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Tailor Made Concrete Structures Walraven & Stoelhorst (eds)
2008 Taylor & Francis Group, London, ISBN 978-0-415-47535-8
Concrete tunnel segments with combined traditional andfiber
reinforcement
G. Tiberti & G.A. PlizzariUniversity of Brescia, Brescia,
Italy
J.C. WalravenDelft University of Technology, Delft, The
Netherlands
C.B.M. BlomDelft University of Technology and Public Works
Rotterdam, The Netherlands
ABSTRACT: The paper deals with the concrete lining behaviour at
Serviceability Limit State (SLS) in order toevaluate the advantages
that result from an optimized reinforcement based on the
combination of rebars and fiberswith respect to the crack behaviour
of segmental lining. For Serviceability Limit State, an analytical
model wasdeveloped to describe the tension stiffening of a concrete
element reinforced with traditional rebars and fibers.A parametric
study was carried out to better understand the behaviour of
segmental lining with different tunneldepth projections. It is
shown that fibers can substitute part of conventional reinforcement
and, as additionalbenefit, significantly improve cracking behaviour
of the segment.
1 INTRODUCTION
Fiber ReinforcedConcrete (FRC) is a compositemate-rial with a
cementitious matrix and fibers as discon-tinuos reinforcement. FRC
is already widely used instructures where fiber reinforcement is
inessential forintegrity and safety, as in industrial pavements or
asshotcrete in early stage linings of conventional tunnel-ing
(Rossi & Chanvillard, 2000; di Prisco et al. 2004).
For structural applications, steel fibers representthe
traditional fiber reinforcement even though severalsynthetic fibers
are nowadays available into the mar-ket. Steel fibers remarkably
enhance concrete tough-ness under tensile loading; therefore, the
material isable to sustain higher tensile stresses after
cracking.
Among the structural applications of FRC (Ahmadet al. 2004),
there is a growing interest in precast tunnelsegments. FRC could be
a competitive design alterna-tive for these precast segments as it
would substitutepart of conventional reinforcement to allow for
timereduction in handling and placing of the curved rebars.
In previous research works (Plizzari & Cominoli,2005), it
was demonstrated that a proper combinationof fibers and rebars
(RC+FRC) could be a competi-tive solution for concrete tunnel
segments at UltimateLimit State (ULS).
In the present paper, the structural behaviour of tun-nel
segments at Serviceability Limit State (SLS) isinvestigated in
order to quantify the benefits in terms
of crack control due to the presence of fibers. In par-ticular,
a simple analytical model is derived in order todescribe the
tension stiffening of a concrete element,including the fiber
contribution.
The results are applied to a case study of a tun-nel lining with
an internal diameter of 14,9m and athickness of 675mm. The tunnel
design depth pro-jection is approximately 27,4m (measured from
thecenter line of the lining); therefore the tunnel over-burden is
equal to 19,3m (1,2 times the internaldiameter D).
A parametric study was carried out by consider-ing several
reinforcement combinations and differenttunnel depth
projections.
2 DESIGNASPECTS
Precast segments for tunnel lining are generally madeof
ordinaryReinforcedConcrete.An open question forthe construction
companies and the designers concernsthe reinforcement for these
precast elements. Gener-ally, the reinforcement should be designed
accordingto two main loading conditions: the embedded soilpressure
and the uplift pressure duringgrouting. In par-ticular, previous
studies (Blom, 2002) show that withthe latter loading case (grout
pressure) the soil supportsignificantly influence the safety of the
lining.
199
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Figure 1. Cracks that typically appear in segmental
tunnellinings during the construction phase.
However, other possible additional local mecha-nisms, which can
cause cracking in the linings, shouldbe taken into account. These
mechanisms are corre-lated to the application of thrust jack forces
or to anumber of phenomena due to the trumpet shape
(Blom,2002).
Previous research works clearly evidence the ben-eficial effects
of Steel Fiber Reinforced Concrete(SFRC) in presence of load
concentrations and split-ting phenomena that arise in tunnel
segments becauseof the introduction of thrust jack forces (deWaal,
1999,Plizzari & Tiberti, 2006). Cracks often appears in
thetunnel lining under the loading conditions mentionedabove. Some
examples of cracks that typically appearin segmental tunnel linings
are shown in Figure 1. Pos-sible causes of these cracks could be
eccentricity orinclination of the thrust jacks (Burgers et al.
2007).
It is desirable to mitigate or reduce these cracksas much as
possible since they determine a loss ofquality, leakage and high
repair costs. Cracking phe-nomena can be limited in tunnel design
by using, forexample, a proper configuration of the thrust jacks
andsupports. Alternatively, they can be reduced by usingan
opportune combination of FRC and conventionalreinforcement
localized in proper regions of the pre-cast tunnel segment, as
shown in Figure 2 (Plizzari &Tiberti, 2007). It consists of an
optimized reinforce-ment based on the combination of fibers and
rebarswhich are localized on the external chords.This under-lines
that the optimized reinforcement of concretestructures can be
obtained by combining conventionalreinforcement (rebars or welded
mesh) for localizedstresses and structural fibers for diffused
stresses.
The term structural fibers refers to fibers havinga high elastic
modulus and adopted with a dosage ableto guarantee a minimum FRC
performance in terms oftoughness.
The concentration of rebars in the external chordsof tunnel
segmentsmay be useful for practical reasons.In fact, it is expected
that segments belonging to thesame ring can hardly stay in a
perfect plane becauseof the irregularities that are normally
present (Fig. 3a).Therefore, the tunnel segments are not supported
uni-formly by the previous ring, as shown in Figure 3a and
Figure 2. Optimized reinforcement proposed for tunnelsegment
based on a combination rebars and fibers in FRC.
gap
crack
gapgap
crackcrackcrack
(a) (b)
Figure 3. Possible gap between rings due to a no-perfectplacing
process (a); possible irregular support configura-tion (b).
a bending moment arises in the segment; this moment,in
unfavorable cases (for example, when only two sup-ports are present
at the extremities) may cause thecracks shown in Figure 1 and in
Figure 3b. It is clearthat, in these cases, the adoption of fiber
reinforcementonly, can not compete with the concentrated rebars ina
load condition governed by bending that produceslocalized stresses.
However, even under very severeload condition, it was proven that
the optimized rein-forcement provides a better behaviour than the
solutionusually adopted in practice (with rebars distributedalong
the segment; Plizzari & Tiberti, 2007).
Moreover, it is well known that, by adding steelfibers, it is
also possible to significantly reduce theamount of stirrups that
are normally placed for increas-ing shear strength as well as the
resistance to splittingstresses that are present under the jacks
during thethrust phase. Since the shear forces in the final
state(embedded soil load condition) are relatively small,the
minimum shear reinforcement required could bereplaced by fiber
reinforcement (Plizzari & Tiberti,2007).
When referring to service conditions (SLS), itshould be observed
that, by using FRC, the lining
200
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Figure 4. Tunnel lining longitudinal section considered
asreference.
behaviour will significantly improve because of thebenefits in
terms of crack control due to the presenceof fibers.
The behaviour of the lining with combined rein-forcement (rebars
and fibers) at SLS will be discussedin the following Sections. It
should be reminded thattunnel linings are generally structures
characterizedby low reinforcement ratios where the crack open-ing
control could play a relevant role in structuraldesign.
3 ANALYTICALAPPROACH
A simple analytical procedure to estimate the crackwidth
expected in the lining under service loads isproposed in this
Section. In particular, an analyticalmodel was developed to
evaluate the maximum bend-ing moment achievable in the longitudinal
section,without exceeding a certain maximum
crack-opening(wmax).
For a tunnel lining, this issue implies the estima-tion of the
bending moment under a specific axialforce (NSLS ). The analytical
model developed hereinis principally based on 3 steps (Tiberti et
al. 2008):
1) study of the sectional response of the tunnel lin-ing:
evaluation of the resistant bending moment-curvature diagram under
a certain axial force,NSLS;
2) determination of the resistant bending moment(MSLS)-average
crack opening diagram;
3) steps 1) and 2) are repeated for different normalaxial forces
(NSLS) that correspond to differenttunnel depth projections. As a
result, a domainMwmaxSLS (corresponding to
amaximumcrackopeningwmax) vs. tunnel depth can be determined.
3.1 Geometrical characteristic of thelining section
The longitudinal section shown in Figure 4, referringto a tunnel
width of 1m, was adopted as reference forthe case study considered
herein. A lining thicknessof 675mm was assumed (it corresponds to
1/22 of thetunnel diameter).The longitudinal steel ratio is equalto
0,21%.
Table 1. Mechanical properties of concrete C45/55.
Des. ValueCharact. Value Av. Value (ULS)
Class of fck Rck fctk fcm fctm Ecm fcd fctdstrength [MPa] [MPa]
[MPa]
C45/55 45 55 2,7 53 3,8 33500 30
s
e
fctm
fctm
=0, Plain
FRC0,80FRC0,50FRC0,25Plain0Typec
Figure 5. Post-cracking behaviour, constitutive lawsadopted for
FRC and Plain concrete.
3.2 Material properties
The study was performed by referring to a normalstrength
concrete C45/55. The mechanical propertiesof concrete were
determined according to Eurocode 2(EC2, 2005; Table 1). The
concrete elastic moduluswas assumed equal to 33500MPa, since the
samevaluewas adopted by Blom et al. (2007) for determining
theinternal actions (axial force and bendingmoment), dis-cussed in
Section 5.Mechanical properties of concreteand steel refer to the
average values in order to betterestimate the crack openings at
SLS.
The constitutive law proposed by EC2 for con-crete under
compression was adopted. A very simpletension softening
constitutive law was assumed todescribe the post-cracking behaviour
of FRC undertension. In fact, after cracking, a constant branchwas
used to describe the residual tensile strength ofFRC. This strength
is obtained by multiplying theaverage tensile strength (fctm) for a
multiplier fac-tor (1; Fig. 5). This performance law was
chosenwithout any explicit correlation to a fiber content. Inthis
way, designers could develop their calculationsjust assuming a
certain FRC performance level, withrespect to its post-cracking
behaviour. Eventually, con-crete technologists should provide an
appropriate mixdesign to achieve the required performance for
FRCpost-cracking behaviour.
The following values were considered in orderto simulate
different FRC performances: = 0 (plainconcrete), = 0,25, 0,50 and
0,80 (Fig. 5).
201
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Figure 6. Scheme of the development of stresses in
thetransmission disturbed area.
The conventional reinforcement consists of twolayers of rebars
B500C with a diameter () equalto 12mm whose characteristic yield
strength (fyk) is500MPa. An average yield strength, fym = 575MPaand
an elastic modulus of 200000MPa were assumed.An ideal
elastic-plastic law was used to describe thebehaviour of steel
under tension and compression.
3.3 Tension stiffening local analytical model
The tension stiffening concerns of the average ten-sile
resistant contribution provided by the uncrackedconcrete present
between two consecutive cracks.
The analytical model proposed byWalraven (1999)was adopted to
properly describe the tension stiffeningof a RC tunnel lining
section. This model describesthe behaviour of a RC tensile bar and
is based on thefollowing hypotheses:
1) a constant bond stress (bm) is present betweenconcrete and
rebar (Fehling and Konig, 1988;Fig. 6);
2) where cracks are present, the stresses in plainconcrete drop
down to zero (Fig. 6).
Fibers link the cracks that exhibit a noticeable localtension
softening behaviour with respect to a plainconcrete (Figs. 5 and
6). In order to study the sec-tional response of RC+FRC tunnel
lining section, itwas necessary to modify the tension stiffening
model,including the FRC residual tensile strength.
Figure 6 shows a scheme representing the behaviourat the
location of cracks of a tensile bar in plain con-crete and in a FRC
concrete element; the transmissionlength (lt) is evidenced.
By adopting Equation 1 that was developed byTiberti et al.
(2008), a considerable reduction of thetransmission length (lt) can
be achieved. Therefore,the use of fibers in combination with
conventionalreinforcement allows for a reduction of the average
Figure 7. Tension stiffening laws adopted to describe
thebehaviour of RC and FRC tensile bar.
Figure 8. Scheme of the sectional response of the tunnellining
longitudinal section.
crack spacing srm (Eq. 2), which result in a more uni-form crack
pattern. As a consequence a smaller crackopening is expected.
As an example, the tension stiffening law vs. theaverage steel
strain are plotted in Figure 7. Noticethat the tension stiffening
contribution was assumedto decrease progressively to zero when
rebars yield atcrack locations (Fig. 7).
In all the derivations it was assumed that the rein-forcing
steel was uniformly distributed over the crosssection (Tiberti et
al. 2008). In order to study the sec-tional response of a tunnel
lining, the behaviour of thetensile bar was adopted for simulating
an effective ten-sile area (around the main reinforcement) of a
beam(Leonhardt 1976; Fig. 8).
The approach introduced by Fehling & Konig(1988) was used in
order to estimate the height of theeffective tensile area, heff
(Fig. 8) that is equal to:
The tunnel lining sectional response at SLS wascalculated by
applying the proposed local tension
202
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stiffening law (for plain and FRC concrete) over theeffective
tensile area, as shown in Figure 8.
4 LINING BEHAVIOURAT SLS
Results presented in this paragraph refers to a shallowtunnel
depth configuration with a tunnel overburdenof 19,3m (1,2 times the
internal diameter).
The following types of reinforcementwere adopted:RC (reference
design solution), RC+FRC by adopt-ing the following values:
0,250,500,80. The lon-gitudinal steel ratio (= 0,21%) was the same
for allthe configurations.
The comparison of the resistant bendingmoment vs.crack opening,
determined with the proposed modelfor the different reinforcement
combinations adopted,is presented in Figure 9.The diagrams clearly
evidencethe benefits provided by fibers in combination withregular
rebars at SLS. In fact, the RC+FRC config-urations exhibit higher
resistant bending moments forthe same crack opening. As expected,
fibers provide abetter crack control. The results are also plotted
in thesame figure in term of percentage of increment. Theincrement
of the resistantmoment (M,expressed as apercentage) was calculated
according to the followingrelationship:
Notice that the RC+FRC solutionwith a value of0,8 is able to
guarantee, for a crack opening of about0,1mm, the maximum increment
of resistant bend-ingmoment (about 45%).The RC+FRCwith =
0,5configuration exhibits an increment of 25% for a crackopening of
0,2mm.
The reinforcement types adoptedwere also checkedat ULS; as
expected, the RC+FRC (= 0,80) con-figuration exhibits a maximum
bending moment only5,3% higher than the one with rebars only. Since
atULS the main issue is the ultimate bearing capacity,it turns out
that the rebars play the major role whilethe fiber resistant
contribution at that limit state isnegligible.
Figure 9 also shows that it is possible to estimate therange of
crack opening where a certain fiber contentcould be effective at
SLS. In fact, for crack openingsfrom 0,2 to 0,3mm, it turns out
that the RC+FRCwith = 0,50 shows an average increment percentage(M)
similar to the one with = 0,80, although thefiber content is
lower.
A parametric study considering several tunnel depthprojections
(range of tunnel overburden from 0,4D to4,51D) was performed. It
was possible to carry out thedomain MwmaxSLS vs. tunnel depth
projection, for a spec-ified maximum crack opening, wmax (the RC
solution
Figure 9. Comparison between different
reinforcementcombinations: resistant bending moment vs. average
crackopening. Diagrams are referred to the design tunnel
depthprojection.
Figure 10. Resistant bending moments achievable for dif-ferent
required crack opening, according to different tunneldepth
projections.RC+FRC (= 0,50) andRC tunnel liningsection.
was adopted as reference). In the domain, the tunneldepth is
measured from the center line of the lining.
A comparison of the proposed domains (forRC+FRC with = 0,50 and
RC) is presented inFigure 10. Notice that, by considering a certain
tun-nel depth and a required crack opening, the RC+FRCsolution
always guarantee higher resistant bendingmoments.
The percentage of bending moment increment(M) vs. the tunnel
depth projection is plotted inFigure 11 for the RC+FRC = 0, 50
solution, refer-ring to different maximum crack openings. It canbe
observed that the RC+FRC configuration is moreeffective for shallow
depths. As an example, by con-sidering a crack opening of 0,2mm and
a tunnel depthof 19,3m (0,7D), it is possible to achieve a
noticeableincrement of about 32%. For deep tunnels, the incre-ment
drops to about 16%. This phenomenon is corre-lated to the
significant normal ring (axial) forces actingon the tunnel lining
at high depths. When the normalring force is high, the tunnel
lining section behaveslike as a pre-stress concrete structure.
Therefore, thelining section is already able to exhibit a
considerable
203
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Figure 11. Percentage of increment of the resistant
bendingmoment vs. fiber content for different required crack
open-ings and according to different tunnel depths. RC+FRCwith= 0,
50.
Figure 12. Increment of the resistant bending moment asa
function of the tunnel depths for a specified maximumcrack opening
(0,1mm and 0,2mm): comparison betweenthe different reinforcement
types adopted.
bending moment bearing capacity without exceedinga required
crack opening.
A final comparison of the reinforcement combina-tions adopted is
presented in Figure 12 that exhibitsthe moment increment for
different tunnel depths. Themaximum crack openings adopted were
0,1mm (con-tinuous line) and 0,2mm (dashed line). The curveshelp to
estimate the most convenient fiber content ()to be combined with
rebars (whose percentage wasfixed to = 0,21% in this example). This
allows tofind the minimum fiber content which can
provideapproximately the maximum increment of resistantbending
moment. It turns out that, by assuming amaximum crack opening of
0,2mm, the use of highfiber content (RC+FRC with = 0,80)
combinedwith rebars tends to be useless. High fiber content(e.g.=
0,80) are convenient for very low crack open-ings (less than 0,1mm)
which are usually not of maininterest for designers. Therefore, a
RC+FRC with= 0,50 seems to be preferable.
The previous results aims to provide a generaltrend since they
are strictly correlated to the longi-tudinal steel ratio ()
adopted. In fact, by assuming alower value of , the range of
average crack openings
where fiber are more effective (at the moment around0,10,2mm)
moves to higher values. On the otherhand, by increasing the value
of , that rangewill moveto very low values, determining fiber
contribution use-less because, generally, the maximum crack
openingsadopted in design are around 0,20,3mm.
5 CONCLUDING REMARKS
The present paper concerns design consideration forsegmental
tunnel linings, by proposed an optimizedreinforcement for both
Ultimate (ULS) and Service-ability (SLS) Limit States.
The combination of traditional reinforcement(rebars) and fiber
reinforcement was investigated bymeans of an analytical approach
based on the tensionstiffening.
The analytical approach adopted enables to quantifythe
significant benefits provided by fibers in combi-nation with
regular rebars at SLS. It has been proventhat it is possible to
estimate approximately the rangeof crack opening where a certain
fiber content couldbe of great benefit. At ultimate Limit State,
fiber con-tribution to bending resistance is negligible since
thelocalized stresses (due to bending moment) are bettercontrasted
by rebars.
A parametric study of different tunnel depth projec-tions
according to several reinforcement combinationswas carried out. It
turns out that, by increasing the tun-nel depth, fiber becomes less
effective and can be usedonly as minimum reinforcement.
ACKNOWLEDGEMENTS
The Authors wish to express their gratitude to theItalian
Ministry of University and Research (MIUR)for financing this
research work within the NationalProject Optimisation of the
Structural, Technologicaland Functional Performance of Construction
Method-ologies and Materials in Tunnel Linings.
The research work was developed within a jointproject between
University of Brescia and Delft Uni-versity of Technology.
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