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Example Application 15

Lined Tunnel Construction

in Saturated Ground

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Conditions and sequence for the lined tunnel construction

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Modeling Procedure

Step 1 Create a circular tunnel. The geometry is symmetric about the tunnel center,

permitting half the tunnel to be modeled. Assign the Mohr-Coulomb material

model and properties for the rock.

Step 2 Set boundary and initial stress conditions. The site is dewatered and initially

unsaturated. Calculate the initial equilibrium stress state. (Stage 1)

Step 3 Excavate the tunnel to produce closure corresponding to 30% relaxation before

the shotcrete liner is installed. (Stage 2)

Step 4 Install the shotcrete liner and advance the tunnel to produce 100% relaxation.

(Stage 3)

Step 5 Install the concrete liner with a 1 cm gap. (Stage 4)

Step 6 Stop dewatering and allow water level to return to original level. Water exerts

a pressure in the gap between the two liners. (Stage 5)

Step 7 Delete the shotcrete liner, simulating degrading of the shotcrete. (Stage 6)

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In the [Model options] dialog, select [GwFlow] and [Adjust tot. stress] configuration options, and [Include structural elements] user interface option.

The system of units are [SI: meter-kilgram-second].

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A project title is assigned, and a project file linedtunnel.prj is created and stored in a working directory.

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Step 1-1 In the [Geometry Builder] create a rectangular box with boundaries at Xmin = 0.0, Xmax = 120.0, Ymin = -80.0, Ymax = 65.0.

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Step 1-2 Select [Circle] and locate the tunnel at Xc = 0.0, Yc = 0.0, with Radius = 6.0 and Segments = 32. Press [OK] to generate the circle.

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Step 1-3 Select [Delete edges] and click on the circle boundary segments outside the model to delete edges.

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Step 1-4 Select [Add] and create a new line group named construction line.

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Step 1-5 Using [Add edges/[Box] draw a box around the tunnel. Add a box inside the tunnel and connect corners to form 4-sided blocks.

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Step 1-6 Add additional construction lines to divide the model into quadrilateral blocks, as shown. A horizontal line is positioned at y=60, which is

the location of the phreatic surface.

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Step 1-7 Select [Blocks] to confirm the model is divided into 14 quad blocks. It may be necessary to use the [Cleanup] stage to produce the model

filled completely with quad blocks. Press [OK] in the Result dialog, and then [OK] to exit the [Builder] tool.

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Step 1-8 The model can now be edited. Select [Edit] to enter the [Edit] tool.

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Step 1-9 Select [Boundary] and [Automatic boundary cond.] to place roller boundaries on the sides and fixed boundary on the base of the model.

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Step 1-10 Select [Mesh]/Block elements] and [Rotate block IJ] option. Rotate the blocks around the tunnel to remove attached boundaries

around the tunnel periphery. The rotated blocks axes should appear as shown, to remove attached edges around the tunnel.

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Step 1-11 Select [Boundaries]/[Mark boundaries] and click on the tunnel boundary segments.

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Step 1-12 Select [Mesh]/[Zone size manual] and click on the red boxes to increase the zone density around the tunnel, as shown.

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Step 1-13 Change the zone density in blocks farther away from the tunnel, by clicking on the red boxes and manually changing zoning. Select

[Adjust ratio] to increase the zone size by a geometric ratio of 1.1 in the i-direction, and 0.9 below the tunnel, 1.1 above the tunnel in

the j-direction.

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Step 1-14 Select [Material]/[Assign] and then [Create] to open the Define Material dialog. Create a material named ground as a Mohr-Coulomb

material and assign properties, as shown.

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Step 1-15 Press [Set all] to assign ground to all zones in the model. Press [OK] to exit the [Edit] tool.

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Step 1-16 Press [Execute] to send the commands to FLAC. Press [Save] to save the state as initial.sav.

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Step 2-1 Enter the [In Situ]/[Initial] tool and assign the initial stress state.

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Step 2-2 Select the [Settings]/[Gravity] tool and input the gravitational magnitude, as shown.

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Step 2-3 Select [Settings]/[GW] and turn off the groundwater flow calculation.

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Step 2-4 Select [Run]/[Solve] and [Solve initial equilibrium as elastic model] to calculate the initial equilibrium state. Save the state as

equilibrium.sav.

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Step 3-1 Enter the [Material]/[Assign] tool. Select [Region]/[range] and then [null] and click on the zone region inside the tunnel to null the tunnel

zones.

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Step 3-2 Enter the [Fish editor] pane and open the FISH function vert_closure.fis. Vertical closure will be calculated between gridpoints i=39, j=19

(tunnel crown) and i=75, j=19 (tunnel invert). Execute the function, and press [OK] to return to the [Record] pane.

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Step 3-3 Enter the [Utility]/[History] tool. Press [Fish->History] and select vert_closure.

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Step 3-4 Press [Gridpoints]/[X components]/[xdisp] and select the gridpoint at the tunnel mid-point. Press [Execute] to send these commands to

FLAC.

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Step 3-5 Enter the [In Situ]/[Apply] tool. Select [Relax] and drag the mouse along the tunnel periphery. Press [Assign] to open the Apply relax

dialog. Set number of steps = 20 and end factor = 0.7. Check [Generate Ground Reaction Table] and select history 1 to write to table 1.

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Step 3-6 Use the [Run]/[Solve] tool to calculate the state at 30% relaxation. The tractions (forces) around the tunnel are shown above.

Save the state as relax_30.sav.

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Step 4-1 Enter the [Structure]/[Liner] tool and select [Add]. Drag the mouse along the tunnel boundary to create shotcrete liner segments

attached to the grid.

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Step 4-2 Enter the [Structure]/[SEProp] tool and assign material properties representing the shotcrete liner material.

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Step 4-3 Enter the [Structure]/[Node] tool and [Fix]/[Rotation] for nodes 1 and 37.

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Step 4-4 Enter the [In Situ]/[Apply] tool and select [Relax]. Drag the mouse along the tunnel periphery and press [Assign]. Set the number of

steps = 20, and the end factor = 0.0. Check [Continue] and [Generate Ground Reaction Table] to continue the ground reaction curve.

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Step 4-5 Enter the [Settings]/[Mech] tool. Press [Large-strain] to continue the run in large strain mode.

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Step 4-6 Use the [Run]/[Solve] tool to calculate the equilibrium state at 100% relaxation of the tunnel with shotcrete support. Save the state as

relax_100.sav.

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Step 5-1 Enter the [Structure]/[Liner] tool and select [Add] to install the concrete liner. Press [Attach nodes:]/[to an interface] and check [Add

gap for grid] with distance = 0.01. Drag the mouse along the tunnel periphery. An Interface properties dialog opens. Enter the

properties for the liner/ground interface. (Normal and shear stiffness = 4 GPa/m, friction angle = 30o.)

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Step 5-2 Select [PropID] and change the liner property to L2. Press [Execute] to send the commands to FLAC.

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Step 5-3 Enter the [Structure]/[SEProp] tool and assign the concrete liner properties, as shown above, to property L2.

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Step 5-4 Enter the [Structure]/[Node] tool and [Fix]/[Rotation] and [X-velocity] to zero for nodes 38 and 74.

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Step 5-5 Use the [Run]/[Solve] tool to calculate the equilibrium state with the concrete liner installed. Save the state as concrete_liner.sav.

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Step 6-1 Enter the [Settings]/[Mech] tool and turn off the mechanical calculation. Enter the [Settings]/[GW] tool. Turn on the groundwater flow

calculation and set water density to 1000 kg/m3 and water bulk modulus to 10,000 Pa.

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Step 6-2 Enter the [Material]/[GWProp/ tool and set porosity = 0.3 and permeability = 1e-10.

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Step 6-3 Enter the [Fish editor] pane. Open ININVT.FIS. Set wth = 60, k0x = 0.5, k0z = 0.5 and syytab = 0. For this setting (syytab=0) only the pore

pressure distribution is calculated and total stress is adjusted from the CONFIG ats command.

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Step 6-4 Use the [Run]/[Solve] tool to calculate the steady state groundwater flow state. The pore pressure distribution is plotted above. Save

the state as water.sav.

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Step 7-1 Use the [settings]/[GW] tool to turn the groundwater flow calculation off and set water bulk modulus to zero. Use the [Settings]Mech]

tool to turn the mechanical calculation back on.

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Step 7-2 Enter the [In Situ]/[Apply] tool and select [Stress]/[pressure]. Drag the mouse along the tunnel periphery and the press [Assign]. When

the Apply value dialog opens, enter the pressure = 660000 Pa., and y-variation = -120000.

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Step 7-3 Enter the [Fish editor] pane and open FISH function apply_gap_press.fis. Execute the function and assign y_wtab = 60, tuncen_x = 0.0

and tuncen_y = 0.0. Press [OK] and return to the [Record] pane.

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Step 7-4 Enter the [In Situ]/[Initial] tool and press Clear? [Displmt&velocity].

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Step 7-5 Enter the [Utility/[History] tool. Press [Reset] and then reassign vert_closure and xdisp histories as done in Steps 3-3 and 3-4.

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Step 7-6 Calculate the equilibrium state using [Run]/[Solve]. Save the state as gap_pressure.sav.

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Step 8-1 Enter the [Structure]/[Segments] tool. Check [Delete] and delete the shotcrete structural element segments. Be careful to not delete

the concrete liner segments.

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Step 8-2 Use the [Run]/[Solve] tool to calculate the equilibrium state with the shotcrete deleted.

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Step 8-3 Save the state as delete_shotcrete.sav.