Statistical Analysis and Preliminary Study on the Mix Proportion Design of Self-Compacting Steel Fiber Reinforced Concrete

With the sustainable development of green construction materials in civil engineering, self-compacting steel fiber reinforced concrete (SC-SFRC) has attracted widespread attention due to its superior self-compacting performance and excellent hardened properties. In this paper, 301 groups of test data from published literatures were collected to quantify the characteristics of the mix proportion of SC-SFRC. The type, aspect ratio and volume fraction of steel fiber commonly used in SC-SFRC are discussed and the effects of steel fiber on the workability and mechanical properties of SC-SFRC are statistically studied. The relationship of cubic compressive strength and water-to-binder ratio and that of the splitting tensile strengths between SC-SFRC and referenced self-compacting concrete (SCC) are also evaluated. Based on these analyses, the reasonable ranges of material components in the mix proportion design of SC-SFRC are determined. The results showed that with several adjusted parameters, the calculation model of the water-to-binder ratio for the mix proportion design of ordinary concrete is suitable for SC-SFRC. The calculation model of tensile strength is suggested for SC-SFRC with various types of steel fiber.


Introduction
Self-compacting steel fiber reinforced concrete (SC-SFRC) is a type of high performance concrete with the benefits of self-compacting performance at the fresh stage and superior mechanical properties at the hardened stage. The composition, production and mechanism of SC-SFRC are more complicated than those of self-compacting concrete (SCC). Due to the large density, elongated shape and large surface area of steel fiber [1], the direct addition of steel fibers in SCC would impair the self-compacting performance and disturb the solid skeleton of fresh concrete [2][3][4]. Nowadays, studies showed that a limited volume fraction of steel fiber could be used in SC-SFRC in order to ensure higher workability and better mechanical performance. Due to the packing effect of the fiber-aggregate solid skeleton, the self-compacting performance could not be achieved once the volume fraction of steel fiber in concrete exceeds the limited value even if the concrete mixture is a homogeneous and stable suspension [5]. The limitation (usually less than 2%) is mainly affected by the characteristics of raw materials [2,6,7] and mix proportion [8][9][10][11][12]. The characteristics of the raw materials include the maximum particle size and surface morphology of coarse aggregate, volume fraction, aspect ratio and geometry of steel fiber, binder paste content and sand ratio. The volume fraction of steel fiber SC-SFRC and SCC are systemically discussed. Moreover, the type, aspect ratio and volume fraction of steel fibers commonly used in SC-SFRC are discussed. The effects of the fiber factor on the workability and mechanical properties are statistically studied. The relationship of w/b and cubic compressive strength of SC-SFRC as well as splitting tensile strengths between SC-SFRC and referenced SCC are studied.

Experimental Database
In this paper, 301 groups of test data for SC-SFRC from previous literatures [2,9,10,[12][13][14][15][16][17][18][19]22,23,[26][27][28][29] were collected to build the database. The range of results used for the experimental database are listed in Table 1. The mineral admixtures of SC-SFRC in the experimental database included parts of fly ash, slag powder, silica fume and stone powder. It should be noted that some values of the cylinder compressive strength used in the experimental database were converted into the cubic compressive strength (f cu ). The conversion factors are followed by the reference [62]. The detailed information of experimental database for SC-SFRC is presented in Appendix A. Steel fiber Length l f (mm) 6 60 Aspect ratio l f /d f 15 120 Volume fraction ρ f (%) 0.08 1.79 Slump flow (SF) (mm) 500 830 The cubic compressive strength (f cu ) (MPa) 20 120 The splitting tensile strength (f ft ) (MPa) 3.0 12.4 Figure 1 displays the variations of the volume content of aggregates, coarse aggregate and fine aggregate (VR A , VR CA and VR FA ) along with the cubic compressive strength f cu for SC-SFRC. SC-SFRCs (A)-(G) form the test data of SC-SFRC with a binary mixture design method, modified DMDA method, modified CPM method, method based on the packing test of steel fiber-aggregates, method of changing water content, method of increasing water and binder contents with w/b constant and method of increasing binder content, respectively. The volume content of their raw materials are distinguished using points of different color. VR a , VR CA and VR FA changed by 45-70%, 10-35% and 25-45% for SC-SFRC, respectively. Both VR A and VR CA show a small decrease with increased cubic compressive strength. VR FA shows little regularity with increased cubic compressive strength. Linear fitting was used to obtain the trendline. Trendlines of VR A , VR CA and VR FA along with f cu for SCC [30] are drawn as black lines where r is the correlation coefficient of the regression equation. It can be seen that VR A and VR CA of SC-SFRC are about 1.49-3.59% and 4.18-4.78% lower than those of SCC, respectively. Compared with SCC, one feature of the mix proportion for SC-SFRC is the lower VR A and VR CA values.

Aggregates
In term of self-compacting performance, a smaller content of coarse aggregate leads to less blocking effect and high flowability of fresh concrete. A suitable volume content of fine aggregate and a certain range of sand ratio would increase the segregation resistance of fresh concrete. However, a higher volume content of coarse aggregate would be beneficial in restricting the shrinkage deformation of hardened concrete, which is consistent with the requirements of the concrete structure performance. Thus, considering the different volume contents of coarse aggregate and fine aggregate, the mix proportion of SC-SFRC is classified into two types, which was named as NC-type SC-SFRC (legends of chamfering triangle in Figures 1 and 2) and LC-type SC-SFRC (legends of triangle in Figures 1 and 2), respectively. NC-type SC-SFRC has a volume content of coarse aggregate that is more than 600 kg/m 3 and volume content of fine aggregate that is less than 1000 kg/m 3 . LC-type SC-SFRC has coarse aggregate content that is less than 600 kg/m 3 and fine aggregate content that is more than 1000 kg/m 3 . LC-type SC-SFRC focuses more on the performance of fresh concrete, while NC-type SC-SFRC focuses on both the workability and volume deformation of hardened concrete. Similar VR A values were observed in NC-type and LC-type SC-SFRC. LC-type SC-SFRC has a VR CA and VR FA that was lower by 10.75-11.59% and higher by 5.64-7.34%, respectively, than NC-type SC-SFRC. However, a higher volume content of coarse aggregate would be beneficial in restricting the shrinkage deformation of hardened concrete, which is consistent with the requirements of the concrete structure performance. Thus, considering the different volume contents of coarse aggregate and fine aggregate, the mix proportion of SC-SFRC is classified into two types, which was named as NC-type SC-SFRC (legends of chamfering triangle in Figures 1 and 2) and LC-type SC-SFRC (legends of triangle in Figures 1 and 2), respectively. NC-type SC-SFRC has a volume content of coarse aggregate that is more than 600 kg/m 3 and volume content of fine aggregate that is less than 1000 kg/m 3 . LC-type SC-SFRC has coarse aggregate content that is less than 600 kg/m 3 and fine aggregate content that is more than 1000 kg/m 3 . LC-type SC-SFRC focuses more on the performance of fresh concrete, while NC-type SC-SFRC focuses on both the workability and volume deformation of hardened concrete. Similar VRA values were observed in NC-type and LC-type SC-SFRC. LC-type SC-SFRC has a VRCA and VRFA that was lower by 10.75-11.59% and higher by 5.64-7.34%, respectively, than NC-type SC-SFRC.
.83-0.015f cu , for SCC, according to Ref [30] VR FA (%) VRA, VRCA and VRFA of SC-SFRC with different mix design methods also showed some differences. SC-SFRC (C), SC-SFRC (D), SC-SFRC (E) and part of SC-SFRC (A) and SC-SFRC (F) can be categorized to LC-type SC-SFRC. In contrast, SC-SFRC (B) and part of SC-SFRC (A) and SC-SFRC (F) can be categorized to NC-type SC-SFRC. Figure 2 shows the variation of sand ratios according to mass βs along with the cubic compressive strength. βs changed by 40-80% for SC-SFRC, which is about 3.0-4.1% higher than that of SCC. Moreover, more than 80% of the sand ratios of SC-SFRC were 47-69%. βs of LC-type SC-SFRC was higher by 15.9-16.2% than that of NC-type SC-SFRC. 20 40 60 80 100 120 20 40 60 80 100 β s =54.3+0.019f cu , for SC-SFRC, data=256, r=0.037 β s =50.0+0.030f cu0 , for SCC, according to Ref [30] NC-type SC-SFRC:     Figure 2 shows the variation of sand ratios according to mass β s along with the cubic compressive strength. β s changed by 40-80% for SC-SFRC, which is about 3.0-4.1% higher than that of SCC. Moreover, more than 80% of the sand ratios of SC-SFRC were 47-69%. β s of LC-type SC-SFRC was higher by 15.9-16.2% than that of NC-type SC-SFRC.   Figure 2 shows the variation of sand ratios according to mass βs along with the cubic compressive strength. βs changed by 40-80% for SC-SFRC, which is about 3.0-4.1% higher than that of SCC. Moreover, more than 80% of the sand ratios of SC-SFRC were 47-69%. βs of LC-type SC-SFRC was higher by 15.9-16.2% than that of NC-type SC-SFRC. 20 40 60 80 100 120 20 40 60 80 100 β s =54.3+0.019f cu , for SC-SFRC, data=256, r=0.037 β s =50.0+0.030f cu0 , for SCC, according to Ref [30] NC-type SC-SFRC:        Figures 1 and 2, the legends of the chamfering triangle are NC-type SC-SFRC and the legends of triangle are LC-type SC-SFRC. In this paper, the binder material is the sum of cement and mineral admixtures while VRBP is the sum of water and binder materials by volume. The influence of hydration reaction on the volume change of binder paste is ignored. VRb and VRBP changed by 12-30% and 30-55% for SC-SFRC, respectively. Similar to SCC [30], VRb and VRBP of SC-SFRC increased in proportion to the cubic compressive strength. VRR and VRBP of SC-SFRC are higher by approximately 0.47-0.97% and 0.92-2.82% compared to that of SCC, respectively. Thus, one feature of the mix proportion for SC-SFRC is the higher VRBP. (a) Figure 3. The probability distribution of maximum particle size of coarse aggregates.  Figures 1 and 2, the legends of the chamfering triangle are NC-type SC-SFRC and the legends of triangle are LC-type SC-SFRC. In this paper, the binder material is the sum of cement and mineral admixtures while VR BP is the sum of water and binder materials by volume. The influence of hydration reaction on the volume change of binder paste is ignored. VR b and VR BP changed by 12-30% and 30-55% for SC-SFRC, respectively. Similar to SCC [30], VR b and VR BP of SC-SFRC increased in proportion to the cubic compressive strength. VR R and VR BP of SC-SFRC are higher by approximately 0.47-0.97% and 0.92-2.82% compared to that of SCC, respectively. Thus, one feature of the mix proportion for SC-SFRC is the higher VR BP .

Binder and Binder Paste
As shown in the red box line of Figure 4, several test data have higher VR b and VR BP values [27,28,51]. All these test data belong to LC-type SC-SFRC. Moreover, the experimental study of Abrishambaf used abundant binder materials of 766 kg/m 3 and a slightly low water content of 140 kg/m 3 [41] with f cu = 63 MPa. The limestone filler was considered as one of the binder materials.    Figures 1 and 2, the legends of the chamfering triangle are NC-type SC-SFRC and the legends of triangle are LC-type SC-SFRC. In this paper, the binder material is the sum of cement and mineral admixtures while VRBP is the sum of water and binder materials by volume. The influence of hydration reaction on the volume change of binder paste is ignored. VRb and VRBP changed by 12-30% and 30-55% for SC-SFRC, respectively. Similar to SCC [30], VRb and VRBP of SC-SFRC increased in proportion to the cubic compressive strength. VRR and VRBP of SC-SFRC are higher by approximately 0.47-0.97% and 0.92-2.82% compared to that of SCC, respectively. Thus, one feature of the mix proportion for SC-SFRC is the higher VRBP.   As shown in the red box line of Figure 4, several test data have higher VRb and VRBP values [27,28,51]. All these test data belong to LC-type SC-SFRC. Moreover, the experimental study of Abrishambaf used abundant binder materials of 766 kg/m 3 and a slightly low water content of 140 kg/m 3 [41] with fcu = 63 MPa. The limestone filler was considered as one of the binder materials.

Binder and Binder Paste
VRb and VRBP of SC-SFRC with different mix design methods also show some differences. Comparing with the trendlines of VRb and VRBP, SC-SFRC (C) and SC-SFRC (G) have similar VRb and VRBP, SC-SFRC (E) and part of SC-SFRC (F) have higher VRb and VRBP due to the same reason discussed in the above paragraph. In contrast, SC-SFRC (B) and SC-SFRC (D) have lower VRBP due to the lower water content.

Steel Fiber
It can be summarized from the experimental database that the hooked-end steel fiber is the most commonly used, which was involved in about 54% of SC-SFRC. This was followed by 23% of SC-SFRC containing crimped steel fibers. All of the other macro steel fibers of straight, milled cut, indentation, twisted and large-end account for about 20%. In contrast, micro steel fiber is only involved in about 3% of SC-SFRC.
The histograms of the probability distributions of length lf, aspect ratio lf/df and fiber factor λf = ρf·lf/df of steel fiber are drawn in Figure 5 where df is the equivalent diameter of the cross-section of steel fiber and ρf is the volume fraction of steel fiber in concrete. More than 75% of lf were less than 42.5 mm, more than 56% of fiber length lf ranged from 30 mm to 35 mm, more than 58% of aspect ratio lf/df ranged from 50 to 70 and more than 80% of the fiber factor λf were less than 0.55.  VR b and VR BP of SC-SFRC with different mix design methods also show some differences. Comparing with the trendlines of VR b and VR BP , SC-SFRC (C) and SC-SFRC (G) have similar VR b and VR BP , SC-SFRC (E) and part of SC-SFRC (F) have higher VR b and VR BP due to the same reason discussed in the above paragraph. In contrast, SC-SFRC (B) and SC-SFRC (D) have lower VR BP due to the lower water content.

Steel Fiber
It can be summarized from the experimental database that the hooked-end steel fiber is the most commonly used, which was involved in about 54% of SC-SFRC. This was followed by 23% of SC-SFRC containing crimped steel fibers. All of the other macro steel fibers of straight, milled cut, indentation, twisted and large-end account for about 20%. In contrast, micro steel fiber is only involved in about 3% of SC-SFRC.
The histograms of the probability distributions of length l f , aspect ratio l f /d f and fiber factor λ f = ρ f ·l f /d f of steel fiber are drawn in Figure 5 where d f is the equivalent diameter of the cross-section of steel fiber and ρ f is the volume fraction of steel fiber in concrete. More than 75% of l f were less than 42.5 mm, more than 56% of fiber length l f ranged from 30 mm to 35 mm, more than 58% of aspect ratio l f /d f ranged from 50 to 70 and more than 80% of the fiber factor λ f were less than 0.55.  As shown in the red box line of Figure 4, several test data have higher VRb and VRBP values [27,28,51]. All these test data belong to LC-type SC-SFRC. Moreover, the experimental study of Abrishambaf used abundant binder materials of 766 kg/m 3 and a slightly low water content of 140 kg/m 3 [41] with fcu = 63 MPa. The limestone filler was considered as one of the binder materials.
VRb and VRBP of SC-SFRC with different mix design methods also show some differences. Comparing with the trendlines of VRb and VRBP, SC-SFRC (C) and SC-SFRC (G) have similar VRb and VRBP, SC-SFRC (E) and part of SC-SFRC (F) have higher VRb and VRBP due to the same reason discussed in the above paragraph. In contrast, SC-SFRC (B) and SC-SFRC (D) have lower VRBP due to the lower water content.

Steel Fiber
It can be summarized from the experimental database that the hooked-end steel fiber is the most commonly used, which was involved in about 54% of SC-SFRC. This was followed by 23% of SC-SFRC containing crimped steel fibers. All of the other macro steel fibers of straight, milled cut, indentation, twisted and large-end account for about 20%. In contrast, micro steel fiber is only involved in about 3% of SC-SFRC.
The histograms of the probability distributions of length lf, aspect ratio lf/df and fiber factor λf = ρf·lf/df of steel fiber are drawn in Figure 5 where df is the equivalent diameter of the cross-section of steel fiber and ρf is the volume fraction of steel fiber in concrete. More than 75% of lf were less than 42.5 mm, more than 56% of fiber length lf ranged from 30 mm to 35 mm, more than 58% of aspect ratio lf/df ranged from 50 to 70 and more than 80% of the fiber factor λf were less than 0.55.   Figure 6 shows the relationship between fiber length lf and the maximum particle size of aggregate MA. To ensure an efficient reinforced effect of steel fibers, lf/MA should be larger than 1.33 in vibrated-compacting SFRC [63]. It can be seen that 99% of lf/MA are larger than 1.33 in SC-SFRC. lf/MA decreases with the increasing MA and 94% of lf/MA are between 1.5 and 6.5. The influences of steel fiber on the fresh and hardened performances of SC-SFRC are shown in Figure 7. SF and SF0 are the slump flows of SC-SFRC and the referenced SCC, respectively. The ratio of the slump flow SF/SF0 forms a linear correlation with fiber factor λf, which decreases with an increase in λf. The type of steel fiber has no obvious influence on SF/SF0. Both the fiber factor and type have no obvious influence on the compressive strength. In this study, fcu and fcu0 are the cubic  Figure 6 shows the relationship between fiber length l f and the maximum particle size of aggregate MA. To ensure an efficient reinforced effect of steel fibers, l f /MA should be larger than 1.33 in vibrated-compacting SFRC [63]. It can be seen that 99% of l f /MA are larger than 1.33 in SC-SFRC. l f /MA decreases with the increasing MA and 94% of l f /MA are between 1.5 and 6.5.   Figure 6 shows the relationship between fiber length lf and the maximum particle size of aggregate MA. To ensure an efficient reinforced effect of steel fibers, lf/MA should be larger than 1.33 in vibrated-compacting SFRC [63]. It can be seen that 99% of lf/MA are larger than 1.33 in SC-SFRC. lf/MA decreases with the increasing MA and 94% of lf/MA are between 1.5 and 6.5. The influences of steel fiber on the fresh and hardened performances of SC-SFRC are shown in Figure 7. SF and SF0 are the slump flows of SC-SFRC and the referenced SCC, respectively. The ratio of the slump flow SF/SF0 forms a linear correlation with fiber factor λf, which decreases with an increase in λf. The type of steel fiber has no obvious influence on SF/SF0. Both the fiber factor and type have no obvious influence on the compressive strength. In this study, fcu and fcu0 are the cubic The influences of steel fiber on the fresh and hardened performances of SC-SFRC are shown in Figure 7. SF and SF 0 are the slump flows of SC-SFRC and the referenced SCC, respectively. The ratio of the slump flow SF/SF 0 forms a linear correlation with fiber factor λ f , which decreases with an increase in λ f . The type of steel fiber has no obvious influence on SF/SF 0 . Both the fiber factor and type have no obvious influence on the compressive strength. In this study, f cu and f cu0 are the cubic compressive strengths of SC-SFRC and the referenced SCC, respectively. We determined that 89.4% of the ratios of cubic compressive strength f cu /f cu0 ranged from 0.85 to 1.15.

Calculation Model of Water-to-Binder Ratio for SC-SFRC
The calculation model of w/b for the vibrated-compacting concrete in Chinese standard JGJ/T 55 [64] is: where fcu,0 is the designed cubic compressive strength of concrete; αa and αb are coefficients mainly related to the type of coarse aggregate; and fb is the compressive strength of binder materials at 28 days (MPa), which can be predicted by formula (2), when there is no measured value. b f s ce f f = γ γ (2) where fce is the compressive strength of cement at 28 days; γf is the influence coefficient of fly ash, which can be taken as values listed in Table 2 [65]; and γs is the influence coefficient of slag powder, which can be taken as the values specified in JGJ/T 55 [64]. With a similar influence, stone powder has the same influence coefficient with fly ash. Moreover, the influence coefficient of silica fume is taken as 1.0 conservatively in the following sections.

Calculation Model of Water-to-Binder Ratio for SC-SFRC
The calculation model of w/b for the vibrated-compacting concrete in Chinese standard JGJ/T 55 [64] is: where f cu,0 is the designed cubic compressive strength of concrete; α a and α b are coefficients mainly related to the type of coarse aggregate; and f b is the compressive strength of binder materials at 28 days (MPa), which can be predicted by Formula (2), when there is no measured value.
where f ce is the compressive strength of cement at 28 days; γ f is the influence coefficient of fly ash, which can be taken as values listed in Table 2 [65]; and γ s is the influence coefficient of slag powder, which can be taken as the values specified in JGJ/T 55 [64]. With a similar influence, stone powder has the same influence coefficient with fly ash. Moreover, the influence coefficient of silica fume is taken as 1.0 conservatively in the following sections.
where β is the replacement ratio by the mass of mineral admixture in binder materials; and γ is the influence coefficient of mineral admixtures. These values are 0.4 and 0.9 for fly ash with β ≤ 0.3 and slag powder with β ≤ 0.4, respectively.
In fact, both Equations (1) and (3) have a form of reciprocal function and are identical in essence, which could be expressed in one form: where κ is the influence coefficient of mineral admixture on the compressive strength of cement. (4) can be transformed to Equation (5).
With b/w as the x-axis and f cu /f b as the y-axis, Figure 8    The different coefficients reflect the different changes in w/b with cubic compressive strength fcu. With the same w/b, fcu of SCC is about 7-10 MPa lower than that of vibrated-compacting concrete [30]. For SC-SFRC, a w/b lower than that of vibrated-compacting concrete and higher than that of SCC is needed to achieve the same fcu. Thus, Equation (1) with αa = 0.270 and αb = −0.522 is advised for the mix proportion design of SC-SFRC.

Designed Tensile Strength of SC-SFRC
Steel fibers obviously strengthen the splitting tensile strength in SC-SFRC [20,60]. The calculation model of designed tensile strength fft for SC-SFRC is shown as Equation (6) [60].
where ft is the tensile strength of referenced SCC, which could be accurately estimated by using the EC-2 model [67][68][69]; αte is the coefficient related to the effective fiber distribution; and αtb is a coefficient that colligated the other factors, which influence the bridging effects of steel fibers in the splitting tensile test.
A total of 89 groups of splitting tensile test data in the experimental database were used to verify Equation (6). There were different advised values of αtbαte for different types of steel fibers according to Chinese standard JGT 472 [63]. The tested splitting tensile strength ft of SCC in the same strength grade was used to calculate the tensile strength fft,c of SC-SFRC. Apart from αtbαte = 0.5, the SC-SFRC with crimped steel fiber and cubic compressive strength of the referenced SCC ranged from 20 MPa to 60 MPa [60]. Moreover, a simple formula (7) was used to calculate the tensile strength of SC-SFRC with hybrid steel fibers based on the previous study of concrete with hybrid steel fibers [70]. Considering the reliability of cubic compressive strength with a probability of 95% in the mix proportion design, α a = 0.270 and α ab = 0.141 for SC-SFRC are obtained. Thus, α b = -α ab /α a = −0.522.
The different coefficients reflect the different changes in w/b with cubic compressive strength f cu . With the same w/b, f cu of SCC is about 7-10 MPa lower than that of vibrated-compacting concrete [30]. For SC-SFRC, a w/b lower than that of vibrated-compacting concrete and higher than that of SCC is needed to achieve the same f cu . Thus, Equation (1) with α a = 0.270 and α b = −0.522 is advised for the mix proportion design of SC-SFRC.

Designed Tensile Strength of SC-SFRC
Steel fibers obviously strengthen the splitting tensile strength in SC-SFRC [20,60]. The calculation model of designed tensile strength f ft for SC-SFRC is shown as Equation (6) [60].
where f t is the tensile strength of referenced SCC, which could be accurately estimated by using the EC-2 model [67][68][69]; α te is the coefficient related to the effective fiber distribution; and α tb is a coefficient that colligated the other factors, which influence the bridging effects of steel fibers in the splitting tensile test. A total of 89 groups of splitting tensile test data in the experimental database were used to verify Equation (6). There were different advised values of α tb α te for different types of steel fibers according to Chinese standard JGT 472 [63]. The tested splitting tensile strength f t of SCC in the same strength grade was used to calculate the tensile strength f ft,c of SC-SFRC. Apart from α tb α te = 0.5, the SC-SFRC with crimped steel fiber and cubic compressive strength of the referenced SCC ranged from 20 MPa to 60 MPa [60]. Moreover, a simple Formula (7) was used to calculate the tensile strength of SC-SFRC with hybrid steel fibers based on the previous study of concrete with hybrid steel fibers [70].
where κ t is a coefficient of the hybrid effect for concrete with hybrid steel fibers. For concrete with hybrid steel fibers, κ t > 1 means a positive hybrid effect between steel fibers while κ t < 1 means a negative hybrid effect between steel fibers. For SC-SFRC mixed with hooked-end and straight steel fibers in this study, κ t ≈ 1. It means that the hybrid effect did not exist in the hooked-end steel fiber and straight steel fiber with lengths that were smaller than 10 mm. Figure 9 and Table 3 provide the detailed comparison of calculated tensile strength f ft,c and tested tensile strength f ft,t of SC-SFRC. The results show that Equation (6) with advised values of α tb α te is suitable for predicting the tensile strength of SC-SFRC with the steel fibers of hooked-end, crimped, milled, indentation and large-end. Equation (6) with advised values of α tb α te obviously underestimates the tensile strength of SC-SFRC with spiral steel fibers and overestimates that of SC-SFRC with straight steel fibers.
where κt is a coefficient of the hybrid effect for concrete with hybrid steel fibers. For concrete with hybrid steel fibers, κt > 1 means a positive hybrid effect between steel fibers while κt <1 means a negative hybrid effect between steel fibers. For SC-SFRC mixed with hooked-end and straight steel fibers in this study, κt ≈ 1. It means that the hybrid effect did not exist in the hooked-end steel fiber and straight steel fiber with lengths that were smaller than 10 mm. Figure 9 and Table 3 provide the detailed comparison of calculated tensile strength fft,c and tested tensile strength fft,t of SC-SFRC. The results show that Equation (6) with advised values of αtbαte is suitable for predicting the tensile strength of SC-SFRC with the steel fibers of hooked-end, crimped, milled, indentation and large-end. Equation (6) with advised values of αtbαte obviously underestimates the tensile strength of SC-SFRC with spiral steel fibers and overestimates that of SC-SFRC with straight steel fibers.

Conclusions
Based on the statistical analyses of test data for SC-SFRC, the following conclusions are drawn: SC-SFRC has differences in the mix proportion compared with SCC. SC-SFRC usually has higher contents of binder paste and fine aggregate, higher sand ratio, lower content and smaller maximum particle size of coarse aggregates. Based on the content of coarse aggregates in the mix proportion, SC-SFRC could be divided into LC-type and NC-type. LC-type SC-SFRC has a significantly lower content of coarse aggregate and higher sand ratio compared with NC-type SC-SFRC. Most of the steel fibers used in SC-SFRC have lengths less than 37.5 mm, aspect ratios less than 70 and fiber factors no more than 0.45. The ratio of slump flows between SC-SFRC and the referenced SCC decreased with an increase in the fiber factor.

Conclusions
Based on the statistical analyses of test data for SC-SFRC, the following conclusions are drawn: SC-SFRC has differences in the mix proportion compared with SCC. SC-SFRC usually has higher contents of binder paste and fine aggregate, higher sand ratio, lower content and smaller maximum particle size of coarse aggregates. Based on the content of coarse aggregates in the mix proportion, SC-SFRC could be divided into LC-type and NC-type. LC-type SC-SFRC has a significantly lower content of coarse aggregate and higher sand ratio compared with NC-type SC-SFRC. Most of the steel fibers used in SC-SFRC have lengths less than 37.5 mm, aspect ratios less than 70 and fiber factors no more than 0.45. The ratio of slump flows between SC-SFRC and the referenced SCC decreased with an increase in the fiber factor.
Based on the calculation model of water-to-binder ratio in Chinese standard JGJ/T 55, suitable coefficients are advised for the mix proportion design of SC-SFRC. The calculation model of the designed tensile strength with advised coefficients according to Chinese standard JGT 472 is suitable for SC-SFRC with steel fibers of hooked-end, milled, indentation and large-end. The calculation model of the designed tensile strength with coefficients proposed in the authors' previous study is suitable for SC-SFRC with crimped steel fibers. More adjustments in the mix proportion design of SC-SFRC, such as determining the dosages of binder materials and water and optimizing sand ratios, need to be further studied.    Note: N is the number of groups in references. A group of test data is a set of results tested from SC-SFRC with the same mix proportion and type and content of steel fiber in the reference.