Tutorial_01_Quick_Start.pdf

Quick Start Tutorial 1-1
Examine2D v.8.0 Tutorial Manual
Quick Start Tutorial
Examine2D is a 2-dimensional plane strain indirect boundary element
program for the elastic stress analysis of underground excavations.
The program is interactive and easy to use, and is ideal for performing
quick parametric analysis, preliminary design and as a teaching tool for
numerical stress analysis in a geotechnical context.
This “quick start” tutorial will introduce you to the basic features of
Examine2D, and demonstrate how easily a model can be created and
analyzed.
The finished product of this tutorial can be found in the Tutorial 01
Quick Start.exa file. All tutorial files installed with Examine2D 8.0 can
be accessed by selecting File > Recent Folders > Tutorials Folder from the
Examine2D main menu.
Topics Covered in this Tutorial
• Project Settings
• Add Excavation Boundary
• Copy Boundary
• Stress Grid
• Move Boundary
• Real Time Contouring
• Query / Graph Query
• Strength Factor
• Displacements
• Stress Trajectories
• Failure Trajectories

Introduction
Before launching into an analysis with Examine2D, it is important to stop
and consider the developmental philosophy of the program, the
assumptions inherent in the analysis and the resultant limitations.
Examine2D is designed to be a quick and simple-to-use parametric
analysis tool for investigating the influence of geometry and in-situ stress
variability on the stress changes in rock due to excavations. The induced
stresses in the plane of the analysis can be viewed by means of stress
contour patterns in the region surrounding the excavations. As a tool for
interpreting the amount of deviatoric overstress (principal stress
difference) around openings, strength factor contours give a quantitative
measure of (strength)/(induced stress) according to a user defined failure
criterion for the rock mass.
Some important limitations of the program which should be considered
when interpreting Examine2D output are described below.
The assumption of plane strain means that the modeled excavation is of
infinite length normal to the plane section of the analysis. In practice, as
the out-of-plane excavation length becomes less than five times the
largest cross-sectional dimension, the stress changes calculated by
Examine2D begin to show some exaggeration since the real stress flow
around the ‘ends’ of the excavation is not taken into account. All of the
stress is ‘forced’ to flow around the excavation parallel to the analysis
plane. This exaggeration becomes more pronounced as the out-of-plane
length approaches the same magnitude as the in-plane dimensions. As
long as this effect is kept in mind, the analysis may still yield useful
insight into behavioral trends in these cases.
The elastic boundary element analysis used in Examine2D dictates that
the material being modeled is assumed to be:
• homogenous
• isotropic or transversely isotropic
• linearly elastic
Obviously, most of the rock masses which will be modeled possess none of
these properties. The degree to which the actual rock mass being modeled
deviates from these assumed properties should be kept in mind when
interpreting Examine2D output. Nevertheless, the induced stresses
calculated and displayed by Examine2D can usually prove useful, for
example, when optimizing excavation geometry and/or sequencing to
avoid overstress and undesirable de-stressing.

The displacements shown by Examine2D are meant to qualitatively
illustrate regional deformation trends only. The actual values of the
displacements calculated by Examine2D include only the elastic
displacements due to the excavation. This, in reality, may constitute a
very small component of the actual measured displacements in the field.
In weak broken rock, the actual magnitude of displacements may be
several orders of magnitude greater than the calculated elastic values. In
addition, the calculated displacements depend directly on the value of the
Deformation (Young's) Modulus for the rock mass, a value difficult to
estimate.
The practice of performing multiple analysis runs using a range of stress
and material properties to study the effect of each parameter is a prudent
one in all cases.
In short, Examine2D is a powerful but, nevertheless, limited tool. Like all
numerical models, it should be used to enhance and supplement, but
never to replace, common sense and good engineering judgement.
New File
Start the Examine2D program by double-clicking on the Examine2D icon
in your installation folder. Or from the Start menu, select Programs →
Rocscience → Examine2D 7.0 → Examine2D.
If the Examine2D application window is not already maximized,
maximize it now, so that the full screen is available for viewing the
model.
Note that when Examine2D is started, a new blank document is already
opened, allowing you to begin creating a model immediately.

Project Settings
The Project Settings option is used to configure the main analysis
parameters for your model (e.g. Units, Field Stress Type, Strength
Criterion etc). Select Project Settings from the toolbar or the Analysis
menu.
Select: Analysis → Project Settings
You will see the Project Settings dialog.
Under the General tab in Project Settings, make sure the following
options are selected:
• Units = Metric, stress as MPa
• Field Stress Type = Constant
• Elastic Properties = Isotropic
• Strength Criterion = Generalized Hoek-Brown, with the Use
GSI, mi, D checkbox selected
Select the Analysis tab in Project Settings. We will use the default
options, which should be as follows:
• Number of Boundary Elements = 100

• Boundary Element Type = Constant
• Analysis Type = Plane Strain
• Matrix Solver Type = Jacobi Bi-Conjugate Gradient
Note: see the Examine2D Help topics for information about these options.
Select the Project Summary tab in Project Settings.
Enter Examine2D Quick Start Tutorial as the Project Title.
TIPS:
• The Project Summary information can be displayed on printouts
of analysis results, by using the Page Setup option in the File
menu and defining a Header and/or Footer.
• You can specify the Author and Company in the Preferences
dialog in the File menu, so that this information always appears
by default in the Project Summary in Project Settings, for new
files.
Select OK to close the Project Settings dialog, and save the selections you
have made.

Add Excavation Boundary
Now let’s add an Excavation Boundary. Select Add Excavation from the
toolbar or the Boundaries menu.
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 or “c” for
close).
Enter vertex [t=table,i=circle,esc=cancel]: 10 10
Enter vertex [...]: 16 10
Enter vertex [...]: 16 20
Enter vertex [...]: a
You will see the Arc Options dialog. Use Arc Definition Method = 3
points on arc, and set the Number of Segments = 8. Select OK. Now you
can enter the second and third points defining the arc.
Enter second arc point [u=undo,esc=cancel]: 13 21
Enter third arc point [...]: 10 20
Enter vertex [...]: c
By entering “c” at the last prompt, the boundary is automatically closed
(i.e. the last vertex is joined to the first vertex). Note that arcs in
Examine2D are actually made up of a series of straight line segments.
The Arc option and other useful shortcuts are also available in the right-
click menu, while you are defining a boundary.

Stress Grid
By default, Examine2D automatically generates a Stress Grid, and
computes the boundary element analysis, as soon as the first excavation
is created.
The Stress Grid defines a grid of points at which stresses and other
results are computed. The contours are generated within the Stress Grid
from the results computed at the stress grid points. (The Stress Grid is
the square bounding box which contains the contours).
You should now see contours of Sigma 1 (major principal stress) as shown
in the following figure.
Figure 1: Sigma 1 contours around excavation.
NOTE:
• The automatic Stress Grid options are configured in the
Preferences dialog in the File menu. If you do NOT see the
Stress Grid and stress contours, then you can generate the
automatic Stress Grid by selecting the Auto Stress Grid option
from the toolbar or the StressGrid menu.
• Stress grids can also be manually drawn at any location using the
Add Stress Grid option.
• The stress contours which you are now viewing, are based on the
default Field Stress values.

Copy Boundary
Now we will create a second Excavation boundary. The second boundary
in this example will be identical to the first boundary, therefore, rather
than entering coordinates again, we will simply use the Copy Boundary
feature of Examine2D, to create a copy of the boundary.
We can use the following right-click shortcut for Copy Boundary:
1. Right click anywhere on the existing excavation boundary, and
select Copy Boundary from the popup menu.
2. We will define the position of the new boundary, by defining a
relative movement of 12 meters in the horizontal direction, and 0
meters in the vertical direction. A relative movement can be
defined by typing the “@” character in the prompt line, followed
by the relative x and y distance from the original object location.
3. Enter @12 0 in the prompt line:
Move from point [@=relative,esc=quit]: @12 0
You will immediately see a second excavation boundary, identical to the
first, located 12 meters to the right of the first boundary.
Figure 2: Second excavation created using Copy Boundary.

Auto Stress Grid
Notice that the Stress Grid is NOT automatically re-generated, when you
add a new boundary. Therefore, let’s re-generate the Auto Stress Grid, so
that the two excavations are at the center of the contours.
Select: StressGrid → Auto Stress Grid
You will see the Grid Spacing dialog.
We will use the default spacing of 40 x 40, so just select OK in the dialog.
The Stress Grid and stress contours will be re-generated, and your screen
should appear as follows.
Figure 3: Stress grid re-generated using Auto Stress Grid.

Field Stress
Now let’s enter the in situ stress values for this example. The Field Stress
Type is Constant, which means that the in situ stress is assumed to be
constant (i.e. does not vary with depth or location in the model).
Enter the following values in the Sidebar at the right of the screen:
• Sigma 1 = 5
• Sigma 3 = 2.5
• Sigma Z = 3.75
• Angle = 90
NOTE: Sigma 1 and Sigma 3 are the IN PLANE major and minor
principal stress. Sigma Z is the OUT OF PLANE principal stress. The
Angle defines the orientation of Sigma 1 with respect to the horizontal
direction. Therefore, the values we have entered define a Constant in situ
stress with a vertical stress which is double the horizontal stress. The
relative magnitude and orientation of the Field Stress is indicated by the
Stress Block icon, displayed in the upper right corner of the screen.
Figure 4: Stress contours for new Field Stress input.
NOTE: the stress contours are automatically re-computed as you entered
the new Field Stress values. In general, Examine2D automatically re-
computes the analysis whenever input data is changed, so that the
displayed contours always correspond to the current input data.

Material Properties
Now let’s enter the elastic and strength properties for the rock mass.
Enter the following Elastic parameters in the Sidebar.
• Em (rock mass Young’s modulus) = 10000
• Poisson’s Ratio = 0.2
Enter the following Strength parameters in the Sidebar.
• Intact Compressive Strength = 80
• GSI = 50
• mi = 17
• D = 0
Notice that the stress contours did NOT change (noticeably) when you
entered the new elastic and strength parameters.
• The strength parameters have NO effect whatsoever on the
calculated stresses or displacements in Examine2D. This is
because the Examine2D analysis is elastic, and material failure
cannot occur. The strength parameters are ONLY used to
calculate the Strength Factor contours (i.e. degree of overstress,
based on the elastic stress analysis).
• Young’s Modulus also has no effect on the elastic stress
distribution (for an isotropic material).
• Poisson’s Ratio does affect the elastic stress distribution, however
the effect is small for this example.
Estimating Input Parameters
For the Generalized Hoek-Brown criterion (GSI, mi, D) option, if you
select the “Pick” buttons beside the strength parameter edit boxes,
this will take you to a chart or table, which allows you to estimate values
for these parameters, according to rock type, rock structure etc.
This is left as an optional exercise to experiment with (if you make any
changes in the dialogs, make sure the above strength parameters are
entered in the Sidebar before proceeding with this tutorial).

Strength Factor
Now let’s view the Strength Factor contours for this model.
Select Strength Factor from the drop-list in the toolbar. You should see
the following contours:
Figure 5: Strength factor contours.
As mentioned in the previous section, the Strength Factor contours
represent the ratio of the material strength, to the induced stress.
If the Strength Factor in Examine2D is LESS THAN ONE, this indicates
that the material would fail, under the given stress conditions. As you can
see from the Strength Factor contours and the Legend, a region of failed
material exists between the two excavations; therefore the excavation
would be unstable, without support or modifications to the geometry.

Real Time Stress Analysis
Now we will demonstrate a unique feature of Examine2D – the ability to
modify the excavation geometry, and view the updated stress analysis
contours, in real time, as you edit the boundaries. Do the following:
1. Left click the mouse on either excavation (just a single click), so
that the excavation boundary is highlighted by a dotted line.
2. Now if you hover the cursor over the excavation boundary, you
will see the four-way arrow icon, which indicates that you can
move the boundary with the mouse. Click and drag the
excavation, and you will see that the analysis contours (in this
case Strength Factor) are immediately updated, in real time, as
you move the boundary. This capability is referred to as real
time contouring or real time stress analysis in Examine2D.
Note: you cannot allow excavation boundaries to intersect or overlap. If
you do this, you will see an error message when you release the mouse
button.
Select Undo from the toolbar or the Edit menu, to undo the move and
place the excavation back in its previous location.
Interactive Arrow Key Move
A useful alternative method of moving the excavation boundaries, is by
pressing the arrow keys, after selecting a boundary. This allows you to
move the boundaries in controlled increments, in the horizontal or
vertical directions. For example:
1. Left click the mouse on either excavation so that the excavation
boundary is highlighted by a dotted line.
2. Now press the arrow keys (left, right, up or down), to move the
excavation boundary. The contours are updated each time you
press an arrow key.
3. Type the letter m followed by Enter in the prompt line. You will
see the Move Increment dialog. This allows you to choose the
move increment used each time you press an arrow key (the
default is 1). Enter a value of 0.2 in the dialog and select OK.
4. Continue to press the arrow keys, and you will see that the
excavation boundary now moves in smaller increments (0.2
meters) for each arrow key press. If you press and hold an arrow
key, the excavation will move continuously, and the contours will
be updated in real time.
Select Undo again, to undo the arrow key move, and place the excavation
in its previous location.

Query
The Query capability of Examine2D allows you to obtain analysis results
along any user-defined line or polyline (e.g. plot the stress along
excavation boundaries).
There are two options for creating queries:
• Add Material Query – allows you to define a Query anywhere in
the model.
• Query Boundary – allows you to automatically create a query
exactly on a boundary.
Let’s first demonstrate Query Boundary. You can use the following right-
click shortcut for Query Boundary:
1. Right click anywhere on either excavation boundary, and select
Query Boundary from the popup menu.
2. The Query will be immediately created on the boundary, as you
will see from the bars displayed along the boundary, which
represent the relative magnitude of the data value (in this case
Strength Factor), on each boundary element.
3. Press F6 as a shortcut to Zoom Excavation, and your screen
should look as follows.
Figure 6: Query created with Query Boundary.

The data which is generated by a Query can be:
• displayed directly on the model
• graphed
• exported to Excel or the clipboard
Let’s first display the query data directly on the model. Right click on the
boundary and select Display Options from the popup menu. You will see
the Display Options dialog, with the Query options tab selected. Select
the Values checkbox and the Draw on Opposite Side checkbox, change
the Size of Largest Value to 20 mm (on screen), and select OK. The
display should look as follows.
Figure 7: Query values displayed on boundary.
The value of the data on the boundary (strength factor) is displayed
directly on each boundary element.
The Query Data can also be graphed. Right click on the boundary and
select Graph Data from the popup menu. A graph of the data will be
immediately generated. Right click on the graph and select Markers from
the popup menu. This will display a marker at the location of each
boundary element along the query.

Figure 8: Graph of query data.
NOTE:
• the distance axis of the graph represents the distance along the
query.
• the starting point of the graph corresponds to a small circular red
dot marker which you will see displayed on the query.
• the data is always generated in a COUNTER-CLOCKWISE
DIRECTION along the boundary, from the starting point.
Select the Tile Vertically option from the toolbar, to tile the Graph and
Excavation views. In the Excavation View, notice the circular red dot
marker on the Query which indicates the starting point of the query.
TIP: a useful property of the query graphs, is that you can click the mouse
at any point on the graph, and the corresponding query location on the
model will be highlighted (i.e. the bar representing the data magnitude at
that location will be highlighted).
Let’s demonstrate this.
1. In the Graph View, double-click the mouse at any location along
the query graph.
2. In the Excavation View, notice that the corresponding bar on the
query is highlighted (i.e. filled with a solid pink/magenta colour).

3. Click at different points along the graph, and notice the
corresponding highlighted location on the query. NOTE: you may
have to move or hide the contour legend, in order to see the entire
excavation.
When you have finished experimenting with this option, close the Graph
view and maximize the Excavation View.
Figure 9: Tiled view of graph and excavations, selected data highlighted on query.
Let’s reset the default Display Options.
• Right-click the mouse anywhere in the view and select Display
Options from the popup menu.
• Select the Defaults button in Display Options, choose Restore
original program defaults in the dialog which appears and
select OK. Select OK to close the Display Options dialog.
NOTE: queries can also be created at any location in the model with the
Add Material Query option. This is left as an optional exercise to
experiment with after completing this tutorial.

Displacements
Now let’s view Displacements for this model.
Select Total Displacement from the drop-list in the toolbar. You should
see the following contours.
Figure 10: Displacement contours near excavations.
Notice that the Query on the boundary now indicates the values of Total
Displacement along the boundary.
You can also view Deformation Vectors and Deformed Boundaries.
These options are available in the Display Options dialog, but are also
available in the toolbar.
• Select the Deformation Vectors toolbar button. The
Deformation Vectors indicate the direction and the relative
magnitude of the elastic displacements.
• Select the Deformed Boundaries toolbar button. This plots the
deformed boundary shape, magnified by a default factor. The
value of this factor can be changed in the Display Options dialog,
with the Scale Factor option, to increase or decrease the apparent
deformation of the boundaries.

Figure 11: Deformation vectors and deformed boundaries displayed.
Turn off the display of Deformation Vectors and Deformed Boundaries, by
re-selecting the toolbar buttons for each option.
It is important to remember that the Displacements calculated by
Examine2D are elastic displacements only, which in reality may
represent only a very small component of the actual displacements
occurring around the excavations. However, the elastic displacements can
still be a useful indicator of the general deformation trends.

Stress Trajectories
You can also display Stress Trajectories on the model, which indicate
the direction and relative magnitude of the in-plane major and minor
principal stresses.
Stress Trajectories is available in the Display Options dialog, but is also
available in the toolbar.
• Select the Stress Trajectories button in the toolbar.
• Change the contour data to Sigma 1.
The screen should look as follows.
Figure 12: Stress trajectories and Sigma 1 contours.
Turn off the Stress Trajectories by re-selecting the Stress Trajectories
toolbar button.

Failure Trajectories
You can also display Failure Trajectories on the model. Failure
trajectories are displayed at grid points where the induced elastic stresses
exceed the strength envelope of the material, as defined by your strength
criterion parameters.
To display Failure Trajectories, select the Failure Trajectories
checkbox under the General tab of the Display Options dialog.
Figure 13: Failure trajectories and Strength Factor contours.
The trajectories are displayed at each grid point where overstress has
occurred, and indicate the potential failure mode of the material (shear or
tension). Shear failure is indicated by two intersecting lines (an “X”) and
tensile failure is indicated by a single line.
Notice the region of overstress between the two caverns. This can be seen
from the strength factor contours (strength factor < 1) and the failure
trajectories (shear failure “X” symbols).
Keep in mind that, because the Examine2D analysis is elastic, “failure”
does not actually occur in the material. The strength factor contours and
failure trajectories indicate where failure would occur, if a plasticity
analysis were carried out. The elastic stresses can exceed the actual
material strength. If elastic overstress occurs, then the true stress and
failure distribution can only be determined from a plasticity analysis.

Let’s increase the region of overstress, by decreasing the strength
parameters. In the sidebar, gradually decrease the Hoek-Brown
parameters (GSI, intact strength, mi) and observe the expanding region
of failure between the two caverns. For example, in Figure 14, the
strength parameters have been lowered to GSI = 30, intact strength = 50,
mi = 10. Notice the expanded region of failure around the caverns.
NOTE: in Figure 14, the number of grid points within the stress grid has
been increased to 75 x 75. Increasing the grid point density results in
smoother contours, and a greater number of visible failure trajectories.
You can change the grid spacing by simply re-selecting Auto Grid and
entering the new spacing, or by using the Modify Grid Spacing option.
Figure 14: Failure trajectories and Strength Factor contours with decreased strength
parameters and increased number of grid points.
That concludes this Quick Start Tutorial. For further information about
program options, see the Examine2D help topics.

Tutorial_01_Quick_Start.pdf

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