chapter 7. tunnel excavation – case study contents

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Chapter 7. Tunnel excavation – case study 56

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


Chapter 7. Tunnel excavation – case study Page 157

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



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.



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.



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



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.



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.



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.



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



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.



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.



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



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



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.



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



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.


Chapter 7. Tunnel excavation – case study 2

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



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



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



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.



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



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



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



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

chapter 7. tunnel excavation – case study contents

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