Tutorial 33 Two Tunnel Lining Design

7/28/2019 Tutorial 33 Two Tunnel Lining Design

1/37

Two Tunnel Lining Design 33-1

Phase2 v.8.0 Tutorial Manual

Two Tunnel Lining Design

In this tutorial,Phase2is used to design two reinforced concrete tunnel

liners in adjacent tunnels. This tutorial combines elements presented in

Tutorial 18 (3D tunnel simulation) and Tutorial 24 (Tunnel LiningDesign) and uses the Distributed load induced stress option to help

determine the tunnel deformation at support installation.

The final model can be found in the Tutorial 33 Two Tunnel Lining

Design 02.fez file. All tutorial files installed withPhase28.0 can be

accessed by selecting File > Recent Folders > Tutorials Folder from the

Phase2main menu.

Topics covered

Reinforced concrete liners

3D tunnel simulation

Adjacent excavations

Distributed loads induced stress option

Support capacity curves


2/37



Problem

Two circular tunnels of radius 7.6 m are to be constructed in Shale at a

depth of 50m. The in-situ stress field is assumed to be isotropic in all

three dimensions, and equivalent to the vertical stress due to gravity,

using a unit weight of 25kN/m3. The strength of the Shale can be

represented by the Generalized Hoek-Brown failure criterion with the

uniaxial compressive strength of the intact rock equal to 25 MPa, the GSI

equal to 30 and mi equal to 6. To compute the rock mass deformation

modulus, the modulus ratio (MR) is assumed to be 200. The support is to

be installed 2m from the tunnel face.

The goal of this tutorial is to design two adjacent reinforced concrete

linings with a factor of safety greater than 1.4.

To design a support system for a single tunnel (see tutorial 24), the

following three steps must be performed:

1. Determine the amount of tunnel wall deformation prior tosupport 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 amountin 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 priorto support installation. For this tutorial, well 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

Hoeks published papers area on the Rocscience website:


3/37



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.

Well start by building a single model that also combines step 2 with step1. Well 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).

In this tutorial well start by opening aPhase2file with predefined

geometry, material properties, boundary conditions, and meshing. The

tunnels and their respective liners will be installed sequentially, with the

second tunnel being installed after the first has been supported with its

liner.

Start thePhase2Model program.

Open Tutorial 33 boundaries.fez from File > Recent Folders >

Tutorials Folder.

Project Settings

Open the Project Settings dialog from theAnalysis menu and select

the Stages tab. Change the number of stages to 11 (see following figure).

Close the dialog by clicking OK.
http://www.rocscience.com/hoek/references/Published-Papers.htmhttp://www.rocscience.com/hoek/references/Published-Papers.htmhttp://www.rocscience.com/hoek/references/Published-Papers.htm


4/37



Excavation

The tunnel is to be excavated in the second stage so click on the Stage 2

tab at the bottom of the screen. Simply place the mouse pointer inside the

right excavation boundary and right-click the mouse. From the menu thatpops up, select theAssign Material > Excavate option.

The material inside the excavation should now be removed.

Adding an Internal Pressure to the Excavat ion

Now lets add a uniform distributed load to the tunnel in Stage 2. The

magnitude and direction of the load will be equal and opposite to the in-

situ 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 3 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


5/37



In the Add Distributed Load dialog, select the Induced stress

orientation option. Select the Stage Load checkbox, and select StageFactors to show the Stage Factors dialog.

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.


6/37



Select OK in both dialogs. You will now be asked to pick the boundary

segments on which the load will be applied.

NOTE: The Field stress vector orientation option could also have been

selected to equally oppose the in-situ stresses around the tunnel (see

tutorial 24) for this first tunnel excavation, as it would yield the same

results as the Induced stress distributed load in the case of a singleexcavation. The two load types differ in that an Induced stress load

opposes the stresses that exist along its surface from the preceding stage,

encompassing both the far field stresses and local stress field

perturbations. The Field stress vector load only opposes the defined far

field stresses, and it opposes the field stresses in the stage in which it is

applied. Thus, an Induced stress distributed load must be used to

oppose redistributed field stresses due to adjacent excavations, as in the

case of the second tunnel excavation later in this tutorial.

Select the excavation line segments to be loaded:

Sel ect boundar y segment s [ ent er=done, esc=cancel ] : use themouse 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 in Stage 2:


7/37



Now click through the stage tabs. You should see the internal pressure

factor reduce as the stage increases beyond Stage 2.

NOTE: the values displayed along the Induced stress distributed load

vectors are factors of the stress at each respective location along theexcavation boundary. Thus, the distributed load will directly oppose the

in-situ stresses around the unexcavated tunnel in Stage 1.

We are now ready to run the analysis.

Compute

Before you analyze your model, lets save this as a new file called

Tutorial 33.fez. (Make sure you select Save As and not Save, or you will

overwrite the initial file.)

Select: File Save As

Save the file as Tutorial 33.fez.

Select: Analysis Compute

ThePhase2Compute 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. Click on the Stage 2 tab. Notice that there is no variation of

stress and that the stress is equal to the 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.

Lets set the reference stage to Stage 1, so that all displacements are

measured relative to those in Stage 1 (which are essentially 0).

Select: Data Stage Settings


8/37



Drag the reference stage slider to Stage 1, and select the

Displacements Only option from the drop-down menu. Press OK.

Change the contours to plot Total Displacement using the pull down

menu in the toolbar. The model for Stage 2 will look like this:

You can see that there no displacement in the first or second stages.

Now click through the stages. Youll see an increase in deformation

around the tunnel as the internal pressure is reduced.


9/37



Step 1 Computing tunnel deformation before supportinstallation using the Vlachopoulos and Diederichsmethod

To compute the tunnel deformation at the point of support installation,

well 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 11 are used since there is zero internal pressure in

this stage.

Switch to the last stage, Stage 11. Look in the lower left corner of the

program window on the status bar. Youll see that the maximum

displacement for this stage is approximately 0.050m. This is the value ofmaximum wall displacement far from the tunnel face. The location of this

displacement is in the 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.

Youll see a number of crosses representing elements in the finite element

analysis that have failed. Zoom Out so that the entire extent of

failed points is visible (see below).


10/37


11/37



For our problem, Rp=10.5m, Rt=7.6m, X=2m, and umax=0.050m. The

Distance from tunnel face/tunnel radius = 2/7.6 = 0.26. The Plastic zone

radius/tunnel radius = 10.5/7.6 = 1.4. From the above plot this gives

Closure/max closure approximately equal to 0.45. Therefore the closure

equals (0.45)*(0.050) = 0.023m.

As computed above, the tunnel floor displaces 0.023m before the support

is installed.

Step 2 - Determining the internal pressure factor

The next step is to determine the internal pressure that yields a

displacement of 0.023m in the floor 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.


12/37



To determine the internal pressure that yields a 0.023m floor

displacement, well plot the displacement versus stage for a point on the

floor of the excavation.

Make sure you have Total Displacement selected as the data type.

Graphing Displacement in the Floor of the Excavation

To create the graph:

Select: GraphGraph Single Point vs. Stage

1. When asked to enter a vertex, type in the value 25,-7.6 for the

location and press Enter. This is a point on the floor of the

excavation.

2. You will see the Graph Query Data dialog.

3. Press the Plot button. The following figure shows the plotgenerated by the program. This is a plot of displacement versus

stage for a point on the floor of the tunnel:


13/37



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 untilthe displacement value on the right side of the plot is equal to 0.023m.

From this plot, you can see that in Stage 4, the wall displacement in the

floor of the tunnel is 0.023m. This represents an internal pressure factor

of 0.4 as was defined in the modeler for the induced stress vectordistributed load.


14/37



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 thePhase2data 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

approximately 0.4 yields the tunnel wall displacement computed above

for the point of support installation (0.023m).

NOTE: to obtain a load stage factor that would more precisely match the

closure at which to apply the liner (0.023m), stage factors of the applied

load could be iterated and recomputed. However, for the purpose of this

tutorial, an error of 2mm is acceptable.

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 thePhase2Model program by pressing

the Model button on the toolbar.


15/37



Model

You should now be in thePhase2Model program with the 11 stage model

you created above loaded into the program.

We will use this file and modify it to do the support design.

Project Settings


the Stages tab. Change the name of Stage 1 to Original In-situ. Change

the name of Stage 2 to Initial Stage. Change the name of Stage 4 to

Tunnel Relaxation. Change the name of Stage 11 to Support Installed.

The dialog should look like this:

Now delete all other stages except these three stages (i.e. stages

3,5,6,7,8,9,10). 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:


16/37



We chose Stage 4 from the old model because it represents the stage in

which the internal pressure in the tunnel yields the necessarydeformation 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 initial stage, should look like:


17/37



Note: you can use the LoadingDistributed LoadsEdit Distributed

Load option to select any of the loads on the boundary to verify that thestage factor is 0.4 for Stage 3.

Stage 4, 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 theReinforcement 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 I-beam. Click OK, and the I-beam reinforcement properties will be

automatically loaded into the Define Liner Properties dialog.


18/37



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.


19/37



Adding a Reinforced Concrete Liner to the Tunnel

We will now line the tunnel with the liner defined above. First make sure

that Stage 4, the Support Installed stage, is selected.

Select: Support Add Liner

1. You will see the Add Liner dialog. Make sure it looks like thefollowing image. Select OK.

2. Click and hold the left mouse button, and drag a selection windowwhich 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 theEnter key. The entire tunnel will now be lined, as indicated bythe thick blue line segments around the excavation boundary (see

below).


20/37



Click through the stages. Notice how the color of the liner changes from

light blue in Stages 1, 2, and 3 to dark blue in Stage 4. This indicates thatthe liner is being installed in Stage 4.


Compute

Before you analyze your model, lets save the file.

Select: File Save




Interpret



If any other files are loaded into the Interpret program, close them. Clickon the tab at the bottom of the program window associated with the file

and use the FileClose menu option to close the file.


on the toolbar.


21/37



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

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 that all of the liner

data points fall well within the 1.4 design factor of safety envelope,

meaning that they have a factor of safety of greater than 1.4. According to

this analysis, this liner should not experience cracking or crushing.


22/37



Refer to Tutorial 24 for an example of an inadequate liner, and the design

steps necessary for the selection of an adequate liner. Tutorial 24 alsoexplores some of the options available with support capacity plots.

Model

Now that the first tunnel liner has been successfully installed, the second

tunnel will now be excavated.

We must add a new set of 10 stages, to repeat the stage factor loading

procedure used to define the critical deformation for the first tunnel.

Project Settings


the Stages tab. Increase the Number of Stages to 14, and insure that the

stages are added after the Support Installed stage. The dialog should look

like this:


23/37



Close the dialog by clicking OK.

Excavation

The tunnel is to be excavated in the second stage so click on the Stage 5tab at the bottom of the screen. Place the mouse pointer inside the left

excavation boundary and right-click the mouse. From the menu that pops

up, select theAssign Material > Excavate option.

The material inside the excavation should now be removed.

Adding an Internal Pressure to the Excavat ion

Lets add a distributed load to the newly excavated tunnel in Stage 5,

with the same initial stage factor sequence as in the case of the first

tunnel. Insure that the Stage 5 tab is selected at the bottom of the screen.


24/37



Select: Loading Distributed Loads Add Uniform Load

Again, select the Induced stress load option, insure the Stage Load

checkbox is selected, and select the Stage Factors button.

In the Stage Factors dialog enter the factors shown in the following

image:

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 using the selection

window.


25/37



Click the Zoom Excavation button on the toolbar. You should see the

following in Stage 2:

Now click through the stage tabs. You should see the internal pressure

factor reduce as the stage increases beyond Stage 5.


Compute

Before you analyze your model, lets save this as a new file called

Tutorial 33 tunnel 2.fez. (Make sure you select Save As and not Save,

or you will overwrite the initial file.)

Select: File Save As

Save the file as Tutorial 33 tunnel 2.fez.




Interpret




26/37



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 the Original In-situ stage. Click on the Stage 5 tab, and compare the

contours to those on the Support Installed tab. Notice that there is no

variation of stress between the two stages. This means that the internal

pressure applied within the second tunnel on the left is equal and

opposite to the field stress and the model is behaving as if the secondtunnel on the left 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 5 will look like this:

Lets set the reference stage to the Support Installed stage, to view

deformation of the rock mass relative to after the installation of the liner

on the first tunnel on the right.

Select: Data Stage Settings


27/37



Drag the reference stage slider to the Support Installed stage, and

select the Displacements Only option from the drop-down menu. Press

OK.

Insure that the Stage 5 tab is selected. Model should look like this:

Step 1 Computing tunnel deformation before support

installation using the Vlachopoulos and Diederichsmethod

Switch to the last stage, Stage 14. Look in the lower left corner of the

program window on the status bar. Youll see that the maximum

displacement for this stage (relative to the Support Installed stage) is

again 0.050m. The location of this displacement is in the floor of the

excavation.


28/37



To determine the radius of the plastic zone, first turn on the display of

yielded elements using the Display Yielded Elements toolbar button.

Youll see a number of crosses representing elements in the finite element

analysis that have failed. Zoom Out so that the entire extent of

failed points is visible (see below).

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 well use the measuring tool.

Select: Tools Add Tool Measure

Pi ck t he l ocat i on t o measur e f r om[ esc=qui t ] : 0,0Pi ck the l ocat i on t o measur e to [ esc=qui t ] : use the mouse toextend the measuring line vertically until you get to the edge

of the yield zone, press the left mouse button.


29/37



As seen above, the radius of the plastic zone is again, approximately

10.5m.

Computing displacement prior to support installation using the Vlachopoulosand Diederichs Method

Since the maximum displacement and the plastic zone radius are

equivalent to those values for the first tunnel, we can also conclude that

the tunnel floor will again experience a displacement of 0.023m before the

support is installed, without repeating the Vlachopoulos and Diederichs

Method.

Step 2 - Determining the internal pressure factor

The next step is to determine the internal pressure that yields a

displacement of 0.023m in the floor 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.

To determine the internal pressure that yields a 0.023m floor

displacement, well plot the displacement versus stage for a point on the

floor of the excavation.

Make sure you have Total Displacement selected as the data type.


30/37



Graphing Displacement in the Floor of the Excavation

To create the graph:

Select: GraphGraph Single Point vs. Stage

1. When asked to enter a vertex, type in the value 0,-7.6 for thelocation and press Enter. This is a point on the floor of theexcavation.

2. You will see the Graph Query Data dialog.

3. Press the Plot button. The following figure shows the plotgenerated by the program. This is a plot of displacement versusstage for a point on the floor 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 0.023m.


31/37



From this plot, you can see that in Stage 7, the wall displacement in the

floor of the tunnel is 0.023m. This again represents an internal pressurefactor of 0.4 as was defined in the modeler for the induced stress vector

distributed load.

From Interpret, switch back to thePhase2Model program by pressing

the Model button on the toolbar.

Model

You should now be in thePhase2Model program with the 14 stage model

you created above loaded into the program.

We will use this file and modify it to do the support design.

Project Settings


the Stages tab. Change the name of Stage 5 to Initial Stage Tunnel 2.

Change the name of Stage 7 to Tunnel Relaxation Tunnel 2. Change the

name of Stage 14 to Support Installed Tunnel 2. The dialog should look

like this:


32/37



Now delete all other stages except these three stages, and the stages from

the installation of the first tunnel (i.e. delete 6,8,9,10,11,12,13). Afterdeleting these stages, the dialog should look like:

We chose Stage 7 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 clickingOK.

Make sure the Initial Stage Tunnel 2 stage tab is selected. Click the

Zoom Excavation button on the toolbar.

You should see the following:


33/37



Click through the stages. Stage 6, the initial stage for tunnel 2, should

look like:

Note: you can use the LoadingDistributed LoadsEdit Distributed

Load option to select any of the loads on the boundary to verify that thestage factor is 0.4 for Stage 3.

Stage 7, the Support Installed Tunnel 2 stage should have no load on

the boundary.


34/37



Adding a Reinforced Concrete Liner to the Tunnel

Since the liner properties have already been defined for the liner of the

first tunnel and this liner was adequate, we do not need to redefine liner

properties.

First make sure that Stage 7, the Support Installed Tunnel 2 stage, isselected.

Select: Support Add Liner

4. You will see the Add Liner dialog. Make sure it looks like thefollowing image. Select OK.

5. Click and hold the left mouse button, and drag a selection windowwhich encloses the entire excavation. Release the left mouse

button. Notice that all excavation line segments are selected.

6. Right-click the mouse and select Done Selection, or just press theEnter key. The entire tunnel will now be lined, as indicated by

the thick blue line segments around the excavation boundary (see

below).


35/37



Click through the stages. Notice how the color of the second liner changes

from light blue in Stages 1 6 to dark blue in Stage 7. This indicates thatthe liner is being installed in Stage 7.


Compute

Before you analyze your model, lets save the file.

Select: File Save




Interpret



If any other files are loaded into the Interpret program, close them. Clickon the tab at the bottom of the program window associated with the file

and use the FileClose menu option to close the file.


on the toolbar. Select Total Displacement as the data type. Your display

should look like this:


36/37



Support Capacity Diagrams

Lets confirm that our support capacity diagrams again show factors of

safety being greater than 1.4.

Select: Graph Support Capacity Plots

Use the spin control to increase the number of envelopes to 3. Deselect

the checkboxes for Stages 4 6, so that only the Support Installed

Tunnel 2 checkbox is selected. The dialog should look like:


37/37


Press OK.

The following plot is generated:

Note that the data points on these plots are from both the first and the

second liner. If you wish to view the data points of a particular liner, you

can right-click in the plot and select Export Data to Excel.

Alternatively, to view the support capacity diagrams for just the first

liner, simply select only the Support Installed stage checkbox in the

Support Capacity Plot dialog shown above.

Notice again that all of the liner data points fall well within the 1.4

design factor of safety envelope, meaning that they have a factor of safety

of greater than 1.4. According to this analysis, this liner should not

experience cracking or crushing.

This concludes the tutorial; you may now exit thePhase2Interpret and

Phase2Model programs.

Documents

Tutorial 33 Two Tunnel Lining Design