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Chapter 7. Tunnel excavation – case study Page 156
CHAPTER 7. TUNNEL EXCAVATION – CASE STUDY
Contents
7.1 Tunnel excavation in urban environment, with initial state 157
7.1.1 Problem definition 157
7.1.2 Drivers 158
7.1.3 Geometry 160
7.1.4 Geometrical input pre-processing 160
7.1.5 Macro model subdomains 162
7.1.6 Meshing 164
7.1.7 Structural elements, boundary conditions and loads 165
7.1.8 Excavation steps, Existence functions, Load functions 167
7.1.9 Materials and initial state data 171
7.1.10 Analysis 171
7.2 Tunnel excavation in urban environment, with flow 172
7.2.1 Data preparation 172
7.2.2 Drivers 172
7.2.3 2-phase boundary conditions 173
7.2.4 Materials 175
7.2.5 Results 175
APPENDIX 7.1 Creation of sections and computation of inflow into tunnel 177
APPENDIX 7.2 Computation of bending moment in continuum elements 179
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The goal of this chapter is to get the ZSOIL user familiar with the main features of the
program in the context of a realistic case study.
7.1 Tunnel excavation in urban environment, with initial state
7.1.1 Problem definition
The simulation of initial state, construction and excavation stages is the main new
feature in this case study, which is described in an engineering draft, Fig. 7.1. The figure
represents a tunnel excavation in urban environment. The case is characterized by
existing surface constructions and a water table. It requires freezing. In this chapter, we
shall first examine the dry case, and then include flow.
Fig. 7.1 Tunnel excavation in urban environment, engineering draft
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The main steps of the analysis are the following:
- We will start with an initial state analysis which includes all loads present
before the beginning of construction: here gravity and loads due to existing
constructions.
- Next we will simulate the excavation of the small pilot tunnel, then the freezing
procedure, the excavation of the main tunnel and safety factors will be
evaluated at the end, but could be evaluated all along the analysis process,
through stability analyses, performed after each excavation step.
- Drivers are used to pilot the different steps, in association with load functions,
which manage the evolution of load amplitudes and existence functions, which
manage the key events.
Open ZSOIL and, under File/Save as save: Ex_7_1_tunnelzh_1ph.inp.
7.1.2 Drivers
The drivers input screen (Fig. 7.2) tells us the essential aspects of the analysis we are
about to perform:
- An Initial state analysis starting with the application of 50% of gravity and 50%
of surface loads present at t=0, progressively increased to 100% by increments
of 10%.
- A Time dependent/Driven load analysis, starting at time t = 0 and progressing
to time t = 10, with time increments of ∆t = 1 this part is split into several
construction stages, as we will see.
- A Stability analysis, starting with a safety factor of 1, tentatively progressing to
30, until instability is detected.
Remarks:
- There is no real time-dependent behavior here, time can be considered fictitious,
just a means to sequence excavation steps.
- Progressive unloading of the medium, which is used to simulate distance to front
in two-dimensional analysis, will be driven by “pseudo-time” driven unloading
functions.
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Fig. 7.2 Control/Analysis & Drivers
Remarks:
- Additional stability analyses could be inserted anywhere in time, in order to define
the safety factor corresponding to a particular construction stage.
- Modifications of the stress state occurring during stability analyses are ignored for
follow-up analyses.
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7.1.3 Geometry
The geometrical data of the finite element model are described in the following figure.
Fig. 7.3 Geometry of planned excavation
7.1.4 Geometrical input pre-processing
Enter the geometrical preprocessor by selecting menu option
Assembly/Preprocessing. We will first create the two tunnels, and define the limit of
the frozen zone.
Select option Macro Model from the method list located on the right hand side of the
screen, then Objects and then Circle (referred to later as Macro
Model/Objects/Circle).
Create three circles from the Circle dialog box, using each time the Apply button:
- The first for the main tunnel, with center (0;0) and radius 6.05 m, see Fig. 7.4
- the second for the limit of the frozen zone with center (0;0) and radius 7.25 m
- the third for the small tunnel, with center (9.65;7.65) and radius 2.4 m
Fig. 7.4 Circle dialog box
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Leave third coordinate of the center z = 0 and number of segments = 20, this defines
the refinement of the discretization of the tunnel.
Now, click on the Close button and press CTRL-F to optimize zoom with the newly
created objects. You should see the following image (see Fig. 7.5).
Fig. 7.5 Circles defining the tunnels
Switch off the grid (press the G key) and the axes (press the A key).
Remark:
- Visualization will show you the list of applicable shortcuts.
Next, we’ll define the contour of the mesh, including the position of the building and the
bottom boundary. For this, move to Macro Model/Point/Create/Point option, and
create the following points, using the Apply button:
Top and building boundary:
(-40; 19.55) (-12; 19.55) (-12; 12.55) (9.65; 12.55) (40; 12.55)
Sides:
(-40; 0) (40; 0)
Bottom boundary:
(-40; -30) (9.65; -30) (40; -30)
Remark:
- Leave third coordinate z = 0.
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Press CTRL-F to optimize zoom with the newly created points.
Now move to Macro Model/Objects/Line and define the contour of the mesh, clicking
on the ten nodes of the mesh contour (as Continue option is switched on in the dialog
box, you don’t have to click twice on each node to indicate the end of a line and the start
of a new one).
Then, uncheck the Continue option, and create two crossing lines between points (-40;
0) (40; 0) and points (9.65; 12.55) (9.65; -30). When prompted, accept the automatic
intersection of objects. Then click on the Close button.
Finally, delete the two lines inside of the tunnels with option Delete/Delete. You should
end up with the following screen, Fig. 7.6.
Fig. 7.6 Macro model
7.1.5 Macro model subdomains
Select option Macro Model/Subdomain/Create/Continuum inside contour, and
click successively inside of the 8 subdomains.
Click on Update/Parameters and assign Initial material number 2 to the three
subdomains which define the frozen zone, as shown below, Fig. 7.7. Notice that
replacement materials can be defined here. These correspond to a situation where the
initial material is replaced by a new one after excavation; the management of activation
is triggered by the corresponding existence function.
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Fig. 7.7 Subdomains
Remark:
- You can use the tool located on the right hand side of the screen, in order to
zoom on this part of the mesh. To come back to a general view, press CTRL-F.
Still using the Update/Parameters tool, assign Existence function 1 and Unloading
function 1 to the small tunnel, and assign Existence function 5 and Unloading function 2
to the main tunnel (see Fig. 7.8). You may check the values assigned to materials,
existence and unloading functions using the selection list located just below the right
method list (see red arrow in Fig. 7.7). Default visualization is set to Initial material.
EF = 1
EF = 5
ULF = 1
ULF = 2
Fig. 7.8 Existence function and unloading function definition
Remark:
- The actual definition of excavation steps and progressive convergence is managed
though existence and load functions, which are defined later.
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7.1.6 Meshing
Now, select the Mesh/Create virtual mesh method and click inside of the small tunnel.
Select Unstructured mesh type, and set approximate element size to 1 m. Click on
Create virtual mesh. Then, click inside of the main tunnel, select unstructured mesh
type, and set approximate element size to 1.5 m. Click on Create virtual mesh.
Then click inside of the upper frozen zone. Structured mesh type is selected by default,
as this subdomain has four control points. Set Edge 1-2 split to 10 and Edge 1-4 split
to 2. Then click on Create virtual mesh. Repeat the same operation for the lower
frozen zone.
Remark:
- As the Adjust split to existing subdomains option is checked On, split along
Edge 1-2 is automatically set to 13 instead of 10 to retain mesh compatibility.
Click successively inside of the two remaining upper subdomains, select unstructured
mesh type, and set approximate element size to 1.6 m. Click on Create virtual
mesh. Click successively inside of the two remaining lower subdomains, select
unstructured mesh type, and set approximate element size to 2 m. Click on Create
virtual mesh. Press CTRL-F. Select Mesh/Virtual -> Real mesh method and click
successively inside of the 8 subdomains. Then, press CTRL-M in order to hide the macro
model, and to leave only the FE model (nodes and elements). You should end up with a
finite element mesh as shown in Fig. 7.9.
Fig. 7.9 Finite element mesh
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7.1.7 Structural elements, boundary conditions and loads
Zoom on the main tunnel zone, and select edges along the tunnel lining with the
button located below the Windows menu, Fig. 7.10.
Fig. 7.10 Selection of edges
Then select FE model/Beam/Create…/On edge(s) method and set Initial material
to 4 and Existence function to 6. Move to Selections/Unselect all Windows menu.
Repeat the same operation for the small tunnel lining. Set Initial material to 3 and
Existence function to 3. Move to Selections/Unselect all Windows menu.
Now select edges along the building’s wall and mat foundation with the button or the
Select edges in zoom box button (located next to the button).
Then select FE model/Beam/Create…/On edge(s) method and set Initial material
to 5 and Existence function to 0. Move to Selections/Unselect all Windows menu.
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Fig. 7.11 Surface Load
Move to FE model/Loads/Surface Loads/PRESSURE/2 nodes (P) method, click on
the two extremity nodes of the building’s mat foundation and set Value 1 and 2 to -150,
Fig. 7.11. Finally, move to FE model/Boundary Conditions/Solid BC/On box
(indicated by the red arrow in Fig. 7.12) in order to create default plane strain box
displacement boundary conditions, and press CTRL-F, Fig. 7.12.
Fig. 7.12 Solid boundary conditions
You may now exit the graphical preprocessor and save your work (File/Exit menu, and
answer Yes). Back in the principal ZSOIL screen, select File/Save menu.
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7.1.8 Excavation steps, Existence functions, Load functions
The excavation sequence is illustrated next (Fig. 7.13).
Fig. 7.13 Excavation steps
A small pilot tunnel is excavated first; its liner is installed next. The area of the main
excavation is then frozen. The main tunnel is excavated next. The liner of the main
tunnel is installed after partial convergence. The key steps are enumerated below (Fig.
7.14). Steps 2, 3, 7 concern the 2-phase case, this will be discussed later.
Fig.7.14 Time schedule
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7.1.8.1 Existence functions
The management of the excavations is done via Existence functions.
Existence functions are multistep Heaviside functions which take value 1 when the
object they are attached to exists and zero when the object disappears. Existence
functions are defined under Assembly/Existence functions by entering one to three
active periods, see Fig. 7.15 and 7.16. For instance, existence function number 5,
associated with the big tunnel excavation has one active period, from t = 0 till t = 4.
Remarks:
- It is important to notice that changes from existance to inexistance, and vice-
versa, indicated at time t will influence computations starting from time t+∆t,
with one exception at t = 0.
- If the time stepping adopted under Analysis/Drivers does not go through the
events identified by existence functions the code will automatically add
intermediate time stepping in order to capture all significant events. For example:
a time stepping like t = 1..2..3..4... etc. in an analysis which uses an existence
function with a switch at t = 1.5, will automatically add a step at 1.5.
- Existence functions can be used to activate/deactivate various things like
elements, prestress etc.
- Default existence function number 0 corresponds to permanent existence.
Fig. 7.15 Existence functions definition
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Fig. 7.16 Existence functions representation
Remark:
- After the definition of the existence functions, use View/Verify excavation
steps option in the pre-processor to view the excavation sequence.
7.1.8.2 Convergence and Load functions
It is often necessary in tunnel construction to delay the installation of the liner in order
to reduce the load carried by the structure, at least if stability allows that. This is
simulated using unloading functions associated with a set of “excavated domain
equivalent” forces which are calculated automatically by the program when the
excavation takes place and which exactly equilibrate the domain, replacing the
excavated part by forces. These forces are then progressively diminished, first till
installation of the liner and then completely.
Load (time) functions are needed to define the evolution in time of loads, imposed
displacements, and tunnel convergence effects, via Unloading functions (unloading of
in situ stress). The load functions needed here are listed in Fig. 7.17.
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Fig. 7.17 Loading/Unloading functions
Remarks:
- Unloading functions 1 and 2 will introduce partial unloading of the domain before
lining is installed; 70% for the small tunnel, 80% for the large one.
- Load functions 3, 4, 5 are associated with the freezing process.
Load functions are introduced under Assembly/Load function. Load functions are
introduced as time-value pairs. Load function 4 is illustrated in Fig. 7.18.
Fig. 7.18 Load function number 4
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7.1.9 Materials and initial state data
Materials present no difficulties in the 1-phase situation, see the input file if details are
needed. However, initial state input deserves a word of explanation.
Fig. 7.19 Materials
We have seen earlier that the initial state driver superposes gravity, which requires
specification of weight for each material (Assembly/Materials/Unit weights, set γ),
gravity direction (Assembly/Materials/Gravity -1 in y direction), and K0 state
(Assembly/Materials/Initial K0 state K0 (x’) = K0 (z’) = 0.45). As illustrated in Fig.
7.19 the K0 state is specified here as material data and not globally under Gravity, as
some materials (beams e.g.) do not require it.
Remark:
- Observe in preprocessor that the load function associated with the surface load,
which represents a preexisting building, has number “0”, see
(Assembly/Preprocessing/FE model/Surface load/update parameters),
which corresponds to a permanent value of “1”. This load is therefore present at
time t = 0 and will be taken into account in the evaluation of the initial state.
7.1.10 Analysis
Analysis of the single phase case Ex_7_1tunnelzh_1ph.inp can be run now, with
Analysis/run analysis, and exploitation of results will be discussed when the 2-phase
problem is analyzed.
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7.2 Tunnel excavation in urban environment, with flow
7.2.1 Data preparation
The single phase data are valid for the 2-phase problem except for the presence of
water. Open ZSOIL and, under File/... menu, first open: Ex_7_1_tunnelzh_1ph.inp
and save it as Ex_7_2_tunnelzh_2ph.inp.
7.2.2 Drivers
The drivers input screen (Fig. 7.20) tells us the essential aspects of the analysis we are
about to perform:
- Switch problem to: Deformation+flow.
- An Initial state analysis starting with the application of 50% of gravity and 50%
of surface loads present at t=0, progressively increased to 100% by steps of
10%.
- A Time dependent/Driven load + Steady state flow analysis, starting at time
t = 0 and progressing to time t = 7, this part is split into several construction
stages, as before.
- A Stability driver could be added.
There is again no real time-dependent behavior here, time can be considered fictitious,
just a means to sequence excavation steps.
Fig. 7.20 Control/Analysis & Drivers
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Remarks:
- A permanent flow solution will automatically be computed at the beginning of
each time-step.
- If we replace the Driven load driver by a Consolidation driver, then the 2-
phase medium will be fully coupled and time considered will be real time, units
become then important.
7.2.3 2-phase boundary conditions
Go back to the geometrical preprocessor by selecting menu option
Assembly/Preprocessing.
Hide Macro model with CTRL-M, axes with A-key and grid with G-key.
You may also hide nodes with N-key and solid boundary conditions with CTRL-B.
Select edges along the right boundary of the domain (x = 40 m) with the button or
the Select edges in zoom box button (located next to the button).
Create seepage elements selecting the FE Model/Seepage/On edge(s) method. Set
material number to 6 and existence function to 0.
Move to FE Model/Boundary Conditions/Pressure BC/Fluid head on selected
edges method, and set water level to 7.65 m. Move to Selections/Unselect all
Windows menu.
Repeat the same steps for the left boundary (x = -40 m). Don’t forget to unselect edges
at the end, using Selections/Unselect all Windows menu.
seepage
elements
seepage
elements
Fig. 7.21 Seepage elements and water boundary conditions
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Now select edges surrounding the small tunnel with the button (Fig. 7.22). You
should select the external edges with respect to the beam elements.
Fig. 7.22 Selection of edges
Create seepage elements selecting the FE Model/Seepage/On edge(s) method. Set
material number to 6 and existence function to 3. Move to Selections/Unselect all
Windows menu. Repeat the same for the main tunnel, with material 6 and existence
function 6 (Fig. 7.23).
Fig. 7.23 Seepage definition
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You may now exit the graphical preprocessor and save your work (File/Exit menu, and
answer Yes). Back in the principal ZSOIL screen, select File/Save menu.
7.2.4 Materials
Make sure that flow data are specified and active for continuum and seepage material,
which is new. See chapter on flow for more information on seepage.
Then, move to Analysis/Run Analysis.
7.2.5 Results
Select menu Results/Postprocessing. We will first take a look at the evolution of the
fluid velocities, during the excavation procedure. For this, move to Time/Select
current time step, select time step 0 and click on OK.
Move to Graph. Option/Fluid velocities and then to Settings/Graph. Contents. Set
scale to 20, and press OK. You may then press the “+” or the “-” keys to navigate
through time steps. Finally, at time t = 7, you should see the following fluid velocities
vectors (Fig. 7.24).
Fig. 7.24 Fluid velocities
To take a look at corresponding water pore pressures, move to Graph Option/Maps
and to Settings/Graph Contents. Select Pore pressure, uncheck the default option,
and set minimal value to -300. Click OK and you should get Fig. 7.25.
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Fig. 7.25 Water pore pressure
Now move to Graph Option/MNT for beams/anchors/rings in order to see bending
moments in the tunnel linings.
To hide foundation beam elements, you can first select them with the
Selections/Elements/List windows menu, selection rule = Material, number = 5,
click on the bottom black arrow, then on the top black arrow, then on Select and Close.
Then you can hide the selected elements with the help of Selections/Hide selected
windows menu.
You may adjust the scale with the Settings/Graph Contents menu, uncheck the
automatic scaling, and set scale to 0.002. Press H-key to show the continuum
elements, and you should get the following bending moments plot (Fig. 7.26).
Fig. 7.26 Bending moments in the main tunnel
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APPENDIX 7.1 Creation of sections and computation of inflow into
tunnel
In this appendix, we’ll see how to define sections around the main tunnel, set the
displayed value to normal fluid velocities, and integrate in order to compute the inflow.
In post-processor, move to Graph Option/Sectional quantities and then to
Sections/Sec. Planes (2D). Click on two points in order to define the position of the
section, here on the left side of the main tunnel (see points 1 and 2 in Fig. 7.27). Then
click on Add button. Repeat the operation for the section below the tunnel (points 3 and
4) and on the right hand side (points 5 and 6). Click on Close.
1
2
3 4
5
6
Fig. 7.27 Fluid velocities
Move to Settings/Graph. Contents and set value to Continuum/Fluid Velocities and
component to N (see Fig. 7.28). Click on OK.
Fig. 7.28 Sectional quantities definition
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Then, under Misc./Sections-2D/Integral INT(rsl) dA, create a file filename.csv and
open it with Excel. The inflow will be integrated from normal fluid velocities for each
section, and also for the sum of the three created sections (see Fig. 7.29).
Fig. 7.29 ASCII file with integral of fluid velocities
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APPENDIX 7.2 Computation of bending moment in continuum elements
Visualization of internal forces in beam elements is straightforward (see Fig. 7.26).
We’ll learn in this appendix how to integrate stresses in order to retrieve bending
moments in continuum elements. Suppose we want to integrate stresses in the upper
part of the frozen zone. First move to Graph.Option/MNT for continuum 2D. Then,
select the continuum elements where you want to integrate stresses with
Selection/Pick Elements and select the end edges on both sides of the “equivalent
beam” with Selection/Edges/Zoom box. Then under Settings/Graph.Contents give
a name to the “equivalent beam” and click on Add beam with label –->. By default,
bending moment Mz is selected. Click on OK and bending moments will be represented
as shown in Fig. 7.30.
Fig. 7.30 Bending moments in continuum elements
Remark:
- Accurate results for structures modeled with aid of continuum elements can
only be obtained selecting the Continuum for structures type in the Material
input screen (Fig. 7.31)
Fig. 7.31 Continuum for structures option defined at the material level