Engineering Fracture Mechanics 74 (2007) 151–167

www.elsevier.com/locate/engfracmech

High performance fibre-reinforced cementitious composite(CARDIFRC) – Performance and application to retrofitting

F.A. Farhat, D. Nicolaides, A. Kanellopoulos, B.L. Karihaloo *

School of Engineering, Cardiff University, Cardiff CF24 3AA, UK

Available online 3 March 2006

Abstract

This paper describes first some of the recent performance checks on the high performance fibre-reinforced cementitiouscomposite CARDIFRC and then its application to the retrofitting of damaged concrete beams. It is shown that an even dis-tribution of fibres throughout the bulk of the material is crucial to its excellent fatigue performance and to the reduction inthe autogenous shrinkage strains. The distribution of fibres in beams, cylinders and strips is examined using computerisedtomography imaging and traditional image analysis. Thin strips of CARDIFRC are used to retrofit damaged concrete beamswhich are subjected to thermal cycling. It is shown that neither the load carrying capacity of the retrofitted beams nor thebond between retrofit strips and concrete deteriorates with thermal cycling. The load carrying capacity of retrofitted beamsis predicted with a model based on fracture mechanics, and the predictions are shown to be in good agreement with test data.� 2006 Elsevier Ltd. All rights reserved.

1. Introduction

New types of concrete are being constantly developed in order to meet the increasing demand for improvedmechanical properties and durability. These new types of concrete are widely known as high strength (HSC),high performance (HPC) and ultrahigh performance concretes (UHPC). The properties of such concretesshow a substantial improvement over conventional concrete. However, the improved and densified micro-structure of these new types of concrete leads to a significant increase in their brittleness as well as in the vol-ume changes which occur during the hardening of the material, i.e. in autogenous shrinkage. Both thesedrawbacks can however be overcome to a large extent by the inclusion of large amounts of short steel fibre.Such fibre-reinforced concretes are called high performance fibre-reinforced cementitious composites(HPFRCCs). One such HPFRCC, known under the trade name CARDIFRC� is the subject of this paper.

The mechanical performance of any HPFRCC depends to a high degree on the even distribution of fibres inthe bulk of the material. Any regions with a low density of fibres or with no fibres are potential sites of weak-ness. The distribution of fibres in the mix depends not only on how the fibres are introduced into the mix butalso on the shape of the object cast from CARDIFRC.

0013-7944/$ - see front matter � 2006 Elsevier Ltd. All rights reserved.

doi:10.1016/j.engfracmech.2006.01.023

* Corresponding author. Tel.: +44 2 20874934; fax: +44 29 20874597.E-mail address: Karihaloob@cardiff.ac.uk (B.L. Karihaloo).

152 F.A. Farhat et al. / Engineering Fracture Mechanics 74 (2007) 151–167

Concrete structures can deteriorate and therefore need repair after long periods in service. To accommodatefor a load carrying capacity higher than the original design value, members may need to be strengthenedthrough retrofitting. A common repair and strengthening technique for concrete beams is by bonding a steelplate to the tension side of the beam. However, several problems have been encountered with this technique,including the occurrence of undesirable shear failures, difficulty in handling heavy steel plates, corrosion ofsteel that can cause deterioration of the bond at a glued steel–concrete interface, and the need of butt jointsystems as a result of limited workable lengths [1,2].

Recently, attention has been directed towards the use of fibre-reinforced plastic (FRP) laminates, whichoffer higher strength/weight and improved durability over their steel counterparts [3–5]. Retrofitting usingFRP is also vulnerable to undesirable brittle failures due to a large mismatch in the tensile strength and stiff-ness with that of concrete. Another problem, which has also been observed with this technique, is the effect oflong exposure to temperature variations [5–7].

A new retrofitting technique using CARDIFRC, a material compatible with concrete, has recently beendeveloped at Cardiff University. It overcomes some of the problems associated with the current techniquesbased on externally bonded steel plates and FRP (fibre-reinforced polymer) which are due to the mismatchof their tensile strength, stiffness and coefficient of linear thermal expansion with that of concrete structurebeing retrofitted [8]. The mix proportions of a mix from the class CARDIFRC (Mix I) are given in Table1, with its typical mechanical properties at room temperature shown in Table 2.

Several studies have previously been undertaken at Cardiff into the feasibility of using CARDIFRC for therehabilitation and strengthening of damaged RC flexural members [8–10]. To predict the moment resistanceand the load–deflection behaviour of the retrofitted beams, two analytical models have been developed byAlaee and Karihaloo [11,12]. One model is based on the classical strength theory, but takes into account fullythe tensile contributions (i.e. pre-peak and post-peak) from concrete and CARDIFRC. The second analyticalmodel is based on the fracture mechanics concepts. This model mimics the initiation and growth of the flexuralcrack that eventually leads to the failure of the retrofitted beam.

It is the aim of this paper first to describe some recent work on the properties of CARDIFRC and then tooutline its performance as a material for retrofitting damaged concrete flexural members at elevated temper-atures. The important role of even fibre distribution in the fatigue behaviour and in the reduction of auto-genous shrinkage of CARDIFRC will be highlighted. It will be shown that thermal cycling of flexural

Table 1Mix proportions for CARDIFRC I

Constituents (kg) Mix I

Cement 855Quartz sand

9–300 lm 470250–600 lm 470

Microsilica 214Water 188Superplasticizer 28Fibres�6 mm 390�13 mm 78

Water/cement ratio 0.22Water/binder ratio 0.18

Table 2Typical material properties of CARDIFRC Mix

Material properties Mix I

Indirect tensile strength (MPa) 27Fracture energy (J/m2) 17,000Compressive strength (MPa) 200Modulus of elasticity (GPa) 48

F.A. Farhat et al. / Engineering Fracture Mechanics 74 (2007) 151–167 153

members retrofitted with this material has no effect either on the bond between concrete and CARDIFRC oron their load carrying capacity.

2. CARDIFRC

CARDIFRC is a new class of high performance fibre-reinforced cementitious composite (HPFRCC) char-acterised by high compressive strength (in excess of 200 MPa), tensile/flexural strength (up to 30 MPa) andhigh energy absorption capacity (up to 20,000 J/m2). This has been made possible by the use of large amounts(up to 8% by volume) of brass-coated short steel fibres (6–13 mm long, 0.16 mm diameter) in a cementitiousmatrix densified by the use of silica fume. The matrix contains only very fine graded quartz sand, instead ofordinary river sand and coarse aggregates. By optimising the grading of fine quartz sands, the water demandwas considerably reduced without affecting the workability of the mix. This was achieved using novel mixingprocedures. Computer tomography imaging and sectioning of specimens have confirmed that these proceduresensure remarkably homogeneous mix with a uniform distribution of fibres [13]. The mix proportion of a mixof the CARDIFRC class is given in Table 1.

3. Effect of thermal cycling

To study the effect of thermal cycling on the mechanical properties of CARDIFRC, specimens made of MixI were heated to a maximum temperature of 90 �C from the room temperature of about 25 �C. Each 24-h ther-mal cycle consisted of a gradual temperature rise period of 30 min, followed by a dwell period of 8 h and end-ing with a slow temperature drop. This thermal cycle mimics a summer’s day in arid hot climate when thetemperature of exposed concrete surface is known to reach the chosen maximum temperature. The numberof thermal cycles varied from 0 to 90 cycles. After the requisite number of thermal cycles, the specimens weretested at room temperature.

Table 3 shows the effect of thermal cycling on the mechanical properties of CARDIFRC Mix I. As can beseen, the mechanical properties of CARDIFRC seem to be unaffected by thermal cycling, thanks to the pres-ence of fibres. The presence of fibres in concrete plays a role in reducing concrete damage by hot and coldcycles in the temperature range from 25 to 150 �C [14].

4. Correlation of CT imaging technique and destructive image analysis

In order to verify that the mixing and compaction procedures used to make CARDIFRC do indeed resultin the steel fibres being uniformly distributed in the hardened CARDIFRC, both destructive and non-destruc-tive techniques were applied. The destructive method consisted of the traditional image analysis, whereas thenon-destructive method was a novel technique of computerised tomography (CT) imaging. A number ofCARDIFRC specimens were cast (namely, 100 · 100 · 500 mm beam, 100 mm diameter cylinder and twotypes of thin strip, 20 mm and 16 mm thickness, respectively) and studied to reveal the effect of the shapeof the specimen and the mixing and compaction procedures on the fibre distribution. The aim of tryingtwo techniques was to check if their results are in some way correlated, because that would open a quickand efficient route to testing the quality of industrially produced CARDIFRC products using only the fastCT imaging technique.

Table 3Mechanical properties of CARDIFRC (Mix I) after thermal cycling

Material properties Thermal cycles

0 30 90

Indirect tensile strength (MPa) 27 31 31Compressive strength (MPa) 200 224 225Modulus of rupture (MPa) 33 33 34Modulus of elasticity (GPa) 48 49 49

154 F.A. Farhat et al. / Engineering Fracture Mechanics 74 (2007) 151–167

The non-destructive technique of CT imaging was used first. A series of CT scans was undertaken in a Gen-eral Electric CTi Helical Scanner at Velindre Hospital, Cardiff, in order to image the test specimens at prede-termined sections along their length, and to log the X-ray absorption density along the depth of the section.Subsequently, the specimens were cut along these predetermined sections and the cross-sections investigatedunder an optical microscope. A fine 10 · 10 mm mesh grid was applied, in order to achieve the best possiblecorrelation between the image analysis data on fibre distribution in the cross-section with the X-ray absorptiondensity data.

Despite the many potential sources of error, a careful examination of the X-ray absorption density contours(Fig. 1a) and the corresponding fibre count contours (Fig. 1b) reveals a reasonable similarity between the twomeasurements in the larger sections examined by the two techniques. In the thin strips the correlation is poorbecause of the beam hardening effect in CT imaging and because the proportion of fibres dislodged during thecutting of the specimens is large relative to the total number of fibres in the cut section. The actual X-rayabsorption densities at grid centres have been plotted against the fibre counts per grid (Fig. 2). It is clear from

Fig. 1. Contour plots showing the X-ray absorption densities (a) and the fibre distribution (b) for the cylinder (100 mm diameter, slice 10).

500

1000

1500

2000

2500

3000

3500

80 100 120 140 160 180 200 220Number of Fibres /cm2

X-r

ay A

bso

rpti

on

(H

ou

nsf

ield

)

Fig. 2. X-ray absorption density vs. number of fibres per cm2 in cylinder slice 10.

F.A. Farhat et al. / Engineering Fracture Mechanics 74 (2007) 151–167 155

this figure that the X-ray absorption density correlates reasonably linearly with the fibre count. This was trueof all the thicker specimens, irrespective of their shapes.

5. Fatigue tests

5.1. Specimens 360 · 90 · 35 mm

The fatigue tests were carried out in three-point bending, with load controlled between two limits (with asinusoidal force variation in time). The minimum stress level, Smin, was 10% of the monotonic flexural strengthand the maximum stress level, Smax, ranged from 80% to 90% of this strength. The tests stopped after specimenfailure or after one million cycles, whichever occurred first. Two specimens were tested up to a very high num-ber of cycles.

Tests have been performed in the load ranges between 10–80%, 10–85% and 10–90% of the ultimate flexuralstrength. Table 4 shows the results of the fatigue life of specimens (i.e. number of cycles to failure, N). It isobserved that there is an excellent consistency in the experimental fatigue life for the load ranges between10–80% and 10–85%, since all of the eight specimens sustained one million or more cycles without failure.

An important observation from the tests performed at the maximum load levels of 80% and 85% Pu, is thatnone of the eight tested specimens developed any visible cracks during one million cycles. This is another con-firmation of the improved distribution of the fibres within the specimens, but it also implies that probably thespecimens will not fail at lower maximum stress levels. From these experimental results, it can be concludedthat the endurance limit of the material is approximately at 85% of its flexural strength. This limit is very high,not very often observed in the relevant literature. This is an indication that CARDIFRC has excellent flawtolerance, which is also confirmed by direct tension tests [15].

In order to check whether internal damage had developed in the specimens that sustained one million ormore cycles without failure, they were tested afterwards in static three-point bending. None of the specimenshad any visible external cracks at the end of the fatigue testing. All the specimens tested in fatigue, showed asmall increase of their flexural strength (about 5%) which can be attributed to ageing as a result of the con-tinued hydration of unhydrated cement.

5.2. Specimens 100 · 100 · 500 mm

The fatigue tests were carried out also on larger beams simply supported over a span of 400 mm. The testswere carried out under load control between two limits (with a sinusoidal force variation in time). The min-imum stress level, Smin, was 10% of the monotonic strength and the maximum stress level, Smax, ranged from70% to 85% of the monotonic strength. The tests stopped after the specimen failure or after one million cycles,whichever occurred first.

Tests have been performed in the load ranges between 10% and 85%, 10% and 80% and 10% and 70% of theultimate flexural strength. A large scatter in the experimental fatigue life of these specimens was observed incontrast to the smaller beam specimens 360 · 90 · 35 mm described above.

The failure surfaces of the tested beams were thoroughly examined visually. It was observed that beamswhich sustained a very small number of cycles had large areas in their planes of failure almost devoid of fibres,

Table 4Flexural fatigue test results on 360 · 90 · 35 mm beams

Load amplitude (% Pu) Fatigue life (N)

N1 N2 N3 N4 Average fatigue life (N)

10–90 1,000,000 21,564 9315 1,000,000 –10–85 1,000,000 1,000,000 1,000,000 20,000,000a 1,000,000b

10–80 1,000,000 1,000,000 1,000,000 1,000,000 1,000,000

a Specimen number 4 had sustained 20,000,000 cycles without failure.b The average fatigue life for the load amplitude 10–85% Pu considers only the first 1,000,000 cycles sustained by specimen number 4.

156 F.A. Farhat et al. / Engineering Fracture Mechanics 74 (2007) 151–167

especially in the zone of tensile stresses. Some other beams had a significant number of fibres in this plane,which however were oriented vertically, without exerting any closure pressure. On the other hand, specimensthat sustained a large number of cycles before failure, had an even distribution of fibres crossing the plane offailure, and most of them applied substantial closure pressure, which extended the fatigue life of the beams. Itwas concluded that the distribution of fibres within the matrix of the beam is a very important parameteraffecting the fatigue life of the tested specimens. Many interesting observations regarding the fibre distributionin CARDIFRC were made by the image analysis of specimens.

6. Image analysis of large beam specimens

Due to the large scatter observed in the fatigue life of large beams (100 · 100 · 500 mm), it was decided toinvestigate the fibre distribution in the planes of failure of six specimens tested under fatigue loading (between10% and 70% Pu). The fatigue life of the selected specimens varied between a few cycles (<10) and a very highnumber of cycles (more than 500,000 cycles). In addition, the distribution of fibres in a section of a specimenwhich did not fail after 1,000,000 cycles was also investigated. This particular specimen was cut along a pre-determined section, located in the centre of the beam, using a diamond saw.

The conclusion from this investigation is that high average number of fibres in the plane of failure results inan extended fatigue life of the specimen. A specimen that sustained just a few cycles (e.g. four cycles) had avery heterogeneous distribution of fibres in the plane of failure. It was easily recognizable that large areasof this section had a significantly low density of fibres, as indicated in Fig. 3. The areas with low density offibres were located in the bottom of the specimen. This is very important, since these parts of the beam weresubjected to tension, and a low number of fibres was a clear reason for a crack to be effortlessly initiated,resulting in extremely low fatigue life. Although the upper part of this section had a high number of fibres,they was not sufficient to prevent the fast failure of this specimen.

On the other hand, in the case of the specimen that did not fail after the application of 1,000,000 cycles, thedistribution of fibres was very even and in combination with the noticeably higher average number of fibres(194 cm�2), satisfactorily explained why the specimen did not fail during testing (Fig. 4).

7. Shrinkage tests

The evaluation and classification of shrinkage in CARDIFRC is the main purpose of this section. For theshrinkage experiments prisms of dimensions 50 · 50 · 250 mm were used. Both fibred and plain specimenswere prepared. The idea of this was to evaluate the effect of the fibres on the shrinkage of plain CARDIFRCmatrix.

Fig. 3. Contour plot showing the fibre distribution for the 100 · 100 mm beam plane of failure, after fatigue testing between 10% and 70%Pu (failure after four cycles).

Fig. 4. Contour plot showing the fibre distribution for the 100 · 100 mm beam plane of failure, after fatigue testing between 10% and 70%Pu (no failure after 1,000,000 cycles).

F.A. Farhat et al. / Engineering Fracture Mechanics 74 (2007) 151–167 157

7.1. Shrinkage specimen preparation

The beam specimen preparation for the shrinkage experiments in terms of mixing, casting and vibrating isthe same as specified in the patent GB 2391010. A very interesting point for the shrinkage specimens is thecuring regime. If the specimens were cured using the traditional curing regime recommended for CARDIFRC(i.e. 7 days at 90 �C) the main dominating period, which is the first 7 days after casting [16], for the autogenousshrinkage would be lost. In order to overcome this problem, the specimens, instead of hot curing immediatelyafter demoulding, were wrapped using thin vinyl acetate sheets.

It is well documented in the literature [16] that for high performance fibre-reinforced cementitious compos-ites it can be assumed that no shrinkage takes place for the first 19 h after placement, i.e. the time required forthe initial setting of the material. Hence, the specimens were left in the steel moulds for about 17 h in order forCARDIFRC to harden sufficiently well for handling. After the specimens were demoulded acoustic vibratingwire gauges were attached to their sides. Each beam specimen carried two of these gauges, which were care-fully aligned to be exactly opposite to each other.

After the gauges were attached, the beams were carefully wrapped, taking care not to damage the gauges.The specimens were wrapped with vinyl acetate sheets and aluminium adhesive tape, preventing any moistureexchange with the surrounding environment. After wrapping the specimens and insulating them properly, theywere connected to the data logger.

7.2. Shrinkage strains

Autogenous shrinkage strains measured will be presented next. For the presentation of the experimentalresults, a distinction is made between the time divisions. Twelve prisms having dimensions 50 · 50 ·250 mm have been made for each type of mix, namely mixes with and without fibres. The graphs illustratedin the following sections are the average values of the 12 prisms for both mixes. From the experimental set-up,the development of the autogenous shrinkage strains is measured as a function of time.

The measurements started at 19 h after casting. In Fig. 5 and elsewhere, SF and SNF are used to designatesmall prisms with and without fibres, respectively. It has to be mentioned that both types of mix have nearlythe same constituents expect for the fibres. It is clear from the first 24 h (Fig. 5(a)) that the presence of fibresreduces the autogenous shrinkage strains, as expected. The mixes without fibres exhibit a rapid development ofautogenous shrinkage strains. This increase in shrinkage strains takes place at a higher rate than for the mixescontaining fibres. The maximum values for mixes with and without fibres, after the first 24 h are about 103 and156 le, respectively. The inclusion of fibres in the matrix has a restraining effect on the development of theautogenous shrinkage strains.

020

4060

80100

120140

160180

0 5 10 15 20 25 30Time (hrs)

Mic

rost

rain

(µ

ε)

SNFSF

0

100

200

300

400

500

600

0 1 2 3 4 5 6 7 8Time (days)

Mic

rost

rain

(µ

ε)

SNFSF

0

100

200

300

400

500

600

700

800

0 4 8 12 16 20 24 28 32Time (days)

Mic

rost

rain

(µ

ε)

SNF SF

SNF SF

0

200

400

600

800

1000

1200

0 10 20 30 40 50 60 70 80Time (days)

Mic

rost

rain

(µ

ε)

(a) (b)

(d)(c)

Fig. 5. Autogenous shrinkage strain variation with time for mixes with and without fibres at different times of the experimental study:(a) 0–24 h, (b) 0–7 days, (c) 0–30 days and (d) up to 75 days.

158 F.A. Farhat et al. / Engineering Fracture Mechanics 74 (2007) 151–167

Fig. 5(b) shows that the autogenous shrinkage strain development continues at a high rate for the first 7 days,especially in mixes without fibres. Mixes containing fibres exhibit a significant decrease in the autogenous strains.The strains on the seventh day are about 317 and 545 le for the mixes with and without fibres, respectively.

The rate of increase of autogenous shrinkage strains slows after the 10th day as seen in Fig. 5(c). This con-firms our earlier observations which are also mentioned in literature; the main dominating period for theautogenous shrinkage is the first 10 days after casting. The strains reached about 754 and 480 le for mixeswithout and with fibres, respectively at the end of the first month.

The autogenous volumetric changes seem to continue even at the end of 75 days. However, it is clear thatthe rate of strain development is slower compared to the early stages. The most probable reason for this phe-nomenon is the relatively coarse type of the cement used (Blaine fineness 290–420 m2/kg), which results in aslow hydration process. Such phenomenon of long lasting hydration and slow autogenous volume deforma-tions have been previously reported in the literature [16–19]. The maximum shrinkage strains for mixes withand without fibres are 577 and 1000.24 le, respectively. Another key issue which may help in the understand-ing of this long lasting phenomenon of autogenous shrinkage is that the material, had not undergone any hotcuring. The specimens after demoulding and attachment of the acoustic vibrating wire gauges were insulatedand placed in a room with controlled environment (constant room temperature of 20 �C). The fact that no hotcuring was used means that chemical reactions, triggered during hydration period, last much longer.

The effect of fibres on the reduction in autogenous shrinkage strains is pronounced. Without fibres the self-induced shrinkage strains are 74% larger. Table 5 summarises the measured autogenous shrinkage strains atthe end of each time interval.

Table 5Measured autogenous shrinkage strains at the end of each time interval for mixes with and without fibres

Autogenous shrinkagestrains mixes with fibres (le)

Autogenous shrinkage strainsmixes without fibres (le)

0–24 h 103.24 156.260–7 days 317.15 545.46Up to 30 days 479.53 754.25Up to 75 days 577.00 1000.24

F.A. Farhat et al. / Engineering Fracture Mechanics 74 (2007) 151–167 159

7.3. Proposed model

During the hardening process of a cementitious system, the degree of hydration and the relative humidity ofthe system continuously change. The relative humidity in the gradually emptying pore space is an unknownparameter that has to be calculated from the actual moisture state in the hardening cement paste. Immediatelyafter mixing, the relative humidity reaches its maximum value, 100%. As hydration proceeds this value willdrop leading to self-desiccation. The thermodynamic equilibrium of the system requires an increase in the sur-face tension in the adsorption layer. This increase in the surface tension is associated with stresses that actfrom the interior of the hardening microstructure and provoke autogenous shrinkage. The constitutive rela-tion that connects the autogenous shrinkage to the surface tension in adsorption layer is the well-known Bang-ham equation:

Fig. 6.adsorp

oea

oa¼ k

oroa

ð1Þ

Here oea is the strain increment that describes the microstructural deformation of the hardening paste – auto-genous shrinkage due to self-desiccation – or the surface tension increment and k a proportionality factor. Thelatter is nothing but the compliance (inverse of stiffness) of the cement paste and is strongly related to the de-gree of hydration. Thermodynamic equilibrium in the gradually emptying pore space can only be establishediteratively. The reason for this is that all the associated equations are implicit functions and therefore no directsolution can be obtained.

As has been mentioned, as the hydration proceeds the relative humidity in the gradually emptying porespace will decrease. From a thermodynamic point of view, the relative humidity can be considered as the mainparameter of the system. A change in the relative humidity of the system, (see Eq. (2)) will result not only in achange of the air (gas) pressure in the empty pore space, (Eq. (3)), but also in a change of the surface tension inthe adsorption layer at the pore wall area (Eq. (4)):

lnðRHÞ ¼ lnpg

p0

� �¼ �4r

RT cw/wat

ð2Þ

pg ¼RTV w

lnðRHÞ ð3Þ

r ¼ RTZ pg=p0¼1

pg=p0

Cd lnpg

p0

� �� �ð4Þ

Eq. (4) gives the surface tension. As can be seen the surface tension is a function of the relative humidity(pg/p0) present in the empty pore volume, and a change of this relative humidity will cause an increase inthe surface tension [17]. Eq. (4) can be used to establish iteratively the thermodynamic equilibrium of the

Thickness of the adsorption layer against RH and some proposed functions for C. Note that for RH = 100% the thickness of thetion layer reaches the maximum of 18 A [17].

160 F.A. Farhat et al. / Engineering Fracture Mechanics 74 (2007) 151–167

hydrating paste. It has to be mentioned that the thickness of the adsorption layer C is also considered to be afunction of this relative humidity (pg/p0) i.e. C ¼ Cðpg

p0Þ. In other words, a change in the relative pressure in the

pore volume not only will cause changes in the surface tension but also to the thickness of the adsorption layer(Fig. 6).

Once the thermodynamic equilibrium has been reached, the increment of the deformation can be simplydetermined by using the modified Bangham concept:

TableExperi

At 10

FNF

At 35

FNF

At 75

FNF

Des ¼ kDr ð5Þ

Note that the pore wall area, the specific mass of the paste and the modulus of elasticity of the paste alsochange throughout the hardening process. In fact, the restraint to the free autogenous shrinkage of CARDI-FRC paste offered by the fibres is estimated through the increase in the modulus of elasticity of the paste withfibres as the hydration proceeds.

7.4. Experimental data versus modelling results

Fig. 7 compares the experimental data and those given by the proposed model.As can be observed, for about the first 10 days for both mixes the model is in good agreement with the

experimental results. As a matter of fact, in the first 7 days the model slightly overestimates the autogenousshrinkage strains. As hydration proceeds the results obtained from the model underestimate somewhat theexperimental data. Table 6 presents the results for both model and experiments at the end of various timeintervals. The reason for this underestimation may be that the model does not take into account the hydrationof dicalcium silicate which normally occurs after that of the primary tricalcium silicate.

0

200

400

600

800

1000

1200

0 10 20 30 40 50 60 70 80Time (days)

Mic

rost

rain

(µ

ε)

SNF SF

Model-NF Model-F

Fig. 7. Experimental and model results for mixes with and without fibres.

6mental and model results at various times (F: mixes with fibres; NF: mixes without fibres)

Experimental values (le) Model values (le)

days

401 401620 574

days

493 453773 727

days

577 5341000 928

F.A. Farhat et al. / Engineering Fracture Mechanics 74 (2007) 151–167 161

7.5. Importance of fibre distribution to autogenous shrinkage

Along with the small prism specimens described above several large beams 100 · 100 · 500 mm were alsotested. These specimens did not give consistent autogenous shrinkage strain readings; there was a very largescatter in the results for mixes with fibres, but not so with the mixes without fibres, as can be seen from Fig. 8.

The spread of the results in beams with fibres can be attributed to the uneven distribution of fibres in thematrix, as in the large fatigue specimens described in Section 6. This has been verified by image analysis ofCARDIFRC sections cut from large beam specimens [20]. Fig. 9 shows a typical result from the imageanalysis.

In Fig. 9(b), dark colour indicates low fibre concentration whereas light colour is used to show high fibreconcentrations. As can be observed from the results of image analysis the distribution of fibres in the specimenis fairly uneven. The fibre concentration is very low at the bottom of the section, whereas a large number offibres is present in the top half. Two possible reasons were identified for this uneven distribution of fibres.First, the specimens were excessively large in size to be well compacted so that the fibres could not distributeuniformly in the matrix. That also explains the fact that CARDIFRC is primarily intended for use as caststrips of relatively small thickness, suitable for retrofitting, and not for casting large structural members.The second reason for the uneven distribution of fibres in the matrix had to do with the vibration frequencyused during compaction, which was initially set at 97 Hz. This frequency proved to be too high and as a resultthe vibration was excessively powerful and caused migration of the fibres in the mix. The vibration frequencyadopted for compacting the small prism specimens was 50 Hz.

0

50

100

150

200

250

300

350

400

450

500

0 10 20 30 40 50 60 70 80 90 100Time (hrs)

Mic

rost

rain

(µ

ε)

Beam 1 Beam 2Beam 3 Beam 4Beam 5

Beam 1Beam 3Beam 5Beam 6

Beam 2Beam 4Beam 6

0

50

100

150

200

250

300

350

400

450

0 10 20 30 40 50 60 70 80 90 100Time (hrs)

Mic

rost

rain

(µ

ε)

(a) (b)

Fig. 8. Autogenous shrinkage strain deformation with time for large beams (a) with fibres and (b) without fibres.

Fig. 9. (a) Section of a CARDIFRC 100 · 100 · 500 mm beam. (b) Contour plot showing the contours of fibre distribution in this section[20].

162 F.A. Farhat et al. / Engineering Fracture Mechanics 74 (2007) 151–167

8. Application of CARDIFRC to retrofitting

Twenty-four under-reinforced RC beams were prepared. Of these, 16 were retrofitted with CARDIFRCand eight left as control. The beams were fabricated in six batches, with each batch consisting of four beams.Along with each batch of beams, three cylinders (100 mm in diameter · 200 mm high) and three cubes(100 mm) were also cast. The beams were allowed to cure in a water bath for 28 days. The cement:fine aggre-gate:coarse proportions in the concrete mix were 1:1.8:2.8 by weight and the water/cement ratio was 0.50.Ordinary Portland cement was used and the maximum size of aggregate was 10 mm.

The beams were reinforced with a single 12 mm rebar 1200 mm long, 100 mm wide and 150 mm deep. Shearreinforcement consisted of 6 mm deformed bars placed at 65 mm spacing. According to the British StandardBS 8110 the beams were over-designed for shear to prevent brittle failure due to the increased shear load onthe strengthened beam so the flexural behaviour could be observed throughout the loading up to failure. Twodifferent configurations of retrofitting were investigated; one strip bonded on the tension face and three strips(one bonded on the tension face and the others on the vertical sides, Fig. 10). Of the 24 beams used in thisprogramme, eight were tested to failure as control beams to compare with the performance of those retrofittedwith CARDIFRC strips. The remaining 16 were pre-loaded to approximately 75% of this failure load toinduce flexural cracking. The beams were tested under four-point bending over a span of 1100 mm. The spac-ing between the applied loads was 400 mm.

8.1. Retrofitting procedure

The retrofit material, CARDIFRC was cast as flat strips in 1030 mm long and 100 mm wide steel mouldswith a well-oiled base and raised border 16 mm high. The strips were left to cure in the moulds for 24 h at20 �C before de-moulding. The retrofit strips were then hot-cured at 90 �C for further 7 days. They were thenbonded to the prepared surfaces of the damaged concrete beam using epoxy based adhesive (Sikadur 31). Inorder to improve the bond between the repair material and the original concrete, the contact surfaces of con-crete were cleaned and roughened using an angle grinder. The repair strip was placed on the adhesive andevenly pressed. The adhesive was then cured for 24 h. The beams were exposed to 30 or 90 thermal cycles

Fig. 10. Configurations of retrofitting. Beams retrofitted with (a) one strip on the tension face and (b) one strip on the tension and fourshort and two continuous strips on sides, fully covering supports and tension strip sides.

Table 7Compressive and splitting strengths of ordinary concrete used in test beams

Thermal cycles Average compressivestrength (MPa)

COV (%) Average splittingstrength (MPa)

COV (%)

0 56.10 1.8 4.46 2.330 66.73 1.7 5.10 7.090 60.67 2.5 4.84 2.7

Fig. 11. Flexural cracking in a beam retrofitted with one strip on the tension face.

F.A. Farhat et al. / Engineering Fracture Mechanics 74 (2007) 151–167 163

and then tested at room temperature in four-point bending. As mentioned earlier, each 24-h thermal cycletried to mimic a temperature cycle in hot dry climate when exposed concrete surfaces are known to reach veryhigh temperatures. It consisted of a temperature rise period from room temperature to 90 �C, followed by adwell period of 8 h at this elevated temperature and a slow cooling period back to room temperature.

8.2. Test results

The test results show that the response of the control beams has very little scatter, especially before theattainment of the maximum load. It appears that thermal cycling has very little effect on the load carryingcapacity of control beams reinforced in flexure and shear. After 90 thermal cycles the shear reinforcementseems to counteract the reduction expected due to the reduction in compressive strength (Table 7).

As expected, all beams retrofitted with one strip failed in pure flexure. The flexural failures observed weregenerally characterised by a single flexural crack occurring in the middle third of the beam extending upwardsto the concrete top fibre between the load points and downwards through the retrofit material (Fig. 11). Allbeams failed at loads higher than the average failure load of control beams. Moreover, both the deflectionbehaviour and failure modes were similar for all exposure conditions.

Of the eight beams retrofitted with three continuous and four short strips only one beam failed in shear.This failure occurred through the joint connecting the long and short strip. Due to the bridging action ofthe tension strip, the crack was arrested in the CARDIFRC tension strip. This type of failure can be classifiedas a ductile shear failure. All the remaining beams failed in pure flexure. The first crack appeared in the middlethird of the tension strip. As the load was increased, this crack propagated vertically in the side strips and themouth of the initial crack in the tension strip opened gradually. As the load was increased further the prop-agation of the cracks on both sides of the beam towards the compression top fibre became visible. After thepeak load, the load–deflection curves descended gently. Finally, the beam exhibited plastic behaviour with theyielding of steel.

8.3. Analytical model

To model the response of a structure based on fracture mechanics, it is necessary to have a good knowledgeof the details of the formation and growth of cracks in the structure.

When the retrofitted beam is under bending, the resistance to crack opening consists of three different com-ponents. The first component is due to the bridging force across the crack faces from the reinforcing steel, the

tt

c

h

b

M

fctm

σc

Fsa M

FP

w

hts

ctt

b

σPFS

a

σc

w

FP

MM

Fig. 12. Free body diagram of the dominant flexural crack in retrofitted beams. Beams retrofitted with (a) one tension strip and (b) onetension and two side strips.

164 F.A. Farhat et al. / Engineering Fracture Mechanics 74 (2007) 151–167

second is from the post-peak tension softening response of concrete, and the third is from the bridging stressesin the retrofit strips (Fig. 12). The closure pressure thus exerted counteracts the opening action of the appliedmoment M. As the stress at the crack tip is finite, the net stress intensity factor at the crack tip must vanish.

In fact, this requires that the crack faces close smoothly near the tip. The net KI at the crack tip is obtainedby superimposing the stress intensity factors produced at the crack tip by the applied moment (KIM), and theclosure forces exerted by steel (KIS), concrete (KIconc), tension retrofit strips (KI(t-strip)), and side retrofit strips(KI(s-strip)) (if they are used). The condition of finite stress at crack tip, i.e. K I = 0 is therefore

KIM � KIS � KIconc � KIðt-stripÞ � KIðs-stripÞ ¼ 0 ð6Þ

In addition to the condition of smooth closure of crack faces at its tip, we must consider the compatibility ofcrack opening displacement of a retrofitted beam [21]. The crack opening displacement can again be written asthe vectorial sum of the contribution from the applied bending moment and the closure forces exerted by steel,concrete and retrofit strips. The compatibility condition of the crack opening need be satisfied only at the levelof the steel reinforcement, because of the assumed known (i.e. linear) variation along the length of the crack:

ðwSÞM � ðwSÞS � ðwSÞconc � ðwSÞt-strip � ðwSÞs-strip ¼ wS ð7Þ

where (wS)i are the crack opening displacement at the level of the steel bar produced by the applied bendingmoment and the closure forces exerted by steel, concrete, tension strip, and side strips, respectively. Note thatthe crack opening wS at the level of the reinforcement is not known, but is to be determined. Each term in theleft-hand side of (7) can be expressed in terms of the corresponding compliance coefficients. For instance, thecrack opening at the level of the steel bar produced by the applied moment is

ðwSÞM ¼ kSMM ð8Þ

F.A. Farhat et al. / Engineering Fracture Mechanics 74 (2007) 151–167 165

where kSM (compliance coefficient) is the crack opening at the level of steel when a unit bending moment isapplied to the crack. The compliance coefficients can be computed from energy principles and Clapeyron’stheorem [22]. These are listed in Alaee and Karihaloo [12].

The force in steel is related to the crack opening at this level by the following formula:

TableCrack90 ther

Configat criti

fS ¼F S

AS

¼ 4:8� 11876:5wS

A1=4ð9Þ

This formula has been established by Alaee and Karihaloo [12] based on the experimental results of Lange-Kornbak and Karihaloo [23]. Due to the similarity between the test beams in Alaee and Karihaloo [12]and those in the present study Eq. (9) was used in the analysis as the bridging force exerted by steel.

The contributions from the tension and side strips (if used) in Eqs. (6) and (7) require a knowledge of thetension softening relation of CARDIFRC. This relation has been obtained from uniaxial tests [15]. A simpli-fied relation can also be found in [12].

To determine the three unknown parameters a, w and M, Eqs. (6) and (7) should be simultaneously satisfiedfor a flexural crack. Each of the two equations are solved for all possible combinations of a and w and M cal-culated. The intersection of the two sets of results for the same pair of given a and w solves the two equations.From this set the maximum moment was chosen as the moment resistance of the beam.

8.4. Model results

The method described above was applied to the critical section of all test beams (i.e. the section in which thedominant crack forms). Their moment resistance MF, crack mouth opening wF and crack depth aF at the

8opening wF, crack depth aF and the moment resistance MF of the beams at the maximum load predicted by the model after 0, 30 andmal cycles

uration of retrofittingcal section

Results Thermal cycles

0 30 90

wF (mm) 0.12 0.11 0.11aF (mm) 112 110 111MF (kN m) 9.25 9.41 9.41

wF (mm) 0.13 0.12 0.14aF (mm) 84 82 82MF (kN m) 13.01 13.52 13.48

0

2

4

6

8

10

12

14

16

18

Max

imum

mom

ent k

Nm

Model results

Test results

1-st

rip

(0)

3-st

rips

(0)

1-st

rip

(90)

1-st

rip

(30)

3-st

rips

(90

)

3-st

rips

(30

)

Fig. 13. Comparison of moment resistance of beams with predictions of model.

166 F.A. Farhat et al. / Engineering Fracture Mechanics 74 (2007) 151–167

maximum load were calculated. Table 8 gives the model results for the retrofitted beams (beams retrofittedwith one strip on the tension face and beams retrofitted with one strip on the tension face, two continuousand four short strips on the sides) after, 0, 30 and 90 thermal cycles.

Fig. 13 compares the moment resistance of the beams predicted by the model with the test results. It can beseen that the model results are in agreement with the test results. For beams retrofitted only with one strip onthe tension face, the model results seem to be in a very good agreement with the test results regardless of thenumber of thermal cycles. For beams retrofitted with one strip on the tension face, two continuous and fourshort strips on the sides, and exposed to no thermal cycles the model is also in a good agreement with the testresults. On the other hand, for beams after 30 and 90 thermal cycles the model results are slightly lower thanthe test.

9. Conclusions

CARDIFRC is very flaw tolerant under repeated flexural cyclic loading with amplitudes reaching 80% ofthe monotonic flexural strength provided the fibres are evenly distributed. To ensure the latter only thinobjects must be made from CARDIFRC and the compaction vibration frequency should be around 50 Hz.The matrix of CARDIFRC because of the very low water to binder ratio is prone to large autogenous shrink-age. However, the use of large volume of fibres reduces these strains by a factor of nearly two, provided againthe fibres are evenly distributed to offer uniform overall restrain to these self-induced volumetric changes.

Retrofitting with thin CARDIFRC strips bonded to the tension face improves the load carrying capacityand the serviceability of the beam. To prevent shear failure, CARDIFRC strips should also be bonded to thesides of the beams. This configuration of retrofitting can increase the failure load by up to 86%. With thermalcycling, the failure load increased by up to 90% and 87% after 30 and 90 thermal cycles, respectively. The roomtemperature figure therefore provides a safe value for design at elevated temperatures.

No visual deterioration or bond degradation was observed after thermal cycling of the retrofitted beams(the bond between the repair material and the concrete substrate remained intact) attesting to the good ther-mal compatibility between the concrete and CARDIFRC. Therefore, this type of retrofit material can be suc-cessfully used in hot climates. The moment resistance of the retrofitted beams is very well predicted by thefracture model.

References

[1] Jones R, Swamy RN, Charif A. Plate separation and anchorage of reinforced concrete beams strengthened by epoxy-bonded steelplates. Struct Engr [Lond] 1988;66(5):85–94.

[2] Ziraba Y, Baluch MB, Basenbul IA, Sharif AM, Azad AK, Al-Sulaimani GJ. Guidelines towards the design of reinforced concretebeams with external plates. ACI Struct J 1994;91(6):639–46.

[3] Meier U, Deuring M, Meier H, Schwegler G. Strengthening of structures with CFRP Laminates: research and application inSwitzerland. Advanced composite materials in bridges and structures. Can Soc Civil Engng 1992:243–51.

[4] Meier U. Post strengthening by continues fibre laminates in Europe, non-metallic (FRP) reinforcement for concrete structures. JpnConcr Inst 1997;1:41–56.

[5] Sen R, Mullins G, Shahawy M, Spain J. Durability of CFRP/epoxy/concrete bond. Composites in the transportation industry. In:Proceedings of the ACUN-2 international composite conference, University of South Wales, Australia, 2000.

[6] Zhen M, Chung DDL. Effects of temperature and stress on the interface between concrete and its fibre-matrix composite retrofit,studies by electrical resistance measurement. Cement Concr Res 2000;30:799–802.

[7] Toutanji HA, Gomez W. Durability characteristics of concrete externally bonded with FRP composite sheets. Cement Concr Compos1997;19:351–8.

[8] Karihaloo BL, Alaee FJ, Benson SDP. A new technique for retrofitting damaged concrete structures. Proc Inst Civil Engrs, BldgStruct 2002;152(4):309–18.

[9] Karihaloo BL, Benson SDP, Didiuk PM, Fraser SA, Hamill N, Jenkins TA. Retrofitting damaged RC beams with high-performancefibre-reinforced concrete. In: Proceedings of the tenth annual BCA, British Cement Association, Birmingham University, 2000.p. 153–64.

[10] Alaee FJ, Benson SDP, Karihaloo BL. High-performance cementitious composites for retrofitting. International Journal of Materialsand Product Technology 2002;17(1/2):17–31.

[11] Alaee FJ, Karihaloo BL. Retrofitting of reinforced concrete beams with CARDIFRC�. J Compos Constr 2003;7(3):174–86.[12] Alaee FJ, Karihaloo BL. A fracture model for flexural failure of beams retrofitted with CARDIFRC�. ASCE J Engng Mech 2003;

129(9):1028–38.

F.A. Farhat et al. / Engineering Fracture Mechanics 74 (2007) 151–167 167

[13] Karihaloo BL, Jefferson AD. Looking into concrete. Mag Concr Res 2001;53:135–47.[14] Rebat KH. Behaviour of fibre reinforced concrete as subjected to thermal cycling. MSc thesis. Irbid, Jordan: Civil Engineering

Department; 1999.[15] Benson SDP. CARDIFRC – development and constitutive behaviour. PhD thesis. UK: Cardiff University; 2003.[16] Cheyrezy M, Behloul M. Creep and shrinkage of ultra-high performance concrete. In: Ulm FJ, Bazant ZP, Wittmann FH, editors.

Proceedings of the 6th international conference on creep, shrinkage and durability mechanics of concrete and other quasi-brittlematerials. Elsevier; 2001. p. 527–38.

[17] Koenders EAB. Simulation of volume changes in hardening cement based materials. PhD thesis. Delft University Press; 1997.[18] Koenders EAB, Breugel Van K. Modelling dimensional changes in low water/cement ratio pastes. In: Tazawa E-i, editor. Proceedings

of the international workshop on autogenous shrinkage of concrete organised by JCI. E & FN Spon; 1999. p. 289–98.[19] Tazawa E, Miyazawa S. Experimental study on mechanism of autogenous shrinkage of concrete. Cement Concr Res 1995;25(2):

1633–8.[20] Nicolaides D. Fracture and fatigue of CARDIFRC. PhD thesis. UK: Cardiff University; 2004.[21] Leung CKY. Delamination failure in concrete beams retrofitted with a bonded plate. In: Mihashi H, Rokugo K, editors. Fracture

mechanics of concrete structures, vol. 3. Freiburg, Germany: AEDIFICATIO Publishers; 1998. p. 1783–92.[22] Bosco C, Carpinteri A. Fracture mechanics evaluation of minimum reinforcement in concrete structures. In: Carpinteri A, editor.

Application of fracture mechanics to reinforced concrete. Proceedings of the international workshop, Turin, Italy, 1990. London:Elsevier; 1992. p. 347–77.

[23] Lange-Kornbak D, Karihaloo BL. Fracture mechanical prediction of transitional failure and strength of singly reinforced beams. In:Carpinteri A, editor. Minimum reinforcement in concrete members, ESIS Publication 24. London: Elsevier; 1999. p. 31–42.