Experimental and numerical investigations about textile-reinforced concrete [603848]

Experimental and numerical investigations about textile-reinforced concrete
and hybrid solutions for repairing and/or strengthening reinforced concrete beams
Amir Si Larbia,⇑, Amen Agbossoub, Patrice Hamelina
aLGCIE, Université Lyon 1, 82 bd Niels Bohr, 69622 Villeurbanne Cedex, France
bUniversité de Savoie, LOCIE, CNRS UMR 5271, Campus Scientifique, Savoie Technolac, 73376 Le Bourget du Lac Cedex, France
article info
Article history:
Available online 20 December 2012
Keywords:
TRC (textile-reinforced concrete)
Reinforced concrete beamsCracksStrengtheningExperimentFinite element analysisabstract
This experimental and numerical study is related to the repair and strengthening of reinforced concrete
beams with TRC (textile-reinforced concrete) and hybrid (TRC + carbon and glass rods) solutions that arepositioned relative to the more traditional ones such as the CFRP (carbon fibre-reinforced polymer) solu-
tions. Beyond the good performances highlighted experimentally, especially in terms of bearing capacity
and different failure modes (e.g., possibility to avoid peeling off), it is clear from this work that the TRC,despite its nonlinear behaviour (multi-cracking), does not allow a significant gain in ductility. From anumerical perspective using numerical modelling (smeared crack approach), the overall behaviour of
beams reinforced with TRC (or the hybrid solutions) based only on the textile ‘‘efficiency factor’’ (or
the average contribution of the filaments) as a calibration coefficient was found to be significantly satis-factory. Numerical modelling performed on all the beams also highlighted the fact that the axial stiffness
of reinforcements (even in the case of a cracking material) governing the overall behaviour of beams
could, at least in part, explain the observed failure modes.
/C2112012 Elsevier Ltd. All rights reserved.
1. Introduction
Techniques of repair and/or strengthening of reinforced con-
crete structures are numerous (shotcrete; bonding of metal plates;
prestressed; bonding sheet or plate of fibre reinforced polymer).
However it is the FRP (especially the carbon reinforced polymer)
which is booming these recent years due, in particular, to very
good mechanical performance coupled with ease of implementa-
tion. Nevertheless, this type of solution suffers from the use of an
epoxy resin which emits toxic organic gas during the manufactur-ing process, and high temperature instability which heavily de-
pends on the glass transition temperature of the resin (usually
lesser than 100 /C176C). From this perspective, the solutions fibres
(short)-mineral matrix could be an interesting alternative if the
mechanical performances were not limited by a relatively small
reinforcement ratio (usually less than 3–4% in volume), condi-
tioned by the workability of the mortar, and the impossibility of
controlling the fibre orientation. The use of fibre cement is essen-
tially limited to the secondary structures [1].
To expand the application of the mineral matrix from the sec-
ondary structures to primary load-bearing structures the use of
textile reinforcement instead of short fibres is an interesting
solution and constitute the textile reinforcement concrete (TRC)completed, if necessary, by additional rods. It allows increasing sig-
nificantly the fibre reinforcement ratio (20–30%, [2]). In addition,
the fibre orientation can be adapted to the planned solicitation.
Although sometimes incomplete and uncertain, there has signifi-
cant progress in recent years with respect to knowledge about
TRC (textile-reinforced concrete). The main related studies have fo-
cused on the mechanical characterisation of TRC, the identification
of interaction mechanisms and the stress transfer between the
weave fabric (textile) and the matrix [3–7] . It is now established
that one of the scientific challenges is the difficulty in preciselyquantifying the (rather weak) textile-mortar interaction, which is
greatly influenced by the conditions of application. Nevertheless,
quantifying the interaction remains a potentially attractive option
as long as only concerns of controlling the cracking guide the
strengthening of the beams. In view of the improved ultimate per-
formance, the use of reinforcing rods seems essential given the low
ultimate strength of TRC compared to CFRP (carbon fibre-rein-
forced polymer) if only realistic and economic TRC reinforcement
thicknesses of less than 15 mm are considered.
Few studies have examined the suitability of TRC in structural
applications [8,9] and, more specifically, in its resistance to bend-
ing moment [10].
The repair and strengthening of bending elements with bonded
CFRP reinforcement has been the subject of numerous studies [11–
13]that allow for the characterisation of the bending behaviour
and highlight the transfer mechanisms between the reinforcement
0263-8223/$ – see front matter /C2112012 Elsevier Ltd. All rights reserved.
http://dx.doi.org/10.1016/j.compstruct.2012.12.005⇑Corresponding author. Tel.: +33 616821691.
E-mail addresses: amir.si-larbi@univ-lyon1.fr ,simirau@yahoo.fr (A. Si Larbi).Composite Structures 99 (2013) 152–162
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and the concrete as well as the factors related to the damage and
failure of the beams. It is worth mentioning that the particular fail-
ure mode that characterises the reinforced concrete beams
strengthened by CFRP, known as peeling-off [14,15] , is the result
of a complex stress state at the end of the beam near the reinforce-
ment. Thus, this aspect does not allow for the full benefit of the
solution as the strength (or strain) rate ratio rarely exceeds 60%.
This aim of this work is as follows:
– To study the technological feasibility and the mechanical per-
formance of a solution based on TRC (with and without using
an epoxy resin).
– To compare qualitatively and quantitatively the innovative
solutions with traditional solutions (e.g., CFRP) in terms of ulti-
mate limit states (bearing capacity, failure modes) and servicelimit state (rigidity, opening crack).
– To model the overall behaviour of the TRC-repaired or TRC-rein-
forced beams by considering only the textile ‘‘efficiency factor’’
in evaluating the influence of the axial stiffness of the reinforce-
ments in terms of local stress distribution and the impact in
terms of overall behaviour.
2. Experimental approach2.1. Properties of reinforcing materials
It should be noted that reinforcements adopted in the case of
damaged beams were designed (first approach) with reference to
the French recommendations [16] relating to the repair and
strengthening of reinforced concrete structures using composite
materials to obtain equivalent ultimate capacities.
2.1.1. Textile Reinforced Concrete (TRC)
The use of the composite TRC as an alternative to possible tra-
ditional composites such as FRP (fibre reinforced polymer) can be
justified. Indeed, in addition to good mechanical performance,
TRC affords a priori better temperature stability (substitution of
the resin bonding by mineral matrix), it can be used with the shot-
crete technique. Finally, the composite TRC has the potential to re-
duce the carbon dependence (significant limitation or avoidance of
the use of carbon) and thus minimise the ecological footprint in
accordance with the concepts of sustainable development.
The TRC that was used in the present study consisted of a se-
lected mortar of fine particles (maximum diameter of aggregate
less than 0.8 mm; Emaco R315 from BASF, which is a thixotropic
repair mortar) and textile reinforcement. The reinforcement was
a knitted textile grid (warp knitting). The meshes are rectangular
and ‘‘open’’ at 3 /C25 mm (frame /C3array) to facilitate penetration
of the mortar and, thus, ensure good yarn/mortar adhesion. The
warp (direction of loading) material is AR glass (for strength and
durability) and the weft material is polyester. Table 1 presents
the details.
To optimise the performance of the TRC, a coating product
(polymer latex) designed to facilitate the impregnation of fibres
[17,18] was applied to the fabric before the mortar was added.
The wet lay-up strengthening method was used to apply the TRC.
Two variants were selected. The first, TRC, consisted of three
layers of alkali-resistant fabric embedded in mortar, while thesecond variant combined two layers of alkali-resistant fabric with
carbon rods (TRC + JV) or a combination of carbon and glass
(TRC + JVC). The rods were treated (surface-scattered with silica)
to improve the roughness of their surface. See Table 2 for the
mechanical and geometrical properties of the rods.
The static characterisation of the TRC and the hybrid solutions
was established with a suitable tensile test [19] (Fig. 1 ).
To obtain representative measurements of the behaviour of the
TRC until failure, two displacement transducers (LVDTs) were cen-
trally placed on each side of the specimen. They cover a distance of
200 mm and a sufficient number of cracks to be representative of
the behaviour of TRC that is multi-cracked and/or has a very open
mesh. A distance of 5 cm around the clamps was excluded from the
measurement zone.
A displacement rate of 1 mm/min was selected. The operating
average stress (force applied to the reported TRC cross-section)
versus the average strain (the average of measured displacements
reported in the measurement height is 200 mm) is consistent with
the instrumentation used.
From plates of dimensions 600 /C3400/C310 mm
3(wet lay-up
application), a width of 50 mm was removed (after 14 days of cur-
ing) from all around the moulded plate to eliminate any
implementation heterogeneity, and three elements of
500/C3100/C310 mm3were obtained, using a diamond saw.
Three configurations were tested
– TRC: 3 glass AR fabric.
– TRC + JC: TRC (2 glass AR fabric) + JC (8 Carbon rods).
– TRC + JVC: TRC (2 glass AR fabric) + JVC (12 Glass rods and 4 car-
bon rods).
The JC configuration (reduced number of rods) was chosen to
facilitate the implementation of in situ.
The JVC configuration was chosen to limit the environmental
impact (with an equal load failure).
The rods (glass and/or carbon) were positioned, as shown in
Fig. 2 , to obtain a symmetrical reinforcement.Table 1
Technical characteristics of AR glass.
Number of
filaments
per rovingRoving
titer
(tex)Filament
diameter
(lm)Roving
strength
(MPa)
AR glass 1600 25000 700 1102Table 2
Properties of the rods.
Diameter (mm) E(GPa) Tensile strength (MPa)
Glass rod 2 40 700
Carbon rod 2 130 2240
Fig. 1. Tensile specimen (geometry, instrumentation, and loading) [19].A. Si Larbi et al. / Composite Structures 99 (2013) 152–162 153

The average result of each configuration is shown in Fig. 2 (a
very low standard deviation, below 6% (3 specimens by group) is
systematically observed).
As shown in Fig. 2 , contrary to what is generally observed in the
literature [4,5] , the TRC used in this study presents an almost linear
elastic behaviour due to the addition of a coating that homogenises
the contribution of the filaments and thus considerably softens the
cracking phase (two phases instead of three commonly identified
in the case of TRC without any coating product). The hybrid rein-
forcement behaviour is linear and is strongly influenced by those
rods. The marked increase of the overall stiffness is mainly the re-
sult of the good interaction (mainly frictional adhesion) between
the mortar and the rods.
The load transfer mechanisms in the case of TRC differ signifi-
cantly from those of CFRP at the micro and meso-scales, among
others. Indeed, the very limited penetration of the mortar in the
bundle generates, schematically, outside filaments that are in di-
rect contact with the mortar (chemical adhesion and frictional
rather continuous) and the inner filaments (the majority), and
the interaction between them is discontinuous, heterogeneous
and primarily frictional. Therefore, the filament contribution issignificantly heterogeneous. The use of an additional resin (latex)
is intended to reduce the heterogeneity (one of the causes of the
non-linear behaviour) and increase the average contribution of
the filaments. Therefore, one of the challenges of this article is to
explore the ability of numerical modelling to account for the con-
tribution of the TRC on the basis of a calibration coefficient (Ctr)
reflecting the average contribution of the filaments or the textile
‘‘efficiency factor’’.
2.1.2. Carbon fibre-reinforced polymer (CFRP)
The main properties of the CFRP, a fabric, are detailed in Table 3 .
2.1.3. Steel and concrete
The steel used in the present study was grade E500. The average
yield stress of the steel based on 10 direct tension tests is
570 ± 13 MPa, with a Young’s modulus of 210,000 ± 5750 MPa
and a yield strain of 2.7 ± 0.04%. The concrete used in the present
study was a ready-mixed concrete, which limited the disparity be-
tween different batches. The average compressive strength of the
concrete at 28 days (NF EN 12390-3) was 30 MPa ± 2.5 (6 speci-
mens). The compression tests were performed on specimens with
a size of 16 /C232 cm2and were carried out in compliance with
ISO 1920-4:2005.
2.2. Specimen geometry and test setup2.2.1. Geometry of beams
Five RC beam specimens were fabricated and tested in this
study. The beams are internally reinforced with two 12 mm rebars
at the bottom and two 8 mm rebars at the top; they are strength-
ened in shear by twenty-eight 6 mm transverse rebars. Test beams
were of rectangular cross-section with a width of 15 cm and a
depth of 25 cm. Their overall length was 2.3 m with a clear span
of 2 m ( Fig. 4 ). The reinforcements were 1.95 m long, which is
intentionally shorter than the span of the beam to avoid contact
between the reinforcement and support system.
To evaluate the performance of the reinforcement in the case of
repair, three reinforced concrete beams were loaded before being
strengthened (CFRP, TRC + JC and TRC + JVC). The beams have been
previously damaged by loading until longitudinal steel yielding.
These loads are controlled via a strain gauge glued on steel. Subse-
quently, these beams have been named damaged beams. The beam
strengthened by TRC has not been previously damaged (undam-
aged beam).
Table 4 summarises the solutions adopted for this study.
The TRC reinforcement was a sanded plate (casted 7 days be-
fore) glued with a structural resin (epoxy, Sikadur31) to the sanded
Fig. 2. Tensile test results and reinforcement configurations.
Table 3
Properties of the CFRP.
Thickness (mm) 0.40Width (mm) 150Tensile strength (MPa) 700Young’s modulus (GPa) 80
Fig. 3. Schematic illustration of the differential impregnation of the roving [20].154 A. Si Larbi et al. / Composite Structures 99 (2013) 152–162

underside of the reinforced concrete beam (undamaged), a slight
pressure is applied, via clamps, during the first 24 h to ensure good
adhesion. The decision to use the epoxy resin reflects the
willingness to consider the prefabrication in the industry (‘‘bond-
ing’’ the prefabricated plates with mortar has to be explored), de-
spite the fact that the use of polymer resin is likely to
compromise the thermal performance of the reinforcement. The
hybrid reinforcement (TRC + JC; TRC + JVC) and CFRP were castedin place on the underside of the beam (damaged) to promote the
in situ implementation without any polymeric resin.
The beams have been repaired or strengthened without any
loading.
2.2.2. Testing device and instrumentation
The test specimens were subjected to a four-point bending test.
The load was applied at intervals of 600 mm ( Fig. 4 ). Static mono-
tonic loads were applied until specimen failure under load control
(1 kN/min). The load was measured by a load cell with a 200 kN
capacity.
To measure specimen-sustained displacement, an LVDT Racing
±100 mm was placed at the centre of the beam, and the beam
was instrumented at this central part with strain gauges, as shown
inFig. 3 . Two strain gauges (length 10 mm) were bonded to (ten-
sile) steel reinforcements.
In the height dimension of the beam ( Fig. 4 ), three strain gauges
(length 70 mm) were implemented on the concrete.2.3. Experimental results and discussions
2.3.1. Analysis of load–displacement curves
The load–deflection curves ( Fig. 5 ) demonstrate the difference
in performance between the initially undamaged beams and the
previously damaged and repaired ones.
In the case of the undamaged beams, there are three phases. The
first phase reflects the integrity of the beam, that is, none of the
Fig. 4. Characteristics of the analysed beams with the used setup and sensors.
Table 4
Beam definitions.
Reinforcement Reinforcement axial stiffness
Ef.Af. (MN)Damage level Dimensions of reinforcement
Beam 1 (reference
beam)Reference beam – Undamaged
beams–
Beam 2 (TRC) TRC (3 glass AR fabric) 1.8 10 /C2150 (mm)
Beam 3 (CFRP) CFRP 4.8 Damaged
beams0.4/C2150 (mm)
Beam 4 (TRC & JC) TRC (2 glass AR fabric) & JC (carbon rod) 3.5 10 /C2150 (mm) & 8 £2 (carbon)
Beam 5 (TRC & JCV) TRC (2 glass AR fabric) & JVC (glass and
carbon rod)3.3 10 /C2150 (mm) & 4 £2 (carbon) & 12 £2
(glass)
Fig. 5. Total applied load versus midspan deflection.A. Si Larbi et al. / Composite Structures 99 (2013) 152–162 155

materials of the beam are damaged. The second phase corresponds
to the propagation of cracks and their multiplication along the
beam. The last phase is that of the steel yielding. The first phase
was not relevant for the previously damaged beams. As for the
gains in terms of ultimate and service load obtained through TRC
reinforcement compared to the reference beam, it can be observed
that hybrid solutions based on TRC associated with carbon and/or
glass exhibit interesting global performances, although the ulti-
mate load level is lower than that for the CFRP solution.
It can be observed that with using beam theory it is quite pos-
sible to approach very significantly the damaged or strengthened
beam service load. However, the ultimate load is considerably
underestimated probably due to the fact that the ultimate proper-
ties of the reinforcement’s materials (TRC, hybrid solutions and
CFRP) have been underestimated. Indeed, in the case of TRC or hy-
brid solutions the ultimate stress is underestimated because of
premature failure due to a complex stress state near the clamps
[19] whereas in the case of CFRP calculations were conducted
based on the properties of the manufacturer, which are may be
underestimated.
Table 5 summarises the global performances and the differ-
ences obtained.
2.3.2. Analysis of the global failure mode of the beams
Apart from the steel yielding failure of the reference beam, two
additional failure modes were observed ( Table 5 ). The first ( Fig. 6 a)
is a failure that occurred in the extremity of the beam; this is acharacteristic failure in beams strengthened by CFRP and con-
cerned the (TRC + JC) beam and the CFRP beam. The second failure
(Fig. 5 b) occurred in the centre of the beam and was accompanied
by a plate strengthening failure.
The explanation of the relocation of the failure could be the rel-
atively low axial stiffness of the reinforcement plate that allows
greater flexibility, a factor which would soften the stress edges. It
follows that the limit value of axial stiffness separating the two
areas of strength (edge peeling-off and central peeling-off) wouldbe limited by the values of the axial rigidity of the TRC + JC and
TRC + JVC, which would also explain their different modes of fail-
ure (This assertion must be validated by performing more tests).
Central failure, while uncommon, is more advantageous in that it
allows calculating an improvement in the efficiency ratio of the
reinforcement as opposed to the fairly weak stress (or strain) effi-
ciency ratio of the CFRP reinforcement. This type of failure is also
independent of the mode of application chosen (bonding of plates
using a structural resin or in situ application without any resin).
Therefore, this finding opens the possibility of direct application
without bonding resin, providing that the mortar is thixotropic
and suitable for in situ application.
2.3.3. Concrete crack analysis
2.3.3.1. Measuring technique. Over the last decade, several types of
full-field techniques have been developed for material character-
isation. The nature of the measurements can be displacement,
strain or temperature. The full-field measurement method consistsTable 5
Loads and displacements results.
Experimentalservice load(kN)Beam theory
service load(kN)Experimental
service deflection(mm)Experimental
ultimate load(kN)Beam theory
ultimate load(kN)Increase
experimentalultimate load(%)Experimental
ultimate deflection(mm)Failure mode
Reference beam 60.03 74.8 9.24 77.03 76.5 – 46.14 Longitudinal steel rebars
failure
CFRP 81.88 84.2 8.69 143.63 106 86.5 28.03 Peeling-offTRC 69.08 79.2 8.59 98.58 91.5 28.1 24.57 Strengthening plate failureTRC & JC 81.35 81.4 9.00 121.10 100.5 57.3 25.78 Peeling-off
TRC & JVC 81.80 82.1 8.98 125.88 105 63.5 29.96 Strengthening plate failure
Fig. 6. Failure modes.156 A. Si Larbi et al. / Composite Structures 99 (2013) 152–162

of placing a well-defined grid of spots or lines on the surface of the
specimen, which is then photographed before and after loading to
determine specimen distortion and, hence, strain. Displacements
are measured with various techniques [21], for instance speckle
imaging [22], speckle interferometry [23], geometric moiré [24],
moiré interferometry, holographic interferometry [25,26] , image
correlation [27] or grid analysis [28]. In this study, the multi-crack-
ing of specimens under four-point bending was studied in terms of
the relationship between loading crack widths.
2.3.3.2. Results of concrete cracks. The image correlation (optical
measurement) method [29] was used to follow the development
of cracks and their propagation in the mid-section of beams.
Images are correlated after an increment of 5 kN during loading
in each case. The precision of the measurements is within 4/
100 mm. The opening of the first crack was analysed as a function
of the applied load ( Fig. 6 ). The analysis is conducted at a distance
of 25 mm from the bottom of the RC beam to measure the crack
opening precisely at the level of the steel rebars.
Fig. 7 permits an assessment of the development of the first
macrocrack appearing (in the constant bending moment) in each
of the beams tested. The correspondences between the overall
behaviour (load–deflection and flexural stiffness-load) and the
development of the crack opening for the two variants considered
can be identified. In damaged beams, two phases are observed. The
first phase (0–80 kN) corresponds to an early, gradually opening
crack with a second phase (80 kN up to failure) corresponding to
a significantly flatter slope associated with the longitudinal yield-
ing of the steel. There is a considerable reduction in crack opening
compared to the reference beam when the reference beam begins
cracking.
As for the beam strengthened with TRC, beyond the additional
initial ‘‘crack-free’’ phase (0–22 kN), a much larger, saw-tooth
development that reflects the stress redistribution conditions,
which are less favourable than in the case of the hybrid TRC rein-
forcements, can be observed. Indeed, the absence of rods in close
proximity, which could support the extra stress generated by the
appearance of a crack, coupled with the relative remoteness of
the TRC from the longitudinal steel rebars, has the effect ofextending the distance travelled by the stress to be redistributed,
thus increasing the saw-tooth development of the crack opening.
However, it is reasonable to assume that the second phase, corre-
sponding to the emergence and propagation of cracks, ranges from
20 kN to 60 kN. In conclusion, it is important to notice that despite
some (variably important) quantitative modifications (whatever
the reinforcement solution), the cracking kinematics are not funda-
mentally affected. The average crack spacing measured only in the
constant moment zone (60 cm) is given in Table 6 . These results
tend to show that the four strengthened and repaired beams exhi-
bit a significant contribution to the reinforcement in comparison to
the reference beam and appear to be related to the former’s axial
stiffness. Thus, it seems that average crack spacing is inversely pro-
portional to the axial stiffness of the reinforcement (the relatively
small variation, however, urges caution and a more completeexperimental study is required to validate this observation).
3. Numerical approach
3.1. Finite element modelling
The developed models are based on the finite element method
(FEM) implemented in commercial software (ANSYS). A specific
non-linear behaviour of concrete and the elasto-plastic behaviour
of steel are taken into account.
Generally, there are two approaches to model concrete or ce-
ment behaviour. These are (i) the discrete approach (or crack prop-
agation approach), which attempts to reproduce the crack
propagation in each element, and (ii) the ‘‘homogenised’’ approach
(smeared crack approach), which simulates a global behaviour of
concrete in tension without taking into account the explicit open-ing of cracks [30]. The main problem with the discrete approach is
that, due to the re-meshing process necessary for each load crack
step, it is a time consuming method.
3.1.1. Element type for concrete
In this paper, the developed finite element (FE) models used iso-
parametric elements (solid65) with a smeared cracking approach
for the concrete. The 3D-solid element was described by eight
nodes and three degrees of freedom at each node (translations in
the nodal x,y, and
zdirections). This element is capable of plastic
deformation, creep, crushing in concrete, and cracking in three
orthogonal directions at each integration point. Time-dependent
nonlinearities (creep and shrinkage) are not considered. Moreover,
to avoid premature failure in the analysis from a significant and
unrepresentative local loss of stiffness from crushing, crushing
capability was disabled.
The used 3D-solid elements simulate the nonlinear material
behaviour with a smeared crack approach [31]. When cracking oc-
curs at an integration point, material properties are adjusted to
effectively model a ‘‘smeared band’’ of cracks, rather than discrete
cracks. With the ‘‘smeared approach’’, mechanical properties of
crack elements are computed using transfer coefficients ( atand
bt). The applied failure criterion of concrete in this study is a crite-
rion in 3D-multiaxial stress developed by William and Warnke
[30]. When a principal stress at an integration point in a concrete
element exceeds the tensile strength, stiffness is reduced to zero
in that principal direction perpendicular to the cracked plane.
Cracking can be simulated at each integration point in three
directions.
The typical stress–strain behaviour of concrete material is pre-
sented in Fig. 8 .
The tensile behaviour of the concrete is assumed linear ( r=Ee)
until the failure stress ftis reached at the point D ( Fig. 8 ). In com-
pression, the stress–strain behaviour of concrete includes threeFig. 7. Load/cracks opening curves.
Table 6
Average crack spacing.
Beam Reference
beamTRC TRC + JVC TRC + JC CFRP
Average macrocrack
spacing (cm)13.3 10.1 9.3 7.8 6.4A. Si Larbi et al. / Composite Structures 99 (2013) 152–162 157

major areas bounded by strain values of /C0e0¼/C02fc
E(point A), /C0ec
(point B), and /C0eu(point C), as shown in Fig. 8 .
The nonlinear behaviour in compression was described in sim-
ulation by the relationship: r¼Ee
1țðe=e0Ț2where e0¼2fc
E.
Table 7 presents the mechanical properties of the used concrete.
3.1.2. Element type for steel rebar
The steel rebars are modelled by a 3D-truss (or spar) element
(LINK8). Such discrete modelling of strengthening elements is de-
scribed by two nodes and three degrees of freedom at each node
(translations in the nodal x,y, and zdirections).
The yield strength of the steels ( fy) is reached for the strain va-
lue of 0.2%. Hooke’s law is valid up to 0.7 fy. The elastic modulus of
steel Esis equal to 200 GPa. The simplified steel behaviour is con-
sidered as a bilinear material (elasto-plastic) with the same behav-
iour in tension and compression. The steel material has a strain
hardening. The tangent modulus ( Et) was assumed to be equal to
20 GPa. The typical stress–strain curve of the steel rebar is shown
inFig. 9 .
3.1.3. Element type for strengthening elements
The modelling of CFRP composite reinforcement was presented
in our previous paper [32]. In this section, we limit our
presentation to the TRC strengthening elements. The developedTRC model is a concrete layer (3D-solid65) reinforced by a 3D-truss
(or spar) element (link 8). The number and section of 3D reinforce-
ment truss elements representative of the TRC strengthening (or
repairing) are determined by the well-known mixture laws oftenused for unidirectional fibre composite materials.
To estimate the section of the link elements representative of
the TRC, the TRC are considered as two layers of unidirectional
reinforcements crossed at 90 /C176. By using the notation ( E:thickness
of layer, n
1: number of yarn per meter in warp direction, n2: num-
ber of yarn per meter in weft direction, k¼n1
n1țn2,vf: fibre volume
fraction) one can deduce the thickness tof equivalent unidirec-
tional layer as: twarp¼n1
n1țn2/C3t¼k/C3tand tweft¼ð1/C0kȚ/C3t. Know-
ing these thicknesses and the size of the TRC strengthening
beam, on can calculate the section of equivalent layers of the uni-
directional TRC. Then, to get the section of one link element of the
model, the equivalent section is divided by the necessary number
of link elements in beam direction imposed by the mesh size of
the beam. Such simplified modelling of TRC could be justified in
this study by the fact that one introduced an experimental coeffi-
cient Ctracting directly on the section of the link element in order
to take into account the effects of TRC wettability. In the study, the
bond between the elements of the model was assumed to be
perfect.
A summary of the TRC properties is presented in the Table 8 .
3.1.4. Typical models of analysed beams
Fig. 10 shows examples of modelled beams. According to the
analysis of the beams, the model had a total of around 5000 ele-
ments. The degrees of freedom at each node are translations in
the nodal x,y, and zdirections. The choice of this number of ele-
ments was based on preliminary studies in which different finite
element sizes were used. For the analysed beams, this number of
elements provides a good balance between the computational time
required and the numerical accuracy of results.
One can see the strengthening elements of the TRC, steel
frames, and concrete elements. The proposed model, especially in
the case of the TRC reinforcements, aims first to evaluate the pos-sibility of modelling the overall behaviour of the strengthened
beams on the basis of a single calibration parameter (load transfer
coefficient; C
tr) and then to analyse the internal stress transfer phe-
nomena in the reinforced beams, thus allowing for a comparison to
the results obtained with the CFRP reinforcement.
For a given TRC system, the calibration coefficient ( Ctr) was
determined in order to get a better fit to typical experimental data.
Then this coefficient was used to model the behaviour of all other
beams made with the same TRC.
A description of the numerical results compared to the experi-
mental results is presented in the following section.
3.2. Numerical results and analysis compared to experimental results3.2.1. Analysis of the stress transfer effects of TRC strengthening
elements
As shown in Section 2.1.1 , the modelling of beams with a TRC
must take into account the load transfer coefficient to the fibres
Fig. 8. Typical stress–strain curve of concrete.
Table 7
Properties of beam and TRC concrete.
Eb(GPa) mb fc(MPa) ft(MPa) at bt
Beam concrete 28 0.2 31 3 0.2 0.9
TRC concrete 23 0.25 29 5.5 0.2 0.9
Fig. 9. Typical stress–strain curve of steel rebar.Table 8
Average properties of the reinforcement elements of the repaired or strengthenedbeams.
Properties CFRP TRC – (AR
glass)Glass
rodCarbon
rod
Dimensions (mm) 0.46 /C2150 ( /C3)( /C3)( /C3)
Longitudinal Young’s
modulus (GPa)80 70 40 130
Ultimate strain (%) 1.8 2.5 – –
(/C3)Value determined by mixture law and data in Tables 1 and 2 .158 A. Si Larbi et al. / Composite Structures 99 (2013) 152–162

of the TRC ( Ctr). To estimate this coefficient for this study, a para-
metric analysis considering three value of Ctr(0.25; 0.5; 0.75) has
been conducted. The results obtained are shown in Fig. 11 .
First, it is evident that the textile ‘‘efficiency factor’’ (or average
contribution of the filaments) of the TRC rate is appropriate and
sufficient to model satisfactorily the overall behaviour of the re-
paired or strengthened beam. The best fit of the load versus deflec-
tion curves is obtained with Ctr(average contribution of the
filaments) equal to 0.25, which reflects a low filament mobilisation
despite the use of an impregnating resin (latex). This low value can
be explained partly by the differentiated contribution of the fila-
ments due to the beam curvature, in addition to the intrinsically
differential behaviour of the filaments, although less pronounced
with the use of a resin, and by the fact that this curvature generates
the degradation of the filaments located on the convex portion of
the bundle.
It is also evident that an increase in Ctrdoes not significantly af-
fect the load cracking beam but induces an increase in the service
load (which corresponds to the longitudinal steel yielding). The
most important effect is observed in the third (plastic) zone where
the increasing of Ctrleads to a significant increase in the slope of
curves. This is consistent with the fact that more fibres of theTRC better support the applied load. Thus, TRC strengthening re-
sults in a higher crack bridging effect and failure load. Therefore,
the axial stiffness of the reinforcement governs the overall behav-
iour of the repaired and strengthened beams through the Ctrcoef-
ficient. The value of 0.25 will be used for all modelling of solutions
that incorporate TRC.
3.2.2. Load–deflection behaviour: experimental and numerical
comparison
Fig. 12 shows the experimental and numerical comparison of
load versus mid-span deflection. The presented numerical results
for the reference beam are terminated for a displacement equal
to about 22 mm, while the test was continued up to about
50 mm. This is due to the need of very low step time to solve the
non-linear problem when displacement goes beyond 22 mm.
Therefore to limit the computation time the simulation of refer-
ence beam was stopped for a displacement equal to about 22 mm.
There is good agreement (except for the initial damage of the
beams which was not taken into account during modelling) be-
tween the experimental and theoretical results, despite curves
with a slight discrepancy for the TRC essentially near the failureload. This slight discrepancy on the curve of the TRC could be
due to the fixed C
trcoefficient, which is most likely not the same
for all samples because of presence of the rods (carbon and/or
glass) seems to slightly change the redistribution efforts near the
failure load. In spite of this, the developed model describes the
experimental observations well and illustrates the fact that both
the CFRP and the TRC reinforcement do not significantly change
the ductility, but they increase the failure load.
This good agreement validates the numerical models, which
will be used in the following section for the analysis of internal
stress, strain and cracks of reinforced beams.
3.2.3. Analysis of strength transfer to steel rebars and strengthening
elements
To better understand the stress redistribution occurring in the
different repaired and/or strengthened beams, the evolution of
the contributions of various materials has been determined high-
lighting the impact of the axial stiffness.
Fig. 10. Typical meshing of the analysed beam. (a) TRC strengthening model with localisation of points used to analyse stress transfer in the beams. (b) 3D trus s elements
(link 8) for steel and FRP rod modelling. (c) Beam with CFRP reinforcement.
Fig. 11. Stress transfer effects of TRC-strengthening elements.A. Si Larbi et al. / Composite Structures 99 (2013) 152–162 159

Fig. 13 illustrates the effect of strengthening on the tensile
stress in the longitudinal steel, the stirrup rebars and the reinforce-
ment (i.e., TRC-or CFRP, as shown in Fig. 10 ).
It is noteworthy that the effect of external strengthening, which
depends more on axial stiffness than the nature of the reinforce-
ment even if there is composite cracking, on the lower part of
the beam is meaningful only in the plastic area (when applied load
F> 70 kN).Indeed, in the plastic area (when F> 70 kN), there are, for a fixed
load value, the following findings:
– Concerning the longitudinal steel rebar in the upper and central
part, the strengthening technique has a very low impact on the
stress in steel rebars (curve in the negative part of Fig. 12 ),
though there is slight increase of compressive stress with an
increase of axial stiffness (ES) of the strengthening elements.
Fig. 12. Experimental and numerical comparison of load versus bending displacement of the analysed beams.
Fig. 13. The stress contribution of the different constitutive materials of the repaired beam (a) in middle of the beam and (b) in stirrup steel in part with shea r load.160 A. Si Larbi et al. / Composite Structures 99 (2013) 152–162

This increase generates a slight increase in the concrete com-
pression strain in the upper and central parts when the axial
stiffness (ES) increases.
– Concerning steel rebar in the lower and central parts, the
strengthening method of the beam yields to significant influ-
ence on tensile stresses in steel rebars. Indeed, the tensile stress
in steel rebar becomes more important as the axial stiffness (ES)
of the strengthening elements is low. Accordingly, tensile fail-
ure (cracking) of the concrete in the lower part will be reached
more quickly when the axial stiffness (ES) is low (as in the case
of the TRC beam). However, the gain in terms of ductility at the
global scale (especially in the case of TRC) is barely noticeable
(curve load versus deflection). Thus, if a substantial plastic
deformation of longitudinal steel reinforcement is a necessary
condition, but insufficient, for obtaining a ductile behaviour.
Indeed, the deflection (in particular in the non-linear domain
reflecting the ductility) is controlled by the curvature, which
is dependent on the opening unit crack (longitudinal steel ten-sile strain), but also by the number of cracks. The magnitude of
the axial stiffness certainly reduces the crack opening unit, but
it also increases the number of cracks (or reduces the average
crack spacing (see Table 7 )). Therefore, the axial stiffness cannot
constitute the only parameter to optimise the ductility of the
repaired or strengthened beams.
– Regarding the steel stirrup in the sheared part of the beam, an
increase of axial stiffness (ES) leads to a reduction of the stress
in the steel stirrup (although the effect is much less sensitive
when the beams JC, JVC and CFRP are compared) because it pro-
motes the aggregate interlock effect.
These mechanisms of load transfer could change the strain and
stress distribution in concrete and, therefore, change cracking den-
sities in the concrete according to the used strengthening
technique.
The following section, aims to present an analysis of the crack-
ing densities of the concrete based on numerical analysis.3.2.4. Crack densities analysis
At each applied load step, the program records a crack pattern.
Fig. 14 shows typical crack patterns developed for the four ana-
lysed beams at fixed loading steps (20 kN, 40 kN and 80 kN).
The program displays circles at locations of cracking or crushing
in concrete elements. Cracking is represented by a circle in the
plane of the crack, and crushing is evidenced by an octahedron.
The first crack at an integration point is shown by a red circle,
the second by a green circle, and the third by a blue circle [28].
In the central part of the beam, both experimental and numer-
ical results show flexural cracks that form vertically up the beam.
Some compression failures, shown as circles, appear near the four
loading points. For the proposed approach, the numerical results
also show an improvement in the bearing capacity of the beams
with a reduction in maximum deflection.
When the CFRP strengthening is used (relatively high axial stiff-
ness), a decrease of the height of the flexural cracks (vertical), par-
ticularly with the increasing load, can be observed. Additionally, itcan be noted that the cracks intensity (compared to the TRC beam
which exhibits the lowest axial stiffness) is only slightly marked in
the centre. Failure cracks are essentially located in the lower part
of the analysed beams. According to the numerical modelling, the
excessive cracking (multi-crack/crush) observed when CFRP
strengthening is used is explained by the concentration of a high
load transfer from the CFRP to the longitudinal steel rebars in the
lower part of the beam and can partially explain the peeling-off
failure. Finally, the reduction of the axial stiffness of reinforcement
is accompanied by a more homogeneous density of cracking.
4. Conclusion
The experimental part of this article has brought out the posi-
tive factors of TRC hybrid solutions in the repair of reinforced con-
crete beams with respect to both ultimate and service behaviourwith performances similar to those of traditional solutions such
as CFRP. The use of TRC alone to strengthen a reinforced concrete
Fig. 14. Crack pattern with the corresponding test load.A. Si Larbi et al. / Composite Structures 99 (2013) 152–162 161

beam seems less advantageous, and while it significantly improves
the ultimate performance, it cannot be considered in the context of
increasing the bearing capacity. It does, nevertheless, appear inter-
esting for the control of cracking in the service phase. However, in
spite of its multi cracking behaviour, TRC does not provide signifi-
cant gain in terms of ductility.
It is important to outline the change of failure mode in the TRC
and TRC + JVC solutions, as it allows a better use of the reinforce-
ment. The change can be explained by the relatively low axial stiff-
ness of these reinforcements, providing there is sufficient
interaction with the concrete surface.
The numerical approach has shown the relevance of the textile
‘‘efficiency factor’’ (or the average contribution of the filaments) as
a calibration coefficient for modelling the overall behaviour of TRC
repaired and/or strengthened beams. This coefficient reflects theratio of filament mobilisation of the textile used for the TRC com-
posite. This observation serves to emphasise that it is the axial
stiffness of reinforcements (irrespective of whether the reinforce-
ment is a cracking material) that governs the overall behaviour
of the repaired and/or strengthened beams. On a more local scale,
it seems that while the distributions of stress are qualitatively very
similar (between CFRP and TRC), which focuses their influence dur-
ing the longitudinal steel yielding, the fact remains that the in-
crease of the reinforcement axial stiffness tends to increase and
concentrate the stress transfer between the longitudinal steel
and the external reinforcement, which can explain, at least in part,
the occurrence of peeling-off failure.
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