Flexural performance of reinforced self-consolidating concrete beams containing hybrid fibers

Construction and Building Materials 174 (2018) 11–23

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Flexural performance of reinforced self-consolidating concrete beams containing hybrid fibers Cong Zhang a,b,⇑, Shicheng Han a, Yuan Hua a a b

School of Environment and Civil Engineering, Jiangnan University, Wuxi 214000, China Key Laboratory of Concrete and Pre-stressed Concrete Structure of Ministry of Education, Southeast University, Nanjing 210000, China

h i g h l i g h t s
Effects of hybrid fibers on flexural performance of SCC beams were investigated.
Macro PP fiber was employed in this study.
A new calculation model for predicting ultimate bearing capacity of SCC beams was proposed.

a r t i c l e

i n f o

Article history: Received 22 December 2017 Received in revised form 1 April 2018 Accepted 9 April 2018

Keywords: Hybrid fiber Self-consolidating concrete Flexural loading Ultimate bearing capacity Crack pattern Prediction model

a b s t r a c t Flexural performances of twelve reinforced self-consolidating concrete (SCC) beams containing steel fiber, macro polypropylene fiber, micro polypropylene fiber, and their combinations were studied at room temperature. The major test variables were fiber types, fiber contents and longitudinal reinforcement ratios. Cracking load, yielding load, ultimate load, mid-span deflection, longitudinal reinforcement strain and crack pattern of the reinforced SCC beams were investigated. It was found that the addition of mono steel fiber and hybrid fibers enhanced the ultimate bearing capacity but reduced the mid-span deflection of reinforced SCC beams. With the increase in fiber content, the longitudinal reinforcement strain, crack width and crack spacing decreased significantly. The hybrid use of steel fiber and micro polypropylene fiber did not have a further beneficial effect on the flexural performance of SCC beams at room temperature. Compared to micro polypropylene fiber, the macro polypropylene fiber displayed a more significant effect on the structural behavior of SCC beams. A calculation method for ultimate bearing capacity of flexural SCC beams at room temperature was proposed, which takes into consideration the effects of hybrid fibers. Comparisons were drawn between the predicted results of this proposed model and other previous models with experimental data in this study and previous literature. The results indicate that the proposed model can reasonably estimate the ultimate bearing capacity of SCC beams containing hybrid fibers subjected to flexural loading at room temperature. Ó 2018 Elsevier Ltd. All rights reserved.

1. Introduction The demands of the construction industry for stronger and more ductile concrete structures have been successfully met by the use of high-strength concrete and dense steel reinforcement. However, more fluid fresh concrete mixture is needed for the highly congested reinforced concrete elements to improve their constructability. Self-consolidating concrete (SCC), a flowing concrete which gives a slump value of over 200 mm and a slumpflow value of more than 600 mm, has been developed in recent ⇑ Corresponding author at: School of Environment and Civil Engineering, Jiangnan University, Wuxi 214000, China. E-mail address: [email protected] (C. Zhang). https://doi.org/10.1016/j.conbuildmat.2018.04.075 0950-0618/Ó 2018 Elsevier Ltd. All rights reserved.

years as a possible solution as it is highly cohesive and can be placed and compacted without external vibration [1–5]. Although SCC has excellent workability, it is still a brittle material with poor tensile performance. The use of randomly distributed short and discrete fibers is one of the most effective ways to improve the tensile properties and cracking behaviors of SCC. There are a variety of commercialized fibers used in SCC (steel fiber, synthetic fiber, etc.) and their feasibility has been clearly documented [6–11]. Usually, steel fibers are used for structural purpose and synthetic fibers (e.g. micro polypropylene fiber) are employed for non-structural applications (shrinkage resistance, fire resistance, etc.). It is recognized that fire usually poses serious damage to concrete structures. Spalling of concrete during fire exposure will further aggravate these damages, especially for high strength concrete

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C. Zhang et al. / Construction and Building Materials 174 (2018) 11–23

Nomenclature

qs qsv SF PPF Pcr Py,b Pu,b du,b

rf a Vf V f ;st V f ;sy f1 f2 r f

sf sf ;st sf ;sy

x df F be F be;st

longitudinal reinforcement ratio stirrup reinforcement ratio steel fiber polypropylene fiber cracking load yielding load ultimate load deflection of simply supported beam at ultimate load tensile stress of fibers fraction ratio of fibers which currently bridging the crack volume fraction of fibers volume fraction of steel fiber volume fraction of macro PP fiber coefficient of friction between fiber and concrete matrix sheared over crack flexural characteristics coefficient average fiber stress for the load-carrying fibers interfacial shear stress between fiber and concrete interfacial shear stress between steel fiber and concrete interfacial shear stress between macro PP fiber and concrete average shear length of fibers bridging over crack diameter of fiber fiber characteristics coefficient characteristics coefficient of steel fiber

(HSC) and SCC due to their high compactness and low permeability [12–15]. Previous studies have confirmed the efficient role of micro polypropylene fibers (micro PP fibers) in reducing the fire spalling risk of SCC [16–19]. However, the hybrid use of steel fibers and micro PP fibers in SCC structural elements exposed to fire is still limited. The hybrid concept of steel and micro PP fibers is that the steel fibers can enhance the structural behavior and the micro PP fibers can improve the fire resistance of SCC structures. In addition, macro PP fibers for structural application have been produced and widely applied in structural elements, especially for tunnel engineering, due to their excellent corrosion resistance [20– 24]. The macro PP fibers usually have a diameter of about 0.7 mm and a length of 45–60 mm. Previous studies demonstrate that the addition of macro PP fibers can significantly improve the mechanical performance of concrete elements. However, relevant research on SCC elements containing hybrid steel and macro PP fiber at both room temperature and high temperature needs further investigation. In this paper, the flexural performances of SCC beam and a series of reinforced SCC beams (with steel fibers, with steel and micro PP fibers, with steel and macro PP fibers, and with steel, micro and macro PP fibers) before exposure to fire, will be thoroughly studied. Relevant investigation of SCC flexural beams with or without fibers, after exposure to fire, will be discussed in the follow-up papers. 2. Experimental 2.1. Materials The raw materials used in this study were cement (PO 52.5R), fly ash, quartz sand (0–5 mm) and crushed stone (5–15 mm). Their basic properties are shown in Table 1. Mix proportion of SCC without fibers is listed in Table 2 [25]. The amount of superplasticizer (Sika, polycarboxylic acid type,

F be;sy Lf k kst ksy

x h c L0

ecr etu fc

e0 ecu

Es fy

es

As h0 x b h c Mpre Mexp

characteristics coefficient of macro PP fiber fiber length aspect ratio of fiber aspect ratio of steel fiber aspect ratio of macro PP fiber crack width depth of the beam cross section depth of neutral axis of reinforced concrete beam span of beam cracking strain of FRC ultimate tensile strain of FRC compressive strength of FRC compressive strain corresponding to compressive strength ultimate compressive strain elastic modulus of rebar yield strength of rebar ultimate tensile strain of longitudinal rebar steel reinforcement area effective height of beam cross section depth of rectangular compressive stress blocks width of the beam cross section depth of the beam cross section depth of neutral axis of reinforced concrete beam predicted moment measured moment

ASTM C494 type F, the highest water reduction is up to 30%) was 1.2 wt% of binder content. Fibers used in this study were steel fiber, micro polypropylene (PP) fiber, macro PP fiber and their combinations. Images and basic properties of different fibers employed in this paper are given in Fig. 1 and Table 3, respectively. Mechanical properties of steel reinforcement bars are shown in Table 4.

2.2. Design of specimen All SCC beams have the same dimensions, as illustrated in Fig. 2. The cross section dimensions of the beams are 150  150 mm2. Reinforcement ratios and fiber contents of the 12 different beams are presented in Table 5.

2.3. Loading program and measurement A displacement-controlled procedure was employed by using a hydraulic servo testing machine (maximum load capacity of 10,000 kN). In order to provide a pure flexural zone, a steel distribution girder having 350 mm spacing on the top face of the test beam was employed, as shown in Fig. 3. The flexural test consisted of two steps, namely a load controlled step and a displacement controlled step, as illustrated in Fig. 4. During the load controlled step, the load increment was 10 kN and the load rate was 0.1 kN/s. After every loading step, the strain of steel rebar and the concrete crack patterns were recorded. When the bottom longitudinal reinforcement bars yielded, the loading process was changed to displacement controlled stage. The displacement rate was kept at 0.5 mm/min until the beam failed. As illustrated in Fig. 3, three linear variable differential transducers (LVDTs) were employed to monitor the displacement of mid-span and loading points. Strain gauges were used to measure the strain of longitudinal reinforcement bars, as illustrated in Fig. 5.

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C. Zhang et al. / Construction and Building Materials 174 (2018) 11–23 Table 1 Properties of raw materials. Materials

Density (g/cm3)

Size

Mechanical property

Origin

3.2

45 lm sieve residue 14.16%

–

Dalian Onoda Cement Co. Ltd., China

2.65

Fineness modulus 2.51 Medium sand

Moh’s hardness 7

Dalian, China

2.6

45 lm sieve residue 9.2%

–

Dalian, China

Cement

Quartz sand

Fly ash

Table 2 Mix proportion of SCC without fibers/(kg/m3). Materials

Cement

Fly ash

Water

Sand 0–5 mm

Crushed stone 5–15 mm

Super plasticizer

W/B ratio

Content

400

160

180

764.8

832

6.72

0.32

Note: W/B is water to binder ratio (binder = cement + fly ash).

Fig. 1. Fibers used in this study (a) Steel fiber; (b) Macro PP fiber; (c) Micro PP fiber.

Table 3 Basic properties of different fibers used in this study. Materials

Density (g/cm3)

Geometric size

Tensile strength (N/mm2)

Quantity (pieces/kg)

Steel fiber Micro PP fiber Macro PP fiber

7.85 0.91 0.91

Hooked lf = 60 mm, df = 0.75 mm Straight lf = 9 mm, df = 18 lm Double duoform lf = 45 mm, df = 0.74 mm

1100 615 465

4600 3.5 billion 50,140

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C. Zhang et al. / Construction and Building Materials 174 (2018) 11–23

Table 4 Mechanical properties of steel reinforcement bars. Diameter/mm

Yield strength/MPa

Ultimate strength/MPa

Elongation/%

Elastic modulus/GPa

6.5 (stirrup) 8 (longitudinal) 10 (longitudinal)

278 491 475

320 651 643

21 13.5 8.5

210 200 200

(a) Reinforcement ratio of 0.56%

(b) Reinforcement ratio of 1.31% Fig. 2. Geometry and reinforcement arrangement of test beams.

Table 5 Reinforcement ratio and fiber content of simple supported beams. Beams

qs/%

qsv/%

SSB-1R SSB-2R SSB-3R SSB-4R SSB-5R SSB-6R SSB-7R SSB-8R SSB-9R

0.56 0.56 0.56 0.56 0.56 0.56 0.56 0.56 0.56

0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38 0.38

SSB-10R SSB-11R SSB-12R

1.31 1.31 1.31

0.76 (60 mm spacing) 0.76 (60 mm spacing) 0.76 (60 mm spacing)

(120 mm (120 mm (120 mm (120 mm (120 mm (120 mm (120 mm (120 mm (120 mm

spacing) spacing) spacing) spacing) spacing) spacing) spacing) spacing) spacing)

Micro PPF/(kg/m3)

SF/(kg/m3)

Macro PPF/(kg/m3)

fc/MPa

0 0 1 0 0.5 0 1 0 0.5

0 30 20 20 20 50 40 40 40

0 0 0 6 3 0 0 4 2

63.2 66.7 63.5 68.4 65.1 65.3 67.3 64.5 62.2

0 0 0

0 30 20

0 0 6

63.2 66.7 68.4

C. Zhang et al. / Construction and Building Materials 174 (2018) 11–23

Fig. 3. Loading and measuring arrangement of test beam.

15

pared to the beam without any fibers. These improvements are further enhanced by increasing the contents of steel fiber and macro PP fiber, but reduced with the increase in reinforcement ratio of the beams. The hybrid effect of steel fiber and macro PP fiber is the most obvious, followed by the combination of steel fiber and micro PP fiber, while the combination of the three fibers shows the lowest effect. This may be related to the poor dispersion of fibers. Moreover, it also shows that although the addition of micro PP fiber can improve the fire resistance of concrete, it cannot be employed to enhance the mechanical properties of reinforced beams. Compared to macro PP fiber and micro PP fiber, the steel fiber has a significant influence on the bearing capacity of reinforced beams. Table 6 presents the test data of deflection at ultimate load. It can be seen that the addition of fiber reduces the deflection of reinforced beams, which indicates that the deformation of reinforced beams is localized. Compared to mono steel fiber, the combination of steel fiber and macro PP fiber can further reduce the beam deflection. However, this reduction effect caused by fibers is weakened with the increase in reinforcement ratio.

3.2. Load-strain behavior of longitudinal reinforcement

Fig. 4. Diagram of imposed load control and displacement control flexural test.

3. Results and discussion 3.1. Load-deflection behavior Fig. 6 shows the load-deflection behavior of SCC beams subjected to flexural loading, followed by the comparison of cracking load, yielding load and ultimate load for each group. It can be seen that the introduction of fibers increases the cracking load, yielding load and ultimate load of reinforced beams com-

Longitudinal reinforcement strain of all the simply supported beams was recorded automatically during the entire testing procedure, as illustrated in Fig. 7. It can be observed that the addition of fibers did not have a significant effect on the longitudinal reinforcement strain before cracking of the beams. After cracking, the longitudinal reinforcement strain of beams with fibers was lower than that of beams without fibers at a given load level. This result indicates that the presence of fibers can reduce the stress of longitudinal reinforcement [26–29]. It can be seen from Fig. 7(a) and (b) that when the reinforcement ratio is 0.56%, the addition of 30 kg/m3 steel fiber (SSB-2R) has an obvious effect on reducing the longitudinal reinforcement strain. This effect is further increased when the steel fiber content is 50 kg/m3 (SSB-6R). The combined use of 20 kg/m3 steel fiber and 6 kg/m3 macro PP fiber (SSB-4R) has a more significant effect than that of SSB-2R. However, with the increase in steel fiber content, the hybrid effect of steel fiber and macro PP fiber becomes less obvious (comparing SSB-8R to SSB-6R). Although the addition of

(a) Strain gauges for longitudinal reinforcement bars having 0.56% reinforcement ratio

(b) Strain gauges for longitudinal reinforcement bars having 1.31% reinforcement ratio Fig. 5. Schematic diagram for the arrangement of strain measuring device.

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C. Zhang et al. / Construction and Building Materials 174 (2018) 11–23

Fig. 6. Load-deflection behavior of reinforced SCC beams with or without fibers subjected to flexural loading.

micro PP fiber (SSB-3R, SSB-5R, SSB-7R and SSB-9R) did not have a positive hybrid effect on increasing the load bearing capacity and reducing the longitudinal reinforcement strain of SCC beams, its potential effect on fire spalling resistance must be considered.

From Fig. 7(c), it can be observed that the effect of fibers on reducing the longitudinal reinforcement strain is negligible when the reinforcement ratio is 1.31%, similar to the hybrid effect of steel fiber and macro PP fiber.

C. Zhang et al. / Construction and Building Materials 174 (2018) 11–23 Table 6 Cracking load, yielding load, ultimate load and the corresponding deflection. Beams

Cracking load Pcr/kN

Yielding load Py,b/kN

Ultimate load Pu,b/kN

Deflection at ultimate load du,b/mm

SSB-1R SSB-2R SSB-3R SSB-4R SSB-5R SSB-6R SSB-7R SSB-8R SSB-9R SSB-10R SSB-11R SSB-12R

10 13 12 13 11 15 14 16 14 17 18 19

45 53 50 52 47 58 57 65 53 101 107 108

55.0 63.2 61.5 67.0 60.4 71.0 66.3 73.1 64.3 126.3 131.4 140.3

20.3 9.7 14.9 12.6 15.7 8.2 7.1 7.7 10.9 34.2 21.5 25.6

3.3. Crack patterns Fig. 8 shows the crack patterns of the tested beams after unloading. It can be seen that the cracks become smaller, narrower, closer and more diffused due to the inclusion of fibers. Steel fibers have a more significant effect on the distribution of cracks than PP fibers. Higher content of steel fiber has a more significant effect.

17

The hybrid effect of steel fiber and macro PP fiber on cracking behavior is not obvious. Also, the addition of micro PP fiber does not have a positive effect on the crack control ability of tested beams, and even causes degradation in some cases. It should be noted that only one large crack was usually found after the yield of steel rebar, which means that the crack shows a localized phenomenon, as reported in previous literature [27,30]. This may be because the addition of fibers can improve the bonding ability between steel rebar and concrete matrix. Moreover, the addition of fibers in flexural beams with low reinforcement ratio (e.g. 0.56% reinforcement ratio in this study) leads to a structural failure likely due to the excessive yielding of steel rebar rather than due to the crushing of concrete in compression zone. Concrete collapses can still occur in flexural beams with high reinforcement ratio (e.g. 1.31% reinforcement ratio in this paper). However, compared to the beams with low reinforcement ratio, the effect of fibers on crack distribution of the beams with high reinforcement ratio is not very noticeable. 3.4. Calculation of ultimate bearing capacity In traditional reinforced concrete beams, the residual tensile strength of concrete in the tension zone is generally neglected

Fig. 7. Load-longitudinal reinforcement strain curves of simply supported beams with various fiber contents.

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C. Zhang et al. / Construction and Building Materials 174 (2018) 11–23

when calculating the flexural bearing capacity of beams. However, in reinforced concrete beams with fibers, the tensile strength of concrete after cracking needs to be considered. ACI 544 [31], Model Code 2010 [32] and Chinese standard CECS 38:2004 [33] all take

the fiber contribution into consideration in flexural bearing capacity calculation. In this paper, the tensile stress of fiber rf in concrete beams is deduced firstly. Then, the ultimate flexural bearing capacity of reinforced concrete beam with hybrid fibers

Fig. 8. Crack patterns of the simply supported beams after unloading.

C. Zhang et al. / Construction and Building Materials 174 (2018) 11–23

19

Fig. 8 (continued)

is predicted based on rf . Finally, the prediction results using the proposed model in this paper are compared with those calculated by ACI 544 and Chinese standard CECS 38:2004. 3.4.1. Tensile stress of fiber rf Based on probability statistics, the tensile strength in concrete matrix can be expressed as Eq. (1).

1 2

rf ¼ aV f r f ð1 þ f 1 Þ

x ¼

rf of fibers ð1Þ

where a is the fraction ratio of fibers bridging the crack; V f is the volume fraction of fibers; f 1 is the coefficient of friction between f fiber and concrete matrix sheared over crack, taken as 1/3; and r is the average fiber stress for the load-carrying fibers, which can be obtained by Eq. (2).

4s x r f ¼ f F be df

which can be expressed as Eq. (3); df is the diameter of fiber, mm; and F be is the fiber characteristic coefficient, taken as 1.2 for hooked steel fiber and 1.0 for smooth fibers.

ð2Þ

where sf is the interfacial shear stress between fiber and concrete, MPa, taken as 2.5 times of concrete tensile strength for hooked steel fiber [34], and taken as 1.1 MPa for Double duoform macro PP fiber [35];  x is the average shear length of fibers bridging over crack, mm,

Lf 4

ð3Þ

 f can be expressed as Eq. where Lf is the fiber length, mm. Then, r (4).

r f ¼ sf kF be

ð4Þ

where k is the aspect ratio of fiber. Therefore, rf can be expressed as Eq. (5).

1 2

rf ¼ asf kV f F be ð1 þ f 1 Þ

ð5Þ

Relationship between crack width x and a can be given as Eq. (6), and x can be expressed as Eq. (7).

a¼1x x¼

4sf x Ef df

2 Lf

ð6Þ

ð7Þ

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C. Zhang et al. / Construction and Building Materials 174 (2018) 11–23

Therefore, the expression for

rf can be rewritten as Eq. (8).

2

1 2

rf ¼ sf kV f F be ð1 þ f 1 Þ 

sf k V f F be Ef

ð1 þ f 1 Þ

ð8Þ

The second part on the right side of Eq. (8) is negligible, so can be simplified as Eq. (9).

1 2

rf ¼ sf kV f F be ð1 þ f 1 Þ

rf ð9Þ

When taking the flexural loading into consideration, Eq. (9) can be rewritten as Eq. (10).

1 2

rf ¼ sf kV f F be ð1 þ f 1 Þð1 þ f 2 Þ

ð10Þ

where f 2 is the flexural characteristic coefficient, expressed as Eq. (11).

f2 ¼

hc L0

ð11Þ

where h is the depth of the beam cross section, mm; c is the depth of neutral axis of reinforced concrete beam, mm; and L0 is the span of beam, mm. 3.4.2. Stress-strain model of materials Tensile stress-strain model for concrete in the tensile zone of beams is given by Eq. (12), as shown in Fig. 9(a).




rct ¼

Ec ect

0 6 ect 6 ecr

rf

ecr < es 6 etu

ð12Þ

where ecr is the cracking strain of FRC, taken as 0.00015; and etu is the ultimate tensile strain of FRC, taken as 0.025 [30]. Compressive stress-strain model for concrete in the compressive zone of beams can be expressed as Eq. (13), as illustrated in Fig. 9(b).

rc

8    
e 6 e0

ð13Þ

e0 6 e 6 ecu

where f c is the compressive strength of FRC, MPa; e0 is the compressive strain corresponding to f c , taken as 0.002; and ecu is the ultimate compressive strain, taken as 0.0035 [30]. Stress-strain relationship of longitudinal rebar is given as Eq. (14).

rs ¼ Es es 6 f y

ð14Þ

where Es is the elastic modulus of rebar, MPa; f y is the yield strength of rebar, MPa; and es is the ultimate tensile strain of longitudinal rebar, taken as 0.01.

(a) Tension

Fig. 10. Stress and strain distribution of FRC beam containing conventional steel rebar.

3.4.3. Ultimate bearing capacity Fig. 10 presents the flexural stress-strain distribution on the cross section of SCC beam containing conventional steel rebar and fibers in the ultimate bearing capacity state. Based on the plane cross-section assumption, equilibrium of force and equilibrium of moment, the ultimate bearing capacity of FRC beam can be expressed as Eq. (15) when taking the contribution of fibers into consideration.

   x h c x þ rf bðh  cÞ þ  Mu ¼ As f y h0  2 2 2 2

ð15Þ

where As is the steel reinforcement area, mm2; h0 is the effective height of beam cross section, mm; x is the depth of rectangular compressive stress blocks, mm; b is the width of the beam cross section, mm; h is the depth of the beam cross section, mm; and c is the depth of neutral axis of reinforced concrete beam, mm. The depth of neutral axis c of reinforced concrete beam and the depth of rectangular compressive stress blocks x can be obtained from Eqs. (16) and (17), respectively.

f y As þ rf bðh  cÞ ¼ a1 f c bx

ð16Þ

x ¼ 0:8c

ð17Þ

For the reinforced SCC beams with steel fiber only, given as Eq. (18).

1 2

rf ¼ sf ;st kst V f ;st F be;st ð1 þ f 1 Þð1 þ f 2 Þ

rf can be ð18Þ

where sf ;st is the interfacial shear stress between steel fiber and concrete, MPa, taken as 2.5 times of concrete tensile strength for hooked steel fiber; kst is the aspect ratio of steel fiber; V f ;st is the volume fraction of steel fiber; and F be;st is the characteristics coefficient of steel fiber, taken as 1.2 for hooked steel fiber. For the reinforced SCC beams with hybrid steel and macro PP fibers, rf can be given as Eq. (19).

(b) Compression Fig. 9. Stress-strain model for FRC.

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C. Zhang et al. / Construction and Building Materials 174 (2018) 11–23 Table 7 Comparison of experimental results and predicted results using various models. Beams

Measured moment Mexp/kNm

SSB-1R SSB-2R SSB-3R SSB-4R SSB-5R SSB-6R SSB-7R SSB-8R SSB-9R SSB-10R SSB-11R SSB-12R

9.6 11.0 10.7 11.7 105. 12.4 11.5 12.8 11.2 20.1 22.9 24.5

Predicted moment, Mpre/kNm

Ratio = Mpre/Mexp

Suggested model

ACI 544

CECS 38

Suggested model

ACI 544

CECS 38

6.3 9.6 8.5 9.2 8.8 11.8 10.7 11.2 10.9 13.9 17.0 16.6

6.3 6.8 6.6 6.6 6.6 7.1 6.9 6.9 6.9 13.9 14.3 14.2

6.3 8.2 7.6 7.6 7.6 9.5 8.8 8.8 8.8 13.9 15.7 15.1

0.655 0.874 0.798 0.781 0.842 0.953 0.930 0.874 0.978 0.629 0.742 0.676

0.655 0.614 0.620 0.564 0.630 0.570 0.600 0.542 0.618 0.629 0.624 0.578

0.655 0.745 0.710 0.646 0.722 0.763 0.766 0.693 0.790 0.629 0.684 0.615

Mean SD CV

0.811 0.117 0.145

0.603 0.033 0.055

0.701 0.057 0.082

Fig. 11. Comparison of experimental results and predicted results for ultimate flexural bearing capacity using various models.

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C. Zhang et al. / Construction and Building Materials 174 (2018) 11–23

Table 8 Comparison of Meda and Dancygie’s experimental results and the predicted results using suggested model in this paper. Reference

Beam No.

Fiber type

Vf/%

k

f0c /MPa

b/mm

h/mm

qs/%

fy/MPa

Mexp/kNm

Mpre/kNm

Mpre/Mexp

Meda [28]

2-PC 2-30 2-60 4-PC 4-30

Hooked steel

0 0.38 0.76 0 0.38

50 50 50 50 50

45.5 45.5 45.5 45.5 45.5

200 200 200 200 200

300 300 300 300 300

0.76 0.76 0.76 1.52 1.52

534 534 534 534 534

54.0 57.6 57.6 100.8 105.6

58.1 62.2 63.8 109.9 113.5

1.077 1.080 1.108 1.090 1.074

Dancygie [27]

4-0-1 4-0-2 5-1-35 5-1-60 8-1-35 8-1-60 4-0-4 5-1-35-3 5-1-35-4

Hooked steel

0 0 0.76 0.76 0.76 0.76 0 0.76 0.76

65 65 65 65 65 65 65 65 65

120.5 114.6 129.4 123.6 124.4 122 118 121.8 121.8

200 200 200 200 200 200 200 200 200

300 300 300 300 300 300 300 300 300

0.28 0.28 0.28 0.28 0.56 0.56 0.28 0.28 0.28

480 480 480 480 480 480 616 616 616

38.7 35.9 35.6 41.0 58.3 55.8 28.9 35.1 33.8

20.2 20.2 33.5 33.5 53.3 53.5 25.9 39.2 39.2

0.522 0.562 0.942 0.818 0.915 0.955 0.895 1.157 1.159

1 2

rf ¼ ð1 þ f 1 Þð1 þ f 2 Þðsf ;st kst V f ;st F be;st þ sf ;sy ksy V f ;sy F be;sy Þ

ð19Þ

where sf ;sy is the interfacial shear stress between macro PP fiber and concrete, MPa, taken as 1.1 MPa for Double duoform macro PP fiber; ksy is the aspect ratio of macro PP fiber; V f ;sy is the volume fraction of macro PP fiber; and F be;sy is the characteristic coefficient of macro PP fiber, taken as 1.2 for Double duoform macro PP fiber. Due to the poor performance of micro PP fiber in improving the structural behavior of reinforced concrete beams, the effect of micro PP fiber on the ultimate flexural bearing capacity of reinforced SCC beams is neglected in this paper. 3.4.4. Comparisons with test results Table 7 and Fig. 11 present the comparison of experimental and predicted results for ultimate flexural bearing capacity of the proposed model, ACI 544 and CECS 38:2004. It can be seen that the predicted results using the proposed model, ACI 544 and CECS 38:2004 are lower than the experimental results. This is mainly because of the potential size effect of relatively small beams used in this study. Moreover, due to the underestimation of fiber contribution, the predicted results of ACI 544 are obviously abnormal. Although the predicted results of CECS 38:2004 are acceptable, its formula is regressed by a large number of test results. Therefore, the reinforcing mechanism of fibers is not clear. The predicted model in this paper not only explains the reinforcing mechanism of different fibers but also provides a more accurate and stable predicted results.

Fig. 12. Comparison of Albert and Dancygie’s experimental results and predicted results.

To extend the validity of the proposed model in this paper, it was applied for the prediction of other experimental ultimate flexural bearing capacity results of reinforced concrete beams with fibers from previous literature, as shown in Table 8 and Fig. 12. It can be seen that the predicted moment and experimental moment are very close with a mean value of 0.951, a standard deviation of 0.199 and a coefficient of variation of 0.210. Therefore, the suggested model in this paper could be employed for the calculation of ultimate flexural bearing capacity of reinforced concrete beams with fibers. 4. Conclusions The effects of steel fiber, micro PP fiber, macro PP fiber and their combinations on the flexural performance of SCC beams with different longitudinal reinforcement ratios at room temperature were investigated in this paper. The following conclusions can be drawn from this study. (1) The addition of steel fibers can enhance the ultimate flexural bearing capacity of reinforced SCC beams, and the hybrid use of steel fiber and macro PP fiber can bring a further improvement. However, along with the increase in longitudinal reinforcement ratio, the above enhancement becomes less pronounced. Compared with macro PP fiber and micro PP fiber, steel fiber has a more significant effect on the bearing capacity of reinforced beams. (2) The addition of fiber reduces the deflection of reinforced beams due to the localized deformation. Compared to mono steel fiber, the combined use of steel fiber and macro PP fiber can further reduce the beam deflection. However, this reduction effect caused by fibers is weakened with the increase in reinforcement ratio. (3) The addition of fibers can decrease the strain, and thus decrease the stress of longitudinal reinforcement. Mono steel fiber and the combination of steel fiber and macro PP fiber have a significant effect on reducing the steel reinforcement strain and stress. Likewise, a higher longitudinal reinforcement ratio means a relatively lower fiber effect on the steel rebars. (4) Cracks in the reinforced SCC beams become smaller, narrower, closer and more diffused due to the inclusion of fibers. Steel fibers play a more predominant role than PP fibers. Higher content of steel fiber has a more significant effect. The combination of steel fiber, macro PP fiber and micro PP fiber does not have an obvious effect on the cracking behavior. For all the tested beams containing fibers, the cracks show a localized phenomenon, which results in a reduction of mid-span deflection of SCC beams.

C. Zhang et al. / Construction and Building Materials 174 (2018) 11–23

(5) A calculation model for ultimate bearing capacity of flexural SCC beams at room temperature was proposed. The model considers the contribution of hybrid fibers to SCC in the tension zone by taking into account the stress transfer behavior of different fibers. The results of the proposed model are found to agree well with experimental data in this study and other literature. The proposed model can be employed to estimate the ultimate flexural bearing capacity of SCC beams containing hybrid fibers at room temperature. Conflict of interest We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work. Acknowledgements The authors gratefully acknowledge the Foundation Research Project of Jiangsu Province (The Natural Science Fund NO. BK20170192) and the Open Foundation of Key Laboratory of Concrete and Pre-stressed Concrete Structure of Ministry of Education (CPCSME2016-10). References [1] A.C. Aydin, Self compactability of high volume hybrid fiber reinforced concrete, Constr. Build. Mater. 21 (6) (2007) 1149–1154. [2] A.S. El-Dieb, M.M. Reda Taha, Flow characteristics and acceptance criteria of fiber-reinforced self-compacted concrete (FR-SCC), Constr. Build. Mater. 27 (1) (2012) 585–596. [3] Y. Ding, S. Liu, Y. Zhang, et al., The investigation on the workability of fibre cocktail reinforced self-compacting high performance concrete, Constr. Build. Mater. 22 (7) (2008) 1462–1470. [4] A. Khaloo, E. Molaei Raisi, P. Hosseini, et al., Mechanical performance of selfcompacting concrete reinforced with steel fibers, Constr. Build. Mater. 51 (2014) 179–186. [5] L. Ferrara, P. Bamonte, A. Caverzan, et al., A comprehensive methodology to test the performance of steel fibre reinforced self-compacting concrete (SFRSCC), Constr. Build. Mater. 37 (2012) 406–424. [6] T.D. Eethar, R. Mahyuddin, High strength characteristics of cement mortar reinforced with hybrid fibres, Constr. Build. Mater. 25 (2011) 2240–2247. [7] F. Kassimi, A.K. El-Sayed, K.H. Khayat, Performance of fiber-reinforced selfconsolidating concrete for repair of reinforced concrete beams, ACI Struct. J. 111 (6) (2014) 1277–1286. [8] C.E. Chalioris, Analytical approach for the evaluation of minimum fibre factor required for steel fibrous concrete beams under combined shear and flexure, Constr. Build. Mater. 43 (2013) 317–336. [9] A. Caggiano, M. Cremona, C. Faella, et al., Fracture behavior of concrete beams reinforced with mixed long/short steel fibers, Constr. Build. Mater. 37 (2012) 832–840. [10] M. Paja˛k, T. Ponikiewski, Flexural behavior of self-compacting concrete reinforced with different types of steel fibers, Constr. Build. Mater. 47 (2013) 397–408. [11] A. Khaloo, E. Molaei Raisi, P. Hosseini, et al., Mechanical performance of selfcompacting concrete reinforced with steel fibers, Constr. Build. Mater. 51 (2014) 179–186.

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