Construction and Building Materials 138 (2017) 12–25

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Construction and Building Materials

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Experimental and numerical study of the flexural behaviour of ultra-highperformance fibre reinforced concrete beams

http://dx.doi.org/10.1016/j.conbuildmat.2017.02.0020950-0618/� 2017 Elsevier Ltd. All rights reserved.

⇑ Corresponding author at: School of Civil, Environmental and Mining Engineer-ing, The University of Adelaide, South Australia 5005, Australia.

E-mail address: manpreet.singh@adelaide.edu.au (M. Singh).

M. Singh ⇑, A.H. Sheikh, M.S. Mohamed Ali, P. Visintin, M.C. GriffithSchool of Civil, Environmental and Mining Engineering, The University of Adelaide, Australia

h i g h l i g h t s

� UHPFRC mix with conventional aggregates is used to manufacture beams.� Stress-strain behaviour of UHPFRC under compression and tension is presented.� Flexural behaviour of large-scale UHPFRC beams is presented.� Finite element analysis of beams is conducted using concrete damaged plasticity model.

a r t i c l e i n f o

Article history:Received 17 May 2016Received in revised form 19 January 2017Accepted 1 February 2017

Keywords:Ultra-high performance fibre reinforced(UHPFRC) concrete beamsFlexural strengthDuctilityFinite element analysisConcrete damaged plasticity model

a b s t r a c t

The development of standard analytical procedures and design guidelines for concrete requires extensivetests at material and structural level. For ultra-high performance fibre reinforced concrete (UHPFRC) thistask is even more complicated than that of conventional concrete due to the potential range of fibre typesand volume fractions. The experimental task of large scale structural members to develop the design pro-cedures can be reduced by adopting an alternative way in which the concrete material model available infinite element packages are validated with the limited number of tests conducted on material and struc-tural members. The validated numerical models can further used to study the effect on the structuralbehaviour due to change in geometry, loading conditions and reinforcement. Therefore the objective ofthe present study is to investigate the efficacy of the hybrid approach of validating the existing concretemodel to study the behaviour of large-scale structural members made up of UHPFRC. For this four full-scale beams with varied spans and cross-sections were fabricated with the indigenously developedUHPFRC using conventional materials and mixing methods and tested under different loading conditionsuntil failure. Numerical models were developed and validated with the test results of the beams forwhich the concrete damaged plasticity (CDP) model was adopted to characterize the behaviour ofUHPFRC material. The material parameters required to define the constitutive model were identifiedby conducting direct/uniaxial tension and compression tests. The results obtained from the numericalmodels shows that the CDP model can accurately predict the load/moment carrying capacities of theUHPFRC beams. The results also show a good capability of the numerical models to predict the overallload deflection behaviour of the UHPFRC beams.

� 2017 Elsevier Ltd. All rights reserved.

1. Introduction

Ultra-high performance fibre reinforced concrete (UHPFRC) isan advanced cement composite material, which is characterisedby high strength, ductility, durability and fracture toughness[1–4]. UHPFRC is generally characterized as the reactive powderconcrete with compressive strength exceeding 150 MPa containing

sufficient fibre content to achieve strain hardening under tension[1]. Since its conception, various proprietary UHPC mixes havebeen developed such as: SIFCON, Ductal, CARDIFRC and CEMTEC,however due to the cost and specialist curing requirements ofthese materials use in practice has been limited to several land-mark structures. In an attempt to further expand the usage ofUHPC by simplifying manufacture techniques and reduce costsrecent research has aimed to develop in-house UHPFRC mixesusing indigenously available materials [5,6].

Most of the reported studies on UHPFRC focus on the character-ization of material properties [7–10] with a few considering the

M. Singh et al. / Construction and Building Materials 138 (2017) 12–25 13

behaviour of full-scale structural members especially with indige-nously developed mixes [11,12,40]. Notable examples of investiga-tions at a member level include that of Graybeal [13] whoinvestigated the potential of constructing of prestressed bridgegirders from UHPFRC designed by Ductal. It was reported thatthe fibre pull out lead to the failure of the girder. At fibre pullout, the flexural stress carried by fibres transferred to the pre-stressing strands that lead to increase of tensile stresses in strandsdue to which the prestressing strands ruptured and the girder col-lapsed. Yang et al. [14,15] investigated the effect of reinforcementratio and concrete placement methods on the flexural strength ofUHPFRC beams. It was found that the method of placement ofUHPFRC in the beams has considerable effect on the ultimatemoment capacities. Recently, Yoo et al. [34] investigated effect ofusing different fibres on the flexural behaviour of reinforcedUHPFRC beams. It was found that the ultimate moment capacitywas not influenced by the fibre geometry whereas the post peakresponse and ductility was considerably improved by long steelfibres.

The flexural behaviour reinforced concrete (RC) beams con-structed with normal strength concrete (NSC) is well understood.The analytical models and standard procedures are also developedfor the analysis of such NS-RC beams. However, the analytical pro-cedures developed for the analysis of NS-RC beams cannot bestraightforwardly adopted for the beams made up of UHPFRCmaterials. For the fact that UHPFRC has substantial tensile strengthand strain capacity that cannot be neglected in the analysis proce-dure. The extensive test regimes are needed to capture the materialcharacteristics such as tensile characteristics, bond-slip and ten-sion stiffening characteristics. The full-scale structural tests arealso required to study the effect of varying geometry, materialproperties and loading conditions on the structural behaviour.The task of empirically developing the analytical procedures forUHPFRC is even more complicated than that of conventional con-crete due to the potential range of fibre types and volume fractions.Such extensive testing regimes will entail time and cost that con-straint the adoption of UHPFRC in real life structures. An alterna-tive way is to conduct a well formulated but limited tests onmaterial and structural level to develop the numerical modelsusing commercially available finite element (FE) software packages[38]. The FE software such as Abaqus is equipped with concreteconstitutive models developed for normal strength concrete(NSC). It is well understood that the material behaviour of UHPFRCis substantially different from NSC hence the adoption of such con-crete constitutive models may not be reliable. The number ofmaterial parameters are also required to define the material modelwhich also needs to be obtained for UHPFRC material through theexperimental tests. The objective of present study is to validate theconcrete constitutive model by conducting the material tests onUHPFRC and to adapt the material model for the analysis of theflexural behaviour of UHPFRC beams.

The concrete damaged plasticity model is based on the classicaltheory of plasticity. The degradation to the stiffness is modelled bydefining the damage variables for tension and compression. Theisotropic damage to the elasticity is considered to model theinelastic behaviour of concrete. Previous studies have shown thatthe use of concrete damaged plasticity (CDP) constitutive modelsavailable in finite element (FE) software such as Abaqus, to be apowerful and reliable predictive tool for the analysis of normalstrength concrete. Recently, Mahmud et al. [16] tested unrein-forced notched UHPFRC beams to study the size effect on the flex-ural strength of UHPFRC. The two dimensional plane stress FEanalysis of beams was conducted using a CDP model for UHPFRC.The overall load versus crack mouth opening displacement(CMOD) captured by the model was in good agreement with anerror ranged from 11.8% to 1.2%. Tysmans et al. [17] adopted a

CDP model to simulate the behaviour of high performance fibrereinforced concrete composite under biaxial tension. It wasreported that the model accurately simulated the strain hardeningbehaviour of fibre concrete but with reduced stiffness. It should benoted that in the above-mentioned studies, only small-scale spec-imens without internal reinforcement are considered and only 2Dfinite element models are developed.

In this investigation an UHPFRC mix developed with conven-tional materials, normal mixing and curing regimes is consideredto study the material characteristics and structural behaviour infull-scale beams. The materials characteristics such as stress strainbehaviour under uniaxial tension and compression is studied forthe developed mix. The uniaxial stress strain data from the testsis used to calibrate the parameters of concrete damaged plasticity(CDP) model. The calibrated CDP model is adapted for the FE anal-ysis of the full-scale beams. The FE models of the beams are vali-dated with the experimental data of the full-scale beam testsobtained from this study. Further the efficiency of the finite ele-ment models is verified with the beam tests conducted by otherresearchers [14]. The methodology of conducting limited but wellformulated material and structural tests to validate the numericalmodels in available finite element packages can expedite the taskof development of design guidelines facilitating the adoption ofUHPFRC in construction industry.

2. CDP model – theoretical background

The damage-plasticity model used for the concrete is based on aplasticity-based continuum damage model [24]. The model uses ascalar (isotropic) damage parameter as an internal variable for thecharacterisation of the damage model which is combined with theelasto-plastic behaviour under tensile and compressive stresses torepresent the inelastic behaviour of the material [23]. It uses a non-associated flow rule with the help of a plastic potential. Formationof tensile micro-cracks is captured macroscopically with a soften-ing stress-strain relationship whereas its plastic response in com-pression is typically represented by strain hardening followed bystrain softening behaviour. The evolution of the yield (or failure)surface is controlled by two hardening parameters (equivalentplastic strains), which are linked to failure mechanisms under ten-sion and compression loading, respectively. The uniaxial stressstrain data in compression and tension data is required by themodel to evaluate the hardening/softening behaviour of the con-crete. In addition, five parameters are required to define the yieldfunction, plastic potential and visco-plastic regularization thatare explained in the following paragraphs.

The damage-plasticity model uses the yield criteria proposed byLubliner et al. [24] along with the modifications proposed by Leeand Fenves [25] to account for different evolution laws of thestrength under tension and compression. The twomain parametersrequired to define the shape of the yield surface are; the ratio ofinitial biaxial compressive strength to initial uniaxial compressivestrength rbo=rco and parameter kc is used to define the shape of thefailure surface in the deviatoric plane. Fig. 1 shows the shape of theyield surface under plane stress condition while the yield functionis defined as

f ¼ 11� a

�q� 3a�pþ b ~epl� �

�rmax

D E� c � �rmax

D E� �� �rc ~epl

� �6 0 ð1Þ

where a and c are dimensionless material constants controlled bythe parameters rbo=rco and kc defined below, �p is the hydrostaticpressure based on effective stresses, �q is the effective von Misesequivalent stress, �rmax is the effective major principal stress, and�rc is the effective cohesive stress in compression, function of the

Fig. 1. Shape of yield surface under plane stress condition.

Fig. 2. Uniaxial stress-strain showing various components of strain (plastic, elastic)and damage.

14 M. Singh et al. / Construction and Building Materials 138 (2017) 12–25

accumulated equivalent plastic strain ~epl, which will be definedlater. The function b ~epl

� �used in the above equation can be defined

as

b ~epl� � ¼ �rc ~epl

� ��rt ~eplð Þ ð1� aÞ � ð1þ aÞ ð2Þ

where �rt is similarly the effective cohesive stresses in tension.The material parameter a can be determined from initial yield

stresses in compression under biaxial and uniaxial stress condi-tions, rbo and rco, as

a ¼ rbo � rco

2rbo � rcoð3Þ

The other material constant c can be defined as

c ¼ 3ð1� kcÞ2kc � 1

ð4Þ

where the parameter kc is used to define the shape of the failuresurface in the deviatoric plane which is the ratio between distancesmeasured from the hydrostatic axis to tensile and compressivemeridians.

The plastic potential used in this study follows a Drucker Pragerhyperbolic function, which requires two parameters: the dilationangle u and n as the potential flow eccentricity parameter, and itmay be expressed as

G ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðnrt0 tanuÞ2 þ �q2

q� �p tanu ð5Þ

where, u is the dilation angle measured in the p–q plane at highconfining pressure; rt0 is the uniaxial tensile stress; and n is aparameter, referred to as the eccentricity of the potential flowwhich defines the rate at which the function approaches theasymptote.

2.1. Stress strain in compression

The stress strain behaviour under uniaxial compression can beobtained from the experimental tests. The inelastic einc

� �strain

(Fig. 2) can be obtained by subtracting the elastic eel0c� �

componentfrom the total strain ðecÞ as follows.

einc ¼ ec � eel0c ð6Þ

eel0c ¼ rc=E0 ð7Þwhere E0 is the initial (undamaged) elastic modulus. Fig. 2 also

shows the plastic strain eplc� �

component which can be obtained

from the damage parameter in compression ðdcÞ. This parametervaries from 0 to 1 which helps to characterize the degradation ofthe material stiffness where it is zero for an undamaged state andone for a complete damage state. With the parameter, the plasticstrain as well as compressive stress and effective compressive stresscan be obtained as follows.

rc ¼ ð1� dcÞE0 ec � eplc� � ð8Þ

M. Singh et al. / Construction and Building Materials 138 (2017) 12–25 15

�rc ¼ rc=ð1� dcÞ ¼ E0 ec � eplc� � ð9Þ

eplc ¼ einc � dc

ð1� dcÞrc

E0ð10Þ

2.2. Stress strain in tension

In order to characterising the hardening and softening phases ofthe material, it is important to get the cracking strain eckt that canbe obtained as

eckt ¼ et � eelt ð11Þ

eelt ¼ rt=E0 ð12ÞThis is practically the inelastic strain einc

� �defined earlier when

the material is under uniaxial compression. Eqs. (8)–(10) derivedfor uniaxial compression are similarly applied to uniaxial tensionto evaluate the plastic strain, tensile stress and effective tensilestress.

3. Experimental program

3.1. UHPFRC mix

In this investigation, an UHPFRC developed in previous studyconducted by the authors (Sobuz et al. [5]) at the University of Ade-laide is considered. The mix design in Table 1 is one of the 40 mixesdeveloped in the study (Sobuz et al. [5]), was used to manufactureall material and beam test specimens. This mix is chosen for thefollowing reasons; a) the fine aggregates used is washed river sandis commonly available in abundance in local market and is inex-pensive; b) the mix achieved a compressive strength of 138 MPaon 56 days and 144 MPa on 90 days under normal curing regimes;c) as the beams consisted of reinforcement hence the mix shouldhave good flow-ability for which this mix has a slump flow of535 mm with fibres in J-ring flow test conducted in accordancewith ASTM C1621 [35].

In Table 1, the binder consisted of sulphate resisting cement andsilica fume. The sulphate resisting cement used had a finenessindex of 365m2/kg and 28 day compressive strength of 60 MPadetermined in accordance with AS 2350.11 (2006). The undensifiedsilica fume locally available under a brand name of Ecotec is used,had a bulk density of 625 kg/m3. The fine aggregate is local washedriver sand with a fineness modulus of 2.34. To ensure adequateworkability, an aqueous polycarboxylate based solution of high-range water reducer retarder (HRWR, ViscoCrete-10) supplied bySika is used. The Dramix 3D steel fibres with hooked ends suppliedby Bekaert is used which were 35 mm in length had an aspect ratioof 64 and yield strength of 1100 MPa as reported by the manufac-turer. The amount steel fibre added is 2.25% by volume.

The planetary concrete mixer of 1000 L capacity was used forthe manufacturing of all the material and beam specimens. Themixing procedure consisted of mixing the cement, silica fumeand sand in dry state for at least 3 min. After which the watermixed with HRWR is added into the dry mixture and allowed tomix until the concrete turns into a flow-able consistent paste,which usually took between 10 and 15 min. Once the mix becomes

Table 1UHPFCR mix detail.

Cement Sand Silica fume

1 1 0.266

visibly flow-able, the steel fibres were then added and mixed forfurther 5 min.

3.2. Test specimens

3.2.1. Compression and tension test specimensIn order to characterize the material properties and to deter-

mine the CDP model parameters, a series compression and tensiontests were conducted. To identify the stress strain behaviour underuniaxial compression, 4 standard cylinder specimens of 100 mm(diameter) � 200 mm (height) were tested. The UHPFRC had self-compacting properties; hence the cylinders were casted verticallywithout providing any compaction. In order to determine thestress strain relationship under direct tension, 3 dog bone speci-mens were casted horizontally and tested under uniaxial tensileloading. The uniaxial tensile specimens that is shown schemati-cally in Fig. 3(a) are similar to those adopted by Redaelli [18] andMoreno et al. [19]. They consist of a central rectangular shank witha cross section of 120 mm square and a length of 300 mm. Outsideof this central region, in order to avoid stress concentrations, thecross section tapers to a total width of 208.6 mm over a totalheight of 604.8 mm. The dog bones were casted horizontally soas to get identical fibre orientation as that of the beams. After 2 hof casting, all the specimens (cylinders and dog bones) were cov-ered with wet hessian and plastic sheets. The specimens weredemoulded after 24 h of casting and cured in a fog room under con-trolled temperature of 24 degrees for 28 days.

3.2.2. Large scale beam specimensFour simply supported beams were fabricated and tested in this

study. The cross section, spans and loading configuration details ofthe all the beams are given in Fig. 4 and Table 2. The beams are des-ignated in accordance to the cross-section size followed by thespecimen number. The beams with cross section of250 mm � 250 mm are named as B25-1 and B25-2. To investigatethe fibre distribution and orientation on the flexural behaviour ofbeams, the beams B25-1 and B25-2 were kept identical in allterms. To ensure the intended flexural failure mode and to preventany premature shear failure of the beam, adequate shear reinforce-ment was also provided, which consisted of 10 mm diameter stir-rups spaced at 90 mm centre to centre up to the load points. Thezone between the load points was not provided with the stirrupsto eliminate the confinement of concrete provided by the stirrups.

The beams B15-1 and B15-2 with cross section of150 mm � 150 mmwere tested to investigate the effect of geomet-rical properties and loading configuration on the flexural behaviourof beams. These beams were provided with 2 bars of 16 mm diam-eter (area = 402 mm2) in both tension and compression faces. Theshear reinforcement is consisted of stirrups of 6 mm diameterspaced at 85 mm centre to centre throughout the beam.

The beams were fabricated one at a time due to the largeamount of material required. The planetary concrete mixer of1000 L capacity was used for the onsite manufacturing of thebeams. The wooden formwork was built for the casting of thebeams and all the beams were casted horizontally. It is a commonpractice to cast the UHPC beams by placing the concrete from oneend and allowing it to flow throughout the beam. However, in thisstudy, the presence of shear reinforcement restricted the free flow

HRWR Water Steel fibre

0.045 0.1775 2.25% by vol.

Fig. 3. (a) Uniaxial tension test specimen; (b) Test set up for direct tension test; (c) Cracking pattern under direct tension.

Fig. 4. Reinforcement detail of beams: (a) B25-1 & B25-2; (b) B15-1; (c) B15-2.

Table 2Test beam details.

Beam Cross-section Effective span Rebar dia Loadingdesignation B � D (mm) (mm) (mm) condition

B25-1 250 � 250 3250 3–20 Four PointB25-2 250 � 250 3250 3–20 Four PointB15-1 150 � 150 1350 2–16 Three PointB15-2 150 � 150 2700 2–16 Four Point

16 M. Singh et al. / Construction and Building Materials 138 (2017) 12–25

of concrete due to which the beams were fabricated by placing theconcrete using back and forth placement method along the span ofthe beam. Cylinders, prisms and dog bones required for the

material property tests were also casted for each batch of concrete.After 2 h of casting all the specimens were covered with wet hes-sian and plastic sheets for at least 24 h. The formwork was then

M. Singh et al. / Construction and Building Materials 138 (2017) 12–25 17

removed and the beams were cured with wet hessian covered withplastic sheets for at least 28 days before testing.

3.3. Test set up and instrumentation

3.3.1. Compression test set upThe cylindrical specimens for compression tests were tested as

per AS1012.9:2014 [36]. The electrical strain gauges of 30 mmlength were attached at the mid height to record the axial and lat-eral strains. Additionally 4 linear variable differential transformers(LVDT) were used to measure the platen to platen displacement soas to measure the strains of the whole specimen. All the straingauges and LVDTs used in this study had an accuracy of ±1%. Theuniaxial compressive load was applied at a constant rate of0.05 mm/minute throughout the test for which a universal testingmachine of 5000kN capacity was used. The load, strain and dis-placement data were recorded continuously at the rate of tworeadings per second.

3.3.2. Tension test set upThe instrumentation of tensile test specimens consisted of four

longitudinal strain gauges of 80 mm length attached on each faceand four LVDTs glued on each face with a gauge length of300 mm. The curved sides of the specimen was pasted with thinlayer of gypsum slurry and was then placed in a specially designedtest rig attached to the Instron testing machine as shown in Fig. 3b.A time lag of 15 min between placement of specimen and start oftest was provided to harden the paste. The displacement controlleduniaxial tensile loading was applied at the rate of 0.01 mm/minutethroughout the test.

3.3.3. Large scale beam test set upBeams B25-1 and B25-2 with an effective span of 3250 mm

were subjected to two equal concentrated loads applied symmetri-cally at a distance of 250 mm from the mid span, so as to inducepure bending stresses in the zone between the load points. Themonotonically increasing load was gradually applied until com-plete failure of the beam; this was facilitated through a singlehydraulically actuated jack to the steel spreader joist placed onthe top face of the beam with its supports 500 mm apart as shownin Fig. 5a. Both the deflections and strains were recorded continu-ously by means of LVDTs and strain gauges as shown in Fig. 5a. Thesimply supported beam B15-1 with an effective span of 1350 mmas shown in Fig. 5b was tested under three point bending. Thebeam was set up on a frame of universal testing machine with acapacity of 1000kN. The monotonic loading is applied and beamis tested until collapse. The beam B15-2 with effective span of2700 mm is subjected to four point bending with 300 mm distancebetween the load points as shown in Fig. 4c. The rest of the setup issimilar to that adopted for B25-1.

To measure the strains in the internal steel rebar, 5 mm electri-cal strain gauges were glued to the bars at mid span before thecasting of the concrete. To prevent the damage of the strain gauges,a polyurethane coating was provided on the strain gauges. Straingauge of 30 mm length was used for the measurement of thestrains of concrete. Three strain gauges were bonded to the sidefaces of the beam at heights as shown in Fig. 5d. As the straingauges cannot record the data once the cracking of the concretecommences, hence to record strain data and crack widths LVDTswere also attached at compression and tension face of the beamsas shown in Fig. 5(a, b, c). Vertical displacements of the beamswere measured at mid span and at other locations as shown inFig. 5(a–c).

4. Experimental results

4.1. Stress strain under compression

In total 12 cylindrical specimens were tested under direct com-pression, from which 4 specimens were strain gauged and instru-mented to get the compressive stress strain behaviour of thematerial. The average compressive strength and standard deviationof 12 specimens is 143 MPa and 6.43, respectively. The strain cor-responding to ultimate strength is 4170 micro-strain and the elas-tic modulus is 38,470 MPa, calculated from the stress strain curvein accordance to AS 1012.17-1997 [37]. The stress strain curves areshown in Fig. 6a, where it can be seen that the relationship is linearup to the peak stress followed by a rapid loss in strength until astable stress plateau is attained.

4.2. Stress strain under tension

The stress strain relationship obtained from the dog bone spec-imens is shown in Fig. 6b. The first cracking occurred at a stress of4.6 MPa, which typically corresponds to the cracking strength ofthe matrix. After first cracking, the fibres resisted the tensile stres-ses by fibre bridging effect until the peak tensile strength isattained. The fibre bridging results in the formation of micro-cracks throughout the specimen and the material resisted the ten-sile stresses until the localization of the crack occurs. The averagepeak tensile strength of the material used in this study is 5.8 MPaand the strain corresponding to the peak strength is 3300 micro-strain. Once the peak strength is achieved, the material undergoesinto a softening stage in which the stress starts to fall rapidly dueto the localization of the crack. The failure zone was located in thecentral region for the tested specimens as depicted in Fig. 3c.

4.3. Tensile strength of reinforcement

Three specimens of each bar diameter were tested under directtension to obtain the stress strain relationship. The tensile rein-forcement of beams B25-1, B25-2 consisted of 20 mm diameterdeformed bars with nominal yield strength of 525 MPa and ulti-mate strength of 625 MPa. The 16 mm tensile reinforcing bars usedfor beams B15-1, B15-2 had a yield strength and ultimate strengthof 520 MPa and 705 MPa, respectively.

4.4. Test results for beams

4.4.1. Cracking pattern and failure modeThe first cracking load for B25-1 and B25-2 is in the range of

20kN whereas for B15-1 and B15-2 is 14kN and 4kN respectively.At this point no visible cracks were observed for all the beams.After first cracking the slope of the load deflection curve becameless steeper compared to initial slope, indicates the formation ofmicro-cracks, although no visible cracks were observed up to loadof 20% of the peak load. With further increase in load, the widelyspaced vertical hairline cracks of an average depth of 0.2D (depthof the beam) measured from the tension face of the beam andspaced at 100 mm apart became visible typically in the middle por-tion of the beam of length span/2. The number of cracks increasedwith the increase of load and new cracks developed between theexisting ones. The increase in the width of the cracks was insignif-icant up to the yield load of the beams whereas a noticeableincrease in the number of cracks was observed.

After steel yielding the increase in the width of the cracksbecame more rapid with little increase in load. The crack widthof one or two cracks, particularly at a location of the yielding ofsteel, became significantly greater than the other cracks. The steel

Fig. 5. Instrumentation details of beams; (a) B25-1 & B25-2; (b) B15-1; (c) B15-2; (d) location of strain gauges on concrete surface.

0

20

40

60

80

100

120

140

160

0 2000 4000 6000 8000 10000

Stre

ss M

Pa

Strain x 10 -6

0

1

2

3

4

5

6

7

0 1500 3000 4500 6000 7500 9000

Stre

ss M

Pa

Strain x 10-6

(a) (b)

Fig. 6. (a) Compressive stress strain of UHPFRC; (b) Stress strain of UHPFRC under direct tension.

18 M. Singh et al. / Construction and Building Materials 138 (2017) 12–25

fibres resisted the opening of the crack allowing the beam to takefurther load until it reaches the ultimate moment capacity of thebeam. After attaining peak load the crushing of top concrete initi-ated lead to sudden drop in load about 8% of the ultimate loadcapacity of the beams. At this stage the crack propagated through-out the depth of the beam.

With further applied displacement the fibres kept pulled outand the load dropped gradually till the strain capacity of the tensilereinforcement was exhausted. All the beams finally collapsed dueto the rupture of tensile reinforcement. The failure pattern indi-cated that the fibres effectively resisted the widening of cracks thatlead to the increased load carrying capacity even after the rein-forcement is yielded.

4.4.2. Load-deflection relationshipThe deflection was measured at mid span for all the beams.

Fig. 7a shows the load-deflection relationship of the tested beams

B25-1 and B25-2. The load-deflection relation can be divided intothree distinct regions, namely initial linear zone before first crack-ing, yield load at the yielding of rebar, peak load and rupture ofrebar. It was observed that initial response of both the beams(B25-1, B25-2) was similar up to the yielding of reinforcement.The peak load for beam B25-1 and B25-2 was 172kN and 167kNand deflection measured for this load was 59 mm and 46 mmrespectively. The beam B25-1 was not tested till collapse whereasbeam B25-2 was tested until complete failure. The failure was dueto the rupture of the tensile reinforcement bars and the ultimatedeflection recorded was 128 mm.

The beam B15-1 was tested under three-point bending and theload versus mid span displacement is shown in Fig. 7b. The load-deflection relation observed to have similar trend as seen forbeams B25-1,2. The ultimate load capacity was 109kN correspond-ing to a deflection of 18 mm. The ultimate deflection at the collapseof beam was 74 mm. Fig. 7b shows the load deflection relationship

Fig. 7. Load-deflection of beams; (a) B25-1 & B25-2; (b) B15-1 & B15-2.

M. Singh et al. / Construction and Building Materials 138 (2017) 12–25 19

of the beam B15-2, tested under four-point bending. In comparisonwith B15-1, B15-2 observed to have several cracks developed nearthe peak load. The peak load for B15-2 is 55kN and the correspond-ing deflection is 79 mm. The test was terminated at a displacementof 131 mm due to the excessing movement of the beam on one ofthe roller support.

The load deflection behaviour of the tested beams (B25-1, B25-2) follows similar trend in terms of post peak flexural behaviour asobtained in the previous study by Yoo et al. [34]. It was found thatthe use of long fibres improved the post peak behaviour of the rein-forced UHPC beams. The similarity between the flexural behaviourof beams tested in present study with the beams tested by Yooet al. [34], shows that the manufactured UHPFRC with conven-tional materials and procedures performed equally well in fullscale structural members.

4.4.3. Discussion of results (beams)The beams B25-1 and B25-2 were identical in all terms whereas

a noticeable difference was observed in their displacement capac-ities and cracking patterns. The beam B25-1 required 28% largerdisplacement to attain its ultimate moment capacity when com-pared to the beam B25-2. At ultimate moment, the beam B25-1observed to have two major cracks developed in constant momentzone whereas B25-2 had one major crack only. The variation in thedisplacement capacities and cracking pattern can be due to differ-ence in the orientation and dispersion of the fibres in the beams.Similar trend was observed in previous study by Yoo et al. [34]in which it was reported that the presence of longitudinal andshear reinforcement disturbed the orientation and dispersion oflonger fibres which resulted in dissimilar results when comparedwith the flexural behaviour of prisms with no internal barreinforcement.

The measure of deformability can be used to evaluate the duc-tility of the beams in terms of ductility index. The ductility index

Table 3Summary of test results.

Beam Initial cracking Yield state Pe

Pcr Dcr Py Dy Pp

(kN) (mm) (kN) (mm) (k

B25-1 20 1 158 26 17B25-2 20 1 161 25 16B15-1 14 0.3 90 9 10B15-2 4 1 40 31 55

Note: Pcr = First crack load, Dcr = first crack deflection, Py = load at steel bar yield, Dy = dedeflection.

can be expressed in terms of deflection, rotational and curvatureductility, from which deflection ductility index is commonlyadopted [14,20,21] due to its simplicity. The deflection ductilityindex can be obtained by taking the ratios of mid span deflectionsat critical stages of load deflection curve such as yield, peak andultimate load state. The expression of ductility index can be theratio of mid span deflection at peak load to the mid span deflectionat yield load whereas the other expression used by Shin et al. [21]considers the ratio of ultimate deflection to the deflection at peakload. The ultimate deflection is defined in different ways by variousresearchers. In this study the ultimate deflection is referred to thestage at which the load bearing capacity is dropped suddenly dueto the rupture of bar. In other words the ultimate deflection isthe deflection measured just before the complete collapse of thebeam.

In this study both definitions of ductility index is used to deter-mine the ductility at different stages of load deflection curve asshown in Table 3. It can be seen that the ultimate state ductilityindex is greater than 4 for all the beams with an exception ofB25-1 that was not tested till collapse. The beams shown greaterductility when compared to the test results reported by Yanget al.[14], where the reinforced UHPFRC beams with short steelfibres had ductility index (ultimate state) ranging from 1.6 to3.75. The higher ductility index values obtained in this studyreflects the advantage of using long steel fibres to improve the postpeak behaviour of UHPFRC beams. Similar results were reported byYoo et al. [34] where beams with long steel fibres shown higherductility than the beams with short steel fibres.

5. Numerical simulation

The concrete damaged plasticity model is adopted in this studyto model the mechanical behaviour of UHPFRC. The parameters

ak state Ultimate state Ductility

Dp Du index

N) (mm) (mm) Dp/Dy Du/Dy

2 59 95 2.27 3.657 46 128 1.80 5.129 18 76 2.00 8.44

79 134 2.55 4.32

flection at steel bar yield, Pp = peak load, Dp = deflection at peak load, Du = ultimate

0

20

40

60

80

100

120

140

160

0 2000 4000 6000 8000 10000

Stre

ss M

Pa

Strain x 10 -6

Experiment

Proposed Eqn

Fig. 8. Comparison of compressive stress strain curve (experiment versus proposedequations).

20 M. Singh et al. / Construction and Building Materials 138 (2017) 12–25

required for the CDP model to accurately represent the materialbehaviour of UHPFRC are calibrated with the test data producedin this research. The uniaxial stress strain curves of UHPFRC undercompression and tension is obtained from the material tests con-ducted in this study, which is an essential component for definingthe material model. The details of the parameter and uniaxialstress strain curves used to model the behaviour of UHPFRC arediscussed as follow.

5.1. Model parameters

5.1.1. Stress strain curve for UHPFRC in compressionThe stress strain curve under uniaxial compression as shown in

Fig. 6a is used to model the compressive behaviour of UHPFRC. Thestress strain curve with a compressive strength of 140 MPa with anelastic modulus of 38GPa obtained from the test data is used todefine the compressive behaviour in the model. In general thestress strain behaviour under compression can also be defined byempirical equations available in literature [32] that are based onthe test data of normal and high strength concretes. These equa-tions may not be suitable for expressing the stress-strain behaviourof the UHPFRC as the pattern of its stress-strain curve is differentdue to a different nature of its failure specifically at the post peakregion [31]. Therefore, the equation for the stress strain curve needsto be developed so that it can accurately predict the response ofUHPFRC material under uniaxial compression. For this purpose,the empirical equation proposed by Lu et al. [32] for high strengthconcrete is modified in the present study that are as follows.

rc ¼ f 0cðE0=EscÞðe=e0Þ � ðe=e0Þ21þ ðE0=Esc � 2Þðe=e0Þ

" #for 0 6 e 6 e0 ð13Þ

rc ¼ f 0c1þ 1=4½fðe=e0Þ � 1g=fðeL=e0Þ � 1g�1:5

" #for e0 6 e ð14Þ

where f 0c is the peak compressive stress and other parameters aredefined below. The strain corresponding to peak stress ðe0Þ, the ini-tial elastic modulus ðE0Þ, the secant modulus ðEscÞ corresponding topeak stress f 0c and the limiting strain ðeLÞ used in the above equa-tions are as follows.

eL ¼ e01:2510

E0

Escþ 45

� �þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1:2510

E0

Escþ 45

� �2

� 45

s24

35 ð15Þ

e0 ¼ 750 f 0c� �0:35 � 10�6 ð16Þ

E0 ¼ 15050 f 0c=10� �1=3 ð17Þ

Esc ¼ f 0c=e0 ð18ÞIn order to check the performance of the proposed empirical

equations, a cylindrical specimen is tested and the experimentalstress-strain curve are compared with that predicted by the pro-posed equations in Fig. 8. It shows a very good agreement betweenthe experimental and the predicted results. The damage parameterðdcÞ proposed by Birtel et al. [33] is used in the present study,which can be defined as

dc ¼ 1� rc=E0

0:2einc þ rc=E0

ð19Þ

Fig. 9. Comparison of compressive stress strain obtained from test and FEM.

5.1.2. Stress strain for UHPFRC in tensionThe stress strain response of UHPFRC under direct tension usu-

ally consists of three phases: linear elastic, strain hardening and

strain softening phase. Once the cracking of the matrix initiates,the fibres resist the opening of micro cracks by fibre bridging andUHPFRC keeps taking stress until the fibres starts pull out fromthe matrix. The gain in strength is nonlinear in strain hardeningzone whereas the fibre pull out leads to the softening phase.

The stress strain curve of UHPFRC under tension is obtainedfrom the dog bone specimen as shown in Fig. 6b is used to definethe tensile behaviour of UHPFRC. The material behaviour is mod-elled as linear elastic up to a tensile stress of 4.6 MPa with an elas-tic modulus of 38GPa followed by strain hardening up to a stress of5.8 MPa. The strain hardening/softening behaviour is implementedusing the stress strain properties shown in Fig. 6b. The damageparameter in tension is assumed to activate once the peak tensilestrength is achieved. For the present study, the damage parameterrecommended by Mahmud et al. [16] is used which is as follows.

dt ¼ 1� rf t

ð20Þ

M. Singh et al. / Construction and Building Materials 138 (2017) 12–25 21

In addition to the stress strain behaviour, there are five otherparameters required to completely define the CDP model whichare discussed as follow:

� rbo=rco is the ratio of biaxial compressive strength to uniaxialcompressive strength. The experimental values of the ratiorbo=rco are in the range from 1.10 to 1.16 for normal strengthconcrete [26]. However, the experimental investigation doneby Curbach et al. [27] found that the strength gain under biaxialloading is less pronounced for UHPFRC material. This ratiorbo=rco reported in their investigation [27] is 1.05, which isadopted in defining the material parameter ðaÞ in the presentstudy.

(a) B25-1

(c) B15-1

Fig. 10. Comparison of load-deflection results (experiment v

Table 4Comparison of experimental results with finite element model.

Beam Peak load Peak defle

PEXP PFEM DEXP

(kN) (kN) (mm)

B25-1 172 177 59B25-2 167 177 46B15-1 109 105 18B15-2 55 58 79

� the parameter kc is used to define the shape of the failure sur-face in the deviatoric plane which is the ratio between distancesmeasured from the hydrostatic axis to tensile and compressivemeridians. The value of kc used in the present study is 2/3 asrecommended by Lubliner et al. [24] and Kmiecik et al. [29] tohave a better prediction. This actually helps to get a shape ofthe yield surface very close to the strength criterion (a combina-tion of three mutually tangent ellipses) of William and Warnke[28] who got a very good model for concrete using fiveparameters.

� / is the dilation angle measured in the p–q plane at high confin-ing pressure which is taken as 30 based on the sensitivity anal-ysis conducted in this study.

(b) B25-2

(d) B15-2

ersus FEA); (a) B25-1; (b) B25-2; (c) B15-1; (d) B15-2.

ction EXP/FEM

DFEM PEXP/PFEM DEXP/DFEM

(mm)

39 0.97 1.5139 0.94 1.1516 1.04 1.1278 0.95 1.01

22 M. Singh et al. / Construction and Building Materials 138 (2017) 12–25

� n is a parameter, referred to as the eccentricity. It is a small pos-itive value (zero to one) which controls the deviation of thehyperbolic plastic potential from its asymptote. It can beobtained from the ratio of tensile strength to compressive initialyield strengths [30] which is taken as є = 0.1 in the presentstudy.

� l is the viscosity parameter used for the a visco-plastic regular-ization scheme, which allows the stresses to go outside theyield surface [22]. It should be noted that the value of the vis-cosity parameter should be as minimum as possible so thatresults will not be affected by this parameter. The value of thisparameter is taken as 0.005 based on a large number of simula-tions are carried out to investigate the effect of this parameteron the results.

5.2. Finite element model built up

5.2.1. Cylinder testThe validation of the concrete model is initially carried out by

simulating a cylinder test under compression. The cylinder havinga 100 mm diameter and 200 mm height is modelled as a 3Ddeformable body using 8 node reduced integration brick elements(C3D8R). The cylinder is sandwiched between two steel platens,which are also modelled with the same element. The load on theconcrete cylinder is applied by imposing a vertically downwarddisplacement of the top steel platen whereas the bottom platenis restricted in all directions at its bottom surface. The interactionbetween cylinder and platen is defined by a surface-to-surfacestandard contact with hard interaction property. The displacementof the top platen and vertical reaction of the bottom platen are postprocessed to get the stress-strain curve.

5.2.2. Four full size beamsThe four beam specimens tested in the present investigation are

analysed using 8 node reduced integration brick elements (C3D8R)to model the concrete. The steel reinforcements are modelled as 3Dtruss elements (T3D2) considering their axial deformations only.The steel reinforcements are embedded in the solid concrete ele-ments where a full bond between reinforcements and concrete isassumed. The supports at the two ends and the two intermediateloading plates are idealised as square prisms of 50 mm sides whichare also modelled with the 8 node brick element (C3D8R) takingmaterial properties of steel. The interaction between beam andsupport is provided as surface to surface standard contact with ahard interaction property and frictional coefficient of 0.1. The dis-placement of the loading plates is imposed incrementally to acti-vate loads on beam specimens. The reaction forces and mid spandisplacement are extracted as primary output for each incrementstep.

Fig. 11. (a) Cracking pattern of test beam B25-1; (b)

6. Validation of the model

6.1. Cylinder test

The cylinder test is analysed with different element sizes of10 mm, 5 mm and 2.5 mm to observe the effect of mesh refine-ment on the numerical results. It is observed that the mesh sizegreater than 5 mm is not able to capture the actual softeningresponse of the stress strain curve whereas the mesh with 5 mmelement size had successfully predicted this response. The cylinderwith 2.5 mm element size predicted the similar response as that of5 mm element size without showing any visible improvement inthe results. Fig. 9 shows the stress strain plot obtained from thefinite element model of 5 mm element size using the proposedCDP material model along with the experimental test data. It canbe seen that the model accurately predicted the overall stressstrain behaviour of UHPFRC under compressive loading. The resultsshow a good predictive capability of the CDP model.

6.2. Full scale beam tests

The effect of mesh refinement on the numerical results is testedby analysing a beam with different element sizes such as 50 mm,25 mm and 15 mm so as to ensure the convergence of results. Itis observed that a mesh size greater than 50 mm leads to conver-gence problem in solving nonlinear equations and may terminatethe analysis prematurely. It is found that the initial part of theload-displacement curve is identical for element size of 50 mmand 25 mmwhereas the post yielding part is considerably differentfor these two cases. The mesh having 50 mm element size is unableto capture the hardening response of the beam whereas the meshwith 25 mm element size could successfully predicted thisresponse. A further reduction in the element size increases thecomputational time significantly but it does not have any visibleimprovement of the results. Based on this observation, an elementsize of 25 mm is used in modelling all the beams in the presentstudy.

The material properties discussed in section 5 are used to definethe uniaxial compressive and tensile response of UHPFRC in thebeam models. It is observed that the ultimate load capacity ofthe FE models is overestimated by more than 25%, when the fibreorientation coefficient (1/K) is taken as 1. This is attributed to thedisturbed fibre orientation in the beams due to the presence ofthe shear reinforcement. AFGC [1] recommendation suggests thatthe fibre orientation coefficient (K) should be determined fromthe tests conducted on the placement methods. In the absence ofsuch test results, it is recommended that the K factor should betaken as 1.25 (for all loadings other than local effects). Therefore,the coefficient K = 1.25 is adopted to account for the disturbed fibreorientation in the beam specimens. The tensile stress strainresponse obtained from the dog bone specimen is reduced by thiscoefficient and adopted in the beam models.

The variation of mid-span deflection with respect to the loadobtained from the finite element analysis and the physical tests

Tensile damage representing cracks from FEM.

M. Singh et al. / Construction and Building Materials 138 (2017) 12–25 23

are presented in Fig. 10a–d for the four beams. Fig. 10 shows thatthe entire load-displacement curve including its post-yield part ofthe four beams is accurately traced by the numerical model. Theultimate load capacity predicted by the FEM model is overesti-mated by 3% to 6% for beams B25-1,2 and 5% for beam B15-2,whereas for beam B15-1 the ultimate capacity is underestimated

(a)

(c) NR2

(e) R14-2

Fig. 12. (a) Compressive stress versus inelastic strain for FEA; (b) Tensile stress vs crackcomparison of beam R13-2; (e) Load deflection comparison of beam R14-2.

by 4%. The overall trend of the load-displacement responseobtained by the FEM models is in good agreement with the exper-imental results. Table 4 compares the peak load and correspondingdisplacement values obtained from numerical and experimentalresults. Fig. 11a, b shows that the cracking pattern captured bythe numerical model is similar to that found in the actual test.

(b)

(d) R13-2

ing strain for FEA; (c) Load deflection comparison of beam NR2; (d) Load deflection

Table 5Comparison of experimental and FEM results of UHPFRC beams tested by Yang et al. [14].

Beam Peak load Peak deflection EXP/FEM

PEXP PFEM DEXP DFEM PEXP/PFEM DEXP/DFEM

(kN) (kN) (mm) (mm)

NR-2 129.5 130 15.03 14.21 0.99 1.06R12-2 147.4 168 14.54 14.7 0.88 0.99R13-2 188.6 188.25 19.21 15.6 1.00 1.23R14-2 206.8 207.62 19.62 15.91 0.99 1.23R22-2 187.1 199.6 17.23 16.1 0.94 1.07

24 M. Singh et al. / Construction and Building Materials 138 (2017) 12–25

6.3. FE models of beams tested by Yang et al. [14]

The finite element model is also validated using the UHPFRCbeams tested by Yang et al. [14]. The material properties used todefine the uniaxial compressive and tensile behaviour of concreteare shown in Fig. 12a and b respectively. The properties in tension(Fig. 12b) are based on the direct tension tests conducted by Willeet al. [39] on the UHPFRC, which had similar properties in termscompressive strength and fibre volume used by Yang et al. [14].As the test data for steel bars is not reported by Yang et al. [14],an elastic perfectly plastic material behaviour is assumed withyield strength of 400 MPa. Fig. 12(c)–(e) shows the load deflectioncurves obtained from the finite element simulation and thosereported by Yang et al. [14] from their experimental tests. It canbe seen the overall trend of the load-displacement response con-forms well to the experimental results. Also, the estimation ofthe peak load for all the beams is in good agreement with theexperimental results. Table 5 compares the results of peak loadsand corresponding peak displacements predicted by numericalmodels with experimental test data.

7. Conclusions

The study in this paper presents the experimental investigationon the flexure behaviour of UHPFRC beams reinforced with con-ventional steel bar reinforcement. All the tested beams exhibitedductile failure and the failure is due to the rupture of steel bar rein-forcement. The steel fibres effectively resisted the widening of thecracks and lead to the increased load carrying capacity even afterthe steel bars are yielded. To predict the flexural behaviour of theUHPFRC beams, the numerical models were developed where con-crete damaged plasticity model is adapted to simulate the materialbehaviour of UHPFRC. The material properties are extracted frommaterial tests conducted on UHPFRC, which served as critical inputfor CDP model. The results obtained from the numerical analysis ofthe beams are validated with experimental data conducted in thisstudy. The numerically obtained load-deflection behaviour agreeswell with the experimental results for all beams. The momentcapacities predicted by the numerical models vary by 5% whencompared to the experimental results. The pre and post peakload-displacement behaviour is well captured by the numericalmodels. The results show that the calibrated CDP model can beused to predict the overall load-displacement behaviour of thereinforced UHPFRC beams when the material properties areobtained from material tests.

Acknowledgements

The research is supported by financial grant from DefenceScience and Technology Organisation (DSTO), Australia.

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