Complete Stress–Strain Curves of Self-Compacting Steel Fiber Reinforced Expanded-Shale Lightweight Concrete under Uniaxial Compression

To expand the structural application of steel fiber reinforced expanded-shale lightweight concrete (SFRELC), a self-compacting SFRELC with high-workability was developed based on previous research. As part of the investigation, the present study focuses on the adaptability of formulas used for the complete stress–strain curves of steel fiber reinforced lightweight-aggregate concrete and conventional concrete under uniaxial compression. On the basis of mix proportion of SFRELC, self-compacting SFRELC was designed with the volume fraction of steel fiber as 0%, 0.4%, 0.8%, 1.2%, 1.6%, and 2.0%. Eighteen cylindrical specimens with dimensions of Φ150 mm × 300 mm were tested to measure the uniaxial compressive stress–strain curves of self-compacting SFRELC. Results indicated that, with the increasing volume fraction of steel fiber, the compressive strain at the peak-stress of the stress–strain curve increased, while the slope of the descending portion decreased. This increased the energy absorption of self-compacting SFRELC with a higher compression toughness. With a comparison of test results between four groups of calculation models, a group of formulas is selected to express the complete stress–strain curves of self-compacting SFRELC under uniaxial compression.


Introduction
In view of the brittleness of lightweight-aggregate concrete [1][2][3], and the utilization of local sintered expanded-shale as fine and coarse aggregates, a new concrete material called steel fiber reinforced expanded-shale lightweight concrete (SFRELC) was developed. To investigate SFRELC with different flowabilities, classified as plastic, flowing, and high flowing with the slump varied from 60 mm to 200 mm, a series of experimental investigations have been performed to study the mechanical properties, including compressive strength and toughness, tensile strength, flexural strength and toughness, deformation and modulus of elasticity, strength developments and complete stress-strain curves [4][5][6][7][8][9][10][11][12], carbonization and freeze-thaw resistance [10,13], as well as autogenous and drying

Raw Materials
Common Portland cement meeting the requirements of China code GB 175 was used [38], of which the physical and mechanical properties are presented in Table 1. Fly ash satisfying the indices of class-II specified in China code GB/T1596 [39] was used as the admixture, the density was 2070 kg/m 3 , the residual amount on a square hole sieve of 45 μm was 20%, and the water demand ratio was about 92%. As in the previous study [9,11] and presented in Figure 1a,b, high-strength sintering expanded shales in continuous gradation of 5-20 mm was used for the coarse aggregate, and the ceramsite sand, the byproduct of sintering expanded shale sieved as continuous gradation within 0.16-5 mm was used for the fine aggregate. The grading curves of coarse expanded-shales and ceramsite sand are drawn in Figure 2, their particle gradation basically met the requirement in China code GB/T 17431.2 [40]. The physical and mechanical properties are listed in Table 2, and the water absorption curves are displayed in Figure 3 to be used as the basis of selecting the presoaking time. At the same time, the 24 h water absorptions of expanded shale and ceramsite sand were measured as 7.45% and 9.75%. Due to the water absorptions within 1 h reaching 93.5%% and 92.6% of 24 h water absorptions for expanded shale and ceramsite sand respectively, the rational presoaking time was chosen as 1 h. The steel fiber exhibited in Figure 1c was crimped cut with thin-plate, the length lf = 36.7 mm, the equivalent diameter df = 1.35 mm, and the aspect ratio lf/df = 27.2. Others included the polycarboxylic acid superplasticizer with a water-reducing rate no less than 30%, and tap water as mixing water.

Mix Proportions
The water/binder ratio (w/b) was chosen as 0.30 to make the self-compacting SFRELC. The volume fraction of steel fiber vf = 0%, 0.4%, 0.8%, 1.2%, 1.6%, and 2.0%, respectively. The volume ratio of ceramsite sand was 50% when vf = 0%, 0.4%, and 0.8%, and then increased 0.2% with the increment of vf = 0.4%. About 30% mass of cement was replaced by fly-ash. The details of mix proportion are presented in Table 3. Where the dosage of super-plasticizer was determined through testing according to the workability of fresh self-compacting SFRELC. As the saturated dry surface condition of expanded shale and ceramsite sand was adopted for the preparation of a fresh mixture of SFRELC, the dosage of presoaking water with 1 h water absorption was added additionally.

Mix Proportions
The water/binder ratio (w/b) was chosen as 0.30 to make the self-compacting SFRELC. The volume fraction of steel fiber vf = 0%, 0.4%, 0.8%, 1.2%, 1.6%, and 2.0%, respectively. The volume ratio of ceramsite sand was 50% when vf = 0%, 0.4%, and 0.8%, and then increased 0.2% with the increment of vf = 0.4%. About 30% mass of cement was replaced by fly-ash. The details of mix proportion are presented in Table 3. Where the dosage of super-plasticizer was determined through testing according to the workability of fresh self-compacting SFRELC. As the saturated dry surface condition of expanded shale and ceramsite sand was adopted for the preparation of a fresh mixture of SFRELC, the dosage of presoaking water with 1 h water absorption was added additionally.

Mix Proportions
The water/binder ratio (w/b) was chosen as 0.30 to make the self-compacting SFRELC. The volume fraction of steel fiber v f = 0%, 0.4%, 0.8%, 1.2%, 1.6%, and 2.0%, respectively. The volume ratio of ceramsite sand was 50% when v f = 0%, 0.4%, and 0.8%, and then increased 0.2% with the increment of v f = 0.4%. About 30% mass of cement was replaced by fly-ash. The details of mix proportion are presented in Table 3. Where the dosage of super-plasticizer was determined through testing according to the workability of fresh self-compacting SFRELC. As the saturated dry surface condition of expanded shale and ceramsite sand was adopted for the preparation of a fresh mixture of SFRELC, the dosage of presoaking water with 1 h water absorption was added additionally.

Test Methods
The expanded shale and ceramsite sand were presoaked for 1 h, and then mixed with cement, fly ash and steel fiber using a horizontal spindle forced mixer. The workability of fresh self-compacting SFRELC was measured according to the specifications in China code JGJ/T283 [41]. Three cubic specimens with dimension of 150 mm were used to test the compressive strength, three cylinder specimens with dimensions of Φ150 mm × 300 mm were used for measuring the uniaxial compressive stress-strain curves, and the mean values were adopted in accordance with the test method in China standards GB/T50081 [42], CECS13:2009 [43], and ACI 544.4R [44]. Specimens were cured in a standard curing room at (20 ± 2) • C temperature and 95% RH for 28 days before testing.
With the requirement of the sufficient rigidity of test machine to get a complete stress-strain curve of concrete under uniaxial compression [11], a 3000 kN electro-hydraulic servo universal testing machine with sufficient rigidity and higher loading control precision made by SANS Co. Ltd., as exhibited in Figure 4, was used as a loading device in this study. The loading speed was maintained as the strain rate among (20-50) × 10 −6 /s. The stress and strain data were measured by a load transducer and two displacement meters on two symmetric sides of each specimen.

Test Methods
The expanded shale and ceramsite sand were presoaked for 1 h, and then mixed with cement, fly ash and steel fiber using a horizontal spindle forced mixer. The workability of fresh selfcompacting SFRELC was measured according to the specifications in China code JGJ/T283 [41]. Three cubic specimens with dimension of 150 mm were used to test the compressive strength, three cylinder specimens with dimensions of Φ150 mm × 300 mm were used for measuring the uniaxial compressive stress-strain curves, and the mean values were adopted in accordance with the test method in China standards GB/T50081 [42], CECS13:2009 [43], and ACI 544.4R [44]. Specimens were cured in a standard curing room at (20 ± 2) °C temperature and 95% RH for 28 days before testing.
With the requirement of the sufficient rigidity of test machine to get a complete stress-strain curve of concrete under uniaxial compression [11], a 3000 kN electro-hydraulic servo universal testing machine with sufficient rigidity and higher loading control precision made by SANS Co. Ltd., as exhibited in Figure 4, was used as a loading device in this study. The loading speed was maintained as the strain rate among (20-50) × 10 −6 /s. The stress and strain data were measured by a load transducer and two displacement meters on two symmetric sides of each specimen.   With the vf increasing from 0% to 2.0%, the slump flow and J-ring slump flow deceased 13.5% and 27.9%, respectively, while the T500 increased from 2.35 s to 7.04 s. The maximum value of T500 took place corresponding to the minimum slump flow at vf = 1.2%. This is due to the insufficient dosage of water reducer. The J-ring slump-flow expressed a faster reduction than the slump-flow, which indicated a fast declination of passing ability of self-compacting SFRELC with the increase of vf. In general, the slump-flows for all mixes of self-compacting SFRELC were 610-780 mm, which met the performance level SF1 and SF2 specified in China code JGJ/T283 [41]. J-ring slump flows were 505-715 mm, and the T500 was longer than 2 s. This met the requirements of a reinforced concrete structure cast by self-compacting SFRELC [34,36].  With the v f increasing from 0% to 2.0%, the slump flow and J-ring slump flow deceased 13.5% and 27.9%, respectively, while the T 500 increased from 2.35 s to 7.04 s. The maximum value of T 500 took place corresponding to the minimum slump flow at v f = 1.2%. This is due to the insufficient dosage of water reducer. The J-ring slump-flow expressed a faster reduction than the slump-flow, which indicated a fast declination of passing ability of self-compacting SFRELC with the increase of v f . In general, the slump-flows for all mixes of self-compacting SFRELC were 610-780 mm, which met the performance level SF1 and SF2 specified in China code JGJ/T283 [41]. J-ring slump flows were 505-715 mm, and the T 500 was longer than 2 s. This met the requirements of a reinforced concrete structure cast by self-compacting SFRELC [34,36]. As presented in Figure 8, the air content of self-compacting SFRELC were more and more sensitive with the addition of steel fiber, especially when vf was over 1.2%. The air content grew slightly when vf = 0-1.2% but had a great increase from 4.4% to 6.2% when vf varied from 1.6% to 2.0%. However, the densities of self-compacting SFRELC increased with vf despite the increase of air content. This is due to the larger density of steel fiber. It should be noted that the higher air content may lead the reduce of the densities of self-compacting SFRELC, as displayed in Figure 9. The dry density of self-compacting SFRELC ranges from 1542 kg/m 3 to 1784 kg/m 3 . It is about 25.7-35.8% lower than that of NWC. As presented in Figure 8, the air content of self-compacting SFRELC were more and more sensitive with the addition of steel fiber, especially when vf was over 1.2%. The air content grew slightly when vf = 0-1.2% but had a great increase from 4.4% to 6.2% when vf varied from 1.6% to 2.0%. However, the densities of self-compacting SFRELC increased with vf despite the increase of air content. This is due to the larger density of steel fiber. It should be noted that the higher air content may lead the reduce of the densities of self-compacting SFRELC, as displayed in Figure 9. The dry density of self-compacting SFRELC ranges from 1542 kg/m 3 to 1784 kg/m 3 . It is about 25.7-35.8% lower than that of NWC. As presented in Figure 8, the air content of self-compacting SFRELC were more and more sensitive with the addition of steel fiber, especially when vf was over 1.2%. The air content grew slightly when vf = 0-1.2% but had a great increase from 4.4% to 6.2% when vf varied from 1.6% to 2.0%. However, the densities of self-compacting SFRELC increased with vf despite the increase of air content. This is due to the larger density of steel fiber. It should be noted that the higher air content may lead the reduce of the densities of self-compacting SFRELC, as displayed in Figure 9. The dry density of self-compacting SFRELC ranges from 1542 kg/m 3 to 1784 kg/m 3 . It is about 25.7-35.8% lower than that of NWC. As presented in Figure 8, the air content of self-compacting SFRELC were more and more sensitive with the addition of steel fiber, especially when v f was over 1.2%. The air content grew slightly when v f = 0-1.2% but had a great increase from 4.4% to 6.2% when v f varied from 1.6% to 2.0%. However, the densities of self-compacting SFRELC increased with v f despite the increase of air content. This is due to the larger density of steel fiber. It should be noted that the higher air content may lead the reduce of the densities of self-compacting SFRELC, as displayed in  Figure 10 presents the uniaxial compressive stress-strain curves of tested self-compacting SFRELC. With the increase of vf, the curves had a trend with a steeper slope at the ascending portion and slower slope at the descending portion. The peak-stress fc,r and corresponding strain εc,r trend increased linearly. 24
The test results of peak-stress (fc,r) and peak strain (εc,r) are summarized in Table 4 and exhibited in Figure 11, while the variation of cubic compressive strength fcu is also displayed, in which the fiber factor λf = lf/df·vf = 27.2vf. It can be seen that the compressive strengths and peak strains increased with the vf due to the enhanced restraining effect of steel fiber on the transversal deformation of the  Figure 10 presents the uniaxial compressive stress-strain curves of tested self-compacting SFRELC. With the increase of vf, the curves had a trend with a steeper slope at the ascending portion and slower slope at the descending portion. The peak-stress fc,r and corresponding strain εc,r trend increased linearly. 24
The test results of peak-stress (fc,r) and peak strain (εc,r) are summarized in Table 4 and exhibited in Figure 11, while the variation of cubic compressive strength fcu is also displayed, in which the fiber factor λf = lf/df·vf = 27.2vf. It can be seen that the compressive strengths and peak strains increased with the vf due to the enhanced restraining effect of steel fiber on the transversal deformation of the  Figure 10 presents the uniaxial compressive stress-strain curves of tested self-compacting SFRELC. With the increase of v f , the curves had a trend with a steeper slope at the ascending portion and slower slope at the descending portion. The peak-stress f c,r and corresponding strain ε c,r trend increased linearly.  Figure 10 presents the uniaxial compressive stress-strain curves of tested self-compacting SFRELC. With the increase of vf, the curves had a trend with a steeper slope at the ascending portion and slower slope at the descending portion. The peak-stress fc,r and corresponding strain εc,r trend increased linearly. 24
The test results of peak-stress (fc,r) and peak strain (εc,r) are summarized in Table 4 and exhibited in Figure 11, while the variation of cubic compressive strength fcu is also displayed, in which the fiber factor λf = lf/df·vf = 27.2vf. It can be seen that the compressive strengths and peak strains increased with the vf due to the enhanced restraining effect of steel fiber on the transversal deformation of the The test results of peak-stress (f c,r ) and peak strain (ε c,r ) are summarized in Table 4 and exhibited in Figure 11, while the variation of cubic compressive strength f cu is also displayed, in which the fiber factor λ f = l f /d f ·v f = 27.2v f . It can be seen that the compressive strengths and peak strains increased with the v f due to the enhanced restraining effect of steel fiber on the transversal deformation of the specimen. With the v f varying from 0% to 2.0%, the increments of f cu , f c,r and ε c,r are 35.5%, 51.3% and 27.1%. According to the fitting formulas in Figure 11, the increment ratio of f cu , f c,r and ε c,r with the increase of v f are 0.562, 1.090 and 0.227, respectively. This indicates that the effect of steel fiber on f c,r is higher than that on the f cu , and the values of f c,r /ε c,r namely the secant modulus increase with the addition of steel fiber. The slope of ascending portion increased with the increasing volume fraction of steel fiber. Values of f c,r are about 0.6-0.8 times of f cu in Table 4, which are lower than that reported in the experiments of Li et al. [7] of flowing SFRELC with the same raw materials and mix proportions. This may be attributed to the slower loading rate having a significant effect on the testing results.   Figure 11. Variation of f cu , f c,r and ε c,r with a varying λ f .
According to China code GB50010 [45], ε cu was defined as the strain corresponding to 0.5f c,r at the descending portion of stress-strain curves. The test results are presented in Table 4, and exhibited in Figure 12 as the relative values of ε cu /ε c,r with a varying λ f . The obvious increasing relationship between ε cu /ε c,r and λ f indicates that the ductility of self-compacting SFRELC after breaking was promoted by the addition of steel fibers. With the v f increased from 0% to 2.0%, ε cu /ε c,r was from 1.87 to 7.11, 2.8 times increase. The maximum value was achieved at v f = 1.2%. specimen. With the vf varying from 0% to 2.0%, the increments of fcu, fc,r and εc,r are 35.5%, 51.3% and 27.1%. According to the fitting formulas in Figure 11, the increment ratio of fcu, fc,r and εc,r with the increase of vf are 0.562, 1.090 and 0.227, respectively. This indicates that the effect of steel fiber on fc,r is higher than that on the fcu, and the values of fc,r/εc,r namely the secant modulus increase with the addition of steel fiber. The slope of ascending portion increased with the increasing volume fraction of steel fiber. Values of fc,r are about 0.6-0.8 times of fcu in Table 4, which are lower than that reported in the experiments of Li et al. [7] of flowing SFRELC with the same raw materials and mix proportions. This may be attributed to the slower loading rate having a significant effect on the testing results.  Figure 11. Variation of fcu, fc,r and εc,r with a varying λf.
According to China code GB50010 [45], εcu was defined as the strain corresponding to 0.5fc,r at the descending portion of stress-strain curves. The test results are presented in Table 4, and exhibited in Figure 12 as the relative values of εcu/εc,r with a varying λf. The obvious increasing relationship between εcu/εc,r and λf indicates that the ductility of self-compacting SFRELC after breaking was promoted by the addition of steel fibers. With the vf increased from 0% to 2.0%, εcu/εc,r was from 1.87 to 7.11, 2.8 times increase. The maximum value was achieved at vf = 1.2%.   Table 4 summarizes the test results of compression absorbed energy (W c,1.0 ) and compression toughness ratio (R e,1.0 ). The W c,1.0 was calculated by the area under the compressive load-deformation curve within the uniaxial compressive deformation of 1.0% standard gauge length of 150 mm, as presented in Figure 13. R e,1.0 was used to evaluate the energy absorption ability of self-compacting SFRELC during compression deformation, which can be calculated as follows [9]. (1) where, N p is the peak compressive load, L 0 is the standard gauge length.  Table 4 summarizes the test results of compression absorbed energy (Wc,1.0) and compression toughness ratio (Re,1.0). The Wc,1.0 was calculated by the area under the compressive load-deformation curve within the uniaxial compressive deformation of 1.0% standard gauge length of 150 mm, as presented in Figure 13. Re,1.0 was used to evaluate the energy absorption ability of self-compacting SFRELC during compression deformation, which can be calculated as follows [9].  This indicates that the crack-bridging effect of smaller amount steel fibers mainly reflects at the pre-peak to arrest the transversal expanded deformation. With the vf varying from 0.4% to 1.2%, the toughening effect of steel fiber was outstanding, and the increments of Wc,1.0 and Re,1.0 were 59% and 54.5%, respectively. When the vf increased to 1.6% or 2.0%, Wc,1.0 and Re,1.0 had no significant promotion. This may be due to the unfavorable effect of large content steel fibers on the compactness of self-compacting SFRELC, which results in the decrease of loading capacities after peak loads. According to previous test results [9], the Re,1.0 of vibro-compacting SFRELC increased, even when vf was up to 2.0%. It can be said that the self-compacting SFRELC has a higher sensibility for steel fibers than the vibro-compacting SFRELC, and the volume fraction of steel fiber in self-compacting SFRELC should not be greater than 1.2%.   Figure 14 presents the variations of compression absorbed energy (W c,1.0 ) and compression toughness ratio (R e,1.0 ). With the v f = 0.4%, the presence of steel fiber improves W c,1.0 about 30% but almost no enhancement on R e,1.0 . This indicates that the crack-bridging effect of smaller amount steel fibers mainly reflects at the pre-peak to arrest the transversal expanded deformation. With the v f varying from 0.4% to 1.2%, the toughening effect of steel fiber was outstanding, and the increments of W c,1.0 and R e,1.0 were 59% and 54.5%, respectively. When the v f increased to 1.6% or 2.0%, W c,1.0 and R e,1.0 had no significant promotion. This may be due to the unfavorable effect of large content steel fibers on the compactness of self-compacting SFRELC, which results in the decrease of loading capacities after peak loads. According to previous test results [9], the R e,1.0 of vibro-compacting SFRELC increased, even when v f was up to 2.0%. It can be said that the self-compacting SFRELC has a higher sensibility for steel fibers than the vibro-compacting SFRELC, and the volume fraction of steel fiber in self-compacting SFRELC should not be greater than 1.2%.  Table 4 summarizes the test results of compression absorbed energy (Wc,1.0) and compression toughness ratio (Re,1.0). The Wc,1.0 was calculated by the area under the compressive load-deformation curve within the uniaxial compressive deformation of 1.0% standard gauge length of 150 mm, as presented in Figure 13. Re,1.0 was used to evaluate the energy absorption ability of self-compacting SFRELC during compression deformation, which can be calculated as follows [9].  This indicates that the crack-bridging effect of smaller amount steel fibers mainly reflects at the pre-peak to arrest the transversal expanded deformation. With the vf varying from 0.4% to 1.2%, the toughening effect of steel fiber was outstanding, and the increments of Wc,1.0 and Re,1.0 were 59% and 54.5%, respectively. When the vf increased to 1.6% or 2.0%, Wc,1.0 and Re,1.0 had no significant promotion. This may be due to the unfavorable effect of large content steel fibers on the compactness of self-compacting SFRELC, which results in the decrease of loading capacities after peak loads. According to previous test results [9], the Re,1.0 of vibro-compacting SFRELC increased, even when vf was up to 2.0%. It can be said that the self-compacting SFRELC has a higher sensibility for steel fibers than the vibro-compacting SFRELC, and the volume fraction of steel fiber in self-compacting SFRELC should not be greater than 1.2%.

The Proposal Model
According to the China code GB50010 and previous report [11,45], the complete stress-strain curve of lightweight aggregate concrete and vibro-compacting SFRELC can be expressed as Formulas (2)-(4). The ascending portion of the curves were calculated by Formula (2), and the coefficient n was determined by Formula (3). The descending portions of curves were fitted using Formula (4), in which α c and b are statistical parameters relating to the shape of descending portion of the stress-strain curve of lightweight aggregate concrete. According to the calculation model in report [11], α c is calculated by Formula (5). For vibro-compacting SFRELC, α cf and b f have the same meanings with α c and b, and can be calculated by Formulas (6) and (7).
where, σ c and ε c are the stress and the strain at any point of stress-strain curve, n is a material parameter that depends on the shape of stress-strain curves, f c,r and ε c,r are the peak-stress and the peak-strain respectively, E c is the modulus of elasticity of concrete. λ f is the fiber factor.
The tested values of α cf /α c and b f /b for self-compacting SFRELC are displayed in Figures 15 and 16. A good fitness can be achieved compared with the calculation results of Formulas (6) and (7). The relationship between εcu/εc,r and αc or αc,f is shown in Figure 17, which fits the formula (8) specified in China Code GB50010 for conventional concrete as follows [45],

Aslani' Model
Aslani's model for compressive stress-strain curves is the same in form with formula (2) [32][33][34]. The material parameter n can be calculated by formulas (9)- (14). The relationship between ε cu /ε c,r and α c or α c,f is shown in Figure 17, which fits the Formula (8) specified in China Code GB50010 for conventional concrete as follows [45], The relationship between εcu/εc,r and αc or αc,f is shown in Figure 17, which fits the formula (8) specified in China Code GB50010 for conventional concrete as follows [45],

Cunha' and FIP Model
The basic form for Cunha's model and the FIP model [35][36][37] is presented as Formulas (15)- (17). When ε c ≤ ε c,lim , When ε c ≥ ε c,lim , where, ε c,lim is the limited strain at stress of αf c,r which may be calculated by Formula (18).
For Cunha's model, the parameter α is related to the curing age t of concrete as presented in Formula (19), and value of α at curing age t = 28d is 0.9. α = 0.9 exp 0.005 1 − ( 28 t ) 1.16 (19) For the FIP model, α = 0.5.

Fitness with Tested Curves
The tested compressive stress-strain curves are compared with the proposed model, Aslani's model, Cunha's model, and the FIP model, respectively. As exhibited in Figure 18, the good fitness by the four calculation models are in the order of the proposed model, Aslani's model, Cunha's model, and the FIP model. Based on the numerical analysis of test data, a similar conclusion will be obtained.
In this paper, the average predictive ratio of calculate to test stress (AVG) and coefficient of variation (COV) at the same strain are used to evaluate the degree of fitting. Formulas (20)-(21) are used to calculate the AVG and COV of fitting curves with the four models and results are displayed in Table 5.
where, σ c is the stress at any point of stress-strain curve,; σ cal is the calculate stress at the same strain with σ c , and SD is the standard deviation of σ cal /σ c .
The tested compressive stress-strain curves are compared with the proposed model, Aslani's model, Cunha's model, and the FIP model, respectively. As exhibited in Figure 18, the good fitness by the four calculation models are in the order of the proposed model, Aslani's model, Cunha's model, and the FIP model. Based on the numerical analysis of test data, a similar conclusion will be obtained.     These results display that nearly all of the four models but Aslani's model have a good prediction for the ascending portion of the test curves. The proposed model is an effective predictor for complete test curves of self-compacting SFRELC. Aslani's model shows a good fitness for curves of v f = 0-0.8%, but slightly worse than the proposed model when v f = 1.2-2.0%. Both Cunha's model and the FIP model are inappropriate for the prediction of the descending portion in compressive stress-strain curves of self-compacting SFRELC.

Conclusions
Based on the test results and analysis, the following conclusions can be drawn: (1) Self-compacting SFRELC with a slump flow of larger than 600 mm was prepared in this experiment.
Slump-flow and J-ring slump-flow decreased while slump-flow time (T 500 ) increased with the increase of v f . Drying densities increased about 12.2% with the v f increased from 0% to 2.0%.
(2) With the increasing v f , the uniaxial compressive stress-strain curves of self-compacting SFRELC trends to be steep at ascending portion and a slower slope at descending portion. With the v f varying from 0% to 2.0%, the increments of f cu , f c,r and ε c,r are 35.5%, 51.3% and 27.1% respectively. Values of f c,r are about 0.6-0.8 times f cu , which may be attributed to the loading rate being slower than that used in the test of axial compressive strength. The residual strengths increased with the increase of volume fraction of steel fiber. (3) With the v f varied from 0.4% to 1.2%, the toughening effect of steel fiber was outstanding, and the increments of W c,1.0 and R e,1.0 are 59% and 54.5%, respectively. When the v f reached to 1.6% and 2.0%, the W c,1.0 and R e,1.0 had no significant promotion. Therefore, the optimal v f for self-compacting SFRELC can be taken as 1.2%. (4) Based on the values of AVG and COV for the predictive ratios, and a comparison of calculations and test curves, the proposed model has a good fitness with the tested curves of self-compacting SFRELC, and Aslani's model is slightly worse. Cunha's model and the FIP model are suitable for the ascending portion, but inappropriate for the descending portion. As such, the proposed model is suggested in this paper.