Flexural performance of layered ECC-concrete composite beam

COMPOSITES

www.elsevier.com/locate/compscitech

Composites Science and Technology 66 (2006) 1501–1512

SCIENCE ANDTECHNOLOGY

Flexural performance of layered ECC-concrete composite beam

Jun Zhang a,*, Christopher K.Y. Leung b, Yin Nee Cheung b

a Department of Civil Engineering, Tsinghua University, Beijing 100084, PR Chinab Department of Civil Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, PR China

Received 20 August 2005; received in revised form 10 November 2005; accepted 25 November 2005Available online 10 January 2006

Abstract

The pseudo strain-hardening behavior of fiber reinforced engineered cementitious composites (ECC) is a desirable characteristic for itto act as a substitute for concrete to suppress brittle failure. The use of ECC in the industry is, however, limited by its high cost. Toachieve higher cost/performance ratio, ECC can be strategically applied in parts of a structure that is under relatively high stress. In thispaper, layered ECC-concrete beams subjected to flexural load are investigated from both theoretical and experimental aspects. Four-point bending tests are performed on beam members with ECC layer at its tensile side. The application of ECC layer leads to increasein both the flexural strength and ductility, and the degree of improvement is found to increase with the ECC thickness. A semi-analyticalapproach for modeling the flexure behavior of layered ECC-concrete beams is also developed. In the model, the stress–crack width rela-tion of both concrete and ECC are employed as fundamental constitutive relationships. The model and experimental results are found tobe in good agreement with one another. Simulation with the model shows that when the ECC thickness goes beyond a certain criticalvalue, both the flexural strength and ductility (reflected by crack mouth opening and crack length at ultimate load) will significantlyincrease. The critical ECC thickness is hence an important design parameter, and it can be determined with the theoretical approachdeveloped in the present work.� 2005 Elsevier Ltd. All rights reserved.

Keywords: A. Fiber reinforced cementitious composite; A. Layered beam; B. Flexural strength

1. Introduction

Concrete is widely used in civil engineering construc-tion. Though concrete is convenient and inexpensive tobe made, its brittle behavior upon tensile loading isone of its adverse properties that lead to the develop-ment of fiber reinforced cementitious composites. Thebrittle behavior of concrete is due to the fast growingof a single crack that leads to the uncontrollable failureof the specimen. This kind of failure mode results in alow ultimate strain around 0.01% and a sudden failurewithout warning. In order to improve the behavior ofconcrete, fiber reinforced concrete (FRC) is made byadding discrete short fibers into the concrete matrix.Fibers used currently include steel, glass, carbon and

0266-3538/$ - see front matter � 2005 Elsevier Ltd. All rights reserved.

doi:10.1016/j.compscitech.2005.11.024

* Corresponding author. Tel.: +86 10 62785836; fax: +86 10 62771132.E-mail address: [email protected] (J. Zhang).

polymer fibers. These fibers act as bridges across thecracks to delay their propagation. Thus, a higher ulti-mate strain and a more ductile failure mode would beattained.

Development of FRCs started in the 1970s. By thattime, only glass fiber and steel fiber were investigated[1]. During the past 10 years, polyvinyl alcohol (PVA)fiber has been introduced in the production of FRC[2]. The resulting composite, which exhibits a pseudo-ductile behavior similar to that of steel, is called ‘‘engi-neered cementitious composites (ECC)’’. The ultimatetensile strain attained by ECC is 2–6%, which is 200–600 times greater than that of concrete [3]. This newkind of material is very effective in transferring stressacross the cracks and fracture occurs with the formationof multiple cracks.

A typical mix of PVA-ECC contains about 2% of PVAfibers. It has been estimated that the cost of this volume of

mailto:[email protected]

1502 J. Zhang et al. / Composites Science and Technology 66 (2006) 1501–1512

PVA fibers used in one-meter cube of ECC is beyond US$250, which is much higher than the cost of conventionalconcrete, which is around US $60 m3 [4]. Table 1 showsthe comparison between the costs of fibers used permeter-cube of FRC and ECC. For the same fiber volumefraction, the numbers indicate that the cost per meter ofECC is higher than that for GFRC/SFRC. In order toachieve better economy, ECC should be used selectivelyin parts of a structure where their advantages can be fullyexploited.

The flexural performance of concrete is important formany current applications such as overlays for highways,bridge decks, airport pavements, roofing tiles, and parti-tion walls. Consider a plain concrete beam subjected toflexural load. The first crack will form when the maxi-mum principal tensile stress exceeds the cracking strengthof the material. The crack then continues to developuntil unstable failure occurring. As mentioned before,ECC is effective in resisting tensile stress and thuschanges the failure mode of concrete from brittle to duc-tile. Based on economic consideration, it is suggestedthat ECC should be applied partially as a layer on thetensile side of a beam. A similar application was donealso by Maalej et al. in 1995 [5].

In the present work, investigations will focus on the flex-ural behavior of layered ECC-concrete beam in which alayer of ECC is applied beneath a layer of concrete. Inthe experimental part, three-point bending tests on pre-notched concrete and ECC beams were carried out toobtain the stress–crack width relationship used in the mod-eling. Four-point bending tests on layered ECC-concretebeams were carried out to investigate the flexural perfor-mance and for the verification of model predictions. Inthe theoretical part, a semi-analytical approach for model-ing the flexure behavior of layered ECC-concrete beams ispresented first. In the model, the stress–crack width rela-tion of both concrete and ECC are employed as the funda-mental constitutive relationship in tension. The completetheoretical load–deformation curves, including load–crackmouth opening displacement (CMOD) and load–cracklength diagrams of ECC-concrete composite beam areobtained in the theoretical analysis. Then, the influencesof the ECC layer thickness on the strength and ductilityof the layered beam are discussed in both theoretical andexperimental aspects. Finally, the model predictions arevalidated in terms of both flexural strength and ductilityby comparison with experimental results of layered beamsunder four-point bending load.

Table 1Comparison of the costs of fibers per meter-cube of FRC and ECC cast

Fiber Type Cost(US $/kg)

Weight of fiberused (kg/m3)

Total costof fiber (HK $/m3)

PVA KII 9.6 26 (2% by vol.) 250AR Glass 1.1 120 (5% by vol.) 130Steel 0.6 108 (1.5% by vol.) 65

2. A model to predict the flexural behavior of layered ECC-

concrete beam

The analysis of flexural behavior of ECC-concrete com-posite beams is based on the method suggested by Zhangand Stang [6], which focused on FRC beams. To applythe same algorithm to layered ECC-concrete compositebeam, the form of the stress–crack width relationship inthe cracked beam section is taken as that of ECC or con-crete, respectively, according to the location along thecrack path. In this section, a model based on the equilib-rium of force in the critical cracked section with multi-lin-ear stress–crack width relation for layered ECC-concretebeam is developed. Before developing the model, the essen-tial material parameters of concrete and ECC for problemformulation will be discussed first.

2.1. Constitutive law of concrete and ECC

It is assumed that the concrete and ECC materials con-sidered here are materials that essentially show a linearresponse in uniaxial tension up to cracking load. Afterthat, one discrete crack is formed. It is further assumedthat the discrete crack propagation is governed by thestress–crack width relationship. Thus the following mate-rial parameters are fundamental in the constitutive rela-tions of concrete and ECC in tension: the Young’smodulus E, the cracking strength rfc, and the stress–crackwidth relationship. It is assumed that the behavior of con-crete and ECC materials in compression is linear elastic,and the Young’s modulus is the same in compressionand tension.

The stress–crack width relationship of concrete and fiberreinforced cementitious composites has been widely inves-tigated during recent years. The experimental results showthat the shape of the stress–crack width curve of fiber rein-forced cementitious composites is complex and stronglyinfluenced by the type and amount of fiber used as wellas the properties of matrix [7,8]. Inverse analysis basedmethod has been developed in recent years [9–11]. In thepresent paper, an inverse analysis based procedure devel-oped by Zhang et al. [12] to determine the stress–crackwidth relationship from three-point bending test onnotched beam are used for the determination of thestress–crack width relation of ECC and concrete. There-fore, three-point bending tests on notched beams of con-crete and ECC were carried out first. Fig. 1(a) shows thethree-point bending test configuration and the experimen-tal setup. The dimensions of specimen used in the test areshown in Fig. 1(b). The CMOD, d was measured by anextensometer of gauge length 8 mm mounted across the10 mm deep and 4 mm wide pre-notched crack. The bend-ing test was conducted at a displacement rate of 0.05 mm/min on an MTS machine. The complete load and CMODrelationship was obtained and then was used to derivethe stress–crack opening law of the material. The mix pro-portion of concrete and ECC used for notched beams,

to MTS machineextensometer for measuring δ

specimen

300mm

400mm

100mm

10mm

4mm

100mm

a

b

Fig. 1. (a) Three-point bending configuration and (b) specimen geometry dimensions.

J. Zhang et al. / Composites Science and Technology 66 (2006) 1501–1512 1503

which is the same with that used in the layered beams testedin the present investigation, is shown in Table 2.

For convenience of numerical calculation, a multiple lin-ear function is used to simulate the stress–crack width rela-tionship, i.e.

rn ¼ knwþ r0n for wn�1 6 w 6 wn ðn ¼ 1; 2; . . . nmaxÞ.ð1Þ

where kn is the slope for w 2 [wn�1,wn]. r01 = rfc, r0n ¼Pn�11 ½ðki � kiþ1Þwi� þ rfc. Usually, 4–5 linear portions are

sufficient to reflect the complete characteristics of thestress–crack width relationship of concrete and ECC. Toobtain the stress–crack width relationship, several parame-ters should be determined, they include: cracking strength,rfc; slope of each linear portion, kn. Cracking strength, rfc,defined as the stress level at which initial crack starts topropagate, is determined directly from the results ofthree-point bending tests on pre-notched beams. Accordingto the elastic theory, for a given initial crack, the CMOD(d) and external load (P) obeys a linear relationship beforethe initiation of cracking. After initial cracking, the linearrelationship between P and d do not exit any longer. Thus

Table 2Mix proportion of notched beam

Constituentcomposition(by weight)

Cementa Water Sand Stone PVAb

Plain concrete 1 0.55 2 2 –ECC 1 0.32 0.4 – 1.7%

a Cement: ordinary Portland.b Cement PVA: polyvinyl alcohol fiber (by volume).

the cracking load, Pfc can be determined by the point wherethe P–d curve deviates from the initial linear portion. Thispoint is regarded as the transition point from the linear-elastic stage to the non-linear-elastic stage, in which a ficti-tious crack starts to develop. Typical graphs illustrating thedetermination of cracking load from three-point bendingtest result on notched specimen for concrete and ECC,respectively, are shown in Fig. 2(a) and (b). Based on thePfc value, the corresponded cracking strength, rfc is calcu-lated using a finite element program by which the effect ofinitial notch on rfc can be taken into account. The slope ofeach linear portion of the stress–crack width relation, kn isdetermined based on the fitting of finite element results tothe results of three-point bending tests. More details ofthe parameter extraction procedures can be found in thereference [12].

Based on the three-point bending test results and theinverse analysis algorithm briefly described above, thebridging stress–crack width relationship of concrete andECC was determined separately and the results are shownin Fig. 3, where three and four linear portions wereadopted for concrete and ECC, respectively. The valuesof rfc, kn and r0n of each linear portion of the two materialsare list in Table 3.

2.2. Derivation of semi-analytical model

A beam composed of a single material rather than layersis considered first. A short segment of the beam with breathb and depth h is subjected to a bending moment M. It isassumed that the beam behaves elastically until the princi-pal tensile stress reaches the cracking strength of the mate-

0.00 0.01 0.02 0.03 0.04 0.05

CMOD (mm)

0

2000

4000

6000

8000

Load

(N

)Lo

ad (

N)

Pfc

0.00 0.05 0.10 0.15 0.20 0.25 0.30CMOD (mm)

0

2000

4000

6000

8000

( daoLN

)

( daoLN

)

0.00 0.01 0.02 0.03 0.04 0.05

CMOD (mm)

0

2000

4000

6000

8000

10000

Pfc

0.00 0.50 1.00 1.50 2.00 2.50 3.00CMOD (mm)

0

2000

4000

6000

8000

10000

12000

(b)

(a)

Fig. 2. Determination of cracking load from notched specimen, (a)concrete and (b) ECC.

0.00 0.20 0.40 0.60 0.80 1.00

Crack width (mm)

0.00

1.00

2.00

3.00

4.00

Str

ess

(MP

a)

Stress-Crack Opening Relationship

Plain Concrete

ECC

Fig. 3. Determined stress–crack width relationship of ECC and concrete.


rial. After that, a single crack is formed. The moment lead-ing to the opening of the first crack is referred to as the firstcracking moment, Mfc and the corresponding load is called

the first cracking load, Pfc. Thus the failure process of thebeam can be divided into two stages: the linear-elastic stageup to first cracking and the fictitious crack developingstage. The assumed stress distribution in the second stageis shown in Fig. 4.

In the first stage, according to classical elastic theory,the Mfc can be calculated by

M fc ¼bh2

6rfc; ð2Þ

where rfc is the cracking strength of the material. In thesecond stage, the crack is opened and the length of thecrack is assumed to be ah, a 2 [0,1] and the crack mouthopening is assumed to be d. Assuming the crack profileto be linear, the crack width w at a distance x from the bot-tom of the beam can be calculated as:

w ¼ d 1� xah

� �. ð3Þ

The stress profile within the uncracked portion of the beamis assumed to be linear and hence the stresses at any loca-tion x from the bottom of the section can be related to ah,bh and d by

rIIðxÞ ¼ rfc 1� x� ahbh� ah

� �; ð4Þ

where bh is the depth of the tensile zone, b 2 [0,1]. For thecracked portion, stress at any location x can be obtained bycalculating the crack width w corresponding to the locationx and then the associated bridging stress is obtained fromthe stress–crack width (r–w) relationship, i.e.

rIðxÞ ¼ rðwÞ ¼ r d 1� xah

� �� . ð5Þ

Stresses obtained above should satisfy equilibrium condi-tions, force equilibrium and moment equilibrium, i.e.Z ah

0

rIðxÞbdxþZ h

ahrIIðxÞbdx ¼ 0; ð6Þ

Z ah

0

rIðxÞðh� xÞbdxþZ h

ahrIIðxÞðh� xÞb dx ¼ M ; ð7Þ

where M is the external moment applied on the beamsection.

A given external bending moment M should be associ-ated with a particular pair of values of d and ah. Hence,there are three unknowns M, d and ah that should besolved. The two equilibrium equations above are notenough for obtaining the solution. Additional informationis required for the calculation. According to the principle ofsuperposition [13], the d under bending load can be decom-posed as

d ¼ dM þ drIðxÞ; ð8Þ

where dM and drI(x) are the crack mouth opening compo-nent caused by external moment M and bridging stressI(x), respectively. On further decomposing drI(x) into twocomponents:

h ecc

ECC

concrete

hhh

ECC

concrete

hhhh

b

a

xx

(concrete)

(concrete)

(concrete)

Fig. 5. Cracked beam section and the normal stress distribution (layeredbeam).

Table 3Parameters of stress–crack width relationship of ECC and concrete

Parameters ECC Concrete

E 23 GPa 25 GParfc 3.8 MPa 3.7 MPa

r–w relationship Four linear portions: (ECC) Three linear portions: (concrete)

w (mm) kn (MPa/mm) r0n (MPa) w (mm) kn (MPa/mm) r0n (Mpa)

Portion 1 0–0.0022 �456 3.8 0–0.0052 �296.9 3.7Portion 2 0.0022–0.045 �34.2 2.872 0.0052–0.0472 �36.0 1.969Portion 3 0.045–0.12 22.04 0.341 0.0472–0.195a �4.3 0.441Portion 4 0.12–0.745a �4.75 3.556 – – –

a The maximum crack opening at which the crack surface traction reduces to zero is 0.745 mm and 0.195 mm, respectively, for ECC and concrete.

σ

σ

h

βh

αh

δ

ω

αh

X

Fig. 4. Cracked beam section and the normal stress distribution (singlematerial beam).


drIðxÞ ¼ dM 0 þ dr0 ; ð9Þ

where dM 0 and dr0 are the crack mouth opening displace-ments obtained from a cracked beam subjected to a bend-ing moment M 0 and an uniform axial stress r 0, respectively.M 0 and r 0 are equivalent effects of the bridging stress whichare given by

M 0 ¼Z ah

0

brIðxÞh2� x

� �dx; ð10Þ

r0 ¼ 1

h

Z ah

0

rIðxÞdx. ð11Þ

The total d then comprises three parts

d ¼ dM þ dM 0 þ dr0 ð12Þ

Applying the results of Tada et al. [14], the total d can beexpressed by

d ¼ 24abhE½MV 1ðaÞ �M 0V 2ðaÞ� �

4r0ahE

V 3ðaÞ; ð13Þ

where

V 1ðaÞ ¼ 0:33� 1:42aþ 3:87a2 � 2:04a3 þ 0:66

ð1� aÞ2;

V 2ðaÞ ¼ 0:8� 1:7aþ 2:4a2 þ 0:66

ð1� aÞ2;

V 3ðaÞ ¼1:46þ 3:42ð1� cos pa

2Þ

cos pa2

� �2.

It should be pointed out that V1(a) as expressed in theequation has been slightly changed based on the finite ele-ment results [6].

The determination of external moment and CMOD fora given crack length is performed according to the follow-ing algorithm. For a given crack length, ah, the appropri-ate combination of M, CMOD (d) are determinedthrough an iteration process. Firstly, a crack mouth open-ing displacement d 0 was assumed. Secondly, based on theassumed d 0, Eqs. (6), (7), (10) and (11) are applied to cal-culate M, M 0 and r 0. Thirdly, the updated crack mouthopening displacement, d, is calculated by substituting theM, M 0 and r 0 as obtained in the previous step into Eq.(13). The updated crack mouth opening displacement, dis then compared with the assumed d 0. If the differencebetween the two values (d and d 0) is larger than a pre-scribed tolerance, the whole iteration process should berepeated by assuming a new crack mouth opening dis-placement as the arithmetic mean of d 0 and d. If the


difference is smaller than the tolerance, the correct combi-nation of ah, M and d is obtained. Then, the crack lengthcan be increased slightly to obtain another set of M andd. The calculation is repeated until the crack lengthreaches the prescribed end value.

The model developed above is based on the assumptionthat the beam is composed of a single material. The samealgorithm as presented in the previous section can beapplied to the analysis of flexural behavior of layered com-posite beam, with the following considerations in mind:

(1) Layered ECC beam is composed of two types ofmaterials, concrete and ECC. Depending on the spe-cific location x along the crack, the stress–crack widthrelationship of either ECC or concrete should beapplied. If the point is within the ECC layer, thestress–crack width relation of ECC should be used.Otherwise, that of concrete should be used.

(2) The cracking strength will be specified as the crackingstrength of ECC or concrete according to the locationof the crack tip.

Fig. 6. Four-point ben

(3) The profile of the crack in this modified algorithm isstill assumed to be linear. The assumed stress distri-bution in the cracked layered beam is shown in Fig. 5.

(4) Since the difference in Young’s modulus of the ECCand concrete is very limited, the difference is neglectedin the numerical calculation. In other words, the sameweight functions given under Eq. (13) can beemployed.

An algorithm with the above considerations would beapplied in the layered beam analysis. For a given cracklength, ah, the appropriate combination of externalmoment, M and CMOD, d are determined through aniteration process. Firstly, if the given crack length, ah issmaller than the thickness of ECC layer, hECC, only thestress–crack width relationship of ECC is used in thecracked part. If the given crack length is larger than hECC,both the stress–crack width relationships of ECC andconcrete are used in the cracked part separately accordingto the location along the crack. Secondly, a crack mouthopening displacement d 0 is assumed. Thirdly, based on the

ding configuration.

0.00 0.40 0.80 1.20 1.60 2.00

Deflection (mm)

0.00

2.00

4.00

6.00

8.00

50mm Layered Beam

Concrete Beam

0.00 0.40 0.80 1.20 1.60 2.00

Deflection (mm)

0.00

2.00

4.00

6.00

8.00

Fle

xura

l str

ess

(MP

a)F

lexu

ral s

tres

s (M

Pa)

ECC Beam

25mm Layered Beam

(a)

(b)

Fig. 7. Flexural stress versus deflection diagrams of layered ECC-concretebeams under four-point bending load, (a) plain concrete and 50 mm ECClayered beams and (b) 25 mm ECC layered and whole ECC beams.


assumed d 0, Eqs. (6), (7), (10) and (11) are applied to cal-culate M, M 0 and r 0. Note that in this step, if the given ah

is smaller than hECC, M, M 0 and r 0 are calculated withrII(concrete), rII(ECC) and rI(ECC) as illustrated in Fig. 5(a).If the given ah is greater than hECC, M, M 0 and r 0 are cal-culated with rII(concrete), rI(concrete) and rI(ECC), as shownin Fig. 5(b). Fourthly, the updated crack mouth openingdisplacement, d is calculated by substituting the M, M 0

and r 0 as obtained in the previous step into Eq. (13). Iter-ation stops for the current crack size when d and d 0 arewithin the prescribed tolerance. One can then move onto the next crack length.

3. Experimental results, model predictions and verification

3.1. Experimental study on flexural performance of layered

ECC-concrete beam

To investigate the flexural performance of layered ECC-concrete composite beams and to verify the model predic-tions, four-point bending tests were carried out on layeredECC-concrete beams with different ECC thickness. In eachbatch, six specimens with dimensions 100 · 100 · 500 mmwere cast. Among the specimens, three of them were testedunder static flexural load, another three were tested underfatigue flexural load. The work regarding the fatigue behav-ior of ECC layered beams will be described in a separatepaper. The mix proportions of concrete and ECC werethe same as those used in the notched beam test which arelist in Table 2. Two different ECC layer thickness, 25 mmand 50 mm were used in the layered beams. During thepreparation of the beams, the ECC layer was cast first.Twenty-four hours after casting the ECC layer, the concretelayer was cast. The reason for not casting concrete immedi-ately after casting ECC material was to prevent the mixingof aggregates (from concrete) with ECC. In the mean timeof casting the layered beams, plain concrete and wholeECC beams were also cast as references. For concrete andECC, three 100 · 300 mm cylinders for compressivestrength test were also prepared. The specimens, bothbeams and cylinders, were vibrated to ensure proper com-paction. All specimens were left covered in their mold for24 h, before they were demolded and cured at 20 �C and98% relative humidity condition until testing. Displacementcontrol, at a rate of 0.15 mm/min, was used in the four-point bending test. The experimental setup is shown inFig. 6. Both the loading and the mid-point deflection wererecorded during test. Mid-point deflection was measuredwith two linear variable differential transducers (LVDT)that sat on the base part of the bending test fixture.

Typical bending test results are displayed in Fig. 7 interm of load–deflection diagrams for different kinds ofbeams. The compressive strengths of the materials usedin each batch are shown in Table 4.

Based on the bending test results, Table 5 shows a com-parison made on the flexural strength of the beams. Theaverage flexural strength of concrete beam is 4.4 MPa.

With the addition of a layer of ECC, the average flexuralstrength has increased to 5.2 MPa for 25 mm layeredECC beam and 6.3 MPa for 50 mm layered ECC beam.The percentage strength improvement with the additionof a layer of ECC as compared to that of plain concreteis 18.2% for 25 mm layered ECC beam and 43.2% for50 mm layered ECC beam. Based on the results, one canconclude that the addition of ECC layer can improve theflexural strength of the beam. Based on the results, onecan see that the addition of ECC layer can improve theflexural strength of the beam. This is consistent with theresults obtained by other researchers [3,5].

In addition to the flexural strength improvement, theaddition of ECC layer can also result in significant ductilityimprovement. A comparison on the deflection reached atultimate load for different types of beam specimens isshown in Table 6. As indicated in Table 6, the averagedeflection value at ultimate load for plain concrete beamwas 0.11 mm. With the addition of a 25 mm layer of

Table 4Compressive strengths of plain concrete and ECC used in layered beams

Type of specimen Material Curingdays

Average compressivestrength (MPa)

Static concrete 1,(CON_1)

Concrete 56 54.8


Concrete 56 54.7


Concrete 56 59.6

Static layered 25 mm 1,(LAY_ECC_25_1)

ECC 114 66.2Concrete 114 52.8


ECC 112 71.9Concrete 112 59.2


ECC 56 62.4Concrete 56 44.2


ECC 112 67.3Concrete 112 55.5





Table 5Flexural strength comparison of different types of beam

Type of specimen Flexuralstrength(MPa)

Averageflexuralstrengthfor eachbatch(MPa)

Averagevalue foreach typeof specimen(MPa)

Percentageincreasecomparedto concrete(%)

(1) (2) (3)

CON_1 4.4 4.4 4.8 4.5 4.4 0CON_2 4.7 4.0 3.7 4.1CON_3 4.5 5.0 4.5 4.7LAY_ECC_25_1 5.5 5.6 5 5.4 5.2 18.2LAY_ECC_25_2 5.3 5.5 6 5.6LAY_ECC_25_3 5 4.5 4.7 4.7LAY_ECC_50_1 6 6.6 8.9 7.1 6.3 43.2LAY_ECC_50_2 5.9 7.4 6.4 6.6LAY_ECC_50_3 5.2 6.5 4.5 5.4ECC_100 7.5 6.6 – 7.1 7.3 65.9ECC_100 7.2 7.6 – 7.4

Table 6A comparison on the deflection at peak load for different types of beam

Type of specimen Deflection at ultimate load(mm)

Averagethe deflec

(1) (2) (3)

CON_1 0.11 0.12 0.12 0.12CON_2 0.08 0.09 0.13 0.10CON_3 0.11 0.13 0.1 0.11

LAY_ECC_25_1 0.17 0.17 0.26 0.20LAY_ECC_25_2 0.12 0.11 0.15 0.13LAY_ECC_25_3 0.12 0.30 – 0.21

LAY_ECC_50_1 0.31 0.36 0.44 0.37LAY_ECC_50_2 0.28 0.40 0.29 0.32LAY_ECC_50_3 0.41 0.30 0.22 0.31

ECC_100 0.35 0.55 – 0.45


ECC, this value increased to an average value of 0.18 mm,with a 64% increase as compared to that of plain concrete.Furthermore, the addition of a 50 mm layer of ECCbrought this value up to an average value of about0.33 mm, with a 200% increase as compared to that of plainconcrete. This increase was due to the effect of fiber bridg-ing across the lower portion (within ECC) of the crack andhence delaying the opening of the upper portion of thecrack (within plain concrete). Hence, the brittle failuremode of plain concrete was prevented. In addition, fromthe results we can see that the ductility improvement ismuch more significant as the ECC layer thickness reaches50 mm in comparison to the case with 25 mm ECC layer(from 64% to 200% improvement over the plain concretebeam). Note that both the strength and ductility improve-ments can be well be explained by the model calculation.More detailed discussions can be found in the next section.

3.2. Model predictions on flexural performance of layer

ECC-concrete beam

Using the obtained stress–crack width relationship andother required parameters in Table 3 as model input, theflexural performance of layered ECC-concrete compositebeam is analyzed with the developed model. In the model-ing, three different beam height, 100, 200 and 300 mm, areassumed which are typical depths normally used in flexuralmembers, such as concrete slabs and beams. The theoreti-cal calculation results regarding the bending behavior ofECC layered beams with different ECC layer thicknessare shown in Figs. 8–11. Plotted in Figs. 8 and 9 are theflexural stress versus crack length and flexural stress versusCMOD diagrams for different thickness of ECC layer used,where the thickness of ECC layer is expressed as the ratiobetween the ECC layer and the whole beam depth. InFig. 10, the flexural strength of the beam is plotted as afunction of the ratio of the thickness of ECC layer andthe total beam depth. Fig. 11 shows the effect of ECC layeron the critical crack length and critical CMOD, defined asthe crack length or CMOD when flexural strength is

value oftion (mm)

Average value foreach type ofspecimen (mm)

Percentage increasecompared to concrete (%)

0.11 0

0.18 64

0.33 200

0.45 309

0 20 40 60 80

Crack length (mm)

0.00

2.00

4.00

6.00

8.00

ECC Layer Ratio0, 0.05, 0.1, 0.15, 0.2, 0.25, 0.3, 0.4, 0.5, 0.6, 0.75, 1

H =100mm

100

0.00 50.00 100.00 150.00 200.00

Crack length (mm)

0.00

2.00

4.00

6.00

8.00

Fle

xura

l str

ess

(MP

a)

Fle

xura

l str

ess

(MP

a)

Fle

xura

l str

ess

(MP

a)

ECC Layer Ratio0, 0.05, 0.1, 0.15, 0.2, 0.25, 0.3, 0.4, 0.5, 0.6, 0.75, 1

H = 200mm

0 50 100 150 200 250 300

Crack length (mm)

0.00

2.00

4.00

6.00

8.00

ECC Layer Ratio:0, 0.05, 0.1, 0.15, 0.2, 0.25, 0.3, 0.4, 0.5, 0.6, 0.75, 1

H=300mm

a

b c

Fig. 8. Flexural stress versus crack length curves of layered beam with different thickness of the ECC layer, (a) H = 100 mm, (b) H = 200 mm and (c)H = 300 mm.


reached, in which the influence of beam height is alsodisplayed.

On inspecting the model results shown in Figs. 8–11,several features of the layered ECC-concrete beam underbending load can be distinguished. First we can see thatwith increase of the thickness of ECC layer, the flexuralstrength of the composite beam increases non-linearly. Byapplying the ECC layer at the bottom of the beam, themaximum flexural strength improvement as compared tothat of plain concrete can be up to 60% (see Fig. 10). A sim-ilar trend of the strength improvement is found in beams ofdifferent depths. As the ECC layer thickness is expressed asa ratio of ECC thickness to total beam depth, the generaltrend of flexural strength improvement with the thicknessof ECC layer takes the characteristic form of three distinctperiods as pictured in Fig. 10, period I with slow rate ofincrease in strength, period II showing much fasterincrease, and finally a period III showing slow increaseagain. Using the case of H = 100 mm as example, periodI corresponds to hECC = 0 to 0.28H (strength improve-ment: 0–10%), period II ranges from hECC = 0.28 to 0.6H(strength improvement: 10–55%) while period III is fromhECC = 0.6 to 1.0H (strength improvement: 55–60%). Thereis some influence of the beam depth on the transition from

period I to period II. The deeper the beam, the lower thetransition boundary. For example, the transition boundaryof period I changes from 0.28H to 0.22H as the beam depthchanges from 100 to 300 mm. Certainly, the absolute ECClayer thickness at this transition point increases with thebeam height. In contrast, the beam depth has very littleinfluence on the transition boundary between period IIand period III, if the ECC thickness/beam depth ratio isconsidered. In addition, a certain effect of beam depth onthe flexural strength can still be observed in the ECC-con-crete layered beam. One can hence say that the layeredbeams exhibit a mild size effect.

Second, by applying ECC layer, the critical CMOD andcrack length are greatly increased comparing to plain con-crete beam, see Fig. 11. This important effect will signifi-cantly improve the ductility of the beam. Furthermore,the theoretical calculations provide one very interestingfinding. From Fig. 11, with gradual increase of the ECClayer thickness, there is a critical point beyond which boththe CMOD and critical crack length becomes much higher.For the beams with 100–300 mm height, the point of jumpcorresponds to ECC thickness around 22–28% of the beamdepth. The ’jump’ value corresponds well with the transi-tion point between flexural strength improvement periods

0.00 0.20 0.40 0.60 0.80 1.00

CMOD (mm)

0.00

2.00

4.00

6.00

8.00

Fl

ts laruxesser

)aP

M(

ECC Layer Ratio1, 0.75, 0.6, 0.5, 0.4, 0.3, 0.25, 0.2, 0.15, 0.1, 0.05, 0

H=100mm

0.00 0.20 0.40 0.60 0.80 1.00

CMOD (mm)

0.00

2.00

4.00

6.00

8.00

elF

xru

ts lare

ss)a

PM(

ECC Layer Ratio:1, 0.75, 0.6, 0.5, 0.4, 0.3, 0.25. 0.2, 0.15, 0.1, 0.05, 0

H=300mm

0.00 0.20 0.40 0.60 0.80 1.00

CMOD (mm)

0.00

2.00

4.00

6.00

8.00

Fl

uxera

lerts

ss(M

aP

)

ECC Layer Ratio1, 0.75, 0.6, 0.5, 0.4, 0.3, 0.25, 0.2, 0.15, 0.1, 0.05, 0

H= 200mm

(a)

(b) (c)

Fig. 9. Flexural stress versus CMOD curves of layered beam with different thickness of the ECC layer, (a) H = 100 mm, (b) H = 200 mm and (c)H = 300 mm.

0.00 0.20 0.40 0.60 0.80 1.00

Ratio of ECC layer

0.00

2.00

4.00

6.00

8.00

Fle

xura

lM

Pa)

(htgnerts

1.00

1.20

1.40

1.60

1.80

2.00

oN

rmilaz

elfde

xur

lats r

neg

ht

H = 300 mm

H = 200 mm

H =100 mm

Fig. 10. Effect of ECC layer on flexural strength, three beam height casesshown together.


I and II, that is discussed above. Therefore, as long as thethickness of ECC layer goes beyond the period I/II transi-tion point, the ductility of the composite beam will improvesignificantly. The above finding can be well explained by

the flexural stress versus crack length or CMOD diagramsof the layered composite beam with different ECC layerthickness. By looking at the diagrams mentioned above(Figs. 8 and 9), one can easily discover that there are twopeaks on each curve. This double peak behavior is mainlydue to the characteristics of the stress–crack width relation-ship of the material. With increase of the ECC layer thick-ness, the stress value at the second peak increases andgradually exceeds that at the first peak. Then, the flexuralstrength is governed by the second peak rather than thefirst. The CMOD and crack length are much larger orlonger at the second peak than those at the first peak. Thisstrength transition happens just at the point where thetransition between period I and II occurs, or in otherwords, at the point where the critical crack length or criti-cal CMOD exhibit the jump. Physically, this ultimate peakload transition means that the flexural strength of the beamis gradually changed from aggregate bridging governed(first peak) to fiber bridging governed (second peak). Thisshould be the reason why there is a jump on the criticalCMOD or critical crack length with ECC layer thickness,as displayed in Fig. 11, which leads to the significant

0.00 0.20 0.40 0.60 0.80 1.00Ratio of ECC layer

0.00

50.00

100.00

150.00

200.00

250.00

300.00

Crti

c lacira

nel kcgt

hm(

)m

H=100 mm

H=200 mm

H=300 mm

0.00 0.20 0.40 0.60 0.80 1.00

Ratio of ECC layer

0.00

0.10

0.20

0.30

0.40

irC

tlaci

mm(

DO

MC

)

H=100 mm

H=200 mm

H=300 mm

(a)

(b)

Fig. 11. Effect of ECC layer on the critical crack length (a) and criticalCMOD (b) of beam under bending load.

0.00 0.20 0.40 0.60 0.80 1.00

Ratio of ECC layer

0.00

2.00

4.00

6.00

8.00

Fl

PM( htgnerts laruxe

a)

Model Prediction

Test Results

Fig. 12. Comparison between model predicted flexural strength andexperimental results of ECC layered beam.

0.00 0.20 0.40 0.60 0.80 1.00

Ratio of ECC Layer

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

)m

m( daol etamitlu ta noit ce lfe

D

Test Data

Linear Fit

Fig. 13. Effect of ECC layer on ductility of beam under bending load.


improved ductility of the beam. Therefore, we may con-clude that for the purpose of strength and ductilityimprovement, the minimum thickness of the ECC layermust be over 22%, 24% and 28% of the beam depth forthe beam with height 300, 200 and 100 mm, respectively.It is important to note that the flexural strength and ductil-ity enhancement of the ECC layered beam is governed bythe bridging law of both plain concrete and ECC materials.For different mix of concrete and ECC, the actual efficiencyof strength and ductility improvement, as well as the min-imum ECC thickness for significant performance enhance-ment are not the same. However, the approach developedin this paper can still be used to analyze the performanceimprovement and identify the minimum required ECClayer thickness.

3.3. Comparison of the experimental results with model

predictions

A critical test for the validity of the proposed model forlayered ECC-concrete composite beam is to compare the

model predictions with experimental results. Particularemphasis is placed on the comparisons of flexural strengthand ductility. The comparison between model predictedflexural strength of layered beams with different thicknessof ECC layer and the experimental results from four-pointbending tests are shown in Fig. 12. The graph shows thatthe model and experimental results agree very well witheach other. In addition to the prediction of increased flex-ural strength with layer thickness, the model also showsthat there is a sudden increase in CMOD or critical cracklength after the ECC thickness goes beyond a certain tran-sition value. Since the CMOD and crack length were notmeasured in our experiment, the theoretical trend can onlybe indirectly verified in a qualitative manner by consideringthe beam deflection at ultimate load, which should be pro-portional to the CMOD and critical crack length. FromTable 6, we can see that the average deflection at ultimateload for plain concrete beam, beam with 25% ECC, beamwith 50% ECC and full ECC beam are 0.11, 0.18, 0.33


and 0.45 mm, respectively. The variation trend of deflec-tion at ultimate load with ECC layer thickness is displayedin Fig. 13. It is quite clear that the data can be fitted withtwo separate lines, with the deflection jump occurringbetween 25% and 50% of beam depth. For the 100 mmdeep beam used in our tests, the theoretical jump positionis at 28% of the beam depth, and that is shown in the figurewith dashed line. Qualitatively, the test results indicate thatthere is a certain ECC layer thickness beyond which theductility can be significantly improved, and this serves asa qualitative verification of the trend predicted by the the-oretical model.

4. Conclusion

In this paper, a combined theoretical/experimentalinvestigation on the bending behavior of layered ECC-con-crete composite beam is carried out. A semi-analyticalapproach for modeling the flexure performance of layeredECC-concrete composite beams is proposed. In the model,the stress–crack width relation of concrete and ECC mate-rials are employed as the fundamental constitutive relation-ship in tension. With the model, the complete flexuralbehavior of the layered beam, such as load–CMOD andload–crack length responses, can be obtained. The modelresults show that flexural strength of the layered beamincreases non-linearly with ECC layer. The variation offlexural strength improvement with the ECC thicknesscan be divided into three periods: period I showing slowrate of strength increase, period II showing much fasterincrease, and finally a period III showing slow increaseagain. At the ECC thickness corresponding to the transi-tion between period I and period II, the member ductility,reflected by the CMOD and crack length as the flexuralstrength is reached, is also found to show a very rapidincrease. Therefore, in the design of ECC/concrete layeredbeams, the ECC thickness should be beyond the criticalvalue given by the period I/II transition for significantimprovements in flexural strength and ductility to beachieved. The flexural performance of layered ECC-con-crete beams was also investigated experimentally by four-point bending test. The experimental results show thatthe application of a layer of ECC on the tensile side of aflexural beam increases its flexural strength and the degreeof improvement increases with the thickness of ECCapplied. The test results are compared to the model interms of both flexural strength and ductility improvements,and good agreement is found.

It should be pointed out that the critical ECC thicknessfor significant performance improvement is dependent onthe stress–crack relation of concrete and ECC materials,as well as the member size. The present investigation pro-vides a general theoretical approach for this importantparameter to be determined.

Acknowledgment

Financial support of the work by the Hong Kong Re-search Grant Council, under CERG UST6138/04E, isgratefully acknowledged.

References

[1] Perumalsamy NB, Surendra PS. Fiber-reinforced cement composites.New York: McGraw-Hill; 1992.

[2] Li VC. Engineered cementitious composites-tailored compositesthrough micromechanical modeling. In: Banthia N, Bentur A, MuftiA, editors. Fiber reinforced concrete: present and the future.Montreal: Canadian Society for Civil Engineering; 1998. p. 64–97.

[3] Zhang J, Li VC. Monotonic and fatigue performance of engineeredfiber reinforced cementitious composite in overlay system. CementConcrete Res 2002;32(3):415–23.

[4] Cheung YN. Investigation of concrete components with a pseudo-ductile layer. MPh thesis, Hong Kong University of Science andTechnology, 2004.

[5] Maalej M, Li VC. Introduction of strain hardening engineeredcementitious composites in the design of reinforced concrete flexuralmembers for improved durability. ACI Struct J 1995;92(2):167–76.

[6] Zhang J, Stang H. Applications of stress–crack width relationship inpredicting the flexural behavior of fiber-reinforced concrete. CementConcrete Res 1998;28(3):439–52.

[7] Li VC, Stang H, Krenchel H. Micromechanics of crack bridging infiber reinforced concrete. Mater Struct 1993;26:486–94.

[8] Li VC, Mishra DK, Wu HC. Matrix design for pseudo strain-hardening fiber reinforced cementitious composites. Mater Struct1995;28(183):586–95.

[9] Roelfstra PE, Wittmann FH. Numerical method to link strainsoftening with failure of concrete. In: Wittmann FH, editor. Fracturetoughness and fracture energy of concrete. Elsevier; 1986. p. 163–75.

[10] Uchida Y. Determination of tension softening diagrams of variouskinds of concrete by means of numerical analysis. In: Wittmann FH,editor. Fracture mechanics of concrete structures. Freiburg, Ger-many: Aedificatio; 1995. p. 17–30.

[11] Kurihara N, Kunieda M, Kamada T, Uchida Y, Rokugo K. Tensionsoftening diagrams and evaluation of properties of steel fiberreinforced concrete. Eng fract mech 2000;65(2–3):235–45.

[12] Zhang J, Liu Q. Determination of concrete fracture parameters froma three-point bending test. Tsinghua sci technol 2003;8(6):726–33.

[13] Maalej M, Li VC. Flexural strength of fiber cementitious composites.J Mater Civil Eng 1994;6(4):390–406.

[14] Tada H. The stress analysis of cracks handbook. Missouri: ParisProd. Inc.; 1985.

Documents

Flexural performance of layered ECC-concrete composite beam