dazio 2008 engineering-structures

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Engineering Structures 30 (2008) 31413150

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Engineering Structures

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Nonlinear cyclic behaviour of Hybrid Fibre Concrete structural walls

Alessandro Dazio a,, Davide Buzzini b,a, Martin Trb a

a Institute of Structural Engineering (IBK), ETH Zurich, CH-8093 Zurich, Switzerlandb Pyry Infra AG. Hardturmstrasse 161, Postfach, CH-8037 Zurich, Switzerland

a r t i c l e i n f o

Article history:

Received 17 September 2007Received in revised form

4 March 2008

Accepted 26 March 2008

Available online 29 May 2008

Keywords:

Fibre concrete

High performance

Structural wall

Cyclic behaviour

Test

Numerical simulation

a b s t r a c t

Hybrid Fibre Concrete (HFC) is a self-compacting high-performance cementitious composite material

with a high-strength mortar matrix reinforced by steel fibres. HFC structural walls are characterized bythe presence of conventional mild steel flexural reinforcement and the absence of shear and confinementreinforcement. The function of the last two reinforcements is taken over by the fibres of HFC. This paperpresentsthe experimental and numerical investigation of the hysteretic behaviourof three HFCstructuralwalls and shows that the proposed structural system is able to provide large inelastic deformationcapacity while ensuring a superior post-earthquake functionality compared to conventional reinforcedconcrete.

The test units were cantilevers featuring either a rectangular (Test Units W1 and W2) or a barbelledcross-section (Test Unit W3). The fibre volume fraction of the HFC used for the construction of the testunits ranged between 3.5 and 6%. In order to ensure the formation of a suitable plastic hinge at the baseof the cantilevers, the flexural reinforcement of all three units was artificially debonded from the HFCby means of steel pipes (sleeves) that were slid onto the reinforcing bars. In order to prevent slidingshear deformations at the construction joint between the footing and the wall, the steel sleeves werepartially embedded into the footing acting as dowels. HFC prevented spalling of the concrete cover,hence preventing buckling of the flexural reinforcement. Despite the absence of shear reinforcement,the test units failed in flexure. Because not only shear but also confinement reinforcement was not usedand because of the self-compacting properties of HFC, the construction of the test units was a lot easiercompared to conventional reinforced concrete structural walls.

Theproposed numericalmodels were able to predict theglobal behaviour of thetestunitswhileat thelocal level the agreement between the experimental results and the numerical simulation was not verygood. The main reason for this disagreement is the lack of accurate information about the cyclic tensilebehaviour of HFC.

2008 Elsevier Ltd. All rights reserved.

1. Introduction

1.1. Statement of the problem

The ability of the capacity design method to ensure depend-

able ductile behaviour of reinforced concrete (RC) structures isproven by a large amount of evidence worldwide [ 1,2]. However,the ductile behaviour of such structures entails some disadvan-tages. To ensure enough inelastic displacement capacity, exten-sive transverse reinforcement for shear, confinementand stabilisa-tion of the longitudinal reinforcement is required in plastic regions,whichoften results in expensive manufacture and time-consumingplacement of the transverse reinforcing bars, in reinforce-ment congestion and in concrete casting difficulties. The post-earthquake functionality of conventional ductile RC structures is

Corresponding author. Tel.: +41 44 633 31 52; fax: +41 44 633 10 44.

E-mail address:[email protected](A. Dazio).

also problematic because their plastic zones are typically affectedby spalling of cover and architectural concrete already at relativelyminor plastic deformations and because residual deformationsafter an earthquake are potentially large.

The use of high-performance fibre-reinforced cementitious

composites (FRCC) to improve the seismic performance ofstructural elements has been investigated by many researchers inthe past and a comprehensive summary of possible applicationscan be found in [3] or in the literature survey presented in [4].As a further contribution towards the development of structuralsystems incorporating FRCC and in an attempt to reduce thedisadvantages of ductile reinforced concrete structures; this paperinvestigates the replacement of concrete with self-compactingHybrid Fibre Concrete (HFC) in the construction of structuralwalls. HFC is a FRCC featuring a high-strength mortar matrixreinforced by steel fibres of different dimensions and shapes. HFCis characterized by a high strength, a strain hardening behaviourand a smooth and controlled post-peak softening behaviour bothin compression and in tension.

0141-0296/$ see front matter 2008 Elsevier Ltd. All rights reserved.doi:10.1016/j.engstruct.2008.03.018
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3142 A. Dazio et al. / Engineering Structures 30 (2008) 31413150

Fig. 1. Schematic representation of a RC (a) and a HFC (b) structural wall.

1.2. Hybrid fibre concrete structural walls

The behaviour of Hybrid Fibre Concrete (HFC) structural wallscan be better understood by making a comparison with thebehaviour of conventional reinforced concrete (RC) structuralwalls.Fig. 1a displays a conventional RC wall that was taken as abenchmark to assess the behaviour of different configurations ofthe HFC wall shown inFig. 1b. For this purpose, the monotonicpushover curve of four different cantilever walls was computednumerically. The walls all had the geometry shown in Fig. 1.The footing was fixed to the ground, a constant axial load N =

200 kN was applied and the pushover curves were computedby increasing the horizontal displacement at the location of theload V in order to track global softening of the walls. The mainproperties of the four walls are: (1) The RC wall is a conventionalRC wall with longitudinal reinforcement, shear reinforcement andconfined boundary elements for plastic deformation capacity. Thebehaviour of this wall was predicted using the software Response-2000 [5]. (2) The HFC wall, no joint, no sleeves is a HFC wallwith longitudinal reinforcement only. The shear transfer and theconfinement of the boundary elements are ensured by the HFC.The wall and the footing are cast at the same time and there areno sleeves on the longitudinal reinforcing bars. All HFC walls weremodelled using the well-known FE code ABAQUS [6]. (3) The HFCwall, with joint, no sleeves is a HFC wall similar to wall no. (2).

However, it is cast in two lifts. The footing is cast first and the wallis cast only after hardening of the footing. This corresponds to theusual construction schedule for a wall on a construction site. (4)The HFC wall, with joint, 500 mm sleeves is a HFC wall similarto wall no. (3). However, 500 mm long plastic pipes (sleeves) areslid onto each reinforcing bar to prevent the bond between thereinforcing bars and the HFC. Further details on these simulationscan be found in [4].

The pushover curves of the four walls are displayed inFig. 2and the following remarks can be made: (1) The RC wall reacheda displacement of 56 mm (2.2% drift) before the outer reinforcingbars reached their ultimate strain, assumed to be 0.07, and failedin tension. The displacement ductility at that point was about 8which is a rather high yet still reasonable value. (2) The elastic

stiffness and the strength of the HFC wall with no joint and nosleeves were significantly higher compared to those of the RC

Fig. 2. Monotonic pushover curves of different RC and HFC structural walls.

wall. This implies a significant contribution of HFC to the strengthand stiffness of the wall which is reasonable considering that theassumed equivalent tensile strength of HFC was 12 MPa at a strainof 0.01 [4]. When the principal tensile strain of HFC reached 0.01,the material started softening andthe load-carrying capacity of thewall dropped. The softening of HFC occurred at one single location

leading to strain concentrations. All the following deformations ofthe wall basically occurred in one single horizontal cross-sectionleading to high local strains in the longitudinal reinforcement. Dueto this strain concentration the ultimate strain of the longitudinalreinforcing bars was reached when the top displacement was

just 28 mm (1.1% drift), implying that the displacement capacityof such a HFC wall would be much lower than that of thepreviously discussed RC wall. At that point of the simulation theresistance of the wall did not drop sharply because the fractureof the reinforcing bars was not modelled. Within the scope ofthis problem no such structural wall with no joint and no sleeveswas tested because the predicted global softening and the reducedplastic deformation capacity were deemed to be unacceptablefor seismic application purposes. For this reason there is no

experimental evidence for the softening behaviour of HFC wallswith no joint and no sleeves. However, a similar phenomenon,


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A. Dazio et al. / Engineering Structures 30 (2008) 31413150 3143

(a) Test unit W1. (b) Test unit W2. (c) Test unit W3.

Fig. 3. Reinforcement of the plastic hinge zone of the HFC structural walls W1 (a), W2 (b) and W3 (c). All dimensions are in [mm].

i.e. a noticeable initial contribution of the fibre concrete to thestrength of the structural element followed by a global softeningbehaviour, is reported by [7]where the axial deformation capacityof large-scale prismatic bars made of conventional fibre-reinforcedconcrete andfeaturing a mild steel longitudinalreinforcement wasinvestigated. (3) In the HFC wall with joint but no sleeves astrain concentration took place already from the beginning of theloading phase. No fibres bridged the construction joint betweenthe footing and the wall, making it significantly weaker than theadjacent sections. All plastic deformations occurred at the jointand, as in the case of jacketed sections [2], the length of the plastichinge canbe assumed to correspond to twice thestrain penetrationlength. Due to the high tensile capacity of HFC it is believed that

strain penetration is reduced compared to conventional reinforcedconcrete. This lead to significant strain concentrations and theultimate strain of the longitudinal reinforcing bars was reachedwhen the computed topdisplacement wasonly 14 mm (0.6% drift),which resulted in a deformation capacity that is a lot lower thanthat of the RC wall. Again, at that point of the simulation theresistance of the wall did not drop sharply because the fractureof the bars was not modelled. For seismic applications this wall isalso unsuitable. (4) To overcome the problem of excessive strainlocalization, 500 mm long sleeves were slid onto the longitudinalreinforcement in order to prevent its bond with the adjacent HFC.The pushover curve of the HFC wall with joint and sleeves isvery similar to the curve of the RC wall with just the shape ofthe curve in the elastic deformation range being slightly different

because of the different cracking patterns. However, the bilinearapproximation of the two curves would be quite similar and,postulating a stable hystereticbehaviour, the seismic displacementdemand would also be similar for both walls[8].

During the simulation with 500 mm long sleeves, the ultimatestrain of the longitudinal reinforcing bars was reached when thetop displacement was 100 mm (4.0% drift). Such a displacementcapacity, especially in terms of displacement ductility (12.5 in thiscase), is verylarge and it is unlikely tobe required tosurvive even asevere earthquake. However, thedisplacement capacity of the wallcan be adjusted to the effective needs by changing the lengths ofthe sleeves, making this wall very suitable for seismic applications.

The intention of this short case study was to qualitativelydescribe the problems arising with the design of HFC structural

walls and to suggest a strategy to overcome them. Parra-Montesinos and co-workers also investigated the behaviour of

structural walls incorporating FRCC and they proposed a differentstructural solution which was better adapted to the mechanicalproperties of the FRCC they used and which differed noticeablyfrom HFC[9]. In the following Sections2 and3 the experimentalbehaviour of three HFC structural walls is presented while inSection4a numerical model for the simulation of such walls isdiscussed. A more detailed description of the experimental resultsand of the numerical model is available in[4].

2. Test units

2.1. Geometry and reinforcement

The test units represent approximately 1:3 scale models ofstructural walls that could be used to stabilise multi-storeybuildings. No specific prototype building was defined. Aspect ratio,nominal axial load and reinforcement content were chosen basedon previous experience making the most of the proposed testsetup[10].

Test Units W1 and W2 had a 900-mm-long and 100-mm-widerectangular cross-section as shown in Fig. 3. Test Unit W3 featuredan I-shaped cross-section with 190-mm-long and 100-mm-wideboundary regions; the web zone was 520 mm long and 52 mmwide. The flexural reinforcement was the same for all test unitsand consisted of 6 reinforcing bars D12 in the end regions of thecross-section and of 10 reinforcing bars D5.2 in the web region.

The location of the flexural reinforcement of Test Units W2 andW3 close to the centreline of the section was chosen in order toallow for a larger thickness of the cover concrete.The shear andtheconfinement reinforcement were provided by thefibres of HFC andno additional horizontal reinforcing bars were placed. In the plasticzone of Test Unit W1 500-mm-long plastic sleeves were usedwhile for Unit W2 and W3 200-mm-long steel sleeves were used.In the first unit the sleeves were located above the construction

joint while in the other units the sleeves were embedded in thefooting over half of their length. The justification for this differencebetween the test units is discussed in Section 3.

The units were all built in the same way. First the footing waspoured. After a curing time of about a week the rest of the wallwaspoured creating a constructionjointjust above thefooting.Thewalls were built in upright position and HFC was poured from thetop.


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Table 1

HFC mix designs

Test Unit W1 W2 W3

Batch V3.3 V4.2 V4.3

Short straight steel [%(kg/m3)] 1.5 (117) 3.0 (234)

fibres(D0.156 mm)

Medium straight stee l [%(kg/m3)] 0.5 (39) 1.5 (117)

fibres(D0.2012 mm)

Long crimped steel [%(kg/m3)] 1.5 (117) 1.5 (117)fibres(D0.6030 mm)

Cement CEM I 52.5R [kg/m3] 1000 961

Fly ash [kg/m3] 168 161

Silica fume [kg/m3] 95 91

Aggregate 0/1 mm [kg/m3] 754 725

Water [kg/m3] 215 218

Superplasticizer [kg/m3] 20 19

Water/binder ratio [] 0.17 0.18

Table 2

Mechanical properties of HFC at day-of-testing (D.o.T)

Test Unit W1 W2 W3

Age [d] 4850 6991 70

Cylinder strengthfc [MPa] 1543.6 1396.4 1354.3

Cube strengthfcw [MPa] 1576.2 1586.7 1589.13-pt. bending strengthfct [MPa] 26.62.0 41.45.7 45.65.5

Modulus of elasticityEc [GPa] 41.41.0 39.90.6 39.90.2

2.2. Material properties

The HFC considered within this project was developed by theInstitute for Building Materials (IfB) at the ETH Zurich [11] and bythe Department of Design and Construction at the Delft Universityof Technology [12]. The mixes thatwereusedto build the testunitspresented in the previous section were designed by the formerinstitution, and their detailed composition is given inTable 1.It isimportant to note, that despite the high fibre content, the HFC hadself-compacting properties. However, several trial batches wereneeded to adjust the rheology of HFC and avoid segregation [4].The mechanical properties of HFC were measured in a series ofdifferent tests and are summarized in Table 2. The compressivestrengthsfcand fcwwere obtained from D150300 mm cylindersand from cube specimens with 150 mm sides, respectively, andthe relevant stressstrain relationships are plotted at the top ofFig. 4.The tensile properties of HFC were characterized by meansof 3-point bending tests on 70 70 280 mm prisms using aspan of 220 mm. The forcedeformation curves for the mid-span

vertical deflection of the prisms are plotted at the bottom ofFig. 4.The tensile strengths given inTable 2were computed by simplydividing the mid-span bending moment by the elastic modulus ofthe section.

For the reinforcement of the test units Grade C reinforcingsteel according to [13] and with the mechanical propertiessummarized inTable 3was used.

2.3. Test setup, instrumentation and loading history

The test setup is depicted in Fig. 5. The test units were fixedto the strong floor by means of a steel footing. The lateral loadwas applied to Test Units W1 and W2 by a 250 kN, 250 mmservo-controlled hydraulic actuator. The actuator was mounted ona reaction frame in line with the strong direction (NorthSouth) ofthe test units and positioned 2500 mm (Aspect ratio of 2.8) abovethe footing of the test units. On the other hand, Test Unit W3 wasloadedby means of a 500 kN,100 mm servo-controlled hydraulicactuator positioned 1700 mm (Aspect ratio of 1.9) above the testunit footing. To prevent out-of-plane deformations a side restraintwas provided at the top of all structural walls. A constant axial loadof200kN was applied toalltestunitsby means ofhollowcorejacks

and two post-tensioning rods running from the steel footing to thetop of the units. The axial load was kept constant during testingby means of a load-follower that was connected to the hollow core

jacks.The instrumentation of Test Unit W2 is shown in Fig. 6. The

instrumentation of the other test units was similar and is givenin [4]. In total, 26 hard-wired devices were used to monitor thebehaviour of the test unit. In addition, Demec measurements(Whitmore gauge measurements) were taken on the east face ofthe wall according to the pattern shown inFig. 6a.

The tests were quasi-static and the test units were subjectedto a fully-reversed cyclic loading history with step-wise increasinghorizontal top displacement. The first four cycles were run inforce control up to respectively 25, 50, 75 and 100% of the force

corresponding to the onset of yielding at the extreme flexuralreinforcing bars of the section (first yield). Afterwards, the nominalyield displacement y corresponding to displacement ductility = 1 was defined and additional cycles in displacementcontrol were carried out. The displacement ductility was thenincreased in steps of 1 up to = 4 and afterwards in steps of2 up to failure. Due to practical difficulties that were encounteredduring testing, Wall W1 was loaded to slightly different targetductilities. While presenting the results relevant to Wall W1 thecorrect ductilities determined at the end of the test are used.

Fig. 4. Stressstrain relationships of the HFC that were used to build Test Units W1 (a), W2 (b) and W3 (c).


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Table 3

Mechanical properties of the reinforcement

Test unit W1 W2 W3

Bar D12 D5.2 D12 D5.2 D12 D5.2

Yield strengthfy [MPa] 528 503 556 511 558 579

Tensile strengthft [MPa] 634 590 689 587 691 670

Hardening ratioft/fy [] 1.20 1.17 1.24 1.15 1.24 1.18

Total elongation at maximum forceAgt [%] 9.9 6.5 10.7 7.1 11.3 8.4

(a) Setup for test units W1 and W2. (b) Setup for test unit W3.

Fig. 5. Test setup for Test Units W1 (a), W2 (b) and W3 (c).

(a) East face. (b) West face. (c) Hard-wired devices.

Fig. 6. Instrumentation of Test Unit W2.

3. Test results

In the following, the test results are presented in termsof forcedisplacement hystereses and displacement componentswith a discussion of the relevant failure mechanisms. Due to space

limitations it is not possible to present all data collected during thetests and for further details the reader is referred to[4].

The hysteretic behaviour of all test units as well as thedisplacementcomponents at thepeak topdisplacement during thefirst cycle of every ductility level are depicted inFig. 7.The threecomponents (1) shear displacements, (2) flexural displacementsand(3) fixed-enddisplacements were computed from thereadings

of the Linear Variable Differential Transformers (LVDTs) mountedon the test units (Fig. 6b). The shear displacements were computed


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Fig. 7. Experimental hysteretic behaviour of Test Units W1 (a, b), W2 (c, d) and W3 (e, f).

using the procedure originally presented in [14], the flexuraldisplacements were computed by integration of the curvaturesobtained from the LVDTs W-V-2 to 7-North and South. Thefixed-end displacement is the component which accounts for therotation of the wall at the construction joint and it was computedby integrating the rotation due to the opening of the crack at the

joint measured by means of the LVDTs W-V-1-North and W-V-1-South over the height of the test unit. If the summation of allthree displacement components is compared to the measured topdisplacement, the error is always less than 10%.

Test Unit W1 failedduring thesecondcycleto ductility8.5 (4.1%drift) due to tensile fracture of several D5.2 and D12 reinforcingbars. However, significant damage occurred well before failure.Spalling of the concrete cover in the compression zone started

at ductility 4 (2% drift) and by the next cycle at ductility 5.7(2.5% drift) the region affected by the spalling was so large thatthe concrete cover was no longer able to prevent buckling of theflexural reinforcement. This insufficient behaviour was caused bythe inappropriate downscaling of the prototypes dimensions tothe test units dimensions.Fig. 3a shows that the thickness of thecover concrete was only about 10 mm. Considering the length ofHFCs mediumand long fibres (12and 30 mm), it is straightforwardto conclude that the cover concrete failed prematurely becauseit was too thin for the fibres to reach a proper distribution. InTest Units W2 and W3 this problem was solved by increasing theamount of fibres in the mix design and especially by increasing thethicknessof theconcretecover (Fig.3b andc). These improvementswere extremely successful totally eliminating spalling and proving

theability of HFC to prevent buckling of theflexuralreinforcement.A direct consequence of the spalling which could be observed in

the hysteresis curve wasthat the peak load reached during thefirstcycle at a ductility of 4 was smaller (push direction) or just slightlyhigher (pull direction) than the peak load that was reached duringthe first cycle at a ductility of 2.5. The spalling of the concretecaused a reduction of the inner lever arm, and hence a reductionof the bending strength which could not be totally compensatedby the hardening of the reinforcing steel.

Test Unit W1 also experienced noticeable sliding at theconstruction joint. The axial load acting on the wall was relativelysmall allowing the wall to grow vertically. Additionally, theconcentration of the deformations at the base of the wall and theminor roughness of the crack at the joint led to a situation whereduring large portions of a loading cycle, the entire base shear hadto be carried by dowel action of the flexural reinforcement and the

reinforcing bars kinkedacross thestillopen joint crack.The kinkingimposed large local inelastic deformations on the bars leading totheir failure. At the same time the sliding also affected the overallshape of the hysteretic loops leading to significant pinching asshown in Fig. 7a. In Test Units W2 and W3 this problem was solvedby using steel sleeves instead of plastic sleeves and by partiallyembedding them into the footing (Fig. 3b and c). The dowel actionexercised by the steel sleeves was enough to transfer the totalityof the base shear across the crack at the joint between wall andfooting.

Test Unit W2 was able to complete a full cycle at ductility8 before failure occurred during the second cycle (see Fig. 7c).However, already during the first cycle a D12 reinforcing baron the south side of the wall fractured causing the base shear

to drop to about 84% of the measured peak value of 185 kNwhich corresponded to a nominal peak shear stress of max =


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Fig. 8. Crack pattern of Test Units W1 (a), W2 (b) and W3 (c) at failure.

Vmax/(0.8bwlw) = 2.4 MPa (0.20fc MPa). The bar fractured

because it experienced a high tensile strain. The strain in the barwas not directly measured. However, a preliminary estimation,based on the maximum crack width of about 31 mm measured atthe joint, shows that the strain had to be around 10%12%. Thisstrain has the same order of magnitude as the total elongation atmaximum force Agtmeasured during the material tests(Table 3).The steel sleeves embedded in the footing prevented sliding ofthe wall and the relevant pinching of the hysteresis loops. Thebehaviour of Wall W2 was significantly better than the behaviourof Wall W1 even if the latter was able to reach a slightlylarger maximum deformation. This is due to the fact that the

unbonded length of the flexural reinforcement was more thantwice the unbonded length of the flexural reinforcement of UnitW2 (Fig. 3). The use of a longer unbonded length in Unit W2as well would have led to a larger displacement capacity. Thiswas not deemed to be necessary; however it is important torecognize that the maximum displacement capacity of the wallscan be largely influenced by the choice of the unbonded length ofthe flexural reinforcement.Fig. 7d shows that shear deformationswere very limited, which is consistent with the crack patterndepicted in Fig. 8b. Flexural displacements are due to crackingalong the wall and Fig. 7d shows that they are proportional tothe base shear. On the other hand, fixed-end displacements aredue to yielding of the flexural reinforcement and are proportionalto the measured top displacement. At displacement ductility 1,

flexural displacements are responsible for more than 50% of themeasured top displacement of Test Unit W2. At higher ductilitiestheir absolute value remains about constant and their percentagecontribution to the measured top displacement reduces.

Test Unit W3 was able to complete two full cycles at ductility8 before failing on its way to ductility 10. However, significantdamage already occurred during the second cycle to ductility 8with the fracture of a D12 reinforcing bar on the south side of thewall. The hysteretic behaviour plotted inFig. 7e is similar to thatof Test Unit W2 and does not require further discussion. On theother hand, the shear deformation of Test Unit W3 is larger thanthe shear deformation of Test Unit W2 (see Fig. 7d and f) and isconsistent with the crack patterns shown in Fig. 8. At displacementductility 1 the total deformation of Test Unit W3 is made up by 44%

fixed-end deformation, 42% flexural deformation and 14% sheardeformation. The peak base shear measured during the test was

262 kN which corresponds to a nominal peak shear stress ofmax =Vmax/(0.8bwlw) = 7.1 MPa (0.61

fcMPa) hence showing that HFC

is potentially capable of transferring large shear forces without theneed for additionalbar reinforcement. However, this large nominalpeak shear stressshouldbe interpreted with caution because of thebarbelled section of Test Unit W3 whose large boundary elementssurely helped resisting shear and because of the relatively lowaspect ratio of the unit which allowed an inclined-strut load-carrying mechanism. In fact, very littleinformation on the ultimateshear strength of HFC is available and additional investigations areneeded.

Fig. 8displays the three test units at failure where the different

crack patterns and the spalling of the concrete cover in theboundary regions of Test Unit W1 can be observed. Two differentkinds of cracks formed in the HFC walls during testing: a largecrack formed at the construction joint and thinner cracks formedalong almost the entire height of the wall. Test Unit W1 showedno cracking along the first 500 mm of the wall because thesleeves prevented bonding between the flexural reinforcementand the HFC. Owing to the shorter sleeves Test Unit W2 hada more extensive crack pattern. After yielding of the flexuralreinforcement the maximum crack width measured on the wallwas about 0.1 mm. All cracks fully closed upon unloading. Thecrack at the construction joint opened considerably and remainedopen after unloading causing almost the totality of the residualdeformations. During the test two kinds of cracks formed in the

plastic hinge zone of Wall W3: bending cracks and shear cracks.Bending cracks appeared in the boundary regions and were almosthorizontal, while shear cracks formed in the web zone of the walland their orientation was diagonal to vertical. The shear cracksopened because of the reduced thickness of the web zone of TestUnit W3, which led to higher shear stresses in this zone than wasthe case for Test Units W1 and W2. The maximum crack widthmeasured during the test was 0.3 mm, which is still very small andcan easily be bridged by the fibres of HFC [15,16].

4. Numerical simulations

4.1. Numerical model and relevant material properties

The behaviour of the test units was simulated numerically bymeans of the fully nonlinear 3D finite element models depicted in


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Fig. 9. Solid element model of Test Units W1 (a, b) and W2 (c, d).

Fig. 9.In this paper only the principal characteristics of the modelsbelonging to Test Units W2 and W3 are discussed, for further

details the reader is referred to[4].The models were built using the well-known general purposefinite element program ABAQUS[6]. The HFC was modelled with3D 8-node solid elements (Type C3D8) and every vertical reinforc-ing bar was modelled using beam elements (Type B31) that weredirectly connected to the nodes of the concrete mesh. To allow forstrain penetration the free length of the beam elements crossingthe construction joint was increased from 200 mm, i.e. the lengthof the steel sleeves, to 300 mm based on a conservative applica-tion of the equation for the estimation of the strain penetrationlength proposed by Paulay and Priestley in [1]. The construction

joint between the wall and the footing was modelled using gap el-ements(Type GAPUNI) which allowed no horizontal slip while fea-turing perfect contact in compression and unrestrained opening intension. The mechanical properties of the reinforcing steel were

described by means of ABAQUSs standard elasto-plastic modelusing nonlinear isotropic/kinematic hardening. The input param-eters for this model were calibrated against the stressstrain re-lationships obtained from the monotonic and cyclic coupon testspresented in [4]. The mechanical properties of HFC were modelledusing ABAQUSs own Concrete Damage Plasticity (CDP) formula-tion. The *CONCRETE COMPRESSION HARDENING curve was fittedto the stressstrain relationship of the cylinder compression testthat was the closest to the average of the three curves plotted inFig. 4.

As no direct tension tests on HFC material samples couldbe conducted in the framework of the structural wall tests, the*CONCRETE TENSION HARDENING curve was computed usingback-analysis on the 3-point bending testspresentedin Section 2.2.

The HFC prisms used for the 3-point bending tests were modelledwith ABAQUS using the CDP material model and making differentassumptions on the tensile behaviour of HFC based on directtensile tests carried out by other researchers on HFC samples witha similar fibre mix [17]. Two of these assumptions are shownin Fig. 10a while the respective forcedeflection curves of thenumerically simulated 3-point bending tests are compared toexperimental evidence inFig. 10b. The simulation of the 3-pointbending test using Assumption 2 as a characterization of thetensile behaviour of HFC yielded a very good agreement betweenthe test results and the numerical simulation up to a verticaldeflection of about 1.8mm which corresponds to 1/122 ofthe spanlength (Fig. 10b). Afterwards a difference between experimentand simulation is noticeable. However, this was not deemed to

be significant because during the test of Walls W2 and W3 muchsmaller strains were reached. Hence, Assumption 2 inFig. 10a was

Fig. 10. Different assumptions regarding the uniaxial tensile behaviour of HFC (a)

and results of the relevant numerical simulations of the 3-point bending tests on

the Test Unit W3 material samples (b).

retained as the better estimate of the actual tensile behaviour ofHFC. These simulations refer to the material that was used to buildTest Unit W3; for Test Unit W2 a similar approach was used.

Unfortunately, in the framework of this research project nomaterial tests could be carried out in order to characterize thecyclic behaviour of HFC. In the literature little information wasfound and for this reason it was decided to choose the parametersgoverning the cyclic behaviour of the CDP model based onthe findings presented in [18] even if they actually refer to adifferent fibre-reinforced cementitious material. A key issue wasthe definition of the unloading and reloading branches after atensile excursion. According to [18] the behaviour after a tensileexcursion is characterized by steep initial elastic unloading toalmost zero stress followed by crack closing with low stiffnessand afterwards by reloading with gradually increasing stiffnessin the region of zero absolute strain. It is not possible to exactlyreproduce this kind of behaviour with ABAQUSs CDP model, hencethe parameter *CONCRETE TENSION DAMAGE (*CTD) governingthe unloading after a tensile excursion was chosen to obtain anunloading stressstrain curve as origin-oriented as possible. It wasnot possible to set the parameter *CTD in such a way as to obtaina perfectly origin-oriented behaviour because in that case thenumerical model did no longer converge.

4.2. Comparison of the numerical and the experimental results

The numerical and the experimental results are compared inFig. 11in terms of forcedeformation relationships. The qualityof the numerical results is similar for Test Units W2 and W3;hence in the following only the results for Test Unit W2 willbe discussed. The initial stiffness in the simulation of Test UnitW2 which is displayed in Fig. 11a with a dotted line accuratelymatches the one observed in the test. The shape of the simulatedhysteresis loops andthe computed strength of the test unit arealsoin fair agreement with the experimentalresults.Only in thesecondcycle at a displacement ductility of 2, the numerical simulationclearly underestimates the maximum strength. This is a direct

consequence of the inability of the nonlinear isotropic/kinematichardening model of the steel to match the hysteretic behaviour


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Fig. 11. Comparison between the experimental and the numerical hysteretic behaviour of Test Units W2 (a) and W3 (b).

Fig. 12. Displacement components of Test Units W2 (a, b, c= test, d, e, f= simulation) and W3 (g, h, i= test,j, k, l= simulation).

of the real reinforcing bars in the strain range occurring duringreloading to ductility 2[4].

A further comparison between numerical and experimentalresults is shown in Fig. 12 where the topdisplacement of Test UnitsW2 and W3 is broken down into its three components. In orderto compute the displacement components from the numerical

results virtual instruments were used. In the numerical modelnodes were defined in correspondence with the fixture of theLVDTs that were mounted on the test units (seeFig. 6b). From therelative displacement of these nodes, virtual readings of the LVDTscould be computed. Afterwards, the displacement componentswere computed using thesame procedure as describedin Section 3for the experimental data.

Due to the proposed structural system for the HFC structuralwalls, the largest part of the top displacement is made up bythe fixed-end component. Its hysteretic behaviour is stronglygoverned by the longitudinal reinforcement and its predictionis quite accurate over the entire deformation range. On theother hand the hysteretic behaviour of the flexural and theshear displacement components is strongly affected by the cyclic

tensile behaviour of HFC and as described in Section 4.1 thisbehaviour is only known and modelled with large uncertainties.

The simulation of Test Unit W2 was able to accurately predict theflexural deformation up to first cracking of the wall. Afterwards,the behaviour of the numerical model was too stiff leading tomaximum flexural deformations (Fig. 12e) of about only 50% ofthe flexural deformations computed from the experimental data(Fig. 12b). A similar observation holds true for the flexural (Fig. 12h

and k) and shear (Fig. 12iand l) deformations of Test Unit W3, thisdespiteFig. 10showing a good agreement between the 3-pointbending tests and their simulation which is also governed by thetensile behaviourof HFC. Owing to the large uncertainties involvedin such a procedure, it was not deemed reasonable and beyondthe scope of this investigation to further improve the numericalsimulation by iteratively adjusting the parameters defining thecyclic tensile behaviour of HFC such as to match the overallbehaviour of the test units.

5. Conclusions and outlook

Hybrid Fibre Concrete (HFC) structural walls are able to un-

dergo large inelastic deformations while ensuring an easier con-structability and superior post-earthquake functionality compared


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to conventional reinforced concrete walls. The tests and the nu-merical simulations on three HFCstructural walls allow thefollow-ing observations:

1. It was possible to build structural walls without any transversereinforcement for shear, confinement and stabilisation of thelongitudinal reinforcement. The HFC used for this purpose hada fibre volume content between 3.5% and 6.0%. Due to the tight

control of the rheology,the HFC hadself-compacting propertiesdespite the high fibre content.

2. The HFC structural walls were able to reach ultimate displace-ment ductilities in excess of 8 corresponding to drifts rangingbetween 3.2 and 4.2% which is comparable to the deformationcapacity of well-detailed capacity designed reinforced concrete(RC) walls and is larger than the capacity demand required tosurvive most severe earthquakes. Furthermore, the deforma-tion capacity of HFC walls can easily be adjusted by changingthe length of the sleeves placed onto the longitudinal reinforc-ing bars.

3. Provided that the thickness of the cover concrete was largeenough to accommodate the biggest fibres, the concrete coverdidnot spall and thereby buckling of the flexural reinforcement

was prevented.4. Test Units W2 and W3 did not suffer any significant structuraldamage up to failure. However, residual displacements uponunloading were of the same order of magnitude as thoseexperienced by RC walls, and they are of course affecting thepost-earthquake functionality and reparability of HFC walls. Inorder to fully exploit the excellent properties of HFC, structuralsystems characterized by small residual displacements shouldbe investigated.

5. For all test units, the cracks remained small (

dazio 2008 engineering-structures

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