# Analysis and Prediction of Compressive Properties for Steel Fiber-and-Nanosilica-Reinforced Crumb Rubber Concrete

Authors: Danying Gao; Tao Zhang; Yihong Wang; Yiming Kong; Dawei Li; Yang Meng
Journal: Advances in Civil Engineering
 (2020)

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## Abstract

The disposal of waste tire rubber has gained more attention from the viewpoint of green, environmental protection, and sustainability. Numerous attempts have been stated on the properties of crumb rubber concrete (CRC) and observed that there is a large reduction of compressive strength and elastic modulus of CRC with the increase of the rubber substitution rate. Based on the CRC with the crumb rubber volume content of 5%, the steel fibers and nanosilica were added to CRC to make steel fiber-and-nanosilica-reinforced crumb rubber concrete (SFNS-CRC) in this paper. The effects of the steel fiber volume content and nanosilica content on the compressive properties of SFNS-CRC were studied, including compressive strength, elastic modulus, peak strain, compression toughness, and failure pattern. The test results indicated that the modulus of elasticity and compressive strength of SFNS-CRC have the increasing tendency with the addition of steel fibers and nanosilica. Moreover, the peak strains have a significant increase with the increase of the steel fiber content and nanosilica replacement ratio. The compressive stress-strain curves of SFNS-CRC gradually plump with the increase of the steel fibers and nanosilica. Finally, the prediction formulas for the compressive strength, elastic modulus, and peak strain of SFNS-CRC were set up. A simple predicted model of the stress-strain curve for SFNS-CRC was proposed, which considers the effect of steel fibers and nanosilica.


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## Body

## 1. Introduction

The rapid development of automobile industry has produced a lot of waste tire rubber. Disposal of waste tires has been a major environmental problem for the countries around the world. Recycling of used tires is becoming more and more important with the increasing landfills for used tires. It is urgent to seek the possible way to take advantage of waste tire rubber. It has been recognized that crushing waste tires into particles of different sizes and adding them to concrete is a sustainable and environmentally healthy way [1]. The concrete containing different rubber crumb particle sizes and contents was studied in depth in the past 30 years. The studies [2–4] found that the rubber content and size have a significant effect on the mechanical properties of concrete, and the compressive strength of rubber concrete decreases with the increase of the rubber content and particle size. Moreover, rubber particles also cause the reduction of concrete elastic modulus. However, it was reported that rubber can improve some mechanical properties of concrete such as brittleness resistance property, freezing-thawing, impact resistance, and toughness [5–9]. Thus, the rubberized concrete and rubberized asphalt were mainly used in roads and bridges due to their impact resistance and buffering properties [10,11]. The application of concrete with high rubber content in the building structure is limited because it greatly reduces the strength of concrete. In order to use CRC for the structural members and layers with high stress, it is necessary to increase the compressive and splitting tensile strength of CRC and to set up its constitutive equation. Li et al. [12] conducted the uniaxial compressive tests on the CRC with low rubber volume content; the uniaxial compressive constitutive models of low-volume rubber concrete were established and further improved through the incorporation of rubber particles equivalent to the sand ratio factor to predict the stress-strain relationship of rubber concrete and promote the application of rubber concrete in structural design.As a new type of reinforced material of concrete, steel fiber has excellent mechanical properties. Considerable studies have shown that adding steel fibers into concrete can improve the mechanical performance of concrete structural components, by delaying the development of microcracks into macrocracks, hindering the development of macrocracks and leading to stress redistribution [13–20]. Li and Li [21] studied the effects of 0.9% steel fiber volume fraction and 5% rubber particle content on the mechanical properties of high-strength concrete, including flexure, compression, and seismic behavior. It was found that, after adding 0.9% steel fibers into CRC, the compressive strength and elastic modulus of CRC increase slightly, while its flexural strength increases significantly. Ahmed et al. [22] compared the compression strength, modulus of elasticity, and stress-strain of rubberized steel fiber concrete with those of rubberized normal concrete. According to the results of analysis for the compressive test, it was reported that crumb rubber and steel fibers considerably affect the toughness of concrete. Moreover, Fu showed that the flexural toughness of steel fiber-reinforced rubberized concrete is highly enhanced due to the combined use of crumb rubber and steel fibers in the concrete mixture and the bridging effect of fibers and high elasticity of rubber [23].Incorporating the waste crumb rubber into the concrete to form CRC is an effective way to realize the resource recycling. Generally, the addition of crumb rubber may increase the deformability, fatigue performance, durability, shock absorption, and noise reduction performance of concrete but decrease its compressive strength and tensile strength. Recently, it has been found that the rubber content does not affect the bridging effect of the steel fibers on the surrounding concrete, and the positive synergy between the steel fibers and the rubber particles has the advantages of enhancing the shrinkage resistance and improving the fracture properties. However, the addition of steel fibers also increases the interfacial area of the concrete, which inevitably increases the presence of microscopic and macroscopic defects between the interfaces and weakens the strength. Adding the nanomaterial into concrete is an efficient means to develop durable and environmentally friendly high-performance concrete because nanosilica can promote the hydration of cement slurry and the formation of early calcium hydroxide, reduce the porosity of cement slurry and the dissolution of calcium, accelerate the pozzolanic reaction, make the microstructure of concrete more dense, and improve the strength, permeability, and wear resistance of concrete [24–31]. In addition, the inclusion of nanomaterials can refine the size of the pores and densify the interfacial transition zone between the cement matrix and the aggregate in hardened rubber concrete [32,33]. Therefore, the high-performance CRC reinforced by steel fibers and nanomaterials has the high compressive and splitting tensile strength, which meets the requirements of the engineering structure for high performance of concrete. In order to probe the coupling effect of crumb rubber, steel fibers, and nanosilica on the properties of concrete, this paper mainly investigated the compressive strength, elastic modulus, compression toughness, and stress-strain curve of steel fiber-and-nanosilica-reinforced crumb rubber concrete (SFNS-CRC) through the uniaxial compression test and finally presented a stress-strain model of SFNS-CRC subjected to uniaxial compression.


## 2. Experimental Program

### 2.1. Materials

The constituents of the CRC mixture used in the test were cement, fine aggregates, coarse aggregates, steel fibers, nanosilica, water, and crumb rubber with a diameter of 1-2 mm [34]. Portland cement (P. O 42.5) was used in all mixtures, which meets the Chinese standard “GB175-2007” [35]. The chemical composition and properties of cement are shown in Table 1. The coarse aggregate with a particle size of 5–20 mm and fine aggregate with a fineness modulus of 3.0 from riversides were used, which is compatible with the Chinese standard “GBT14684-2011” [36]. The rubber particle size was 1∼2 mm, which was made by the mechanical crushing of the discarded rubber tire. The particle size distributions of the fine aggregate, coarse aggregate, and crumb rubber are shown in Figure 1. The steel fiber used was a kind of hooked one at both ends with the tensile strength of 1345 MPa. Table 2 lists the geometrical and mechanical characteristics of the steel fiber. The nanosilica was white powder with an average particle size of 30 nm, and its apparent density was 40–60 g/l. The properties of nanosilica are given in Table 3. The amorphous structure of nanosilica was revealed by the XRD pattern, as shown in Figure 2. The brown yellow powder of the naphthalene water reducer with 25% water-reducing ratio was adopted to ensure that the slump of concrete was within the range of 20∼70 mm. The used materials and CRC mixture slump test are shown in Figure 3.Table 1
Chemical composition and properties of cement.
Specific surface area (m2/kg)
Specific gravity (kg/m3)
Setting time (min)
SO3 (%)
MgO (%)
Cl (%)
Loss on ignition (%)
Mortar strength (MPa)
350
3100
Initial
Final
2.26
2.21
0.015
3.82
3 days
28 days
172
230
25.6
45.8Figure 1
Particle size distribution of aggregates.Table 2
Geometrical and mechanical specifications of the steel fiber.
Fiber type
Lengthdf (mm)
Diameterlf (mm)
Aspect ratio (lf/df)
Tensile strength (MPa)
3D 35
0.55
35
65
1345Table 3
Properties of nanosilica.
Appearance
Purity (%)
Diameter (nm)
Specific surface area (m2/g)
Density (g/L)
pH value
High-dispersive white powder
≥99.5
30
200 ± 10
40∼60
5.0∼7.0Figure 2
XRD pattern of nanosilica.Figure 3
(a) Materials. (b) Concrete slump test.
(a)
(b)


### 2.2. Experimental Design and Mixing Proportion

The research for the reinforcing effects of the steel fibers and the nanosilica on the compression properties of CRC is the main purpose of the test. The strength grade C35 of CRC with 5% crumb rubber and the compressive strength of 35 MPa to 45 MPa was chosen as the control group. The mix proportions of crumb rubber were designed by following the principle of the volume percentage method, where 5% crumb rubber meant adding 50 kg crumb rubber into 1 m3 concrete. Based on CRC with 5% of the crumb rubber volume content, four steel fiber volume contents (νf) (0%, 0.5%, 1.0%, and 1.5%) were taken into consideration. Moreover, when the volume percentage of the steel fiber was 1.0%, three nanosilica replacement ratios (νN) (0%, 1%, and 2% by replacing the cement) were adopted. Details of the mixture proportion of SFNS-CRC are listed in Table 4.Table 4
Mix proportions of SFNS-CRC (unit: kg/m3).
Group
Crumb rubber
Cement
Coarse aggregate
Fine aggregate
Water
Water reducer
Steel fiber
Nanosilica
CR5SF0
50
400
703
1004
169
4
0
—
CR5SF0.5
50
419
705
1060
177
4.5
39 (0.5%)
—
CR5SF1
50
438
654
1045
185
5
78 (1%)
—
CR5SF1.5
50
457
604
1029
193
5
117 (1.5%)
—
CR5SF1NS1
50
433.62
654
1045
185
5
78 (1%)
4.38 (1%)
CR5SF1NS2
50
429.24
654
1045
185
5
78 (1%)
8.76 (2%)
Note: CR5SF1NS1 means the specimen with CR = 5%,νN = 1%, and νf = 1%.


### 2.3. Specimen Preparation and Curing

SFNS-CRC was mixed through a shaft mixer with 60 L capacity. All aggregates and steel fibers were put together and mixed for 2 minutes to ensure the steel fibers were uniformly dispersed. For the mixture of SFNS-CRC with the steel fiber content of 1.5% (117 kg/m3), the mixing times were extended until the mixture was dispersed to reduce the possibility of fiber balling due to uneven stirring. Then, the crumb rubbers and cement were added and mixed for another 2 minutes. Additionally, for the mix proportion including nanosilica, the nanosilica was added to water in advance and stirred uniformly. Then, the water reducer was added into water and stirred evenly. Finally, the water was added to the mixture and mixed for another 2 minutes. After the end of the mixing process, the slumps of concrete mixtures were tested immediately. For each group of SFNS-CRC, nine 150 mm × 150 mm × 300 mm prism specimens were cast for testing the prism compressive strength fc, elastic modulus Ec, and stress-stain curves, respectively, and three 150mm × 150mm × 150 mm cube specimens for testing cubic compressive strength fcu. All specimens were cast by using steel moulds and put on a vibration table for 20-second vibration to ensure compaction, demoulded after 24 hours, and then cured in a moisture room at approximately 95% relative humidity and 20°C temperature. The tests were performed after 28 days.


### 2.4. Test Procedures

The compressive strength, the modulus of elasticity, and the stress-strain curves were tested according to the specifications in Chinese standards GB/T50081 [37] and CECS13:2009 [38], respectively. Both the tests of compressive strength and modulus of elasticity were conducted in an electrohydraulic servo-controlled machine with a capacity of 3000 kN. The loading rate for the tests of compressive strength and modulus of elasticity tests was 0.5 MPa/s. Whitney [39] pointed out that sudden failure of the specimen was caused by the insufficient rigidity of the testing machine. In this paper, the four strong springs, as shown in Figure 4, were used as a rigid element to improve the stiffness of the whole test device, and the complete stress-strain curves were obtained. The specific loading scheme of the test was as follows: firstly, the specimens were taken out from the curing room, wiped to make them clean, checked whether the appearance was intact, and measured for the size to the accuracy of 1 mm; secondly, two displacement transducers were attached to the opposite sides of the section of the prism specimen to measure the deformation, and the measured load and deformation were recorded with a data acquisition system at a rate of once per second; thirdly, the preloading up to the 40% of prism compressive strength was carried out before formal loading at the loading speed of 0.6 MPa/s, while the displacement transducers on both sides were observed. The difference between the measured values of two displacement transducers could not exceed 30%. Otherwise, the adjustment for specimens should be carried out; fourthly, the formal loading was carried out after the preloading was completed. In the formal loading, the loading speed of 0.5 MPa/s was first used to 30% of the peak load, and then the loading speed was taken as 0.2 mm/min by displacement control, as shown in Figure 4.Figure 4
Testing arrangement for stress-strain curves: (a) general view; (b) layout.
(a)
(b)


## 2.1. Materials

The constituents of the CRC mixture used in the test were cement, fine aggregates, coarse aggregates, steel fibers, nanosilica, water, and crumb rubber with a diameter of 1-2 mm [34]. Portland cement (P. O 42.5) was used in all mixtures, which meets the Chinese standard “GB175-2007” [35]. The chemical composition and properties of cement are shown in Table 1. The coarse aggregate with a particle size of 5–20 mm and fine aggregate with a fineness modulus of 3.0 from riversides were used, which is compatible with the Chinese standard “GBT14684-2011” [36]. The rubber particle size was 1∼2 mm, which was made by the mechanical crushing of the discarded rubber tire. The particle size distributions of the fine aggregate, coarse aggregate, and crumb rubber are shown in Figure 1. The steel fiber used was a kind of hooked one at both ends with the tensile strength of 1345 MPa. Table 2 lists the geometrical and mechanical characteristics of the steel fiber. The nanosilica was white powder with an average particle size of 30 nm, and its apparent density was 40–60 g/l. The properties of nanosilica are given in Table 3. The amorphous structure of nanosilica was revealed by the XRD pattern, as shown in Figure 2. The brown yellow powder of the naphthalene water reducer with 25% water-reducing ratio was adopted to ensure that the slump of concrete was within the range of 20∼70 mm. The used materials and CRC mixture slump test are shown in Figure 3.Table 1
Chemical composition and properties of cement.
Specific surface area (m2/kg)
Specific gravity (kg/m3)
Setting time (min)
SO3 (%)
MgO (%)
Cl (%)
Loss on ignition (%)
Mortar strength (MPa)
350
3100
Initial
Final
2.26
2.21
0.015
3.82
3 days
28 days
172
230
25.6
45.8Figure 1
Particle size distribution of aggregates.Table 2
Geometrical and mechanical specifications of the steel fiber.
Fiber type
Lengthdf (mm)
Diameterlf (mm)
Aspect ratio (lf/df)
Tensile strength (MPa)
3D 35
0.55
35
65
1345Table 3
Properties of nanosilica.
Appearance
Purity (%)
Diameter (nm)
Specific surface area (m2/g)
Density (g/L)
pH value
High-dispersive white powder
≥99.5
30
200 ± 10
40∼60
5.0∼7.0Figure 2
XRD pattern of nanosilica.Figure 3
(a) Materials. (b) Concrete slump test.
(a)
(b)


## 2.2. Experimental Design and Mixing Proportion

The research for the reinforcing effects of the steel fibers and the nanosilica on the compression properties of CRC is the main purpose of the test. The strength grade C35 of CRC with 5% crumb rubber and the compressive strength of 35 MPa to 45 MPa was chosen as the control group. The mix proportions of crumb rubber were designed by following the principle of the volume percentage method, where 5% crumb rubber meant adding 50 kg crumb rubber into 1 m3 concrete. Based on CRC with 5% of the crumb rubber volume content, four steel fiber volume contents (νf) (0%, 0.5%, 1.0%, and 1.5%) were taken into consideration. Moreover, when the volume percentage of the steel fiber was 1.0%, three nanosilica replacement ratios (νN) (0%, 1%, and 2% by replacing the cement) were adopted. Details of the mixture proportion of SFNS-CRC are listed in Table 4.Table 4
Mix proportions of SFNS-CRC (unit: kg/m3).
Group
Crumb rubber
Cement
Coarse aggregate
Fine aggregate
Water
Water reducer
Steel fiber
Nanosilica
CR5SF0
50
400
703
1004
169
4
0
—
CR5SF0.5
50
419
705
1060
177
4.5
39 (0.5%)
—
CR5SF1
50
438
654
1045
185
5
78 (1%)
—
CR5SF1.5
50
457
604
1029
193
5
117 (1.5%)
—
CR5SF1NS1
50
433.62
654
1045
185
5
78 (1%)
4.38 (1%)
CR5SF1NS2
50
429.24
654
1045
185
5
78 (1%)
8.76 (2%)
Note: CR5SF1NS1 means the specimen with CR = 5%,νN = 1%, and νf = 1%.


## 2.3. Specimen Preparation and Curing

SFNS-CRC was mixed through a shaft mixer with 60 L capacity. All aggregates and steel fibers were put together and mixed for 2 minutes to ensure the steel fibers were uniformly dispersed. For the mixture of SFNS-CRC with the steel fiber content of 1.5% (117 kg/m3), the mixing times were extended until the mixture was dispersed to reduce the possibility of fiber balling due to uneven stirring. Then, the crumb rubbers and cement were added and mixed for another 2 minutes. Additionally, for the mix proportion including nanosilica, the nanosilica was added to water in advance and stirred uniformly. Then, the water reducer was added into water and stirred evenly. Finally, the water was added to the mixture and mixed for another 2 minutes. After the end of the mixing process, the slumps of concrete mixtures were tested immediately. For each group of SFNS-CRC, nine 150 mm × 150 mm × 300 mm prism specimens were cast for testing the prism compressive strength fc, elastic modulus Ec, and stress-stain curves, respectively, and three 150mm × 150mm × 150 mm cube specimens for testing cubic compressive strength fcu. All specimens were cast by using steel moulds and put on a vibration table for 20-second vibration to ensure compaction, demoulded after 24 hours, and then cured in a moisture room at approximately 95% relative humidity and 20°C temperature. The tests were performed after 28 days.


## 2.4. Test Procedures

The compressive strength, the modulus of elasticity, and the stress-strain curves were tested according to the specifications in Chinese standards GB/T50081 [37] and CECS13:2009 [38], respectively. Both the tests of compressive strength and modulus of elasticity were conducted in an electrohydraulic servo-controlled machine with a capacity of 3000 kN. The loading rate for the tests of compressive strength and modulus of elasticity tests was 0.5 MPa/s. Whitney [39] pointed out that sudden failure of the specimen was caused by the insufficient rigidity of the testing machine. In this paper, the four strong springs, as shown in Figure 4, were used as a rigid element to improve the stiffness of the whole test device, and the complete stress-strain curves were obtained. The specific loading scheme of the test was as follows: firstly, the specimens were taken out from the curing room, wiped to make them clean, checked whether the appearance was intact, and measured for the size to the accuracy of 1 mm; secondly, two displacement transducers were attached to the opposite sides of the section of the prism specimen to measure the deformation, and the measured load and deformation were recorded with a data acquisition system at a rate of once per second; thirdly, the preloading up to the 40% of prism compressive strength was carried out before formal loading at the loading speed of 0.6 MPa/s, while the displacement transducers on both sides were observed. The difference between the measured values of two displacement transducers could not exceed 30%. Otherwise, the adjustment for specimens should be carried out; fourthly, the formal loading was carried out after the preloading was completed. In the formal loading, the loading speed of 0.5 MPa/s was first used to 30% of the peak load, and then the loading speed was taken as 0.2 mm/min by displacement control, as shown in Figure 4.Figure 4
Testing arrangement for stress-strain curves: (a) general view; (b) layout.
(a)
(b)


## 3. Test Results and Discussion

The test results of the slump, cube compressive strength (fcu), prism compressive strength (fc), modulus of elasticity (Ec), peak deformation (dc) corresponding to the peak load, and peak strain εc corresponding to the peak stress of SFNS-CRC are listed in Table 5, in which each value is an average of the test results from three specimens.Table 5
Test results.
Group
Slump (mm)
f
cu (MPa)
f
c (MPa)
f
c
/
f
cu
d
c (mm)
E
c (GPa)
R
e
.1.0
ε
c (×10−3)
CR5SF0
70
35.6
26.8
0.73
0.224
22.2
0.349
1.50
CR5SF0.5
68
38.6
29.2
0.75
0.294
23.6
0.538
1.96
CR5SF1
65
40.3
31.9
0.79
0.393
25.2
0.716
2.62
CR5SF1.5
50
37.6
28.4
0.75
0.439
25.6
0.761
2.93
CR5SF1NS1
43
45.1
35.4
0.78
0.459
28.7
0.741
3.06
CR5SF1NS2
28
46.4
36.2
0.78
0.581
30.4
0.811
3.87
Note:Re.1.0 stands for the toughness index.


### 3.1. Effects of Steel Fibers and Nanosilica on Compressive Properties

The relationships between compressive properties of SFNS-CRC and steel fiber content are shown in Figure5. As shown in Figure 5(a), compared with CRC without steel fibers, as νf increases from 0 to 0.5%, 1.0%, and 1.5%, the increment rate for fcu is 8.4%, 13.2%, and 5.6%, respectively; it is 8.9%, 19.0%, and 6.0% for fc. The ratio of the compressive strength of the prism to that of the cube is about 0.76 for SFNS-CRC and CRC, which is slightly lower than the value of 0.85 for normal concrete [37]. Zheng et al. [40] reported the ratio of cylinder compressive strength to cube compressive strength for rubberized concrete is related to the rubber content and size. In addition, with the addition of steel fibers, the steel fiber has a similar effect on the compressive properties of CRC and normal concrete [41]. The effect of addition of steel fibers on compressive strength ranges from 0 to 25% as reported by Balaguru and Shah [42]. However, Fu et al. [23] found that the effect of concrete containing rubber crumbs on compressive strength depends on the rubber content. The decline in compressive strength due to a high amount of fiber dosage in CRC might be associated with the poor compactness [43].Figure 5
Effects of the steel fiber content: (a)fcu and fc; (b)Ec; (c)εc.
(a)
(b)
(c)As shown in Figures5(b) and 5(c), the values of Ec and εc also gradually increase with the increase of νf. Ec increases from 22.2 GPa to 25.6 GPa and εc increases from 1.5 × 10−3 to 29.3 × 10−3 with the increase of νf from 0 to 1.5%, and the increasing rate is 15% and 95%, respectively. Obviously, the steel fiber has little effect on Ec of CRC, and the value of Ec for CRC with steel fibers was still smaller than that for plain concrete. This is due to the fact that steel fibers play a minor role in the elastic phase of the concrete. Fu et al. [23] pointed out that the modulus of elasticity of CRC is dominated by the crumb rubber content. However, the growth of peak strain is much higher than that in other literature studies [16]. For rubber and steel fiber addition, the effect of rubber [12] and steel fibers on the deformation of concrete exceeds the effect of rubber and steel fibers on the strength of concrete, which causes a large deformation of SFNS-CRC. This is attributed to the fact that steel fibers can inhibit the development of cracks in concrete and hinder the development of macrocracks. The stress concentration in SFNS-CRC can be avoided by changing the direction of major fractures through the bridging action of steel fibers.For a group of specimens withνf = 1%, as νN increases from 0% to 1% and 2%, the increment rate for fcu is 11.9% and 15.1%, respectively; it is 11% and 13.5% for fc, as shown in Figure 6(a). The increment rate for Ec is 13.9% and 20.6% and that for εc is 16.8% and 47.7%, respectively, as shown in Figures 6(b) and 6(c). The measured interfacial transition zone (ITZ) between the rubber particle and concrete is shown in Figure 7. It can be found that the thickness of the ITZ becomes thinner with the addition of nanosilica. The loss in strength of concrete with incorporation of crumbs is attributed to the increased thickness of the ITZ between the hardened paste matrix and crumb rubber particles which causes poor bonding between them and leads to the formation of microcracks and consequently premature failure [4,32,33]. This is due to the hydrophobic properties of crumb rubber, which traps air around it, leading to an increase in the air content and consequently an increase in the ITZ thickness. However, as the nanosilica amount increases, the ITZ thicknesses decrease, as shown clearly in Figure 7(b). The main reason is that nanosilica has the ability to fill up nanovoids and also refine the pore system which makes the hardened microstructure of the concrete mix denser [31]. In addition, the high pozzolanic reactivity of nanosilica enables it to react and consume the surplus Ca(OH)2 and produce extra C-S-H gel which is the main compound for the strength development and densification of the interfacial transition zone [32,33].Figure 6
Effects of the nanosilica content: (a)fcu and fc; (b)Ec; (c)εc.
(a)
(b)
(c)Figure 7
Representative SEM images of SFNS-CRC: (a)vN = 0%; (b)vN = 1%.
(a)
(b)


### 3.2. Effects of Steel Fibers and Nanosilica on Load-Deformation Curves

The load-deformation curves of SFNS-CRC with different steel fiber volume contents are compared in Figure8(a). It is found from the test that the ascending shape of SFNS-CRC load-deformation curves is similar, while the slope of descending portions on the curves is decreasing with the increase of νf and going to converge to the horizontal. It can also be seen from the figure that, with the increase of νf, both the peak load and the peak deformation of SFNS-CRC increase significantly. With the addition of steel fibers, the curves are plumper and have better energy absorption capacity. This similar morphological change can be found in previous research [22,23].Figure 8
Load-deformation curves of SFNS-CRC with different (a)νf and (b)νN.
(a)
(b)For a group of specimens withνf=1%, the load-deformation curves of SFNS-CRC with different nanosilica contents are compared in Figure 8(b). It is found that the ascending and descending branches of these curves are similar, but the curvature of the curves near the peak load decreases with the increase of νN. It can also be seen from the figure that, with the increase of νN, both the peak load and the peak deformation of SFNS-CRC increase significantly. In addition, the descending segment has a larger area with the increase of νN. This indicates that the addition of nanosilica can significantly improve the prepeak and postpeak deformability of SFNS-CRC.


### 3.3. Effects of Steel Fibers and Nanosilica on Compression Toughness

The area under the stress-strain curve is a measure of toughness of the material. The most significant effect of adding steel fibers and nanosilica is to improve the toughness of concrete. Compression work (W1.0) and toughness index (Re.1.0) can be used to evaluate the axial compression toughness of steel fiber-reinforced concrete [38], where W1.0 is defined as the area under the load-deformation curve with the deformation range from 0 to l0×1.0%, in which l0 is the gauge length (150 mm in this study). The toughness index Re.1.0 is an indicator of the energy absorption capacity of the specimen and is defined as follows:(1)Re.1.0=W1.0Fmax×l0×1.0%,where Fmax is the peak load.The results of the toughness indexRe.1.0 calculated by equation (1) for each group are listed in Table 5. Compared with the toughness index of CRC, the increasing ratios of the toughness index of CRC with fibers are 54%, 105.2%, and 118.1% when νf increases from 0 to 1.5%. When the nanosilica content increases from 0 to 2%, the toughness index increases from 0.716 to 0.811 and the increasing ratio reaches 13.2%. It means that steel fibers and nanosilica can remarkably improve the toughness and energy absorption capability of CRC. The toughening effect of steel fibers on CRC is greater than that of nanosilica. The previous research has shown that the toughness index can be increased with the increase of the fiber volume and aspect ratio [44].


### 3.4. Effects of Steel Fibers and Nanosilica on Failure Mode

From the failure modes of prism specimens shown in Figure9, it can be observed that the addition of steel fibers has a significant effect on the failure mode of CRC. For CRC, when approaching to the peak load, one crack or several longitudinal parallel cracks start to appear in the central portion of the specimen and then propagate quickly. Finally, the specimens are split into several parts. The CRC specimens with steel fibers show the typical oblique shear failure mode. With the increasing steel fiber content, the number of cracks increases and the width of the major macrocracks enlarges. Compared to the one without steel fibers, the CRC specimens with steel fibers exhibit more and thinner vertical cracks at failure. This is because steel fibers with adequate anchorage can be used to bridge cracks and prevent catastrophic collapse [18] and further promote the cracks to develop and widen. When nanosilica is added into CRC, the cracks are distributed more evenly and more scattered rather than being relatively concentrated and more small cracks appear near the macrocracks. The cement mortars on the surface of concrete are peeled, which do not fell off, as shown in Figures 9(e) and 9(f). The phenomenon may be mainly attributed to the formation of stronger ITZs due to the pozzolanic and filler effects of nanosilica.Figure 9
Failure modes of specimens. (a) CR5SF0. (b) CR5SF0.5. (c) CR5SF1.0. (d) CR5SF1.5. (e) CR5SF1NS1. (f) CR5SF1NS2.
(a)
(b)
(c)
(d)
(e)
(f)


## 3.1. Effects of Steel Fibers and Nanosilica on Compressive Properties

The relationships between compressive properties of SFNS-CRC and steel fiber content are shown in Figure5. As shown in Figure 5(a), compared with CRC without steel fibers, as νf increases from 0 to 0.5%, 1.0%, and 1.5%, the increment rate for fcu is 8.4%, 13.2%, and 5.6%, respectively; it is 8.9%, 19.0%, and 6.0% for fc. The ratio of the compressive strength of the prism to that of the cube is about 0.76 for SFNS-CRC and CRC, which is slightly lower than the value of 0.85 for normal concrete [37]. Zheng et al. [40] reported the ratio of cylinder compressive strength to cube compressive strength for rubberized concrete is related to the rubber content and size. In addition, with the addition of steel fibers, the steel fiber has a similar effect on the compressive properties of CRC and normal concrete [41]. The effect of addition of steel fibers on compressive strength ranges from 0 to 25% as reported by Balaguru and Shah [42]. However, Fu et al. [23] found that the effect of concrete containing rubber crumbs on compressive strength depends on the rubber content. The decline in compressive strength due to a high amount of fiber dosage in CRC might be associated with the poor compactness [43].Figure 5
Effects of the steel fiber content: (a)fcu and fc; (b)Ec; (c)εc.
(a)
(b)
(c)As shown in Figures5(b) and 5(c), the values of Ec and εc also gradually increase with the increase of νf. Ec increases from 22.2 GPa to 25.6 GPa and εc increases from 1.5 × 10−3 to 29.3 × 10−3 with the increase of νf from 0 to 1.5%, and the increasing rate is 15% and 95%, respectively. Obviously, the steel fiber has little effect on Ec of CRC, and the value of Ec for CRC with steel fibers was still smaller than that for plain concrete. This is due to the fact that steel fibers play a minor role in the elastic phase of the concrete. Fu et al. [23] pointed out that the modulus of elasticity of CRC is dominated by the crumb rubber content. However, the growth of peak strain is much higher than that in other literature studies [16]. For rubber and steel fiber addition, the effect of rubber [12] and steel fibers on the deformation of concrete exceeds the effect of rubber and steel fibers on the strength of concrete, which causes a large deformation of SFNS-CRC. This is attributed to the fact that steel fibers can inhibit the development of cracks in concrete and hinder the development of macrocracks. The stress concentration in SFNS-CRC can be avoided by changing the direction of major fractures through the bridging action of steel fibers.For a group of specimens withνf = 1%, as νN increases from 0% to 1% and 2%, the increment rate for fcu is 11.9% and 15.1%, respectively; it is 11% and 13.5% for fc, as shown in Figure 6(a). The increment rate for Ec is 13.9% and 20.6% and that for εc is 16.8% and 47.7%, respectively, as shown in Figures 6(b) and 6(c). The measured interfacial transition zone (ITZ) between the rubber particle and concrete is shown in Figure 7. It can be found that the thickness of the ITZ becomes thinner with the addition of nanosilica. The loss in strength of concrete with incorporation of crumbs is attributed to the increased thickness of the ITZ between the hardened paste matrix and crumb rubber particles which causes poor bonding between them and leads to the formation of microcracks and consequently premature failure [4,32,33]. This is due to the hydrophobic properties of crumb rubber, which traps air around it, leading to an increase in the air content and consequently an increase in the ITZ thickness. However, as the nanosilica amount increases, the ITZ thicknesses decrease, as shown clearly in Figure 7(b). The main reason is that nanosilica has the ability to fill up nanovoids and also refine the pore system which makes the hardened microstructure of the concrete mix denser [31]. In addition, the high pozzolanic reactivity of nanosilica enables it to react and consume the surplus Ca(OH)2 and produce extra C-S-H gel which is the main compound for the strength development and densification of the interfacial transition zone [32,33].Figure 6
Effects of the nanosilica content: (a)fcu and fc; (b)Ec; (c)εc.
(a)
(b)
(c)Figure 7
Representative SEM images of SFNS-CRC: (a)vN = 0%; (b)vN = 1%.
(a)
(b)


## 3.2. Effects of Steel Fibers and Nanosilica on Load-Deformation Curves

The load-deformation curves of SFNS-CRC with different steel fiber volume contents are compared in Figure8(a). It is found from the test that the ascending shape of SFNS-CRC load-deformation curves is similar, while the slope of descending portions on the curves is decreasing with the increase of νf and going to converge to the horizontal. It can also be seen from the figure that, with the increase of νf, both the peak load and the peak deformation of SFNS-CRC increase significantly. With the addition of steel fibers, the curves are plumper and have better energy absorption capacity. This similar morphological change can be found in previous research [22,23].Figure 8
Load-deformation curves of SFNS-CRC with different (a)νf and (b)νN.
(a)
(b)For a group of specimens withνf=1%, the load-deformation curves of SFNS-CRC with different nanosilica contents are compared in Figure 8(b). It is found that the ascending and descending branches of these curves are similar, but the curvature of the curves near the peak load decreases with the increase of νN. It can also be seen from the figure that, with the increase of νN, both the peak load and the peak deformation of SFNS-CRC increase significantly. In addition, the descending segment has a larger area with the increase of νN. This indicates that the addition of nanosilica can significantly improve the prepeak and postpeak deformability of SFNS-CRC.


## 3.3. Effects of Steel Fibers and Nanosilica on Compression Toughness

The area under the stress-strain curve is a measure of toughness of the material. The most significant effect of adding steel fibers and nanosilica is to improve the toughness of concrete. Compression work (W1.0) and toughness index (Re.1.0) can be used to evaluate the axial compression toughness of steel fiber-reinforced concrete [38], where W1.0 is defined as the area under the load-deformation curve with the deformation range from 0 to l0×1.0%, in which l0 is the gauge length (150 mm in this study). The toughness index Re.1.0 is an indicator of the energy absorption capacity of the specimen and is defined as follows:(1)Re.1.0=W1.0Fmax×l0×1.0%,where Fmax is the peak load.The results of the toughness indexRe.1.0 calculated by equation (1) for each group are listed in Table 5. Compared with the toughness index of CRC, the increasing ratios of the toughness index of CRC with fibers are 54%, 105.2%, and 118.1% when νf increases from 0 to 1.5%. When the nanosilica content increases from 0 to 2%, the toughness index increases from 0.716 to 0.811 and the increasing ratio reaches 13.2%. It means that steel fibers and nanosilica can remarkably improve the toughness and energy absorption capability of CRC. The toughening effect of steel fibers on CRC is greater than that of nanosilica. The previous research has shown that the toughness index can be increased with the increase of the fiber volume and aspect ratio [44].


## 3.4. Effects of Steel Fibers and Nanosilica on Failure Mode

From the failure modes of prism specimens shown in Figure9, it can be observed that the addition of steel fibers has a significant effect on the failure mode of CRC. For CRC, when approaching to the peak load, one crack or several longitudinal parallel cracks start to appear in the central portion of the specimen and then propagate quickly. Finally, the specimens are split into several parts. The CRC specimens with steel fibers show the typical oblique shear failure mode. With the increasing steel fiber content, the number of cracks increases and the width of the major macrocracks enlarges. Compared to the one without steel fibers, the CRC specimens with steel fibers exhibit more and thinner vertical cracks at failure. This is because steel fibers with adequate anchorage can be used to bridge cracks and prevent catastrophic collapse [18] and further promote the cracks to develop and widen. When nanosilica is added into CRC, the cracks are distributed more evenly and more scattered rather than being relatively concentrated and more small cracks appear near the macrocracks. The cement mortars on the surface of concrete are peeled, which do not fell off, as shown in Figures 9(e) and 9(f). The phenomenon may be mainly attributed to the formation of stronger ITZs due to the pozzolanic and filler effects of nanosilica.Figure 9
Failure modes of specimens. (a) CR5SF0. (b) CR5SF0.5. (c) CR5SF1.0. (d) CR5SF1.5. (e) CR5SF1NS1. (f) CR5SF1NS2.
(a)
(b)
(c)
(d)
(e)
(f)


## 4. Prediction of Compressive Properties

### 4.1. Compressive Strength

Based on the test data from this paper and previous research [22,23,30,32,33,43,45–48], the relationship between the ratio of fcu−fc0/fc0 and λf and vN is shown in Figure 10, where fcu and fc0 are the cube compressive strength of SFNS-CRC and CRC and λf is the characteristic coefficient of steel fibers. Although the experimental data look like dispersed, the ratio of fcu−fc0/fc0 has an increasing tendency with the increasing λf and vN, respectively. Through the regression of test data mentioned above, an empirical formula of fcu is put forward as follows:Figure 10
Relationship offcu with (a)λf and (b)vN.
(a)
(b)(2)
f
cu
=
f
0
1
+
0.22
λ
f
−
0.12
λ
f
2
1
+
0.11
v
N
.The comparison offcu calculated by equation (2) with the test results is shown in Figure 11. It can be seen that the calculation results are in good agreement with the test data. In this paper, the obtained data were corresponding to 0.42 water/cement ratio. For the purpose of extending the applicability of equations, the data of specimens with different water/cement ratios were collected from the different experiments finished by other researches to be employed for establishing the equations. They confirmed that the calculated value matches the experimental values well, which indicates equation (2) can be used to calculate fcu of SFNS-CRC when fcu is below 60 MPa.Figure 11
Comparison offcu between test and calculated data.It can be seen from the test results in Figure5(a) that the ratio of the compressive strength of the prism to that of the cube for SFNS-CRC is the same as that for CRC, and there is a consistency between the compressive strength of the cube and the prism for SFNS-CRC and CRC. Therefore, the prism compressive strength of SFNS-CRC can be calculated in the same model as that for cube compressive strength of SFNS-CRC as follows:(3)fc=f01+0.22λf−0.12λf21+0.11vN,where fc and f0 are the prism compressive strength of SFNS-CRC and CRC, respectively.


### 4.2. Modulus of Elasticity

Modulus of elasticity is usually used in structure design. Many relationships betweenfcu and Ec have been set up in many studies. For example, the elastic modulus for normal concrete can be calculated as follows according to the Chinese standard “GB/T50081-2010” [49]:(4)Ec=1052.2+34.7/fcu.Zheng et al. [40] put forward a relationship between modulus of elasticity and compressive strength for rubberized concrete based on the ACI equation:(5)Ec=4213.6671.25fcu.Using the available data from the tests as well as those available from the database, Bompa et al. [50] suggested a prediction of Ec for rubberized concrete by using the compressive strength:(6)Ec=120.8×fcu102/3×103.Based on the regression of the experimental data from this paper and previous studies [22,23,32,45,47], a formula of Ec for SFNS-CRC is proposed as follows:(7)Ec=1051.5+90.5/fcu.The comparison of calculated results by equations (5)–(7) with test results between fcu and Ec is drawn in Figure 12. It can be seen from the figure that equations (5)–(7) are in line with the test results well, which can be used to calculate the elastic modulus for SFNS-CRC by fcu. It needs to be underlined that equation (7) is suitable for predicting Ec of SFNS-CRC when fcu is less than 60 MPa.Figure 12
Relationship betweenEc and fcu.


### 4.3. Peak Strain

It is observed from Table2 that the peak strain εc has the relationship with steel fiber volume contents νf and nanosilica replacement ratios νN. Through the regression of test results from this paper, an empirical formula of εc is put forward as follows:(8)εc=ε01+0.55λf1+0.23vN,where εc and ε0 are the peak strain of SFNS-CRC and CRC, respectively. Generally, ε0 increases with the increase of fc. An empirical formula developed by Li et al. [51] for predicting the peak strain for CRC is used in this paper as follows:(9)ε0=1065.91+117.955fc×10−6,where fc is the prism compressive strength of CRC.


### 4.4. Stress-Strain Curve

The recorded load-deformation curves are transformed into the dimensionless form to analyze the characteristics of stress-strain curves, as shown in Figure13. There are various equations to predict the stress-strain curve of concrete [52–59], in which the model proposed by Ezeldin and Balagaru [57] is brief and easy to use, that is,(10)y=βxβ−1+xβ,where y=σ/fc, in which σ is the stress under uniaxial compression and fc is the peak stress of SFNS-CRC under uniaxial compression; x=ε/εc, in which ε is the strain under uniaxial compression and εc is the peak strain of SFNS-CRC under uniaxial compression; and β is the material parameter that depends on the shape of the stress-strain diagram.Figure 13
Normalized stress-strain curves of SFNS-CRC with different (a)νf and (b)νN.
(a)
(b)According to the characteristics of the stress-strain curve, the following geometric boundary conditions are determined:ε=0, σ=0; ε=0, dσ/dε=0; ε=εp, dσ/dε=Ec; and σ=σp, dσ/dε=0. Through satisfying the geometric boundary conditions mentioned above, the parameter β of stress-strain curves can be calculated as follows:(11)β=11−fc/εcEc.The values ofβ can be determined by values of fc, εc, and Ec from the measured stress-strain curves of SFNS-CRC or calculated by the equations of fc, εc, and Ec established previously in this paper, as illustrated in Figure 14. It can be seen that β decreases with the increase of steel fiber volume contents and slightly decreases with the increase of the nanosilica content. The descending part of the stress-strain curve is affected by the β value. As the value of β decreases, the area under the stress-strain curve increases, which means the curve becomes flatter. It indicates β can reflect the influence of λf and vN on the strength and toughness of SFNS-CRC. Through regression analysis, the equation of β can be set up as follows by using λf and vN as variables:(12)β=2.94−1.34λf−0.12vNk,R2=0.95.Figure 14
Relationship ofβ with (a)λf and (b)νN.
(a)
(b)The stress-strain curve can be predicted by using equations (3), (10), and (12). The comparison of fitted curves with experimental curves is shown in Figure 15. It can be observed that the calculated results by equation (10) fit well with the experimental results and the fitting coefficients are more than 0.9 except for that of CR5SF0.5.Figure 15
Comparison of the fitting curve and experiment curve. (a) CR5SF0. (b) CR5SF0.5. (c) CR5SF1.0. (d) CR5SF1.5. (e) CR5SF1NS1. (f) CR5SF1NS2.
(a)
(b)
(c)
(d)
(e)
(f)


## 4.1. Compressive Strength

Based on the test data from this paper and previous research [22,23,30,32,33,43,45–48], the relationship between the ratio of fcu−fc0/fc0 and λf and vN is shown in Figure 10, where fcu and fc0 are the cube compressive strength of SFNS-CRC and CRC and λf is the characteristic coefficient of steel fibers. Although the experimental data look like dispersed, the ratio of fcu−fc0/fc0 has an increasing tendency with the increasing λf and vN, respectively. Through the regression of test data mentioned above, an empirical formula of fcu is put forward as follows:Figure 10
Relationship offcu with (a)λf and (b)vN.
(a)
(b)(2)
f
cu
=
f
0
1
+
0.22
λ
f
−
0.12
λ
f
2
1
+
0.11
v
N
.The comparison offcu calculated by equation (2) with the test results is shown in Figure 11. It can be seen that the calculation results are in good agreement with the test data. In this paper, the obtained data were corresponding to 0.42 water/cement ratio. For the purpose of extending the applicability of equations, the data of specimens with different water/cement ratios were collected from the different experiments finished by other researches to be employed for establishing the equations. They confirmed that the calculated value matches the experimental values well, which indicates equation (2) can be used to calculate fcu of SFNS-CRC when fcu is below 60 MPa.Figure 11
Comparison offcu between test and calculated data.It can be seen from the test results in Figure5(a) that the ratio of the compressive strength of the prism to that of the cube for SFNS-CRC is the same as that for CRC, and there is a consistency between the compressive strength of the cube and the prism for SFNS-CRC and CRC. Therefore, the prism compressive strength of SFNS-CRC can be calculated in the same model as that for cube compressive strength of SFNS-CRC as follows:(3)fc=f01+0.22λf−0.12λf21+0.11vN,where fc and f0 are the prism compressive strength of SFNS-CRC and CRC, respectively.


## 4.2. Modulus of Elasticity

Modulus of elasticity is usually used in structure design. Many relationships betweenfcu and Ec have been set up in many studies. For example, the elastic modulus for normal concrete can be calculated as follows according to the Chinese standard “GB/T50081-2010” [49]:(4)Ec=1052.2+34.7/fcu.Zheng et al. [40] put forward a relationship between modulus of elasticity and compressive strength for rubberized concrete based on the ACI equation:(5)Ec=4213.6671.25fcu.Using the available data from the tests as well as those available from the database, Bompa et al. [50] suggested a prediction of Ec for rubberized concrete by using the compressive strength:(6)Ec=120.8×fcu102/3×103.Based on the regression of the experimental data from this paper and previous studies [22,23,32,45,47], a formula of Ec for SFNS-CRC is proposed as follows:(7)Ec=1051.5+90.5/fcu.The comparison of calculated results by equations (5)–(7) with test results between fcu and Ec is drawn in Figure 12. It can be seen from the figure that equations (5)–(7) are in line with the test results well, which can be used to calculate the elastic modulus for SFNS-CRC by fcu. It needs to be underlined that equation (7) is suitable for predicting Ec of SFNS-CRC when fcu is less than 60 MPa.Figure 12
Relationship betweenEc and fcu.


## 4.3. Peak Strain

It is observed from Table2 that the peak strain εc has the relationship with steel fiber volume contents νf and nanosilica replacement ratios νN. Through the regression of test results from this paper, an empirical formula of εc is put forward as follows:(8)εc=ε01+0.55λf1+0.23vN,where εc and ε0 are the peak strain of SFNS-CRC and CRC, respectively. Generally, ε0 increases with the increase of fc. An empirical formula developed by Li et al. [51] for predicting the peak strain for CRC is used in this paper as follows:(9)ε0=1065.91+117.955fc×10−6,where fc is the prism compressive strength of CRC.


## 4.4. Stress-Strain Curve

The recorded load-deformation curves are transformed into the dimensionless form to analyze the characteristics of stress-strain curves, as shown in Figure13. There are various equations to predict the stress-strain curve of concrete [52–59], in which the model proposed by Ezeldin and Balagaru [57] is brief and easy to use, that is,(10)y=βxβ−1+xβ,where y=σ/fc, in which σ is the stress under uniaxial compression and fc is the peak stress of SFNS-CRC under uniaxial compression; x=ε/εc, in which ε is the strain under uniaxial compression and εc is the peak strain of SFNS-CRC under uniaxial compression; and β is the material parameter that depends on the shape of the stress-strain diagram.Figure 13
Normalized stress-strain curves of SFNS-CRC with different (a)νf and (b)νN.
(a)
(b)According to the characteristics of the stress-strain curve, the following geometric boundary conditions are determined:ε=0, σ=0; ε=0, dσ/dε=0; ε=εp, dσ/dε=Ec; and σ=σp, dσ/dε=0. Through satisfying the geometric boundary conditions mentioned above, the parameter β of stress-strain curves can be calculated as follows:(11)β=11−fc/εcEc.The values ofβ can be determined by values of fc, εc, and Ec from the measured stress-strain curves of SFNS-CRC or calculated by the equations of fc, εc, and Ec established previously in this paper, as illustrated in Figure 14. It can be seen that β decreases with the increase of steel fiber volume contents and slightly decreases with the increase of the nanosilica content. The descending part of the stress-strain curve is affected by the β value. As the value of β decreases, the area under the stress-strain curve increases, which means the curve becomes flatter. It indicates β can reflect the influence of λf and vN on the strength and toughness of SFNS-CRC. Through regression analysis, the equation of β can be set up as follows by using λf and vN as variables:(12)β=2.94−1.34λf−0.12vNk,R2=0.95.Figure 14
Relationship ofβ with (a)λf and (b)νN.
(a)
(b)The stress-strain curve can be predicted by using equations (3), (10), and (12). The comparison of fitted curves with experimental curves is shown in Figure 15. It can be observed that the calculated results by equation (10) fit well with the experimental results and the fitting coefficients are more than 0.9 except for that of CR5SF0.5.Figure 15
Comparison of the fitting curve and experiment curve. (a) CR5SF0. (b) CR5SF0.5. (c) CR5SF1.0. (d) CR5SF1.5. (e) CR5SF1NS1. (f) CR5SF1NS2.
(a)
(b)
(c)
(d)
(e)
(f)


## 5. Conclusions

The mechanical characteristics of CRC with different nanosilica replacement ratios and steel fiber volume contents have been experimentally studied through the uniaxial compressive tests on prism specimens. Based on the extensive test data and analysis, the following conclusions can be drawn:(1)
For the SFNS-CRC specimens with the different steel fiber and nanosilica contents, the ascending shapes of load-deformation curves are similar, while there is a difference in the descending part of the curves. With the addition of steel fibers, the SFNS-CRC specimens exhibit more ductile failure and maintain their integrity during testing. With the addition of nanosilica, the surface cracks of SFNS-CRC specimens become fine and dense.(2)
Both steel fibers and nanosilica have the better reinforcing effects on the compressive characteristics of CRC. The toughness index and energy dissipation capacity of SFNS-CRC in compression increase with the increasing steel fiber and nanosilica contents, respectively. The critical compressive strain of SFNS-CRC significantly increases with the combined effect of steel fibers and nanosilica.(3)
By considering the effects of the characteristic parameter of steel fiber and nanosilica contents upon the compressive characteristics of CRC, the equations for compressive strength, modulus of elasticity, and critical compressive strain of SFNS-CRC were proposed by regression of experimental data, respectively. Then, a simple predicted model of the stress-strain curve for SFNS-CRC was proposed, which only contains one parameter (β) and is easy to be used.



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*Source: 9693405-2020-03-05.xml*