# Supported Tunnel

Problem Statement

Note

To view this project in 3DEC, use the menu command . Choose “3DEC/ ExampleApplications/ Supported_tunnel” and select “Supported_tunnel.prj” to load. The main data files used are shown at the end of this example. All data files are found in the project.

Problem Description

This example shows how to create a simple supported tunnel in fractured rock. The joints are simulated using the Discrete Fracture Network (DFN) logic, and the tunnel is supported using hybrid bolts.

3DEC Model

**Model Geometry**

The 3DEC model is shown in Figure 1. The model is built by first creating a 20x10x20 m brick and then making cuts to define the region of interest in the center. Three cuts are also made in the y direction to define the stages of tunnel excavation.

The tunnel is created by importing a dxf and using the command `block cut geometry`

.

A DFN is generated with a power-law size distribution with an exponent of 3. The minimum and maximum fracture sizes are 0.5 m and 20 m respectively.

Tetrahedral zones are generated with an edge length of 0.25 m in the region of interest and 0.5 m outside of that.

**Properties**

The zones are assigned the Mohr-Coulomb material model with the following properties:

Friction, \(\phi\) = 30° Tension, T = 0

Model Solving

**Initial State**

All boundaries were fixed and the following initial compressive stress was applied:

\(\sigma_{xx}\) = 40 MPa \(\sigma_{yy}\) = 30 MPa \(\sigma_{zz}\) = 10 MPa

The model was then solved to initial equilibrium.

**Excavation and Support**

The first two meters of the tunnel are excavated and the model is solved. Hybrid bolts are then added with a spacing of approximately 0.5 m the bolts in the side walls were assigned a length of 2 m, and the bolts in the roof had a length of 4 m. No bolts were installed in the floor. A total of 11 bolts were used for each round of excavation (see Figure 2).

Dowel segments are automatically generated where each bolt crosses a joint. The dowel length is set to 5 cm.

After installation of the bolts, another 2 m of tunnel is excavated and the model is solved. This is repeated three more times to excavate and support the entire 10 m length of the tunnel.

Results and Discussion

The 3DEC simulation yields displacement as shown in Figure 3. Figure 4 shows the axial forces in the hybrid bolts and Figure 5 shows the shear forces in the dowels. The support is successful at stabilizing the tunnel and the model reached equilibrium after each stage of excavation.

Data Files

**tunnel-1.dat**

```
model new
model random 10000
model large-strain on
model domain extent -20 20 -20 20 -20 20
block tolerance 1e-3
block create brick -10 10 -5 5 -10 10
; define region of interest
; construction joints have id of 99
block cut joint-set origin 0 0 -5 joint-id 99
block cut joint-set origin 0 0 5 joint-id 99
block cut joint-set dip 90 dip-dir 90 origin 5 0 0 joint-id 99
block cut joint-set dip 90 dip-dir 90 origin -5 0 0 joint-id 99
geometry import 'tunnel.dxf'
block cut geometry 'tunnel' joint-id 99
block group 'tunnel' range geometry-space 'tunnel' count odd
; define excavation rounds
block cut joint-set dip 90 origin 0 -3 0 spacing 2 joint-id 99
block join
; add fractures in region of interest
block group 'center' slot 'construction' range pos-x -5 5 pos-z -5 5
block hide range group 'center' not
fracture template create "dfn-template" size power-law 3 size-limits 0.5 20
fracture generate dfn "dfn1" template "dfn-template" fracture-count 30000
block cut dfn name "dfn1"
; generate zones - smaller in region of interest
block zone generate edgelength 0.25
block hide off
block zone generate edgelength 0.5
;; new zoning logic
;block hide off
;block zone size edgelength 0.25 range group 'center'
;block zone size edgelength 0.5 range group 'center' not
;block zone gcm2 min-edge 0.25 max-edge 0.5
==================================================
block zone cmodel assign mohr-coulomb
block zone prop dens 2500 young 1e9 poiss 0.25
block zone prop cohesion 1e7 friction 35 tension 1e6
; make construction joints elastic
block contact jmodel assign elastic
block contact prop stiff-norm 1e11 stiff-shear 1e11
; make joints mohr-coulomb
block contact jmodel assign mohr range dfn-3dec 'dfn1'
block contact prop stiff-norm 1e10 stiff-shear 1e10 friction 30 ...
range dfn-3dec 'dfn1'
; default contact props
block contact material-table default prop stiff-norm 1e10 ...
stiff-shear 1e10 friction 30
model save 'zoned'
```

**tunnel-2.dat**

```
model rest 'zoned'
; initial state
block insitu stress -40e6 -30e6 -10e6 0 0 0
; boundary conditions
block gridpoint apply vel 0 0 0 range pos-x -10
block gridpoint apply vel 0 0 0 range pos-x 10
block gridpoint apply vel 0 0 0 range pos-z -10
block gridpoint apply vel 0 0 0 range pos-z 10
block gridpoint apply vel-y 0 range pos-y -5
block gridpoint apply vel-y 0 range pos-y 5
model solve convergence 1
model save 'initial'
```

**tunnel-exc.dat**

```
model restore 'initial'
block gridpoint ini dis 0 0 0
block excavate range group 'tunnel' pos-y -5 -3
model solve
model save 'exc-1'
==============================================
fish def add_cables(ypos)
; left side
command
sel hybrid create by-line (-1,[ypos],-0.5) (-3,[ypos],-0.5) ...
prop 1 segments 10 dowel-length 0.05
sel hybrid create by-line (-1,[ypos],0) (-3,[ypos],0) ...
prop 1 segments 10 dowel-length 0.05
sel hybrid create by-line (-1,[ypos],0.5) (-3,[ypos],0.5) ...
prop 1 segments 10 dowel-length 0.05
end_command
; right side
command
sel hybrid create by-line (1,[ypos],-0.5) (3,[ypos],-0.5) ...
prop 1 segments 10 dowel-length 0.05
sel hybrid create by-line (1,[ypos],0) (3,[ypos],0) ...
prop 1 segments 10 dowel-length 0.05
sel hybrid create by-line (1,[ypos],0.5) (3,[ypos],0.5) ...
prop 1 segments 10 dowel-length 0.05
end_command
; top
loop i (1,5)
local angle = math.pi/6.0*float(i)
p1x = math.cos(angle)
p1z = 1.0 + math.sin(angle)
p2x = 4.0*math.cos(angle)
p2z = 1.0+4.0*math.sin(angle)
command
sel hybrid create by-line [(p1x,ypos,p1z)] [(p2x,ypos,p2z)] ...
prop 1 segments 10 dowel-length 0.05
end_command
end_loop
end
[add_cables(-4)]
sel hybrid prop 1 cross-sectional-area 181e-6 young 98.6e11 yield-tension 5e6 ...
grout-stiffness 1.12e9 grout-cohesion 1.75e9
; dowel properties
sel hybrid prop 1 dowel-stiffness 2e10 dowel-yield 5e5 dowel-strainlimit 0.1
block excavate range group 'tunnel' pos-y -3 -1
model solve
model save 'exc-2'
=======================================
[add_cables(-2)]
block excavate range group 'tunnel' pos-y -1 1
model solve elastic
model save 'exc-3'
=======================================
[add_cables(0)]
block excavate range group 'tunnel' pos-y 1 3
model solve
model save 'exc-4'
=======================================
[add_cables(2)]
block excavate range group 'tunnel' pos-y 3 5
model solve
model save 'exc-5'
```

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