Date post: | 17-Jan-2016 |
Category: |
Documents |
Upload: | carmine-tranfa |
View: | 67 times |
Download: | 7 times |
Computers and Geotechnics 31 (2004) 171–183
www.elsevier.com/locate/compgeo
Three-dimensional modelling of tunnel excavation and lining
G. Galli *, A. Grimaldi, A. Leonardi
Department of Civil Engineering, University of Rome,‘‘ Tor Vergata’’, Viale del politecnico n.1, Rome, Italy
Abstract
In this study, a 3D finite element model is applied to simulate the conventional procedure of tunnel excavation and lining. Both
shallow and deep tunnels are considered in soils modelled with Mohr–Coulomb elasto-plastic constitutive equation.
A polycentric tunnel cross-section with temporary lining and soil-nailing of the face excavation is studied.
The numerical results show the influence of the soil properties and excavation procedures on face deformation and ground
settlements.
The model allows to evaluate the lining–soil interaction and the stress distribution in both the lining and the reinforcing
structural elements.
� 2004 Published by Elsevier Ltd.
1. Introduction
Tunnel design and construction sets relevant issues,
especially for shallow tunnels in urban environment.
The main problems are the evaluation and the control ofground settlements, deformations and stability of the
excavation front, loads and stresses in the lining. A great
variety of excavation techniques has been developed
[1–3], which employ different methods to reinforce and
support the excavation front. It is therefore important to
evaluate and compare the effect of these methods.
Usually the excavation process is simulated step by
step with FEM modelling. The numerical modellingoften relies on a 2D analysis, implementing elasto-
plastic constitutive models, which are supposed to cap-
ture the limit-state behaviour of drained and undrained
soils. Complete reviews of numerical analyses of tunnels
have been presented in [4,5]. These reviews make it ap-
parent how popular 2D modelling is with respect to 3D
modelling [6].
However, the use of 3D modelling is almost manda-tory if one wants to correctly evaluate the effects of the
excavation process, so that 3D models are under con-
tinuous development, and are being applied to increas-
ingly complex problems [7].
* Corresponding author.
E-mail address: [email protected] (A. Grimaldi).
0266-352X/$ - see front matter � 2004 Published by Elsevier Ltd.
doi:10.1016/j.compgeo.2004.02.003
Specifically, 3D schemes have been used to model
shallow excavations with TBM tunnelling, where the soil
has been modelled in order to simulate time-dependent
consolidation effects [9]. Three-dimensional analysis at
different stages of tunnel excavation has been developed,for instance, in [10] for the Heathrow Express Trial
Tunnel (the first tunnel excavated by the New Austrian
Tunnelling Method in the London Clay, with a poly-
centric section) and in [11] for the case of circular
shallow tunnels, where the effects of sub-horizontal
pipes and umbrella of pipes have been analysed, with
special attention to displacements at the excavation face.
In [12], excavation-induced displacements for shallowtunnels in sandy soils have been analysed both with
experiments and with 3D numerical simulations.
Moreover, a 3D analysis for shallow tunnels is presented
in [13], which investigates K0-influence both on the ini-
tial deformation and on the lining stresses.
In this paper we are concerned with 3D analysis of
shallow and deep tunnels. More specifically, we will
study a full-section-excavated tunnel with polycentricsection, the excavation process being performed with the
use of soil nails and temporary lining.
The Mohr–Coulomb elasto-plastic constitutive model
has been employed; this model is used to describe both
drained and undrained limit conditions. Simulations
have been implemented with the commercial finite ele-
ments code-LUSAS 13.5 [16].
172 G. Galli et al. / Computers and Geotechnics 31 (2004) 171–183
The main aim of the numerical investigations is to
evaluate:
1. Influence of the protection measures (lining and face
reinforcing) on the ground settlements and face
deformations.2. Soil–structure interaction and stresses in the lining
elements.
In the FEM simulation, standard eight-node volume
elements have been used. Therefore, limit conditions of
stability at the excavation face [14] and localized plastic
deformations are excluded (this case has been investi-
gated, for instance, in [8]).
In the following, the modelling of the excavation andlining phases is illustrated.
The results proposed are referred to various soil
mechanical properties and different procedures of ex-
cavation and lining with or without face-protective
measures.
Finally, a comparison with the simpler 2D model is
given [8,15].
Cross section at the excavation face
Step 1
1
1
Step 2
2
2
Step 3
33
Step 4
44
Step 5
5
5
Step 6
6
Fig. 1. Excavation and lining
2. Modelling of excavation and lining
Excavation and lining cases studied in this work are
referred to the highway and railway tunnel typologies,
with polycentric cross-section (surface 100–150 m2, dia-meter 10–15 m), excavated with conventional methods
(open face, hand mined) and subsequent lining phases.
The first numerical model refers to the shallow tunnel
case with cover height equal about the medium diameter
of the cross-section. A simple numerical procedure is de-
veloped, suitable to evaluate the excavation effects on the
ground settlements and on the stresses in temporary and
final lining. The excavation procedure includes reinforc-ing elements at the excavation face to assure face stability.
The protective measures for the excavation face are
longitudinal fibber-glass nails grouted in the tunnel face
and umbrellas of longitudinal fibber-glass pipes (circular
crone with internal diameter 0.04 m and external di-
ameter 0.06 m), designed to prevent localized break-ups
and front extrusion.
Longitudinal profile
Protective measures forface stability
Temporary lining
6
Final concrete lining
procedure (see Table 1).
Table 1
Protective measures and lining elements
Excavation and lining procedure
1. Umbrella of pipes
2. Soil nailing at face
3. Steel ring beam
4. Shotcrete support
5. Invert arch
6. Final concrete lining
G. Galli et al. / Computers and Geotechnics 31 (2004) 171–183 173
The temporary lining is given by steel ring beams with
standard double-T section (two coupled IPE-180),
shotcrete support (thickness 0.3 m) and concrete invert
arch (thickness 0.8 m).
The arrangement of these elements in the typicalcross-section is illustrated in Fig. 1 and Table 1.
3. Three-dimensional final element modelling
The 3D model of Fig. 2 shows a shallow tunnel case
with a polycentric section (D ¼ 11 m) assuming sym-
metric loading conditions.Excavation and lining phases are simulated through
72 different analysis steps.
In the first step, all the representative elements of the
lining and soil reinforcing are deactivated; in the second
step, the soil-weight is applied to the ground elements; in
the third step, the soil reinforcing elements of the front
(umbrella of pipes and soil nails at face) are activated
and tunnel excavation starts at the end cross-section ofthe model.
70 m
Fig. 2. Three-dimen
Table 2
Lining elements and protective measure parameters
Lining material properties
Ring steel beams E ¼ 2:1Eþ 08 kPa, v ¼ 0:3
Shotcrete support E ¼ 2:5Eþ 07 kPa, v ¼ 0:1
Invert arch E ¼ 2:85Eþ 07 kPa, v ¼ 0:2
Umbrella of pipes E ¼ 1:3Eþ 07 kPa, v ¼ 0:3
Soil nails at face E ¼ 1:5Eþ 07 kPa, v ¼ 0:3
In the subsequent phases, the tunnel excavation is
developed and the lining elements are activated (steel
beams, shotcrete support and invert arch).
The constitutive law used for the soil elements is the
elasto-plastic associated Mohr–Coulomb model with thefollowing material parameters: E ¼ 40; 000 kPa,
m ¼ 0:334, / ¼ 26� (friction angle), cohesion c ¼ 20 kPa,
density c ¼ 20 kN/m3. The lining elements and the
protective measures are assumed to have a linearly
elastic behaviour.
The lining geometrical material parameters are given
in Table 2.
The excavation sequence are:• Construction of soil nails and umbrella of pipes.
• Excavation of 1 m of soil and subsequent installation
of the temporary lining, which includes a steel ring
beam at 1 m distance from the excavation face, a
shotcrete support at 2 m distance from the excavation
face and an invert arch at a variable distance (4–16 m)
from the excavation face.
The numerical procedure simulates an excavationstarting from the end section of the soil model and
stops at the middle section. The excavation crosses 15
soil layers with different thicknesses. The element
thickness (1 m) in the central layers of the model is
reduced with respect to the mesh thickness (4 m) of
the lateral first layers, in order to increase the nu-
merical accuracy in the central part of the model,
where the simulation is assumed representative of theactual excavation phase.
The details of the subsequent analysis steps (load
cases in Lusas 13.5) are as follows:
∼4D
∼3D
D
∼D
sional model.
A ¼ 47:8 cm2, l ¼ 2634 cm4/m
Thickness¼ 0.3 m
Thickness¼ 0.8 m
Circular crown section 0.06/0.04 m
Circular crown section 0.06/0.04 m
174 G. Galli et al. / Computers and Geotechnics 31 (2004) 171–183
Load case 1. Initialisation of the procedure: deactiva-
tion of all lining and reinforcing elements.
Load case 2. Soil weight; lithostatic condition.
Load case 3. Activation of the steel ring beams and
the shotcrete support elements (3D beams) locatedin the first soil layer. Activation of the soil pipes um-
brella and soil nails at the face (3D-bars).
Load case 4. Deactivation of the soil elements in-
cluded in the first layer (release of 100% of the bound-
ary nodal forces).
Load case 5. Activation of the steel ring beams and
the shotcrete support elements located on the sec-
ond layer. Activation of the invert arch in the firstlayer.
Load case 6. Deactivation of the soil elements in-
cluded in the second layer (release of 100% of the
boundary nodal forces).
The procedure (load cases 5–6) is repeated to simulate
the first 20 m of tunnel excavation and lining.
Fig. 3. Stresses and displacement (excavatio
In this first part, the length of the excavation step is 4
m corresponding to the thickness of the soil elements
(load cases 7–13).
In the central part of the model the length of the
excavation step is reduced to 2 m between 20 and 30 m,and to 1 m between 30 and 35 m (middle section of the
model). In this part of the excavation (20–35 m), a more
precise lining procedure is adopted with the subsequent
activation of steel ring beams and shotcrete support
(load cases 13–72).
We assume that final concrete lining is placed at large
distance from the excavation face, hence it does not
appear in the numerical simulations.
3.1. Soil stresses and displacements
The results obtained from the 3D model are relative
to the final situation after completing the excavation and
lining (Fig. 3).
n and lining completed, load case 72).
G. Galli et al. / Computers and Geotechnics 31 (2004) 171–183 175
In this example all the protective measures have been
considered. The numerical results show the spreading of
a plastic zone near the excavation face and under the
invert arch.
3.2. Stresses in lining
The numerical results show the interaction between
lining elements and surrounding soil, and allow to val-
uate the stress resultant in the steel ring beams (Fig. 4),
shotcrete support (Fig. 5) and invert arch (Fig. 6).
The small bending stiffness of the ring steel beams
and shotcrete support implies that the stresses produced
Fig. 6. Stress resultants in the invert arch
Fig. 5. Stress resultants in the shotcrete supp
Fig. 4. Stress resultants in the steel ring beams (doub
by axial force are prevailing on the bending moment
effects. More precisely, the compression stress in the
steel beams is almost constant with the maximum value
r ¼ 142; 600 kPa. In the shotcrete, the maximum com-
pression stress is r ¼ 2600 kPa. In the invert arch, bothaxial force and bending moment are relevant, and the
maximum compression stress in the concrete is r ¼ 1800
kPa.
3.3. Soil nails
The model gives the distribution of the tensile axial
force in the nails at the excavation face (Fig. 7). The
(1 m of lining, thickness¼ 0.8 m).
ort (1 m of lining, thickness¼ 0.3 m).
le T section; A ¼ 47:8 cm2/m, I ¼ 2634 cm4/m).
176 G. Galli et al. / Computers and Geotechnics 31 (2004) 171–183
tensile force in the nails is extinguished at a distance of
about two diameters (D ¼ 11 m) from the excavation
front. The maximum tensile stress in the fibber glass
nails is about r ¼ 17; 707 kPa.
3.4. Ground settlements and face deformation
The numerical simulation has been repeated for three
different procedures of excavation and lining:
Fig. 8. Face mo
Fig. 9. Settlements at the tunn
50
10
15
20
25
0
0
0
0
0
300
0 10 20 30 4
EExxccaavvaattiioonn ffaaccee
Distan
Axial Force in the soilnails (kN
)A
xial Force in the soilnails (kN)
Fig. 7. Axial force in s
• Face with soil nailing at face and construction of the
invert arch at 4 m distance from the excavation face.
• Face without nails at face and construction of the in-
vert arch at 4 m distance from the excavation face.
• Face with soil nailing at face and construction of theinvert arch at 16 m distance from the excavation face.
The excavation face movements are plotted in Fig. 8.
These results show that face movements are reduced
by the soil nails at face (Fig. 8); the analysis shows also a
vements.
el cross-section heading.
0 50 60 70 80
N=278 kN
ce (m)
oil nails at face.
Fig. 11. Vertical displacements at ground surface.
Table 3
Mechanical properties of soil
Soil E (kPa) v c (kPa) u (�)
Case 1 40,000 0.334 20 26
Case 2 40,000 0.334 5 38
Case 3 20,000 0.334 40 26
Fig. 10. Heading displacements at the excavation face cross-section.
G. Galli et al. / Computers and Geotechnics 31 (2004) 171–183 177
reduction of the total displacements near the excavation
face. In Figs. 9 and 10, the effects of the excavation andlining procedure on the tunnel heading settlements are
examined. The strong reduction of the settlements due
to soil nails and invert arch is emphasized.
The distribution of the ground settlements is given in
Fig. 11.
4. Influence of soil parameters
With the subsequent model cases, the influence of
different mechanical properties of the soil (Table 3),
corresponding to the Mohr–Coulomb criterion with
associated flow, has been analysed. Both a shallow
tunnel (Fig. 2) example (with an additional surface load
of 40 kN/m2 that simulates the influence of a four-stories
building) and a deep tunnel example (Fig. 14) are ex-amined.
The excavation and lining procedures are the same
used for the first model.
The numerical results for the shallow tunnel exampleare given in Figs. 12 and 13, and Table 4.
The influence of the soil mechanical properties on the
maximum values of the stress resultants in the lining
elements is shown in Table 4.
Similarly in Fig. 13, the influence of soil parameters
on the settlements (at the heading and at the ground
surface), face displacements and on the maximum values
of the axial force in the soil nails at face is investigated.
Fig. 12. Stress and settlements in the model before excavation and lining procedure and after excavation and lining procedure (case 2).
178 G. Galli et al. / Computers and Geotechnics 31 (2004) 171–183
The next example is a deep tunnelling excavation andlining, corresponding to the three soil cases (Table 3) but
without the asymmetrical surface load in the previous
case.
The mesh is similar to that of the shallow case, but
the tunnel location is about 53 m below the soil plane
(Fig. 14).
The comparison of soil movements and stress in the
soil nails are reproduced in Fig. 15.In these cases, the ground settlements are negligible.
The stress resultant in the lining elements are given in
Table 5.
The previous results have been obtained assuming the
simple Mohr–Coulomb model with associated flow. The
use of this criterion is diffused in practice, and the cor-
responding finite element numerical iterative solution is
generally stable. Some numerical results using the non-associated Mohr–Coulomb model are also shown in
Figs. 16 and 17, where the vertical displacements are
plotted corresponding to different values of the dilatancy
(Table 6).
The comparison shows the increment of the groundsettlements for the cases of non-associative flux.
5. Two-dimensional modelling
The most frequent modelling used for tunnelling ex-
cavation is the 2D finite element analysis [4].
In this case a soil layer, orthogonal to the tunnel andsufficiently far from the excavation front, is considered
(Fig. 18). The excavation and lining phases are analysed
with subsequent load cases corresponding to deactiva-
tion of soil elements and activation of lining elements.
The nodal forces acting on the tunnel cross-section
boundary are gradually relaxed to simulate the interac-
tion between the soil and the lining elements. However,
for the 2D model it is necessary to assume the fraction ofnodal forces release in the subsequent load cases.
On the contrary, the 3D model can automatically
simulate the real procedure of excavation and lining. A
comparison between 2D model predictions and the re-
Fig. 13. Soil displacements and axial force in the soil nails.
Table 4
Axial force (kN) and bending moment (kNm) in the lining elements
Case Steel ring Shotcrete support Invert arch
Nmax Mmax Nmax Mmax Nmax Mmax
1 )634 )29 )188 )167 )509 )1612 )591 )28 )188 )151 )424 )1633 )354 )30 )208 )195 )358 )134
Fig. 14. Three-dimensioinal model of deep excavation.
G. Galli et al. / Computers and Geotechnics 31 (2004) 171–183 179
sults of the corresponding 3D model can be useful to
define the correct nodal forces release in 2D model.
This comparison has been developed for the shallow
tunnel case of Fig. 18.
The excavation and lining procedure (Fig. 18), is
simulated with nine load cases:
Load case 1. Deactivation of all beams elements.
Load case 2. Soil weight application.Load case 3. Deactivation of ground elements and
relaxation of 30% of the nodal forces.
Load case 4. Activation of steel beams.
Load case 5. 20% further relaxation of the nodal
forces.
Load case 6. Activation of shotcrete support.
Fig. 15. Soil displacements and axial force in the soil nails (deep excavation).
Table 5
Axial force (kN) and bending moment (kNm) in the lining elements (deep excavation)
Case Steel ring Shotcrete support Invert arch
Nmax Mmax Nmax Mmax Nmax Mmax
1 )447 )24 )172 )167 )509 )1612 )520 )33 )188 )151 )424 )1633 )745 )49 )208 )195 )358 )134
Fig. 16. Settlements at the tunnel cross-section heading.
180 G. Galli et al. / Computers and Geotechnics 31 (2004) 171–183
Fig. 17. Vertical displacements at ground surface.
Table 6
Mechanical properties of soil (different values of dilatancy)
Soil w (�) c (kPa) u (�)
Case 1 26 20 26
Case 2 12 20 26
Case 3 6 20 26
Fig. 19. Stresses and displacement (excavati
~4D
~3D
D
~D
Fig. 18. Two-dimensional model, cross-section dimension.
G. Galli et al. / Computers and Geotechnics 31 (2004) 171–183 181
Load case 7. 10% further relaxation of the nodal
forces.
Load case 8. Activation of concrete invert arch.
Load case 9. Relaxation of 40% of the nodal forces.
The 2D model results are given in Figs. 19 and 20,
and show that the stress and displacement distribution
in the soil is similar to the corresponding 3D distribu-
tion.Specifically, with the assumed sequence of nodal force
release, the settlement values at the tunnel cross-section
heading are almost coincident for 2D and 3D model.
In this sense the 3D and 2D model results can be
correlated.
However, the results of the 2D model generally
strongly dependent on the choice of the fraction of no-
dal forces release, as shown in Fig. 21, where the exca-vation and lining procedure, is simulated with the
following load cases:
Load case 1. Deactivation of all beams elements.
Load case 2. Soil weight application.
Load case 3. Deactivation of ground elements and
relaxation of 40% of the nodal forces.
Load case 4. Activation of steel beams.
on and lining completed, load case 9).
Fig. 20. Heading displacements in 2D model.
Fig. 21. Heading displacements in 2D model, second procedure.
182 G. Galli et al. / Computers and Geotechnics 31 (2004) 171–183
Load case 5. 30% further relaxation of the nodal
forces.
Load case 6. Activation of shotcrete support.
Load case 7. 20% further relaxation of the nodal
forces.
Load case 8. Activation of concrete invert arch.
Load case 9. Relaxation of 10% of the nodal forces.
This numerical simulation gives values of the settle-ments at the tunnel cross-section heading very different
with respect to the values of the 3D model.
6. Conclusions
The numerical investigation developed in this study
has shown the possibility to simulate the tunnelling ex-cavation and lining phases using a standard FEM
commercial software.
The use of 3D models can be useful to analyse the real
sequence of soil excavation, face reinforcing and tunnel
lining.
The FEM technique of activation/deactivation of the
structural elements is helpful to develop a simple pro-
cedure for the excavation phases.The numerical results show the efficiency of 3D model
to analyse the face deformation and the ground settle-
ments in the soil, and to evaluate the stress in the lining
elements in the subsequent construction phases.
References
[1] Pelli F, Kaiser PK, Morgernstern NR. Three dimensional
simulation of rock liner interaction near tunnel face. In: Proceed-
ings of the 2nd International Symposium on Numerical Models in
Geomechanics, Ghent; 1986. p. 359–68.
[2] Geisler H, Wagner H, Zieger O, Mertz W, Swoboda G. Practical
and theoretical aspects of the three dimensional analysis of finally
lined intersections. In: Proceedings of the 5th International
Conference on Numerical Methods in Geomechanics, Nagoya;
1985. p. 1175–83.
[3] P€ottler R. Three-dimensional modelling of junction at the channel
tunnel project. Int J Numer Anal Methods Geomech 1992;16:683–
95.
[4] Gioda G, Swoboda G. Developments and applications of the
numerical analysis of tunnel in continuous media. Int J Numer
Anal Methods Geomech 1999:1393–405.
[5] Negro A, de Queiroz PIB. Prediction and performance: a review
of numerical analyses for tunnels. In: Kusakabe O, Fujita K,
Miyazaki Y, editors. Geotechnical aspects of underground con-
struction in soft ground. Rotterdam: Balkema; 2000. p. 409–18.
[6] Swoboda G, Mertz W, Schmid A. Three-dimensional numerical
model to simulate tunnel excavation. In: Proceedings of the 3rd
International Conference on Numerical Models in Geomechanics.
Niagara Falls; 1989. p. 536–48.
[7] Swoboda G, Abu-Krisha A. Three-dimensional numerical mod-
elling for TBM tunnelling in consolidated clay. Tunnel Under-
ground Space Technol 1999;14(3):327–33.
[8] Callari C. The application of a strong-discontinuity FEM to the
analysis of strain localization induced by underground openings.
In: Pande GN, Pietruszczak S, editors. Proceedings of the 8th
International Symposium on Numerical Models in Geomechanics
– NUMOG VIII. Rotterdam: Balkema; 2002. p. 163–70.
G. Galli et al. / Computers and Geotechnics 31 (2004) 171–183 183
[9] Dias D, Kastner R. Three dimensional simulation of slurry shield
tunnelling. In: Kusakabe O, Fujita K, Miyazaki Y, editors.
Geotechnical aspects of underground construction in soft ground.
Rotterdam: Balkema; 2000. p. 351–6.
[10] Tang DKW, Lee KM, Ng CWW. Stress paths around a 3-D
numerically simulated NATM tunnel in stiff clay. In: Kusakabe O,
FujitaK,MiyazakiY, editors.Geotechnical aspects ofunderground
construction in soft ground. Rotterdam: Balkema; 2000. p. 443–9.
[11] Yoo CS, Shin HK. Behaviour of tunnel face pre-reinforced with
sub-horizontal pipes. In: Kusakabe O, Fujita K, Miyazaki Y,
editors. Geotechnical aspects of underground construction in soft
ground. Rotterdam: Balkema; 2000. p. 463–8.
[12] Nakai T,MatsubaraH,Kusunoki S. Effects of excavation sequence
on 3-D settlement of shallow tunnels. In: Kusakabe O, Fujita K,
Miyazaki Y, editors. Geotechnical aspects of underground con-
struction in soft ground. Rotterdam: Balkema; 2000. p. 403–8.
[13] Guedes deMeloPFM,SantosPereiraC.The role of the soilK0 value
in numerical analysis of shallow tunnels. In: Kusakabe O, Fujita K,
Miyazaki Y, editors. Geotechnical aspects of underground con-
struction in soft ground. Rotterdam: Balkema; 2000. p. 379–
84.
[14] Kielbassa S, Duddeck H. Stress–strain fields at the tunnelling
face – three dimensional approach for two-dimensional
technical approach. Rock Mech Rock Engrg 1991;24:115–
32.
[15] Pierau B. Tunnel design with respect to the three-dimensional
state of stress and displacements around the temporary face. In:
Proceedings of the 4th International Conference on Numerical
Methods in Geomechanics. Edmonton; 1992. p. 1221–
31.
[16] Fea Ltd. 66, High Street Kingston Upon Thames,
Surrey.