between the fine mesh around the tunnel, and the coarser mesh of the rest of the boundary. (If we did not do this, a poor mesh would be generated where the fine to coarse transition is too abrupt.)

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Boundary Conditions In most of the tutorials so far, we have not been specifying any boundary conditions. We were using the default boundary condition, which is a fixed (zero displacement) external boundary. For an axisymmetric model, the external boundary conditions are very important, and must be user specified. We cannot simply leave the boundary fixed, or else nothing would happen (i.e., no displacements could take place).

Figure 6-2: Displacement boundary conditions for axisymmetric model. First, let’s ‘free’ the tunnel boundaries.

Select: Displacements → Free Select boundary segments to free [enter=done,esc=cancel]: Use the mouse to select the 2 segments marked FREE in Figure 6-2. When finished, right-click and select Done Selection, or press Enter.

The triangular pin symbols are now gone from the two boundary segments (representing the end of the tunnel and the length of the tunnel), indicating that they are free to move with no restriction in any direction. Now let’s specify the boundary segments at the upper left edge as restrained in the X direction, but free to move in the Y direction. (These segments are located on the axis of symmetry, and therefore must have zero X displacement).

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Select: Displacements → Restrain X Select boundary segments to restrain in X direction [enter=done,esc=cancel]: Use the mouse to select the three segments marked FIXED X in Figure 6-2. Right-click and select Done Selection, or press Enter.

Observe that the triangular pins on these segments have been replaced by vertical rollers. Now let’s specify the boundary segments along the bottom as restrained in the Y direction, but free to move in the X direction.

Select: Displacements → Restrain Y Select boundary segments to restrain in Y direction [enter=done,esc=cancel]: Use the mouse to select the three segments marked FIXED Y in Figure 6-2. Right-click and select Done Selection, or press Enter.

Observe that the triangular pins on the bottom segments have been replaced by horizontal rollers. Now we have a bit of tidying up to do.

Select: Displacements → Restrain X,Y 1. Right-click the mouse and select Pick by Boundary Nodes from the popup menu. This will change the mode of restraint application from boundary segments to boundary nodes. (The mode can also be changed in the Selection Mode sub-menu of the Displacements menu). 2. Select the upper left corner of the model, i.e. the vertex at (0 , 18). 3. Select the lower right corner of the model, i.e. the vertex at (28 , 24). 4. Right-click and select Done Selection. 5. A triangular pin symbol should now replace the roller symbol at these two vertices. The above steps were necessary, since the upper left and lower right vertices required a Restrained XY condition. This leads us to an important point – after applying restraints to boundary segments, you should always check that nodes at the ends of segments have the correct conditions applied. TIP: restraints can also be applied directly with a right-click shortcut, by right-clicking on segments or vertices and selecting a restraint option from the popup menu.

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Field Stress For this example, we will be using the default hydrostatic stress field of 10 MPa. However, let’s look at the field stress option, to see how an axisymmetric field stress is specified.

Select: Loading → Field Stress

Only two independent principal stresses (Horizontal and Vertical) are specified for an axisymmetric problem, and no angle is allowed. Select OK or Cancel. Note the following correspondences between Plane Strain and Axisymmetric field stress, as defined in Phase2: PLANE STRAIN

AXISYMMETRIC

Sigma 1 (in-plane)

‘Horizontal’ stress

Sigma 3 (in-plane)

‘Horizontal’ stress

Sigma Z (out-of-plane)

‘Vertical’ stress

Angle

not applicable

Table 6-1: Equivalent plane strain and axisymmetric field stress components. NOTE: •

The Horizontal (axisymmetric) field stress can also be thought of as a uniform radial stress around the excavation.

•

An angle cannot be specified for the axisymmetric field stress, because this would require a true 3-dimensional analysis, which is beyond the scope of the Phase2 axisymmetric analysis.

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It should be emphasized that the terms Horizontal and Vertical refer strictly to the setup of your model in Phase2, and not necessarily the true orientation of your excavation. The Vertical stress is the stress in the axial direction (i.e. the axis of rotational symmetry), and the Horizontal stress is the field stress perpendicular to this axis.

Properties 9 Enter: Name = Material 1

In this tutorial, we will not be defining or assigning any properties, therefore all default properties will be in effect. We have dealt with defining and assigning properties in previous tutorials.

Init.El.Ld.=Fld Stress Only Material Type = Isotropic Young’s Modulus = 20000 Poisson’s Ratio = 0.2

For reference purposes, the default rock properties which will be in effect are shown in the margin. (If you want, you can verify this by selecting Properties→ Define Materials).

Failure Crit. = Mohr Coul. Material Type = Elastic Tens. Strength = 0

Note that our analysis will therefore be elastic, and also note the values of Young’s Modulus and Poisson’s ratio.

Fric. Angle (peak) = 35 Cohesion (peak) = 10.5

We have now completed the modeling, your finished model should appear as shown below.

Figure 6-3: Finished model – Phase2 Axisymmetric Tutorial

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Compute Before you analyze your model, save it as a file called axi1.fez.

Select: File → Save Use the Save As dialog to save the file. You are now ready to run the analysis.

Select: Analysis → Compute The Phase2 Compute engine will proceed in running the analysis. When completed, you will be ready to view the results in Interpret.

Interpret To view the results of the analysis:

Select: Analysis → Interpret This will start the Phase2 Interpret program.

Sigma 1 On the Sigma 1 contours, notice the stress concentration at the ‘corner’ of the tunnel (remember the tunnel is circular). Toggle the stress trajectories on by selecting the Stress Trajectories button in the toolbar. The principal stress trajectories illustrate the “stress flow” around the end of the tunnel.

Figure 6-4: Principal stress trajectories around axisymmetric excavation.

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The square dot markers in the upper right corner of the model indicate nodes where the difference between Sigma 1 and Sigma 3 is less than a certain tolerance, so that the conditions are effectively hydrostatic, and a distinction between ‘major’ and ‘minor’ principal stress is not warranted. Toggle the stress trajectories off by re-selecting the Stress Trajectories toolbar button. As an optional step, look at Sigma 3 and Sigma Z, and consider the significance of the principal stress results from an axisymmetric analysis. As with plane strain, Sigma 1 and Sigma 3 are the major and minor ‘inplane’ principal stresses. Sigma Z is therefore the ‘out-of-plane’ stress, however, since the problem is axisymmetric, Sigma Z is really the induced circumferential or hoop stress around the excavation.

Displacement Now let’s view the displacements.

Select: Note the maximum total displacement displayed in the status bar is 0.00228 m, or just over 2 mm. This is quite small, but remember our analysis was elastic and we used a relatively high Young’s modulus. Now let’s view the deformation vectors. Right-click the mouse and select Display Options. In the Display Options dialog, toggle Deformation Vectors on, enter a Scale Factor of 600, and select Done. The deformation vectors show the inward displacement along the length and face of the tunnel. Notice how the “corner” of the tunnel effectively restrains the displacements in both x and y directions.

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Figure 6-5: Displacement contours and vectors around axisymmetric excavation. Toggle the deformation vectors off by selecting the Deformation Vectors button in the toolbar.

Query Data Phase2 allows the user to query data anywhere in the rock mass, to obtain values interpolated from the contour plots. A query can be a single point, a line segment, or an arbitrary polyline. Let’s first create a query along the length of the tunnel.

Select: Query → Add Material Query 1. It will be handy to use the Snap option, so right-click the mouse and make sure the Snap option is selected. While in Snap mode, if you place the cursor near a vertex, you can snap exactly to the location of a vertex. 2. Use the mouse to select the vertex at (4 , 0). 3. Use the mouse to select the vertex at (4 , -24). 4. Right-click the mouse and select Done. You will see the following dialog:

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Enter 50 locations, toggle off Display Queried Values, and select OK. A query has now been created along the length of the tunnel. The 50 locations at which data will be generated are indicated by black cross markers.

Graphing a Query Graphs are created from queries with the Graph Material Queries option. However, a convenient shortcut to graph data for a single query, is to simply right-click on a query and select Graph Data. 1. Right-click on the query you just created (i.e. anywhere along the length of the tunnel), and select Graph Data from the popup menu. 2. You will see the Graph Query Data dialog. Select the Create Plot button in this dialog. 3. You should see the graph in Figure 6-6. Since we were viewing the Total Displacement contours, we obtained a graph of total displacement vs. distance along the query. The data graphed always corresponds to the contoured data being viewed.

Figure 6-6: Total displacement along length of tunnel.

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As you can see, the displacement levels off and becomes constant at a certain distance away from the tunnel face. This curve is useful in that it allows us to see the distance at which end effects can be ignored, and plane strain conditions can be assumed. Also, this curve can be used to estimate the “load split” factors, as described in the Support Tutorial, Step 2.

Deleting a Query Queries are deleted with the Delete Material Query option. However, a convenient shortcut to delete a single query, is to simply right-click on the query and select Delete Query. 1. First close the graph if you are still viewing it. 2. Right-click on the query and select Delete Query, and the query will be removed from the model.

Graphing Multiple Queries Now let’s create two more queries, this time perpendicular to the tunnel, and plot them on the same graph.

Select: Query → Add Material Query 1. The Snap option should still be in effect, so use the mouse to select the vertex at (4 , -24), and then select the vertex at (28 , -24). Right-click the mouse and select Done. 2. In the Specify Query Locations dialog, enter 50 locations and select OK. Add another query.

Select: Query → Add Material Query 1. Use the mouse to select the vertex at (4 , 0). 2. Now enter the coordinates (28 , 0) in the prompt line. Alternatively, you can right-click and select the Ortho snap option, which will allow you to snap the query exactly along a horizontal line, and also to the external boundary (at the point 28,0) because the Snap option is also enabled. Right-click the mouse and select Done. 3. In the Specify Query Locations dialog, enter 50 locations and select OK. You have created two new queries, one along the lower edge of the model, and a parallel one at the face of the tunnel.

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This time, to graph the queries, we will use the Graph Material Queries option, since we want both queries on the same graph. (The right-click shortcut can only be used to graph a single query).

Select: Graph → Graph Material Queries 1. Select the two queries by clicking on them with the left mouse button. (Alternatively, you could right-click the mouse and choose Select All from the popup menu.) 2. Right-click and select Graph Selected (or just press Enter), and you will see the Graph Query Data dialog. 3. Select the Create Plot button in the dialog, and you should see the following graph.

Figure 6-7: Total displacement perpendicular to tunnel, at face (lower curve), and at 24 meters from face (upper curve). The total displacement decreases as we move away from the tunnel. Note: •

the Total Displacement along the lower boundary is exactly equivalent to the Horizontal (X) Displacement, since the Vertical (Y) Displacement along this boundary is zero. (If you graphed this query while viewing Horizontal Displacement instead of Total Displacement, you could verify this for yourself.)

•

The Total Displacement curve at the face of the tunnel includes both X and Y displacement components.

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Now close the graph view by selecting the X in the upper right corner of the view.

Writing a Query to a File Finally let’s save one of the queries to a file using the Write Query File option, so that we can use it in the last part of this tutorial.

Select: Query → Write Query File 1. Select the query at the bottom edge of the model with the mouse. 2. Right-click and select Write Selected. 3. In the Save As dialog, save the query in a file called axidisp. 4. You will then see a dialog allowing you to add a comment which identifies the file. This is optional, you can add a comment if you wish. You have just saved the data in a Phase2 “points value” file. A .pvf file is a simple text file format, which can be read back into Phase2. We will be demonstrating that in the final part of this tutorial.

Plane Strain Comparison with Axisymmetric Results To further illustrate the significance and meaning of an axisymmetric model, we will create a plane strain model which is equivalent in all respects to our axisymmetric model (except of course that the tunnel will now be infinite, with no ‘end effects’), and compare the analysis results. From Interpret, switch back to Model.

Select: Analysis → Model (Or if you quit the program and are just re-starting the tutorial at this point, then start the Phase2 Model program.)

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Model If you have been following this tutorial from the beginning, and the axisymmetric model is still open:

Select: File → New to open a new document window, so that you can begin creating a new model. Plane strain is the default analysis type, so you do not have to set this in Project Settings, it will already be in effect. Let’s first create a circular tunnel of radius 4 meters (i.e., the same radius as the axisymmetric tunnel).

Select: Boundaries → Add Excavation 1. Right-click and select the Circle option from the popup menu. 2. In the Circle Options dialog, select the Center and radius option, enter radius = 4, enter Number of segments = 60, and select OK.

3. At the prompt, enter 0,0 as the circle center, and the circular excavation will be created. Now add the external boundary.

Select: Boundaries → Add External

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We will use the default parameters, so just select OK to automatically create a BOX external boundary with an expansion factor of 3. NOTE: this external boundary is the same distance away from the excavation, as the right edge of the external boundary for the axisymmetric problem (i.e. 28 meters from the center of the tunnel).

Mesh Now discretize and mesh the model. First select Mesh Setup.

Select: Mesh → Setup In the Mesh Setup dialog, set the Number of Excavation Nodes to 60. Select the Discretize button in the Mesh Setup dialog (this is equivalent to using the Discretize option in the Mesh menu). The status bar will indicate: Discretizations: Excavation=60, External=68

Select the Mesh button in the Mesh Setup dialog (this is equivalent to using the Mesh option in the Mesh menu). The status bar will indicate: ELEMENTS = 1492 NODES = 781

Select OK in the Mesh Setup dialog.

Boundary Conditions We will use the default boundary condition, which is a fixed (i.e. zero displacement) condition on the external boundary. This corresponds to the Fixed XY condition of the right edge of the external boundary in the axisymmetric model.

Field Stress We will use the default Field Stress (i.e. hydrostatic conditions σ1=σ3=σZ = 10MPa, which is the same field stress we used for the axisymmetric problem), so you do not need to use the Field Stress option.

Properties We will use the default rock material properties, so you do not have to enter or assign any properties. The default properties are Material Type = Elastic, Young’s Modulus = 20,000 MPa, Poisson’s ratio = 0.2. However, we do have to excavate the tunnel. Let’s do this with a rightclick shortcut.

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1. Right-click the mouse inside of the circular excavation. 2. In the popup menu, go to the Assign Material sub-menu, and select the Excavate option. 3. The circular tunnel is now excavated. The model should appear as below.

Figure 6-8: Infinite tunnel, 4 meter radius, plane strain problem.

Compute Before you analyze your model, save it as a file called axi2.fez.

Select: File → Save Use the Save As dialog to save the file. You are now ready to run the analysis. (Alternatively, if you select Compute before saving a new file, Phase2 will recognize this, and display the Save As dialog).

Select: Analysis → Compute The Phase2 Compute engine will proceed in running the analysis. When completed, you will be ready to view the results in Interpret.

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Interpret We will now wrap up this tutorial with a few comparisons between the axisymmetric and plane strain models we have created. Switch back to Interpret.

Select: Analysis → Interpret View the total displacement contours.

Select: Notice the maximum displacement displayed in the status bar. Maximum Total Displacement = 0.002265 m

This is almost identical to the maximum displacement from the axisymmetric problem (0.00228). Now let’s use the Query and Graph options again to plot the displacement vs. distance from the tunnel boundary.

Select: Query → Add Material Query 1. Enter the point (4 , 0) at the first prompt and (28 , 0) at the second prompt. Right-click and select Done, or just press Enter. 2. In the Specify Query Locations dialog, enter 50 locations, and select OK. 3. Notice the query created from the right edge of the tunnel to the right edge of the external boundary. Right-click on the query and select Graph Data. 4. You will see the Graph Query Data dialog. Select the Create Plot button, and a graph of total displacement will immediately be generated. You can see the displacement decreasing from the maximum at the tunnel boundary, to zero at the fixed, external boundary. Finally, let’s compare this curve with the one we saved using Write Material Query at the end of the axisymmetric analysis. First close the graph you just created.

Select: Graph → Graph Material Queries 1. Select the query with the left mouse button. (Notice that it is highlighted with a dotted line when selected).

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2. Right-click the mouse and select Add from File. In the Open file dialog, open the axidisp file. (This is the query you saved earlier on the axisymmetric model). 3. You should see an information dialog, informing you that the query was successfully read. Select OK. 4. Now right-click and select Graph Selected, or press Enter. In the Graph Query dialog, select the Create Plot button, and the graph will be generated. The graph should show two Total Displacement curves which overlap almost exactly. •

One curve represents the query along the lower edge of the axisymmetric model, which we read in using Step 2 above.

•

The other is the query added on the plane strain model.

This illustrates the relationship between the axisymmetric and plane strain models – although the two models look very different, we can extract the same results from either one.

Additional Exercises When you plotted the total displacement contours for the plane strain tunnel model, you may not have noticed, but the contours begin to get “square” as you get further from the tunnel (immediately around the tunnel they are circular). The displacements are conforming to the shape of the external boundary and the fixed boundary condition we imposed on it.

Radial Mesh For circular problems such as this one, there is a more appropriate meshing option we could have used, called Radial meshing. Radial meshing produces a symmetric, reproducible radial mesh for symmetric problems such as this. As an additional exercise, re-do the plane strain circular tunnel analysis, with the following changes: •

After you add the excavation, DO NOT add the external boundary, but select Mesh Setup instead.

•

In the Mesh Setup option, toggle the Mesh Type to Radial, the Element Type to 4 Noded Quadrilaterals, and enter the #Excavation Nodes = 60. Note that for a Radial mesh, an Expansion Factor for the external boundary is entered, rather than a Gradation Factor.

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9 Enter: 9 Mesh Type = Radial 9 Elem. Type = 4 Node Quad Expansion Factor = 3 9 # Excavation Nodes = 60

•

Discretize and Mesh. The external boundary will appear when the radial mesh is generated.

•

Carry out the analysis and data interpretation as before.

When you plot the displacement versus distance from the tunnel, you should get nearly identical results as when you used the BOX external boundary. However, the displacement contours are no longer distorted, and are circular at any distance from the excavation. Also note that quadrilateral elements, in conjunction with Radial meshing, are very efficient, and give very good results.

Figure 6-9: Total displacement contours with radial mesh.

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Distance of External Boundary from Excavation As pointed out in other tutorials, the distance of the external boundary from the excavation(s), and the boundary conditions we impose on it, are very important. Create another Radial mesh, as described above, except this time use an Expansion Factor of 5 (in the Mesh Setup dialog). Re-run the analysis and plot the displacement versus distance from the tunnel. You will see that actually our previous Expansion Factor of 3 was too low, because displacements increase significantly when we move the fixed external boundary farther from the tunnel.

Upper curve Expansion factor = 5 Lower curve Expansion factor = 3

Figure 6-10: Moving the fixed external boundary farther from the excavation results in increased displacements. The displacements near the excavation are comparable, but diverge towards the external boundary. For example, at about 18 meters from the excavation, the displacement for the Expansion Factor = 5 curve is about double the Expansion Factor = 3 curve (see Figure 6-10). The restraining effect of a fixed external boundary should therefore always be considered. When comparing with analytical solutions, as in the Phase2 verification manual, it is very important to take this into account. One final suggested exercise: Re-do the axisymmetric problem and move the right edge of the external boundary over to 44 meters. This gives an equivalent distance from the excavation as the plain strain model with an expansion factor of 5. Compare results with the equivalent plain strain model.

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Finite Element Groundwater Seepage Phase2 has the capability to carry out a finite element groundwater seepage analysis, for saturated / unsaturated, steady state flow conditions. This tutorial will demonstrate the basic features of performing a groundwater seepage analysis with Phase2, and how this functionality is fully integrated with the stress analysis functionality of Phase2. •

After a groundwater seepage analysis is computed, the results (pore pressures), are automatically utilized in the Phase2 stress analysis to calculate effective stress.

•

The seepage analysis capability in Phase2 can also be used as a standalone groundwater program, independently of the stress analysis functionality of Phase2.

Topics Covered •

Hydraulic boundary conditions

•

Hydraulic material properties

•

Ponded water loading

•

Groundwater + Stress Analysis

•

Computed Water Table

•

Flow Vectors

•

Flow Lines

•

Iso-Lines

•

Discharge Sections

Geometry

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Model Start the Phase2 Model program.

Project Settings The first thing you must do before you can start defining a finite element groundwater model, is to set the Groundwater Method = Finite Element Analysis in Project Settings. Select Project Settings from the Analysis menu, select the Groundwater tab, and set the Method = Finite Element Analysis.

Also, select the General tab and make sure that the Units are set to Metric, stress as MPa, as that’s what we will be using for this tutorial. Select OK.

External Boundary This model only requires an External boundary to define the geometry. Select the Add External option from the Boundary menu, and enter the following coordinates in the prompt line at the bottom right of the screen. Enter Enter Enter Enter Enter Enter Enter Enter Enter

vertex vertex vertex vertex vertex vertex vertex vertex vertex

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Entering c at the last prompt automatically closes the boundary and exits the Add External Boundary option. Select Zoom All from the toolbar (or press the F2 function key) to zoom the model to the center of the view.

Mesh Now generate the finite element mesh. Select the Mesh Setup option in the Mesh menu. Change the Mesh Type to Uniform. Leave the default element type (3 Noded Triangles) and the number of elements (1500). Click the Discretize button followed by the Mesh button.

Close the Mesh Setup dialog by selecting the OK button.

Hydraulic Boundary Conditions Now define the hydraulic boundary conditions. Select the Set Boundary Conditions option from the toolbar or the Groundwater menu. NOTE: the stress analysis boundary conditions are automatically hidden when you are defining groundwater boundary conditions. You will see the Set Boundary Conditions dialog, which allows you to define the hydraulic boundary conditions for the groundwater analysis.

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Let’s first set the Total Head boundary conditions: 1. Make sure the Total Head boundary condition option is selected in the Set Boundary Conditions dialog, as shown above. 2. In the dialog, enter a Total Head Value = 26 meters. Also make sure the Selection Mode is set to Boundary Segments. 3. Now you must select the desired boundary segments, by clicking on them with the mouse. 4. Click on the THREE segments of the external boundary indicated in the following figure. (i.e. the left edge of the external boundary, and the two segments at the toe of the slope).

5. When the segments are selected, right-click the mouse and select Done Selection. A boundary condition of Total Head = 26 meters is now assigned to these line segments. NOTE: the hatch pattern represents ponded water which is defined by the Total Head boundary condition of 26 meters on the selected segments. 6. Now enter a Total Head Value = 31.8 meters in the dialog. Select the lower right segment of the external boundary, as shown below. Rightclick and select Done Selection.

The Total Head boundary conditions represent the elevation of the phreatic surface (ponded water) at the left of the model (26 m), and the elevation of the phreatic surface at the right edge of the model (31.8 m).

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Now we need to assign the Unknown (P=0 or Q=0) boundary condition to the upper two segments of the slope. 7. In the Set Boundary Conditions dialog, select the Unknown (P=0 or Q=0) boundary condition option.

8. Select the upper two segments of the slope, as shown below. Rightclick and select Done Selection.

9. The necessary hydraulic boundary conditions are now assigned.

Stress Analysis Boundary Conditions Although this tutorial is primarily concerned with how to define a groundwater seepage analysis model, we will also discuss the stress analysis aspects of the model, since in many cases you will be performing both a groundwater and a stress analysis. When you selected the Set Boundary Conditions option (in the previous section), the stress analysis boundary conditions were automatically hidden. To restore the display of the stress analysis boundary conditions, select the Show Boundary Conditions option from the toolbar or the Groundwater menu. NOTE: the Show Boundary Conditions option can be selected at any time to toggle the display between stress analysis and groundwater boundary conditions.

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Notice that the stress analysis boundary conditions (in this case, Fixed X,Y conditions on the external boundary) are now displayed. First we have to free the segments of the external boundary representing the slope surface. 1. Select the Free option from the toolbar or the Displacements menu. 2. Select the four line segments defining the ground surface of the slope, as shown below.

3. Right-click and select Done Selection. The slope surface is now free, however, this process has also freed the vertices at the upper left and upper right corners of the model. Since these edges should be restrained, we have to make sure that these two corners are restrained. We can use a right-click shortcut to assign boundary conditions: 4. Right-click the mouse directly on the vertex at (15,25). From the popup menu select the Restrain X,Y option. 5. Right-click the mouse directly on the vertex at (65,35). From the popup menu select the Restrain X,Y option. The restraint boundary conditions are now correctly applied.

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Ponded Water Load An important point to remember when you are defining a Phase2 model which includes Ponded Water, and you are carrying out both a groundwater seepage analysis and a stress analysis: •

The weight of the Ponded Water must be defined by adding a Ponded Water distributed load to the model.

The total head boundary conditions that you use to define the hydraulic boundary conditions DO NOT define the weight of the ponded water. Conversely, the Ponded Water distributed load DOES NOT define the total head boundary conditions required by the groundwater analysis. The Ponded Water load is defined as follows: 1. Select the Add Ponded Water Load option from the toolbar or the Distributed Loads sub-menu of the Loading menu. 2. You will see the Add Ponded Water Load dialog. Enter a Total Head value of 26 meters and select OK.

3. Select the slope segment between the vertices at (15,25) and (30,25) and the slope segment between vertices (30,25) and (32,26). Right-click and select Done Selection. 4. The ponded water load will be added to the model, and is represented by blue arrows applied normal to the selected boundary segments. NOTE: Phase2 automatically determines the magnitude of the load based on the value of Total Head, the elevation of the line segments, and the unit weight of water entered in the Project Settings dialog. 5. Your model should appear as in the following figure.

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Field Stress A surface model usually requires Gravity field stress, so let’s quickly define that. Select the Field Stress option from the Loading menu, select the Gravity field stress option, and also select the Use Actual Ground Surface checkbox. Select OK.

Define Hydraulic Properties Now define the hydraulic properties (permeability) of the slope material. Select the Define Hydraulic option from the toolbar or the Properties menu.

In the Define Hydraulic Properties dialog, enter a saturated permeability Ks = 5e-8. Select OK. NOTE: since we are dealing with a single material model, and since you entered properties with the first (default) tab selected, you do not have to Assign these properties to the model. The properties are automatically assigned by Phase2.

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Define Material Properties Since we are primarily concerned with the groundwater analysis for this tutorial, we will just use the default material strength and stiffness properties in the Define Material Properties dialog.

Discharge Section A Discharge Section allows you to compute the steady-state, volumetric flow rate through a user-defined line segment. Let’s add a Discharge Section to the model. 1. Select Add Discharge Section from the toolbar or the Groundwater menu. 2. Right-click the mouse and make sure that the Snap options are enabled (checkbox is displayed beside each option). 3. Click the mouse on the vertex at the crest of the slope at (50,35). 4. Click the mouse at the point (50,20) on the lower edge of the external boundary to create a vertical discharge section between the crest of the slope and the lower edge of the model.

Compute Now save the model. Select Save from the toolbar and use the Save As dialog to save the file. You are now ready to run the analysis. To compute the groundwater seepage analysis, you have two choices: Compute Groundwater Only If you only wish to compute the groundwater analysis, without computing the stress analysis, then you can select the Compute (Groundwater Only) toolbar button. This is useful if you wish to check groundwater results before running the stress analysis, or if you are not interested in the stress analysis. Compute Groundwater and Stress If you select the main Compute option, then the groundwater seepage analysis will be computed first, and the stress analysis will be computed next. The stress analysis will utilize the pore pressures calculated from the groundwater analysis. Select the main Compute option, so that both groundwater and stress analysis results will be calculated. The analysis should only take a few seconds.

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Interpret We can now view the results of the groundwater and stress analysis in the Phase2 Interpret program.

Select: Analysis → Interpret Your screen should appear as follows.

By default, if your model includes finite element groundwater seepage analysis, you will initially see contours of Pressure Head on the model when you view the results in Interpret. The Legend in the upper left corner of the view, indicates the values of the contours. The contour display can be customized with the Contour Options dialog, which is available in the toolbar, the View menu, or the right-click menu. Also note that by default the groundwater boundary conditions are displayed (Total Head etc). TIP: you can turn off the display of the Total Head values in the Display Options dialog (select the Groundwater tab and turn off the Show BC Values checkbox). This is also available as a toolbar shortcut.

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Discharge Section The Discharge Section (the vertical green line segment) displays the steady-state, volumetric flow rate of water, normal to the plane of the discharge section. The flow rate is approximately 8e-8 m3/s across the discharge section, in the direction indicated by the arrow.

Display of flow across Discharge Section The display of Discharge Sections can be turned on or off in the Display Options dialog or the toolbar. You can also use a right-click shortcut. Right-click on the Discharge Section and select Hide All Discharge Sections from the popup menu, to hide the discharge section.

Water Table You will notice on the plot, a pink line which is displayed on the model. This line highlights the location of the Pressure Head = 0 contour boundary. By definition, a Water Table is defined by the location of the Pressure Head = 0 contour boundary. Therefore, for a slope model such as this, this line represents the position of the Water Table (phreatic surface) determined from the finite element analysis. The display of the Water Table can be turned on or off using the toolbar shortcut, the Display Options dialog, or the right-click shortcut (rightclick ON the Water Table and select Hide Water Table). Notice that the contours of Pressure Head, above the Water Table, have negative values. The negative pressure head calculated above the water table, is commonly referred to as the “matric suction” in the unsaturated zone. This is discussed later in the tutorial.

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To view contours of other data (Total Head, Pressure, or Discharge Velocity), simply use the mouse to select from the drop-down list in the toolbar. Select Total Head contours from the drop-down list.

Flow Vectors Right click the mouse and select Display Options. Select the Groundwater tab. Toggle ON the Flow Vectors option. Toggle OFF all of the Boundary Condition options. Select Done. (Flow Vectors and other Display Options can also be toggled on or off with shortcut buttons in the toolbar.)

Total Head contours and flow vectors. As expected, the direction of the flow vectors corresponds to decreasing values of the total head contours. NOTE: the relative size of the flow vectors (as displayed on the screen), corresponds to the magnitude of the flow velocity. Select Total Discharge Velocity contours (from the toolbar list), and verify this. The size of the flow vectors can be scaled in the Display Options dialog. This is left as an optional exercise. Turn off the flow vectors by re-selecting the flow vectors option from the toolbar.

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Flow Lines Select Total Head contours again. We can also add Flow Lines to the plot. Flow lines can be added individually, with the Add Flow Line option. Or multiple flow lines can be automatically generated with the Add Multiple Flow Lines option. Let’s do that. 1. Select Add Multiple Flow Lines from the toolbar or the Groundwater menu. 2. Make sure the Snap option is enabled in the Status Bar. If not, then right click the mouse and enable Snap from the popup menu, or click on the word Snap in the Status Bar. 3. Click the mouse on the upper right corner of the external boundary, i.e., the vertex at (65,35). 4. Click the mouse on the lower right corner of the external boundary, i.e., the vertex at (65,20). 5. Right click and select Done. 6. You will then see a dialog. Enter a value of 8 and select OK.

The generation of the flow lines may take a few seconds. Your screen should look as follows.

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Total Head contours and flow lines Notice that the flow lines are perpendicular to the Total Head contours. (Note: only 6 flow lines are displayed, although we entered a value of 8, because the first and last flow lines are exactly on the boundary, and are not displayed.) Now delete the flow lines. Select Delete Flow Lines from the toolbar, right click and select Delete All, and select OK in the dialog which appears. TIP: Flow Lines (and Iso-Lines, discussed in the next section) can be saved by selecting the Save Tools and Lines option. This will save all drawing tools, Flow Lines and Iso-lines, so that you don’t have to recreate them each time you open a file in Interpret.

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Iso-Lines An iso-line is a line of constant contour value, displayed on a contour plot. As we discussed earlier, the pink line which is displayed on the model, represents the Water Table determined by the groundwater analysis. By definition, the Water Table represents an iso-line of zero pressure head. Let’s verify that the displayed Water Table does in fact represent a line of zero pressure (P = 0 iso-line), by adding an iso-line to the plot. 1. First, make sure you select Pressure Head contours. 2. Select the Add Iso-Line option from the toolbar, or the Iso-Line sub-menu in the Analysis menu. 3. Click the mouse on the Water Table line. You will then see the Add Iso-Line dialog.

4. The dialog will display the exact value (Pressure Head) of the location at which you clicked. It may not be exactly zero, so enter zero in the dialog, and select the Add button. 5. An Iso-Line of zero pressure head, will be added to the model. It overlaps the displayed Water Table exactly, verifying that the Water Table is the P = 0 line. 6. Press Escape or right-click and select Cancel to exit the Add IsoLine option.

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Queries Let’s now add a query to plot the Pressure Head along a vertical profile. The query will consist of a single vertical line segment, from the vertex at the crest of the slope, to the bottom of the external boundary. 1. Select Add Material Query from the toolbar or the Query menu. 2. The Snap option should still be enabled. Click the mouse on the vertex at the crest of the slope, at coordinates (50,35). 3. Enter the coordinates (50,20) in the prompt line, as the second point (or if you have the Ortho Snap option enabled, you can enter this graphically). 4. Right click and select Done, or press Enter. You will see the following dialog.

5. Enter a value of 20 in the edit box. Enable the Show Queried Values checkbox (if it is not already selected). Select OK. 6. The query will be created, as you will see by the vertical line segment, and the display of interpolated values at the 20 points along the line segment. 7. Zoom in to the query, so that you can read the values. 8. We can graph this data with the Graph Material Queries option in the Graph menu or the toolbar. Let’s use a shortcut instead. 9. A shortcut to graph data for a single query, is to right click the mouse ON the Query line. Do this now, and select Graph Data from the popup menu. 10. You will see the Graph Query Data dialog. Select the Create Plot button, and the graph will be generated, as shown in the following figure.

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Pressure Head profile along vertical section. The Query we have created, gives us the pressure head along a vertical line from the crest of the slope to the bottom of the external boundary. The data is obtained by interpolation from the Pressure Head contours. Notice the negative Pressure Head (i.e., matric suction) above the Water Table. Although we have only used a single line segment to define this Query, in general, a Query can be an arbitrary polyline, with any number of segments, added anywhere on or within the external boundary. Close the graph, and select Zoom All (if you previously zoomed in to read the query values). Also, delete the Query (right-click on the Query and select Delete Query from the popup menu).

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Stress Analysis Results Let’s just have a quick look at the stress analysis results before we conclude this tutorial. First let’s hide the groundwater boundary conditions, and display the stress analysis boundary conditions, by selecting the Show Boundary conditions option (available in the toolbar or the Groundwater menu). The stress analysis boundary conditions are now displayed. This includes the Fixed X,Y restraints on the external boundary, as well as the distributed load due to Ponded Water (represented by the blue arrows applied normal to the boundary at the toe of the slope). Because we have computed the stress analysis as well as the groundwater seepage analysis, all of the data from both analyses is available for plotting, by selecting a data type from the drop-list in the toolbar. For example, you can select the following stress analysis results for plotting: •

Principal stresses (Sigma1, Sigma3, SigmaZ)

•

Displacements (Total, Horizontal, Vertical)

•

Strength Factor

•

Effective Stress

Contours of effective Sigma1

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The effective stress results in Phase2 utilize the pore pressures obtained from the groundwater seepage analysis. The effective stress results are used in the failure criterion for each material, when computing Strength Factor and yielding.

More Groundwater Examples Many more examples of groundwater seepage analysis with Phase2 are presented in the Phase2 Groundwater Verification Manual. The files used for the verification examples, can be found in the Groundwater Verification sub-folder, in the Examples folder in your Phase2 installation folder. These examples demonstrate more advanced features of the Phase2 groundwater analysis, including material permeability functions, infiltration boundary conditions, and other features. For more information see the Groundwater Verification manual, which can be accessed through the Phase2 Help system.

Pressure head contours in dam with full reservoir

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Shear Strength Reduction Analysis In this tutorial, Phase2 is used to determine the safety factor of a simple homogeneous slope using the shear strength reduction (SSR) method. This tutorial covers the basics of setting up a model for an SSR analysis in Phase2, and interpreting the SSR analysis results. Topics Covered •

Project Settings

•

Shear Strength Reduction

•

Boundary Conditions

•

Field Stress

•

SSR Analysis Results

•

Critical SRF

Geometry

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Model Start the Phase2 Model program.

Project Settings Open the Project Settings dialog from the toolbar or the Analysis menu. Under the General tab, define the units as being “Metric, stress as kPa”. Do not change the number of stages and do not exit the dialog. Note: if you have a multi-stage model, the Phase2 strength reduction analysis is only carried out at the final stage of the model. If you want to do SSR at an intermediate stage of a multi-stage model, you will have to remove the stages after the stage of interest. You can do this by simply rolling back the number of stages in the Project Settings dialog. SSR should be used to determine the factor of safety against failure at a particular point in time (i.e. at a particular Stage). Thus, we only do SSR at one stage, not for each stage (of a multi-stage model).

In the Project Settings dialog, select the Strength Reduction tab. Turn on the Determine Strength Reduction Factor checkbox. This enables the SSR analysis. Leave the various SSR settings at the default values. Close the Project Settings dialog by pressing the OK button.

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Boundaries This model only requires an External boundary to define the geometry. Select the Add External option in the Boundaries menu and enter the coordinates shown in the figure at the beginning of this tutorial.

Mesh Now generate the finite element mesh. Before we do this, let’s define the parameters (type of mesh, number of elements, type of element) used in the meshing process. 1. Select the Mesh Setup option in the Mesh menu. 2. In the Mesh Setup dialog, change the Mesh Type to Uniform, the Element Type to 6 Noded Triangles and the number of elements to 800. 3. Close the Mesh Setup dialog by selecting the OK button. Based on our experience with numerous SSR models, we suggest using a uniform mesh with 6 noded triangles for all SSR analyses. The number of elements depends on the complexity of your model. If it is a simple model, 800 elements is fine. If the model is more complicated, then the default 1500 elements should be adequate. You can always try different mesh densities to make sure you are using enough elements to capture the correct behavior.

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Mesh the slope by selecting the Discretize and Mesh option from the toolbar or the Mesh menu.

Mesh and default boundary conditions

Boundary Conditions Now we can set the boundary conditions. The portion of the external boundary representing the ground surface (0,30 to 50,30 to 80,50 to 130,50) must be free to move in any direction. 1. Select the Free option in the Displacements menu. 2. Use the mouse to select the three line segments defining the ground surface of the slope. 3. Right-click and select Done Selection. TIP: you can also right-click on a boundary to define its boundary conditions.

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The slope surface is now free, however, this process has also freed the vertices at the upper left and upper right corners of the model. Since these edges should be restrained, we have to make sure that these two corners are restrained. Let’s use the right-click shortcut to assign boundary conditions: 1. Right-click the mouse directly on the vertex at (0,30). From the popup menu select the Restrain X,Y option. 2. Right-click the mouse directly on the vertex at (130,50). From the popup menu select the Restrain X,Y option. The displacement boundary conditions are now correctly applied.

Free boundary condition applied to ground surface NOTE: in general, the displacement boundary conditions for an SSR analysis of a slope will be a Free ground surface, and Fixed XY for the remainder of the external boundary.

Field Stress Now define the in-situ stress field. 1. Select the Field Stress option in the Loading menu. 2. Change the Field Stress Type from Constant to Gravity (gravitational stress distribution throughout the slope). 3. Check the Use actual ground surface checkbox. By using this option, the program will automatically determine the ground surface above every finite-element and define the vertical stress in the element based on the weight of material above it.

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4. Leave the horizontal stress ratios as 1, meaning hydrostatic initial stresses (i.e. horizontal stress = vertical stress). If you know the actual horizontal stress ratio when doing your own slope model, you can use this information. However, the horizontal stress distribution within a slope is rarely known, so leaving the default hydrostatic stress field has shown to be a good assumption.

Material Properties Define the material properties of the soil that comprises the slope. Select Define Materials from the toolbar or the Properties menu. Type Till for the name. Make sure the Initial Element Loading is set to Field Stress & Body Force (both in-situ stress and material self weight are applied). Enter 19 kN/m3 for the Unit Weight. For Elastic Properties, enter 50000 kPa for the Young’s Modulus and 0.4 for the Poisson ratio. For Strength Parameters, make sure the Failure Criterion is set to MohrCoulomb. Set the Material Type to Plastic, meaning the material can yield/fail. Set the Tensile Strength to 5 kPa (same as the cohesion). Set the peak and residual Cohesion to 5 kPa. Set the peak and residual Friction Angle to 30°. Leave the dilation angle at 0° (no volume increase when sheared, non-associated flow rule). Press the OK button to save the properties and close the dialog.

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You have completed the definition of the model. Save the model using the Save option in the File menu.

Compute Run the model using the Compute option in the Analysis menu. The analysis should take under a few minutes to run. Once the model has finished computing (Compute dialog closes), select the Interpret option in the Analysis menu to view the results.

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Interpret After you select the Interpret option, the Interpret program starts and reads the results of the analysis. You should see the following screen with the critical strength reduction factor (SRF) of 1.16 displayed at the top of the window. NOTE: if this same model is computed in Slide the limit equilibrium safety factor is 1.14 compared to a critical SRF of 1.16 in Phase2.

Note the different values of SRF (strength reduction factor) in the tabs along the bottom of the screen. The tab that is selected by default is the critical SRF. By default the maximum shear strain dataset is selected and contoured. Maximum shear strain will give you a good indication of where slip is occurring, especially if you change the view to higher SRF values. By cycling through the various SRF tabs, you get a good indication of the progression of failure through your slope. Use the Zoom and Pan options to center the slope in the view. TIP: if you have a mouse wheel, you can use it to zoom in and out by turning the wheel. You can also pan using the mouse wheel by holding it down while you move the mouse (cursor must be inside the view). Change the SRF to 1.5 by clicking on the SRF: 1.5 tab. Note the well formed shear band. The view should look like the following image.

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Now switch to SRF: 1. Another useful feature is the ability to animate the progression of failure. Select Display Options in the View menu. Choose the Stress tab. Turn on the Deform Contours and Deform Boundaries options. Select the Relative, All Stages scaling option. Select Done to save and exit the dialog. Now choose the Animate Tabs option in the Data menu.

Press the Escape key to stop the animation.

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NOTE: the timing of the Animation can be specified in the Stage Settings dialog in the Data menu. Select the critical SRF tab (SRF: 1.16). Another dataset of interest is Total Displacement. Use the combobox in the toolbar to select the Total Displacement dataset. The displacement contours clearly highlight the zone of failure.

Another important feature when doing an SSR analysis, is the ability to plot maximum deformation versus SRF. As the SRF is increased, the strength properties are decreased. As the strength decreases the maximum displacement increases. At some point, the slope will fail, and deformations will increase rapidly and the finite-element analysis will not converge. It is this point of non-convergence that defines the critical SRF. To view this plot, select the Graph Shear Strength Reduction option in the Graph menu. The following plot is generated. Notice the inflection in the displacements and the point where the solution does not converge.

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Close the graph. You may have noticed that the stress analysis results of Stage 1 are not available to look at. Only the data for the different SRF values are available. It is possible to view the results from the stage or stages prior to the SSR analysis. To view the results from these stages: 1. Select the Stage Settings option in the Data menu. 2. Move the reference stage slider all the way to the left so that it reads “Not Used”. 3. Select OK.

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A Stage 1 tab now exists along with the SRF tabs at the bottom of the view. You can now see the results of Stage 1 by selecting the Stage 1 tab. You may wonder why SRF: 1 was used as a reference stage for displacements. In order to factor out the elastic displacements due to rebound and stress redistribution (initial stresses and body forces are rarely in equilibrium to start with), the displacements at the minimum SRF stage are factored out. Thus all SRF displacements are relative to the displacements that occur at the minimum SRF stage. Note: The results of Stage 1 and SRF: 1 are slightly different even though the material properties are the same for both. The reason is the different tolerance and iteration count used for each. To accelerate the SSR analysis, speed optimized values of tolerance and number of iterations are used. •

You can edit the tolerance and number of iterations used in the SSR analysis, under the Strength Reduction tab in the Project Settings dialog of the Phase2 modeler.

•

You can edit the tolerance and number of iterations used for stages prior to the SSR analysis (in this case Stage 1), under the Stress Analysis tab in Project Settings.

This concludes the tutorial, you may now exit the Phase2 Interpret and Phase2 Model programs.

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Importing Slide Files / SSR Analysis

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Importing Slide Files / SSR Analysis Slide is a 2D limit equilibrium slope stability program produced by Rocscience. Phase2 version 6 can import files written by version 5 of Slide. This allows you to perform a finite element stress analysis and slope stability analysis on a Slide model, using Phase2. This tutorial will provide an overview of Slide file import and the Shear Strength Reduction method in Phase2, and then demonstrate the procedure with an example. Topics Covered •

Importing a Slide file

•

Slide options which are supported in Phase2

•

Slide options which are not supported in Phase2

•

Shear Strength Reduction (SSR) analysis

Importing a Slide Data File To import a Slide data file (.sli file), there are two possible methods: 1. You can use the File > Import > Import Slide File option. 2. Or you can use the File > Open option and set the Files of Type to Slide File Format (*.sli), as shown below.

Both methods provide identical functionality for importing Slide data files into Phase2.

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After selecting the Slide data file that you wish to import, you will see a dialog with options pertaining to how you wish to import the file.

In general, you will simply press OK, but there might be instances where you wish to modify boundaries, customize the mesh, or not start by running a Shear Strength Reduction (SSR) analysis to determine the factor of safety of your slope. In which case, you can use this dialog to customize how the Slide file is imported. After the import, you might see a warning dialog such as:

Not all functionality in Slide is supported by Phase2. Certain material and support models are not supported (see below). If a Slide model contains unsupported functionality, a warning dialog is issued. In this case, the user must change the material or support models to one supported by Phase2. The method for defining material and support models is very similar between Slide and Phase2, so the user should have no problem changing the model.

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Shear Strength Reduction Method The Shear Strength Reduction (SSR) method is widely used to determine the factor of safety of a slope using the finite-element method and is used in Phase2 version 6. The method simply reduces the shear strength of the material until the model becomes unstable. The point of instability is taken as the factor of safety of the slope. It is not the purpose of this document to describe the method. However, to understand the applicability of the method, it is important to understand its advantages and disadvantages. Some of the advantages of the SSR method include: 1) you do not have to define a failure surface or search for a minimum failure surface, how the slope fails is a result of the SSR method 2) equations of equilibrium are all satisfied, 3) strains and displacements in the soil and/or rock can be calculated, 4) strains, displacements, axial force and moment distributions in support can be calculated 5) progressive failure can be modeled. The disadvantages include: 1) Not as widely known or trusted as the limit-equilibrium methods, 2) requires more data such as material modulus, stiffness, plasticity parameters, in-situ stress, boundary conditions etc. 3) Mesh generation and model setup can be difficult and may require a high level of modeling expertise, 4) Limit equilibrium has more material models and is numerically simpler, 5) Finite-element is prone to convergence, tolerance, and numerical instability issues, 6) It is much slower and compute time intensive. Phase2 version 6 tries to remove a lot of the complexity of defining a finite-element model by directly importing a Slide data file, automatically meshing the model, automatically defining in-situ stress states, boundary conditions and material models. Thus limiting the disadvantages talked about above. In the majority of cases, little or no effort is required by the user in order to run a SSR analysis. However, the user must still be aware of what assumptions are made when setting up the finite-element model for a SSR analysis and how the finite-element model is actually created. Below is a description of how a Slide file is imported, along with a description of the assumptions made and under what circumstances the user might have to modify the model to accurately calculate the factor of safety. It is important to note that the import of Slide files and the automatic model setup is NOT fool-proof. In the majority of cases, the user should only have to import the file and click compute, but be aware that this might not always work.

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How Slide Options are Imported into Phase2 The following is a listing of Slide version 5 features which are imported into Phase2, and those features which are not currently imported into Phase2. Files written with a version of Slide prior to 5.0 are not supported but may read correctly depending on what you are trying to model.

Slide Project Settings Phase2 now supports Imperial English units and will properly read Slide files with imperial units (pounds and feet). Other project settings such as failure direction, method, tolerances etc. have no meaning in Phase2 and are not read. The groundwater setting is read. Sensitivity and probability settings are not read since Phase2 does not support these types of analyses.

Groundwater Phase2 supports the definition of pore pressures using piezometric lines, Ru, water pressure grids, and integrated steady-state groundwater seepage analysis. The properties and settings for all these techniques are properly read from the Slide file during import.

Sensitivity and Probabilistic Analyses Sensitivity and probabilistic analyses are currently NOT supported in Phase2. Data pertaining to these analyses is not imported.

Boundaries The Slide external boundary and material boundaries are all read into Phase2. The water table is read into Phase2 but since Phase2 does not support a specific water table entity, it is converted to a piezometric line with id equal to 1. Piezometric lines are read directly into Phase2. Water pressure grids are read into Phase2. Tension crack polylines are NOT read into Phase2.

Tension Cracks The explicit modeling of a tension crack region is not directly supported in Phase2 since no facilities exist in the finite-element method for a zero strength material with possible hydrostatic forces applied to the surface of a tension crack. Consequently, how one models a tension crack zone using a finite-element analysis is open to debate. One method that has been used successfully (see Verification#27 in the Phase2 Slope Stability Verification manual), is to represent the soil in the tension crack region as a distributed load applied to the soil underlying the tension crack zone. This works well for dry tension cracks but water filled tension cracks is another issue.

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Tutorial Manual

Importing Slide Files / SSR Analysis

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Distributed and Line Loads Distributed loads (uniform and triangular) and line loads are imported into Phase2.

Pseudo-static Seismic Loads Phase2 supports the import of pseudo-static seismic load coefficients from Slide.

Material Properties The following Slide material models are supported: 1) Mohr-Coulomb, 2) Undrained (Constant), 3) Undrained F(datum), 4) Infinite Strength, 5) Shear-Normal Function, 6) Hoek-Brown, 7) Generalized Hoek-Brown, 8) Power Curve. The following Slide material models are not supported: 1) Undrained F(depth), 2) No Strength, 3) Anisotropic Strength, 4) Anisotropic Function, 5) Vertical Stress Ratio, 6) Barton-Bandis, 7) Hyperbolic, 8) Discrete Function, 9) Drained-Undrained. The Shear-Normal function is supported by fitting a Generalized HoekBrown envelope to the discrete data points. The Power Curve function is supported by converting it to the Generalized Hoek-Brown failure criterion. The Anisotropic Strength and Anisotropic Function set the material type to Mohr-Coulomb and set the strength as being the minimum of the different directions. Anisotropy in strength is not supported in Phase2.

Support and Support Properties Phase2 will read Slide support elements. All support elements in a Slide file are read in as Phase2 bolt elements EXCEPT for geotextiles. Geotextiles are read in as structural interface elements. Structural interfaces have two components: 1) A structural beam element to model the tensile behavior of the geotextile, 2) Two interface elements on either side of the geotextile to model slip between the geotextile and the soil. Active and passive force application methods for Slide support models have no meaning in a Phase2 finite-element analysis, and are therefore ignored. An equivalent behavior can be defined by setting a PreTensioning force in the Phase2 bolts. Slide support models that are imported into Phase2 are: 1) End Anchored, 2) Geotextiles, 3) Grouted Tieback, 4) Soil Nail.

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Importing Slide Files / SSR Analysis

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Support models which are NOT imported: 1) Grouted Tieback (with friction), 2) Micro-Pile. End anchored or deadman anchors are read in as Phase2 end-anchored bolts. Peak capacity of the Phase2 bolt is set to the Slide anchor capacity, the residual capacity is set to zero. The bolt spacing is read from the Slide file. Geotextiles will convert to structural interfaces with Phase2 liner elements being defined as geotextiles with a default tensile modulus and a peak tensile capacity. The peak tensile capacity is read from the Slide geotextile support properties. The residual tensile strength is set to zero. The tensile modulus is given a default value equal to 100 times the tensile strength. The user should define the appropriate tensile modulus for the geogrid/geotextile they are using. See the online help for a description of this parameter. If the Slide Shear Strength Model for the geotextile-soil interface is linear, the Phase2 joint interface properties for the structural interface are given a Mohr-Coulomb slip criterion with cohesion and friction angle equal to the adhesion and friction angle defined for the Slide geotextile. If the Slide Shear Strength Model for the geotextile-soil interface is hyperbolic, the Phase2 joint interface properties for the structural interface are given a Geosynthetic Hyperbolic slip criterion with adhesion and friction angle equal to the adhesion and friction angle defined for the Slide geotextile. Interface normal and shear stiffnesses between the geotextile and the soil are also required. Default values of Kn=100000KPa/m and Ks=10000KPa/m are used. These are based on a number of published values and can be changed in the Joint Properties dialog. Material dependant geotextile properties are not read from the Slide file but can be manually defined in Phase2. Slide anchorage methods are supported through the different finite-element mesh end conditions of the structural interface. See the online help for more information on these parameters. Strip coverage is not supported for values other than 100%. You will have to factor the interface and tensile strength properties to account for strip coverage. Slide Grouted Tiebacks and Soil Nails are both converted to Phase2 tieback bolts. The only difference between the two is the grouted length. Soil Nails have 100% grouted length. The Phase2 tieback peak tensile capacity is taken as the minimum of the Slide plate capacity and tensile capacity. The residual capacity is set to zero. The bolt spacing is read from the support spacing in the Slide file. In the case of tiebacks, the grouted length is properly read. For both Slide soil nails and grouted tiebacks, the bond strength is properly read.

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Importing Slide Files / SSR Analysis

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Slide Grouted Tiebacks with friction are not properly read into Phase2. They are read as Phase2 tieback bolts but no bond capacity is defined. The user must either define an equivalent bond capacity to the frictional characteristics, thus accounting for the depth of the anchor, or use structural interface elements instead. In the case of structural interface elements, the debonded length of the bolt should be given different material properties than the bonded length. In particular, the debonded length should be given joint stiffness properties (normal and shear) equal to zero. You will require a vertex on the structural interface to separate the bonded from the debonded length. Micro-piles are not supported in Phase2. Piles should be modeled using structural interfaces or liner elements. User-defined support properties in Slide are not supported in Phase2.

Mesh Generation The complete finite-element mesh is automatically created during the import of the Slide file. No user intervention is required. The mesh, by default, will contain approximately 800 uniformly distributed 6 noded triangular elements.

Boundary Conditions The import facility automatically determines the top, bottom and sides of the external boundary used in the Slide model. The boundary conditions applied to these surfaces are: 1) the top boundary (ground surface) is free to move in the x and y directions, 2) the sides are fixed in the x and y directions (pinned), 3) the bottom surface is fixed in the x and y directions (pinned). The following image shows a typical mesh and boundary conditions after import of a Slide model.

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Importing Slide Files / SSR Analysis

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Initial Stress and Body Force By default, each finite-element is given both an initial stress and a body force (self weight). The initial vertical stress is estimated from the weight of the material above the element. Phase2 automatically determines the ground surface above the element and automatically determines the stress due to the material above the element. The horizontal initial stress is set equal to the vertical stress (hydrostatic stress state). The body force is equal to the unit weight defined for the material in Slide. Since Phase2 allows for only one unit weight, when reading a Slide file, the greater of the moist or saturated unit weight is taken. This system of element loading (the combination of initial stress and body force) is defined in the material properties dialog by defining the Initial Element Loading as being Field Stress & Body Force. Initial Element Loading is one of the more complicated concepts in Phase2 and it is highly recommended for people who do not understand it, to review the online help on the subject. Since the initial stress and body force does not define an equilibrium state for a slope (or any non-horizontal ground surface), the material within the slope will deform under the influence of its own self weight and initial stress. In general, the material will deform horizontally away from the slope surface since the initial horizontal stresses are not in equilibrium. The final vertical stress distribution within the slope will be a gravitational stress distribution while the horizontal stress will be due to some unloading and redistribution of stress due to the poisson effect. By default, all materials are given a poisson ratio of 0.4. If you know your material’s poisson ratio, you may change the default value inside the Phase2 material properties dialog. Horizontal stress plays a very important role in the stability analysis. In general, little is known about the horizontal stress distribution within a soil or rock mass. So assuming that the material has an initial hydrostatic stress state is not unreasonable. This is the assumption made in a large number of the slope stability verification examples. Results from these examples show good agreement with the Slide results. If knowledge of the initial vertical and horizontal stress state is known, it should be used in defining the initial stress state for the model.

Ponded Water In Phase2, ponded water is replaced by an equivalent distributed load (pressure) normal to the submerged portion of the external boundary. The distributed load, which varies according to the submerged topology, is defined using a series of “Ponded Water” loads which are oriented normal to the external boundary. When importing a Slide file with ponded water, Phase2 will automatically replace the ponded water by these ponded water distributed loads.

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Importing Slide Files / SSR Analysis

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Groundwater Finite-Element Analysis Both Slide and Phase2 have integrated steady-state unsaturated groundwater modeling capabilities. Thus Phase2 will read the hydraulic properties (i.e. permeability, unsaturated hydraulic parameters), boundary conditions, and finite-element mesh from the Slide data file. By default, if a Slide model contains a groundwater mesh, Phase2 will use this mesh for both stress and groundwater analysis and will not generate a new mesh on import of the Slide file. The only exception to this rule is if a distributed load exists in the Slide file as well. In this case, the mesh must be created during import but the boundary conditions of the groundwater mesh are preserved.

Phase2 v.6.0

Tutorial Manual

Importing Slide Files / SSR Analysis

9-10

Slide File Import / Shear Strength Reduction Example We will now give a quick demonstration of the Import Slide File option, and the Shear Strength Reduction method in Phase2.

Import Slide File 1. In the Phase2 Model program, select File…Import…Import Slide. 2. Navigate to the Examples > Tutorials folder of your Phase2 6.0 installation folder. 3. You will find a Slide file named Tutorial 09 Slide File.sli. Open this file. 4. You will see the Slide Import Options dialog. Just select OK in this dialog (leave the default checkbox selections). 5. The file will be imported into Phase2 and you should see the following model.

Slide file imported into Phase2 NOTE: •

This Slide file already included finite element groundwater seepage analysis, therefore the existing groundwater mesh from Slide was imported directly into Phase2.

•

The groundwater boundary conditions in Slide defined ponded water at the toe of the slope. As you can see in the above figure, this has been converted into an equivalent distributed load (blue arrows) in Phase2.

•

As an optional exercise, you can compare the material properties of this model in both Slide and Phase2. Open this file in Slide (assuming you have the Slide program). Compare the Material (strength and hydraulic) properties in Slide and Phase2. You will find that the properties are the same.

•

Note that the filename (in Phase2) now has a .FEZ filename extension. This is the filename extension used for Phase2 files.

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Importing Slide Files / SSR Analysis

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Compute (with Shear Strength Reduction) This model does not need any modifications, and can be computed immediately. If this model is computed in Phase2, the following computations will be carried out: 1. The finite element groundwater seepage analysis will be run first, to determine pore pressures (this will be virtually instantaneous, you will not notice it). 2. Then the Phase2 stress analysis will be run, which will include the pore pressures from the groundwater seepage analysis (also very quick for this file). 3. Lastly, the Shear Strength Reduction slope stability analysis will be computed. This will take some time (perhaps 5 to 10 minutes or more, depending on the speed of your computer).

Shear Strength Reduction Analysis Results Select the Interpret button in the Phase2 Model program, to view the analysis results. You should see the following:

Results of SSR analysis for imported Slide file. Notice the following:

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1. By default, after an SSR slope stability analysis has been performed in Phase2, the Maximum Shear Strain contours will be displayed. The Maximum Shear Strain contours highlight the “failure” of the slope at the critical Strength Reduction Factor. 2. The critical SRF represents the Strength Reduction Factor at which the slope becomes unstable (i.e. the stress analysis approaches non-convergence). 3. You will notice that the Stage tabs at the bottom of the screen indicate “SRF: (value)”. Each tab corresponds to ONE iteration of the SSR analysis, using the indicated value of Strength Reduction Factor. 4. By default, the tab with the critical Strength Reduction Factor will be displayed initially. In this case, the critical SRF = 1.56. (Note: this compares with a minimum safety factor slip circle in Slide = 1.52, which is in good agreement). 5. By default after an SSR analysis in Phase2, only the SSR results are displayed. If you wish to view the regular Phase2 analysis results (i.e. the results of the stress analysis without applying the Strength Reduction Factor), you must select Data…Stage Settings (in Phase2 Interpret), and set the Reference Stage = 0 (Not Used). You will then see the results for all stages before the SSR analysis (e.g. the Stage 1 tab) followed by the SSR tabs.

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Importing Slide Files / SSR Analysis

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Graphing the Strength Reduction Factor If you select Graph … Graph Shear Strength Reduction, you will see the following graph.

This graph summarizes the essential results of the SSR analysis. The Strength Reduction Factor is plotted against the Maximum Displacement (at any point in the model). The critical Strength Reduction Factor corresponds to the point at which the Maximum Displacement shows a sudden increase (i.e. the model becomes unstable).

Importing Surfaces between Slide and Phase2 Before we conclude this quick introduction to SSR analysis with Phase2, we will mention a useful feature common to both Slide and Phase2. If you wish to compare a limit equilibrium slip surface (determined by Slide) with the zone of Maximum Shear Strain contours (after the Phase2 SSR analysis), you can easily import surfaces (polylines) between Slide and Phase2. To import a surface from Slide to Phase2: 1. Run the model in Slide. 2. In the Slide Interpret program, right-click the mouse on the critical slip circle/surface. 3. Select Copy (slide modeler format) from the right-click menu. 4. Now, in the Phase2 Interpret program, go to the Edit menu and select Paste from Slide Interpret. 5. You will see the slip circle/surface from Slide Interpret, imported into Phase2 Interpret. NOTE: the surface is imported as a Polyline Drawing Tool entity.

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If you carry out these steps for the current example model, you will see the following:

Notice the critical slip circle (from Slide) corresponds approximately to the zone of Maximum Shear Strain contours in Phase2. A similar procedure can be used to import a drawing polyline from the Phase2 Interpret program, into the Slide Model program. In the Slide Model program, it can be imported as an actual slip surface, which allows you to run a Slide analysis on a surface imported from Phase2. That concludes this tutorial, for more examples of the Shear Strength Reduction method, see the Phase2 Slope Stability Verification manual, and the accompanying example files, which are installed with the Phase2 program.

Phase2 v.6.0

Tutorial Manual

SSR Search Area

10-1

SSR Search Area In this tutorial, Phase2 is used to determine the factor of safety of an embankment using the shear strength reduction (SSR) method. The slope stability analysis is restricted to one side of the embankment by defining an SSR search area. Topics covered •

Import from Slide

•

Shear strength reduction

•

SSR search area

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Add failure surface from Slide

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SSR Search Area

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Model In this tutorial we will import a model that was constructed in Slide. Slide is a 2D limit equilibrium slope stability program available from Rocscience. If you are not familiar with Slide, see the Rocscience website for information. To import the model file into Phase2, select Import from the File menu and click on Import Slide. Open the file Tutorial 10 Slide File.sli found in the Examples > Tutorials folder in your Phase2 installation directory. TIP: You can also import a Slide file by simply choosing Open from the File menu. At the bottom of the Open dialog, for Files of type, select Slide File Format (*.sli) from the drop down menu. Once you have opened the Slide file, you will see the following dialog.

This allows you to set various options for the finite element analysis. We want to perform a shear strength reduction (SSR) analysis to determine the factor of safety for slope stability so leave this option on. We also want Phase2 to automatically generate a finite element mesh and appropriate boundary conditions so leave these options on as well (Slide analyses do not require a finite element mesh so the mesh must be generated by Phase2). Click OK to accept the defaults. You should now see a model that looks like this.

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This model represents a sloped embankment built upon a sand layer overlying a foundation clay layer that sits on top of bedrock. The water table is 25 feet below the top of the embankment and ponded water exists at the left side of the model. The ponded water exerts a force on the soil as shown by the blue arrows.

SSR Analysis – Default Region The model is already completely built so we can perform the shear strength reduction analysis. Save the file in Phase2 format by selecting Save As from the File menu. Now select Compute from the Analysis menu. The computation will take several minutes. When it is finished click on the Interpret button to see the results. You will now see a plot showing the maximum shear strain in the model for the critical shear strength reduction factor (SRF = 1.52). If you click on the tabs for higher SRF factors, you will see the development of a clear failure surface on the right side of the embankment. The plot for SRF = 1.75 is shown below.

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If you display the deformation vectors you will clearly see the displacement of the slope on the right side with very little deformation on the left side. In an SSR analysis, Phase2 automatically finds the slope failure mechanisms associated with the minimum shear strength reduction (minimum factor of safety). In this case, the most likely failure occurs on the right side of the embankment. What if we are only interested in failure on the left side? We need to somehow restrict the analysis to the left side of the model. In Slide, you can simply choose the failure to proceed from right to left. In Phase2 we can define an SSR search area.

Define SSR Search Area Go back to the Phase2 modeller program by clicking on the Open Modeler button. We will now specify the area over which we would like to perform the SSR analysis. Go to the Analysis menu and select SSR Search Area > Define SSR Search Area. You will now see cross hairs and you will be asked to enter the first point of the search area. You will need to enter two points to define two diagonally opposite corners of a rectangular area. We wish to encompass the left side of the model so choose a first point above and to the left of the model (near −250, 100. The exact coordinates do not matter so you can use the mouse to choose the point). Now choose a second point below the model and just to the right of the embankment plateau (around 40, −60). Be sure to include the entire flat top of the embankment since it is likely that the failure surface will intersect somewhere on this plateau. The model should now look like this.

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You can easily resize the search area by right clicking on one of the corner points and clicking on Move To. You will now see the cross hairs again and you can move the point to a new location. Click the left mouse button to finish the move. You can delete the search area by going to the Analysis menu and selecting SSR Search Area > Delete SSR Search Area. TIP: You can also define the SSR Search Area by choosing Project Settings from the Analysis menu and clicking on the tab for Strength Reduction. At the bottom of the dialog, turn on the option Limit SSR Search Area and click on the Define button. You can now enter the limits of the search area as shown.

You have now finished defining the SSR search area. Save the file with a different name and run Compute. Open the Interpreter.

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Interpret A screen is now displayed with the critical strength reduction factor (SRF) of 2.01 written at the top of the window. Click through the higher SRF plots and you will see the development of a failure zone on the left side. The plot below shows the maximum shear strain for SRF = 2.12.

Note that the critical SRF for this analysis (2.01) is higher than the critical SRF of the previous analysis with no search area defined (SRF = 1.52). This indicates that the left side of the embankment is more stable than the right. This is why Phase2 did not show failure on the left in the previous analysis since it only looks for the failure mode with the lowest factor of safety, unless you restrict the search area as we have done here. The reason for the different stability of the right and left sides, is due to the stabilizing effect of the ponded water force on the left side of the embankment. TIP: You can animate the viewing of the different SRF stages by choosing Animate Tabs from the Data menu. Hit the Esc key to stop the animation. If you are a Slide user, you can directly compare the Slide analysis with the Phase2 analysis. If you run the Slide model and you are looking at the Interpret window you will see a circular failure surface as shown.

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Note the factor of safety calculated by Slide is 2.03, which is very close to the value calculated by Phase2 (2.01). In the Slide Interpreter, right click on the failure surface and select Copy (Slide modeler format). Go back to the Phase2 Interpret window and choose the plot for SSR: 2.12. Go to the Edit menu and choose Paste from Slide Interpret. You will now see the failure surface appear on the plot as a black line. You can modify the appearance of the line by right clicking on it and choosing Format. Change the colour to red and the weight to 3. Click OK and your plot should now look like this.

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You can see the very good agreement between the Slide limit equilibrium analysis and the Phase2 finite element analysis. This concludes the tutorial, you may now exit the Phase2 Interpret and Phase2 Model programs.

Phase2 v.6.0

Tutorial Manual

Geogrid Reinforced Embankment (No Slip)

11-1

Geogrid Embankment (no slip) This tutorial will demonstrate the use of geosynthetics in Phase2, by performing a shear strength reduction (SSR) analysis for a sand embankment on top of a soft clay layer with a geogrid liner in between. The geogrid liner is considered to be fully bonded to both soil layers to prevent slip at the geogrid/soil interface. Topics Covered •

Shear strength reduction

•

Slope stability

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Multiple materials

•

Liner support (Geogrid)

•

Graphing liner data

Geometry

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Geogrid Reinforced Embankment (No Slip)

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Model Start the Phase2 Model program.

Project Settings Open the Project Settings dialog from the Analysis menu and make sure the General tab is selected. Define the units as being “Metric, stress as kPa”. Do not change the number of stages and do not exit the dialog.

In the Project Settings dialog, select the Strength Reduction tab. Turn on the Determine Strength Reduction Factor checkbox. This enables the SSR analysis. Leave the various SSR settings at the default values. Close the Project Settings dialog by pressing the OK button.

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Geogrid Reinforced Embankment (No Slip)

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Boundaries This model requires an External boundary to define the geometry, and a material boundary between the sand and clay layers. Generate these boundaries as follows: 1. For the external boundary, select the Add External option in the Boundaries menu and enter the coordinates shown in the figure at the beginning of this tutorial. 2. For the material boundary, select the Add Material option in the Boundaries menu and enter the coordinates (0,3) and (21,3) or simply click on these points on the existing boundary. Hit enter to finish.

Mesh Now generate the finite element mesh. Before we do this, let’s define the parameters (type of mesh, number of elements, type of element) used in the meshing process. 1. Select the Mesh Setup option in the Mesh menu. 2. In the Mesh Setup dialog, change the Mesh Type to Uniform, the Element Type to 6 Noded Triangles and the number of elements to 800. 3. Close the Mesh Setup dialog by selecting the OK button.

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Mesh the model by selecting the Discretize and Mesh option in the Mesh menu.

Mesh and default boundary conditions

Boundary Conditions Set the boundary conditions on the slope portion of the model. What we want to do is define the portion of the exterior boundary representing the ground surface (0,9 to 10,9 to 21,3 to 30,3) as being free to move in any direction. 1. Select the Free option in the Displacements menu. 2. Select the three line segments defining the ground surface of the slope. 3. right-click and select the Done Selection menu option (or hit Enter). TIP: you can also right-click on a boundary to define boundary conditions. We now want the exterior boundaries on the left, right and bottom sides to be restrained in the x and y direction (pinned/fixed) so that these points will not move. By default these boundaries are fixed when the model is created, however freeing the surface boundaries also caused the freeing of the corner nodes (0,9 and 30,3). To re-fix these points, select the Restrain X,Y option in the Displacements menu. Select the two line segments defining the top-left and right sides, and hit enter. The following image represents what the model should now look like.

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Free boundary condition applied to ground surface

Field Stress Now define the in-situ stress field. 1. Select the Field Stress option in the Loading menu. 2. Change the Field Stress Type from Constant to Gravity (gravitational stress distribution throughout the slope). 3. Check the Use actual ground surface checkbox. By using this option, the program will automatically determine the ground surface above every finite-element and define the vertical stress in the element based on weight of the material above it. 4. Leave the horizontal stress ratios as 1, meaning hydrostatic initial stresses. If you know the horizontal stress ratio when doing your own slope model, you can use this information. However, the horizontal stress distribution within a slope is rarely known, so leaving the default hydrostatic stress field has shown to be a good assumption.

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Geogrid Reinforced Embankment (No Slip)

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Material Properties Define the material properties of the soft clay layer and the overlying sand fill. Select the Define Materials option in the Properties menu. Make sure the first tab (Material 1) is selected. Type Sand Fill for the name. Change the colour to a sandy yellow if you wish. Make sure the Initial Element Loading is set to Field Stress & Body Force (both insitu stress and material self weight are applied). Enter 17 kN/m3 for the Unit Weight. For Elastic Properties, enter 50000 kPa for the Young’s Modulus and 0.4 for the Poisson ratio. For Strength Parameters, make sure the Failure Criterion is set to Mohr-Coulomb. Set the Material Type to Plastic, meaning the material will yield/fail. Set the Tensile Strength, Cohesion and residual cohesion to 0 kPa. This is representative of a dry, unconsolidated sand embankment. Set the peak and residual Friction Angle to 37°. Leave the dilation angle at 0° (no volume increase when sheared, non-associated flow rule). Do not press the OK button. The dialog should appear as shown.

Now define the properties of the clay layer. Click on the second tab (Material 2). Change the name to Soft Clay. Enter the material properties as shown in the following diagram. Press the OK button to save the properties and close the dialog.

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Assigning Properties Assign the different material properties to different layers in the model. Select Assign Properties in the Properties menu. By default the entire model is set to Material 1 (Sand Fill). Change the bottom layer to Soft Clay by selecting Soft Clay in the dialog and clicking anywhere in the lower layer of the model. Close the dialog. The model should now appear as shown. TIP: you can also assign material properties by right clicking in the desired material layer and choosing Assign Material from the pop-up menu.

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Geogrid Reinforced Embankment (No Slip)

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Geogrid We now wish to add a geogrid between the clay layer and the sand fill to increase the strength of the slope. A geogrid is a flexible planar reinforcement that offers no resistance to bending or compression. The geogrid has a tensile strength only. In this case the geogrid is modeled in Phase2 as a simple liner. Note that this is only true when there is assumed to be no slip between the reinforcement layer and the soil. For geosynthetics with slip allowed see Tutorial 12 (Geogrid Embankment with Slip). To create the geogrid in the model, first assign its properties. From the Properties menu, choose Define Liners. For Liner 1, change the name to Geogrid. At the top right of the dialog under Liner Type, select Geosynthetic. NOTE: you must change the Liner Type from Beam to Geosynthetic prior to filling in any other properties, since the geosynthetic does not possess flexural rigidity like a regular beam or liner. Now set the Tensile Modulus to 50000, set the Material Type to Plastic and set the Tensile Strength (peak) to 60. Click the OK button to save the settings and close the dialog.

Now we must add a geogrid to the model. Select Add Liner from the Support menu. Ensure that Geogrid is selected for the Liner Property. Click OK to close the box. Now click anywhere on the material boundary to install the geogrid. Right click and choose Done Selection or hit Enter to finish. Your geogrid is now installed and the model should appear as in the following figure.

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NOTE: If your liner appears under the material boundary rather than above it, this is likely because you entered the points for the material boundary from right to left rather than from left to right. Although this will not affect the results, you may wish to flip the liner around so that your plots will be consistent with the plots in this tutorial. To do this, right click on the liner and choose Reverse Liner Orientation.

You have completed the definition of the model. Save the model using the Save option in the File menu.

Compute Run the model using the Compute option in the Analysis menu. The analysis should take a few minutes to run. Once the model has finished computing (Compute dialog closes), select the Interpret option in the Analysis menu to view the results.

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Interpret After you select the Interpret option, the Interpret program starts and reads the results of the analysis. The following screen is displayed with the critical strength reduction factor (SRF) of 1.45 written at the top of the window. TIP: Click and drag the legend to the right side of the screen so as not to cover up the model.

The Interpret view lists the various computed reduction factors in tabs along the bottom of the screen. The tab that is selected by default is the critical SRF. The maximum shear strain dataset is selected and contoured. Maximum shear strain will give you a good indication of where slip is occurring, especially if you change the view to higher SRF values. By cycling through the various SRF tabs, you get a good indication of the progression of failure through your slope. Display the yielded elements in the geogrid by clicking the Display Yielded Liners button. You should see no change, indicating that none of the geogrid elements have failed.

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Change the SRF to 1.46 by clicking on the SRF: 1.46 tab at the bottom of the window. Observe that two of the geogrid elements have failed and that large shear strains accompany this failure. Clearly the tensile failure of the geogrid has resulted in unstable sliding of the slope (lack of convergence in the model).

Now switch to SRF: 1.75. The view should look like the following image. Note the two well-formed shear bands in the model. Methods for further interpretation of SSR models are presented in Tutorial 8 “Shear Strength Reduction Analysis”.

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Graphing Geogrid Data A graph of the tensile force acting on the geogrid can be easily obtained. Select the Graph Liner Data option in the Graph menu, then click on the geogrid line and hit Enter. A dialog will appear asking which data you would like to plot. Use the defaults for the Vertical Axis and Horizontal Axis. Under Stages to Plot, turn on SRF: 1.45 and SRF: 1.46. Turn off the other ‘stages’. Recall that the different SRF models are considered as different stages in Phase2. TIP: you can perform the same task by right clicking on the geogrid liner and choosing Graph Liner Data.

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Select Create Plot to generate a graph of axial force along the length of the geogrid liner for the two SRF models.

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This graph shows the tensile (negative) forces supported by the geogrid. Recall that the geogrid cannot support compressive forces. You can see that the failure of two elements in the SRF: 1.46 model has caused a drastic drop in the tensile forces compared with the SRF 1.45 model. This loss of support in the geogrid is what leads to the slope failure in the model.

Additional Exercise Try re-running the model with no geogrid liner. You should observe that the critical SRF is 1.27 and that the failure surface is less localized.

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Geogrid Embankment (with slip) In Tutorial 11, we performed a shear strength reduction (SSR) analysis for a sand embankment on top of a soft clay layer with a geogrid liner in between. We will now proceed with the same model and add the following features: 1. Allow slip between the geogrid liner and the soil layers. 2. Construct the model in two stages. The first stage simulates only the clay layer. The geogrid and the sand fill embankment are added in the second stage. Topics Covered •

Shear strength reduction

•

Slope stability

•

Staging

•

Multiple materials

•

Initial element loading

•

Structural interfaces

•

Joints

•

Liner support (geogrids)

Geometry

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Model Start the Phase2 Model program and open the .fez file you created in Tutorial 11. If you did not do Tutorial 11 then open the file Tutorial 11 Geogrid Embankment (no slip).fez from the Examples > Tutorials folder of your Phase2 installation folder.

Project Settings Open the Project Settings dialog from the Analysis menu and make sure the General tab is selected. Change the number of stages from 1 to 2. Click OK to save and close the dialog.

Staging In this tutorial we wish to build the model in a more realistic way than in Tutorial 11. The first stage will consist of only the clay layer. In the second stage we will then add the geogrid and the sand fill embankment. We do this by applying the following steps: 1. Click on the Stage 1 tab at the bottom of the window. Right click inside the Sand Fill layer and choose Assign Material. A list of possible materials will now appear. Choose Excavate. This will delete the sand fill layer. 2. Right click on the geogrid liner. Choose Delete Liner from the popup menu. Your model should now appear as in the following figure.

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3. Click on the Stage 2 tab. Add the sand fill embankment by right clicking in the excavated zone, choosing Assign Material, and then choosing Sand Fill. 4. Since the sand fill is manually deposited on top of the existing clay layer, the sand fill will not have an in-situ stress associated with it. The stress that develops in the sand fill will be purely due to its own weight. Therefore we need to change the sand fill properties. Right click inside the sand fill. Select Material Properties. For Initial Element Loading select Body Force Only as shown. For more information on initial element loading consult the Phase2 Help.

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5. The sand fill will likely settle under its own weight. To enable this settlement, we need to allow the left boundary to move in the vertical direction. To do this, right click on the left boundary of the sand embankment. Select Restrain X. The clay layer will also compact under the weight of the sand so right click on the left boundary of the clay layer and select Restrain X. Finally, we want the bottom left corner to be restrained both in X and Y, therefore right click on the bottom boundary and select Restrain X,Y. The model should now look like this.

The model will now simulate the deposition of a sand fill embankment in the second stage.

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Geogrid We now wish to add a geogrid between the clay layer and the sand fill in Stage 2 of the simulation. In Tutorial 11, we modelled the geogrid as a simple liner. This is a good method if there no slip between the reinforcement layer and the soil. To simulate a geosynthetic with slip, we need to create a Structural Interface. The Structural Interface option in Phase2 allows you to model support which has a sliding interface (joint) on BOTH sides of the support element. We therefore need to assign Joint properties as well as Liner properties.

Properties The Liner properties should already be assigned. Check by choosing Define Liners from the Properties menu. Ensure that for Liner 1 (Geogrid) the Liner Type is set to Geosynthetic, the Tensile modulus is 50000, the Material Type is Plastic and the Tensile peak and residual strengths are 60 and 0 respectively. Now go to the Properties Menu and select Define Joints. For Joint 1, change the name to Support 1. Set the Slip Criterion to Mohr-Coulomb and change the friction angle to 30 degrees. Leave all other parameters at their default values. The window should look like this:

Click OK to close the window.

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To assign properties to the Structural Interface, choose Define Structural Interface from the Properties menu. You can see how the Structural Interface is composed of a Liner sandwiched between two joints. You can specify different combinations of Liner and Joints to make up a Structural Interface. You can also change the properties of the liner or joints from this window by clicking on the ellipses (…) next to the joint or liner name. We will use the existing values so click OK to close the window.

Add Support Now we must add the Structural Interface to the model. Choose Add Structural Interface from the Boundaries Menu. You will be asked if you wish to reset the mesh as shown.

The reason that Phase2 needs to reset the mesh is that the structural interface is composed of multiple nodes that initially overlap but may separate as slip occurs on the joints. The following schematic diagram illustrates the point.

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Click OK to reset the mesh. You will now see the Add Structural Interface dialog. Choose Structural 1 for the Property. Now select First point closed / last point open for the end condition. If a Joint end is Closed, this means that the end of the Joint boundary is represented by only ONE node in the finite element mesh, and therefore relative movement (sliding or opening) cannot occur at the joint end. If a Joint end is Open, this means that the end of the Joint boundary is represented by TWO nodes in the finite element mesh, which can move with respect to each other. In our model, one end of the joint will terminate at a free surface (the toe of the embankment) so this end should be set to Open. The end of the structural interface within the embankment will be defined as Closed. We only want the geogrid to be installed at Stage 2 of the simulation. Therefore set the Install at stage option to 2. The dialog should look like this.

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TIP: After you have installed the structural interface, you can still change the stage at which it is installed. To do this, view the desired stage and then right click on the Structural Interface and select Install At This Stage. Click OK to close the dialog and begin selection of the boundary points. Click on the two end points of the existing material boundary (coordinates 0,3 and 21,3). Be sure to click the left point first to ensure that this is the closed end of the Structural Interface. Right click and choose Done or hit Enter to finish. The Structural Interface will now appear as a green line with a circled triangle indicating the closed end and an open circle representing the open end as shown.

HINT: You can also add the Structural Interface by using the Phase2 Convert Boundary option to convert a Material boundary to a Structural Interface boundary. This is performed by selecting Convert Boundary from the Edit sub-menu of the Boundaries menu. See the Phase2 Help for more information. NOTE: in the Phase2 Interpret program, the 3 components of the Structural Interface (joint/liner/joint) will be expanded and drawn with thick line segments for easy viewing. You have now finished installing the geogrid.

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Mesh The model was unmeshed in order to add the Structural Interface. However this does not affect the mesh parameters. You therefore do not need to re-enter the mesh parameters. To remesh the model simply choose Discretize and Mesh from the Mesh menu. You have now completed building the model. Save the model using the Save option in the File menu.

Compute Run the model using the Compute option in the Analysis menu. The analysis should take a few minutes to run. Once the model has finished computing (Compute dialog closes), select the Interpret option in the Analysis menu to view the results.

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Interpret After you select the Interpret option, the Interpret program starts and reads the results of the analysis. The following screen is displayed showing the Maximum Shear Strain contours at the critical Strength Reduction Factor (SRF = 1.45). TIP: Click and drag the legend to the right side of the screen so as not to cover up the model.

Before looking at the Shear Strength Reduction analysis, you may want to check the effect of the staging. You will see that the stress analysis results of Stage 1 and Stage 2 are not available to look at. Only the data for the different SRF values are available. To view the results from the different stages: 1. Select the Stage Settings option in the Data menu. 2. Move the reference stage slider all the way to the left so that it reads “Not Used”. 3. Press the OK button to exit the dialog.

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Stage 1 and Stage 2 tabs now exist along with the SRF tabs at the bottom of the view. You can now see the results of Stage 1 by selecting the Stage 1 tab. After selecting the Stage 1 tab, plot contours of maximum stress by choosing Sigma 1 from the drop down menu on the tool bar. Your model should now look like this.

You can see that the stress increases with depth in the clay layer due to gravitational load as you would expect. This stress is mostly due to the initial element loading. If you plot displacements, you will see that virtually no displacement has occurred.

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Click on the Stage 2 tab, and you can see larger stresses under the sand embankment. Change the contours to plot displacements by choosing Total Displacements from the drop down menu on the tool bar. Show the deformation vectors by selecting the Display Deformation Vectors button. Clearly a large amount of vertical displacement occurred in the sand and the clay as the soil layers compacted under the weight of the sand.

Click on the SRF=1 tab and you will see the same results. This is because SRF: 1 means that no strength reduction has been applied so these results are the same as the Stage 2 results. If you wish to look at deformations caused by strength reduction, rather than by settlement, you must go back to the Stage Settings item in the Data menu and set the reference stage back to SRF 1. Now go back to the plot of SRF: 1.45 and change the contours back to Maximum Shear Strain. Turn off the displacement vectors. Display the yielded elements in the geogrid by clicking the Display Yielded Liners button. You will see that joint elements at the toe of the embankment have failed (slipped). Slippage has occurred on both sides of the geogrid, i.e. between the liner and the sand, and also between the liner and the clay. If you go back to the plot for SRF: 1 you will see the same slippage even before any shear strength reduction. This shows that the weight of the sand material has caused slip along the geogrid-material interfaces but that this slip is not responsible for the failure of the slope.

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Now change the SRF to 1.46 by clicking on the SRF: 1.46 tab at the bottom of the window. Observe that one element in the geogrid itself has failed and that large shear strains accompany this failure. Clearly the tensile failure of the geogrid has resulted in unstable sliding of the slope (lack of convergence in the model).

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Click through the other SRF plots and you will see further failure in the geogrid and the evolution of two localized shear bands as in the model from Tutorial 11.

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Groundwater Flow in a Coffer Dam

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Groundwater Flow in a Coffer Dam In this tutorial, finite element groundwater seepage analysis is used to determine the quantity of seepage entering a cofferdam. The problem is solved in three stages as follows: 1. Installation of sheet pilings to hold back water 2. Excavation of soil inside the dam 3. Pumping of water inside the dam The example is based on problem 2.4 from Craig (1997). The problem is constructed and solved entirely with Phase2. Topics Covered •

Seepage analysis

•

Renaming stages

•

Multiple materials

•

Relative coordinates

•

Boundary copying

•

Discharge sections

•

Groundwater only calculation

•

Flownets

Geometry

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Model Start the Phase2 Model program.

Project Settings Open the Project Settings dialog from the Analysis menu and make sure the General tab is selected. Define the units as being “Metric, stress as kPa”. Change the number of stages to 3. Now click on the Rename Stages… button. We will perform the simulation in three stages. Name the first stage “Dam”, the second stage “Excavate” and the third stage “Pump” as shown.

Click OK to close the Rename Stages dialog. Back in the Project Settings dialog, select the Groundwater tab. Under Method choose Finite Element Analysis. This enables steady state finite element analysis of groundwater flow. Under Compute choose Groundwater Only since we are not interested in solid deformations and stresses in this tutorial. Close the Project Settings dialog by pressing the OK button.

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Boundaries First add an external boundary. Select the Add External option in the Boundaries menu and enter the four corner coordinates shown in the figure at the beginning of this tutorial. Now we need to add boundaries to separate the ponded water from the soil and to delineate the impermeable sheet piling. First draw a horizontal material boundary across the model by choosing Add Material from the Boundaries menu. Enter the coordinates (0,10) and (27,10). Hit Enter to finish. The sheet piling is assumed to be very thin. To create the boundary for the sheet piling therefore, it is easier to enter relative distances instead of absolute coordinates. Go to the Boundaries menu and select Add Material. Enter the top left coordinate for the right sheet piling (18,13) and hit enter. Now you can enter a relative distance from this point for the next point. Enter @ 0.2 , 0 in the prompt line and hit enter. This will put the next point 0.2 m away in the x direction and 0 m in the y direction. Now enter @ 0 , −8 to plot the next point 8 m below. Now enter @ −0.2 , 0 and finish with @ 0 , 8 to close the boundary. To create the left sheet pile, simply right click on the right sheet pile, select Copy Boundary, and enter the relative coordinates @ −9 , 0. Hit Enter. Finally, enter another horizontal material boundary to delineate the water level inside the dam for stage 2 (excavation). Select Add Material from the Boundaries menu and enter the coordinates 9.2 , 7.5 and 18,7.5. Hit Enter to finish. Your model should now look like this:

TIP: When you need to enter a lot of complicated geometry to your model, it can be useful to see the distance between points and the angles between lines. You can do this by going to File and choosing Preferences and turning on the option Show segment length, radius, angles when adding geometry.

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Material Properties Select Define Materials from the Properties menu. You will now see all of the default material properties for Material 1. In this tutorial we don’t care about the strength and stiffness of the solid material therefore leave all the default values. Change the name of Material 1 to Soil. Now click on the Material 2 tab. Change the name of Material 2 to Sheet Pile. Click OK to close the dialog. We now need to define the fluid flow properties of the soil. To do this, go to the Properties menu and choose Define Hydraulic. Click on the Soil tab at the top of the dialog. Enter 4e−7 for Ks. Ks is the saturated permeability in m/s (also called hydraulic conductivity). You may specify anisotropic permeability by specifying K2/K1 ≠ 1 and an angle to indicate the directionality. However we will assume isotropic permeability so do not change the default values. The Model option at the top of the dialog refers to the function used to calculate the permeability in the unsaturated zone as a function of matric suction. Different models may be chosen, including a user-defined model. However we will use the default Simple option. See the Phase2 Help for more information on permeability models. Your dialog should now look like this.

Now select the Sheet Pile tab. The sheet piling is assumed to be essentially impermeable. We wish to set the permeability to a very low value, however we cannot choose 0 since this will lead to numerical instability. Therefore set the permeability, Ks, to 1e−20. Click OK to close the window.

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Assign Material Properties By default, the entire model is assigned the properties of Soil (material 1). In our model, the top left and top right sections will represent ponded water and the top middle section will be empty space. We therefore need to remove the soil material from these areas. Ensure that you are looking at Stage 1 (Dam). Select Assign Properties from the Properties menu. Click on the Excavate button and then select the top left, top middle and top right sections of the model. Do not close the dialog. We now wish to assign the Sheet Pile properties to the sheet pilings. Select Sheet Pile from the Assign dialog and click inside the 4 sections representing the 2 sheet pilings. Do not close the dialog. Your model for Stage 1 should now look like this.

Now click on the Stage 2 (Excavate) tab at the bottom of the Phase2 window. Click the excavate button in the Assign dialog and then click in the middle section of the model to excavate the area between the sheet pilings. Close the assign dialog. Your model for Stage 2 (Excavate) should appear as below.

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Mesh Now generate the finite element mesh. Select the Mesh Setup option in the Mesh menu. Change the Mesh Type to Uniform. Leave the default element type (3 Noded Triangles) and the number of elements (1500). Click the Discretize button followed by the Mesh button.

Close the Mesh Setup dialog by selecting the OK button. Your model should now appear as shown.

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Boundary Conditions The model shows the default boundary conditions for the solid soil (all external boundaries fixed in the x and y directions). Since we are only performing a groundwater analysis, we don’t care about the stress and displacement boundary conditions. To set the boundary conditions for the groundwater analysis, select Show Boundary Conditions from the toolbar or the Groundwater menu. Make sure you are looking at Stage 1 (Dam). For all stages we wish to simulate ponded water to the left and right of the sheet piling. The elevation of the top of the sheet piling is 13 m. Therefore we will set the total head for these boundaries to 13 m. To do this, choose Set Boundary Conditions from the Groundwater menu. For BC Type choose Total Head. Enter a Total Head Value of 13.

Now select the four boundary segments that enclose the ponded water: Line 1: from (0,10) to (9,10) Line 2: from (9,10) to (9,13) Line 3: from (18.2,10) to (18.2,13) Line 4: from (18.2,10) to 27,10)

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Click Apply and your model should look like this.

The soil surface inside the coffer dam has zero pore pressure (it is at atmospheric pressure). Therefore we need to set the pressure on this surface to zero. In the Set Boundary Condition Dialog, choose Zero Pressure for the BC Type. Click on the ground surface between the pilings and hit Enter (or right click and choose Done Selection). Now close the dialog box. Your model will appear as shown.

Boundary conditions applied at Stage 1. TIP: you can also right-click on a boundary to define its boundary conditions. Now select the Stage2 (Excavate) tab at the bottom of the window. Set the pore pressure for the top of the soil layer to zero as you did for Stage 1. You may also remove the zero pressure BC for the boundary where the soil used to be in Stage 1 (although this is not necessary).

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Boundary conditions applied at Stage 2. Finally, select Stage 3 (Pump). In this stage we wish to simulate pumping such that the water table will be below the surface. To do this set the Total Head for the soil surface between the pilings to 7 m. This is slightly below the actual elevation of 7.5 m. The model should now appear as shown.

Boundary conditions applied at Stage 3. We are now done applying the boundary conditions so close the Set Boundary Conditions Dialog.

Discharge Sections If we wish to calculate flow quantities, this is done by defining a Discharge Section. A Discharge Section in Phase2 is a user-defined line segment, through which the steady state, volumetric flow rate, normal to the discharge section, will be calculated during a groundwater seepage analysis.

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We wish to add discharge sections at the soil surface. To do this, choose Add Discharge Section from the Groundwater menu. Enter a start point on the left boundary just below the ponded water. Add a finish point on the left edge of the left sheet piling just below the ponded water. After the second point is entered, the discharge section will be added to the model, and you will automatically exit the Add Discharge Section option. You can enter the coordinates using the keyboard but it is easier to just click on the model since the cursor will snap to the boundaries (if the cursor does not snap to the boundaries go to the View menu, select Snap and ensure all of the options are selected). The discharge section is displayed as a green line, with small circles marking the endpoints as shown. The value of the flow rate across this line will be displayed in the Phase2 Interpret program, when you view the analysis results.

TIP: you can delete a discharge section by right-clicking on it and choosing Delete Discharge Section. Now perform the same steps to set three more discharge sections: one below the soil surface on the other side under the ponded water, one below the soil surface between the sheet pilings in Stage 1 and one below the soil surface between the sheet pilings in Stage 2. NOTE: It doesn’t matter at what stage you add the discharge sections. They will persist throughout the whole model. You final model should now appear as shown.

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Cofferdam model – Stage 1 (Dam) You have completed the definition of the model. Save the model using the Save option in the File menu.

Compute Recall that the model is set up for groundwater computation only. Therefore you must run the model using the Compute (groundwater only) option in the Groundwater menu (or click the Compute groundwater only button in the toolbar). The analysis should take a few seconds to run. Once the model has finished computing (Compute dialog closes), select the Interpret option in the Analysis menu to view the results.

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Interpret After you select the Interpret option, the Interpret program starts and reads the results of the analysis. The following screen is displayed showing the pressure head results for Stage 1 (Dam).

You can also see the volumetric flow rate and direction through each of the discharge sections. As you would expect, the water is flowing down from the ponded water and up into the dam. The sum of the volumetric downwards flow is equal to the volumetric upwards flow between the sheet pilings. To see the magnitude and direction of flow throughout the model, plot the Flow Vectors by clicking the Flow Vectors button. It is clear that the groundwater is flowing around the impermeable sheet pilings with high flow rates directly below the pilings.

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Pressure head and flow vectors for stage 1 Now click on the Stage 2 tab (Excavate). You can now see the flow conditions after some soil has been excavated. This geometry corresponds to Problem 2.4 in Craig (1997). This problem asks for the quantity of seepage entering the cofferdam. From the figure below, the volumetric flow into the dam is 2.0234e-6 m3/s. The value given in Craig (1997) is 2.0e-6 m3/s.

Pressure head and flow vectors for stage 2 TIP: you can hide the display of the discharge section that is no longer in the soil by right clicking on it and selecting Hide This Discharge Section.

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The problem also asks for a flow net to be constructed. This can also be done with Phase2. First turn off the flow vectors by pressing the flow vector button again. Now change the quantity being plotted from Pressure Head to Total Head using the drop down menu on the tool bar. Now right-click on the model and select Contour Options. Under Mode select Filled (with lines) and then select Done. You will now see the equipotential lines of the flownet. To plot the flow lines, go the Groundwater menu and select Add Multiple Flow Lines. Select the top left corner of the soil as the first point (you may need to move the legend out of the way prior to this). If the cursor does not snap to the node point go to the View menu, select Snap and ensure that all snap options are turned on. Now move horizontally until you intersect the sheet piling and click to establish the second point. Hit enter to finish. You will now see the Flow Lines Options dialog. Here you can choose how many flow lines you wish to plot. Under Flow Line Start Locations select the first option and leave the default value (10 locations, evenly spaced along the polyline).

Click OK to close the dialog. You will now see 10 flow lines plotted as shown. To complete the flownet you could repeat these steps for the right side of the model.

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Now select the Stage 3 tab (Pump). For this stage, pumping was simulated by applying a total head lower than the elevation. You can see that the volumetric discharge at the bottom of the dam is higher than in Stage 2. You can also see that the water table has been lowered. The water table is shown as a pink line (your water table line may be obscured by the green discharge line. To hide the discharge line, right click on it and choose Hide This Discharge Section).

This concludes the tutorial, you may now exit the Phase2 Interpret and Phase2 Model programs.

References Craig, R.F., 1997. Soil Mechanics, Spon Press, London and New York, 485 pp.

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Geotextile Reinforced Ramp

14-1

Geotextile Reinforced Ramp In this tutorial, a ramp is constructed and its performance under loading is assessed. The model is created in four stages as follows: 1. Foundation soil layer is brought to equilibrium. 2. Fill is added on top of the soil interlayed with geotextile support layers. Precast concrete liners are added to support the fill. 3. The concrete road bed is constructed on top of the fill. 4. Load is applied to the road surface. Topics Covered •

Import DXF

•

Geotextiles

•

Liners

•

Structural Interfaces

•

Selection Windows

•

Selection Filter

•

Discretization Density

•

Mapped meshing

•

Staged Loading

•

Liner Bending Moments

Geometry

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Model Start the Phase2 Model program.

Project Settings Open the Project Settings dialog from the Analysis menu and make sure the General tab is selected. Define the units as being “Metric, stress as kPa”. Change the number of stages to 4. Close the dialog by clicking OK.

If you changed the Units from some other system, then you will see a warning window telling you that default values will change to reflect the new units. Click Yes to verify the unit change.

Boundaries To save typing in many coordinates, we will import the boundary geometry from a DXF file (AutoCAD Drawing Exchange File). This technique is useful if a problem geometry has already been constructed in Autocad and you do not wish to re-enter the geometry in Phase2. To import the file, select Import DXF from the Import sub-menu of the File menu. In the DXF Options dialog, select External Boundary, Materials and Stages as shown.

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Select the Import button, and you will see an Open File dialog. Select the file Tutorial 14 boundaries.dxf from the Examples > Tutorials folder in your Phase2 installation folder. Click OK. You will see a model with external, material and stage boundaries as shown.

NOTE: Stage boundaries perform the same function as material boundaries but are plotted grey instead of green. In previous versions of Phase2, stage boundaries were used to delineate excavations between stages and material boundaries were used to separate different materials. You can now use them interchangeably.

Material Properties Select Define Materials from the Properties menu. Change the name of Material 1 to Foundation Soil. For Initial Element Loading choose Field Stress & Body Force. This choice reflects that the soil layer is in-situ with both self weight and stress. See the Phase2 Help for more information on initial element loading. Set the Unit Weight to 20 kN/m3. Leave all other properties as the default values. Note that the Material Type is set to elastic, meaning that there can be no failure in this layer.

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Now click on the Material 2 tab. Change the name of Material 2 to Fill. Change the Initial Element Loading to Body Force only. This is the logical choice if the fill is to be manually added such that it settles under its own weight. Change the Unit Weight to 23 kN/m3, the Young’s Modulus to 10000 kPa and the Poisson’s ratio to 0.3. Under Strength Parameters, set the Material Type to plastic to enable failure in the Fill. Set the peak and residual friction angle to 35 degrees and the peak and residual cohesion to 0 kPa as shown.

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Now click on the tab for Material 3. Change the Name to Concrete and enter the parameters as shown below. Note the high value for Young’s Modulus indicating a very stiff material. Observe also that the Material Type is elastic, indicating that there is no failure allowed in the Concrete.

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Click OK to close the dialog.

Assign Material Properties By default, the entire model is initially assigned the properties of Foundation Soil (material 1). We now need to build up the road material stage by stage. Click on the Stage 1 tab at the bottom of the Phase2 window. Choose Assign Properties from the Properties menu. Select excavate and click in all areas above the soil material boundary. This should leave just the Foundation Soil as shown.

Assigned materials for Stage 1. Now click the Stage 2 tab. Select Fill from the Assign Materials dialog and click inside the three sections that make up the fill as shown.

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Assigned materials for Stage 2. Click on the Stage 3 tab. Select Concrete from the Assign Material dialog and click inside the three sections making up the concrete road surface as shown.

Assigned materials for Stage 3. Close the Assign Materials dialog.

Support Properties First we will set the properties of the precast concrete support. Choose Define Liners from the Properties menu. Change the name from Liner 1 to Precast Concrete. Change the Young’s modulus to 20000000 kPa and the thickness to 0.15 m as shown.

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Click OK to close the dialog. The geotextile reinforcement layers must be modelled using Structural Interfaces. These allow slip to occur between the fill material and the geotextile. To set the properties of the Structural Interface select Define Structural Interface from the Properties menu. You will now see how a structural interface is composed of a liner sandwiched between two joints (slip elements). We don’t want the use the precast concrete as our geotextile liner, so for the Liner choose Liner 2 from the drop down menu. To set the properties of the Liner, click on the ellipsis (…) to the right of Liner 2. You will now see the Define Liner Properties dialog with Liner 2 selected. Change the Name to Geotextile. Under Liner Type select Geosynthetic. Now set the tensile modulus to 4000 kN/m, the Material Type to Plastic and the peak Tensile strength to 80 kN/m as shown. Leave the residual tensile strength at 0.

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Click OK to close the dialog. You now need to set the properties of the joints on either side of the liner. In the Define Structural Interface Properties dialog, click on the ellipsis (…) to the right of Joint 1. You will now see the Define Joint Properties dialog. Change the Slip Criterion to Mohr-Coulomb and set the Friction Angle to 32 degrees as shown.

Click OK to close the dialog.

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Your Structural Interface Properties dialog should now appear as shown.

Click OK to close the dialog.

Assign Geotextiles The geotextile supports are a series of horizontal Structural Interfaces within the Fill. The coordinates are already defined from reading in the DXF file. To add the Structural Interfaces, select Add Structural Interface from the Boundaries menu. In the Add Structural Interface dialog, select First point closed / last point open. Under Staging, set Install at stage to 2. The dialog should appear as shown.

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Click the OK button. Select the point with coordinates (11 , 9). You may enter the point with the keyboard but it is easy to select the point with the mouse since the cursor will snap to existing points. Now click on the point at (14.7 , 9). Right click and choose Done. You will now have one structural interface that cannot slip on the outside edge (indicated by a circle with a triangle in it) and is free to slip on the inside edge (marked by an open circle).

TIP: to enable snapping to existing geometry, select Snap from the View menu and turn on all options. You can perform the same task by clicking on the words in the status bar at the bottom of the Phase2 window next to the coordinates, or use the right-click menu. The easiest way to add the remaining Structural Interfaces is by copying and pasting. Right click on the Structural Interface you just constructed. Select Copy Boundary. You now need to enter a point from which to copy (base point), so select the left point of the existing Structural Interface. Enter the point to copy to by selecting the next point directly below (11 , 8). A copy of the Structural Interface should now appear. Repeat these steps for the remaining points on the left side of the Fill until your model appears as shown.

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Now we need to add Structural Interfaces to the right side of the fill. You could repeat the above technique (be careful to ensure that the outside point is closed and the inside point is open). Alternatively you could use the multiple copying capability of Phase2. To do this, go to the Boundaries menu, select Edit and choose Copy. You can now select all of the Structural Interfaces by drawing a selection window around them (click the left mouse button and hold it down while moving the mouse to expand the size of the box). Hit Enter to finish the selection. Now select a base point to copy from (say 11 , 9) and then a point to copy to (15.3 , 9). You should now have an exact copy of the Interfaces on the right side of the fill. TIP 1: For selecting multiple boundaries, the default option is Select Inside Only, meaning that only line segments completely inside the selection window will be selected. You can change this to select line segments that cross the selection window as well by right clicking while you are making your selection, choosing Selection Window, and choosing Select Inside or Crossing. TIP 2: When trying to select the Structural Interfaces, you may enclose other boundaries with your Selection Window. Since we only want to copy the Structural Interfaces, we can use a Selection Filter. Just before you draw your Selection Window, right click and choose Selection Filter. Now uncheck everything except for Structural Interfaces as shown. This will ensure that only Structural Interfaces are selected.

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Notice that the Interfaces you have just copied are oriented the wrong way, with the closed points on the inside and the open points on the outside. To flip them around, go to Boundaries, select Edit and choose Convert Boundary. Select all of the Interfaces on the right side using a Selection Window (don’t forget to apply the Selection Filter again to ensure only Structural Interfaces are selected). You will now see the Convert To dialog box. We do not wish to change the type of boundary so select Structural Interface and click OK. In the Add Structural Interface dialog, select First point open / last point closed. Click OK. Your model should now look like this.

Finally we need to add the precast concrete liner. However you cannot add Liners until the finite element mesh exists. The next step is therefore to build the mesh.

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NOTE: Structural interfaces must be added before the mesh since the joints will affect the mesh generation. See the Phase2 Help for more information.

Mesh Select the Mesh Setup option in the Mesh menu. Change the Mesh Type to Uniform. Leave the default element type (3 Noded Triangles) but set the number of elements to 1200). Click the Discretize button followed by the Mesh button.

Close the Mesh Setup dialog by selecting the OK button. Your model should now appear as shown.

Initial mesh We would like to improve the quality of the mesh in the region of interest (the ramp construction). To increase the density of the mesh in this area, first make sure you are looking at Stage 3 or Stage 4. Select Increase Discretization Density from the Mesh menu. Draw a box around the road construction. You will now see a higher density mesh in the Fill and Concrete layers as shown.

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Mesh after increasing discretization density in the ramp construction To improve the mesh further, we can use the Mapped Meshing capability in Phase2. This generates a geometrically regular mesh in triangular or quadrilateral regions of the model, sometimes called a Structured Mesh. See the Phase2 Help for more details. From the Mesh menu, select Mapped Meshing and then Automatic Mapped Mesh. You will see a dialog box with information about the Mapped Meshing. Click OK and your model should now look like this.

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Mesh after mapped meshing We have finished generating the finite element mesh so we can now add the precast concrete liners.

Assign Liners Click on the Stage 2 tab. From the Support menu select Add Liner. Ensure that the Liner property is Precast Concrete and the Install at stage is set to 2.

Click OK. Now select all of the boundary segments on the left side of the Fill layer. You can select them all at once by encompassing them in a box as described above. Do the same for the right side of the fill. Right click and choose Done Selection. Your model should now appear as shown.

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Boundary Conditions The model now shows the default boundary conditions (all external boundaries fixed in the x and y directions). In our model, only the edges and bottom of the Soil layer need to be fixed. To free the other boundaries, select Free from the Displacements menu. Click on all of the outer boundaries except the sides and edges of the Soil layer. Be sure to select the very small boundary segments that form the top edges of the road (you may need to zoom in to select these). Hit Enter to finish selecting. The top left and top right nodes of the soil layer have now been freed. To re-fix them, select Restrain X,Y from the Displacements menu and click on the left and right edges of the sol layer. Hit Enter to finish. Your model should now look like this.

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We now need to add the loading to the road surface. Click on the Stage 4 tab. Under the Loading menu choose Distributed Loads and then Add Uniform Load. Leave the orientation as Normal to boundary and enter 6 kN/m for the magnitude. We only wish to apply the load during Stage 4, so turn on the Stage Load option and click the Stage Factors button. Enter 0 for the Stage 1, 2 and 3 Factors as shown.

Click OK. Now click OK in the Add Distributed Load dialog. Click on the stage boundary that is the road surface. Hit Enter and your model should now look like this.

Boundary conditions for Stage 4. You can click through the other stages to ensure that load is only being applied in Stage 4.

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Field Stress The last step is to specify the field stress in the model. Select Field Stress from the Loading menu. Set the Field Stress Type to Gravity and turn on the option Use actual ground surface as shown.

Click OK to close the dialog. You have completed the definition of the model. Save the model using the Save option in the File menu.

Compute Run the model using the Compute option in the Analysis menu. The analysis should take under a few minutes to run. Once the model has finished computing (Compute dialog closes), select the Interpret option in the Analysis menu to view the results.

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Interpret After you select the Interpret option, the Interpret program starts and reads the results of the analysis. The following screen is displayed showing the maximum stress in the Foundation Soil layer for Stage 1.

This reflects the initial element loading of the soil layer. If you plot displacements you will see no displacement has occurred. Click on the Stage 2 tab. You will now see the maximum stress after the fill has been added. To make the plot clearer you may want to shrink the size of the plotted Structural Interfaces. Right click anywhere in the window and choose Display Options. Click on the Stress tab and turn off the option for Expand Composites under the Support heading. Your plot should now look like this.

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Plot displacements by choosing Total Displacement from the drop down menu on the toolbar. Plot the deformed boundaries by clicking the Display Deformed Boundaries button. You will see significant downward displacement in the fill since it has settled under its own weight. There is less displacement at the edges where the fill is being supported by the precast concrete liner.

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Click through the other stages and you will see increased deformation as the concrete road bed is added and then when the load is applied in Stage 4. If you wish to see the effect of only the load, you can set Stage 3 as the reference stage. Do this by going to the Data menu, selecting Stage Settings and pushing the slider for Reference Stage to Stage 3.

Click OK. You will now see the effect of just the loading in the final stage.

Note the buckling of the structure as the middle displaces downwards and the edges bulge outwards. Check if any of the supports have failed by clicking on the Display Yielded Liners button. You will see that the outside edges of the upper geotextiles have failed. The precast concrete liners have remained intact since we set them to be elastic.

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NOTE: If you want to know the manner in which the geotextile liners have failed then turn on the Expand Composites option in the Display Options dialog. You will see that the liner failure is in fact slipping of the joints of the structural interface. The actual geotextile component of the structural interface has not failed (i.e. its tensile strength has not been exceeded). You can easily plot the bending moments associated with the concrete supports. First turn off the deformed boundaries. Now go to Show Values in the Analysis menu and select Show Values. Beside the Liners check box, choose Bending Moment from the drop down menu.

Click OK and you will see the bending moments plotted graphically on the model.

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The maximum and minimum moments are shown. Note that the geotextiles cannot support moments so all of their values are 0. If you want to see the true minimum moment for the concrete supports, then turn off the plots for the geotextiles by going to Show Values from the Analysis menu and choosing Toggle Show Values. Now click on each of the geotextiles to turn them off. This concludes the tutorial, you may now exit the Phase2 Interpret and Phase2 Model programs.

Additional Exercise Try setting the Material Type of the Foundation Soil to Plastic and see if there is any change in the results.

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Composite Liner Tutorial

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Composite Liner Tutorial This tutorial describes the support of a tunnel using composite liners. A Composite Liner in Phase2, is a liner which may consist of multiple layers of material. The different layers of a Composite Liner may have different material properties, and may be applied at different stages. A joint may also be included in the Composite Liner, which will exist between the rock mass and the first liner layer. There are a total of four stages in the simulation. The tunnel will be excavated in three stages. After each excavation, shotcrete is added for support. A layer of concrete is added one stage later on top of the shotcrete layer to form a composite liner. The installation of the concrete liner is finished in the fourth stage. Topics Covered •

Composite Liners

•

Staged liner installation

•

Selection Window

•

Selection Filter

•

Graph composite liner data

•

Show values

Geometry

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Model Start the Phase2 Model program. To save typing in boundaries and material properties we will start with an existing model and then excavate it and add support. Open the file Tutorial 15 boundaries.fez located in the Examples > Tutorials folder in your Phase2 installation folder. Zoom into the excavation and the model should look like this.

Project Settings Click the Project Settings button on the toolbar. Change the number of stages to 4. Close the dialog by clicking OK.

Excavation Click on the Stage 1 tab. Select the Assign Properties button on the toolbar. From the Assign Properties dialog, select Excavate. Click anywhere within the upper tunnel section. Your screen should look like the following:

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In Stage 2 we will excavate the middle section of the tunnel. Click the Stage 2 tab. Click anywhere within the middle tunnel section. (Note that the Excavate option you selected from the previous step is still active.) Your screen should look like the following:

In Stage 3 we will excavate the lower section of the tunnel. Click the Stage 3 tab. Click anywhere within the lower tunnel section.

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We are now finished excavating the tunnel. Close the Assign dialog.

Composite Liner Properties Composite Liners are made up of two or more single liners and possibly a joint (slip element) between the rock and the first liner layer. Before specifying the properties of the composite liner, we will set the properties of the individual liner layers. Click the Define Liner Properties button on the toolbar. In our model, the composite liner will be made up of a shotcrete layer and a concrete layer. Change the Name of Liner 1 to Shotcrete and change the Young’s modulus to 25000 MPa. The dialog should look like this.

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We will now define the properties of the second layer of the composite liner. Click on the tab for Liner 2. Change the name to Concrete, the Young’s Modulus to 35000 MPa, and the Thickness to 0.15 m. The dialog should look like this.

Click OK to close the dialog. Now we can set up the composite liner. Click the Define Composite Properties button on the toolbar.

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Our composite liner is to be made up of the shotcrete layer and concrete layer we have already defined, so ensure that the First Liner is set to Shotcrete and change the Second Liner to Concrete. In our model we want the second layer to be placed one stage after the first. This means that if for example the first shotcrete layer of the composite liner is installed at Stage2, the second concrete layer will be applied at Stage 3. To accomplish this, go to the drop down menu next to the word installed. Select “1 stage after” from this menu. Your dialog should now look like this.

Click OK to close the dialog. NOTE: You can also specify that slip may occur between the rock and the composite liner by choosing “2 liners (with slip)” from the Composite Type drop down menu, but we will not be doing that for this example.

Add Support In this model, we will add the entire liner at Stage 1 and then stage the installation later. To add the composite liner first go to Stage 1. Click the Add Liner toolbar button. In the Add Liner dialog, click the Composite Liner checkbox so that the Liner Property is Composite 1. The value for Install at stage should be 1 as shown.

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Click OK to close the dialog. Now select all of the segments that make up the large tunnel. Be sure to select the parts of the tunnel that are unexcavated at Stage 1 – we will deal with the staging later. Hit Enter to finish selection. TIP: You can easily select all the sections of the tunnel using a Selection Window. Hold down the left mouse button and drag a window to encompass the entire tunnel. If you do this, you will find you have selected the internal stage and material boundaries as well as the excavation boundary. To prevent this from happening you can use a Selection Filter. Before drawing your Selection Window, right click and choose Selection Filter. Deselect everything except Excavation Boundary as shown. Now click OK and draw the Selection Window.

Your model should look like this.

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To assign the composite liner installation to the correct stages, first click the Assign Properties button on the toolbar. Select Composite Liners from the drop down menu at the top. Now click the Remove button and click on all sections of the tunnel that have not been excavated in Stage 1. Hit Enter. The sections you selected will turn grey and your model should look like this.

Now select the Stage 2 tab. Click the Install button on the Assign dialog. Select the liner segments that become exposed at this stage of excavation (this includes the two exposed vertical walls and floor ledge) and hit the enter key.

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Click the Stage 3 tab and select the additional liner segments that become exposed at this stage of excavation. Hit the enter key. Close the Assign dialog. The model for Stage 3 should now look like this.

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NOTE: in Stage 4, the concrete layer will be installed on the bottom section of the tunnel since the second layer of the composite liner is installed one stage after the first (shotcrete) layer. Save your model by choosing Save As from the File menu and give the file a different name.

Compute Run the model by pressing the Compute button on the toolbar. The analysis should take under a few minutes to run. Once the model has finished computing (Compute dialog closes), click the Interpret button to view the results.

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Interpret After you select the Interpret option, the Interpret program starts and reads the results of the analysis. Zoom into the excavation using the Zoom Excavation button. You should see a screen similar to the following that shows the maximum compressive stress for Stage 1.

You can see the installation of the shotcrete liner around the excavation (marked as light blue rectangles). Select the Stage 2 tab.

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Purple rectangles show a second layer of support has been added (concrete) to the top of the tunnel that was excavated in Stage 1. This plot shows low stresses directly below the tunnel with high stresses shed into the sandstone layer further below. This suggests failure has occurred below the tunnel. To observe the failure in the rock, click on the Display Yielded Elements button. The plot should now look like this.

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You can see that there is significant rock failure around the excavation. Observe however that the installation of the liners at the top of the tunnel have prevented extensive failure in this area, while at the bottom of the tunnel, where a liner has not been applied, the failure is severe. This is not too worrying since much of this failed rock will be excavated in the next stage. Stage 3 shows further excavation and liner installation. Stage 4 completes the installation of the concrete liner. You will see that the addition of the concrete liner in stage 4 has virtually no effect on the stress or failure in the rock. We can examine the role of the composite liner by plotting axial forces and bending moments. Click on the Graph Liner Data button. Click on the boundary of the tunnel and hit Enter. First we will look at the effect of the shotcrete only. So click on the Select Support Layer button. You will see under Liner that “Layer 1: Shotcrete” is selected.

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Since this is what we want, click OK to close the window. Now select all stages in the Graph Liner Data dialog.

Click Create Plot. The graph should look like this.

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You will see that the axial force increases after Stage 1 at the top of the tunnel (between 30 m and 45 m). This reflects increased stress in this area as the tunnel excavation proceeds. The numbers on the lines display the node numbers from the model so you can determine which points on the graph correspond to which sections of the tunnel boundary. Go back to the plot of the tunnel. You will see labels along the liner showing the node numbers. We can also plot the effect of the two different liners on the same graph. Click on the Graph Liner Data button again and select the tunnel boundary. Hit Enter. Now under Composite / Structural Layer in the bottom right corner of the dialog, select Plot All Layers. Under Lines on Graph select Lines on graph same colour as liner. Turn on Stage 4 and turn off all of the other stages.

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Click Create Plot. Your graph should look like this.

You can see that the shotcrete (Layer 1) is generally taking more load than the concrete. This is because the shotcrete was installed first. When the concrete is installed on top, it takes no load until further excavation occurs and stresses around the tunnel are redistributed. This is the reason that the concrete shows zero axial force along the bottom of the tunnel (the left side of the graph) – there is no further excavation after it is installed and therefore no load is shifted to the concrete support layer.

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To make interpretation easier, you may want to graph the loads directly on the plot of the tunnel. Go back to the plot of the tunnel. Ensure you are looking at Stage 4. Turn off the Yielded Elements. Turn off the liner numbers by right clicking on the liner and clicking on Liner Numbers. Click on the Show Values button. In the Show Values dialog, select the Liners checkbox, and make sure Axial Force is the data type. Select OK.

Minimum and maximum forces are shown by blue text and red text respectively. To change the options select Show Values again. Next to Liners, choose Bending Moment from the drop down menu as shown.

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Now click on the Select Support Layer button. Under the Liner heading, click in the box and select “Layer 2: Concrete”.

Click OK. Now click OK in the Show Values dialog. TIP: you can also Show Values by right clicking on the liner and using the options in the Show Values sub-menu. You should now see the bending moments in the concrete liner plotted around the tunnel. If you want, you can plot the exaggerated displacement of the tunnel by clicking on the Display Deformed Boundaries button. The plot should now look like this.

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You can see the large bending moments at the top corners of the tunnel. You may want to turn off the text showing the minimum and maximum moments since they are obscuring some of the data. You can do this by going to the Show Values dialog and clearing the checkbox next to the Minimum and Maximum Values option. This concludes the tutorial, you may now exit the Phase2 Interpret and Phase2 Model programs.

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Retaining Wall Tutorial

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Retaining Wall Tutorial In this tutorial, Phase2 is used to simulate the construction of an earth retaining wall. The wall is subjected to forces from backfill and from ponded water. Joint elements are included between the wall and the soil so the wall may slip relative to the soil. The model is built in four stages: 1. Bring the foundation soil to equilibrium 2. Add a layer of fill and a retaining wall 3. Add water 4. Add another layer of fill on top of the first Topics covered •

Joints

•

Add vertex

•

Staged piezometric lines

•

Ponded water load

•

Staged loading

•

Graph joint data

•

Reference stages

Geometry

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Model We will start this tutorial by importing a file in which geometry, materials and boundary conditions have already been assigned. Start the Phase2 Model program. Go to the File menu and click Open. Open the file called Tutorial 16 boundaries.fez located in the Examples > Tutorials folder of your Phase2 installation folder. You will see a model that looks like this.

This is Stage 1 of the model – just the foundation soil. Click through the other stages and you will see the addition of the retaining wall and a layer of fill in stage 2 and another layer of fill in stage 4. In this tutorial we will be adding a joint between the retaining wall and the soil layer and also adding ponded water to the left of the wall.

Add Joint Click on the tab to show Stage 2. Go to the Boundaries menu and choose Add Joint. If you see a warning that the mesh is going to be reset, click OK to reset the mesh. You will now see the Add Joint dialog. Our joint is man-made and will start and finish at a free surface. Therefore for Joint End Condition, choose the option Both ends open. Note that for natural joints found in geological formations you would usually choose both ends closed. We want the joint to be installed at Stage 2 so ensure that the Install at stage option is set to 2. The dialog should look like this:

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Click OK. You will now see a cross-hair cursor with which you can select the points that make up the joint. With the mouse, select the point at the bottom left of the retaining wall (6 , 5). The cross-hairs should snap to the existing point. If it does not snap, right click and turn on all of the Snap options. Now select the point at the bottom right of the wall (8.5 , 5) and then at the top of the wall (8.5 , 11). Right click and choose Done. You should now see a joint represented by an orange line as shown.

The open circles at the ends of the joint indicate that it is open at both ends. If you click through the stages then you will see the joint is a light colour in Stage 1 indicating that it is not installed. It is a dark orange (installed) in all other stages. We now need to set the properties of the joint. Select Define Joints from the Properties menu. For Joint 1, change the criterion to Mohr-Coulomb and the friction angle to 27 degrees as shown.

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Click OK to close the dialog. We do not need to assign the Joint 1 properties to our existing joint because it is Joint 1 by default.

Add Piezometric Line In Stage 3 there will be ponded water to the left of the wall. To draw the piezo line, we should first add a vertex on the wall at the water surface. Go to the Boundaries menu and select Edit > Add Vertices or click the Add Vertices button. The water will be at an elevation of 8 m, so enter the coordinates 7 , 8. Hit Enter. Hit Enter again to finish entering points. You will see a new vertex about half way up the wall on the left side. NOTE: It is not necessary to add the vertex before drawing the piezometric line, however the new vertex will make adding loads easier later in the tutorial. Now select Add Piezometric Line from the Boundaries menu. Enter 0 , 8 for the first point and hit enter. Now click on the new vertex you just created at 7 , 8. Click on the bottom right corner of the wall at 8.5 , 5 and finally click on the top right corner of the foundation soil at 20 , 5. Hit Enter to finish entering points. NOTE: even though the retaining wall is considered impermeable, the piezo line is defined through the retaining wall so that the pore pressures will be correctly calculated in the foundation soil layer. You will now see a dialog that lets you choose which materials are affected by the piezometric water level. Select the checkbox next to Foundation and click OK. You should now see the piezometric line as shown.

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We only want the water to be added at Stage 3. To do this, select Define Hydraulic from the Properties menu. For the Foundation material, turn on the Stage Piezo Lines option. Next to Stage 1 change the Piezo # to none. Stage 2 should now read none as well. Click on Add Stage. Next to Stage 3 change the Piezo # to 1. The dialog should look like this.

There is no need to set stage 4 since it will automatically be the same as stage 3. Click OK to close the dialog. If you click through the stages you will still see the piezo line plotted at every stage. To change this, you can select View Piezos by Stage from the Groundwater menu. Now you should only see the piezo line in stages 3 and 4.

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Mesh Before we can add the forces caused by the ponded water, we need to generate the mesh. The mesh options are already set up so simply select Discretize and Mesh from the Mesh menu.

Distributed Load The water to the left of the wall will exert a hydrostatic force on the wall and foundation soil. We will simulate this by a distributed load. Go to the Loading menu and choose Distributed Loads. Select Add Ponded Water Load from the sub menu. You will now see a dialog asking for the total head. Enter 8 m. Since we only want the water to be added at stage 3, click on the Stage Load option. Click on the Stage Total Head button and unclick the Apply boxes for stages 1 and 2 as shown.

Close both dialogs by clicking OK. You now have to select the boundary segments on which to apply the load. Click the bottom of the pond and the bottom left boundary of the retaining wall below the piezo line. Right click and choose Done. Your model should now look like this for Stage 4.

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Note the triangular load applied to the side of the wall. This shows how the hydrostatic force increases with depth. You have completed the definition of the model. Save the model with a different name using the Save As option in the File menu.

Compute Run the model using the Compute option in the Analysis menu. The analysis should take under a few minutes to run. Once the model has finished computing (Compute dialog closes), select the Interpret option in the Analysis menu to view the results.

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Interpret After you select the Interpret option, the Interpret program starts and reads the results of the analysis. You will see the maximum stress in the foundation soil layer for stage 1. Change the display to show contours of Total Displacement. You should see virtually no displacement in the layer since the field stress and body force of the finite elements are in equilibrium in the first stage. Click on the tab for Stage 2. You will see significant deformation in the fill layer as it settles due to gravity. There is little displacement in the retaining wall since it is made of stiff concrete and does not deform much under gravitational loading. Click on the button to display deformed boundaries. You will see how the retaining wall is being pushed outwards and rotated as shown.

If you click on the button to Display Yielded Joints, you will see all of the vertical joint sections turn red indicating that this entire section of the joint has slipped. It is clear that sliding along the vertical joint is responsible for the displacement contours behind the retaining wall. Click on the tab to view Stage 3. You can see that the wall is being pushed back to the right slightly due to the force applied by the ponded water. To see this more clearly you can plot the displacement of this stage relative to stage 2. Go to the Data menu and choose Stage Settings. Set the Reference Stage to Stage 2 and click OK. Your plot for Stage 3 will now look like this.

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It is clear that the bottom of the wall is being pushed by the water and this is causing displacement and rotation. Stage 4 shows significant displacement back in the other direction as the second layer of fill is added.

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To look at the joint behaviour in more detail, you can graph the joint data. First turn off the reference stage by choosing Stage Settings from the Data menu and setting the Reference Stage to Not Used. Select Graph Joint Data from the Graph menu, or simply right click on the joint and choose Graph Joint Data. In the Graph Joint Data dialog, select Shear Stress for the vertical axis and turn on stages 2, 3 and 4 as shown.

Select Create Plot and you should now see a graph that looks like this.

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The first four points show the stress on the horizontal portion of the joint. These show positive values indicating stress causing left lateral motion. You can see how Stage 2 shows the highest shear stress on this segment and how the stress decreases when the water is added in Stage 3. Stage 4 then shows an increase in stress when the extra fill is added. For the vertical section of the joint, the stresses are negative indicating a stress tending to cause right lateral motion. On the graph you can see a number 1 just to the right of the last point. If you go back to the model plot, you will see a number 1 displayed at the top of the joint. This number 1 corresponds to the number 1 on the graph so that you can determine where the start and finish of the joint is. You may find it easier to plot the joint data directly on the model. To do this, click on the Show Values button on the toolbar. Under the Data heading, turn on the Joints option. For this plot choose Shear Displacement from the pull down menu. Click OK and you will see the shear displacements plotted on the joint. Turn off the deformed boundaries by clicking on the Display Deformed Boundaries button. Turn off the distributed loads by right clicking and choosing Display Options and unchecking the option for Distributed Loads under the Stress tab. You will now see a plot like this for stage 4.

The maximum and minimum values are denoted with red text and blue text respectively. Note the negative (right lateral) slip on the vertical section of the joint as the soil is moving downwards relative to the wall. The bottom of the joint shows positive (left lateral) displacements since the wall is shifting left relative to the foundation. This concludes the tutorial, you may now exit the Phase2 Interpret and Phase2 Model programs.

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Trench Tutorial In this tutorial, Phase2 is used to simulate the excavation of a trench into a sloped embankment. The trench is supported by soldier piles and struts. The model is built in five stages: 1. Bring soil layers to equilibrium 2. Install a pile on the high side of the trench 3. Excavate the first section of the trench and lower the water table 4. Install a pile on the low side of the trench and install a strut between the two sides 5. Excavate the final section of the trench and lower the water table Topics covered •

Soldier piles

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Strut with cross-sectional area and moment of inertia

•

Staged support

•

Staged piezometric lines

•

Staged excavation

•

Automatic Liner Removal option = OFF

•

Show Values

•

Plot Liner data

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Model We will start this tutorial by importing a file in which geometry, materials and boundary conditions have already been assigned. Start the Phase2 Model program. Go to the File menu and click Open. Open the file called Tutorial 17 boundaries.fez located in the Examples > Tutorials folder in your Phase2 installation folder. You will see a model that looks like this:

This is Stage 1 of the model showing the soil layers prior to excavation.

Project Settings The first thing to do is change the number of stages in the model. Go to the Analysis menu and choose Project Settings. Set the Number of Stages to 5. Click OK to close the dialog.

Automatic Liner Removal Option Before we proceed with the modeling, go to the Support menu, and notice the Automatic Liner Removal option. In order to model strut support in Phase2, the Automatic Liner Removal option must be turned OFF. This allows you to excavate the material on both sides of the strut (liner), without automatically removing the support. We will be doing this in Stage 5. For the file you have just read in, the Automatic Liner removal option has already been turned off. (When the option is ON a checkmark appears beside the menu option, when it is OFF, no checkmark appears). Make sure the option is OFF. For more information about the Automatic Liner Removal option, it is recommended that you read the Phase2 Help.

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Stage 1 – Initial Conditions For Stage 1 we only need to add a piezometric line to delineate the water table. Go to the Boundaries menu and choose Add Piezometric Line. Enter the following coordinates: 0 , 6 (existing vertex) 4 , 6 (existing vertex) 8 , 7.5 12 , 7.5 Hit Enter to finish entering the points. NOTE: For existing vertices it is easier just to click on them than enter the numbers – if the cursor doesn’t snap to existing vertices then right click and turn on the Snap options. For the final point you also will not have to type it in. The cursor should snap to the right boundary making a horizontal line. You will now see a dialog asking to which materials you would like to assign the piezo. Click on the check boxes beside Material 1 and Material 2 as shown.

Click OK. Your model for Stage 1 should now look like this:

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Stage 2 – Install pile support Select the Stage 2 tab. In Stage 2 we will add a pile to the right side of the future trench. We will implement this as a liner element. Another possible approach would be to implement this as a structural interface with a joint on either side of the liner allowing slip to occur between the liner and the soil. See Additional Exercises at the end of this tutorial. First we need to set the properties of the pile. Select Define Liners from the Properties menu. Change the name of Liner 1 to Pile. Change the thickness to 0.2 m as shown.

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Click OK to close the dialog. Install the liner by selecting Add Liner from the Support menu. You will see the Add Liner dialog as shown.

Ensure that the Liner Property is Pile and Install at stage is set to 2. Click OK. Now select the three stage boundaries to the right of the future trench at x = 8 m. Hit Enter to finish selecting boundary segments. Your model should look like this for Stage 2.

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Stage 3 – Excavate soil and lower piezometric line Click on the Stage 3 tab. In this stage we will excavate the first part of the trench and lower the water table. Select Assign Properties from the Properties menu. Make sure that Materials is selected from the pull-down menu at the top. Now click on Excavate. Click in the triangular section at the top-middle of the model to excavate the first part of the trench. Close the Assign dialog. We now need a new piezo line that runs below the new surface. Click the Add Piezo Line button. Enter the following points: 0 , 6 (existing vertex) 8 , 6 (existing vertex) 10 , 7.5 12 , 7.5 (existing vertex) Hit Enter to finish entering points. In the Assign Piezometric Line to Materials dialog, do not check any of the materials. The materials need to be assigned different piezo lines at different stages. We will sort this out in Stage 5. Click OK to close the dialog. You will now see both piezo 1 and piezo 2 plotted. We need to stage the piezo lines but it will be easier to do this at the end of model building when all of the piezo lines are in place. For now just leave the two piezo lines as shown. The model for Stage 3 should look like this.

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Stage 4 – Install second pile and strut support Click on the Stage 4 tab. The properties of the pile have already been set up so we only need to install it. Click on the Add Liner button. Ensure the Liner Property is Pile and Install at Stage is set to 4. Click OK. Now select the stage boundaries to the left of the trench at x = 4 m as shown.

We will now install a strut between the two piles to support the excavation that will occur in Stage 5. First we need to set the properties of the strut. Click the Define Liner Properties button on the toolbar. Click on the tab for Liner 2. Change the name to Strut. Under Geometry, turn on the Area option. Change the Area to 0.2 m2 and the Moment of Inertia to 1e−20 m4 as shown.

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Setting a very low moment of inertia ensures that the beam will experience no flexure or torsion – only axial forces. Now add the strut by selecting Add Liner from the Support menu. In the Add Liner dialog, select Strut from the pull-down menu for the Liner Property. Ensure that the Install at Stage option is set to 4.

Click OK. Now click on the boundary segment at the top of the soil between the two piles. Right click and choose Done Selection. Your model should now look like this:

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TIP: You may wish to hide the piezo lines prior to installing the strut. To do this right click anywhere in the Phase2 window and choose Display Options. Now uncheck Piezometric Lines. You will also need to hide the piezo lines if you wish to access the liner strut information by right clicking on it, since the strut is “underneath” piezo line 2.

Stage 5 – Excavate soil and lower piezometric line Click on the tab to show Stage 5. In this stage we will excavate the remainder of the trench and add another piezo line. Click on the Assign Materials button. Click the Excavate button in the dialog and then click inside the lower section of the trench between the piles and just below the strut. Close the Assign dialog. NOTE: because the Automatic Liner Removal option is turned OFF, this allows us to excavate the material on both sides of the strut, without automatically removing the strut. See the section earlier in this tutorial for more information. We now need to add another piezo line below the new soil surface. From the Boundaries menu select Add Piezometric Line. Enter the following points: 0 , 6 (existing vertex) 3,6 4 , 4 (existing vertex) 8 , 4 (existing vertex) 9,6 10.5 , 7 12 , 7.5 (existing vertex) Hit Enter to finish entering points. In the resulting dialog, do not select any materials and click OK. It is now time to assign the piezo lines to the correct stages. From the Properties menu select Define Hydraulic. For Material 1, turn on the option for Stage Piezo Lines. For Stage 1, set the Piezo # to 1. For Stage 2, set the Piezo # to 1. Now click the Add Stage button. For Stage 3 set the Piezo # to 2. Click Add Stage 2 more times to add stages 4 and 5. Set the Piezo # for Stage 5 to 3. The dialog should now look like this.

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Material 2 is affected by the piezo lines in the same way as Material 1. Therefore click on the Material 2 tab and repeat the above steps to stage the piezo lines. TIP: you can also use the Copy To button in the dialog to copy the properties from one material to another. Click OK to close the dialog. NOTE: You do not need to define the piezo # for every stage. If a stage is not listed it will automatically adopt the piezo # of the previous stage. Therefore in this example you could have only specified stages 1, 3 and 5. This can be done by setting up only 3 rows in the table and changing the stage numbers by clicking on the stage numbers in the first column. You will still see 3 piezo lines on your model. To only see the piezo line for the relevant stage, go to the Groundwater menu and choose View Piezos by Stage. Your model should now look like this for Stage 5.

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Click through the other stages to ensure that the piezo lines are where they should be. You have now completed the definition of the model. Save the model with a different name using the Save As option in the File menu.

Compute Run the model using the Compute option in the Analysis menu. The analysis should take a few minutes to run. Once the model has finished computing (Compute dialog closes), select the Interpret option in the Analysis menu to view the results.

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Interpret After you select the Interpret option, the Interpret program starts and reads the results of the analysis. You will see the maximum stresses for Stage 1. Change the contours to Total Displacement and turn on the deformed boundaries by clicking the Display Deformed Boundaries button. The plot should look like this:

You will see that some deformation has occurred already. If you press the Display Yielded Elements button, you will see that significant failure has occurred at the top of the slope. Turn off the yielded elements and click on the Stage 2 tab. You will see that the addition of the soldier pile has no effect until the trench is excavated. Click on the Stage 3 tab. You will now see significant displacement at the right side and bottom of the trench. The pile appears to be bending due to the weight of the soil it is holding back. Verify this by right clicking on the liner and selecting Show Values > Bending Moment. Your plot should now look like this:

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You can see positive bending moments just below the surface of the trench. Click on the Stage 4 tab. You should see very little difference as the other pile and the strut are added. Click on the tab for Stage 5.

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Now you can see even larger bending moments in the two soldier piles. Note the moment change from positive to negative in the right pile as it passes the strut, showing how the pile bends around the supporting strut. It is also interesting to observe how the left side of the trench is deformed to the left as it is being pushed by the strut. The strut shows no moment because we set its moment of inertia to a very small value to prevent bending and twisting. To observe the effect of the strut, right click on it and select Graph Liner Data. Ensure that the Vertical Axis is set to Axial Force as shown.

Click Create Plot. You will now see a graph of the axial force in the strut that looks like this:

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You can see the constant positive axial force experienced by the strut, clearly indicating that it is providing support to the excavation. TIP: If you find the line hard to see, right click inside the graph and choose Chart Properties. Set the Chart Interior colour to grey. Alternatively, if you have Microsoft Excel software then you can right click on the graph and choose Plot in Excel. This concludes the tutorial, you may now exit the Phase2 Interpret and Phase2 Model programs.

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Additional Exercises 1. Try running the model again without the strut. You should see significantly more deformation and failure on the right side of the trench as shown below. Notice there is little deformation on the left side since the left side is not providing any support to the failing right side via the strut.

2. Try using structural interfaces for the soldier piles instead of liners. The structural interfaces should be composed of a Pile sandwiched between two joints. Set the joint Slip Criterion to Mohr-Coulomb and you should see slippage between the piles and the soil.

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3D Tunnel Simulation using the Core Replacement Technique

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3D Tunnel Simulation using the Core Replacement Technique In this tutorial, Phase2 is used to simulate the three-dimensional excavation of a tunnel. In three dimensions, the tunnel face provides support. As the tunnel face advances away from the area of interest, the support decreases until the stresses can be accurately modelled with a two-dimensional plane-strain approach. This procedure is necessary in order to determine the amount of deformation prior to support installation. The complete model can be found in the Tutorial 18 3D Tunnel Simulation using Core Replacement.fez file located in the Examples > Tutorials folder in your Phase2 installation folder. Topics covered •

3D tunnel simulation

•

Core Replacement Technique (Material Softening)

•

Reinforced concrete liners

•

Support capacity curves

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Problem A circular tunnel of radius 4m is to be constructed in Schist at a depth of 550m. The in-situ stress field has been measured with the major in-plane principal stress equal to 30 MPa, the minor in-plane principal stress equal to 15 MPa and the out-of-plane stress equal to 25 MPa. The major principal stress is horizontal and the minor principal stress is vertical. The strength of the Schist can be represented by the Generalized HoekBrown failure criterion with the uniaxial compressive strength of the intact rock equal to 50 MPa, the GSI equal to 50 and mi equal to 10. To compute the rock mass deformation modulus, the modulus ratio (MR) is assumed to be 400. The support is to be installed 2m from the tunnel face. The goal of this tutorial is to demonstrate how to model the tunnel deformation prior to support installation using the core replacement (material softening) approach. To design a support system, the following procedure can be used: 1. Determine the amount of tunnel wall deformation prior to support installation. As a tunnel is excavated, there is a certain amount of deformation, usually 35-45% of the final tunnel wall deformation, before the support can be installed. Determining this deformation can be done using either a) observed field values, or b) numerically from 3D finite-element models or axisymmetric finite-element models, or c) by using empirical relationships such as those proposed by Panet or Vlachopoulos and Diederichs. 2. Using the core replacement technique, determine the modulus reduction sequence that yields the amount of tunnel wall deformation at the point of and prior to support installation. This is the value determined in step 1. 3. Build a model that relaxes the boundary to the calculated amount in step 2. Add the support and determine whether a) the tunnel is stable, b) the tunnel wall deformation meets the specified requirements, and c) the tunnel lining meets certain factor of safety requirements. If any of these conditions are not met, choose a different support system and run the analysis again.

Model The first step is to determine the amount of tunnel wall deformation prior to support installation. For this tutorial, we will use the relationship proposed by Vlachopoulos and Diederichs. The Vlachopoulos and Diederichs method is documented in Appendix 1 of the Kersten Lecture by Hoek, Carranza-Torres, Diederichs and Corkum. The paper is in the Hoek’s published papers area on the Rocscience website: http://www.rocscience.com/hoek/references/Published-Papers.htm

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This method requires that we build a model of the tunnel and determine a) the deformation far from the tunnel face using a simple plane strain analysis, and b) for the same model determine the plastic zone radius. In this tutorial we’ll start by building a single model that also combines step 2 with step 1. We’ll build a plane strain model that sequentially replaces and reduces the modulus of the material inside the excavation over a number of stages. The final stage, with the material excavated inside the tunnel, will be used to determine the amount of deformation prior to support installation (step 1). The factoring of the modulus over a number of stages will be used to determine the modulus that yields the amount of tunnel wall deformation at the point of support installation (step 2). Start the Phase2 Model program.

Project Settings Open the Project Settings dialog from the Analysis menu and make sure the General tab is selected. Define the units as being “Metric, stress as MPa”.

Select the Stages tab. Change the number of stages to 9 (see following figure). Fill in the stage names as seen below. Close the dialog by clicking OK.

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Geometry Now enter the circular tunnel.

Select: Boundaries → Add Excavation 1. Right-click the mouse and select the Circle option from the popup menu. You will see the following dialog.

2. Select the Center and radius option, enter Radius = 4 and enter Number of Segments = 96 and select OK. 3. You will be prompted to enter the circle center. Enter 0,0 in the prompt line, and the circular excavation will be created.

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Select Zoom All (or press the F2 function key) to zoom the excavation to the center of the view.

Now we will create the external boundary. In Phase2, the external boundary may be automatically generated, or user-defined. We will use one of the ‘automatic’ options.

Select: Boundaries → Add External You will see the Create External Boundary dialog. We will use the settings of Boundary Type = Box and Expansion Factor = 5. Select OK, and the external boundary will be automatically created.

The boundaries for this model have now been entered.

Mesh Add the finite element mesh by selecting Mesh Setup from the Mesh menu. In the mesh setup dialog, change the Element Type to 6 Noded Triangles.

Click the Discretize button and then the Mesh button. Click OK to close the dialog. The mesh will look like this:

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Boundary Conditions For this tutorial, no boundary conditions need to be specified by the user. The default boundary condition will therefore be in effect, which is a fixed (i.e. zero displacement) condition for the external boundary.

Field Stress Field Stress determines the initial in-situ stress conditions, prior to excavation. As described earlier in this tutorial, the in-situ stress field has been measured with the major in-plane principal stress equal to 30 MPa, the minor in-plane principal stress equal to 15 MPa and the out-ofplane stress equal to 25 MPa. The major principal stress is horizontal and the minor principal stress is vertical.

Select: Loading → Field Stress

Enter Sigma 1 = 30, Sigma 3 = 15, Sigma Z = 25, Angle = 0, and select OK.

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Materials Go to the Properties menu and select Define Materials. For Material 1, change the Failure Criterion to Generalized Hoek-Brown and the Material Type to Plastic. Now define the strength parameters and the Young’s Modulus using the GSI calculator. Press the GSI calculator button (see below).

In the GSI calculator dialog, set the uniaxal compressive strength of the intact rock equal to 50 MPa, the GSI equal to 50 and mi equal to 10. To compute the rock mass deformation modulus, set the modulus ratio (MR) to 400. The dialog should look like:

Press the OK button. The material properties dialog should now be updated with the new strength and modulus values.

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Change the Name of Material 1 to E=6143. Click on the Material 2 tab and change the name to E=3000. Change the Initial Element Loading to None. Change the Young’s Modulus to 3000 MPa. See below.

Now follow the same procedure and set the Young’s modulus of Materials 3 thru 8 to 1000, 250, 100, 50, 20 and 10 MPa respectively. Change the names to reflect the value of the modulus. Make sure that the Initial Element Loading for Materials 3 thru 8 is set to None. Click OK when done.

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Now a little explanation as to what we did. The first material, with modulus 6143 MPa, and Generalized Hoek-Brown failure criterion, is the in-situ rock mass. Materials 2 thru 8 will be used inside the excavation (excavation core). The core material is progressively replaced over a number of stages. This replacement, along with the modulus reduction, allows the boundary to progressively deform. In each of the eight stages, the material inside the excavation is replaced by a material with zero internal stress (i.e. Initial Element Loading = None) and with a lower modulus than the proceeding stage. In the final stage, the material inside the excavation is removed. This process models the advancement of the tunnel face. Each stage (and corresponding core modulus) represents some distance from the tunnel face, either in front of or behind the face. The final excavated stage represents the deformed state far away from the tunnel face, at a distance where the face has no influence on stresses or displacements. What’s left is determining the correspondence between core modulus and distance from the tunnel face. In particular, the modulus sequence that yields the deformation at the support installation distance. The support installation distance being the distance between the tunnel face and where the support is installed. To determine the correspondence between core modulus and distance from the tunnel face, one must first know the relationship between tunnel wall deformation and distance from the tunnel face. As mentioned previously, there are a number of methods for doing this. Knowing the relationship between tunnel wall displacement and distance from the tunnel face, and knowing the relationship between core modulus and tunnel wall displacement, you can then determine the relationship between core modulus and distance from the tunnel face. Knowing this relationship allows you to determine the modulus reduction sequence that gives the tunnel wall displacement prior to support installation.

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Core Replacement Technique Click the Zoom Excavation button on the toolbar. You should see the following:

Select: Properties → Assign Properties 1. Make sure the Stage 2 tab, E=3000, is selected (at the bottom left of the view). 2. Select the “E=3000” button in the Assign dialog. 3. Click the left mouse button inside the tunnel. The material inside the tunnel should change to green, the color representing the E=3000 material. 4. Change to Stage 3, E=1000, by clicking the stage tab at the bottom of the screen. 5. Select the “E=1000” button in the Assign dialog. 6. Click the left mouse button inside the tunnel. The material inside the tunnel should change to light blue, the color representing the E=1000 material. 7. Change to Stage 4, E=250. 8. Select the “E=250” button in the Assign dialog. 9. Click the left mouse button inside the tunnel. 10. Change to Stage 5, E=100.

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11. Select the “E=100” button in the Assign dialog. 12. Click the left mouse button inside the tunnel. 13. Change to Stage 6, E=50. 14. Select the “E=50” button in the Assign dialog. 15. Click the left mouse button inside the tunnel. 16. Change to Stage 7, E=25. 17. Select the “E=25” button in the Assign dialog. 18. Click the left mouse button inside the tunnel. 19. Change to Stage 8, E=10. 20. Select the “E=10” button in the Assign dialog. 21. Click the left mouse button inside the tunnel. 22. Change to Stage 9, Excavated. 23. Select the “Excavate” button at the bottom of the Assign dialog. 24. Click the left mouse button inside the tunnel. The material inside the excavation should now be removed. 25. Close the Assign dialog by clicking on the X in the upper right corner of the dialog. Now select stage 1 – the in-situ condition stage. Turn on the minimum data tips mode using the following command.

Select: View → Data Tips → Minimum Hover the mouse inside the excavation. After a second, a data tip should appear. You should see the following:

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Notice that the data tip shows all the materials inside the excavation as a function of stage. We are now ready to run the analysis.

Compute Before you analyze your model, let’s save this as a new file called CoreSoftening.fez

Select: File → Save Save the file as CoreSoftening.fez.

Select: Analysis → Compute The Phase2 Compute engine will proceed in running the analysis. When completed, you will be ready to view the results in Interpret.

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Interpret From Model, switch to the Interpret program.

Select: Analysis → Interpret After you select the Interpret option, the Interpret program starts and reads the results of the analysis. You will see the maximum stress, sigma 1 for Stage 1. Notice that there is no variation of stress and that the stress (30 MPa) is equal to the major in-situ field stress. This is expected since in the first stage the material inside and outside the tunnel boundary is the in-situ E=6143 material. Now click the Zoom Excavation button on the toolbar. Change the contours to plot Total Displacement using the pull down menu in the toolbar. The model for Stage 1 will look like this:

You can see that there no displacement in the first stage. Now click through the stages. You’ll see an increase in deformation around the tunnel as the core material is replaced and softened (modulus reduced).

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Step 1 – Computing tunnel deformation before support installation using the Vlachopoulos and Diederichs method To compute the tunnel deformation at the point of support installation, we’ll use the empirical relationship developed by Vlachopoulos and Diederichs. To use the Vlachopoulos and Diederichs method, you need two pieces of information from the finite-element analysis. You need to know a) the maximum tunnel wall displacement far from the tunnel face, and b) the radius of the plastic zone far from the tunnel face. Both of these values can be computed from a plane strain analysis with zero internal pressure inside the excavation. In the model we just built, the results from stage 9 are used since the material inside the excavation is completely removed in this stage. Switch to the last stage, stage 9. Look in the lower left corner of the program window on the status bar. You’ll see that the maximum displacement for this stage is approximately 0.062m. This is the value of maximum wall displacement far from the tunnel face. The location of this displacement is in the roof and floor of the excavation. The location of this displacement is important since any comparisons of displacement for various core moduli must be made at the same location. To determine the radius of the plastic zone, first turn on the display of yielded elements using the Display Yielded Elements toolbar button. You’ll see a number of crosses representing elements in the finite element analysis that have failed. Zoom Out failed points is visible (see below).

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The extent of this failed zone represents the extent of the plastic zone around the tunnel. To determine the radius of the plastic zone, you can use either the measuring tool or the dimensioning tool to measure the distance from the center of the tunnel to the perimeter of the yielded/plastic zone. In this tutorial we’ll use the measuring tool. Select: Tools → Add Tool → Measure Pick the location to measure from [esc=quit]: 0,0 Pick the location to measure to [esc=quit]: use the mouse to extend the measuring line vertically until you get to the edge of the yield zone, press the left mouse button.

As seen above, the radius of the plastic zone is approximately 9.5m.

Computing displacement prior to support installation using the Vlachopoulos and Diederichs Method The following plot was created using the Vlachopoulos and Diederichs equations (Vlachopoulos and Diederichs, 2009). The equations can also be found in the Kersten Lecture, appendix 1 (Hoek et. al., 2008). Using this plot, you can estimate the amount of closure prior to support installation if you know the plastic radius and displacement far from the tunnel face.

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For our problem, Rp=9.5m, Rt=4m, X=2m, and umax=0.062m. The Distance from tunnel face/tunnel radius = 2/4 = 0.5. The Plastic zone radius/tunnel radius = 9.5/4 = 2.4. From the above plot this gives Closure/max closure approximately equal to 0.44. Therefore the closure equals (0.44)*(0.062) = 0.027m. As computed above, the tunnel roof displaces 0.027m before the support is installed.

Step 2 - Determining the core modulus The next step is to determine the core modulus that yields a displacement of 0.027m in the roof of the tunnel. It is important to maintain the same location as is used to determine umax, since the location of maximum displacement can change depending on the magnitude of the internal pressure. This can be seen in this model as larger core moduli produce larger displacement in the sidewall while smaller core moduli produce larger displacements in the roof and floor.

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To determine the internal pressure that yields a 0.027m roof displacement, we’ll plot the displacement versus stage for a point on the roof of the excavation. Make sure you have Total Displacement selected as the data type.

Graphing Displacement in the Roof of the Excavation To create the graph:

Select: Graph → Graph Single Point vs. Stage 1. When asked to enter a vertex, type in the value 0,4 for the location and press Enter. This is a point on the roof of the excavation. 2. You will see the Graph Query Data dialog.

3. Press the Create Plot button. The following figure shows the plot generated by the program. This is a plot of displacement versus stage for a point in the roof of the tunnel.

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Right-click in the plot and choose the Sampler option. Move the sampler by moving the mouse with the left mouse button. Move the sampler until the displacement value on the right side of the plot is equal to 0.027m.

From this plot, you can see that in stage 4, the wall displacement in the roof of the tunnel is approximately 0.027m. This represents a 3 stage material replacement and reduction of core modulus from E=6143(insitu), to 3000, 1000 and finally 250 MPa. Creating a convergence confinement graph in Excel Often you want to create a convergence confinement graph which plots displacement versus core modulus. This is easily done by exporting the above graph to Microsoft Excel™. This requires that you have Excel installed on your computer.

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Right-click in the Graph you just created and choose the Plot in Excel option. Excel will launch with a plot of stage number versus displacement. You can easily modify the plot to change the stage number data to the core modulus. A sample of the Excel file for this example is included in the Tutorials folder with the Phase2 data files. The following image shows the convergence-confinement plot in Excel for this example. You can see by this plot that modulus reduction to 250MPa yields the tunnel wall displacement computed above for the point of support installation (0.027m).

We have now completed steps 1 and 2 as defined in the Problem section at the beginning of this tutorial. It is now time to actually design our support system. From Interpret, switch back to the Phase2 Model program by pressing the Model button on the toolbar. IMPORTANT: see the note at the end of this tutorial, about how to carry out the analysis if the required modulus value lies between two values in your initial modulus reduction sequence.

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Model You should now be in the Phase2 Model program with the 9 stage model you created above loaded into the program. We will use this file and modify it to do the support design.

Project Settings Open the Project Settings dialog from the Analysis menu and select the Stages Tab. Delete stages 5,6,7, and 8. Note: you can select multiple stages by scrolling down the number column with the left mouse button depressed. Use the Delete Stages button to delete the stages. Change the name of stage 5 from Excavated to Support Installed. The dialog should look like:

It is important that we keep all the core softening stages up to the stage that represents support installation. This is because the replacement and softening of the core material in stages 2 and 3 affect the final displacement result. These stages directly influence the stress path and displacement of the material around the excavation. Close the dialog by clicking OK. Make sure the Stage 5, Support Installed stage tab is selected. Click the Zoom Excavation button on the toolbar. You should see the following:

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Setting the Reinforced Concrete Liner Properties Now define the liner properties. The properties we enter will correspond to a 200 mm thick layer of concrete reinforced with W150X18 I-beams spaced at 2 meter intervals along the tunnel axis.

Select: Properties → Define Liners 1. Change the Name of the liner to Tunnel Liner 2. Change the Liner Type to Reinforced Concrete 3. Click on the Common Types button. You will see the Reinforcement database dialog shown below. For the Reinforcement, we will select an I-beam from a list of standard reinforcement types. 4. In the Reinforcement database dialog, select the W150 x 18 Ibeam. Click OK, and the I-beam reinforcement properties will be automatically loaded into the Define Liner Properties dialog.

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5. In the Define Liner Properties dialog, for the Reinforcement, enter a spacing of 2m. 6. Enter the properties for the concrete. Thickness=0.2m, Modulus=25000MPa, Poisson Ratio=0.15, Compressive Strength=45MPa, Tensile Strength=5MPa. The liner properties dialog should look like:

7. Press OK to save your input and exit the dialog.

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Adding a Reinforced Concrete Liner to the Tunnel We will now line the tunnel with the liner defined above. First make sure that Stage 5, the Support Installed stage, is selected.

Select: Support → Add Liner 1. You will see the Add Liner dialog. Make sure it looks like the following image. Select OK.

2. Click and hold the left mouse button, and drag a selection window which encloses the entire excavation. Release the left mouse button. Notice that all excavation line segments are selected. 3. Right-click the mouse and select Done Selection, or just press the Enter key. The entire tunnel will now be lined, as indicated by the thick blue line segments around the excavation boundary (see below).

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Click through the stages. Notice how the color of the liner changes from light blue in stages 1 thru 4 to dark blue in stage 5. This indicates that the liner is being installed in stage 5. We are now ready to run the analysis.

Compute Before you analyze your model, let’s save this as a new file called CoreSofteningLinerDesign.fez. (Make sure you select Save As and not Save, or you will overwrite the internal pressure reduction file).

Select: File → Save As Save the file as CoreSofteningLinerDesign.fez.

Select: Analysis → Compute The Phase2 Compute engine will proceed in running the analysis. When completed, you will be ready to view the results in Interpret.

Interpret From Model, switch to the Interpret program.

Select: Analysis → Interpret If any other files are loaded in the Interpret program (i.e. the CoreSoftening.fez file), close them. Click on the tab at the bottom of the program window associated with the file and use the File→Close menu option to close the file. Make sure the Stage 5 tab is selected. Click the Zoom Excavation button on the toolbar.

Support Capacity Diagrams Support capacity diagrams give the engineer a method for determining the factor of safety of a reinforced concrete liner. For a given factor of safety, capacity envelopes are plotted in axial force versus moment space and axial force versus shear force space. Values of axial force, moment and shear force for the liner are then compared to the capacity envelopes. If the computed liner values fall inside an envelope, they have a factor of safety greater than the envelope value. So if all the computed liner values fall inside the design factor of safety capacity envelope, the factor of safety of the liner exceeds the design factor of safety.

Select: Graph → Support Capacity Plots

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The Support Capacity Plot dialog allows you to choose the support element (i.e. liner type), the number of envelopes, and the stages from which the liner data is taken. Use the spin control to increase the number of envelopes to 3. The dialog should look like:

Press OK. The following plot is generated. The dark red lines represent the capacity envelopes for the 3 factors of safety (1, 1.2, 1.4).

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Right away you’ll notice that all the data points fall within the factor of safety=1.4 envelope, on all four plots. This means that the support system chosen has a factor of safety greater than 1.4. For further information on some of the tools that can be used with support capacity plots, see tutorial 24.

Note about determining the final core modulus Before we conclude this tutorial, it is important to note the following. In this example, the required core modulus which gives the displacement required at the point of support installation, just happens to be exactly equal to one of the original modulus values chosen for the initial reduction sequence (i.e. 250 MPa). In general this will not be the case. That is, the required core modulus will probably lie between two of the values chosen for your initial modulus reduction sequence. If this occurs, you should do the following: 1. Use the convergence-confinement graph to determine the required core modulus at the point of support installation, as discussed earlier in this tutorial. 2. Then you can either insert a new stage of core replacement, with the required modulus value, or simply use the nearest stage with a HIGHER modulus value, and lower the material modulus at this stage to the required value (e.g. if the required modulus is 350 MPa, but your initial sequence goes from 500 to 250, then change the 500 value to 350). 3. Re-run the analysis and check if the new modulus value does in fact give the desired displacement at the point of support installation. It should be close. If not, then repeat steps 1 to 3 until you determine the required modulus value. This concludes the tutorial; you may now exit the Phase2 Interpret and Phase2 Model programs.

References Hoek, E., Carranza-Torres, C., Diederichs, M.S. and Corkum, B. (2008). Integration of geotechnical and structural design in tunnelling – 2008 Kersten Lecture. Proceedings University of Minnesota 56th Annual Geotechnical Engineering Conference. Minneapolis, 29 February 2008, 153.

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Vlachopoulos, N. and Diederichs, M.S. (2009). Improved longitudinal displacement profiles for convergence-confinement analysis of deep tunnels. Rock Mechanics and Rock Engineering (Accepted - In Press) 16 pgs.

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Joint-Liner Interaction Tutorial This tutorial demonstrates how to model liner support in a jointed rock mass, when joints intersect excavation boundaries on which liner support will be installed. In order to correctly model the interaction of the jointliner intersections, we must define a Composite Liner which includes a joint at the liner-rock interface. In this case, the liner will resist slip on the joints such that it remains intact and continuous around the excavation. The analysis will be conducted in two parts. The first part shows the response of a tunnel in jointed rock without a liner. The second part shows the effect of adding the liner support. Topics Covered •

Rock joints

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Composite Liner with joint

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Generalized Hoek-Brown failure criterion

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Copying boundaries and relative coordinates

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Graph joint data

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Liner bending moments

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Model Start the Phase2 Model program.

Project Settings Open the Project Settings dialog from the Analysis menu and make sure the General tab is selected. Set the Number of Stages to 2. In this analysis, the first stage will bring the unexcavated rock to equilibrium and the tunnel will be excavated in the second stage. Define the units as being “Metric, stress as MPa”. Click OK to close the Project Settings dialog. If you see a warning about the unit system then hit OK.

Boundaries First we will define the excavation. Select Add Excavation from the Boundaries menu. Type the letter i to indicate you wish to draw a circle (or right click and choose Circle) and hit Enter. You will now see the dialog for entering a circle. Select the Centre and radius option and set the radius to 3.2. Set the Number of segments to 40 as shown.

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Click OK. You will now see a circle that you can drag around with the mouse. Enter 0,0 for the centre coordinates and hit Enter. The excavation geometry is now defined. To define the external boundary, select Add External from the Boundaries menu. The default boundary is a box around the excavation and the default expansion factor is 3. Click OK to accept these defaults. The model should now look like this.

Joints From the Boundaries menu, select Add Joint. You will see the Add Joint dialog, which allows you to select a Joint property type, end condition and installation stage. We will use the default selections, so just select OK. NOTE: see the Phase2 Help system for a discussion of the Joint End Condition option. Now enter the following coordinates defining the joint. −23 , −17 23 , 0.5 Enter The joint is now added to the model. Note that the “closed” Joint End Condition is indicated by an icon of a circle with a triangle inside, at both ends of the joint.

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Note that the two points defining the joint were actually entered just outside of the external boundary, and Phase2 automatically intersected the boundaries and added new vertices. We now wish to generate a series of parallel joints. The easiest way to accomplish this is to “copy and paste” the original joint. To do this, right click on the joint and select Copy Boundary from the resulting menu. You can now enter relative coordinates to make a copy of the joint shifted by some amount. At the prompt enter: @0,3 This will create a copy of the joint shifted 0 m in the x direction and 3 m in the y direction. Repeat these steps by right clicking on the original joint each time and entering the following relative coordinates: @0,5 @0,7 @ 0 , 10 @ 0 , 11 @ 0 , 13 @ 0 , 16 Your model should now appear as shown.

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Mesh Now that all of the boundaries have been defined we can generate the finite element mesh. Select the Mesh Setup option in the Mesh menu. The default options should be sufficient for this model. Ensure that the Mesh Type is Graded, the Element Type is 3 Noded Triangles, the Gradation Factor is 0.1 and the Default Number of Nodes on All Excavations is 75. Click the Discretize button and then the Mesh button. Click OK to close the dialog. The model should now look like this:

Field Stress Select Field Stress from the Loading menu. The tunnel is assumed to be deep underground and the stress is assumed to be caused by the overburden. Select Gravity for the Field Stress Type and enter 1100 m for the Elevation. All other values can be left as default values. The dialog should appear as shown.

Click OK to close the dialog.

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Material Properties Select Define Materials from the Properties menu. For Material 1, change the name to Graphitic Phyllite. For Initial Element Loading select Field Stress & Body Force. Leave the Unit Weight at the default value (0.027 MN/m3). For Young’s Modulus enter 1645 MPa and for Poisson’s ratio enter 0.3. Under Strength Parameters select Generalized HoekBrown for the Failure Criterion. Set the Material Type to be Plastic. Enter the Generalized Hoek-Brown parameters as shown below:

Click OK to close the dialog. NOTE: see the Phase2 Help system for a discussion of the meaning of the different Generalized Hoek-Brown parameters.

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Joint Properties Select Define Joints from the Properties menu. Change the name of Joint 1 to Rock Joints. For Criterion, select Mohr-Coulomb and change the friction angle to 20 degrees. Leave all other values as default. Note that leaving the Initial Joint Deformation option turned on means that the joints will deform due to the field stress as well as stresses induced by excavations. The dialog should appear as below:

Click OK to close the dialog.

Excavation The tunnel is to be excavated in the second stage so click on the Stage 2 tab at the bottom of the screen. From the Properties menu select Assign Properties. From the Assign Properties dialog, select Excavate. Because of the joint boundaries passing through the tunnel, the easiest way to excavate all sections of the tunnel is by using a selection window. Click and hold down the left mouse button at a point above and to the left of the tunnel. Drag the mouse to draw a box completely enclosing the tunnel. Release the button and all sections of the tunnel should be excavated as shown.

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You can also excavate the tunnel by clicking inside each section that is separated by joints – but you must be careful to click inside all sections. You have now completed modelling the tunnel without support. Save the model by choosing Save As from the File menu.

Compute Run the model by pressing the Compute button on the toolbar. The analysis may take several minutes to run since the unsupported tunnel will experience extensive failure and large deformations. Once the model has finished computing (Compute dialog closes), click the Interpret button to view the results.

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Interpret (unsupported) After you select the Interpret option, the Phase2 Interpret program starts and reads the results of the analysis. You should see a screen similar to the following that shows the maximum compressive stress for Stage 1.

You can see that stress generally increases with depth as expected. There are some discontinuities in stress across the joints, however the variations in observed stress are small. Click on the Stage 2 tab. You will now see low stresses around the tunnel with higher stresses further out. This suggests that the rock around the tunnel has failed and cannot support high stresses. Confirm this by plotting the failed elements using the Display Yielded Elements button on the toolbar. You can also plot the sections of joints that have yielded by clicking on the Display Yielded Joints button. The model should appear as follows.

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There is obviously extensive failure around the tunnel that extends a significant distance into the rock mass. Also, most of the joints close to the tunnel have failed. Now plot the deformation by changing the contours to Total Displacement and clicking on the Display Deformed Boundaries button. Turn off the Yielded Elements and zoom in on the excavation. The model will appear as shown.

You can see how the tunnel has been squeezed under stress and also how its shape has changed to become more elliptical. The joints are also showing some slip, as can be observed from the offset between opposite sides of each joint, where each joint intersects the tunnel boundary.

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You can examine the slip on the joints by plotting the shear displacement. Right click on the joint that intersects the top of the tunnel. Select Graph Joint Data. For the Vertical Axis select Shear Displacement and click Create Plot. The graph should look like this:

This plot shows almost 10 cm of slip on the joint near the tunnel surface. NOTE: the “gap” in the joint displacement graph (no data points) is due to the excavated section of the joint passing through the tunnel. We now wish to minimize the deformation and failure in the tunnel by adding support in the form of a shotcrete liner.

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Liner Support Go back to the Phase2 Model program. Open the saved file from the previous part of this tutorial if necessary. We will use the same model as before but now we will add liner support and observe the effect.

Modeling Joint-Liner Interaction To summarize the model so far – we have an excavation which is intersected by rock joints, and the excavation requires liner support in order to prevent collapse. IMPORTANT!!! In order to correctly model the interaction of the jointliner intersections, we must define a Composite Liner which includes a joint at the liner-rock interface. As you will see when you plot the liner forces, this correctly models the shear force which is applied to the liner by the differential slip of the joint endpoints at the joint-tunnel intersections.

Composite Liner Properties For the purpose of this example, it will be sufficient to define a Composite Liner which is composed of a single liner and a joint. First we will specify the properties of the single liner. Select Define Liners from the Properties menu. Change the Name of Liner 1 to Shotcrete and leave all other values as the default. The dialog should look like this:

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Click OK to close the dialog. Now we need to define the properties of the joint between the liner and the rock. Select Define Joints from the Properties menu. Click on the tab for Joint 2. Change the name to Liner Joint and leave all other selections as default values as shown.

Click OK to close the dialog. Now we can set up the composite liner. Select Define Composite from the Properties menu. Our composite liner is to be made up of the shotcrete layer and a joint. For Composite Type, select “1 liner (with slip)” from the pull-down menu. Change the Joint to Liner Joint and ensure that the First Liner is set to Shotcrete. The dialog should look like this:

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Click OK to close the dialog. NOTE: it is very important in this model that you use a composite liner with a joint. If you only use a single liner then it will not resist slip on the rock joints and the liner will segment and become discontinuous around the tunnel.

Add Support In this model, we will add the liner in Stage 2. To add the composite liner, first go to Stage 2. Select Add Liner from the Support menu. In the Add Liner dialog, make sure the Composite Liner checkbox is selected. The Liner Property should be Composite 1. The value for Install at stage should be 2 as shown.

Click OK to close the dialog. Now select all of the segments that make up the tunnel, by clicking and dragging a selection window (hold down the left mouse button and drag a window to encompass the entire tunnel). Hit Enter to finish selection. Your model should look like this for Stage 2.

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Your model is now finished. Save your model by choosing Save As from the File menu.

Compute Run the model by pressing the Compute button on the toolbar. The analysis should take under a minute to run. Once the model has finished computing (Compute dialog closes), click the Interpret button to view the results.

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Interpret (with support) The model behaviour for Stage 1 will be the same as before. Select the Stage 2 tab. You will now see a ring of high stress around the tunnel but slightly away from the tunnel boundary. This suggests that the rock directly adjacent to the boundary has failed and cannot support high stresses. Confirm this by plotting the failed elements using the Display Yielded Elements button on the toolbar. You can also plot the sections of joints that have yielded by clicking on the Display Yielded Joints button. Zoom in on the excavation and it should appear as shown.

You can see that elements around the tunnel have failed in shear and also that joints near the top and bottom of the tunnel have failed (shown as red lines). However the failure of elements and joints is much less severe than observed in the unsupported model. Note that none of the liner elements can fail since we set the liner material type to be elastic. Now plot the deformation by changing the contours to Total Displacement and clicking on the Display Deformed Boundaries button. Turn off the Yielded Elements and Yielded Joints. You can see that the tunnel (and liner) have displaced inwards and that there is little slip on the joints compared with the amount of tunnel closure. The tunnel has also maintained its circular shape.

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The amount of slip on the joints is small but it is not zero. You can examine the slip on the joints by plotting the displacement. Right click on the joint that intersects the top of the tunnel. Select Graph Joint Data. For the Vertical Axis select Shear Displacement and click Create Plot. The graph should look like this:

It is clear that the amount of slip is increasing as the joint approaches the tunnel, however, the slip on the joint is about 50 times less than the slip observed in the unsupported tunnel. Now examine the behaviour of the liner. Go back to the window showing the tunnel in Stage 2. Turn off the deformed boundaries display. Right click on the liner and select Show Values → Bending Moment. The screen should look like this:

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You can see that there are very large bending moments where the liner is intersected by the rock joints. The joints are trying to slip but they are being resisted by the liner, which undergoes shear deformation causing the large observed bending moments. It is clear that the liner is responsible for maintaining the integrity of the tunnel.

Additional Exercise Repeat the previous analysis, but instead of applying a Composite Liner with a joint, apply a regular (single layer) liner. If you run the analysis, you will see the difference in the liner behaviour. As you can see from the following figure, the Liner bending moment results are completely different from the Composite Liner (with joint) bending moments.

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Liner bending moment (single layer liner, with no joint between liner and rock). At the tunnel / rock joint intersections, the liner bending moments decrease to minimum values, rather than maximum values. This is because the liner is effectively discontinuous at these locations, and does not resist differential movement of opposite sides of each joint. If you view the Deformed Boundaries, you will see that differential movement of the joint ends takes place, similarly to the model with no liner support. The reason that the Composite Liner (with joint) gives such different results from a single layer liner (with no joint), is due primarily to the way in which Phase2 assigns node numbering at the intersections of joints. When a joint is present between the liner and the rock, this correctly models the physical interaction of the joints, tunnel boundary and liner. Finally, the following figure illustrates the deformations for all three cases (unsupported, single liner, composite liner). NOTE: the scale factors used to display the deformed boundaries are as follows: unsupported (Scale Factor = 1), single liner (Scale Factor = 1), composite liner (Scale Factor = 20).

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As you can see, the overall deformation for the single liner is not much different from the unsupported case. The differential movement at the joint ends is actually more pronounced for the single liner compared to the unsupported case. For the composite liner, the overall deformations are about 20 times less than the unsupported case, and the deformation pattern is relatively uniform and circular.

Deformed boundaries for (left to right) – unsupported, single liner, composite liner. Scale factor for deformations = 1, 1, 20, respectively. This concludes the tutorial; you may now exit the Phase2 Interpret and Phase2 Model programs.

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Liner with Sliding Gap This tutorial describes the support of a tunnel using a circular steel-set liner which includes sliding gaps. The steel-sets are constructed with sliding gaps that enable a squeezing tunnel to contract with little resistance until the gap is closed, at which time the liner will resist further tunnel squeezing. This technique enables the installation of the liner near the tunnel face before large deformations have occurred, but prevents very large forces from building up in the liner since the liner is able to deform a significant amount before it takes axial load. The analysis will be conducted in two parts. The first part shows the response of the tunnel with a regular liner (no sliding gap). The second part shows the effect of using a liner with sliding gaps. Topics Covered •

Liners with Sliding Gap

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Simulated three-dimensional tunnel excavation

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Staged tractions

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Liner axial forces

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Graph Single Point vs Stage

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Background Steel sets are sometimes used to support tunnels subjected to high squeezing stresses (see Figure 1). If these supports are installed before much deformation has occurred, the steel sets will be subjected to very large stresses as the tunnel deforms and the supports may fail (see Figure 2). However, it is often necessary to install support as close as possible to the tunnel face to ensure the safety of the workers. For this reason, sliding joints (gaps) may be added to the steel sets (see Figure 3). These gaps allow the liner to easily deform in the axial direction, until a predetermined amount of deformation has occurred, at which time the support will “lock” and will begin resisting axial stresses. This system allows the installation of the steel sets close to the tunnel face when little tunnel deformation has occurred. The sliding joints will allow further tunnel deformation before the steel sets pick up axial load. This system will prevent extreme deformations in the tunnel but will also prevent failure of the supports by ensuring that they are not subjected to very high stresses.

Figure 1. Steel sets for supporting a 5.2 m diameter tunnel.

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Figure 2. Plot of support pressure versus roof displacement for a squeezing tunnel. The red line shows the pressure on a liner with no sliding joints installed after a small amount of roof displacement. The blue line shows a liner with sliding joints installed at the same time.

Figure 3. A sliding joint. TIP: plots such as Figure 2 can be obtained from the program RocSupport available from Rocscience. For more information about RocSupport see the Rocscience website.

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Model Start the Phase2 Model program.

Project Settings Open the Project Settings dialog from the Analysis menu and make sure the General tab is selected. Set the Number of Stages to 20. In this analysis, the three-dimensional effects of tunnel excavation will be simulated by gradually decreasing tractions on the surface of the tunnel, therefore many stages are required. Define the units as being “Metric, stress as MPa”. Click OK to close the Project Settings dialog. If you see a warning about the unit system then hit OK.

Boundaries and Mesh First we will define the circular tunnel. Select Add Excavation from the Boundaries menu. Type the letter i to indicate you wish to draw a circle (or right click and choose Circle) and hit Enter. You will now see the dialog for entering a circle. Select the Centre and radius option and set the radius to 2.6. Set the Number of segments to 64 as shown.

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Click OK. You will now see a circle that you can drag around with the mouse. Enter 0,0 for the centre coordinates and hit Enter. The excavation geometry is now defined. The finite element mesh and external boundary can be constructed at the same time by generating a Radial mesh. Select Mesh Setup from the Mesh menu. For Mesh Type choose Radial, for Element Type choose 4 Noded Quadrilaterals and for Expansion Factor enter 6. Click the Discretize button and then the Mesh button to generate the mesh and the external boundary.

Click OK to close the dialog. Your model should appear as shown below. Note the default boundary conditions for the external boundary are fixed (zero displacement), which is what we want.

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Figure 4. Circular tunnel with radial mesh.

Field Stress Select Field Stress from the Loading menu. For this model we will assume a constant hydrostatic stress. Enter a value of 30 MPa for σ1, σ3 and σZ as shown.

Click OK to close the dialog.

Material Properties Select Define Materials from the Properties menu. For Material 1, change the name to Rock Mass. For Initial Element Loading select Field Stress Only. For Young’s Modulus enter 2570 MPa and for Poisson’s ratio enter 0.3. Under Strength Parameters select Generalized Hoek-Brown for the Failure Criterion. Set the Material Type to be Plastic. Enter the Generalized Hoek-Brown parameters as shown below:

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Click OK to close the dialog. NOTE: the Generalized Hoek-Brown parameters mb, s, and a, as well as the rock mass modulus, were obtained using the program RocData, based on the following Hoek-Brown classification parameters for the rock mass: •

Sigci (intact uniaxial compressive strength) = 30 MPa

•

GSI (Geological Strength Index) = 35

•

mi (intact m parameter) = 7

•

D (disturbance factor) = 0

The rock mass modulus was computed from the Simplified HoekDiederichs (2005) equation. RocData is a program for the analysis of strength data. For more information about RocData see the Rocscience website.

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Excavation The tunnel is to be excavated in the first stage so ensure you are looking at Stage 1. From the Properties menu select Assign Properties. From the Assign Properties dialog, select Excavate. Click inside the tunnel. The model should now appear as shown.

TIP: you can also right click inside the tunnel and select Assign Material → Excavate from the popup menu.

Boundary Pressure When a tunnel is excavated in three dimensions, the full deformation does not occur immediately at the tunnel face. The rock ahead of the tunnel face begins to deform before it is excavated due to the stresses caused by the nearby excavation. As excavation progresses, the boundary will continue to deform as the tunnel face moves away and stresses continue to change. In general, a tunnel does not reach its “twodimensional” state of deformation until the tunnel face is several diameters away. This is shown schematically below.

Roof Displacement Tunnel face

Figure 5. Schematic diagram showing the side view of a tunnel and the roof displacement.

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To simulate this effect on the 2-dimensional model, we will apply a traction (distributed load) to the inside of the tunnel boundary, that gradually decreases through the stages. Ensure you are looking at Stage 1. Go to Loading → Distributed Loads → Add Uniform Load. Ensure that the Orientation is Normal to boundary, and enter 30 MN/m2 for the Magnitude. This should exactly balance the field stress so that very little deformation will occur at the initial stage.

Now click on the Stage Load check box as shown above, and select the Stage Factors button. You will now see a dialog asking for the Stage Factor for each stage. The stage factor is multiplied by the initial magnitude to get the actual load magnitude for each stage (e.g., in this case a factor of 1 will apply a load of 30 MN/m2 and a factor of 0.5 will apply 15 MN/m2). We wish to gradually decrease the applied load so enter the values for each stage as shown below.

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Click OK to close the Stage Factors dialog and click OK to close the Add Distributed Load dialog. You will now be asked to select the boundary segments on which to apply the load. Select all of the segments that make up the tunnel by using a selection window. Click somewhere above and to the left of the tunnel and hold down the left mouse button. Drag a window to encompass the entire tunnel and release the mouse button. Hit Enter (or right click and choose Done). You should now see the distributed load applied to the inside of the tunnel as shown (you may need to zoom in).

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Click through the stages 1 to 20 to ensure the load is decreasing. Since we entered a stage factor of 0 for stage 20, there should be no load displayed for the final stage. TIP: to quickly view different stages, you can select the Page Down or Page Up keys to increase or decrease the stage.

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Liner Properties Now let’s define the properties of the steel set liner. For the first part of this tutorial we will define a steel-set liner with no sliding gap. From the Properties menu select Define Liners. Change the name of Liner 1 to Steel Set. Change the Young’s Modulus to 3133 MPa and the thickness to 0.24 m. Leave all other default values. Click OK to close the dialog. NOTE: •

IMPORTANT!!! The liner properties which we enter (Young’s Modulus and Thickness) are actually the properties of an equivalent liner of uniform cross-section, which has the same elastic response as a series of equally spaced steel sets. See below for more information.

•

Also note that the liner is Elastic. This means that the liner will not fail, it will respond elastically regardless of the stress applied to the liner. (To consider liner failure, we would need to set the liner Material Type = Plastic, and enter the liner Compressive and Tensile Strength. This is beyond the scope of this tutorial, and is left as an optional exercise to explore after completing this tutorial).

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Equivalent Uniform Liner Properties It is very important to understand how we arrived at the liner properties (Young’s Modulus and Thickness) for this example. When we have a liner which is composed of a series of discrete, equally spaced support elements (in this case, steel sets), then to define the equivalent liner properties in Phase2, we can define the properties of a liner of uniform cross-section which is equivalent in behaviour to the actual liner system. For details about how these equivalent liner properties can be calculated, see the Theory section in the Phase2 Help system (see Theory > Liners > Equivalent Properties for Steel Set and Shotcrete Liners). This document describes how to obtain equivalent liner properties for multicomponent liners such as steel set and shotcrete support systems. The same equations can also be used to determine the equivalent uniform properties of a steel-set only support system, by setting the modulus of one of the liner components to zero. For this example, the modulus and thickness of the equivalent uniform liner section is derived from a support system consisting of CP 160 steel sets spaced at 1.5 meters along the length of the tunnel, with 0.2 meter thick shotcrete in between the steel sets. (NOTE: in this tutorial we have not discussed the shotcrete component of the liner, however in practice the steel set rings would normally be augmented by shotcrete support).

Add Liner We will now add the liner. We need to determine the stage at which the liner will be applied. Remember that the staging in this model is intended to simulate the 3-dimensional advance of the tunnel face, by gradually decreasing the applied load on the tunnel boundary. One could perform a true three-dimensional or axisymmetric analysis to determine the state of stress and deformation near the tunnel face and therefore accurately determine the stage (i.e. deformation) at which the support should be added. For this example we will estimate that the deformation at the face is between one quarter and one third of the final deformation. However, the liner cannot be installed immediately at the face. The deformation at which the support is installed is approximately one third to one half of the final deformation. This corresponds to Stage 5 (i.e. 60% applied traction). Click on the tab for Stage 5 and from the Support menu select Add Liner. Ensure the chosen liner is Steel Set and the application stage is Stage 5 and click OK. Select the entire tunnel with a selection window. Hit enter to finish entering boundary segments. The model for Stage 5 should now look like this:

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You have now completed the modeling. Select Save As from the File menu and save the model.

Compute Run the model by pressing the Compute button on the toolbar. The analysis will take a couple of minutes to run. Once the model has finished computing (Compute dialog closes), click the Interpret button to view the results.

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Interpret (no sliding gap) After you select the Interpret option, the Interpret program starts and reads the results of the analysis. You will see a screen showing the maximum compressive stress for Stage 1. Since we specified the initial traction inside the tunnel to exactly balance the field stress, you should see a constant stress of 30 MPa throughout the rock mass. Now plot displacements by selecting Total Displacement from the dropdown menu on the toolbar. All displacements should be 0 at Stage 1. To facilitate comparison between stages we should fix the contour range to be the same for all stages. To do this, right click on the model and select Contour Options. Select Custom Range and set the maximum to 0.074 (7.4 cm) as shown.

Click Apply and then Done. Now click through the remaining stages. You will see the displacement around the tunnel increasing as the applied tractions decrease. If you turn on the displacement vectors by clicking the Display Deformation Vectors button, you will see that all of the deformation is radially inwards. The displacements for Stage 10 are shown below.

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Figure 6. Displacements, Stage 10, no sliding gap. It is interesting to plot the displacement through the stages. From the Graph menu select Graph Single Point vs. Stage. Select any point on the tunnel boundary. In the resulting dialog ensure that the Vertical Axis is Query Data and the Horizontal Axis is Stage Number. Click Create Plot. You will see a graph as shown.

Figure 7. Displacement versus stage number. You can see the displacement increasing through the stages. The change in slope after stage 10 is due to the fact that we changed the rate at which applied tractions decreased after Stage 10 (from 10% per Stage to 1% per stage).

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Interestingly, after stage 5 there appears to be an increase in the rate of displacement even though we installed the liner at Stage 5. This is because after Stage 5 the rock begins to fail. You can observe this by going back to the plot of the model, turning off the displacement vectors and turning on the failed elements (click the Display Yielded Elements button). The model in Stage 6 is shown below.

Figure 8. Yielded elements, Stage 6, no sliding gap. Note that even though some failure occurs in this model, significantly more failure would occur if the liner were not in place (try rerunning the model without the liner. You will see massive failure around the tunnel and displacements > 50 cm by Stage 20).

Liner Loading Now click on the tab for Stage 5. Recall that we installed the liner at Stage 5. The displacements are still increasing but now the liner is starting to take up some of the load. To see this, right click on the liner and select Show Values → Axial Force. Turn off the yielded elements and your screen should look like this.

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Figure 9. Liner axial force, Stage 5, no sliding gap. At Stage 5 the liner is taking an axial force of about 1 MN. Note that the bending moments on the liner are zero since the stresses are hydrostatic and the excavation is a circle (you can test this by selecting Bending Moment from the Show Values menu when you right click on the liner). Click through the subsequent stages. You will see the axial force on the liner increasing with each stage. In stage 20, the axial force on the liner is about 18.5 MN. This force is likely large enough to cause failure of the support system. This rough analysis suggests that the liner is likely to fail if installed as a rigid entity without sliding gaps. We will now run the model using a liner with sliding gaps to try to decrease the axial stress in the liner while still maintaining the integrity of the tunnel. .

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Model (with sliding gap) Go back to the to Phase2 Model program. Open the saved file from the previous part of this tutorial if necessary. We will use the same model as before but now we will include a sliding gap in the liner and observe the effect.

Liner Properties Select Define Liners from the Properties menu. At the bottom right of the dialog select the Sliding Gap checkbox.

Figure 10. Sliding Gap option in Define Liner Properties dialog. Enabling the Sliding Gap option means that: 1. There will be no axial force in the liner until the locking strain has been reached. 2. However, the liner can resist bending moments before the locking strain has been reached. So in general, the bending moment can be non-zero even prior to locking. The point at which locking occurs is determined from the Strain at Locking value. The definition of the Strain at Locking value in Phase2 is as follows.

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Calculating Strain at Locking for a Liner with Sliding Gaps The strain at locking refers to the circumferential strain that the liner goes through after installation to the point of locking. This strain is calculated by:

∆L Σ(gap lengths ) = L initial circumference For a steel set with two sliding gaps as shown, the strain at locking is calculated as follows:

D g1

g2

∆L g1 + g 2 = × 100% L πD

In our model, we will assume that we have two gaps of 0.5 m each (see Figure 1 and Figure 3). The diameter of the tunnel is 5.2 m, therefore the value for Strain at Locking is ~6% by the equation above. Enter this value in the dialog as shown. Click OK to close the dialog.

Sliding Gap Location It is important to note the following: •

In the actual steel set support system, the sliding gap(s) are located at certain positions on the circumference of the liner. Typically, 2 or more sliding gaps will be used around the circumference.

•

In the Phase2 model, the liner sliding gap does not have any specific physical location along the liner. Locking occurs when the total average strain along the liner is equal to the locking strain. There is no actual physical location to the liner sliding gap(s).

Your modified model is now finished. Save your model by choosing Save As from the File menu.

Compute Run the model by pressing the Compute button on the toolbar. The analysis should take a couple of minutes to run. Once the model has finished computing (Compute dialog closes), click the Interpret button to view the results.

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Interpret (with sliding gap) The model behaviour up until Stage 5 will be the same as before. Select the Stage 5 tab. Change the contours to show Total Displacement. Now right click on the liner and select Show Values → Axial Force. You will see that the axial force is 0 MN. This is because the liner gaps are sliding and have not yet locked. It is useful to know the exact roof displacement at each stage. Select Add Material Query from the Query menu. Click on a point on the tunnel roof and hit Enter. Check the box to Show Queried Values.

Click OK and you will now see the radial displacement at the tunnel roof as shown (1.58 cm).

Figure 11. Stage 5 results with sliding gap If you click through the subsequent stages, you will see that the liner does not start taking axial stress until Stage 11. At this point the displacement at the tunnel roof is 17.4 cm as shown.

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Figure 12. Stage 11 results with sliding gap. We can use these values to calculate the circumferential strain and check against the Strain at Locking value (6%) that we entered in the Define Liner Properties dialog. To get the circumferential strain we need to know the change in the circumference from the time of liner installation. So we need the value of displacement at Stage 5 when the liner was installed (0.0158 m) and at Stage 11 when the liner starts taking load (0.174 m). Assuming that all of the displacement is radial, ∆Circumference

= π × ∆Diameter

= 2π× ∆Radius

= 2π × (0.174 – 0.0158) = 0.994 m ∆Circumference ×100% Circumference = 6.1%

% Strain =

=

0.994 × 100% π × 5.2

This is very close to the 6% value of circumferential strain specified for the Strain at Locking (the calculated value is slightly higher because some strain has occurred past the point of locking, at Stage 11). Click through the remaining stages. You will see the displacements increasing as the tractions decrease. The maximum displacement in Stage 20 is ~20 cm. This is higher than that observed for the liner with no sliding gap (7.3 cm) but much less than the displacement that would occur with no liner at all (~ 50 cm).

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Let’s compare the effect of the sliding gap on the rock mass yielding. 1. Open the file from the first part of the tutorial (liner with NO sliding gap). 2. Tile the views vertically so that you can easily compare results for the two files, with and without the sliding gap. 3. For each view: select Stage 20, show the Strength Factor contours, display the yielded elements, and use Show Values to display the liner axial force. 4. Your screen should look similar to the following (zoom in or out as required).

Figure 13. Comparison of rock mass yielding and liner axial force with NO sliding gap (left) and WITH sliding gap (right). As you can see, including a sliding gap in the liner allows substantially greater failure of the rock mass. However, the final axial force in the liner is much lower. At Stage 20, the liner with sliding gaps is supporting an axial force of 6.9 MN, compared to 18.5 MN with no sliding gap. The following table summarizes some key results for the 3 different cases (no liner, liner with no sliding gap, and liner with sliding gap).

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Maximum Radial Displacement (m)

Maximum Axial Force in Liner (MN)

Number of Yielded Elements

No Liner

0.514

n/a

1152

Liner (no sliding gap)

0.073

18.5

512

Liner (with sliding gap)

0.194

6.9

832

This concludes the tutorial; you may now exit the Phase2 Interpret and Phase2 Model programs.

Additional Exercises

30

30

25

25

Axial force in liner without joints

20

20

15

15

Displacement of tunnel roof (liner with joints)

10

10

Axial Force in Liner (MN)

Applied Traction (MPa)

You can create a plot similar to Figure 2 for the two models by extracting the displacements, tractions and liner axial loads for each stage. Plot the applied tractions and liner axial forces versus displacements. The plot should appear as shown.

Axial force in liner with joints 5

5 Displacement of tunnel roof (liner without joints)

0

0 0

0.05

0.1

0.15

0.2

Displacement (m)

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This is not exactly the same as Figure 2 since we don’t know the support pressure provided by the liner (only the axial forces); however the plot is still informative. Notice how the displacement curve for the model with sliding gap turns sharply downwards when locking is achieved and the liner begins to take on axial load. Since the curve is becoming quite flat at this point, it is clear that the liner is preventing significant further deformation without a large amount of extra support pressure.

Liner Capacity Envelopes If we know the specifications for the capacity of our support system, we can check if the force on the liner falls within acceptable limits. A program that can generate such capacity diagrams is Response 2000 (http://www.ecf.utoronto.ca/~bentz/r2k.htm). The capacity envelope for the liner considered in this tutorial is shown below. Liner without sliding joints

Liner with sliding joints

Points lying inside the blue envelope are acceptable, whereas states outside the envelope represent potential failure of the support system. In our models, the bending moments are zero since the stresses are hydrostatic. The liner forces for the two models are plotted on the diagram. According to this diagram, the force on the liner without sliding gaps will result in failure of the liner, whereas the liner with sliding gaps is safely within the design limits. The following reference provides a useful overview and discussion of liner capacity envelopes:

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Sauer, G., Gall, V., Bauer, E and Dietmaier, P. 1994. Design of tunnel concrete linings using capacity limit curves. in Computer Methods and Advances in Geomechanics, Eds.: Siriwardane & Zaman, page 2621 - 2626 Rotterdam, NL.

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Levee with Toe Drain In this tutorial, finite element groundwater seepage analysis is used to simulate a levee with a horizontal toe drain. Toe drains are often used to prevent capillary rise on the downstream sloping surface. Phase2 can be used to test the effectiveness of different drain configurations. The finished tutorial can be found in the Tutorial 21 Levee with Toe Drain.fez file located in the Examples → Tutorials folder in your Phase2 installation folder. Topics Covered •

Seepage analysis

•

Levee drainage

•

Multiple materials

•

Phreatic surface

•

Groundwater only calculation

•

Flownets

Geometry

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Model Start the Phase2 Model program.

Project Settings Open the Project Settings dialog from the Analysis menu and make sure the General tab is selected. Set the Units of Measurement to “Metric, stress as kPa”. Click the Groundwater tab. Under Method choose Finite Element Analysis. In this tutorial we are not interested in performing a stress analysis, so under Compute, select Groundwater Only. Close the Project Settings dialog by pressing the OK button.

Boundaries First add the external boundary. Select the Add External option in the Boundaries menu and enter the following coordinates: 0,0 36 , 18

*

40 , 20 45 , 20

This point is required to specify the height of the ponded water later in the tutorial.

*

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85 , 0 100 , 0 100 , -15 -15 , -15 -15 , 0 c (to close the boundary) Hit Enter to finish entering points. This defines the external boundary, which includes the levee sitting on top of low permeability soil (see figure at the start of the tutorial). Select View → Zoom → Zoom All to center and maximize the model in the view. Now we need to add material boundaries. Firstly, we will define the boundary between the levee and the underlying soil. Go to the Boundaries menu and select Add Material. Enter the following points: 0,0 85 , 0 Hit Enter to finish entering points. TIP: when you are entering boundary points, the cursor should snap to existing points. Therefore you do not need to type in coordinates if a point already exists at that location. If your cursor does not snap to existing points, right click with the mouse when you are creating a boundary and select Snap in the popup menu to turn on the snapping option. To define the toe drain material boundary, add another material boundary with the following coordinates: 100 , -1 65 , -1 65 , 0 Hit Enter. Your model should now look like this:

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Material Properties Select Define Materials from the Properties menu. You will see the default material properties for Material 1. In this tutorial we don’t care about the strength or stiffness of the solid material therefore leave all the default values. Change the name of Material 1 to Levee. Now click on the Material 2 tab. Change the name of Material 2 to Soil. Similarly, change the name of Material 3 to Drain. Click OK to close the dialog. We now need to define the fluid flow properties of the soil. Go to the Properties menu and choose Define Hydraulic. Click on the Levee tab at the top of the dialog. Enter 1.16e-9 for Ks. Leave all other values as the default values as shown.

The underlying soil is assumed to be essentially impermeable, so click on the Soil tab and enter a value for Ks of 1.0e-20 m/s. For the Drain material, enter a permeability of 1e-6 m/s to simulate a high permeability sand drain.

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Assign Material Properties By default, the entire model is assigned the properties of Levee (material 1). To assign the correct material properties to the different parts of the model, go to the Properties menu and select Assign Properties. Select Soil from the Assign dialog and click near the bottom of the model. Now select Drain and click inside the drain region (the narrow rectangle at the toe of the levee). Alternatively you can assign material by simply rightclicking inside the region of interest and choosing Assign Material. Your model should now look like this:

Mesh Now generate the finite element mesh. Select the Mesh Setup option in the Mesh menu. Set the Mesh Type to Uniform. Leave the default number of elements (1500) but set the Element Type to 6 Noded Triangles. Here we wish to use 6-noded triangles to get more degrees of freedom in the narrow drain region. Click the Discretize button followed by the Mesh button.

Close the Mesh Setup dialog by selecting the OK button. Your model should now appear as shown.

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Boundary Conditions To set the boundary conditions, we first need to display the groundwater boundary conditions. From the Groundwater menu, select Show Boundary Conditions. The model shows the default boundary conditions (no flow across any external boundary segment). We wish to simulate ponded water to the left of the levee and a seepage face on the right. The ponded water has a depth of 18 m, therefore we will set the total head for these boundaries to 18 m. To do this, choose Set Boundary Conditions from the Groundwater menu. For BC Type choose Total Head. Enter a Total Head Value of 18.

Now select the two boundary segments that enclose the ponded water: Line 1: from (-15,0) to (0,0) Line 2: from (0,0) to (36,18) Click Apply.

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To set up the seepage face on the right of the levee, choose Unknown for the BC Type. Click on the right slope of the levee (line from 45,20 to 85,0) and the horizontal surface at the right (line from 85,0 to 100,0). Click Apply.

We will assume that the drain provides a drained boundary such that the pressure along the top of the drain is 0. Therefore choose Zero Pressure for the BC Type.

Click on the top of the drain material (line from 65,0 to 85,0) and click apply. Close the dialog and your model should look like this:

TIP: you can also right-click on a boundary to define its boundary conditions.

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You have now completed the definition of the model. Save the model using the Save option in the File menu.

Compute Since we are only interested in the groundwater results, we only need to run the groundwater computation. Select Compute (groundwater only) from the Groundwater menu (or click the Compute groundwater button in the toolbar). The analysis should take a few seconds to run. Once the model has finished computing (Compute dialog closes), select Interpret in the Analysis menu to view the results.

Interpret After you select the Interpret option, the Interpret program starts and reads the results of the analysis. A screen is displayed showing the pressure head results. Your plot should look like this:

The purpose of the toe drain was to prevent the phreatic surface from intersecting the right (downstream) side of the levee. The phreatic surface is shown as a pink line on the plot and it is clear that it does not intersect the boundary, meaning that the drain performed as desired. We can easily construct a flow net to examine the results in more detail. Change the quantity being plotted from Pressure Head to Total Head using the drop down menu on the tool bar. Now right-click on the model and select Contour Options. Under Mode select Filled (with lines) and then select Done. You will now see the equipotential lines of the flownet.

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To plot the flow lines, go the Groundwater menu and select Add Multiple Flow Lines. Select the top left corner of the levee as the first point (40,20). Now select the bottom left corner of the levee (0,0). Hit enter to finish. You will see the Flow Line Options dialog. Here you can choose how many flow lines you wish to plot. Under Flow Line Start Locations select the first option and leave the default value (10 locations, evenly spaced along the polyline).

Click OK to close the dialog. You will now see 10 flow lines plotted as shown.

This concludes the Levee with Toe Drain tutorial.

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Modeling Comments If you display the flow vectors for this model, and view the discharge velocity contours (see figure below), you will observe that there is apparently no flow taking place within the drain material. This is because the zero pressure boundary condition along the top of the drain, acts as a “sink”, and this is what simulates the drainage condition. The high permeability of the drain material does not create the drainage condition, in this case.

However, if you remove the zero pressure boundary condition at the top of the drain, and re-run the analysis, you will then see actual flow through the drain material, as shown in the figure below. This is due to the difference in permeability of the drain and levee materials.

For this particular model, the analysis results (pressure head, total head, location of water table) are very similar, with or without the boundary condition. However, this will not always be the case, and in general it is recommended that the zero pressure boundary condition is used to enforce the drainage condition at the desired location.

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Another modeling alternative is to exclude the base and drain material altogether, and just model the levee material with boundary conditions, as shown in the next figure.

If you are only interested in groundwater results, and the base material is assumed to be impermeable, then it is sufficient to only model the levee as shown in the above figure. NOTE: one reason you may wish to include the base material in the model, is that a slope stability analysis can be easily carried out on the entire model, if desired.

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Additional Exercises We can simulate a levee with a low permeability core by specifying material boundaries to define the core and setting up a new material with a lower permeability (say 1e-11 m/s). An example is shown below:

Another possibility is to construct a levee with a non-horizontal toe drain as shown.

This type of model is described in Groundwater Verification Problem #4.

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SSR Polygonal Search Area In this tutorial, Phase2 is used to determine the factor of safety of a slope using the shear strength reduction (SSR) method. The SSR Polygon Search Area option is used to focus the SSR analysis to a specific region of the slope, in order to filter out local bench failures and determine a more important global failure mechanism. The finished tutorial can be found in the Tutorial 22 SSR Polygonal Search Area.fez file, located in the Examples > Tutorials folder in your Phase2 installation folder.

Topics Covered •

Shear Strength Reduction

•

SSR Polygonal Search Area

Geometry

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Model Start the Phase2 Model program.

Project Settings Open the Project Settings dialog from the Analysis menu and make sure the General tab is selected. Define the Units of Measurement as being “Metric, stress as kPa”. Select the Strength Reduction tab. Turn on the Determine Strength Reduction factor checkbox. This enables the SSR analysis. Leave the various SSR settings at the default values. Close the Project Settings dialog by pressing the OK button.

Boundaries This model only requires an External boundary to define the geometry. Select the Add External option in the Boundaries menu and enter the coordinates shown in the figure at the beginning of this tutorial.

Material Properties Select Define Materials from the Properties menu. You will see the default properties for Material 1. Make sure the Initial Element Loading is set to Field Stress & Body Force (both in-situ stress and material selfweight are applied). Enter 20 kN/m3 for the Unit Weight. For Elastic Properties, make sure that Isotropic is the selected Elastic Type, and then enter 50000 kPa for the Young’s Modulus and 0.3 for the Poisson ratio. For Strength Parameters, make sure the Failure Criterion is set to Mohr-Coulomb. Set the Material Type to Plastic, meaning the material can yield/fail. Set the Tensile Strength to 0 kPa. Set both the peak and residual Cohesion to 5, and the peak and residual Friction Angle to 30. Leave the dilation angle at 0. The dialog should look like this:

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Press the OK button to save the properties and close the dialog.

Field Stress Because the top of the model represents the true ground surface, we want to use a gravity field stress. Go to the Loading menu and select Field Stress. For Field Stress Type select Gravity and click the check box for “Use actual ground surface”. Leave all other values as default.

Click OK to close the dialog.

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Mesh Now generate the finite element mesh. Select the Mesh Setup option in the Mesh menu. Set the Mesh Type to Uniform. Leave the default number of elements (1500) but set the Element Type to 6 Noded Triangles. Click the Discretize button followed by the Mesh button.

Close the Mesh Setup dialog by selecting the OK button.

Boundary conditions By default, all of the external boundary segments are fixed. Since the top of this model represents the actual ground surface, we need to free the top surface. Go to the Displacements menu and select Free. Click on the seven sections that make up the top boundary and hit Enter. You will now see that the fixed boundary conditions have disappeared from the top boundary. We must, however, re-establish the fixed boundary condition for the upper left and upper right vertices of the slope. Select Restrain X,Y from the Displacement menu and click on the right and left vertical boundaries. Your model should now look like this:

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Save the model using the Save option in the File menu.

Compute We will first analyze the model without specifiying any SSR search region. Press Compute to perform the SSR analysis. Once the model has finished computing (Compute dialog closes), select Interpret in the Analysis menu to view the results.

Interpret The Interpret program starts and reads the results of the analysis. By default the maximum shear strain contours are displayed. The critical shear strength reduction factor (SRF) = 1.37.

If you click on the tabs for higher SRF factors, you will see the development of a clear failure surface, for the bench in the middle of the slope. However, there may be other slope failures with very similar SRF values which a global search, or a rectangular SSR search window, will fail to find. We will now demonstrate how to use the polygonal SSR search window option to focus the SSR analysis on a specific region.

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Model with polygonal search area Go back to the Phase2 model program by clicking on the Model button. We now wish to perform an SSR analysis that excludes the small ‘local’ failure observed in the previous analysis. This can be done by specifying a polygonal SSR Search Area. In general, an SSR Search Area is implemented in the SSR analysis as follows: 1. A material can only fail if the Material Type = Plastic in the Define Material Properties dialog. If a Material Type = Elastic then the material cannot "fail", and the material strength parameters are not applicable. 2. In general, the SSR analysis is only applicable for materials which have Material Type = Plastic. 3. When you define an SSR Search Area, what this does is effectively make the Material Type = Elastic for all finite elements which are outside of the SSR Search Area. NOTE: •

This is done on an individual element basis. The original material properties are not actually changed. Instead, a new "elastic" version of each material is created, and assigned to each element which is outside of the SSR Search Area.

•

All finite elements within OR crossing an SSR Search area, are considered to be part of the SSR Search Area. Only elements which are entirely outside of a search area are given Elastic properties.

4. Therefore, failure can only occur within an SSR Search Area, during the SSR analysis, since all finite elements outside of the search area(s) are assumed to be Elastic. The use of a rectangular SSR search area is described in Tutorial 10. However, for this problem, we need to define a more complicated shape for the search area – hence a polygon.

Define SSR Polygon Search Area In order to avoid the minimum SRF value bench failure, we need to define a polygon which misses this section of the slope. Go to the Analysis menu and select the SSR Search Area > Define SSR Search Area (polygon) option. Enter the following coordinates:

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5, 5 5, 12 17, 12 27, 15 36, 19 42, 30 48, 30 43, 19 30, 9 ‘c’ to close the boundary. The model will now look like this:

Save the file under a different name and then hit Compute. Once the model is done computing, hit the Interpret button to go back into the Interpreter.

Interpret Examining the results, you can see the Critical SRF is now 1.41. Click through the higher SRF tabs. It is apparent that the SSR Search polygon has revealed a more important global failure mechanism which includes the entire slope, rather than just a single bench. The figure below shows the Maximum shear strain at SRF = 1.5. Without the polygonal search area, we wouldn’t be able to find this failure (i.e. a rectangular search window that included this large area would also include the bench in the middle of the slope, which has only a slightly lower critical SRF).

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This concludes the SSR Polygonal Search Area tutorial.

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Anchored Sheet Pile Wall Tutorial In this tutorial, Phase2 is used to simulate the construction of an excavation supported by a sheet pile wall anchored with grouted tiebacks. The complete model can be found in the Tutorial 23 Anchored Sheet Pile Wall.fez file located in the Examples > Tutorials folder in your Phase2 installation folder. Topics covered •

Liners

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Joints

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Structural interface

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Grouted tieback bolts

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Surcharge pressure

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Insert stage

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Model Start the Phase2 Model program.

Project Settings Open the Project Settings dialog from the Analysis menu and make sure the General tab is selected. Define the units as being “Metric, stress as kPa”. Select the Stages tab and change the number of stages to 5. Close the dialog by clicking OK.

Geometry The problem consists of two soil layers and two stages of excavation. Therefore an external boundary, a material boundary, and a stage boundary are required as shown below. Start by creating a rectangular external boundary. Select the Add External option in the Boundaries menu and enter the following coordinates: 0,0 30 , 0 30 , 18 20 , 18 0 , 18

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(to close the boundary)

Now we need to delineate the different material layers within the model. Go to the Boundaries menu and select Add Material. Enter the following points: 0 , 14 30 , 14 Hit Enter to finish entering points. Next we will define the boundaries of the two stages of excavation. We do not need to explicitly define the bottom of the first excavation since this is coincident with the material boundary. Therefore we will just draw the bottom of the second excavation and the vertical line that defines the lateral extent of the excavation. From the Boundaries menu, select Add Stage (we use a stage boundary instead of an excavation boundary because an excavation boundary requires a fully enclosed space). Enter the following points: 0 , 10 10 , 10 10 , 18 Enter The model should now look like this:

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Sheet pile wall Before we generate the mesh, we need to define the boundary that delineates the sheet pile wall. The top part of the wall will be coincident with the excavation but the wall will extend below the excavated soil. We wish to allow slip between the soil and the wall. Therefore we will need a sliding interface (joint) on both sides of the wall. The way to do this in Phase2 is to use a Structural Interface boundary. The wall will be installed in Stage 2, so first click on the Stage 2 tab at the bottom of the screen. Go to the Boundaries menu and select Add Structural Interface. You will see the Add Structural Interface dialog. We want to set up the interface so that the top is open (the joint ends are free to slip past each other) and the bottom is closed (the joint ends are attached and cannot slip past each other). Assuming that we draw the interface from the top down, select the option for ‘First point open / last point closed’. Ensure that ‘Install at stage:’ equals 2 as shown.

Click OK and you can enter points to define the structural interface. Enter the following points: 10 , 18 (or click on the existing point on the top boundary) 10 , 8 Enter The model should now look like this:

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Mesh Go back to Stage 1. Add the finite element mesh by selecting Mesh Setup from the Mesh menu. In the mesh setup dialog, change the Default Number of nodes to 120 as shown.

Click the Discretize button and then the Mesh button. Click OK to close the dialog. The mesh will look like this:

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Boundary conditions By default, all segments of the external boundary are fixed. Since the top of this model represents the actual ground surface, we need to free the top surface. Go to the Displacements menu and select Free. Click on the three sections that make up the top boundary and hit Enter. You will see that the fixed boundary conditions have disappeared from the top boundary. The left and right edges should be fixed only in the x-direction to allow vertical movement. Select Restrain X from the Displacements menu and select all the sections of the left and right boundaries. These boundaries will now be showing rollers instead of pins. Finally, we need to re-establish the fixed boundary condition on the bottom corners. Select Restrain X,Y from the Displacement menu, click on the bottom boundary and hit Enter. Your model should now look like this:

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Field Stress Because the top of the model represents the true ground surface, we want to use a gravity field stress. Go to the Loading menu and select Field Stress. For Field Stress Type select Gravity and click the check box for “Use actual ground surface”. Leave all other values as default.

Click OK to close the dialog.

Materials We now need to define the material properties and assign the correct materials to the correct parts of the model. Go to the Properties menu and select Define Materials. Change the name of Material 1 to Sand. Enter the other material parameters as shown.

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Click on the tab for Material 2, change the name to clay and enter the following properties:

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Click OK to close the dialog. To assign the materials to the model, select Properties → Assign Properties. Be sure you are looking at the first stage. By default, everything is set to Sand material. Select Clay from the assign dialog and click in the sections of the model below the green material boundary.

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This sets up the initial state for the first stage. In the second stage, we will add support so there is no change in material. In the third stage we will start excavating. Click on the Stage 3 tab. Choose Excavate from the Assign menu and click inside the top left section of the model as shown:

In Stage 4 we will install another tieback and excavate further. Click on the tab for Stage 4 and then click inside the next area to be excavated as shown.

Close the Assign dialog and click through the stages to ensure that the excavation proceeds correctly.

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Sheet pile wall The sheet pile wall will be installed in Stage 2 so click on the tab to show Stage 2. In our model, the sheet pile wall is sandwiched between two joints. The wall plus the joints together make up a structural interface. Right click on the structural interface (dark green line) and select Structural Interface Properties. You will now see a dialog that gives the default properties of the liner (wall) and the two joints.

To modify the properties of the joints, click on the button (…) to the right of Joint 1. We want to allow slip on the joint so change the Slip Criterion to Mohr-Coulomb. Leave all other properties as the default properties as shown.

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Click OK to close the dialog and go back to the Structural Interface dialog. Click on the button (…) next to Liner 1 to set its properties. In the Define Liner Properties dialog, change the name to Sheet Pile Wall. Set the thickness to 0.2 m as shown.

Click OK to close the dialog. Click OK in the Define Structural Interface Properties dialog.

Grouted tiebacks The first tieback will be added in Stage 2 prior to the excavation so click on the tab for Stage 2. Go to the Support menu and select Add Bolt. You will see the Add Bolt dialog. Ensure the Bolt Property is Bolt 1 and ‘Install at Stage:’ is 2.

Click OK to start entering bolt coordinates. Click on the point at the top of the sheet pile wall (10,18). Enter the coordinates 18 , 15 for the second point. Hit Enter to stop entering points. The model will look like this:

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Click on Stage 4 to add the next tieback. Select Add Bolt again from the Support menu and choose Bolt 2 for the Bolt Property.

Click OK to close the dialog and then click on the intersection point between the material boundary and the sheet pile wall (10,14). Enter 18 , 11 for the second point. Hit Enter. The model should now look like this:

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To set the tieback properties, select Define Bolts from the Properties menu. For Bolt 1, change the bolt type to Tieback. Change the PreTensioning force to 5 kN and the Percent of Length to 40%. Leave all other properties.

Click on the tab for Bolt 2. Change the Bolt Type to tieback, the PreTensioning force to 10 kN and the Percent of Length to 40%.

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Click OK to close the dialog. You will now see that 40% of the bolt is grouted (shown as an increased line width of the bolt).

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Inserting a stage Now that the model is nearly done, we realize (oops!!) that we meant to install the second bolt prior to the second round of excavation. We can remedy this by inserting a stage. Open the Project Settings dialog from the Analysis menu. Select the Stages tab. Click on Stage 4 (where we install the second bolt and excavate) and then click the Insert Before button. The dialog will look like this:

Click OK to close the dialog. If you click through the stage tabs, you will see that a stage has been added and that the new stage (Stage 4) appears the same as the previous stage (Stage 3). We wish to install the second bolt in Stage 4 so click on the tab for stage 4. Right click on the green bolt and select ‘Install bolt at stage 4’. The model should now look like this for Stage 4.

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Surcharge We wish to apply a small surcharge to the soil surface behind the wall. Click on the tab for Stage 6. Go to Loading → Distributed Loads → Add Uniform Load. Set the magnitude to 10 kN/m3 as shown and click the checkbox for Stage Load.

Click on the button for Stage Factors. Set all Stage Factors to 0 except for Stage 6 as shown.

Click OK to close the dialog. Click OK to close the Add Distributed Load dialog. You will now be prompted to select a boundary on which to apply the load. Select the top boundary just to the right of the excavation and hit enter. You final model for Stage 6 should now look like this:

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You have completed the definition of the model. Save the model using the Save As option in the File menu.

Compute Run the model using the Compute option in the Analysis menu. The analysis should take under a few minutes to run. Once the model has finished computing (Compute dialog closes), select the Interpret option in the Analysis menu to view the results.

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Interpret The Interpret program starts and reads the results of the analysis. You will see the maximum stress for Stage 1. Stage 1 only shows the stress due to gravity in the undisturbed material. Click the tab for Stage 2 to observe the stress after the installation of the sheet pile wall and grouted tieback. There is not much change from Stage 1. Change the contours to plot Total Displacement (using the pull down menu at the top). The model for Stage 2 will look like this:

You can see that there is some displacement since a pre-tension force was applied to the anchor bolt and this pulls on the sheet pile wall. Click on the tab for Stage 3 and display the deformed boundaries by clicking on the Display Deformed Boundaries button on the toolbar at the top. Now you can see a slight bulge in the sheet pile wall and the heave of the bottom of the excavation, due to removal of the excavated material.

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Click the tab for Stage 5 to show the results of the second level of excavation. Here the bulging of the wall is more pronounced. To see the actual displacement of the wall we can add a query point. Go to Query → Add Material Query and select the point at the head of the lower bolt (10,14) and hit enter. Specify the query locations as shown in the dialog below and click OK.

You will now see the total displacement at the point (in metres).

You will see a displacement of ~3.4 cm. Click on the tab for Stage 6 and you will see a displacement of ~3.6 cm. You may decide that this is too large for your specifications, in which case you may want to try applying a larger pretension force to the bolts. Delete the query by right clicking on it and choosing Delete Query. Right click on one of the bolts and select Show Values → Axial Force. You can now see the axial force distribution throughout the bolts.

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The maximum axial force in the second bolt (~ 79 kN) is below the tensile strength (100 kN) so you could perhaps apply a slightly larger pretension without causing bolt failure. Right click on the bolts and select Show Values → Show Values (all bolts off). Now click the Display Yielded Liners button on the toolbar. The wall itself was set to be elastic so it won’t exhibit any failure. However the joint between the liner and soil shows some failure (red elements), indicating that the joint is slipping.

We can look at the joint slippage by following these steps. Right click on the wall and select Show Values → Joint Shear Displacement. You will see values only at the very bottom of the wall. This suggests that we are seeing the slip on the left side of the wall rather than on the right. To remedy this, right click on the wall and select Choose Support Layer. Click under the Joint heading and select ‘negative side: Joint 1’.

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Click OK. You will now see the shear displacement between the joint and the soil to the right of the wall.

Finally, we can look at the moments in the sheet pile wall. Right click on the wall and select Show Values → Bending Moment. You can see a maximum moment of ~85 kNm.

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This concludes the tutorial, you may now exit the Phase2 Interpret and Phase2 Model programs.

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Tunnel Lining Design In this tutorial, Phase2 is used to design a reinforced concrete tunnel liner. The complete model can be found in the Tutorial 24 Tunnel Lining Design.fez file located in the Examples > Tutorials folder in your Phase2 installation folder. Topics covered •

Reinforced concrete liners

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3D tunnel simulation

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Distributed loads – field stress vector option

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Support capacity curves

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GSI calculator

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Problem A circular tunnel of radius 4m is to be constructed in Schist at a depth of 550m. The in-situ stress field has been measured with the major in-plane principal stress equal to 30 MPa, the minor in-plane principal stress equal to 15 MPa and the out-of-plane stress equal to 25 MPa. The major principal stress is horizontal and the minor principal stress is vertical. The strength of the Schist can be represented by the Generalized HoekBrown failure criterion with the uniaxial compressive strength of the intact rock equal to 50 MPa, the GSI equal to 50 and mi equal to 10. To compute the rock mass deformation modulus, the modulus ratio (MR) is assumed to be 400. The support is to be installed 2m from the tunnel face. The goal of this tutorial is to design a reinforced concrete lining with a factor of safety greater than 1.4. To design a support system, the following three steps must be performed: 1. Determine the amount of tunnel wall deformation prior to support installation. As a tunnel is excavated, there is a certain amount of deformation, usually 35-45% of the final tunnel wall deformation, before the support can be installed. Determining this deformation can be done using either a) observed field values, or b) numerically from 3D finite-element models or axisymmetric finite-element models, or c) by using empirical relationships such as those proposed by Panet or Vlachopoulos and Diederichs. 2. Using either the internal pressure reduction method, or the modulus reduction method (see tutorial 18), determine the internal pressure or modulus that yields the amount of tunnel wall deformation at the point of and prior to support installation. This is the value determined in step 1. 3. Build a model that relaxes the boundary to the calculated amount in step 2 using either an internal pressure or modulus. Add the support and determine whether a) the tunnel is stable, b) the tunnel wall deformation meets the specified requirements, and c) the tunnel lining meets certain factor of safety requirements. If any of these conditions are not met, choose a different support system and run the analysis again.

Model The first step is to determine the amount of tunnel wall deformation prior to support installation. For this tutorial, we’ll use the relationship proposed by Vlachopoulos and Diederichs. The Vlachopoulos and Diederichs method is documented in Appendix 1 of the Kersten Lecture by Hoek, Carranza-Torres, Diederichs and Corkum. The paper is in the Hoek’s published papers area on the Rocscience website:

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http://www.rocscience.com/hoek/references/Published-Papers.htm This method requires that we build a model of the tunnel and determine a) the deformation far from the tunnel face using a simple plane strain analysis, and b) for the same model determine the plastic zone radius. In this tutorial we’ll start by building a single model that also combines step 2 with step 1. We’ll build a plane strain model that relaxes an internal pressure on the tunnel boundary from a value equal to the applied in-situ stress to zero. The final stage, with zero internal pressure, will be used to determine the amount of deformation prior to support installation (step 1). The factoring of the applied internal pressure over a number of stages will be used to determine the pressure that yields the amount of tunnel wall deformation at the point of support installation (step 2). Start the Phase2 Model program.

Project Settings Open the Project Settings dialog from the Analysis menu and make sure the General tab is selected. Define the units as being “Metric, stress as MPa”.

Select the Stages tab. Change the number of stages to 10 (see following figure). Close the dialog by clicking OK.

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Geometry Now enter the circular tunnel.

Select: Boundaries → Add Excavation 1. Right-click the mouse and select the Circle option from the popup menu. You will see the following dialog.

2. Select the Center and radius option, enter Radius = 4 and enter Number of Segments = 96 and select OK. 3. You will be prompted to enter the circle center. Enter 0,0 in the prompt line, and the circular excavation will be created.

Select Zoom All (or press the F2 function key) to zoom the excavation to the center of the view.

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Now we will create the external boundary. In Phase2, the external boundary may be automatically generated, or user-defined. We will use one of the ‘automatic’ options.

Select: Boundaries → Add External You will see the Create External Boundary dialog. We will use the settings of Boundary Type = Box and Expansion Factor = 5. Select OK, and the external boundary will be automatically created.

The boundaries for this model have now been entered.

Mesh Add the finite element mesh by selecting Mesh Setup from the Mesh menu. In the mesh setup dialog, change the Element Type to 6 Noded Triangles.

Click the Discretize button and then the Mesh button. Click OK to close the dialog. The mesh will look like this:

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Boundary Conditions For this tutorial, no boundary conditions need to be specified by the user. The default boundary condition will therefore be in effect, which is a fixed (i.e. zero displacement) condition for the external boundary.

Field Stress Field Stress determines the initial in-situ stress conditions, prior to excavation. As described earlier in this tutorial, the in-situ stress field has been measured with the major in-plane principal stress equal to 30 MPa, the minor in-plane principal stress equal to 15 MPa and the out-ofplane stress equal to 25 MPa. The major principal stress is horizontal and the minor principal stress is vertical.

Select: Loading → Field Stress

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Enter Sigma 1 = 30, Sigma 3 = 15, Sigma Z = 25, Angle = 0, and select OK.

Materials Go to the Properties menu and select Define Materials. For Material 1, change the Failure Criterion to Generalized Hoek-Brown and the Material Type to Plastic. Now define the strength parameters and the Young’s Modulus using the GSI calculator. Press the GSI calculator button (see below).

In the GSI calculator dialog, set the uniaxal compressive strength of the intact rock equal to 50 MPa, the GSI equal to 50 and mi equal to 10. To compute the rock mass deformation modulus, set the modulus ratio (MR) to 400. The dialog should look like:

Press the OK button. The material properties dialog should now be updated with the new strength and modulus values.

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Click OK to close the dialog. Since you entered properties with the first (Material 1) tab selected, you do not have to Assign these properties to the model. Phase2 automatically assigns the Material 1 properties for you.

Excavation The tunnel is to be excavated in the first stage so click on the Stage 1 tab at the bottom of the screen. Simply place the mouse pointer inside the excavation and right-click the mouse. From the menu that pops up, select the Assign Material > Excavate option.

The material inside the excavation should now be removed.

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Adding an Internal Pressure to the Excavation Now let’s add a uniform distributed load to the tunnel in stage 1. The magnitude and direction of the load will be equal and opposite to the insitu stresses thus forming a balance between the stresses in the rock and the pressure inside the tunnel. Since the pressure is equal and opposite to the in-situ stress, no deformation should occur. However, in stage 2 and after, we will factor the load and gradually reduce the magnitude of the pressure. As a result, tunnel deformation will increase as the pressure is lowered to zero.

Select: Loading → Distributed Loads → Add Uniform Load

In the Add Distributed Load dialog, select the Field stress vector orientation option. Select the Stage Load checkbox, and select the Stage Factors button. In the Stage Factors dialog enter the factors shown in the following image.

Factor = 1 means the magnitude will be the same as the field stress while a Factor = 0 means no load will be applied at that stage. Other values of Factor can be used to increase or decrease the magnitude of a load at any stage of a model.

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Select OK in both dialogs. You will now be asked to pick the boundary segments on which the load will be applied. Select the excavation line segments to be loaded: Select boundary segments [enter=done,esc=cancel] : use the mouse to draw a selection window around the entire excavation. After the excavation segments are selected, right-click and select Done Selection, or press Enter.

Note: to draw a selection window, simply pick one of the window corners by moving the mouse cursor to a point, and press AND HOLD DOWN the left mouse button. Now move the cursor while still holding down the left mouse button, you should see a window forming. Now move the mouse cursor to the opposite corner of the window and release the left mouse button when done. Click the Zoom Excavation button on the toolbar. You should see the following:

Now click through the stage tabs. You should see the internal pressure reduce as the stage increases. NOTE: a useful feature of the Field stress vector loading option is that any change to the field stress through the field stress dialog will also automatically update the internal pressure inside the tunnel. We are now ready to run the analysis.

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Compute Before you analyze your model, let’s save this as a new file called InternalPressureReduction.fez

Select: File → Save Save the file as InternalPressureReduction.fez.

Select: Analysis → Compute The Phase2 Compute engine will proceed in running the analysis. When completed, you will be ready to view the results in Interpret.

Interpret From Model, switch to the Interpret program.

Select: Analysis → Interpret After you select the Interpret option, the Interpret program starts and reads the results of the analysis. You will see the maximum stress, sigma 1 for Stage 1. Notice that there is no variation of stress and that the stress (30 MPa) is equal to the major in-situ field stress. This means that the internal pressure is equal and opposite to the field stress and the model is behaving as if the tunnel did not exist. Now click the Zoom Excavation button on the toolbar. Change the contours to plot Total Displacement using the pull down menu in the toolbar. The model for Stage 1 will look like this:

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You can see that there no displacement in the first stage. Now click through the stages. You’ll see an increase in deformation around the tunnel as the internal pressure is reduced.

Step 1 – Computing tunnel deformation before support installation using the Vlachopoulos and Diederichs method To compute the tunnel deformation at the point of support installation, we’ll use the empirical relationship developed by Vlachopoulos and Diederichs. To use the Vlachopoulos and Diederichs method, you need two pieces of information from the finite-element analysis. You need to know a) the maximum tunnel wall displacement far from the tunnel face, and b) the radius of the plastic zone far from the tunnel face. Both of these values can be computed from a plane strain analysis with zero internal pressure inside the excavation. In the model we just built, the results from stage 10 are used since there is zero internal pressure in this stage. Switch to the last stage, stage 10. Look in the lower left corner of the program window on the status bar. You’ll see that the maximum displacement for this stage is approximately 0.065m. This is the value of maximum wall displacement far from the tunnel face. The location of this displacement is in the roof and floor of the excavation. The location of this displacement is important since any comparisons of displacement for various internal pressures must be made at the same location. To determine the radius of the plastic zone, first turn on the display of yielded elements using the Display Yielded Elements toolbar button. You’ll see a number of crosses representing elements in the finite element analysis that have failed. Zoom Out failed points is visible (see below).

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The extent of this failed zone represents the extent of the plastic zone around the tunnel. To determine the radius of the plastic zone, you can use either the measuring tool or the dimensioning tool to measure the distance from the center of the tunnel to the perimeter of the yielded/plastic zone. In this tutorial we’ll use the measuring tool. Select: Tools → Add Tool → Measure Pick the location to measure from [esc=quit]: 0,0 Pick the location to measure to [esc=quit]: use the mouse to extend the measuring line vertically until you get to the edge of the yield zone, press the left mouse button.

As seen above, the radius of the plastic zone is approximately 9.5m.

Computing displacement prior to support installation using the Vlachopoulos and Diederichs Method The following plot was created using the Vlachopoulos and Diederichs equations. The equations can be found in the Kersten Lecture, appendix 1. Using this plot, you can easily estimate the amount of closure prior to support installation if you know the plastic radius and displacement far from the tunnel face.

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For our problem, Rp=9.5m, Rt=4m, X=2m, and umax=0.065m. The Distance from tunnel face/tunnel radius = 2/4 = 0.5. The Plastic zone radius/tunnel radius = 9.5/4 = 2.4. From the above plot this gives Closure/max closure approximately equal to 0.44. Therefore the closure equals (0.44)*(0.065) = 0.028m. As computed above, the tunnel roof displaces 0.028m before the support is installed.

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Step 2 - Determining the internal pressure factor The next step is to determine the internal pressure that yields a displacement of 0.028m in the roof of the tunnel. It is important to maintain the same location as is used to determine umax, since the location of maximum displacement can change depending on the magnitude of the internal pressure. This can be seen in this model as larger internal pressures produce larger displacement in the sidewall while smaller internal pressures produce larger displacements in the roof and floor. To determine the internal pressure that yields a 0.028m roof displacement, we’ll plot the displacement versus stage for a point on the roof of the excavation. Make sure you have Total Displacement selected as the data type.

Graphing Displacement in the Roof of the Excavation To create the graph:

Select: Graph → Graph Single Point vs. Stage 1. When asked to enter a vertex, type in the value 0,4 for the location and press Enter. This is a point on the roof of the excavation. 2. You will see the Graph Query Data dialog.

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3. Press the Create Plot button. The following figure shows the plot generated by the program. This is a plot of displacement versus stage for a point in the roof of the tunnel.

Right-click in the plot and choose the Sampler option. Move the sampler by moving the mouse with the left mouse button. Move the sampler until the displacement value on the right side of the plot is equal to 0.028m.

From this plot, you can see that in stage 5, the wall displacement in the roof of the tunnel is 0.028m. This represents an internal pressure factor of 0.1 as was defined in the modeler for the field stress vector distributed load.

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Creating a convergence confinement graph in Excel Often you want to create a convergence confinement graph which plots displacement versus internal pressure. This is easily done by exporting the above graph to Microsoft Excel™. This requires that you have Excel installed on your computer. Right-click in the Graph you just created and choose the Plot in Excel option. Excel will launch with a plot of stage number versus displacement. You can easily modify the plot to change the stage number data to the internal pressure factor. A sample of the Excel file for this example is included in the Tutorials folder with the Phase2 data files. The following image shows the convergence-confinement plot in Excel for this example. You can see by this plot that an internal pressure factor of 0.1 yields the tunnel wall displacement computed above for the point of support installation (0.028m).

We have now completed steps 1 and 2 as defined in the Problem section at the beginning of this tutorial. It is now time to actually design our support system. From Interpret, switch back to the Phase2 Model program by pressing the Model button on the toolbar.

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Model You should now be in the Phase2 Model program with the 10 stage model you created above loaded into the program. We will use this file and modify it to do the support design.

Project Settings Open the Project Settings dialog from the Analysis menu and select the Stages Tab. Change the name of stage 1 to Initial Stage. Change the name of Stage 5 to Tunnel Relaxation. Change the name of Stage 10 to Support Installed. The dialog should look like this:

Now delete all other stages except these three stages (i.e. stages 2,3,4,6,7,8,9). Note, you can select multiple stages by scrolling down the number column with the left mouse button depressed. Use the Delete Stages button to delete the stages. After deleting these stages, the dialog should look like:

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We chose stage 5 from the old model because it represents the stage in which the internal pressure in the tunnel yields the necessary deformation before we install the support. Close the dialog by clicking OK. Make sure the Stage 1 tab is selected. Click the Zoom Excavation button on the toolbar. You should see the following:

Click through the stages. Stage 2, the tunnel relaxation stage, should look like:

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Note: you can use the Loading→Distributed Loads→Edit Distributed Load option to select any of the loads on the boundary to verify that the stage factor is 0.1 for Stage 2. Stage 3, the Support Installed stage should have no load on the boundary.

Setting the Reinforced Concrete Liner Properties Now define the liner properties. The properties we enter will correspond to a 100 mm thick layer of concrete reinforced with W100X19.3 I-beams spaced at 2 meter intervals along the tunnel axis.

Select: Properties → Define Liners 1. Change the Name of the liner to Tunnel Liner 2. Change the Liner Type to Reinforced Concrete 3. Click on the Common Types button. You will see the Reinforcement database dialog shown below. For the Reinforcement, we will select an I-beam from a list of standard reinforcement types. 4. In the Reinforcement database dialog, select the W100 x 19.3 Ibeam. Click OK, and the I-beam reinforcement properties will be automatically loaded into the Define Liner Properties dialog.

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5. In the Define Liner Properties dialog, for the Reinforcement, enter a spacing of 2m. 6. Enter the properties for the concrete. Thickness=0.1m, Modulus=25000MPa, Poisson Ratio=0.15, Compressive Strength=45MPa, Tensile Strength=5MPa. The liner properties dialog should look like:

7. Press OK to save your input and exit the dialog.

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Adding a Reinforced Concrete Liner to the Tunnel We will now line the tunnel with the liner defined above. First make sure that Stage 3, the Support Installed stage, is selected.

Select: Support → Add Liner 1. You will see the Add Liner dialog. Make sure it looks like the following image. Select OK.

2. Click and hold the left mouse button, and drag a selection window which encloses the entire excavation. Release the left mouse button. Notice that all excavation line segments are selected. 3. Right-click the mouse and select Done Selection, or just press the Enter key. The entire tunnel will now be lined, as indicated by the thick blue line segments around the excavation boundary (see below).

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Click through the stages. Notice how the color of the liner changes from light blue in stages 1 and 2 to dark blue in stage 3. This indicates that the liner is being installed in stage 3. We are now ready to run the analysis.

Compute Before you analyze your model, let’s save this as a new file called LinerDesign.fez. (Make sure you select Save As and not Save, or you will overwrite the internal pressure reduction file).

Select: File → Save As Save the file as LinerDesign.fez.

Select: Analysis → Compute The Phase2 Compute engine will proceed in running the analysis. When completed, you will be ready to view the results in Interpret.

Interpret From Model, switch to the Interpret program.

Select: Analysis → Interpret If any other files are loaded into the Interpret program (i.e. the InternalPressureReduction.fez file), close them. Click on the tab at the bottom of the program window associated with the file and use the File→Close menu option to close the file. Make sure the Stage 3 tab is selected. Click the Zoom Excavation button on the toolbar.

Support Capacity Diagrams Support capacity diagrams give the engineer a method for determining the factor of safety of a reinforced concrete liner. For a given factor of safety, capacity envelopes are plotted in axial force versus moment space and axial force versus shear force space. Values of axial force, moment and shear force for the liner are then compared to the capacity envelopes. If the computed liner values fall inside an envelope, they have a factor of safety greater than the envelope value. So if all the computed liner values fall inside the design factor of safety capacity envelope, the factor of safety of the liner exceeds the design factor of safety.

Select: Graph → Support Capacity Plots

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The Support Capacity Plot dialog allows you to choose the support element (i.e. liner type), the number of envelopes, and the stages from which the liner data is taken. Use the spin control to increase the number of envelopes to 3. The dialog should look like:

Press OK. The following plot is generated. The dark red lines represent the capacity envelopes for the 3 factors of safety (1, 1.2, 1.4). Notice the number of liner data points that fall outside the 1.4 design factor of safety envelope, meaning they have a factor of safety less than 1.4. This occurs for both the capacity diagrams for the concrete and the capacity diagrams for the I-beam. In fact, a number of points fall outside the factor of safety=1.0 envelope. This liner would most likely experience cracking and crushing if used in this tunnel. Later, we’ll have to improve on this design.

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Let’s investigate some of the things you can do with the support capacity envelopes.

Select: Window → Tile Vertically The window should look like:

Make sure the Support Capacity Plot view is selected, not the contour view of the tunnel. If you are interested in just the concrete moment capacity plot, you can expand this plot using the following option.

Select: View → Concrete Moment Capacity Plot

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The four plots are replaced by a single plot of the moment capacity for the concrete. Alternatively, you can maximize any single plot interactively by double-clicking on the plot. Double-clicking on the moment capacity for the concrete returns you to the four plots. Right-clicking also gives you a context menu that enables you to choose viewing options. Make sure you have a single plot of the moment capacity for the concrete. Your display should look like:

Select: View → Zoom → Zoom Support Capacity Data The view is zoomed so that the extents of the plot are determined by the extents of the moment and axial force data for the concrete.

Select: View → Zoom → Zoom All The plot is returned to the default extents. If you have a mouse wheel, you can use it to zoom in and out on the data. Holding down the mouse wheel and moving the mouse results in panning of the plot. There are a number of options for manipulating the plot. Return to the default extents.

Select: View → Zoom → Zoom All Try right-clicking in the plot view and choosing the Chart Properties option.

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A dialog containing a number of options for changing the format of the plots is displayed. Close this dialog. Now use the mouse to click on one of the red liner data points. The data point is highlighted in the support capacity plot view and the liner associated with this data is highlighted in the main contour view. This is shown in the following figure.

Right-click in the support capacity plot view and select the Filter Data by FS option. The following dialog is displayed. Change the Factor of safety used for filtering to Concrete moment. Change the Maximum value to 1 and turn on the Highlight filtered liners. What this does is plot all the data points with factor of safety between 0 and 1 for the concrete moment, and show the associated liner elements in the contour view.

Press the OK button after making these changes. In the following image, only the liner elements with factor of safety between 0 and 1 for the concrete are displayed. The liner elements associated with these data points are highlighted on the contour view by drawing a grey circle around each element. As you can see, the areas of minimum factor of safety for the concrete are in the roof and floor of the excavation.

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Now let’s go back to the Modeler and pick a better support system for the tunnel. From Interpret, switch back to the Phase2 Model program:

Select: Analysis → Model

Model – Improving the Support System

Select: Properties → Define Liners 1. Make sure the Tunnel Liner tab is selected. Click on the Common Types button. 2. In the Reinforcement dialog that is displayed, select the W150 x 18 I-beam. Click OK. 3. Increase the thickness of the concrete to 0.2m. The liner properties dialog should look like:

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4. Press OK to exit the dialog. We are now ready to re-run the analysis.

Compute Before you analyze your model, let’s save this as a new file called LinerDesign2.fez. (Make sure you select Save As and not Save, or you will overwrite the LinerDesign.fez file).

Select: File → Save As Save the file as LinerDesign2.fez.

Select: Analysis → Compute The Phase2 Compute engine will proceed in running the analysis. When completed, you will be ready to view the results in Interpret.

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Interpret From Model, switch to the Interpret program.

Select: Analysis → Interpret

Select: Graph → Support Capacity Plots Use the spin control to increase the number of envelopes to 3. The dialog should look like:

Press OK. The following plot is generated.

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Right away you’ll notice that all the data points fall within the factor of safety=1.4 envelope, on all four plots. This means that the support system chosen has a factor of safety greater than 1.4 thus achieving the design factor of safety. You can also use some of the tools previously demonstrated to filter out points with a factor of safety less than 1.4. You’ll see that none exist. This concludes the tutorial; you may now exit the Phase2 Interpret and Phase2 Model programs.

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Editing the Reinforcement Database In this tutorial, the procedure for adding user-defined reinforcement types to the Phase2 reinforcement database is covered. The reinforcement is used when defining reinforced concrete liners.

Topics covered •

Reinforced concrete liners

•

Reinforcement database

•

Customizing the database

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Problem

When designing reinforced concrete liners, Phase2 offers a database of common reinforcement types. These include I-beams, lattice girders, hollow sections, rebar, wire mesh, and channels. Typical properties for a number of common sections are available for the user to choose from. If your particular section is not in the database, it is possible to add it to a custom version of the database. This makes it easy to define the section in any future models. This custom reinforcement database can also be shared so that other engineers within your company can easily use the section in their analysis. In this tutorial, an I-beam section commonly used in tunnels in Venezuela is added to the database. This section has the following properties: Designation

Weight kg/m

Height mm

Width mm

Area cm2

Ix cm4

Sx cm3

Sy cm3

CP 160

29.3

160

160

37.5

1790

223

615

To define a new entry in the database you need to define the following quantities: Shape Type Designation (Imperial) Weight (lbf/ft) Area (in2) Depth (in) Moment of Inertia (in4) Designation (Metric) Weight (kg/m) Area (mm2) Depth (mm) Moment of Inertia (mm4*10^6) As you can see, you need both the metric and imperial properties of the section. The units for each are in brackets. The shape and type are user defined descriptions. If you look at the dialog on the first page of this tutorial, you’ll see the various shapes and types used as descriptions in the default database that comes with the program.

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For the above section, the parameters are as follows: Shape

I-beam

Type

CP

Designation (Imperial)

CP160 x 29.3 (Metric)

Weight (lbf/ft)

0

Area (in2)

0

Depth (in)

0

Moment of Inertia (in4)

0

Designation (Metric)

CP160 x 29.3

Weight (kg/m)

29.3

Area (mm2)

3750

Depth (mm)

160

Moment of Inertia (mm4*10^6)

17.9

Notice the imperial quantities are set to zero. If a weight, area, depth or moment of inertia value is zero, it is automatically calculated from its equivalent metric (or imperial) value. So in the above example, the weight in lbf/ft is automatically calculated from the weight in kg/m. So if all you use is imperial or metric units, and you only have the weight, area, depth and moment of inertia in one of these unit systems, you do not have to do the conversion. If you do have these quantities in both unit systems, by all means enter the values in both unit systems.

Creating a New User Reinforcement Database Start the Phase2 Model program. The default reinforcement database is saved in a file called Reinforcement.xls that is installed in your Phase2 7.0 installation folder. This file is a Microsoft Excel™ format file and contains a spreadsheet with all the section information. This file should NOT be edited or changed in any way. The reason for this is that future updates of Phase2 7.0 will most likely update this file. So any changes you make to this file will be lost after an update.

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Phase2 7.0 allows the customization of the reinforcement database by allowing the user to create a new database. This new database is a copy of the default database, in a user specified location, that you can modify and add your custom support to. You can also share this database with other people in your company by 1) specifying the location of the database as a shared location that all people can gain access to or 2) simply by giving a copy of the database file to the other people and having them use it privately on their own computer. The following procedure sets up a custom database on your computer.

Select: Properties → Define Liners 1. Change the Liner Type to Reinforced Concrete 2. Click on the Common Types button. 3. In the dialog that is displayed (see below), press the Edit Database button.

4. In the User Reinforcement Database dialog (see below), press the Create New button.

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5. A warning dialog will appear explaining that the default reinforcement database will be copied to another location for editing (see below), press the OK button.

6. In the Save As dialog, navigate to a folder in which you want to save the database. In the following figure, the database is being saved in the My Documents folder with the filename P2UserRDB.xls. You must have read/write privileges for files in the folder you choose. Press the Save button.

7. You’ll now find yourself back in the User Reinforcement Database dialog. Press the OK button to exit the dialog. Phase2 is now set up to use a custom reinforcement database. The database is a simple Excel™ spreadsheet; its name and location as you defined in step 6 above. You can edit this file with Microsoft Excel™ independently of Phase2, or use the User Reinforcement Database dialog to Edit the file.

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Editing the Current User Reinforcement Database

From within the Reinforcement dialog: 1. Press the Edit Database button. 2. In the User Reinforcement Database dialog (see below), press the Edit button.

3. Microsoft Excel™ will launch, and read in the custom database that you defined in the previous section. Scroll up to the top of the spreadsheet. You’ll see the following:

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Editing the Reinforcement Database

Notice the column headers match the quantities that we defined earlier in this tutorial. 4. Scroll down to the last line in the spreadsheet. Now append the following information into the Excel™ spreadsheet. Place each cell value in the appropriate column as listed below. Data

Excel Column

Cell Value

Shape

A

I-beam

Type

B

CP

Designation (Imperial)

C

CP160 x 29.3 (Metric)

Weight (lbf/ft)

D

0

Area (in2)

E

0

Depth (in)

F

0

Moment of Inertia (in4)

G

0

Designation (Metric)

H

CP160 x 29.3

Weight (kg/m)

I

29.3

Area (mm2)

J

3750

Depth (mm)

K

160

Moment of Inertia (mm4*10^6)

L

17.9

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The Excel™ spreadsheet should look something like:

5. Save and close the Excel spreadsheet. Press OK in the User Reinforcement Database dialog. You’ll now see that CP type has been added to the I-beam shape. Select this reinforcement section (see below) and you’ll see that all the properties that you entered into the database are now displayed.

If you press OK after selecting the CP section in the reinforcement dialog, you’ll see that the liner properties dialog is updated with the CP section data.

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Opening a User Reinforcement Database If someone sends you a reinforcement database file, or sends you a link to a database file in a shared folder on your company’s network file system, you can easily open this file in Phase2 7.0. In the User Reinforcement Database dialog (see below), press the Open Existing button. Now use the Open File dialog to navigate to the folder containing the reinforcement database file. Select the database file and press Open. Press OK in the User Reinforcement Database dialog. The new sections should now be seen in the Reinforcement dialog.

This completes the tutorial. You may now exit the Phase2 Modeler.

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Drawdown Analysis for Slope In this tutorial, two different methods of modeling the staged drawdown of ponded water against a slope are examined, and an SSR slope stability analysis is performed. The drawdown is implemented in two ways: 1) by lowering the water table, and 2) by running a finite element groundwater analysis with changing boundary conditions. The complete models can be found in the Tutorial 26 Slope Drawdown (piezo).fez and Tutorial 26 Slope Drawdown (finite).fez files located in the Examples > Tutorials folder in your Phase2 installation folder.

Topics covered •

Drawdown

•

Staged piezo lines

•

Staged groundwater analysis

•

Shear strength reduction

•

Importing coordinates

•

Ponded water loading

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Model Start the Phase2 Model program. In this tutorial we will start with a model that has already been constructed. Select File → Open and choose Tutorial 26 Slope Drawdown (initial).fez from the Examples > Tutorials folder in your Phase2 installation folder. You will see a model that looks like this:

This is a two-stage model of a slope upon which a Shear Strength Reduction analysis will be performed. The geometry, material properties and mesh have already been specified for this model. The purpose of this tutorial is to examine how to simulate groundwater drawdown. This can be done in two different ways: using piezo lines or finite element groundwater analysis. We will start with the piezo line approach.

Drawdown with piezometric lines Go to Analysis → Project Settings and select the Groundwater tab. Ensure that the Method is set to Piezometric Lines and that the Pore Fluid Unit Weight is 9.81 kN/m3 as shown:

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Click on the Strength Reduction tab and you will see that Shear Strength Reduction has been turned on.

Click OK to close the dialog.

Piezometric Lines In the first stage, there will be 10 m of ponded water at the base of the slope. In the second stage, the ponded water will drop down 5 m. Ensure you are looking at Stage 1. Go to Boundaries → Add Piezometric Line. Enter the following coordinates: 0 , 40

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65 , 40 66.35 , 40.6 67.7 , 41 78.3 , 42.4 89.4 , 43.5 130 , 47 Enter Now select Soil 1 in the dialog as shown:

Click OK. Your model should now look like this:

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TIP: If you don’t want to type in all of these coordinates, you can import a table stored in a text file. After you select Add Piezometric Line, type t for table and hit Enter. You will now be prompted to enter coordinates in a table. Click the Import button and choose the file Tutorial 26 piezo 1.txt in your Examples > Tutorials folder in your Phase2 installation folder. The coordinates should then fill the table as shown. Click OK to close the dialog and draw the piezo, hit Enter to finish.

In the second state we want to drop the ponded water by 5 m. Click on the tab for Stage 2. Go to Boundaries → Add Piezometric Line. Enter the following coordinates (or import Tutorial 26 piezo 2.txt as described in the tip above): 0 35 57.5 35 58.7 35.8 60.1 36.3 65.3 37.3 76.6 39 93.5 41.1 110 43 130 45 Enter Select Soil 1 in the ‘Assign Piezometric Line to Materials’ dialog and click OK. The model should now look like this:

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Notice that the new water table (piezo 2) has superceded the old water table (piezo 1). Go back to Stage 1. You will see that Stage 1 is the same as Stage 2; the active water table is piezo 2, and piezo 1 is inactive. We now need to stage the piezo lines. From the Properties menu, choose Define Hydraulic. Click on the Stage Piezo Lines checkbox. For Stage 1, choose Piezo #1 and for Stage 2, choose Piezo #2. For Hu, choose Custom from the pull-down menu. Leave the custom value as 1.

Click OK to close the dialog. Now click through the stages and you will see that piezo 1 is active in Stage 1 and piezo 2 is active in Stage 2.

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Ponded Water Load In this model there is ponded water at the left side of the model. This applies a stress to the soil surface due to the weight of the water. To account for this, go to Loading → Distributed Loads → Add Ponded Water Load. In Stage 1, the y-coordinate of the water table is 40 m. So enter a Total Head of 40 m. Now select the Stage Load checkbox.

Click the Stage Total Head button. In Stage 2, the water table is at 35 m, so change the Total Head for Stage 2 to 35 m as shown:

Click OK and then click OK to close the ‘Add Ponded Water Load’ dialog. You will now be prompted to select the boundary segments on which to apply the ponded water load. Select the horizontal surface between (0,30) and (50,30). Also select the two segments on the slope below piezo 1. Hit Enter to finish choosing segments. The model for Stage 1 should look like this:

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You can see the load due to the weight of the water in Stage 1 ranges from 0 to 98.1 kPa. In Stage 2, the depth of ponded water is reduced by half so the maximum load is 49.05 kPa. The model definition is now complete. Save the model using the Save As option in the File menu.

Compute Run the model using the Compute option in the Analysis menu. Because it is performing a Shear Strength Reduction analysis, the model will take several minutes to run. Once the model has finished computing (Compute dialog closes), select the Interpret option in the Analysis menu to view the results.

Interpret The Interpret program starts and reads the results of the analysis. The Shear Strength Reduction analysis is only performed on the last stage of your model, so what you are seeing is the maximum shear strain for the critical strength reduction factor (1.28) for the second stage.

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If you click the tab for SRF: 1.29 you get a better picture of the critical failure surface as shown.

If you want to look at the stage data prior to the SSR analysis, select Stage Settings from the Data menu. Set the Reference Stage to Not Used, and the Visible Stage to Stage 1.

Click OK. You will now see the maximum shear strain in stage 1. Change the plot to Pore Pressure using the pull-down menu at the top. You can see the pore pressure due to the water table in Stage 1. Click the tab for Stage 2. It is clear how the pore pressure decreases as the water table is lowered.

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Drawdown with finite element groundwater analysis We can perform the same analysis using finite elements to compute the pore pressures in the model instead of Piezometric lines. Go back to the Phase2 Model program. Go to Analysis → Project Settings and select the Groundwater tab. Change the method to Finite Element Analysis. Leave all other options as shown:

Click OK to close the dialog. Phase2 will ask you if you want to delete the Piezometric lines. Click Yes.

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Groundwater boundary conditions From the Groundwater menu, select Show Boundary Conditions. Ensure you are looking at Stage 1. Choose Set Boundary Conditions from the Groundwater menu. For the BC Type, choose Total Head. Set the Total Head Value to 47 m.

Use the mouse to select the right vertical boundary of the model. Click Apply in the dialog. The right side of the model should display a total head boundary condition as shown:

In the dialog, change the Total Head Value to 40. Click on the left vertical boundary, the horizontal segment at the base of the slope and the bottom two segments of the slope and click apply. The model should look like this:

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You can see how Phase2 displays the ponded water based on the specified total head boundary conditions. Finally, we need to set unknown boundary conditions for the rest of the slope face, since we don’t know where the water table will intersect the slope. In the Set Boundary Conditions dialog, select Unknown (P=0 or Q=0) for the BC Type. Click the top segment of the slope face and click Apply. Click the Close button and the model should look like this:

Now click the tab for Stage 2. In Stage 2 we want to lower the ponded water. Choose Set Boundary Conditions from the Groundwater menu again. Follow these steps: •

Select Total Head (H) for the BC Type. Set the Total Head to 45 m. Select the right vertical boundary and click Apply.

•

Set the Total Head Value to 35 m. Click on the left vertical boundary, the horizontal boundary at the base of the slope, and the bottom section of the slope face and click Apply.

•

Change the BC Type to Unknown (P=0 or Q=0). Click on the section of the slope just above the water table (the middle section of the slope face) and click Apply.

Select the Close button to close the dialog. The model should look like this for Stage 2.

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Hydraulic material properties From the Properties menu, choose Define Hydraulic. Here you can select the model that dictates the permeability transition from saturated to unsaturated soil. Leave the model as the default (Simple). You can also change the permeability here. Leave the default value of 1e-7 m/s.

Click OK to close the dialog. The model definition is now complete. Save the model using the Save As option in the File menu. Choose a different name from the model that you created using Piezometric lines.

Compute Run the model using the Compute option in the Analysis menu. Because it is performing a Shear Strength Reduction analysis, the model will take several minutes to run.

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Once the model has finished computing (Compute dialog closes), select the Interpret option in the Analysis menu to view the results.

Interpret The Interpret program starts and reads the results of the analysis. You are now looking at the maximum shear strain for the critical strength reduction factor (1.25) for the second stage.

This is slightly lower than the SRF of 1.28 calculated for the model with Piezometric lines. If you click the tab for SRF: 1.26 you get a better picture of the critical failure surface as shown.

This looks basically the same as the failure surface in the model with piezo lines. If you want to look at stage data prior to the SSR analysis, select Stage Settings from the Data menu. Set the Reference Stage to Not Used, and the Visible Stage to Stage 1.

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Click OK. You will now see the maximum shear strain in Stage 1. Change the plot to Pore Pressure using the pull-down menu at the top. You can see the pore pressure in stage 1. Click the tab for Stage 2. It is clear how the pore pressure decreases as the boundary conditions change. If you still have the previous model open in Interpret (with the piezo lines), you can view them both simultaneously by selecting Tile Vertically from the Window menu. Click on the window showing the pore pressures in the piezo line model. Ensure you are looking at Stage 2. You can’t see the piezo line because it is the same colour as the contours. To change the piezo line colour, select Display Options from the View menu. Under Boundaries, change the Piezometric line colour to pink as shown.

Click Done.

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To facilitate comparison between the two models, we want the contour range to be the same. Select Contour Options from the View menu and select Custom Range. Set Min to -120 and Max to 480.

Click Done and the screen should look like this:

You will see the pore pressures are basically the same for the two models. The main difference is that the finite element groundwater model exhibits negative pore pressures (suction) above the water table. Note that the negative pore pressures have no effect on the slope stability, unless you specify an unsaturated shear strength parameter phi_b for the material. See the Phase2 help for more information.

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The other difference between the models is that the contours are a bit smoother for the finite element groundwater analysis. The results from this model are likely more accurate than the results from the model with piezo lines. In the piezo line model, we had to guess at the water table profile and the water table was then used to compute pore pressures. In the finite element groundwater model, pore pressures are calculated based on the boundary conditions, and the water table shows where the pore pressure is 0. This concludes the tutorial; you may now exit the Phase2 Interpret and Phase2 Model programs.

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Drawdown due to tunnel excavation In this tutorial, Phase2 is used to simulate tunnel excavation in a saturated soil. The tunnel is assumed to have a permeable liner so there is a drawdown in the water table as water drains into the tunnel. The model is based on a study presented by Shin et al. (2002). The complete model can be found in the Tutorial 27 Tunnel Drawdown.fez file located in the Examples > Tutorials folder in your Phase2 installation folder.

Topics covered •

Staged tunnel excavation

•

Groundwater drawdown

•

Permeable tunnel liner

•

User defined permeability function

•

3D tunnel simulation

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Model Start the Phase2 Model program.

Project Settings Open the Project Settings dialog from the Analysis menu and make sure the General tab is selected. Define the units as being “Metric, stress as kPa”. Click on the tab for Stages. Change the number of stages to 3.

Click on the tab for Groundwater. Set the Method to Finite Element Analysis. Leave all other options as default.

Click OK to close the Project Settings dialog.

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Geometry The problem consists of four soil layers and an excavation. Therefore an external boundary, three material boundaries, and an excavation boundary are required. Start by creating a rectangular external boundary. Select the Add External option in the Boundaries menu and enter the following coordinates: −100 , 0 100 , 0 100 , −50 −100 , −50 c

(to close the boundary)

Now we need to delineate the different material layers within the model. Go to the Boundaries menu and select Add Material. Enter the following points: −100 , −5 100 , −5 Hit Enter to finish entering points. All of the material layers are horizontal, so we will simply copy this boundary. Right click on the green material boundary and select Copy Boundary. Click on the point at (−100,−5). Enter −100 , −35 at the prompt and hit Enter. Repeat, entering −100 , −40 for the second point. The model should look like this:

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Now we will create the tunnel. From the Boundaries menu, select Add Excavation. Type i followed by Enter to create a circular boundary. In the resulting dialog, choose the option ‘Centre and Radius’. Set the radius to 2 m. Leave the Number of Segments as 40.

Click OK to close the dialog. Enter the coordinates 0 , −20 for the centre of the circle. Hit Enter. The model should now look like this:

Mesh Generate the finite element mesh by selecting Discretize and Mesh from the Mesh menu. The mesh will look like this:

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Boundary conditions By default, the entire external boundary is fixed. Since the top of this model represents the actual ground surface, we need to free the top surface. Go to the Displacements menu and select Free. Click on the ground surface and hit Enter. You will now see that the fixed boundary conditions have disappeared from the top boundary. We now need to re-establish the fixed boundary condition on the top corners. Right click on the top left corner and select Restrain X,Y. Repeat for the top right corner. Your model should now look like this:

Field Stress Because the top of the model represents the true ground surface, we want to use a gravity field stress. Go to the Loading menu and select Field Stress. For Field Stress Type select Gravity and click the check box for “Use actual ground surface”. Leave all other values as default.

Click OK to close the dialog.

Materials We now need to define the material properties and assign the correct materials to the correct parts of the model. Go to the Properties menu and select Define Materials. Change the name of Material 1 to Thames gravels. Enter the material parameters as shown.

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Click on the tab for Material 2, change the name to London clay and enter the following properties:

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Enter the following properties for materials 3 and 4.

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Click OK to close the dialog. To assign the materials to the model, select Properties → Assign Properties. Be sure you are looking at the first stage. By default, everything is set to Thames gravel material. Select London clay from the assign dialog and click in the second layer. Be sure to click inside the tunnel as well.

Now choose Lambeth Group clay and click in the third layer, and Lambeth Group sand and click in the fourth layer. The model should look like this:

Click on the Stage 2 tab near the bottom left of the window. Choose Excavate from the Assign menu and click inside the tunnel. Close the Assign dialog. The model will now look like this:

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Excavation and support In general, a tunnel must be excavated before structural support is added. Therefore, some deformation will occur before the support is installed. The amount of deformation depends on the distance of the tunnel face from the location of support installation. The tunnel face provides some support, so if the liner is installed close to the tunnel face, then not much deformation will have occurred. In essence, this is a threedimensional problem that we are trying to simulate in two dimensions. For this problem, let’s assume that we are installing the liner 2 m behind the face. To simulate the supporting effect of the nearby tunnel face, we will apply a load to the perimeter of the tunnel equal to some proportion of the in-situ stress. The amount of load required to correctly simulate the 3D effect of the tunnel face can be determined by following procedures outlined in Tutorial 24. In the third stage, we will install the liner and remove the load. Removing the load will simulate the advance of the tunnel face away from our two-dimensional slice. Ensure you are looking at Stage 2. Go to Loading → Distributed Loads → Add Uniform Load. Under Orientation, choose the option for Field Stress Vector. This will automatically work out the traction required to perfectly balance the in-situ stress. Now click the checkbox for Stage Load.

Click on the Stage Factors button. Through the type of analysis described in Tutorial 24, we can determine that a load of 0.16 times the in-situ stress will simulate the effective support of the tunnel face 2 m away. Therefore for Stage 2, set the Stage Factor to 0.16. For Stage 3, we assume that the tunnel face is far away so set the Stage Factor to 0.

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Click OK to close the dialog. Click OK to close the ‘Add Distrubted Load’ dialog. You will now be prompted to select a boundary on which to apply the load. Click somewhere above and to the left of the tunnel. Hold down the left mouse button and draw a window around the tunnel. Release the left mouse button and hit Enter to select the tunnel boundary. Zoom in using the middle mouse wheel, or click the Zoom Excavation button. The model for Stage 2 should now look like this:

You can see how the applied traction is not constant. It is calculated to balance the in-situ stress, which increases with depth. Click on the tab for Stage 3. Go to Support → Add Liner. Ensure ‘Liner Property’ is Liner 1 and ‘Install at stage’ is 3.

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Click OK and draw a window around the tunnel as you did when applying loads above. Hit Enter and your model should look like this:

To see the properties of the liner, right click on it and select Liner Properties.

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The default values are suitable so click OK to close the dialog.

Groundwater boundary conditions The water table for this site is 2.5 m below the ground surface. We will use groundwater boundary conditions to set this up. Go back to Stage 1. Zoom out to see the entire model using the mouse wheel or the Zoom All button. From the Groundwater menu, select Show Boundary Conditions. Choose Set Boundary Conditions from the Groundwater menu. For the BC Type, choose Total Head. Set the Total Head Value to −2.5 m.

Select all sections of the left and right vertical boundaries. Click Apply. The model will appear as shown:

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We will now simulate the effect of a permeable liner by setting the pressure at the surface of the tunnel to 0. Click on the tab for Stage 2. Zoom in on the tunnel. From the Set Boundary Conditions dialog, select BCType = Zero Pressure.

Draw a window around the tunnel as described above. Click the Apply button and then the Close button. The model should look like this:

Click on the tab for Stage 3 to ensure that the zero pressure boundary condition also exists in this stage.

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Hydraulic material properties From the Properties menu, choose Define Hydraulic. Ensure you are looking at the properties for Thames gravel. Here you can select the model that dictates the permeability transition from saturated to unsaturated soil. Leave the model as the default (Simple). You can also change the permeability here. Set the value to 1e-10 m/s.

ASIDE: Obviously, the permeability of gravel is much higher than we have specified. However, in this problem, we want to observe the drawdown of the water table due to the tunnel excavation. Drawdown will only occur if the recharge rate is low, i.e. water does not quickly enter the system to replace the water lost into the tunnel. If we set a permeability for the top layer higher than the underlying layer, then rapid recharge will occur and we will not see drawdown of the water table. Click on the tab for London clay. The base permeability for the London clay is 1e-10 m/s. The permeability decreases by two orders of magnitude between 50kPa and 100 kPa of suction. We can simulate this behaviour with a user-defined permeability model. For Model, click the New button. Set the Name to Clay model and fill in the chart as shown:

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Click OK to return to the Define Hydraulic Properties dialog. Click on the tab for Lambeth Group clay. Leave the model as Simple and set the permeability to 1e-10 m/s.

Click on the tab for Lambeth Group sand. Set the permeability to 1e-6 m/s as shown.

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Click OK to close the dialog. The model definition is now complete. Save the model using the Save As option in the File menu.

Compute Run the model using the Compute option in the Analysis menu. The model should take a couple of minutes to compute. Once the model has finished computing (Compute dialog closes), select the Interpret option in the Analysis menu to view the results.

Interpret The Interpret program starts and reads the results of the analysis. You are now looking at the Pressure Head in Stage 1.

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As expected, the water table (pink line) is at 2.5 m below the surface and the pressure increases monotonically with depth. Click on the tab for Stage 2.

Here you can see the obvious drawdown of the water table due to the drained boundary around the tunnel. Show the flow vectors by clicking on the Show Flow Vectors button in the toolbar. Zoom in on the tunnel and you can see how the fluid is flowing into the tunnel.

Turn off the Flow Vectors. Change the plot to show Total Displacement contours. Zoom out until you can see the ground surface. Click the button to Display Deformed Boundaries. Click the button to Display Yielded Elements. The plot should look like this:

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You can see some shear failure around the tunnel and at the ground surface. You can also see how there is some subsidence at the surface. To determine the exact value, go to Query → Add Material Query. Enter 0,0 for the query point. Hit Enter. In the resulting dialog, choose At Each Vertex and Show Queried Values.

Click OK. You will see that the displacement directly above the tunnel is about 8.8 cm. Click on the tab for Stage 3. You will see that there is little change in the displacement or failure pattern (there is actually a small amount of rebound since removing the load is equivalent to removing material inside the tunnel).

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The liner has successfully accommodated the load without any more failure. To evaluate the performance of the liner, go to Analysis → Show Values → Show Values. Check the box for Liners and choose Bending Moment from the pull-down menu.

Click OK. Zoom in on the tunnel to see the moments as shown.

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Finally, you can check the volume loss due to the tunnel excavation. The volume loss is the volume change due to surface subsidence divided by the volume of the excavation. Go to Analysis → Info Viewer. Scroll down to the heading for Stage 3. You can see the Volume Loss to Excavation is 35.5 %.

This concludes the tutorial; you may now exit the Phase2 Interpret and Phase2 Model programs.

References Shin, J.H., Addenbrooke, T.I. and Potts, D.M., 2002. A numerical study of the effect of groundwater movement on long-term tunnel behaviour. Géotechnique, 52 (6), 391-403.

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Development of a Stope in a Coal Mine This tutorial will model the development of a stope and access roads in a coal mine. The tutorial demonstrates the use of multiple materials and staging in Phase2, including specification of different in-situ stresses for each material layer. The complete model can be found in the Tutorial 28 Coal Mine Stope.fez file located in the Examples > Tutorials folder in your Phase2 installation folder.

Topics covered •

Staged excavation

•

Multiple materials

•

Custom field stresses

•

Locked-in horizontal stress

•

Advanced discretization

•

Copy boundary

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Model Start the Phase2 Model program by double-clicking on the Phase2 icon in your installation folder.

Project Settings For staged models, the first thing we must always do is to set the Number of Stages in the Project Settings dialog.

Select: Analysis → Project Settings With the General tab selected, set the Units to “Imperial, stress as ksf” as shown. Note that Phase2 remembers the most recently selected Units in Project Settings, and uses it as the default setting for all new documents.

Select the Stages tab. Change the Number of Stages to 3 as shown.

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Select OK to close the dialog.

Entering Boundaries We will enter the external boundary for the model.

Select: Boundaries → Add External Enter the following information in the command (prompt) line at the bottom right corner of the Phase2 Model window. Enter Enter Enter Enter Enter

vertex[t=table,i=circle,esc=cancel]: 0 0 vertex[...]: 2000 0 vertex[...]: 2000 597 vertex[...]: 0 597 vertex[...,c=close,esc=cancel]: c

Press F2 to Zoom All. We will now add the material boundaries, which will define the rock mass layers.

Select: Boundaries → Add Material Enter vertex [t=table,i=circle,esc=cancel]: 2000 400 Enter vertex [...]: 0 400 press Enter

Because the material boundaries in our model are all parallel, we can specify the other boundaries by copying the first boundary.

Select: Boundaries → Edit → Copy

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Click on the material boundary to select it and hit Enter. We are now prompted to select one of the vertices of the material boundary and specify its new location. Select the vertex with coordinates (2000, 400), then specify its new location as (2000, 247) and hit Enter. The new boundary is created. To specify the last material boundary, we will repeat the copy procedure. Right-click the mouse on the previously created material boundary and choose Copy Boundary from the resulting pop-up menu. Select the vertex at (2000, 247) and then enter the new location as (2000, 232). The model should now look like this:

We will now add stage boundaries to define the location of the stope and access roads within the coal seam.

Select: Boundaries → Add Stage Enter vertex [t=table,i=circle,esc=cancel]: 1330 232 Enter vertex [...]: 1330 247 press Enter

Select the stage boundary that was just created by right-clicking on it with the mouse and choosing Copy Boundary (you may need to zoom in to do this. Zoom in by spinning the wheel on your mouse). Select the vertex with coordinates (1330, 232). Next enter the location (1280, 232) to which it should be copied. These two boundaries delineate one of four access roads. We will generate three more access roads by copying the two boundaries we just created and placing them at the appropriate locations.

Select: Boundaries → Edit → Copy Select both stage boundaries and press Enter. Select vertex (1330, 232) and then enter its new location as (1250, 232). Repeat the procedure two more times, using new locations of (800, 232) and (720, 232). The model should look like this:

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This completes the definition of boundaries for this model.

Meshing For this model, we will initially use the default Mesh Setup parameters. Select the Discretize and Mesh shortcut. A single mouse click on this button automatically discretizes the boundaries and generates the mesh.

Select: Mesh → Discretize & Mesh The mesh is generated (see the image below) and the status bar will show the total number of elements and nodes in the mesh. You should get the number of nodes and elements indicated below. ELEMENTS = 676 NODES = 370

This mesh needs to be refined in the area of the pillars. To do so, we will use the Advanced Discretization option in the Mesh Setup dialog.

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Choose Mesh Setup from the Mesh menu. Click the Advanced button and select the Use Discretization Regions checkbox. To create a new discretization region select the Add button. The mouse cursor turns into a cross with which we will be able to draw our window of interest. Move the mouse to a location with coordinates close to (600, 320), press and hold the left mouse button, and start dragging the mouse to a second point at approximately (1400, 150). A window is drawn on the screen once the mouse begins to move. Release the mouse button once the mouse gets to the indicated coordinate. In the Mesh Setup dialog, change the Number of Nodes to 250 as shown:

Press the "Discretize" button followed by "Mesh" button. Click OK to close the dialog. Your mesh should look similar to the following.

Now, the mesh is refined and has more elements in the area of interest.

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Boundary Conditions Now we can set the boundary conditions. The portion of the external boundary representing the ground surface (0, 597 to 2000, 597) must be free to move in any direction. 1. Select the Free option in the Displacements menu. 2. Use the mouse to select the line segment defining the ground surface. 3. Right-click and select Done Selection. TIP: you can also right-click on a boundary to define its boundary conditions. The surface is now free, however, this process has also freed the vertices at the upper left and upper right corners of the model. Since these edges should be restrained, we have to make sure that these two corners are restrained. Let’s use the right-click shortcut to assign boundary conditions: 1. Right-click the mouse directly on the vertex at (0,597). From the popup menu select the Restrain X,Y option. 2. Right-click the mouse directly on the vertex at (2000,597). From the popup menu select the Restrain X,Y option. The displacement boundary conditions are now correctly applied.

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Define Material Properties We will now specify the properties of the different materials in the model.

Select: Properties → Define Materials With the first tab selected at the top of the Define Material Properties dialog, create a Sandstone material and enter the following properties:

Select the second, third and fourth tabs, respectively, and enter properties for a Siltsone, Coal and Shale as indicated in the next three screen captures. Select OK when you are finished.

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This completes the definition of material properties.

Field Stress Now define the in-situ stress field. 1. Select the Field Stress option in the Loading menu. 2. Change the Field Stress Type from Constant to Gravity (gravitational stress distribution throughout the model). 3. Select the Use actual ground surface checkbox. By using this option, the program will automatically determine the ground surface elevation above every finite element and define its vertical stress based on the weight of material overlying it.

4. We wish to specify a different horizontal field stress for each

material. Click on the “Advanced” button in the dialog. Tabs with the names of the materials in our model appear. This option enables us to further customize the in-situ stress field. Select the Apply Custom Field Stress checkbox.

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5. The default horizontal to vertical stress ratios of 1 indicate a hydrostatic initial stress state. For our example, we will change the ratios to 0.428 for the four materials in the model. So enter 0.428 for the two Stress Ratios for each material. Note that these values override the stress ratios of 1 shown in the main dialog. 6. Due to previous tectonic stress history, we will apply locked-in horizontal stresses for each layer of material. Use the following table to enter tectonic in-plane and out-of-plane horizontal stresses for the four materials. Material

Locked-in-horizontal stresses

Sandstone

120

Siltstone

90

Coal

50

Shale

70

The dialog for sandstone should appear as shown

We are finished defining the material properties. Select OK to close the Define Material Properties dialog.

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Assigning Properties Select: Properties → Assign Properties The Assign Properties dialog allows you to specify the stratigraphy of material layers in our model. In conjunction with the Stage Tabs at the bottom left of the view, it also allows us to assign the sequence in which openings are excavated and supports are installed. •

At the first stage we will only have the material stratigraphy.

•

At the second stage we will excavate the road gates on both sides of the stope.

•

At the third stage we will excavate the stope.

Assign Materials 1. Make sure the Stage 1 tab is selected (at the bottom left of the view). 2. Select the “Siltstone” button in the Assign dialog. (Notice that the material names you entered when you defined the four materials appear on the list). 3. Click the left mouse button in the second layer from the top. Notice that these elements are now filled with the colour representing the Siltstone material. Stage 1 – material assignment

4. Assign "Coal" and "Shale" to the third and fourth layers, respectively. For the coal layer, you will need to click inside each section of the layer since it is separated by stage boundaries. NOTE: Since we defined the “Sandstone” properties using the first tab in the Define Materials dialog, the “Sandstone” properties do not need to be assigned by the user. The properties of the first material in the Define Materials dialog, are always automatically assigned to all elements of the model.

5. Select the Stage 2 tab. Stage 2 – excavation of four access roads

6. Select the “Excavate” button in the Assign dialog. 7. Place the cursor in each of the four access roads, and left click to excavate them as shown (zoom in if necessary).

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8. Select the Stage 3 tab. 9. Place the cursor in the middle section of the coal layer and click the left mouse button, and the elements will disappear. 10. You are finished assigning materials. Now select each Stage Tab, starting at Stage 1, and verify that the excavation staging and material property assignment is correct. You have now completed the model building phase of the analysis; the model should appear as in the following figure for Stage 3.

Before you analyze your model, save it as coalstope.fez.

Select: File → Save

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Use the Save As dialog to save the file. You are now ready to run the analysis.

Select: Analysis → Compute The Phase2 Compute engine will perform the required finite element calculations. The analysis should take less than a minute. Once the computations are done, we will view the results in Interpret.

Interpret To view the results of the analysis:

Select: Analysis → Interpret This will start the Phase2 Interpret program.

Sigma 1 You are now viewing Sigma 1 (major principal) stress contours for Stage 1. You may want to zoom in on the excavations (use the middle mouse wheel or select Zoom Window and draw a window around the region of interest). Select the Stage 2 and 3 tabs and observe the changes in stress distribution. TIP: you can also use the Page Up / Page Down keys to change between stages. The figure below shows Sigma 1 for Stage 3. Note the high stress in the pillars on either side of the stope.

Toggle on the principal stress trajectories, using the button provided in the toolbar. Again select the stage tabs 1 to 3, and observe the stress flow around the excavation.

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If you want to compare results at different stages on the same screen, it can easily be done as follows. 1. Select Window→New Window TWICE, to create two new views of the model. 2. Select the Tile Vertically button in the toolbar, to tile the three views vertically. 3. Zoom in on the excavation in each view. 4. Select the Stage 1 tab in the left view, the Stage 2 tab in the middle view, and the Stage 3 tab in the right view. 5. Display the stress trajectories in each view. 6. Hide the legend in the right and middle views (use View → Legend Options, or right-click on a Legend and select Hide Legend). 7. Right-click in any view and select Contour Options. Click in each view, and select Auto-Range (all stages), to ensure that the same contour range is used for all stages. Close the Contour Options dialog. Your screen should appear as shown below.

Strength Factor Let’s look at the Strength Factor contours. 1. Display the Strength Factor in each view. 2. Turn OFF the stress trajectories and Toggle Yielded Elements ON, using the Display toolbar buttons, in each view.

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Observe the development of strength factor and yielding around the excavation. Note that the yielding is in the roof of the stope. Note: the strength factor is the rock strength divided by the rock stress. For a plastic analysis such as this, the strength factor is always greater than or equal to 1, but the strength factor contours can indicate regions that are close to failure (the lower the value, the closer to failure). See the help files for more information.

Let’s view the model full screen again. Maximize one of the views (it doesn’t matter which one). Re-display the legend if necessary (View → Legend Options), and select the Stage 3 tab, if necessary. Display the mesh by selecting the Elements button in the toolbar. Note that each Yielded Element symbol corresponds to a single finite element. As an optional step, use the arrow keys (up / down / left / right), to pan the model around the view. View the contours and yielded elements around the entire excavation. You can also pan by holding down the mouse wheel and moving the mouse. Toggle off the Mesh and select Zoom All.

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Strength Factor contours and yielded elements, Stage 3. Select the Stage tabs 1 to 3, and observe the strength factor contours on the whole model. Toggle off the Yielded Elements.

Total Displacement Plot contours of total displacement by selecting Total Displacement from the pull-down menu in the toolbar. Select the Stage 1 tab. The maximum total displacement for Stage 1 is virtually 0, as indicated in the status bar. Maximum Total Displacement = 4.81444e-012 ft

Select the Stage 2 tab. Maximum Total Displacement = 0.0846895 ft

Select the Stage 3 tab. Maximum Total Displacement = 1.41063 ft

You can see how the displacement increases as excavation proceeds. (You might see slightly different numbers in your model due to different meshing). As you can see from the displacement contours, the maximum total displacement at Stage 3 occurs at the center of the stope roof.

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Differential Results So far, we have always used a Reference Stage = 0. Differential results between any two stages can be viewed by setting the Reference Stage > 0 in the Stage Settings dialog. For example:

Select: Data → Stage Settings

Set the Reference Stage to 1 and select OK. Notice that the Stage Tabs now allow you to view results relative to the reference stage you just entered. If you change the contours back to Sigma 1, you will now see the stresses due to excavation only – the plots are relative to Stage 1, so the gravity stresses are subtracted out. The plot below shows Sigma 1 in Stage 3 relative to Stage 1. See the Phase2 Help system for more information about how to interpret differential results.

This concludes the tutorial.

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Application of Joint Networks This tutorial will demonstrate how to specify joint networks or discrete fracture networks (DFN) in Phase2 using the automatic joint network generator. It will also demonstrate a few techniques for analyzing the effects of the joints on model results. The model involves the stability analysis of a transportation tunnel near a slope in blocky rock. There are three different zones of blocky rock in the model. The finished Phase2 model of this tutorial can be found in the Tutorial 31 Application of Joint Networks.fez file, located in the Examples > Tutorials folder in your Phase2 installation folder. Topics Covered •

Adding joint networks to different model regions

•

Specifying joint end conditions

•

Interpreting joint movements

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Model If you have not already done so, run the Phase2 Model program by double-clicking on the Phase2 icon in your installation folder. Or from the Start menu, select Programs → Rocscience → Phase2 7.0 → Phase2. Open the file Tutorial 31 Joint Networks (initial).fez.

Figure 31-1: Basic geometry (startup model) for the tutorial example. As seen in Figure 31-1 above, the model consists of three material zones. (For the rest of the tutorial we will refer to these zones as Zones I, II and III as labeled on the figure.) In each of these zones we will be applying a joint network.

Adding a Voronoi Joint Network to Zone I We will apply a joint network to the zone at the upper right corner of the model.

Select: Boundaries → Joint Networks → Add Joint Network Notice that the mouse cursor immediately changes shape. Click the left mouse button at any location within Zone I. A hatched pattern appears in the selected zone. Hit Enter or right-click and select Done to complete zone selection. The Add Joint Network dialog (Figure 31-2) pops up. In the dialog, input data fields are grouped under headings. Labels (descriptions) of the input fields are shown on the left cells while the corresponding actual input fields are on the right.

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Figure 31-2: Input dialog for joint networks. Towards the bottom of the dialog, there are three checkboxes. We shall examine their roles in subsequent sections of this tutorial.

Automatic Preview of Joint Networks The third checkbox in the lower section of the joint network dialog is labeled Update Preview. A preview of the currently active joint network is displayed on the Phase2 model being developed, as soon as the joint network dialog appears. When the Update Preview checkbox is on (the default status) a joint network is immediately redrawn the moment any change is made to a parameter in the dialog. When it is off, the preview remains but will not be updated until the dialog is closed. Leave the Update Preview checkbox on.

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The network is shown in a rectangular window slightly larger than the selected zone. In addition to allowing you to see the geometry of the joint network you are specifying, the preview feature allows you to zoom into any part of a model for a closer look without leaving the joint network dialog. We will zoom into an area of the model around Zone I to take a closer look at the currently displayed joint network. You can use key strokes and shortcuts shown in the table below to zoom around Zone I. Action Zoom In Zoom Out Pan to the Left Pan to the Right Pan Up Pan Down Zoom All Zoom Excavation

Shortcut Key Home End Left arrow Right arrow Up arrow Down arrow F2 F6

Click anywhere on the Phase2 model. Use any combination of the Home and Arrow keys to zoom into Zone I. Press F2 when you are done to reset the view to the model extents.

Specifying Input for Voronoi Joint Network Under the General Settings heading in the dialog, click on the Joint Model input field (the cell on the right with the descriptor Parallel Deterministic). From the resulting dropdown list select the Voronoi joint model. Notice that the joint network displayed on the model immediately changes. (Depending on the speed of your computer the preview may not be as quick.) Change the Density (number of Voronoi cells per unit area) to 0.4. Once the network of Voronoi cells is displayed, click on the Regularity input field and change the option from Irregular to Medium Regular.

Changing Joint End Conditions By default, the ends of all joints in a network are assumed to be closed, i.e. no relative movement (joint sliding or opening) can occur at a joint end. Options exist in the joint network dialog for removing this constraint. In our example, we will specify that joint ends be open at the ground surface and at intersections with the excavation (tunnel). Click on the input data cell (cell with the default end condition setting of All Closed). Select Open at Boundary Contacts from the dropdown list. Once this option is selected, five new rows of data appear. Each row describes end conditions for joints that intersect a type of boundary. (There are five types of boundaries in Phase2.)

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In a model, the first time the Open at Boundary Contact option is selected, joint ends are specified as open at the ground surface and at excavation boundaries. Since this is what we are interested in, we will accept these defaults. Your dialog should now look like exactly like that shown on Figure 31-3 Select the OK button to close the dialog. This completes the specification of a joint network for Zone I.

Figure 31-3: Appearance of dialog after input of all parameters for Voronoi joint network.

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Adding a Network Comprising 2 Joint Sets to Zone II We shall next apply a joint network to Zone II of the model. This time the network will comprise two sets of parallel joints.

Select: Boundaries → Joint Networks → Add Joint Network Click the left mouse button anywhere within Zone II and hit Enter to complete selection. The joint networks dialog pops up with the details of the Voronoi network previously specified for Zone I. As mentioned earlier, there are three checkboxes towards the bottom of the joint networks dialog. We already looked at the function of the third (Update Preview) checkbox. We shall now examine the roles of the first two in the specification of our new joint network. The first checkbox with the label Use Multiple Joint Sets allows us to specify a network with more than one joint set. The second checkbox, with the description Auto Min/Max 3x Std. Dev., is on by default. It automatically calculates lower and upper bounds (relative minimum and relative maximum values) for the values generated from a statistical distribution based on the specified standard deviation. As its name suggests, the Auto Min/Max 3x Std. Dev. option calculates both relative minimum and relative maximum as three times the standard deviation. However there are exceptions. If a relative minimum or maximum calculated this way will result in an invalid bounding value (for example, if it leads to negative spacing) the minimum or maximum will be assigned a lower value that maintains a valid bound. Select the Use Multiple Joint Sets checkbox. A new panel appears on the left side of the dialog as soon as the option is turned on. The panel shows an automatically selected joint set – Joint Set 1.

Setting the Parameters for Joint Set 1 For Joint Set 1, change the joint model from Voronoi to Parallel Statistical. Leave the joint property field as Joint 1. Under the Orientation section of the dialog leave the Use Trace Plane option as the default of No. Enter an inclination angle of 45o. Next, we are going to specify a distribution for the spacing of the parallel joints in Set 1. Enter a mean spacing of 3 m. Leave the choice of distribution as Normal. Set the standard deviation to 0.8. Because the Auto Min/Max 3x Std. Dev. option is on, the relative minimum and relative maximum values for the distribution are automatically calculated. Both relative minimum and relative maximum are automatically set to a value of 2.4 (3 x 0.8).

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The next set of parameters we will input relate to the lengths of the joints. Change the Infinite Length option from Yes to No. Once you do this several new input data fields appear for entering parameters for the distribution of joint lengths. Specify the following values: • • •

Mean = 4 m Distribution = Lognormal, and Standard deviation = 1 m.

The relative minimum and maximum values are again set automatically. For persistence, specify the following distribution parameters: • • •

Mean = 0.7 Distribution = Normal, and Standard deviation = 0.1.

The relative minimum is automatically set to 0.3 (3 x 0.1). The relative maximum is however set to only 0.2. This is because a persistence of 1 is not allowed. Due to the fact that the joint end conditions currently displayed on the dialog correspond to the values of interest to us, we will simply accept them. This completes the definition of Joint Set 1.

Setting the Parameters for Joint Set 2 When we selected the Use Multiple Joint Sets option, two buttons labeled Add and Delete appeared beneath the left panel with joint sets information. These buttons are for adding sets to a network or deleting them. Click on the Add button. A second joint set labeled Joint Set 2 shows up on the left panel just below Joint Set 1. It is highlighted. This indicates that Joint Set 2 is active and its parameters can be specified or altered. Notice that there are checkmarks beside the joint set labels. A checkmark indicates that a joint set is actually drawn (or applied) in the selected material zone. If it is deselected, although the data (parameters) for the joint set remain, joints from the set are not applied to the material zone. We will leave the checkmarks as they are. For Joint Set 2 input the parameters shown in Table 31-1. Leave all other parameters as the defaults provided in the dialog. Click on the OK button to complete the definition of the joint network for Zone II.

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Table 31-1: Input parameters for Joint Set 2 (for Zone II) Parameter Value General Settings Joint Model Joint Property Orientation Use Trace Plane Inclination Spacing Mean Distribution Standard deviation Length Infinite Length Mean Distribution Standard deviation Persistence Mean Distribution Standard deviation

Parallel Statistical Joint 1 No -10o 2m Normal 0.5 No 2m Normal 1m 0.5 Normal 0.1

Adding a Cross-Jointed Network to Zone III We shall next apply a fracture network consisting of bedding planes with cross joints to Zone III.

Select: Boundaries → Joint Networks → Add Joint Network Click the left mouse button anywhere within Zone III and hit enter to complete selection. The joint network dialog pops up with the details of the network previously specified for Zone II. Specify the parameters indicated in Table 31-2 for the cross-jointed network. Leave any other parameters not specified as the defaults provided in the dialog. Click on the OK button to close the joint network dialog and apply the joint network to Zone III. This completes the specification of joint networks for our model.

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Table 31-2: Input parameters for Cross-Jointed Network (for Zone III) Parameter Value General Settings Joint Model Bedding Joint Property Cross Joint Property Orientation Use Trace Plane Bedding Inclination Cross Joint Inclination Bedding Spacing Mean Distribution Standard deviation Cross Joint Spacing Mean Distribution Standard deviation

Cross Jointed Joint 2 Joint 3 No -21o 69o 2m Normal 0.8 5m Normal 1.0

Meshing We will use the Discretize and Mesh option in Phase2 to automatically discretize the boundaries in our model and generate a mesh with one mouse click.

Select: Mesh → Discretize & Mesh While the mesh is being generated the mesh generation status window shown below opens up.

Figure 31-4: Status window indicating progress of mesh generation. Upon completion of the mesh generation process the status window disappears, and your model should appear like the image in Figure 31-5.

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Figure 31-5: Appearance of model at end of mesh generation.

Boundary Conditions In Figure 31-5 we see that the slope (ground) surface is not free; it has pinned (fixed, zero displacement) boundary conditions. This occurs because by default all nodes on the external boundary are pinned. To remove these conditions select the Free option in the Displacements menu.

Select: Displacements → Free The following message appears in the status window at the bottom right corner of the program: Select boundary segments to free [enter=done, esc=cancel]:

Use the mouse to select all the line segments that define the ground surface. When finished, right-click on the mouse and select Done Selection, or simply press Enter. The triangular pin symbols should now be gone from the slope surface. It may be necessary to re-apply the pinned boundary conditions to the uppermost nodes of the left and right external boundaries of the model. To do so:

Select: Displacements → Restrain X,Y

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1. Right-click the mouse. Select Pick by Boundary Nodes from the resulting popup menu. This will change the mode of application of boundary conditions from segments to nodes. 2. Select the topmost vertex of the left external boundary with coordinates (-50, 34.5) and the corresponding vertex on the right boundary with coordinates (70, 73.761). 3. Right-click and select Done Selection. Triangular pin symbols now appear at these vertices. Your final model should now look like Figure 31-6 below:

Figure 31-6: Final slope with tunnel model after specification of all appropriate boundary conditions.

Field Stress For this tutorial we will specify a gravitational field stress. This assumption is reasonable for slope problems or surface and near-surface excavations.

Select: Loading → Field Stress

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Figure 31-7: Dialog with field stress properties specified for the tutorial. Enter the parameters indicated in the field stress dialog (Figure 31-7) above. Select OK. (Notice that in this tutorial we assume horizontal stresses to be larger than the vertical stresses.)

Material and Joint Properties The material and joint strength and deformation properties used in this tutorial have already been provided in the starting file Tutorial 31 (initial).fez. If you would like to see the material properties assumed in the model you can do the following:

Select: Properties → Define Materials Click on the tabs named Zone I, Zone II and Zone III to see what the properties are. To review the joint properties:

Select: Properties → Define Joints Note that all the materials and joints are assigned plastic properties, i.e. they will fail if the stresses at a location exceed the material or joint strength.

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Figure 31-8: Representation of open ended joints with concentric circles.

Visual Representation of Joint End Conditions Because we specified joint ends to be open at the ground surface and at excavation boundaries, any such ends (nodes) are represented by a symbol of two concentric circles. As an example, we shall zoom in on the tunnel to look how the ends of joints that intersect the excavation boundary are represented.

Select: View → Zoom → Zoom Excavation Your view should be similar to that in Figure 31-8. The concentric circle symbols representing open joint ends are visible on the excavation boundary, wherever a joint intersects the excavation.

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Compute Before you analyze the model, you must save it under any name of your choice.

Select: File → Save As Enter your file name (e.g. Tutorial 31 – Final Model .fez). You are now ready to run the analysis.

Select: Analysis → Compute The Phase2 Compute engine will begin to run the analysis. Since we are using Plastic materials and joints, depending on the speed of your computer, the analysis may take some time. Once the computation is done, you can view the results in the Phase2 Interpret.

Interpret To view the results of the analysis:

Select: Analysis → Interpret This will start the Phase2 Interpret program. We will briefly look at aids for interpreting how networks of joints affect stresses, strains and displacements in the model.

Contours of Major Principal Stress – Sigma1 When Interpret first opens up it displays contours of major principal stress, Sigma 1. Go to Contour Options, choose Custom Range, change the Max value to 3 and the number of Intervals to 20, and select Done. You should see the following contours (Figure 31-9). The effects of the joints on the Sigma 1 contours are visible – the contours are jagged and not as smooth as those for models without joints.

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Figure 31-9: Sigma 1 contours. Notice the jagged nature of the contours.

Contours of Maximum Shear Strain We will next look at contours of maximum shear strain. On the Interpret toolbar

Click on Sigma 1: From the resulting list of quantities

Select: The contours reveal that very little shear strain occurs in the intact rock materials (most of the model is coloured in blue). Most of the shear displacements must be occurring along the joints. We shall zoom in on the excavation and examine the distribution of shear straining in that region.

Select: View → Zoom → Zoom Excavation

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Figure 31-10: Contours of maximum shear strain in vicinity of tunnel. In Figure 31-10 it can be seen that concentrations of shear strain occur at some joint ends and joint intersections with the tunnel.

Deformed Boundary The Phase2 Interpret program can display an exaggerated view of the deformed shapes of excavation, joint and external boundaries. This feature is very useful in understanding behaviour.

Select: View → Display Options In the resulting dialog select the Deform Boundaries checkbox. You can access the Deform Boundaries option quicker by simply clicking on the Display Deformed Boundaries toolbar button shown in the margin.

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Figure 31-11: Plot of (exaggerated) deformed boundaries. Notice the differential movements of some joint ends which intersect the tunnel. Gray lines that show how boundaries deform are drawn on the screen. From the deformed boundaries (shown on Figure 31-11), slip at joint ends that intersect the tunnel is visible. If we had left the joint end conditions as closed, these differential displacements would not have occurred. This concludes the tutorial; you may now exit the Phase2 Interpret and Phase2 Model programs.

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Slope Angle Optimization In this tutorial, Phase2 is used to examine the stability of an open pit mine. The Change Slope Angle editing option is used to help optimize the open pit design to make the slope as steep as possible while maintaining a suitable factor of safety. The complete models can be found in the Tutorial 32 Slope Angle 0.fez to Tutorial 32 Slope Angle 15.fez files located in the Examples > Tutorials folder in your Phase2 installation folder.

Topics covered •

Importing Slide files

•

Change slope angle editing option

•

Batch compute

•

Slope angle optimization

•

Shear strength reduction

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Problem An open pit mine is excavated through weak rock. The specification of the mine design states that the factor of safety must be greater than 1.25. The goal is to create as steep a slope as possible (to minimize costs) while maintaining a factor of safety greater than 1.25. This can be done in Phase2 by constructing a series of models with different slope angles and observing the factors of safety. By plotting the slope angle versus the factor of safety, we can obtain the optimum slope angle for the mine.

Model Start the Phase2 Model program. In this tutorial we will start by importing a model created in the slope stability program Slide (see http://www.rocscience.com/products/Slide.asp for more information on Slide). You do not need to have Slide installed to import this model. Go to File → Import → Import Slide. Open the Slide file Tutorial 32 Slope Angle.sli found in the Tutorials folder, which is a subfolder of the Examples folder in the Phase2 installation directory. TIP: You can also import a Slide file by simply choosing Open from the File menu. At the bottom of the Open dialog, for Files of type, select Slide File Format (*.sli) from the drop down menu. Once you have opened the Slide file, you will see the following dialog.

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This allows you to set various options for the finite element analysis. We want to perform a shear strength reduction (SSR) analysis to determine the factor of safety for slope stability so leave this option on. We also want Phase2 to automatically generate a finite element mesh and appropriate boundary conditions so leave these options on as well (Slide analyses do not require a finite element mesh so the mesh must be generated by Phase2). Click OK to accept the defaults. You will see a model that looks like this:

This is a model of an open pit mine in which there is a layer of sediments and a layer of weak weathered rock on top of the bedrock. To determine the overall angle of the slope, go to Tools → Add Tool → Dimension Angle. Click on the crest of the slope (near 122, 120) and then click on the toe (at 30, 40). Now move the mouse to the right to draw a horizontal line. Click the mouse button to finish drawing the angle and you should see that the overall slope is approximately 41°.

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Material properties The material properties used by Slide are imported along with the model. However, the finite element analysis performed by Phase2 requires some additional properties. Go to the Properties menu and select Define Materials. Be sure you are looking at the properties for Surficial sediments. Slide does not require Young’s modulus, Poisson’s ratio or Tensile strength to perform a slope stability analysis, so default values are assigned to all materials in Phase2. For the Surficial sediments, change the Young’s Modulus to 10000 kPa, the Poisson’s Ratio to 0.3 and the Tensile Strength to 0 as shown:

Now click on the tab for the Weathered Rock. Change the Poisson’s Ratio to 0.3 and the Tensile Strength to 5.

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Now for the Rock material, change the Young’s Modulus to 200000, the Poisson’s Ratio to 0.3 and the Tensile Strength to 40 kPa.

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Click OK to close the dialog. The model definition is now complete. Save the model using the Save As option in the File menu.

Compute Run the model using the Compute option in the Analysis menu. Because it is performing a Shear Strength Reduction analysis, the model will take several minutes to run. Once the model has finished computing (Compute dialog closes), select the Interpret option in the Analysis menu to view the results.

Interpret The Interpret program starts and reads the results of the analysis. You will now see the maximum shear strain contours for the critical strength reduction factor of 0.98.

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If you click the tab for SRF: 1 you get a better picture of the critical failure surface as shown.

The critical SRF is equal to the factor of safety. A value of 0.98 is clearly unacceptable. We will now proceed to modify the slope angle to produce a higher factor of safety.

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Changing slope angle Go back to the Phase2 Model program. First delete the Dimension Angle drawing tool by right clicking on it and selecting Delete Tool. Go to Boundaries → Edit → Change Slope Angle. You will be asked if you wish to reset the mesh.

Click OK and the current mesh will be deleted. You are now prompted to pick the starting vertex at the toe of the slope. Click on the point at 30 , 40. You are now asked to pick the vertex at the crest of the slope. Click on the point at the top of the slope (close to 122 , 120). Crest

Toe

After clicking on the top point, you are presented with the Change Slope dialog. The default action is to Project Horizontally. This is what we want since we have flat benches in our slope and we do not want them to be rotated (try clicking on the option for rotate and see what happens). We want to make the slope shallower so choose clockwise for the rotation. The default value of 5° is suitable for a first guess.

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Click OK to close the dialog. You will now see that the overall slope angle is shallower.

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Mesh Remesh the model by selecting Discretize and Mesh from the Mesh menu. The model will look like this:

Boundary conditions You can see that the boundary conditions on the slope face have reverted to the default (fixed in x and y direction). We must free these boundaries. Choose Free from the Displacements menu. Click on all of the segments of the slope face. Hit Enter to finish selecting segments. The model should now look like this:

Save the model using the Save As option in the File menu (give it a different name from the previous model).

Compute Run the model using the Compute option in the Analysis menu. Because it is performing a Shear Strength Reduction analysis, the model will take several minutes to run.

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Once the model has finished computing (Compute dialog closes), select the Interpret option in the Analysis menu to view the results.

Interpret You will see the maximum shear strain contours for the critical strength reduction factor of 1.08.

This is still less than the desired factor of safety (1.25), so we will continue to decrease the slope angle.

Slope optimization We now want to determine what slope angle will give a factor of safety of 1.25. The best way to do this is to run a few more examples and then plot a graph of factor of safety versus slope angle. We can then interpolate to get the desired slope angle. Go back to the Phase2 Model program. Repeat the above analysis and rotate the slope by another 5° clockwise. Then repeat again rotating by another 5°. This fourth model will have a slope that has been rotated 15° from the original. NOTE: in general, it is better to start with the maximum slope angle, and use the Change Slope Angle option to decrease the slope angle. If you do this, Phase2 will simply crop any material boundaries at the new slope face. If you start with a shallow slope and make it steeper, Phase2 will automatically extend any material boundaries which intersect the slope, however the results may not be as you intended, and you may have to perform additional editing to achieve the correct boundaries.

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TIP: you can create multiple Phase2 models and then run them all in batch mode. For example, after you have created your models, go the windows Start menu, and select All Programs → Rocscience → Phase2 → Utilities → Compute (or Compute (Fast Intel)). In the Compute dialog, you can open multiple files and then hit Compute. The program will then compute them all sequentially.

After you have finished running the models, open them in the Interpret program to determine the factors of safety. Use a spreadsheet program (e.g. Microsoft Excel) to plot Factor of Safety versus Change in Slope Angle. The plot should look like this:

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1.4

Factor of Safety

1.3 1.2 1.1 1 0.9 0

5

10

15

20

Change in Slope Angle

You can now interpolate to estimate the change in slope angle that will produce a factor of safety of 1.25 (shown with dashed lines in the above plot). It appears that a value of 13° should produce the desired results.

Final pit design In the Phase2 Model program, open the original model and rotate the slope by 13° clockwise following the steps outlined above. Measure the overall angle of the slope as you did for the first model (go to Tools → Add Tool → Dimension Angle and click on the crest, toe and a third point to the right of the toe). You will see that the overall angle is now 28°.

Run Compute and view the results in Interpret. You should see a factor of safety of 1.25 as expected.

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This concludes the tutorial; you may now exit the Phase2 Interpret and Phase2 Model programs.

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