A Completely 3D Model For The Simulation of Mechanized Tunnel Excavation
A Completely 3D Model For The Simulation of Mechanized Tunnel Excavation
A Completely 3D Model For The Simulation of Mechanized Tunnel Excavation
DOI 10.1007/s00603-012-0224-3
ORIGINAL PAPER
Received: 20 October 2011 / Accepted: 4 February 2012 / Published online: 9 March 2012
Springer-Verlag 2012
Abstract For long deep tunnels as currently under construction through the Alps, mechanized excavation using
tunnel boring machines (TBMs) contributes significantly to
savings in construction time and costs. Questions are,
however, posed due to the severe ground conditions which
are in cases anticipated or encountered along the main
tunnel alignment. A major geological hazard is the
squeezing of weak rocks, but also brittle failure can represent a significant problem. For the design of mechanized
tunnelling in such conditions, the complex interaction
between the rock mass, the tunnel machine, its system
components, and the tunnel support need to be analysed in
detail and this can be carried out by three-dimensional (3D)
models including all these components. However, the stateof-the-art shows that very few fully 3D models for
mechanical deep tunnel excavation in rock have been
developed so far. A completely three-dimensional simulator of mechanised tunnel excavation is presented in this
paper. The TBM of reference is a technologically advanced
double shield TBM designed to cope with both conditions.
Design analyses with reference to spalling hazard along the
Brenner and squeezing along the LyonTurin Base Tunnel
are discussed.
apeak
ares
B
c
Cc
CI
D
E
f
F
fck
Ks
Ksn
List of Symbols
A
Surface area
Kst
Ff
FN
FR
G
g
K
K
Kn
Kns
Knt
Kt
Ktn
K. Zhao M. Janutolo (&) G. Barla
Department of Structural and Geotechnical Engineering,
Politecnico di Torino, Turin, Italy
e-mail: michele.janutolobarlet@polito.it
URL: http://www.polito.it\rockmech
Kts
mdil
123
476
mpeak
mres
N
N
n
Ni
P
p
p
r
R
RPM
speak
sres
t
T
Ttot
Tf
Tr
fug
u
ucrown
uf
ufin
uinvert
un
us
ut
UCS
fvg
fvgtop
fvgbot
DD
Dg
Dr
Dzmin
c
di
dei
dpi
{d}
ds
dt
dn
ep
epi
epl
k
K. Zhao et al.
123
l
m
r
r1
r3
rh
rv
s
u
w
Friction coefficient
Poissons ratio
Stress
Maximum principal stress
Minimum principal stress
Horizontal stress
Vertical stress
Shear stress
Friction angle (MohrCoulomb)
Dilation angle (MohrCoulomb)
1 Introduction
Today, almost all rock mass conditions can be bored by
modern TBMs with tunnel diameter varying from less than
3 m to more than 15 m. Long deep tunnels such as Alpine
Tunnels are excavated mainly by mechanised tunnelling, as
TBMs contribute significantly to savings in construction
time and costs. TBMs have already been used in the
Lotschberg and the Gotthard Base Tunnel and will be
employed in future tunnels to be excavated through the
Alps such as the Brenner and LyonTurin Base Tunnels.
However, open issues remain when dealing with critical
hazards encountered in these tunnels relating mainly to
stress-induced brittle failure of hard rocks (spalling, rock
bursting), squeezing ground behaviour, structurally controlled failures and water inflows, also in view of identifying the possible countermeasures to be applied (Loew
et al. 2010). Use of TBMs in very severe ground conditions
is yet under discussion due to some negative experiences
which resulted in very low rates of advancement and even
in standstill, as in the case of the YacambuQuibor Tunnel
(Hoek and Guevara 2009) or in the Headrace Tunnel of the
Gilgel Gibe II Hydroelectric Project (Barla 2010).
For the design of mechanised tunnelling in such conditions, the complex interaction between the rock mass, the
tunnel machine, its system components, and the tunnel
support has to be analysed in detail and three-dimensional
models including all these components are suitable to
correctly simulate this interplay and avoid the errors
introduced by assumption of plane strain conditions
(Cantieni and Anagnostou 2009). This is even more so in
the case of the double shield universal TBM (DSU TBM),
which is indeed a more complex machine than the gripper
or the single shield TBM.
This paper is intended to describe an advanced 3D
model which has been recently developed for the detailed
simulation of the DSU TBM, with specific problems in
mind as in the case of excavation of deep tunnels through
rock masses which exhibit either spalling or squeezing
477
2006) and Nagel et al. (2008). The model includes the soil,
the shield machine, the hydraulic jacks, the tunnel lining
and the tail void grout as separate components. The
advancement is simulated by a step-by-step procedure. It
should be noted, however, that excavation with closed
system shield TBMs in shallow soil tunnels is rather different with respect to rock TBMs such as double shield
TBMs, especially if attention is paid to the ground
behaviour, to the interplay between the ground, the TBM
and the support components (e.g., absence of grippers,
different cutterhead pressures, different methods of annulus
grouting) and to the design objectives (e.g., surface
settlements).
A worldwide trend towards the increased use of segmentally lined tunnels (Asche et al. 2011), excavated by single
or double shield TBMs, is to be noted. Today, single shield
TBMs are mainly used in soils or soft and weak rocks.
Double shield TBMs have come into common use as they
can cope with hard rocks as well as weak and unstable
rocks. As shown in Fig. 1, they consist of the front shield
with a cutterhead, main bearing and drive and a gripper
shield with clamping unit (gripper plates), tail shield and
auxiliary thrust cylinders. Both parts are connected by a
section (the telescopic shield) with telescopic thrust cylinders, which operate as the main thrust cylinders. The
basic principle (conventional mode) is that the machine is
clamped radially to the tunnel wall through the grippers
and the excavation and installation of the segmental lining
are performed at the same time.
Where the rock is weak and it is not possible to clamp
radially through the grippers, the necessary thrust forces
can either be provided by the telescopic cylinders or by the
auxiliary thrust cylinders. In the first mode with the telescopic cylinders, the auxiliary cylinders only transfer the
thrust forces to the segmental lining. In the second mode,
which is also called single shield mode, the front and
gripper shield form a stiff unit and the auxiliary cylinders
produce the necessary forward thrust (Maidl et al. 2008).
Recently, the range of application has been extended:
(a) downwards, even more in the direction of incompetent and squeezing rock formations as well as
(b) upwards, even more in the direction of very competent and extremely hard rock formations. In case
(a) there is an extended cutter head torque and thrust force
required whereas in case (b) an extended cutterhead thrust
capacity would be necessary in order to achieve appropriate penetration rates.
123
478
K. Zhao et al.
123
479
Table 1 TBM main features (assumed)
Description
Unit
Lining
Inner diameter
mm
8,100
Thickness
mm
450
Outer diameter
mm
9,000
GPa
3036
Cutterhead
Excavation diameter
mm
9,300
MN
17 (18.3 if
overboring)
MW
4.9
Overboring
mm
140
mm
9,440
No.
64 (?5 for
overboring)
MN
50
00
MN
80
Weight
kN
13,000
Pads dimensions H, B
Maximum pressure
mm
MPa
6,600, 2,000
4
Re-gripping
mm
2,000
mm
9,230
mm
9,230
mm
9,170
Gripper shield
mm
9,170
Grippers
Shield
Tail shield
mm
9,170
mm
5,000
mm
6,000
4 Modelling Approach
4.2 FEM Model
4.1 Foreword
4.2.1 Modelling the Rock Mass
In this paper, a simulator of TBM excavation of deep
tunnels has been developed using 3D FEM modelling and
the midas GTS (Geotechnical and Tunnel analysis System)
computer code (TNO DIANABV). This simulator is intended to be more general than the previous 3D models
123
480
K. Zhao et al.
elements; (2) obtain a mesh size with only one variation (in
the transversal plane, i.e., perpendicular to the tunnel axis);
and (3) improve the mesh geometric quality, that is, the
internal angles are close to 90o, the aspect ratios close to 1,
also by choosing an appropriate grading (in the transversal
123
481
123
482
K. Zhao et al.
Cutterhead
Front shieldInvert
Gripper
Lining
123
in the second step, the TBM enters the model and the
cutterhead is activated;
in the third step, the first slice of the shield is activated;
in the thirteenth step, the grouting with a softening
phase, the relevant pressure, the lining and the jack
pressure are activated. The excavation and the placing
of the rings are simulated in the same phase, assuming a
stroke of 1 m;
since the fifteenth step, the properties of the grouting
are changed into the hardening phase;
the stages proceed until a steady-state condition is
reached.
483
Rear shield
Cutterhead
Front shield
(a) 12 th step
The rock mass is considered to be continuous, homogeneous and isotropic. Any constitutive law based on these
assumptions for rock masses can be implemented in the
model. In this paper, the problems in mind are the spalling
and squeezing phenomena; therefore, two constitutive
models for reproducing them in a consistent and simple
way are illustrated in the following.
4.4.1 Brittle Behaviour (Spalling)
Lining
Groutingsoftening phase
Auxiliary thrust force
(b) 13 th step
X
Z
Groutinghardening phase
Fig. 8 Constitutive law for brittle behaviour: Diederichs (2007) criterion and stressstrain relationship. The intact rock criterion is shown for
comparison
123
484
K. Zhao et al.
1
apeak
1
2
123
485
Fig. 10 Constitutive law for squeezing behaviour: MohrCoulomb criterion and stressstrain relationship
fugT f us1
ut1
B N1
N2
un1
. . . us8
N3
N4
ut8
un8 gT
N1
N2
N3
7
N4
8
123
486
K. Zhao et al.
un
us
ut
Fig. 11 Interface topology
between the rock mass and the support elements near the
interface and no slip before yielding of the interface is
assumed (Fakharian and Evgin 2000; Cai and Ugai 2000),
the stiffnesses are actually penalty numbers that approximately enforce contact-surface compatibility consisting of
impenetrability and pre-sliding stick constraints. The normal and shear stiffnesses are therefore set to be much
greater than the stiffness of the softer neighbouring zone.
It is noted that too high values of Kn, Ks and Kt may
produce numerical errors related to the computer precision.
The values should be less than 100 times the stiffness of the
adjacent element according to Day and Potts (1994). A
rule-of-thumb is suggested in the FLAC manual (Itasca
2006), where the normal and shear stiffness can be set
equal to ten times the equivalent stiffness of the softer
neighbouring zone, which is given by:
K 4=3G
DZmin
11
d_ ei
d_ pi 0
d_ pi
12
if f \0 or f_\0
og
d_ pi k_
ori
if f f_ 0
13
14
15
g jsj r tan w
16
123
DD
DD 2Dr
17
487
18
Before the closure of the gap, only the invert of the front
shield is in contact with the rock mass as in the case of hard
rock, while the gap is simulated by the special interface
elements described in Sect. 4.5.1. Then, when the gap is
closed, the entire shield starts to support the rock mass. This
19
20
21
22
123
488
K. Zhao et al.
123
the remaining surface pea gravel and later cement grout are
injected. It is important, in the case of spalling, to correctly
fill this gap which could even be bigger due to the stressinduced notches. The elastic modulus of the pea gravel
with mortar injection is taken to be equal to 1 GPa. The
backfilling is usually performed at a certain distance behind
the shield. Therefore, as shown in Fig. 14a, the backfilling
is modelled in only one stage. The pea gravel and the lining
are activated 2 m behind the shield.
When tunnelling through weak rock, a grout annulus is
injected via the shield tail with a very fast hardening mortar
and simultaneously with the shield advance. In this case, as
shown in Fig. 14b, the tail gap grouting is modelled in two
phases as follows:
1.
2.
5 Applications
In order to illustrate in detail the 3D simulation model of
TBM excavation in brittle and squeezing rock conditions,
respectively, the case studies of the Brenner and the Lyon
489
Rock mass
25 GPa
0.25
UCS
130 MPa
8.1 MPa
CI
58.5 MPa
Generalised HoekBrown
apeak
0.25
speak
0.041
mpeak
0.656
ares
mres
0.75
9
sres
10-6
0.5
mpeak
1.4
sres
0.2
ares
0.5
mres
sres
10-6
123
490
K. Zhao et al.
350
6 Results
300
250
Intact rock
Brittle peak modified
1 [MPa]
200
150
100
50
-10.0
0.0
10.0
20.0
30.0
40.0
3 [MPa]
e_ p1 e_ p1 e_ p2 e_ p2 e_ p3 e_ p3
24
3
Dt
It is noted that this softening parameter has not been
introduced in the constitutive law; the equivalent plastic
strain is thus only a variable describing the degree of
damage in the rock mass.
The spalling zones are shown to occur at the invert and at
the crown with a maximum depth of approximately 1 m (the
uncertainty in the assessment of the depth of failure prediction is half of the element size, i.e., 0.15 m). The v-shape is
less pronounced than in other cases, as the stress ratio is
rather small. In intrinsic conditions, failure zones start right
behind the face. Any failure zone occurs at the face.
Also, failure occurs at the sidewalls. This is a shear
failure (i.e., in the high confinement range) which develops
Shield
Lining
Grippers
Pea gravel
Diameter
9.3 m
Diameter
9.3 m
Diameter
9m
Base
2m
Maximum
thickness
18.5 cm
Thickness
3 cm
Thickness
3 cm
Thickness
45 cm
Height
6.6 m
Minimum
thickness
11.5 cm
1 GPa
5m
Thickness
5 cm
6m
Regripping
2m
200 GPa
200 GPa
30 GPa
200 GPa
0.3
0.3
0.2
0.3
0.3
Density
312 kN/m3
Density front
shield elements
14,128 kN/m3
Density
30 kN/m3
Density
78 kN/m3
Density
24 kN/m3
Pressure at
the face
0.25 MPa
Pressure
4 MPa
Friction coefficient
rock-shield skin
123
0.3
Friction coefficient
backfilling-lining
0.3
491
123
492
K. Zhao et al.
123
7 Results
Figures 20 and 21 show the plastic strain contours and
compare the results for intrinsic conditions (a) and for the
complete model (b) when the interaction between the TBM
and ground is considered (again in terms of the equivalent
plastic strain given by Eq. 23 above). The plastic zones are
shown to be reduced in extent but are still all around the
excavation (the plastic radius is reduced from 12.9 m in
intrinsic conditions to 10 m for the complete model). It is
also noted that in the complete model the plastic strain at
the invert is smaller than that at the roof (there is a
reduction of 29% at the front shield invert). It is clear that
the presence of the shield invert (in this case, both front and
rear shield) before the gap is closed, associated with the
self-weight of the machine, provides an additional confinement near the tunnel face.
Figure 22 depicts the results in terms of LDP (a) and
contact pressure (b) on both the shields and the lining. The
493
closure of the entire gap between the front shield and the
ground is shown to occur 4 m behind the face. For the rear
shield this occurs at a distance of 9 m at the invert and
10 m at the crown, where complete closure takes place.
Given the value of the pressure acting on the shield, one is
in position to carry out the structural design of the shield
(and therefore of the machine). It is of interest to note that
the shape of the LDP and the contact pressure distribution
are very similar to those given by Ramoni and Anagnostou
(2011). Also to be noted is the greater pressure computed at
the shield invert with respect to the crown value, as shown
by Graziani et al. (2007).
When the grout reaches the hardening phase, the stresses
due to the excavation advancement are gradually
2 GPa
0.25
2 MPa
24
4
123
494
K. Zhao et al.
Shield
Lining
Grouting
softening phase
Diameter
9.44 m
Diameter
9.44 m
Diameter
9m
Thickness
3 cm
Thickness
3 cm
Thickness
45 cm
5m
6m
Grouting
hardening phase
200 GPa
200 GPa
36 GPa
0.5 GPa
1 GPa
0.3
0.3
0.2
0.3
0.3
Pressure at
the face
0.25 MPa
0.875 MN/
m
Pressure
(rock
and lining)
0.2 MPa
Density
312 kN/m3
Density
24 kN/m3
Density
24 kN/m3
Density shield
elements
2,757 kN/m3
Density
30 kN/m3
Friction coefficient
rock-shield skin
0.3
Friction coefficient
grouting-lining
0.3
123
N
X
25
i1
495
0
-10
-5
(a)
10
15
20
25
y [m]
-50
u [mm]
-100
crown
invert
-150
-200
-250
Tr
3.5
(b)
26
p [MPa]
2.5
2
1.5
Lining
Tf l
0.5
ZR
2
p 2pr dr r l p p R3 16;826 KNm
3
y [m]
0
-10
-5
10
15
20
27
25
25
-5
28
30
-10
RPM
T
60
20
15
10
Crown
Invert
8 Conclusions
y [m]
0
0
10
15
20
25
123
496
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