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Materials and Structures (2006) 39:365–377DOI 10.1617/s11527-005-9009-4

Stress-strain characteristic of SFRC using recycled fibres

H. Tlemat · K. Pilakoutas · K. Neocleous

Received: 2 March 2005 / Accepted: 24 May 2005C© RILEM 2006

Abstract This paper presents work from a compre-hensive study on the development of a flexural designframework for concrete reinforced with steel fibres thatare recovered from used tyres. The experimental flex-ural behaviour of notched concrete prisms reinforcedwith these fibres is initially presented. For comparisonpurposes, prisms reinforced with industrially producedfibres are also considered. An attempt to adopt an ex-isting RILEM design framework to derive appropriatetensile stress-strain blocks is made, but problems areidentified with key parameters of the framework. Theinfluence of crack propagation and location of neutralaxis depth on the tensile stress distribution is exam-ined. Following an analytical study, it is concluded thatthe uniaxial stress-strain model, proposed by RILEMoverestimates the load-carrying capacity and should bemodified by utilising more advanced analytical tech-niques.

Resume Cet article presente l’etude sur ledeveloppement d’un cadre en beton aux fibresd’acier recuperees des pneus utilises. Le comporte-ment experimental en flexion des prismes en betonentaillees, renforcees avec des fibres, est initiallementpresente. A fin de comparer les resultats, les prismes

H. Tlemat, Buro Happold, Birmingham, UK

K. Pilakoutas · K. Neocleous, Centre for Cement andConcrete, Department of Civil and Structural Engineering,The University of Sheffield, Sheffield, UK

renforcees avec des fibres produites industriellementsont egalement considerees. Pour deduire les blocscontrainte-deformation en tension appropries, unetentative d’adopter un cadre existant de conceptionRILEM est effectuee, mais des problemes avec lesparametres cles du cadre ont ete identifies. L’influencede la propagation des fissures ainsi que la profondeurde l’axe neutre sur la distribution des efforts de tensionest examinee. A la suite d’une analyse analytique, onpeut conclure que le modele de contrainte-deformationuniaxial propose par RILEM surestime la capaciteportante et il doit etre modifie en utilisant destechniques analytiques plus elaborees.

1. Introduction

Waste arising from used tyres is currently being man-aged through the implementation of environmental leg-islation. In the European Union, the driving force be-hind the waste management of tyres is the imple-mentation of a number of directives, especially the1999 Landfill directive [1]. This directive has alreadystopped the disposal of whole tyres to landfill, and willprohibit the disposal of tyre constituents by 2006. As aresult, tyre recycling has become much more popularsince it is one of the most environmentally friendly andeconomically viable ways of managing waste tyres.

Tyre shredding, pyrolysis and cryogenic reductionof tyres are currently the main processes used for therecycling of used tyres. The first process reduces tyres

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to rubber crumb and steel fibres. In pyrolysis, tyresare thermally decomposed to their constituents in theabsence of air such as oil, gases (hydrogen, methane,and other hydrocarbons), carbon, and steel wires. Inthe cryogenic process the tyre is fractured after beingfrozen to a suitable temperature.

Research at the University of Sheffield [2–5] demon-strated that steel fibres recycled from used tyres (RSF)can be effectively used to reinforce concrete. In ad-dition, it was indicated that the mechanical behaviourof concrete reinforced with tyre-recycled steel fibres(RSFRC) is comparable to that of conventional steelfibre reinforced concrete (SFRC). Therefore, it can bepresumed that the design models developed to evaluatethe flexural resistance of conventional SFRC are alsoapplicable for RSFRC.

An attempt to use the RILEM design model [6–8]in FEA simulation for the derivation of flexural be-haviour of RSFRC was not successful due to the fol-lowing reasons. The RILEM model considers almostconstant tensile stress in the fracture zone, which isclearly not the case for all fibres, since failure is mainlythrough pull-out and not yield.

The value used for the load at the limit of proportion-ality, Fu, directly affects the determination of the designparameters such as the stress at the limit of proportion-ality, ffct, and the equivalent flexural strengths, feq2 andfeq3. The authors found that the RILEM procedure fordetermining Fu [6] does not give consistent results. ABrite-Euram project on SFRC developed an iterativeprocedure for determining Fu, where a reasonable es-timate of the initial slope (between 0.1 and 0.4 of thepeak load) is necessary [9]. This project demonstratedthat the iterative technique leads to more uniform re-sults, but attempts by the authors to use the proceduredid not lead to consistent results. It is noted that thefinal RILEM recommendation for the σ -ε model usesresidual flexural tensile strengths and, hence, the modelis independent of Fu.

Finally, two fixed values are considered for the neu-tral axis depth for the determination of post-crackingflexural tensile strengths (σ 1 and σ 2) after cracking,independent of the amount and type of fibre reinforce-ment.

This paper describes an experimental study, carriedout on RSFRC and SFRC prisms to investigate theabove issues. The effect of crack propagation and lo-cation of neutral-axis depth on the tensile stress distri-bution are examined.

The study was carried out on notched prisms by util-ising the RILEM bending test [6]. It is noted that a four-point load arrangement was used instead of three-pointload. The use of four-point load arrangement createda region of constant moment and, hence, minimisedthe overestimation of bending resistance, caused at thepoint of load application by the load-spreading effect[10].

The first part of this paper presents the type of fibresused in this study, and describes the tests performedon prismatic specimens. The second part of the paperexamines the effect of fibre type and content on theflexural behaviour of RSFRC and attempts to evaluateappropriate stress-strain relationships by consideringthe RILEM design model [7, 8].

2. Experimental examination

2.1. Methodology

2.1.1. Types of fibres and mixes

Two types of RSF were considered: a) pyrolysed andb) shredded. Steel fibres obtained from virgin tyre cordand two types of industrially produced steel fibres werealso examined.

The pyrolysed steel fibres (PRSF) were obtained bycutting recycled steel tyre-cord to 50 mm pieces. Thecord was obtained from the microwave-induced pyrol-ysis of whole tyres [11]. The recycled cord was undam-aged, since the tyres were decomposed at relatively lowtemperatures (about 350 ◦C). However, it is noted thatthe cord was not entirely clean, as it contained a layerof carbon on its surface. In addition, the steel fibre di-ameter depends exclusively on the type of cord usedin the tyre. The typical fibres shown in Fig. 1a wereobtained from super-single tyres. The fibres comprised12 wires of 0.23 mm diameter, twisted together into acore strand of 0.85 mm diameter, and surrounded withanother 15 twisted wires. On the cord surface thereis a single twisted wire with a twist pitch of 5.33 mm(Fig. 1b). The fibre overall external diameter is 1.55 mmwith effective diameter 1.16 mm and a tensile strengthin excess of 1250 MPa. In general, the PRSF were notconsistent in diameter (ranging 0.8 to 1.55 mm) andshape (Fig. 1a).

The virgin steel fibres (VSF) were obtained by cut-ting virgin steel tyre-cord to 50 mm pieces. The VSF

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Fig. 1 (a) Pyrolysed and virgin steel fibres, (b) Construction ofone pyrolysed fibre.

Fig. 2 Un-sieved shredded steel fibres.

Fig. 3 Types of industrially produced steel fibres.

fibres were free from any contaminates and had a con-sistent diameter of 1.55 mm. Their surface and tensilestrength were similar to those of PRSF fibres (Fig. 1a).

The shredded RSF (SRSF) were obtained from thethird stage of mechanical shredding of discarded tyresand, hence, they were inconsistent in diameter andshape (Fig. 2). The SRSF were sieved to avoid usingfibres containing rubber crumb on their surface and toremove the larger pieces of steel. In general, the sievedSRSF were more consistent in size and shape and had anaverage diameter of 0.23 mm, a length averaging over20 mm and a tensile strength of around 2000 MPa.

Two types of industrially produced steel fibres (ISF)were used and both had a hooked end as illustrated inFig. 3. The fibres with a flattened end, here called ISF-

Table 1 Summary of geometry and tensile strength for eachtype of fibre

Length (l) Diameter (d) Tensile strengthFibre type [mm] [mm] N/mm2

SRSF 20a 0.23a ∼ 2000PRSF 50 0.80 – 1.55 >1250VSF 50 1.55 >1250ISF-1 50 1.00b 1050ISF-2 50 1.05 1000

aaverage, bnominal

1, had a length of 50 mm, a nominal diameter of 1 mm,and a tensile strength of 1050 MPa. The ISF-2 fibreswere made of cold drawn wires, 50 mm long, 1.05 mmthick, and a tensile strength of 1000 MPa (Fig. 3). Thegeometry and tensile strength of each fibre type aresummarised in Table 1.

Six groups of prisms were cast in the study (seeTable 2). In these groups, all sets comprised of threespecimens. Group one comprised one set of plain con-crete prisms, which were used as control specimens.Group two included three sets of prisms containingSRSF for three fibre ratios (0.5, 1 and 2% by mass).Groups three and four included three sets of prismsreinforced with PRSF and VSF, respectively, havingfibre ratios of 1.5, 3 and 6% by mass. Groups fiveand six each comprised of one set of prisms reinforcedwith high fibre ratio (6% by mass) of ISF-1 and ISF-2,respectively.

A mix design (SPFA 40/30) with a cement content of236 kg/m3 and a water to cement ratio of 0.66 was usedfor all types of prisms. The coarse and fine aggregateused in this work was fluvial dragged gravel. For practi-cal mixes, the maximum size of coarse aggregate is rec-ommended not to be larger than 2/3 of the length of thesteel fibre and should not exceed 1/5 of the minimumsize of the specimen [12]. Hence, the aggregates usedfor plain and SRSF specimens had a maximum size of10 mm. Two sizes of coarse aggregates were used forthe remaining fibres: a) one with a maximum size of10 mm, and b) one with a maximum size of 20 mm.To improve workability, 30% (by cement mass) of aspecial SPFA (superpozzolan fly-ash) and various per-centages of superplasticizer (Sulphonated Napthalene-Formaldehyde Condensate) were used. Each mix re-sulted in a set of three prisms and six cubes.

As expected, Table 2 shows that increasing the fi-bre ratio reduces the workability as measured by the

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Table 2 Material information for each type of prism

Aggregates

Fibre ratio Aspect ratio d/l SPc Sand 10 mm 20 mm SlumpGroups: Type of Prism [%]a [–] [%]b [kg/m3] [kg/m3] [kg/m3] [mm]

Plain 0.0 – 0.1 865 345 690 200SRSF 0.5 ≤87 0.2 860 1035 0 160

1.0 ≤87 0.4 855 1035 0 1502.0 ≤87 0.75 744 1035 0 55

PRSF 1.5 ≈32 0.2 851 345 690 2003.0 ≈32 0.4 837 345 690 1506.0 ≈32 0.75 807 345 690 140

VSF 1.5 32 0.2 853 345 690 1603.0 32 0.4 841 345 690 906.0 32 0.75 815 345 690 70

ISF-1 6.0 50 0.75 815 345 690 150ISF-2 6.0 48 0.75 815 345 690 150

a% by mass, b% by cement mass, cSuperplasticizer

Table 3 Averaged test results

Fibre ratio fcm Age Fu Ppeak COVPp1 δu ffct, u feq,2 feq,3 fR,1 fR,4

Groups: Type of Prism [%] [MPa] [Day] [kN] [kN] [%] [mm] [MPa] [MPa] [MPa] [MPa] [MPa]

Plain 0.0 51.5 101 18.0 18.0 9 0.03 3.45 – – – –SRSF 0.5 49.5 90 18.5 18.5 22 0.05 4.26 1.4 1.6 1.1 0.8

1.0 50.0 94 23.1 23.1 5 0.06 5.32 2.0 2.8 3.9 1.72.0 45.0 105 27.1 27.1 6 0.08 6.24 2.4 4.1 6.0 2.5

PRSF 1.5 44.0 112 25.1 27.1 7 0.07 5.78 3.3 4.6 5.4 3.73.0 38.5 113 31.7 34.0 15 0.11 7.30 4.3 6.1 7.8 5.86.0 50.0 115 37.4 58.3 15 0.11 8.62 6.3 11.0 12.6 11.2

VSF 1.5 54.1 163 28.7 28.6 11 0.09 6.61 3.2 5.8 6.6 4.33.0 62.0 162 33.4 40.7 23 0.07 7.7 5.2 7.7 10.2 5.26.0 66.2 161 41.6 61.6 23 0.07 9.6 5.9 12.6 14.1 10.4

ISF-1 6.0 52.9 66 44.8 64.6 14 0.09 10.3 6.6 12.4 14.1 12.7

ISF-2 6.0 63.9 196 46.8 61.3 6 0.12 10.78 5.6 11.8 13.8 11.5

Coefficient of variation for Ppeak

slump test. To obtain a reasonable workability the su-perplasticizer was increased when the fibre ratio wasincreased.

2.1.2. Specimen preparation

The prismatic specimens (150 mm deep, 150 mm wide,and 550 mm long) were cast in timber moulds. Thespecimens were cast in two layers, and were vibratedin the moulds during casting. A day after casting, thespecimens were demoulded and then placed in the mistroom until the day of testing. A notch (25 mm high and5 mm thick) was sawn at mid-span, a day before testing,

using rotating diamond blades into the tensile face ofeach beam (perpendicular to the top casting surface)[4, 5]. The purpose of the notch was to act as a crackinducer. All tests were performed at an age shown inTable 3.

2.1.3. Testing procedure

Results from flexural tests on such concrete prismsare prone to significant experimental errors (due tospurious support displacements, machine stiffness andload rate) and, hence, accurate deflection measure-ments need to be made [13]. To avoid these errors and

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Fig. 4 Instrumentation and test set up.

the effect of torsion on the deflection measurements,it was decided to use a yoke (Fig. 4) as specified bythe Japanese standard [14]. The rollers were pinnedand, hence, free to rotate and to allow the expansionof concrete. The specimens were tested in a 100 kNservo-hydraulic machine under displacement controlat a constant rate of 0.2 mm/min [4, 5].

Average mid-span beam deflections were measuredon both sides of the beam (δ1 and δ2) using two trans-ducers fixed to the yoke (LVDT5) and, hence, any tor-sional effects (due to the roller arrangement) were can-celled out.

One transducer (LVDT4) was mounted across thenotch mouth to monitor the crack mouth opening dis-placement (CMOD). Furthermore, three transducerswere used to measure the crack propagation at differ-ent height locations, and one transducer was used onthe compressive face to measure the compressive strain(Fig. 5).

2.2. Results

2.2.1. Effect of fibre content and type

2.2.1.1. Compressive strength. For the compressivestre-ngth, cubes were placed according to BS 12 [15]

Fig. 5 Testing arrangement and instrumentation.

with the cast face not in contact with the platens ofthe testing machine The load was applied at a constantrate of stress within the range of 0.2 to 0.4 kN/s, andthe compressive strength was measured to the nearest0.5 MPa.

The cylinder compressive strength and the secantmodulus needed for the subsequence analysis were cal-culated according to Eurocode-2 [16] as follows.

ffcm = 0.85∗ fcm [MPa] (1)

Efcm = 9.5 f 2/3fcm [MPa] (2)

where, Efcm secant modulus of concrete in com-pression; ffcm mean compressive cylinder strength inSFRC; fcm measured mean compressive cube strengthin SFRC.

Table 3 shows the cube compressive strength as theaverage of six specimens tested on the same day asthe corresponding set of prisms. Since different con-stituents are used in the different mixes, a direct com-parison between groups is not easy to make. However,within groups, increased fibre reinforcement appearsto increase the compressive strength in all fibres exceptSRSF. The reduction of strength shown for SRSF 2%may be associated with the reduced workability in thatset. Between groups there is only one direct compar-ison that can be made relating to the sets having 6%fibres. If date of testing is taken into account, no majordifferences are noted.

2.2.1.2. Flexural strength. Figure 6 shows the aver-age load-deflection curve for the plain concrete prisms.Point A indicates the load when the first crack is con-sidered to have initiated. On further loading, the plain

370 Materials and Structures (2006) 39:365–377

Fig. 6 Average load versus mid-span deflection for controlbeam.

Fig. 7 Fracture of plain concrete prism.

Fig. 8 Flexural behaviour of SRSF prisms with different% offibres.

concrete prism broke suddenly in two halves (Fig. 7).The testing machine was not stiff enough to measurethe softening region of plain concrete and no furthermeasurements were recorded.

Figure 8 shows the average load versus average mid-span deflection for all the SRSF prisms. As expected,the flexural behaviour of the prisms improves as thefibre fraction increases. Fibres act as crack arrestors,giving a substantial increase in toughness, even whenfibres debond and are pulling out. In the case of 0.5%fibre ratio, only the toughness was increased. The peakload is 10% lower than of plain concrete, but that can beattributed to the lower compressive strength. However,

Fig. 9 Effects of PRSF and VSF fibre ratios on flexural resis-tance.

overall the peak load and the toughness increase withthe amount of fibres used.

A comparison between PRSF and VSF is shown inFig. 9. The VSF were tested to examine the effect ofcarbon black on the surface of PRSF. The virgin fibresappear to give higher strength and energy absorption ca-pacity. However, the concrete strength of PRSF (whichwas tested mush earlier than VSF) is on average 20%less than for VSF, and this on its own may accountfor this difference. The carbon black on the surface ofPRSF appears to increase the workability of the mixesas seen in Table 1. This is surprising since carbon blackis a fine powder with a large surface area. However, thediameter of this powder may be such that it leads to abetter packing of the particles of wet concrete. The car-bon black may also have an effect on the bond strengthof the fibres. However, there is no physical evidence tosupport that. Since the fibres are mixed by weight andthe PRSF fibres have carbon black, this means that lessPRSF fibres are used in comparison to VSF. A den-sity examination showed a difference between the twofibres at up to 15%. As less PRSF fibres are used incomparison to VSF, this may explain both the small re-duction in energy absorption capacity and the increasein workability

Figure 10 shows that the behaviour of the prism re-inforced with 6% ISF-1 and ISF-2 fibres is similar tothat of VSF and PRSF prisms. Fibres are pulled outrather than broken during the softening regime. Pro-vided that the fibre bond with concrete is good enough,there should not be much difference between the be-

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Fig. 10 Flexural behaviour of prisms containing 6% ISF, PRSF,and VSF.

Fig. 11 Initial behaviour for prisms containing PRSF.

haviour of prisms with different fibres, despite the verydifferent nature of the fibres.

2.2.2. Pre-crack behaviour

Figure 11a shows that the initial load-CMOD behaviourof prisms containing various ratios of PRSF was linear(region 0-A) until the point of fracture, when the microcracking phase started (Point A). The region (A-B) isidentified as a fracture zone, within which the crackingincreases and the stress at the notch tip decreases as thedeformation increases.

On further deformation, the load also decreasesdue to complete fibre pull out. The experiments werestopped after the crack exceeded 4 mm. On unloading,the cracks were still visible as shown in Fig. 12.

Fig. 12 Fracture of PRSF prism.

Fig. 13 LVDTs Locations and assumed strain distribution.

2.2.3. Flexural strain and crack measurements

To determine the complete strain/crack-width profiles,gauges were used to measure the displacement atfixed points along the depth at mid-span as shown inFig. 13.

The distance between Gauge 5 and Gauge 2 is equalto hsp. The displacement measured at each gauge canbe used to estimate the elastic strain prior to crack ini-tiation and the crack width after crack initiation, asfollows.

ui = wi,el = li · εi Prior to crack initiation (3)

where, li length of the gauge, εi longitudinal strain.After crack initiation, the displacement may be ob-

tained as the sum of the elastic displacement and thecrack opening (Eq. (4)).

u(i) = wi,el + wi,c After crack initiation (4)

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The compressive strain can be determined by divid-ing the displacement measured by gauge 5 by the lengthof the transducer l5 (50 mm). The tensile strain prior tocrack initiation, at locations h2, h3 and h4 (30, 66 and117 mm from the bottom surface), respectively, can bedetermined by dividing the displacement measured bygauges 2, 3 and 4 by a gauge length of 55 mm.

Using the cracked hinge model proposed by Ulfkjaeret al. [17] and adopted for fibre reinforced concreteby Olesen [18], the tensile strain can be obtained byEq. (5).

εt,i = σi,max

E+ wi.c

s(5)

Where, σ i,max maximum stress at first crack; wi,c de-formation measured after crack initiation; s length ofthe hinge.

Obviously, the determination of the length of thehinge is critical in the calculation of strain. Ulfkjaer etal. [17] applied the hinge model to a three-point bendingbeam and obtained a value of s equal to hsp/2. This wasbased on simulated elasto-plastic analysis and compar-ison with experiments. This result was also confirmedby Olesen [18].

Figure 14 shows the load versus mid-span deflectionand strain at locations 2, 3, 4 and 5 versus mid-spandeflection. It can be seen that the compressive strainεc0,s5 and the tensile strain εt0,s2 prior to crack initiation(at a deflection corresponding to point A) are more orless equal. The first crack at gauges 2, 3 and 4 wasinitiated at a load P0,s2, P0,s3 and P0;s4 of 21.4, 28.5and 32.0 kN, respectively. After crack initiation, thetensile strains εc1,s2; εc1,s3; and εc1,s4 at peak loads (ata deflection corresponding to point B) were 1.31, 0.84and 0.03 ‰, respectively.

Fig. 14 Strain measurements for VSF 1.5%.

Fig. 15 Variation of neutral axis depth for VSF prisms.

Fig. 16 Strain profile over the prism depth.

2.2.4. Position of neutral axis depth

The position of the normalised neutral axis (y =1−x/hsp) shown in Fig. 15 for a prism reinforced with1.5% VSF fibres, was calculated using the assumptionplane sections remain plane (Bernoulli). The calculatedvalue of y varied between 0.61 and 0.82 at first microcrack and peak-load, respectively. The maximum depthof the neural axis was 0.95 h at a deflection of 3.2 mm.For prisms with higher fibres ratio (3% and 6%), lessvalues were registered, as shown in Fig. 15 for the loadsat first-crack, peak and at 3 mm deflection. Similar re-sults were reported by Schnuetgen and Dam [19]. It isclear, that the simple approach taken by the RILEMmodel [7, 8] that the value of y is independent of thefibre volume is not right.

Using the strain values determined at peak load(Point B, Fig. 14) and the corresponding neutral axisposition, the strain profile over the prism’s depth canbe determined as illustrated in Fig. 16.

It can be seen that the method to determine the strainsand neutral axis position was accurate. This vindicates

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the choice of hinge length of hsp/2 and can be used as abuilding block for the development of design models.

2.2.5. Parameters for the determinationof stress-strain relationship

To predict the stress-strain curve recommended byRILEM TC 162-TDF [7], the parameters associatedwith the bending test of the same standard [5] werestudied. The limit of proportionality ffct and the equiv-alent tensile strengths feq1 and feq3 were determinedfrom the load-deflection curve for four-point load testsat several specific deflection values (δu, δ2 and δ3) asshown in Fig. 17. These values were determined ac-cording to DVB [20], from where they were adoptedby RILEM.

Fu is the highest value of the load when deflectionδu does not exceed 0.05 mm. The moment at mid spanfor the four point test arrangement corresponding to Fu

is as follows:

Mu = Fu

2∗ L

3(Nmm) (6)

where, L Support span (mm).

Fig. 17 Determination of Fu and equivalent tensile strength.

Assuming a linear stress distribution, the limit ofproportionality ffct,u can be calculated by Eq. (7).

ffct,u = Fu ∗ Lb ∗ h2

sp(N/mm2) (7)

where, b width of the specimen (mm); hsp distance be-tween the notch tip and the top of the cross section(mm).

The energy absorption capacities DBZ,2 and DBZ,3

are equal to areas ABCD and ABEF under the load-deflection curve up to deflection δ2 and δ3, respectively.The mean force recorded in the areas DBZ,2 and DBZ,3

can be calculated as follows.

F2 = DBZ,2

L/1200(N) (8)

F3 = DBZ,3

L/200(N) (9)

The moment at mid span of the corresponding to F2

and F3 are determined by Eqs. (10) and (11), respec-tively.

M2 = F2

2∗ L

3= DBZ,2

L/1200∗ L

6(Nmm) (10)

M3 = F3

2∗ L

3= DBZ,3

L/200∗ L

6(Nmm) (11)

The equivalent flexural tensile strength feq,2 and feq,3

can be determined by means of the following expres-sions.

feq,2 = M2

bh2sp/6

= F2Lbh2

sp(N/mm2) (12)

feq,3 = M3

bh2sp/6

= F3Lbh2

sp(N/mm2) (13)

In addition, the residual flexural tensile strengths fR,1

and fR,4, provided by RILEM as a final recommenda-tion [8], were calculated from the load-CMOD curveat CMOD equal to 0.5 mm and 3.5 mm, respectively asshown in Fig. 18.

fR,i = FR,iLbh2

sp(N/mm2) (14)

It should be noted that the CMOD at the bottom sur-face is calculated using CMOD1 measured at a distance

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Fig. 18 Determination of Fu and residual tensile strengths.

ξ (5 mm) below the prism using the following relation-ship [21].

CMOD = CMOD1h

h + ξ(mm) (15)

feq,2 or fR,1 is used in the verification of the serviceabil-ity limit states, while feq,3 or fR,4 is taken into account atthe ultimate limit state. These design parameters weredetermined for all tested specimens and are tabulatedin Table 3.

The results shown in Table 3 indicate that the equiv-alent tensile strengths (feq,2 and feq,3) or the residualstrengths (fR,1 and fR,4) of PRSF are slightly lower thanfor VSF (due to reasons explained earlier). However,the strength characteristics of prisms reinforced with6% VSF are similar to those for prisms containing 6%of ISF-1 or ISF-2. This can lead to the conclusion thatcleaned PRSF fibres are as good as industrial fibres.

The feq,2 and fR,1 values for the prism reinforcedwith 2% SRSF are comparable to those obtained forprisms reinforced with 1.5% of the other types of fi-bres. However, this is not true for feq,3 or fR,4. Thisindicates that SRSF can be used in applications wherebridging of micro cracks is more important than flexuralstrength.

3. Discussion on parameters

The results in Table 3 suggest that the relationship be-tween the equivalent flexural tensile strengths (feq,2 andfeq,3) and the residual flexural tensile strengths (fR,1 andfR,4) differs significantly. The residual flexural tensilestrength values (fR,1) were higher than the values ob-tained for the equivalent flexural tensile strength feq,2.This is probably as much to do with the definitionof these values and the test method as with the ac-

Fig. 19 Correlation between equivalent tensile strength andresidual tensile strength parameters.

Fig. 20 Correlation between fR and feq.

curacy. This difference ranged from 1.6 to 2.5 times.This means that the use of both parameters for designpurposes, in a similar way as recommended by RILEM,can lead to different results. This problem is related tothe fact that the RILEM method for determining theload at the limit of proportionality Fu and the corre-sponding δu is not consistent. Therefore, the evaluationof DBZ,2 is inaccurate. The effect of errors in the de-termination of the initial slope on feq,3 is minor. Fig. 19shows the relationship between feq,2 and feq,3, and be-tween fR,1 and fR,4.

Fig. 20, on the other hand, reveals that the residualtensile strength parameter fR,4 and equivalent tensilestrength feq,3 have similar values but fR,1 is greater thanfeq,2. This indicates that fR,4 and feq,3 parameters areinsensitive to initial errors and are more appropriatefor design purposes.

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4. Analytical investigation of RILEM

stress-strain approach

The design recommendation proposed by RILEM ap-pears to overestimate the load-carrying capacity ofprisms tested by the Brite-EuRam Project BRPR-CT98-0813 [22]. To investigate the reliability of theRILEM stress-strain model, it is necessary to calcu-late the load mid-span deflection. For the finite elementanalysis undertaken by Dupont and Vandewalle of theBrite-EuRam project BRPR-CT98-0813 [22] a rela-tively simple approximation of the stress-crack widthcurve was used as input for tensile stiffening. The finalstress-strain relationship was then calculated by simplydividing the crack width by the characteristic length,which was assumed to be the length of one finite ele-ment. Dupont and Vandewalle [24] assumed the charac-teristic length to be 0.79hsp (hsp, prism effective depth)and the strains were determined by dividing the crackwidth by two times the assumed characteristic length.

The French recommendation on FRC [25] calculatesthe strains by dividing the crack width by an assumedcharacteristic length equal to 2h/3. However, the deter-mination of the value of h is not clearly defined in therecommendation.

The characteristic length (or the width of the frac-ture zone in a smeared tensile test) is defined by Bazantand Pijaudier-Cabot [26] as the ratio GF/WF. The sur-face fracture energy, GF, expresses the energy absorbedto create a unit crack area. WF represents the energyabsorbed by a volume of material during a smearedtensile test, where a high number of microcracks arecreated. Both the surface fracture energy and the vol-umetric fracture energy are determined from the com-plete area enclosed by the stress-displacement or stress-strain curves.

In this work, the tested VSF beam with 1.5% fibre ra-tio was analysed using ABAQUS FE-package [27]. Dueto the symmetric boundary, only one half of the prismwas analysed. The tension softening effect was modi-fied using the stress-strain curve based on the RILEMdesign parameters provided in Table 1. Figure 21 showsthe distribution of the principal stresses at peak load.The position of the neutral axis is about 0.8hsp at a peakload of 35 kN. This load is higher than that achievedexperimentally (Table 3).

A comparison of the load-deflection curves obtainedexperimentally and analytically, is shown in Fig. 22.The use of the RILEM stress-strain approach leads to

Fig. 21 Distribution of the principal stress.

Fig. 22 Load-deflection behaviour (result of testing and FEA).

an over estimation of the peak response. In addition, theFE-program was not able to converge after a deflectionof 0.12 mm. The overestimation of the load-curryingcapacity highlights the deficiencies of the RILEM iden-tified earlier and underlines the need for the develop-ment of more robust models.

5. Conclusions

The SRSF and PRSF can form a viable alternativeto commercially-available steel fibres for use in SFRC.The majority of steel fibre reinforced concrete speci-mens failed in flexure due to pull-out rather than yield-ing. The displacement controlled load application leadto stable results throughout the load history.

The equivalent flexural tensile strength for PRSF isslightly lower than that of VSF, due to the lower com-pressive strength and the black carbon on the PRSFsurface. Both ISF prisms and VSF prisms are similarin behaviour. This indicates that cleaned PRSF fibrescan be as effective as ISF fibres. Concrete prisms rein-forced with 2% SRSF fibre behave similarly to prismsreinforced with 1.5% ISF fibres. SRSF concrete canbe used in applications where a high resistance againstmicro cracking is required.

376 Materials and Structures (2006) 39:365–377

It is demonstrated here that the neutral axis depth ofSFRC migrates with load and should differ for differenttypes and amounts of steel fibres.

The equivalent hinge length of hsp/2 was shown tolead to reasonable results when converting displace-ment measurements to equivalent strains.

The load at limit of proportionality can not be ac-curately determined and its use can lead to erroneousestimation of feq,2. The parameter feq,3 can be deter-mined with greater accuracy and are better parametersfor design. The values of the parameters feq,2 and fR,1

have great differences contrary to feq,3 and fR,4.A finite element analysis has shown that the stress-

strain approach proposed by RILEM overestimates thepeak response. A discussion on the characteristic lengthfor determination of strain from crack width shows thatthere is a diversity of opinions among the researchersand this is also reflected in code equations.

Acknowledgements The authors wish to acknowledge theMarie-Curie EU Community program “Improving Human Re-search Potential and the Socio-Economic Knowledge Base” un-der contract number HPMF-CT-2002-01825, the UK Govern-ment’s Department of Trade and Industry for the partners in In-novation project “Demonstrating steel fibres from waste tyres asreinforcement in concrete” (contract: CI 39/3/684, cc2227) andthe University of Sheffield for their financial support.

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