Numerical simulations of SFRC precast tunnel segments

Underground Space Use: Analysis of the Past and Lessons for the Future – Erdem & Solak (eds)
© 2005 Taylor & Francis Group, London, ISBN 04 1537 452 9
Numerical simulations of SFRC precast tunnel segments
G.A. Plizzari & L. Cominoli
Department of Engineering Design and Technologies, University of Bergamo, Italy
ABSTRACT: The paper addresses precast tunnel segments for the new Line 9 of the Barcelona (Spain) Metro
where the conventional reinforcement (rebars) may be partially substituted by steel fibers.
After the experimental determination of the material properties, NonLinear Fracture Mechanics analyses
allowed to study the structural behavior of the tunnel segments with different types of reinforcement. Finally, an
optimized reinforcement, based on a combination of rebars and steel fibers, is proposed.
1 INTRODUCTION
Fiber Reinforced Concretes (FRC) are composite materials
with a cementitious matrix and a discontinuous
reinforcement (the fibers) that may be made of metal,
glass, synthetic or natural materials.
After almost four decades of research, mechanical
properties of FRC have become well known, Standards
for material characterization are widely available and
design guidelines have been recently proposed
(Naaman & Reinhardt, 2003; di Prisco et al., 2004;
RILEM, 2002).
Among the structural applications of FRC, there is
a growing interest in precast tunnel segments to be
used with the Tunnel Boring Machine (TBM), where
steel fibers may substitute, partially or totally, the
conventional reinforcement (rebars).
In the present paper, the structural behavior of the
tunnel segments for the new Metro line (Line 9) of
Barcelona (Spain) are numerically simulated with FE
analyses based on Non Linear Fracture Mechanics
(NLFM; Hillerborg et al., 1976).
The new TBM-excavated tunnel of Barcelona has a
diameter of about 12 m, a length of more than 40 km
and is located from 30 to 70 m below the surface. The
tunnel is made of 7 segments with a length of about
4.70 m and 1 key segment of half that length (Fig. 1).
According to the original design project, the segments
are made of conventional reinforcement with
an addition of steel fibers whose contribution to the
bearing capacity of the segment was not taken into
account. In fact, the fibers were incorporated only to
control cracking that may occur during handling and
placing of the segments.
After the experimental characterization of the
material properties of FRC with two types of steel
1105
Figure 1. Transverse section of the tunnel for the new
line (9) of the Barcelona Metro with evidenced the 8 tunnel
segments (Gettu et al., 2004).
fibers, NLFM analyses allowed to study the structural
behavior of the segments with several combinations
of reinforcement under different loading conditions.
The numerical model was previously validated by
using the experimental results on full-scale tests performed
in Barcelona (Gettu et al., 2004).
Finally, an optimized reinforcement, based on a
combination of rebars and steel fibers, is proposed.

Table 1. Concrete composition (quantities refer to 1 m 3 ).
2 MATERIALS
Weight [Kg] Volume [l]
Cement Portland 52,5R 425 134,92
Water 142 142
Superplasticiser – 3,20
Aggregates 1885 699,88
Air assumed – 20,00
Water/cement ratio 0,33 –
Table 2. Geometrical characteristic of the fibers.
Fiber L f � f L f/� f
code [mm] [mm] [-] Fiber shape
Wirand 50.0 1.00 50.0
FF1
Wirand 50.0 0.75 67.0
FF3
The concrete matrix was made with cement CEM I
52.5R (UNI-ENV 197) and a natural river gravel with
a rounded shape and a maximum diameter of 15 mm;
its composition is summarized in Table 1. The grain
size distribution of aggregates was chosen very close
to the Bolomey curve by using nine classes of aggregates.
An acrylic based super-plasticizer was used.
The two different types of fibers that were considered
in this research are reported in Table 2 where
the fiber length (L f), the fiber diameter (� f) and the
aspect ratio (L f/� f) are shown. All the fibers are cold
drawn, have a hooked shape, a rounded shaft and a
tensile strength higher than 1100 MPa.
Fibers with an aspect ratio equal to 50 (FF1) were
used with two different volume fractions (V f), equal
to 0.45% (35 kg/m 3 ) and to 0.58% (45 kg/m 3 ). Fibers
with a higher aspect ratio (FF3) were used with a
lower dosage, equal to 25 kg/m 3 (V f � 0.32%) and to
35 kg/m 3 (V f � 0.45%).
Eight beam specimens were made for each type of
SFRC; in addition, 8 beams of plain concrete were
used as reference specimens.
The slump(s) of the fresh concrete was always
greater than 150 mm.
Specimens were stored in a fog room (R.H. � 95%;
T � 20 � 2°C) until 24 hours before testing.
Table 3 reports the mechanical properties of concrete
(average values), as determined after about
60 days of curing; in particular, tensile strength (f ct)
from cylinders (� �80 mm, L � 240 mm), compressive
strength from cubes (f c,cube) having 150 mm side
and Young’s modulus (E c) from compression tests on
cylinders (� �80 mm, L � 240 mm), are reported.
1106
Table 3. Mechanical properties of concrete (average values).
f c,cube [MPa] f ct [MPa] E c [GPa]
FF1 64.7 64.1 4.11 4.07 38.8 38.1
FF3 63.5 4.04 37,4
Figure 2. Geometry (a) and instrumentation (b) of the
notched specimen for the beam tests.
Fracture properties were determined from notched
beams (150 � 150 � 600 mm) tested under four point
bending according to the Italian Standard (UNI, 2003;
Fig. 2a). The tests were carried out with a closed-loop
hydraulic testing machine by using the Crack Mouth
Opening Displacement (CMOD) as a control parameter,
which was measured by means of a clip gauge
positioned astride a notch in the mid-span, having a
depth of 45 mm (Fig. 2a). Additional Linear Variable
Differential Transformers (LVDTs) were used to
measure the Crack Tip Opening Displacement (CTOD)
and the vertical displacement at the beam mid span
and under the load points (Fig. 2b).
Figure 3 shows typical experimental results from
bending tests on beams with fibers FF1.
Inverse analyses of the bending tests, based on
NLFM, allowed to determine the best-fitting softening
law for the SFRCs adopted in the present research
(Roelfstra & Wittmann, 1986). The Young’s modulus
(E c) was the one experimentally measured from the

Nominal Stress σ N [MPa]
Nominal Stress σ N [MPa]
6
5
4
3
2
1
R60- FF1 - 35 kg/m 3 - V f =0,45%
0
0.0 0.1 0.2 0.3 0.4 0.5
9
8
7
6
5
4
3
2
1
CTOD m [mm]
Experimental
Numerical
R60- FF1 - 45 kg/m 3 - V f =0,57%
Experimental
Numerical
0
0.0 0.1 0.2 0.3 0.4 0.5
CTOD m [mm]
Figure 3. Experimental and numerical results obtained
from beam tests on beams with fibers FF1.
Figure 4. Bilinear law for the approximation of the postcracking
behavior of SFRC.
cylinders while the Poisson ratio (�) was assumed
equal to 0.15. The softening law was approximated as
bilinear where the first steeper branch can be associated
with (unconnected) micro-cracking ahead of the
stress-free crack while the second branch represents
the aggregate interlocking or the fiber bridging (Fig. 4).
The numerical analyses were initially performed by
assuming both a discrete crack approach with Merlin
(1994) and a smeared crack approach with Abaqus
(release 6.4.1; 2003); the latter was also used for the
numerical simulations of the tunnel segments.
(a)
(b)
1107
Figure 5. Mesh adopted for the numerical simulations of
the beam tests based on a discrete crack approach.
Table 4. Parameters for the bilinear softening law for
cracked concrete.
SFRC V f (%) f ct [MPa] w 1 [mm] � 1 [MPa] w cr [mm]
FF1 0.45 4.1 0.031 1.450 3.50
0.58 4.1 0.023 2.134 5.35
FF3 0.32 4.1 0.031 1.227 3.2
0.45 4.1 0.028 1.505 3.9
Figure 5 shows the mesh used for Merlin with triangular
plain stress elements and interface elements
for the crack. The material parameters identified from
the bending tests (f ct, � 1, w 1, w cr) are summarized in
Table 4. The best-fitting numerical curves obtained
with Merlin are compared with the experimental ones
in Figure 3.
2 VALIDATION OF THE FE MODEL
Experimental studies on the tunnel segments for the
Barcelona Metro were carried out by Gettu and
co-workers (2004) at the Universitat Politècnica de
Catalunya. The studies aimed to study the possibility
of using only fiber reinforcement in the tunnel segments
(without any conventional reinforcement). The
experimental program included the material characterization
and structural scale tests under critical loading
conditions: flexure, concentrated in-plane loads and
possible stress concentrations in the joints between
segments of the same ring.
The experimental results were used to validate the
FE model used in the present research work. In particular,
the simulation of the bending tests performed
under three point loading is presented herein. These
tests aimed to simulate the inadequate filling of the
space between the lining and the excavated surface
(Gettu et al., 2004; Fig. 6). Figure 7 shows the configuration
of a bending test.
Figure 8a shows a comparison between the experimental
and the numerical load-deflection curve for
specimens reinforced with both conventional and
fiber reinforcement as well as for specimens with
steel fibers only. The good agreement between the
numerical and the experimental results should be
noticed. A further comparison, shown in Figure 8b,

Figure 6. Motivation for the flexure tests performed at
UPC (Gettu et al., 2004).
Figure 7. Configuration of the flexure test (Gettu et al.,
2004).
Figure 8. Comparison between the numerical curves and
the experimental load displacement (a) and load-crack opening
(b) curves obtained by Gettu et al., (2004) for two different
materials.
1108
concerns the crack opening displacement measured
in the mid-section (Fig. 7); once again, the numerical
curves fit the experimental ones quite well.
4 DESIGN ASPECTS
An open question for the construction companies and
the precast industry concerns the reinforcement for
these precast elements. In fact, a heavy conventional
reinforcement is undesired in the construction process
due to the placement of many curved rebars and for
pouring the fresh concrete. Figure 9 shows the conventional
reinforcement adopted for the segments of
the Barcelona Metro that, as already mentioned, also
included 30 kg/m 3 of steel fibers (FF1).
In order to verify the structural behavior of the tunnel
segments towards an optimization of the reinforcement,
several NLFM analyses were performed
in the present research work. Based on the material
properties described in §2, the damaged plasticity
model provided in ABAQUS 6.4.1 (2003) was adopted
for the FE simulations of the tunnel segments. The
numerical analyses were carried out by adopting a 3D
solid model with 4032 first order hexahedral elements
(C3D8-eight node linear brick elements). The
constitutive law for concrete under compression was
assumed according to EC2 (2003).
The actions on the tunnel segments result from transportation,
placing process and soil pressures in the
final state. The numerical results concerning the high
compression force exerted by the 30 TBM actuators
on the ring during excavation are presented herein.
The service load applied by a single actuator for the
Barcelona Metro was 3 MN.
One single segment with four actuators was considered
for the numerical analyses and its boundary
conditions (i.e. presence of the adjacent segments)
were simulated by elastic springs whose stiffness was
calibrated with previous FE analyses of the full ring.
Figure 9. Caption of a typical figure. Photographs will be
scanned by the printer. Always supply original photographs.

Structural behavior of segments with different types
of reinforcement was compared. Numerical results
from segments with conventional reinforcement only
(RC), with rebars and 35 kg/m 3 of fibers (RC35FF1,
similar to the reinforcement adopted in Barcelona), or
with 45 kg/m 3 of fiber reinforcement only (45FF1),
are presented. To better evaluate the reinforcement
effects, a reference specimen of plain concrete was
also considered. Figure 11 shows the numerical results
in terms of load (from four actuators) versus the longitudinal
displacement of the middle section (average
value under the four loading areas). One can notice
the brittle failure of the plain concrete specimen and
the minor contribution of fibers to the bearing capacity
of the segment with conventional reinforcement.
Specimens with fibers only have the same ultimate
load but it is reached with larger displacements and,
therefore, larger crack openings.
To better understand the structural behavior of segments
with fiber-reinforcement only, Figure 12 shows
the load-displacement curve of the specimen with
45 kg/m 3 of fibers FF1, without conventional reinforcement.
It can be noticed that a splitting crack starts
to open at the service load and that, because of the
stress-redistribution along the longitudinal direction
Figure 10. Scheme of a segment with the load from four
actuator and the springs representing the neighbor segments.
Load [kN]
30000
25000
20000
15000
10000
5000
0
Tunnel Segments: Non Linear Analyses, Comparison
45FF1 Plain
RC RC35FF1
RCO35FF1
0 1 2 3 4 5 6
Displacement [mm]
Figure 11. Comparison between the load-displacement
curves as obtained from specimens with different types of
reinforcement.
1109
of the segment, this crack can propagate in a stable
way up to the ultimate load which is almost twice the
service load.
The distribution of radial stress � r (see Fig. 13)
along the longitudinal section at the service load is
represented in Figure 14; one can notice the tensile
stresses under the actuator (on the left side) up to a
distance from the segment surface of about 400 mm.
Figure 12. Caption of a typical figure. Photographs will be
scanned by the printer. Always supply original photographs.
Figure 13. Reference system adopted for stresses and
strains.
Stress σ R [MPa]
3
2
1
-2
-3
-4
Radial Stress, Fiber FF1-45
0
0 200 400 600 800 1000 1200 1400 1600 1800
-1
Distance [mm]
Service Load
Figure 14. Distribution of radial strains � r along the longitudinal
section of the element under service loads.

Figure 15. Distribution of radial strains � r under service
loads.
Stress σ R [MPa]
2,5
2
1,5
1
0,5
0
Radial Stress, Fiber FF1-45
Point 1
Point 2
Point 3
0 1000 2000 3000 4000 5000 6000
Force of the hydraulic jack [kN]
Figure 16. Distribution of the radial stresses (� r) at three
different distances under the loading area of the actuator.
Figure 17. Optimized rebars proposed for the tunnel segment
(the reinforcement in the middle of the specimen is
provided by 35 kg/m 3 of fibers FF1.
Figure 15 shows the 3D distribution of the radial
strains (in plane x-r of Figure 13) in the element under
service load (3 MN in 4 actuators), and evidences
the strain concentration under the actuators (some
1110
Table 5. Reinforcement and maximum load obtained form
the segments.
Reinforcement [kg/m3 ]
Rebars Fibers Total
Max. Load
[kN]
Plain – – – 21024
45FF1 – 45 45 24016
RC35FF1 97 35 132 24234
RC 97 – 97 24232
RCO35FF1 31 35 66 24943
elements are removed to better show the strains inside
the element).
The load increase in the SFRC elements is possible
because of the stress distribution along the longitudinal
section of the segment. This is clearly evidenced
in Figure 16 that reports the radial stresses vs. the
load at three different distances under the loading
area (100, 200 and 300 mm; Fig. 13).
The previous numerical results showed that the
use of fiber reinforcement with only 3 MN actuators
may provoke larger crack openings and that tensile
stresses are mainly concentrated in the first 30–40 cm
under the actuators. In order to optimize the reinforcement
of the tunnel segment, the rebars could be
limited to the chords along the two longer sides (that
are loaded by the actuators), as shown in Figure 17.
The corresponding numerical results are shown in
Figure 11 (RCO35FF1); note that the load displacement
curve is very similar to the one related to the full
conventional reinforcement with steel fibers. These
results evidence that, although the considered loading
condition is very severe, a lot of conventional reinforcement
adopted in Barcelona may be substituted
by steel fibers.
Table 5 reports the different amounts of steel reinforcement
(fibers and rebars) considered for the tunnel
segments and the corresponding ultimate load. It can
be noticed that the proposed optimized reinforcement
guaranties the same ultimate load and allows a savings
of half of the reinforcement adopted in Barcelona.
5 CONCLUDING REMARKS
The present paper shows results of a numerical study
of precast tunnel segments for the new Line 9 of the
Barcelona Metro. Numerical analyses were performed
under the assumptions of NLFM.
The numerical model allows a good approximation
of the experimental results from full-scale tests
obtained at the Universitat Politècnica de Catalunya.
The total reinforcement adopted in Barcelona may
be reduced by using an optimized combination of
conventional and fiber reinforcement.

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ACNKNOWELEDGEMENTS
The research project was financed by Officine
Maccaferri S.p.A. (Bologna, Italy) whose support is
gratefully acknowledged. A special thanks goes to
Prof. Paolo Riva for his useful suggestions for the
numerical model and to Engineer Giuseppe Tiberti
for his assistance in carrying out the beam tests and
the numerical analyses.