Effect of steel fibers on the compressive and splitting-tensile behaviors of cellular concrete with millimeter-size pores

Construction and Building Materials 221 (2019) 60–73

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Effect of steel fibers on the compressive and splitting-tensile behaviors of cellular concrete with millimeter-size pores Xiao-hua Wang, She-rong Zhang, Chao Wang ⇑, Ke-lei Cao, Pei-yong Wei, Jia-xin Wang State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin 300072, China School of Civil Engineering, Tianjin University, Tianjin 300072, China

h i g h l i g h t s

g r a p h i c a l a b s t r a c t


A new steel fiber reinforced cellular

concrete (SFRCC) is introduced in this study.
Steel fiber reinforcement is obvious in the mechanical behaviors of SFRCC.
Fiber characteristics affect the distributions of steel fibers and pores in SFRCC.
Correlation between compressive and splitting-tensile strengths of SFRCC is studied.

a r t i c l e

i n f o

Article history: Received 14 April 2019 Received in revised form 28 May 2019 Accepted 7 June 2019

Keywords: Steel fiber reinforced cellular concrete Compressive behavior Splitting-tensile behavior Steel fiber reinforcement Distribution characteristic

a b s t r a c t A high-performance steel fiber reinforced cellular concrete (SFRCC) with millime-size pore structure is recently suggested as an attractive material in structural engineering because of its desirable engineering characteristics. However, the influence of the steel fibers on the mechanical properties of SFRCC are still very limited in literature. Therefore, before the structural applications, it is necessary to learn the mechanical behaviors of SFRCC under compression and splitting-tension, as well as their relationship. To this end, a detailed experimental program has been performed to research the effect of fibers’ shape (i.e., crimped, straight and hooked end) and aspect ratio (i.e., 33.33, 44.44 and 55.56) on the compressive and splitting-tensile behaviors of the new SFRCC utilizing saturated superabsorbent polymer (SAP) under different volume fraction of steel fibers (i.e., 0.5%, 1.0% and 1.5%). Experimental results show that higher compressive strength and splitting-tensile strength of SFRCC are tightly related to higher volume fraction or aspect ratio of steel fibers, corresponding to the more ductile behaviors and higher loading levels in the post-peak behaviors. Moreover, it is important to consider the influence of fibers’ shape on the mechanical properties of SFRCC. Based on the cracked planes of SFRCC specimens after splitting-tensile tests, it is confirmed that the procedures of specimen fabrication and material characterization significantly influence the distributions of steel fibers and pores and some empirical formulae are proposed to describe the dependence of their distributions on the fiber characteristics. Ó 2019 Elsevier Ltd. All rights reserved.

⇑ Corresponding author at: State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin 300072, China. E-mail address: [email protected] (C. Wang). https://doi.org/10.1016/j.conbuildmat.2019.06.069 0950-0618/Ó 2019 Elsevier Ltd. All rights reserved.

X.-h. Wang et al. / Construction and Building Materials 221 (2019) 60–73

1. Introduction Lightweight cellular concrete is composed of cement, water, aggregate and pore structure. The entrapment of pore structure is usually obtained by the usage of foaming agents. The complex pore structure makes the cellular concrete lightweight but may compromise its strength and durability, hindering its practical applications [1]. Based on the mechanical tests, Rasheed and Prakash [2] suggested that the flexure strength of cellular concrete was 1/3–1/5 of its compressive strength. Higher proportion of pore structure used to replace concrete matrix indicates a greater drop in the compressive strength of cellular concrete [3]. However, due to the special engineering characteristics, such as low density, heat insulation and high energy absorption, cellular concrete is used widely for building panels, fire protection wall, energy-absorbing pads, and so on [1,4,5]. Especially, because of high energy absorption, cellular concrete is capable to be used as the construction material of protective structures for impact resistance [6,7]. Different from the traditional methods described above to produce the pore structures in concrete, an ideal has been put forward to replace concrete matrix fully or partially with spherical saturated superabsorbent polymer (SAP), whose diameter is in the range of 4 mm to 8 mm, thus forming a completely new cellular concrete [6]. In a relatively dry environment, the saturated SAP beads can slowly dehydrate and separate from the concrete matrix, eventually leaving closed millimeter-size pores uniformly distributed in the concrete. It is also confirmed that osmotic pressure and humidity gradient are two important factors affecting the moisture movement between SAP and cement paste [8–10]. Therefore, compared with the conventional cellular concrete, there exists some special structural characteristics, such as standard spherical pore structure, larger pore size in diameter and higher strength for the mortar matrix, when millimeter-size saturated SAP is introduced to form the pore structure [6]. Although cellular concrete utilizing millimeter-size saturated SAP has numerous advantageous engineering characteristics, its low strength characteristic has hindered its broader practical applications. The concept of using fibers to improve the mechanical properties of concrete has been widely accepted for many decades [11–14]. By introducing all kinds of fibers into the concrete composites, it has been widely accepted that the loading-carrying capacity, energy absorption capacity, abrasion resistance, stability and flexibility of fiber reinforced concrete can be significantly improved by the addition of fibers [15–17]. Among them, steel fiber is the most popular one to be used in the fiber reinforced concrete and extensive researches have been performed to explore the usage of steel fiber in producing high strength fiber reinforced concrete [11,18,19]. In this way, a fighting strategy has come into use to counteract the pore structure in cellular concrete by the addition of discrete steel fibers. Due to the mixing action, the steel fibers are distributed evenly and in different directions throughout the concrete matrix, which have a positive impact to resist the formation of plastic deformation and microcracks [20]. The reinforcement mechanism of steel fibers can be expressed as the steel fibers evenly distributed in concrete matrix not only are capable to disallow the micro-defects from developing into macrocracks, but also can hold the existing pore structures together and reinforce the concrete against collapsing. In this condition, steel fiber reinforced cellular concrete (SFRCC) with low density but high performance can be easily achieved through adding steel fibers into cellular concrete. Therefore, SFRCC, consisting of concrete matrix, pores and fibers, is proposed as a potential construction material with some expected engineering characteristics, such as low density, well sound and thermal insulation, high impact resistance, as well as high resistance to cracking [21,22].

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However, limited works have been done regarding the cellular concrete reinforced with different types of steel fibers, in terms of fiber parameter, fiber content and fiber-matrix interaction, especially for the new SFRCC utilizing saturated SAP. Therefore, before the practical application of SFRCC, understanding the behaviors of SFRCC under compression and tension is the primary issue to be solved since the addition of steel fibers may significantly change the mechanical behaviors of SFRCC, as well as the correlation between the compressive strength and the splitting-tensile strength [23,24]. On the other hand, most of the published studies are related to the fiber reinforcement effect on the mechanical properties, while limited literatures can be found dealing with the distribution of steel fibers in the concrete. However, the contributions of steel fibers to the mechanical properties of SFRCC depends on their distribution within the concrete matrix [11,25]. It is confirmed by Gettu et al. [25] that a preferential horizontal orientation of the steel fibers together with segregation can be caused by the excessive vibration and the obvious wall effect can be found in the prism specimens, resulting in higher concentration of steel fibers at the molded faces. So that, the assumption of the uniform distribution of steel fibers in SFRCC cannot always be guaranteed due to the compaction procedure and material characterization. The influences of the specimen fabrication and material characterization on the distributions of steel fibers and pores in standard SFRCC specimens are, thus, of great importance, which hinders the practical applications of SFRCC. In sum, although cellular concrete has many advantages, its shortcomings, such as low strength, cracking, water absorption and so on, are also cannot be ignored and restrict its wide application in construction industry. This study tries to verify the feasibility of the new cellular concrete reinforced with steel fibers and replacing concrete matrix fully or partially with SAPs, since SAPs have been verified to be a useful internal curing material. The moisture emission from SAPs during curing or in relatively dry environment can mitigate the racking caused by shrinkages, especially autogenous shrinkage, which is a common issue in lightweight cellular concrete. On the other hand, regarding the low strength of light-weight cellular concrete, steel fibers are introduced to restrict the generation and development of cracks, as well as the remaining coarse aggregate. Besides the enhancement effect, steel fibers also can restrict the non-uniform distributions of SAPs in the SFRCC, avoiding the floating of SAPs. The aim of this study is to develop a high-performance SFRCC to provide a better alternative for structural applications. A detailed experimental program has been performed to research the effect of fibers’ shape (i.e., crimped, straight and hooked end) and aspect ratio (i.e., 33.33, 44.44 and 55.56) on the compressive and splitting tensile behaviors of the new SFRCC utilizing saturated SAP under different volume fraction of steel fibers (i.e., 0.5%, 1.0% and 1.5%). The research, the correlation between compressive strength and splitting-tensile strength of SFRCC is also discussed and compared with the findings from other researchers. Moreover, an effort has been made in this experimental study to investigate the distribution characteristics of steel fibers and pores in the SFRCC so that the restriction effect of steel fibers on the floating of SAP beads can be further understood. The results, obtained in this study, are expected to form a basis for the selection of suitable fiber types and contents for their most efficient applications in the reinforcement of cellular concrete utilizing millimeter-size saturated SAP. 2. Experiment procedures 2.1. Materials The moderate heat ordinary Portland cement of 42.5 Grade was used in this study, having a Blaine fineness of 318 m2/kg. The

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The other two types of steel fibers differed in shape (i.e., straight and hooked end, denoted as F2L1 and F3L1) but had the same length (i.e., 30 mm), whose aspect ratios were both 33.33. These fibers have a same tensile strength of 1100 MPa.

chemical compositions of cement have shown in Table 1. As the fine aggregate, the artificial sand was medium sand with a fineness modulus of 2.8, special gravity of 2.62 and moisture content of 3%. In this study, the pore structure in the cellular concrete was controlled by the saturated SAP beads presoaked in the NaCl solution with a certain concentration. To avoid the SAP beads releasing water into the cement paste during specimen fabrication, it was necessary to control the concentration of NaCl solution to be higher than the equilibrium concentration, where the saturated SAP beads would reach an equilibrium state as soon as they were mixed in the cement paste. Therefore, the equilibrium concentration between SAP and cement paste was investigated at first to be 0.5 mol/L NaCl solution via the test method proposed by Wang et al. [9]. In this study, to prepare the saturated SAP beads, the dry SAP with a diameter of 1.5 mm–2.0 mm was used and pre-soaked in 1.0 mol/L NaCl solution for more than 12 h [6]. The water absorptivity of SAP in 1.0 mol/L NaCl solution trended to be stable after 6 h and the maximum diameter of saturated SAP beads was about 7.5 mm. As discussed by Deng et al. [6], due to the difference in density, the saturated SAP beads whose density is near to that of water show a clear trend of floating when mixed with the concrete matrix. In order to achieve a more uniform distribution of pore structure and the higher mechanical properties of SFRCC, five types of steel fibers differing in shape or aspect ratio were used in this study. The detailed properties of the steel fibers are shown in Table 2. As shown in Table 2, three crimped fibers had different length (i.e., 30 mm, 40 mm and 50 mm), denoted as F1L1, F1L2 and FlL3, respectively. Their aspect ratios lf =df (ratio between fiber length and its equivalent diameter) were 33.33, 44.44, and 55.56.

2.2. Mix proportion Sixteen concrete mixtures were used for casting the specimens in this experimental study. Table 3 shows the compositions of concrete mix designs for unreinforced cellular concrete and SFRCC, where the superscript of the mix code represents the volume fraction of steel fibers. The mix design R in Table 3 is defined as a reference cellular concrete without fiber reinforcement. In this study, the basic compositions of SFRCC remains the same as the reference cellular concrete, as shown in Table 3, but the major differences in the concrete mixture for SFRCC lie in the fiber type and its volume fraction. In fact, the fiber length and maximum aggregate size are closely related to guarantee the distribution uniformity and effectivity of steel fibers. For this reason, the maximum aggregate size should not exceed 0.5 times the fiber length. It has been reported that the steel fiber content in SFRC should be in the range of 0.5% to1.5% as the addition of steel fibers may lead to a drop in the workability of concrete mixture and result in balling or matting, which is difficult to be separated during the specimen compaction by vibration [21]. Based on the mix design of reference cellular concrete, the SFRCC in this study were made with the fiber volume fraction of 0.5% to 1.5%, specifying that there were three fiber contents (i.e., 40 kg/m3, 80 kg/m3 and 120 kg/m3) for SFRCC reinforced with each kind of steel fibers. Moreover, a certain proportion of superplasticizer (i.e., 2.34 kg/m3)

Table 1 Chemical compositions of cement. Testing object

SiO2

Fe2O3

Al2O3

CaO

MgO

K2O

Na2O

Alkali content

SO3

Loss on ignition

Cement

19.92%

5.32%

3.55%

57.48%

4.07%

0.57%

0.14%

0.52%

2.20%

1.34%

Table 2 Summary of investigated steel fiber types. Description

Fiber type F1L1

F2L1

F3L1

F1L2

F1L3

Geometry

Shape Surface Cross-section Anchorage

Crimped Plane Circular Continuous

Straight Plane Circular Continuous

Hooked end Plane Circular Hooked end

Crimped Plane Circular Continuous

Crimped Plane Circular Continuous

Parameters

Length (lf ) Diameter (df ) Aspect ratio (lf =df ) Tensile strength

30 mm 0.9 mm 33.33 1100 MPa

30 mm 0.9 mm 33.33 1100 MPa

30 mm 0.9 mm 33.33 1100 MPa

40 mm 0.9 mm 44.44 1100 MPa

50 mm 0.9 mm 55.56 1100 MPa

Table 3 The concrete compositions (kg/m3). Components

Cement Water Sand Aggregate

Concrete compositions

<4 mm 4 mm–7 mm 7 mm–10 mm

Superplasticizer Superabsorbent polymer (SAP) Steel fiber

R0.0

F1L10.5/1.0/1.5

F2L10.5/1.0/1.5

F3L10.5/1.0/1.5

F1L20.5/1.0/1.5

F1L30.5/1.0/1.5

390.00 175.50 716.30 110.40 260.00 377.00 2.34 159.26 0.00

390.00 175.50 716.30 110.40 260.00 377.00 2.34 159.26 40/80/120

390.00 175.50 716.30 110.40 260.00 377.00 2.34 159.26 40/80/120

390.00 175.50 716.30 110.40 260.00 377.00 2.34 159.26 40/80/120

390.00 175.50 716.30 110.40 260.00 377.00 2.34 159.26 40/80/120

390.00 175.50 716.30 110.40 260.00 377.00 2.34 159.26 40/80/120

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was used to improve the workability of the mixtures due to the addition of steel fibers. For a simplification, the mix code for different concrete mixture is denoted by the fiber type and its volume fraction in following research, such as F1L1-0.5%, F1L1-1.0% and F1L1-1.5% for SFRCC reinforced with the fiber type of F1L1 but different fiber contents of 40 kg/m3, 80 kg/m3 and 120 kg/m3, respectively. In sum, there are three fiber contents (40 kg/m3, 80 kg/m3 and 120 kg/m3) and five fiber types (F1L1, F2L1, F3L1, F1L2 and F1L3), a total of fifteen mix designs of SFRCC, have been studied in this paper to gain the deeper understandings of steel fiber reinforcement to the compressive and splitting-tensile behaviors of SFRCC. 2.3. Procedure of specimen fabrication To make the SAP beads and steel fibers distribute uniformly in SFRCC, a standard gravity mixer was used and the mix procedure was adopted as following: The cement, superplasticizer, sand and aggregate were first put into the mixer and stirred for 2 min, meanwhile the steel fibers were added into the mixer gradually. Then, the saturated SAP beads were drained by a sieve and added into the mixer, followed by stirring for another 1 min. Finally, the water was added into the mixer and stirred for 1 min and the whole mix procedure was considered complete. Next, during specimen fabrication, the mold was half-filled and vibrated for 10 s at first, and then fully-filled and vibrated for another 15 s [25]. In this study, a vibrating table was used to compact the specimens at a determined frequency of 50 Hz. During specimen compaction, the top surface of the fresh concrete matrix was covered with a hard plate and pressured by hand to avoid the spilling of SAP beads. After 1 day, the specimens were demolded and cured in the standard curing room for 28 days, in which the room temperature was controlled in the range of 20 ± 2 centigrade degrees and the relative humidity was maintained higher than 95%. After curing, these hardened SFRCC specimens were placed in the indoor environment (i.e., 25 ± 2 centigrade degrees and 50 ± 5% relative humidity) until mechanical tests. 2.4. Testing methods 2.4.1. Physical properties test on fresh concrete According to the Chinese standard [26], the workability of each mixture was tested by a slump bucket within the lapse of 5 min when the whole mix procedure was considered complete. Moreover, the mass and volume of each cubic specimen were measured soon after specimen demolding, and the fresh concrete density was obtained easily from the mass divided by the volume of the cubic specimen. 2.4.2. Compressive and splitting-tensile tests The compressive strength and splitting-tensile strength of unreinforced cellular concrete and SFRCC were averaged from three cubic specimens with an edge length of 150 mm for each mix design. The quasi-static compressive tests on the prepared cubic specimens were carried out with a constant loading rate of 1 mm/min delivered by an electro-hydraulic servo-controlled loading test machine at Tianjin University. For the purpose of minimizing the end friction, grease was applied on the interfaces between specimen and apparatus before quasi-static compressive tests. During the compressive tests, the load and displacement versus time were all recorded by the logging system. The splitting-tensile tests were also carried out by the electrohydraulic servo-controlled loading test machine. A high-strength steel fixture was used between the apparatus platen and specimen, so that the uniformly distributed pressure could be applied on the midline of the two relative surfaces. In order to further investigate

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the distributions of steel fibers and pores during specimen fabrication, the loading surfaces were perpendicular to the casting direction. During the splitting-tensile tests, a constant loading rate of 1 mm/min was also delivered by the testing machine and the crack opening displacement was recorded in real time by two LVDTs placed at both sides of the tested specimen. It is worthy to be pointed out that many researchers have confirmed the influence of the width of the loading strip on the splitting-tensile strength [27,28]. Rocco et al. [29] verified that the splitting-tensile test could reflect the true tensile strength if the width of the loading strip did not exceed 4% of the diameter of specimen. Therefore, the width of the loading strip was selected as 6 mm and then the uniformly distributed tensile stress could be produced in the vertical plane under the action of external forces. 3. Experimental results 3.1. Physical properties of fresh concrete The properties of fresh concrete including fresh concrete density and slump value are indicated in Fig. 1. As shown in Fig. 1 (a), the density of fresh SFRCC is not affected by the shape and aspect ratio of steel fibers, but mainly depends on the volume fraction of steel fibers. In theory, the density of fresh SFRCC follows the
 equation of Dc ¼ Dm 1  v f  v p þ Df v f þ Dp v p , where Dc = density of fresh SFRCC; Df and v f denote the density and volume fraction of steel fibers, respectively; Dp and v p are the density and volume fraction of SAP beads, respectively. It is also pointed out by other researchers that increasing the aspect ratio of steel fibers would lead to the mixing problems, where concrete usually has a lower fresh density for the same volume fraction of steel fibers [30]. However, this phenomenon is not obvious in our study as the largest aspect ratio is only 55.56. It is worth noting that the fresh density of SFRCC without fibers is about 2150 kg/m3 before curing and its hardened density decreases to nearly 2030 kg/m3 due to the moisture emission from SAPs and concrete matrix in the indoor environment. Thus, the advantage of the reduction in self-weight is meager when compared to the density of conventional light-weight concrete (300 kg/m3 – 1800 kg/m3). It is noted that this paper focuses on the steel fiber reinforcement effect on the cellular concrete, and the effect of volume fraction of SAP needs further study. Slump of concrete mixture is another important parameter for fresh SFRCC, which reflects the effect of steel fibers on its workability. As shown in Fig. 1(b), it is obvious that the slump values for different mix design of SFRCC is relatively lower than that of unreinforced cellular concrete, indicating the restriction in workability from the addition of steel fibers. Larger volume fraction or higher aspect ratio of steel fibers used in the mixture shows more significant restriction in the workability of fresh SFRCC. Moreover, the fiber shape, to some extent, shows a little influence on the slump of fresh SFRCC and straight fibers show less restriction in workability than the other two fibers. For example, the slump of fresh SFRCC reinforced with straight fibers is 55 mm relatively higher than those reinforced with crimped and hooked end fibers when the volume fraction of steel fibers reaches 1.5%. 3.2. Effect of steel fibers on the compressive behaviors of SFRCC The typical stress-strain curves from compressive tests on specimens with different fiber contents are given in Fig. 2. It is obvious from Fig. 2 that the compressive strength for SFRCC specimens to some extent is depended on the content and length of fibers, as well as the fiber type. Following these figures, the stress-strain curve under compression for the unreinforced cellular concrete

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Fig. 1. Effect of steel fibers’ shape and aspect ratio on the properties of fresh SFRCC: (a) Fresh density; (b) Slump.

Fig. 2. Effect of steel fibers on the compressive behaviors of SFRCC under axial compression tests: (a) Fiber content; (b) Aspect ratio of fibers; (c) Variability in compressive strength.

shows a nonlinear compaction stage up to 30% of the peak stress, which also occurs in SFRCC due to the existence of large pore structures. Compared to the SFRCC, the unreinforced cellular concrete exhibits more brittleness as the post-peak strength decreases rapidly with the increasing strain, indicating less energy absorption capacity. Higher content and longer length of fibers corresponding to a slightly higher compressive strength, while their post-cracking behavior will be enhanced significantly due to the increase in the content and length of steel fibers. On the other hand, the ultimate strain at the peak load increases gradually with the continuous addition of steel fibers, along with the decreasing slope of the descending branch, which is mainly caused by the growing resistance to cracking from the addition of steel fibers. This phenomenon is consistent with the experimental results by Yoo et al. [31]. Moreover, Fig. 2(c) also shows that the straight steel fibers has less reinforcement effect on the compressive strength of SFRCC that the hooked end fibers and crimped fibers. In general, the fiber enhancement effect on the compressive strength of SFRCC is not obvious. Thus, it is not a wise approach to improve the compressive strength of cellular concrete by the addition of steel fibers. To solve this problem, some methods can be used to improve the mix design of concrete matrix under the premise of maintaining the volume fraction of pores for the SFRCC, such as the usage of lower water-to-cement ratio and silica fume. The average results for the uniaxial compressive tests on SFRCC are summarized in Table 4. It is found that the steel fiber reinforcement effect on compressive strength is not obvious, even a slight decrease can be found when the steel fiber content is relatively

lower, as shown in Table 4. The conflicting result may be caused by the comprehensive influence of the addition of steel fibers and SAP beads at the same time, since higher volume fraction of pores from SAP beads restricts the strength enhancement effect of steel fibers. Moreover, the elastic modulus of SFRCC is defined as Eq. (1) and the average elastic modulus for each mix design

Table 4 The average results for uniaxial compressive tests on SFRCC. Mix code

f c (MPa)

Ec (GPa)

ecf ðmm=mmÞ

RIw

b

R F1L1-0.5% F1L1-1.0% F1L1-1.5% F2L1-0.5% F2L1-1.0% F2L1-1.5% F3L1-0.5% F3L1-1.0% F3L1-1.5% F1L2-0.5% F1L2-1.0% F1L2-1.5% F1L3-0.5% F1L3-1.0% F1L3-1.5%

17.60 17.59 18.59 21.89 17.34 17.85 19.62 18.01 20.14 22.37 18.52 19.84 21.74 18.47 21.68 21.41

1.78 1.81 1.79 1.88 1.74 1.79 1.86 1.83 1.89 1.91 1.77 1.74 1.85 1.91 1.84 1.95

0.01286 0.01399 0.01502 0.01577 0.01336 0.01358 0.01603 0.01344 0.01481 0.01596 0.01376 0.01416 0.01629 0.01293 0.01490 0.01707

0.00 0.53 1.07 1.60 0.53 1.07 1.60 0.53 1.07 1.60 0.71 1.42 2.13 0.89 1.78 2.67

4.410 3.676 3.283 2.270 4.397 4.322 4.050 3.257 2.494 1.642 3.541 2.486 1.810 2.939 1.902 1.735

Note: f c ¼ compressive strength, Ec ¼ elastic modulus, ecf ¼ ultimate strain at the peak load, RIw = reinforcing weight index, b ¼ material parameter depending on the descending branch of stress-strain curve.

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has been listed in Table 4. It can be found that the elastic modulus is also insignificantly affected by the addition of steel fibers, less than 10% for the mix design in this study. The ultimate strain corresponding to the peak stress shows relatively more obvious increasing trend as the fibers’ content and length increase. To sum up, the compressive properties of SFRCC is also depended on the characteristics of steel fibers, in terms of volume fraction and the aspect ratio, which has been widely accepted in traditional normal concrete and SFRC [21,31].

Ec ¼

f 30  f 60

ð1Þ

ec30  ec60

where f 30 and ec30 are the stress and strain corresponding to 30% of the peak compressive strength for SFRCC after the non-linear compaction stage. f 60 and ec60 are the stress and strain corresponding to 60% of the peak compressive strength for SFRCC before the yield stage. To estimate the steel fiber reinforcement effect on the compressive behaviors, the normalized stress-strain curves are applied as shown in Fig. 3(a) and (b). It is clearly noted that the normalized stress-strain curves are tightly dependent on the steel fiber content and the aspect ratio. The present experimental investigation shows that steel fibers have little impact on the compression behavior of SFRCC before peak compressive strength, but more effective contribution can be found on the compressive stress-strain curve in the descending branch, which is also accepted for SFRC [31–33]. Higher steel fiber content and higher aspect ratio will contribute to gain a gentler post-peak behavior, corresponding to higher ductility of SFRCC under uniaxial compression. To further investigate the steel fiber effect on the compressive behaviors of SFRCC, an analytical model for the steel fiber reinforced concrete to reflect the stress-strain curve is necessary, especially for its descending branch. After investigation of various analytical models from different researchers, it is found that the analytical model, expressed as Eq. (2), can describe the complete compressive behaviors of normal-strength SFRC [34].

bðec =ecf Þ f ¼ f c b  1 þ ðec =ecf Þb

ð2Þ

where f c and ecf are the compressive strength of concrete and the corresponding ultimate strain, respectively; f and ec denote the stress and strain on the curve, respectively; b is the material parameter depending on the shape of the stress-strain curve under compression, especially for its descending branch. As widely reported, a higher b can be obtained when lower volume fraction of steel fibers is used, and the suggested equations for material parameter b usually are the function of the reinforcement index (RIw ¼ wf lf =df ), where wf is the weight fraction and equals to

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3.2 times the volume fraction of steel fibers (wf ¼ 3:2V f ) [31,32]. Moreover, the material parameter b is tightly dependent on the descending branch of normalized stress-strain curves [31–33]. However, the analytical model in Eq. (2) is not able to describe the complete normalized compressive behaviors of SFRCC due to the existence of compaction stage from the pore structure, which will restrict the fitting accuracy when the coefficient b is obtained by the least-square error method. Thus, in this study, the analysis model is only used to describe the descending branch of the normalized stress-strain curve under uniaxial compression, since the addition of steel fibers almost has no impact on the shape of normalized stress-strain curve under compression before the peak compressive strength. In Fig. 3(a) and (b), the analytical curves show a good consistency with the measured stress-strain curves. The material parameter b calculated by the descending branch of normalized stress-strain curves is listed in Table 2, and the relationship between b and RIw for SFRCC is shown in Fig. 3, compared with some empirical formulae for SFRC and high-strength steel fiber reinforced concrete (HSSFRC) with different fiber shapes. It is obvious in Table 2 that higher RIw usually leads to a lower b, indicating more ductility in the post-peak behavior of SFRCC. Fig. 3(c) also shows the coefficient b of SFRCC is strongly influenced by not only the reinforcement index but also the fiber shape. SFRCC reinforced with straight fibers has more brittleness after the peak compressive strength is reached, while the post-peak behaviors of SFRCC reinforced with hooked end fibers has more ductility. Thus, the previous equations of coefficient b, only taking the reinforcement index RIw into consideration, cannot precisely predict the compressive behaviors for both SFRC and SFRCC when they are reinforced with different shaped fibers. Thus, further research is required to develop a rational model. 3.3. Effect of steel fibers on the splitting-tensile behaviors of SFRCC Usually, once the peak load is reached under splitting-tensile tests, a crack usually generates at the center of specimen and propagates toward the loading points, during which the crack opening increases with the increasing transversal displacement. In this study, as for the unreinforced cellular concrete specimens, there exists a sudden energy release soon after the peak splittingtensile load is achieved, indicating a brittle failure. However, after the peak splitting-tensile load, the crack opening of SFRCC specimens can be delayed by the steel fibers embedded in the concrete matrix, since the steel fibers bridge the crack and prevent its further propagation. After the SFRCC specimens are completely failed under splitting-tensile tests, further investigation into the distributions of steel fibers and pores has been carried out on the cracked planes of SFRCC specimens. The cracked planes of SFRCC specimens

Fig. 3. Effect of steel fibers on the behavior of SFRCC under axial compression tests: (a) Fiber content; (b) Fiber length; (c) Fiber type.

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after splitting-tensile tests have been shown in Fig. 4, along with the numbers of steel fibers and pores on the planes. It can be found that the failure of steel fibers mainly lies in the fiber pulling out, while a few fibers are broken under splitting tension. Generally, steel fibers and pores do not distribute uniformly as expect. Due to the difference in density, the steel fibers are apt to sink, while the pores exhibit a floating trend. Fig. 5 shows the load-displacement curves under splittingtensile tests on the SFRCC specimens, compared to the cellular concrete specimens. For the unreinforced specimens, the loaddisplacement curves under tension show a nearly linear behavior up to the peak load and almost no resistance to cracking can be found after the peak load. However, for the SFRCC specimens, the magnitude of splitting-tensile load transferred by the steel fibers drops rapidly soon after the main crack forms, and then it stabilizes at a lower level and further decreases gradually with the increasing transversal displacement. The reason for the rapid drop in tensile capacity after the peak load may lie in the brittle failure of concrete matrix, and the following more gradual reduction of tensile capacity may be related to the continuous pulling out of the steel fibers from the concrete matrix. Fig. 5(a) and (b) show that the peak splitting-tensile load of SFRCC increases with the increase in volume fraction and aspect ratio of steel fibers. Some characteristic values to describe the splitting-tensile behaviors of SFRCC have

been illustrated in the diagrammatic sketch of Fig. 5(c), and the average mechanical properties have been summarized in Table 5. It is obvious in Table 5 that the fiber reinforcement effect on splitting-tensile behaviors of SFRCC is remarkable with the addition of steel fibers, especially for hooked end steel fibers. For example, the SFRCC reinforced with hooked end steel fibers shows 37%–177% strength enhancement in splitting-tensile test when the volume fraction of fibers increases from 0.5% to 1.5%. Moreover, steel fibers with higher aspect ratio show more significant fiber reinforcement effect on splitting-tensile behaviors of SFRCC. In this study, the splitting-tensile strength for F1L1-1.5% is 2.38 MPa and 169%, while the splitting-tensile strength for F1L3-1.5% reaches 2.97 MPa and 236% strength enhancement. Generally, since the fiber reinforcement effect on splitting-tensile strength is more remarkable than that on the displacement at the peak load, SFRCC also shows an enhancement of the secant stiffness. It is worth noting that the enhancement effect of steel fibers on splitting-tensile strength of SFRCC is still obvious even if the fiber content is relatively lower. This phenomenon may be related to the existence of pore structure in SFCRCC. The pore structure in cellular concrete will significantly decrease the load capacity, since pores will collapse and penetrate easily under loadings. However, adding steel fibers can effectively bridge the concrete skeleton among pores, emphasizing the fiber reinforcement effect on SFRCC. Moreover,

Fig. 4. The pores and steel fibers distributing on cracked planes of SFRCC under splitting-tensile tests.

Fig. 5. Effect of steel fibers on the splitting-tensile behaviors of SFRCC under splitting-tensile tests: (a) Fiber content; (b) Aspect ratio of fibers; (c) Diagrammatic sketch for the splitting-tensile behaviors of SFRCC.

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X.-h. Wang et al. / Construction and Building Materials 221 (2019) 60–73 Table 5 The summary of the mean mechanical properties for splitting-tensile tests on SFRCC. Mix code

F t (kN)

dt (mm)

K t (kN/mm)

F r (kN)

dr (mm)

f t (MPa)

ft

TTI (kN  mm)

TTI

R F1L1-0.5% F1L1-1.0% F1L1-1.5% F2L1-0.5% F2L1-1.0% F2L1-1.5% F3L1-0.5% F3L1-1.0% F3L1-1.5% F1L2-0.5% F1L2-1.0% F1L2-1.5% F1L3-0.5% F1L3-1.0% F1L3-1.5%

31.26 45.92 72.26 84.17 44.38 45.58 56.82 42.97 76.82 86.60 50.70 68.80 92.90 52.86 85.44 104.95

0.25 0.25 0.26 0.27 0.26 0.30 0.47 0.32 0.34 0.31 0.32 0.35 0.43 0.51 0.60 0.84

126.91 184.63 288.46 306.62 172.00 153.46 119.80 132.63 226.61 277.58 160.20 197.69 217.31 103.34 142.04 124.72

— 41.06 54.90 71.23 29.84 35.73 44.19 36.21 65.60 75.76 41.42 47.34 75.83 50.56 78.43 96.90

— 0.35 0.34 0.37 0.41 0.53 0.66 0.46 0.56 0.37 0.39 0.53 0.56 0.55 0.84 0.95

0.88 1.30 2.04 2.38 1.26 1.29 1.61 1.22 2.17 2.45 1.43 1.95 2.63 1.50 2.42 2.97

1.00 1.47 2.31 2.69 1.42 1.46 1.82 1.37 2.46 2.77 1.62 2.20 2.97 1.69 2.73 3.36

6.74 141.48 162.96 223.66 77.58 114.59 152.00 123.53 210.79 230.21 169.61 182.51 308.10 206.58 341.10 398.64

1.00 20.99 24.18 33.18 11.51 17.00 22.55 18.33 31.27 34.16 25.16 27.08 45.71 30.65 50.61 59.15

*

Note: F t ¼ peak splitting-tensile load, dt = displacement at the peak load, K t = secant stiffness at peak load, F r ¼ peak bridging load at the crack tip singularity, dr = displacement at the crack tip singularity, f t = splitting-tensile strength, f t = normalized splitting-tensile strength, TTI ¼ tension toughness index, TTI ¼ normalized tension toughness index.

the nonuniformly distributed pore structure will lead to a lower peak splitting-tensile load especially for the cellular concrete without fiber content, accompanied by the much more significant discreteness. To further compare the energy absorbed by SFRCC, the tension toughness index (TTI) is proposed and calculated as the area under the load-displacement curve. However, the SFRCC reinforced with long fibers but low volume fraction of steel fibers also has large crack opening before complete failure, which will lead to a conflict in comparing the TTI obtained by the integrating the complete load-displacement curve. Thus, in this study, the TTI is generated by the area of load-displacement curve up to 20 times displacement corresponding to the peak splitting-tensile load, which has been verified to describe the splitting-tensile behavior of the post-peak branch [27]. Moreover, the normalized tension toughness index (TTI), calculated as the ratio of the area under the load-displacement curve for SFRCC to that for cellular concrete, is also used to compare the energy absorption under splittingtensile test. Both the TTI and TTI have been shown in Table 5. In general, for the SFRCC, higher tension toughness (or energy absorption) is tightly related to its higher splitting-tensile strength and ductility from the addition of steel fibers, i.e. higher fiber volume fraction and larger aspect ratio. The TTI for SFRCC reinforced with hooked end fibers increases from 20.99 for F1L1-0.5% to 33.18 for F1L1-1.5% and 30.65 for F1L3-0.5%. It is also obvious that the fiber reinforcement effect is tightly dependent on the fiber shape and the SFRCC reinforced with hooked end fibers has more remarkable toughness enhancement than that reinforced with straight fibers. Moreover, the fiber enhancement on the tension toughness is extremely significant. For example, although the SFRCC for F2L10.5% only has 42% increase in splitting-tensile strength, its tension toughness reaches 11.51 times that of cellular concrete without steel fiber reinforcement. Fig. 6(a) shows the variability in splitting-tensile strength of SFRCC with different mix design. Comparing Fig. 6(a) with Fig. 2 (c), we can find that the fiber enhancement effect on splittingtensile strength is more significant than that on compressive strength, especially for steel fibers with higher aspect ratio or volume fraction. After the formation of the main crack, the steel fibers in SFRCC are capable to bridge the cracked surfaces and restrict the increase in crack opening, since the addition of steel fibers improves the possibility of stress redistribution during the continuous pulling out of steel fibers. At this stage, most of the energy can

be absorbed by the deformation of steel fibers and the SFRCC can continue to bear the loads, which is identified as the bridging effect. In this study, the peak bridging load is used to reflect the load capacity of post-peak region for SFRCC, which is conductive to restricting the development of cracks and enhancing the toughness of concrete. This is important to improve the impact resistance of concrete when the SFRCC is used in the protection engineering. It has been confirmed in Fig. 6(b) that the peak bridging load has a tightly linear correlation with the peak splittingtensile strength. Therefore, for the purpose of the increase in peak tensile strength and better post-peak behavior, it is a wise approach to design the addition of steel fibers to gain higher peak bridging load and widen the application of cellular concrete especially in the conditions of undergoing dynamic loads. In sum, adding steel fibers into cellular concrete can not only effectively restrict the development of microcracks in concrete matrix, but also improve the strength of cellular concrete, compensating the self-defect of cellular concrete. The main functions of steel fibers in concrete matrix lie in: (1) Crack resistance: The internal defects are the inducing factors of concrete failure. The addition of steel fibers can prevent the expansion of original defects (microcracks) in the concrete matrix and effectively delay the appearance of new cracks; (2) Enhancement effect: In the process of loading, the steel fibers and concrete matrix bear the load and deform together, reducing the stress concentration at crack tips. Moreover, the steel fibers can continue to bear the load even after cracking, so that the compressive and tensile strengths of SFRCC can be enhanced to a certain extent; (3) Toughening effect: even if the SFRCC cracks under loads, the steel fibers can also cross the cracks and bear a certain tensile stress to hinder the rapid expansion of cracks, so that the concrete has a higher residual strength and post-peak strain. In fact, the bridging load of SFRCC under splitting-tension has been discussed by many researchers, in which the Variable Engagement Model (VEM) has been widely accepted to investigate the fiber reinforcement [16]. From the VEM, the bridging load is tightly related to the shear stress between steel fibers and concrete matrix. Fig. 7 shows the diagrammatic sketch for a hooked end steel fiber pulling out from concrete to illustrate the shear contributions from different fiber performance zones. For hooked end steel fibers, the component of shear stress in the straight zone between the hooked and snubbing zones is small in comparison to that in the hooked and snubbing zones, even can be ignored.

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Fig. 6. Strength enhancement mechanism of steel fibers on the splitting-tensile behavior for SRFCC: (a) Variability in splitting-tensile strength; (b) Relationship between peak splitting-tensile load and peak bridging load.

Fig. 7. Shear contributions of a hooked end steel fiber from different fiber performance zones.

Thus, the bridging load of a hooked end fiber mainly comes from the hooked and snubbing zones and the bridging load of a straight fiber only benefits from the snubbing zone, leading to a low fiber reinforcement effect on splitting-tensile behaviors of SFRCC in terms of splitting-tensile strength and tension toughness. As for the crimped steel fibers, although the hooked zone also does not exist, the straight zone has remarkable friction effect between steel fiber and concrete matrix, leading to a significant bridging load and fiber reinforcement effect. 4. Discussion 4.1. Distribution characteristics of steel fibers and pores in SFRCC It has been confirmed that the procedure of specimen fabrication and material characterization have great impacts on the distribution of steel fibers, leading to the variability in mechanical properties of SFRCC [25]. As for SFRCC, due to the difference in densities of different components, it has been observed on the cracked planes that the steel fibers are apt to sink, while the pores exhibit a floating trend. Thus, the primary issue to be solved before the practical application of SFRCC is learning the distribution characteristics of steel fibers and pores in SFRCC.

To further evaluate the distribution of steel fibers, the two cracked planes of each specimen after splitting-tensile tests were divided into four rows (Z1–Z4) along the casting direction, as shown in Fig. 8(a). The fiber count on each row region is the average from the two pieces. Table 6 gives the statistical results of the steel fiber distributions for SFRCC specimens reinforced with F1L1 as an example. As shown in Table 6, the number of steel fibers in the same statistical region changes obviously from one specimen to another for each mix design. Moreover, in general, there is a steady increase of fiber percentage along the casting direction relative to the entire fiber distribution, indicating the segregation of steel fibers. For example, the mean distribution density of fibers in SFRCC specimens of FL1L-0.5% is 0.67 fibers/cm2 over the entire cracked plane, while the mean distribution density is 0.36 fibers/ cm2 for Z1 and 1.03 fibers/cm2 for Z4. As the volume fraction of steel fibers increases, there exists a nearly proportional growth in the mean distribution density. The percentage of fibers for different row region has been shown Fig. 8(b). It seems that higher volume fraction of fibers has more segregation resistance and stability of steel fibers. In the same way, the distribution characteristics of steel fibers in casting direction for SFRCC specimens reinforced with different steel fibers have been shown in Fig. 8(b)–(f). It can be concluded in this study that the steel fibers distributed in SFRCC

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Fig. 8. Distribution characteristics of steel fibers in casting direction for SFRCC specimens reinforced with different steel fibers: (a) Discretization of the cracked plane (b) F1L1; (c) F2L1; (d) F3L1; (e) F1L2; (f) F1L3.

Table 6 Steel fiber counts on the cracked planes of SFRCC specimens reinforced with F1L1 after splitting-tensile tests. Mix code

Region

Specimen 1

Specimen 2

Specimen 3

No. of fibers (mean and std. dev.)

Mean distribution density (fibers/cm2)

Percentage of fibers (%)

F1L1-0.5%

Z1 Z2 Z3 Z4 Total

19 31 51 58 159

24 26 42 45 137

18 34 32 71 155

20 ± 3 30 ± 3 42 ± 8 58 ± 11 150 ± 10

0.36 0.54 0.74 1.03 0.67

13.53 20.18 27.72 38.58 100.00

F1L1-1.0%

Z1 Z2 Z3 Z4 Total

42 59 81 119 301

34 65 72 102 273

43 45 73 89 250

40 ± 4 56 ± 8 75 ± 4 103 ± 12 275 ± 21

0.71 1.00 1.34 1.84 1.22

14.44 20.51 27.43 37.62 100.00

F1L1-1.5%

Z1 Z2 Z3 Z4 Total

64 77 104 119 364

54 93 136 155 438

72 87 120 127 406

63 ± 7 86 ± 7 120 ± 13 134 ± 15 403 ± 30

1.13 1.52 2.13 2.38 1.79

15.73 21.27 29.80 33.20 100.00

shows a more obvious sinking trend and more fibers occur at the bottom of specimen when specimens reinforced with lower volume fraction or aspect ratio of fibers. In this study, the non-uniformity coefficient (ff ) is introduced to evaluate the fiber segregation for different mix design of SFRCC. The non-uniformity coefficient of fiber distribution can be expressed as Eq. (3), wherel = 25% andn = 4 in this study. Therefore, higher non-uniformity coefficient of steel fibers indicates a more serious fiber segregation. Based on the statistical analysis of the fiber distribution on the cracked plane of SFRCC, the nonuniformity coefficient can be obtained easily for each mix design, and some potential influencing factors that may determine the non-uniformity coefficient have been shown in Fig. 9.

ff ¼

Xn   l  l=ðnlÞ i i

ð3Þ

where ff represents the non-uniformity coefficient of fiber distribution; li is the percentage of fibers of the ith row region; l is the expected percentage of fibers for each region; n denotes the total number of row regions on the cracked plane of SFRCC. From Fig. 9(a), it can be found that higher slump of the fresh concrete mixture will lead to higher non-uniformity coefficient of fiber distribution (i.e., more serious fiber segregation). As explained in Subsection 3.1, the workability of fresh concrete is generally determined by the volume fraction and aspect ratio of steel fibers. Thus, in this study, we attempt to establish the relationship between the characteristics of steel fibers and fiber distribution,

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Fig. 9. Some factors influencing the fiber distribution: (a) Slump of fresh concrete; (b) Fiber characteristics.

which can be generalized as Eq. (4). Based on the statistical analysis of fiber distribution on the cracked plane, the fitting parameters can be determined as a1 ¼ 0:06, a2 ¼ 3:70 and a3 ¼ 1:43. The fitting result has been shown in Fig. 9(b), exhibiting a good regression effect. a

ff ¼ a1 ln½Nf ðlf =df Þ 2  þ a3

ð4Þ

where a1 , a2 and a3 are the fitting parameters; N f denotes the fiber number on the cracked plane. As shown in Fig. 10, the addition of steel fibers in the concrete mixture contributes to effectively restrict the floating of saturated

SAP beads. More fibers added into the concrete mixture will make the pores distributed more uniformly. In order to quantitatively analyze the effect of steel fibers on the pore distribution, the non-uniformity coefficient of pore distribution (fp ) is introduced, whose definition is similar to that of steel fibers in Eq. (4). Then, in the same way, a relationship between pore distribution and fiber characteristics as shown in Fig. 10(f), based on which the nonuniformity coefficient of pore distribution can be determined by the fiber number on the cracked plane and the aspect ratio of steel fibers. Therefore, the choice of suitable volume fraction and aspect ratio of steel fibers is of great importance in the mix design of the

Fig. 10. Distribution characteristics of pores in casting direction for SFRCC specimens reinforced with different steel fibers: (a) F1L1; (b) F2L1; (c) F3L1; (d) F1L2; (e) F1L3; (f) Effect of fiber characteristics on pore distribution.

X.-h. Wang et al. / Construction and Building Materials 221 (2019) 60–73

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suggested SFRCC, which is tightly related to the distributions of steel fibers and pores. 4.2. Relationship between strength and splitting-tensile strength of SFRCC Compressive strength and splitting-tensile strength of SFRCC are the most important indices in structural design, where compressive strength usually is necessary and splitting-tensile strength is needed for some specific applications, such as structures exposed to earthquake and airfield runway. As reported, the compressive strength of concrete can be used to estimate the splitting-tensile strength, and various empirical relations have been proposed to describe their tight correlation [23,24]. Meanwhile, most of the empirical relations are proposed for normal concrete, while few are for fiber reinforced concrete. Behnood et al. [24] investigated their correlation for SFRC through different meth0 ods, such as non-linear regression (NLR), M5 model tree (MT), support vector machine (SVM). The few empirical formulae to predict the splitting-tensile strength of fiber reinforced concrete have been listed in Table 7, as well as some typical formulae for normal concrete. These published prediction formulae for normal concrete and all kinds of fiber reinforced concrete in Table 7 are primarily used to predict the splitting-tensile strength of SFRCC in this study. The integral absolute error (IAE), defined as Eq. (5), can be applied to evaluate the gap between results from experiments and prediction. As shown in Table 7, the IAE values of prediction formulae are all near or above 20%, which verifies their inapplicability to SFRCC. Fig. 11 shows the remarkable differences more graphically, where both the normal concrete and fiber reinforced concrete usually has a relatively higher splitting-tensile strength than SFRCC when the fiber reinforcement is not remarkable for SFRCC with straight steel fibers or a relatively lower FRI.

IAE ¼

X ½ðQ i  Pi Þ2 1=2 P  100 Qi

ð5Þ

where Qi represents the experimental result; Pi is the predicted result. The reason for this phenomenon not only lies in the complex pore structure in concrete matrix significantly changing the mechanical properties of SFRCC but also the fiber shape effect

Fig. 11. Comparation the experimental results of SFRCC with published prediction formulae.

not reflected in these prediction formulae. Moreover, it has been confirmed in this study that the shape of steel fibers has a significant influence on both compressive behaviors and splitting-tensile behaviors of SFRCC. Moreover, the steel fiber reinforcement effect can be reflected by the peak bridging load, which has a tight correlation with various mechanical properties of SFRCC. In previous studies, a shape coefficient of steel fibers sf has been introduced into the VEM model to considering the effect of steel fiber shape on the residual load capacity of cracked SFRC before failure, only from the contributions of steel fibers. In VEM model, the shape coefficient of steel fibers is 0.5 for straight fibers, 0.75 for crimped fibers and 1.00 for hooked end fibers, which is also adopted in this study [40]. Considering the effect of fiber shape, Fig. 12 shows the relationships between fiber coefficient (F) and mechanical properties of SFRCC, where F ¼ sf v f lf =df . It is obvious that both compressive strength and splitting-tensile strength have a nearly linear relationship with the fiber coefficient, although the high discreteness exists in compressive strength. In order to achieve a more accurate prediction model for SFRCC, the fiber shape effect is taken into consideration. In this study, the splitting-tensile strength of SFRCC is taken to be proportional to the square root of its compressive strength, since the simple 0.5

Table 7 Empirical relationships between compressive strength and splitting-tensile strength for concrete. Sources

Empirical relation

ACI 363R-92 [35]

ft ¼

ACI 318R-99 [36]

ft ¼

CEB-FIP [37]

ft ¼

Behnood et al. [24]

ft ¼

Behnood et al. [24]

ft ¼ ft ¼

Behnood et al. [24]

ft ¼

Choi and Yuan [38]

ft ¼

Choi and Yuan [38]

ft ¼

Xu and Shi [23]

ft ¼

Abbass et al. [39]

ft ¼

Behnood et al. [24]

ft ¼

Behnood et al. [24]

ft ¼ ft ¼

Behnood et al. [24]

ft ¼

In this study

ft ¼

0:5 0:59f c 0:5 0:56f c 2=3 0:30f c 0:750 0:219f c 0:908 0:166f c Age0:074 , when f c  22:33 0:554 0:423f c Age0:026 , when f c > 22:33 0:681 0:269f c Age0:015 0:5 0:60f c 0:5 0:55f c 0:83 0:21f c 0:4989 0:5079f c 0:853 0:205f c Age0:048 ðw=cÞ0:043 FRI0:012 0:941 0:144f c Age0:153 ðw=cÞ0:215 FRI0:002 , if f c  16:18 0:527 0:474f c Age0:014 ðw=cÞ0:163 FRI0:011 , iff c > 16:18 0:781 0:246f c Age0:027 ðw=cÞ0:016 FRI0:013 0:50 0:77f c ðsf FRIÞ0:46

IAE

Remark

38.70

For normal concrete (NC)

32.83

For NC

22.43

For NC

20.85

NLR1 model proposed by non-linear regression (NLR) for NC

20.61

MT2 model proposed by M50 model tress (MT) for NC

21.79

SVM2 model proposed by support vector machine (SVM) for NC

40.69

For polypropylene fiber reinforced concrete (PFRC)

31.16

For glass fiber reinforced concrete (GFRC)

32.49

For steel fiber reinforced concrete (SFRC)

24.75

For SFRC

19.68

NLR6 model proposed by NLR for SFRC

43.09

MT6 model proposed by MT for SFRC

22.57

SVM6 model proposed by SVM for SFRC

6.62

Proposed for SFRCC considering fiber shape effect

Note: Age= curing age of concrete; w/c = ratio of water to cement; FRI ¼ v f lf =df ; sf ¼ shape coefficient of steel fibers.

*

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X.-h. Wang et al. / Construction and Building Materials 221 (2019) 60–73

Fig. 12. Relationships between fiber coefficient and mechanical properties of SFRCC: (a) Compressive strength; (b) Splitting-tensile strength.

power law model has been widely used in the analytical models evaluating the splitting-tensile strength with compressive strength for all kinds of concrete materials [38]. The general form of the proposed prediction model for SFRCC is given as: 0:50

f t ¼ b1 f c

ðsf FRIÞb2

ð6Þ

where b1 and b2 are the fitting parameters. The fiber shape coefficient sf has been introduced to modify the effect of steel fibers. Based on many tests, these parameters in the prediction model for SFRCC are determined as b1 ¼ 0:77 and b2 ¼ 0:46. The IAE value for the proposed prediction model is only 6.62, indicating a high fitting accuracy to the experimental results of SFRCC in this study. It is worthy to be pointed out that the proposed prediction model is only adapted to the SFRCC with a certain pore structure in this study. Further researches should be carried out to consider the effect of pore structure in SFRCC, especially the volume fraction of pores, on the relationship between compressive strength and splitting-tensile strength. 5. Conclusions In order to develop a high-performance SFRCC utilizing millimeter-size saturated SAP for engineering applications, an extensive experimental program has been carried out to study the effects of adding steel fibers with different shape, volume fraction and length on the mechanical properties of SFRCC under compression and tension. In addition, distribution characteristics of steel fibers and pores in the SFRCC are also emphasized in this study, which are confirmed to have great influences on the mechanical properties of SFRCC. Based on the previous discussions, the following conclusions can be drawn: (1) In general, the steel fiber shows great reinforcement effect on mechanical behaviors of SFRCC proposed in this study. Moreover, the splitting-tensile strength of SFRCC shows more obvious fiber reinforcement effect than that its compressive strength. Higher tension toughness (or energy absorption) is tightly related to its splitting-tensile strength and ductility from the addition of steel fibers. In order to achieve higher splitting-tensile strength and better postpeak behavior of SFRCC, it is a wise approach to design the addition of steel fibers to gain higher peak bridging load due to its tight correlation with the peak splitting-tensile strength.

(2) The distributions of steel fibers and pores in SFRCC are verified to be tightly related to fiber type and its volume fraction, not distributing uniformly as expect. Generally, in SFRCC, the steel fibers are apt to sink, while the pores exhibit a floating trend. Some empirical formulae have been proposed to form a basis for selection of suitable fiber type and content to achieve the relatively uniform distribution of steel fibers and pores. (3) Fiber characteristics play an important role in affecting the relationship between compressive strength and splittingtensile strength of SFRCC. Previous prediction models for normal concrete and SFRC are inapplicable to the SFRCC, due to the lack of comprehensive consideration about fiber characteristics, especially for the fiber shape. Based on the experimental data in this study, the prediction model suggested for SFRCC has taken the steel fiber characteristics into consideration, such as fiber shape, volume fraction and aspect ratio.

Declaration of Competing Interest None. Acknowledgements This research is supported by the National Natural Science Foundation of China, China (No. 51779168). The corresponding author acknowledges the support from open Foundation (No. 2017SGG02) from State Key Laboratory of Water Resources and Hydropower Engineering Science, Wuhan University, China. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.conbuildmat.2019.06.069. References [1] D.K. Panesar, Cellular concrete properties and the effect of synthetic and protein foaming agents, Constr. Build. Mater. 44 (2013) 575–584, https://doi. org/10.1016/j.conbuildmat.2013.03.024. [2] M.A. Rasheed, S.S. Prakash, Mechanical behavior of sustainable hybridsynthetic fiber reinforced cellular light weight concrete for structural applications of masonry, Constr. Build. Mater. 98 (2015) 631–640, https:// doi.org/10.1016/j.conbuildmat.2015.08.137.

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