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Mechanical properties of high performance concrete reinforced with basalt fiber and polypropylene fiber
Construction and Building Materials 197 (2019) 464–473
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Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Mechanical properties of high performance concrete reinforced with basalt fiber and polypropylene fiber Dehong Wang ⇑, Yanzhong Ju ⇑, Hao Shen, Libin Xu School of Civil Engineering and Architecture, Northeast Electric Power University, Jilin 132012, China
h i g h l i g h t s An experimental study is conducted on hybrid fiber reinforced high performance concrete (HPC). The influence of basalt fiber (BF) and polypropylene fiber (PF) on the mechanical properties of HPC are determined. A formula for calculating the flexural strength of hybrid fiber HPC is developed. The mathematical expression of compressive stress-strain of hybrid fiber reinforced HPC is derived.
a r t i c l e
i n f o
Article history: Received 9 July 2018 Received in revised form 18 October 2018 Accepted 23 November 2018
Keywords: High performance concrete Basalt fiber Polypropylene fiber Mechanical properties Stress-strain relationship
a b s t r a c t The mechanical properties of high performance concrete (HPC) reinforced with basalt fiber and polypropylene fibers were investigated in this study. The influence of single basalt fibers (BFs), single polypropylene fibers (PF) and hybrid fibers with different contents on the compressive strength, flexural strength, splitting tensile strength and stress-strain curve of HPC were investigated. A formula for calculating the flexural strength of hybrid fiber HPC was developed, and a conversion relationship between flexural strength and cube compressive strength was proposed. On the basis of experimental data analysis, the mathematical expression of the compressive stress-strain of hybrid fiber reinforced HPC was derived. Test results indicate that, the strength of HPC reinforced with single doped basalt fibers or polypropylene fibers increases with the increase of the fiber volume fraction. However, the compressive strength increases slightly, while the flexural strength and splitting tensile strength are improved significantly. When the two types of fibers are mixed into HPC simultaneously, there are two kinds of synergy effects (positive and negative synergy effects). When the basalt fiber content is 0.15% and polypropylene fiber content is 0.033%, the synergy effect of fiber mixing is the best. At this time, the compressive strength, flexural strength and splitting tensile strength increased by 14.1%, 22.8% and 48.6%, respectively, when compared with those of HPC without fibers. Ó 2018 Elsevier Ltd. All rights reserved.
1. Introduction Concrete is a widely used material in civil engineering construction. However, normal concrete exhibits poor tensile properties and low ductility [1,2]. The addition of fibers to the concrete mixture can significantly improve the concrete’s mechanical properties, especially for tensile strength [3,4]. High performance concrete (HPC) reinforced with fibers was developed for high strength, toughness, and durability [5,6]. The addition of single fiber can only improve the performance of a single aspect of the concrete, and enhancing the overall performance of concrete, can be achieved by mixing with different fibers [7]. Different types or ⇑ Corresponding authors. E-mail addresses: [email protected] (D. Wang), [email protected] (Y. Ju). https://doi.org/10.1016/j.conbuildmat.2018.11.181 0950-0618/Ó 2018 Elsevier Ltd. All rights reserved.
sizes of fibers are mixed into concrete with a specific admixture to form a hybrid fiber concrete. Different types of fiber can be rationally combined in a concrete matrix, which reinforce the performance of hybrid fiber reinforced concrete at multi-scale [8,9]. Moreover, the cost can be reduced by using cheaper synthetic fibers instead of metal fibers [10]. Walton et al. [11] reported that adding hybrid mixed inorganic fibers and organic fibers into concrete can improve the impact resistance and tensile properties of the concrete matrix. Soroushian et al. [12] investigated the performance of concrete reinforced with two different types of fiber. The experimental results show that the flexural toughness and impact resistance of hybrid fiber concretes are enhanced to some extent, but when compared with plain concrete the compressive strength has slightly decreased. Yew et al. [13] investigated the performances of concrete reinforced with various polypropylene fibers.
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Polypropylene fibers can be used to enhance the tensile and flexural strength and the elasticity modulus of concrete. Moreover, the addition of a 0.5% volume fraction of polypropylene fibers resulted in a 95.8% reduction in the slump. Park et al. [14] investigated the influence of hybrid steel fibers on the tensile behavior of UHPHFRC. The results indicated that the shape of the tensile stress strain curves of UHPHFRC is mainly affected by the type of macro-fiber rather than micro fiber. The utilization of favorably affected the multiple cracking behaviors and strain hardening of UHPHFRC, and. Lawler et al. [15] investigated the flexural toughness, restrained shrinkage and permeability of microfiber and macrofiber hybrid fiber reinforced concrete. The results showed that the microfibers improved the first-crack strength and delayed the development of macrocracks, and thus the strength and crack resistance of the hybrid fiber concrete was better than the resistance of the concrete containing the macrofiber only. Aslani et al. [16] investigated the mechanical properties of hybrid steel fiber and polypropylene fiber. The experimental results showed that the compressive strength and modulus of elasticity of the hybrid fiber reinforced self-compacting concrete of that was 91 days old were higher than those of the steel and polypropylene fiber selfcompacting concrete at the same age. Basalt fiber is a new type of eco-friendly, green and highperformance fiber, it has excellent performance, and has been widely used in many areas [2,17,18]. Basalt fiber can improve the flexural strength, toughness as well as the fracture energy of cement matrix composites [19]. The elastic modulus of basalt fiber can reach 93–115 GPa, which is considerably larger than that of chemical fibers like polypropylene fiber, polyvinyl alcohol fiber and so on. Basalt fiber and polypropylene fiber can form complementary advantages in the concrete matrix, and make up for the defects of each individual fiber, improve the tensile strength of concrete matrix in different scale. Hybrid of basalt fiber and polypropylene fiber instead of steel fiber into HPC matrix have attracted great interests to improve the defect of steel fiber HPC corrosion, which can also reduce the material costs (see Table 3). The research on the mechanical properties of HPC reinforced with basalt fiber and polypropylene fiber is not adequate in the past. The quantitative relationship between mechanical properties of hybrid fiber HPC and fiber content are not clear, and the constitutive relationship of HPC reinforced with basalt fiber and polypropylene fiber has not been investigated. Thus, the main objective of this study is to investigate the mechanical properties of HPC reinforced
with basalt fiber and polypropylene fiber. The interest of this study is to quantify and discuss the effect of basalt fiber and polypropylene fiber and hybrid fibers in enhancing the mechanical properties of HPC, proposed the formulas for predicting the strengths of HPC reinforced with different basalt fiber and polypropylene fiber volume fraction, and established the stress-strain relationship model of hybrid fiber HPC. This research also aims to find the optimum basalt fiber and polypropylene fiber contents that could significantly enhance the mechanical properties of HPC. 2. Experimental program 2.1. Materials Hybrid fiber HPC was prepared by the following ingredients: Grade 42.5 ordinary Portland cement, silica fume, quartz sand, basalt fiber, polypropylene fiber, water reducer and water. The chemical compositions and physical properties and of the cement are shown in Table 1. Silica fume used in this study has a particle size of less than 2 lm, a density of 2.214 kg/m3, and a specific surface area of 143,100 cm2/g. Table 2 summarizes the chemical compositions of the silica fume. The diameter of quartz sand ranges from 0 to 1.25 mm. Table 3 summarizes the main performance indexes and price of basalt fiber and polypropylene fiber, the properties and cost steel fibers are also presented in Table 3 for the purpose of comparing the cost of different types of fiber. Fig. 1 shows the appearance of two types of fibers. Water reducer utilized in this study is a non-naphthalene high-performance water reducer, and the water reduction rate is 29%. 2.2. Mix proportions To study the influence of different contents of the two types of fibers on HPC, 16 different test mixture proportions were designed in this study. The two fibers are nonmetallic fibers, and when the fraction is too large they easily agglomerate. Therefore, the volume fraction of basalt fiber was varied in three groups as 0.10%, 0.15%, 0.20%, and the polypropylene fiber volume fraction was varied in groups as 0.025%, 0.033%, 0.042% [19]. The ratio of water to cement was 0.22, the ratio of silica to cement was 0.3, and the ratio of sand to cement was 1.3 [20]. For the sake of comparative analysis, a mixture of HPC without any fibers, and six mix proportions were
Table 1 The chemical compositions and physical properties of the cement. Mineral compositions (%)
Physical properties
C3S
C2S
C3A
C4AF
f-CaO
f-MgO
Density (g/cm3)
fct,f,3 /MPa
fct,f,28 /MPa
fct,f,3 /MPa
fct,f,28 /MPa
60.5
18.1
7.4
8.9
0.9
1.8
3.18
5.17
9.62
29.2
61.5
Table 2 The chemical compositions of silica fume.
*
Mineral compositions
SiO2
Fe2O3
Al2O3
CaO
MgO
LO.I*
K2O
Na2O
FC
SO3
Content/%
82.22
1.81
0.97
0.36
1.31
1.45
0.84
0.16
0.92
0.27
LO.I = Loss on ignition.
Table 3 The performance indexes of two types of fibers. Fiber type
Density/ gcm3
Elastic modulus/GPa
Tensile strength /MPa
Length /mm
Length-to-diameter ratio
Fibers price (USD/m3-0.042%Vf)
Basalt fiber (BF) Polypropylene fiber (PF) Steel fiber (SF)
2.75 0.91 7.86
80–110 3.5 201
3000–4000 650 2850
12 12 13
1000 600 65
3.00 0.33 9.04
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(a) basalt fiber and (b) polypropylene fiber Fig. 1. The fibers used in the study.
Table 4 The mix proportions of HPC. Specimen
Cement (kg)
Silica fume (kg)
BF0PF0 BF0.10PF0 BF0.15PF0 BF0.20PF0 BF0PF0.025 BF0PF0.033 BF0PF0.042 BF0.10PF0.025 BF0.10PF0.033 BF0.10PF0.042 BF0.15PF0.025 BF0.15PF0.033 BF0.15PF0.042 BF0.20PF0.025 BF0.20PF0.033 BF0.20PF0.042
756.89 756.16 755.80 755.43 756.71 756.65 756.58 755.98 755.92 755.86 755.62 755.56 755.50 755.25 755.19 755.13
227.07 226.85 226.74 226.63 227.01 226.99 226.98 226.79 226.78 226.76 226.68 226.67 226.65 226.58 226.56 226.54
Quartz sand/(kg) 0.63–1.25 (mm)
0.32–0.63 (mm)
0.16–0.32 (mm)
738.12 737.41 737.05 736.70 737.94 737.88 737.82 737.23 737.17 737.11 736.88 736.82 736.76 736.52 736.46 736.40
371.18 370.82 370.64 370.47 371.09 371.06 371.03 370.73 370.70 370.67 370.55 370.52 370.49 370.38 370.35 370.32
169.54 169.38 169.30 169.22 169.50 169.49 169.48 169.34 169.33 169.31 169.26 169.24 169.23 169.18 169.16 169.15
BF (kg)
PF (kg)
Water reducer (kg)
Water (kg)
0.00 2.75 4.13 5.50 0.00 0.00 0.00 2.75 2.75 2.75 4.13 4.13 4.13 5.50 5.50 5.50
0.00 0.00 0.00 0.00 0.23 0.30 0.38 0.23 0.30 0.38 0.23 0.30 0.38 0.23 0.30 0.38
68.12 68.05 68.02 67.99 68.10 68.10 68.09 68.04 68.03 68.03 68.01 68.00 67.99 67.97 67.97 67.96
169.09 168.93 168.85 168.76 169.05 169.03 169.02 168.89 168.87 168.86 168.80 168.79 168.78 168.72 168.71 168.70
[Note] BF = basalt fiber (fraction = 0.1%, 0.15%, 0.2%), PF = polypropylene fiber (fraction = 0.025%, 0.033%, 0.042%).
performed with only one type of fiber. The mix proportions are shown in Table 4, and abbreviations are used for mixtures according to the BF and PF content. BF and PF contents were also given in the abbreviations of mixtures. For instance, BF0.10PF0.025 means that the volume fraction of BF is 0.1% and the volume fraction of PF is 0.025%. 2.3. Fabrication of specimen and loading methods First the quartz sand was mixed for 2–3 min without water in the mixer, then cement and silica fume were added into the mixer and remixed for 3 min. The next step was to add half water and water reducer, and then, the mixture was remixed for approximately 3 min. Subsequently, the remaining half of the water and the fibers were added and remixed for approximately 4 min. Then, the mixture was cast into molds and vibrated on high-frequency vibration table. The specimens were kept in the molds for 24 h under the standard conditions (room temperature of approximately 20 °C and humidity of 95%), then the molds were removed, and specimens were cured in steam of approximately 90 °C for 3 days in the concrete accelerated curing box. The heating rate of the curing box was controlled to increase by no more than 15 °C per hour, and gradually increased to 90 °C. After the steam curing was finished, the specimens were moved into the standard curing room for 24 days. The Chinese code GB/T 31387-2015 Reactive powder Concrete was used to determine the mechanical properties of hybrid fiber HPC. Cube specimens of 100 mm 100 mm 100 mm were used for cube compression and splitting tensile strength tests. Prismatic
specimens of 100 mm 100 mm 300 mm were used for compression stress-strain tests, and prismatic specimens of 100 mm 100 mm 400 mm with a span of 300 mm were used for flexural strength tests. The compression strength test and stress–strain test were loaded by a 5000 kN electro-hydraulic servo pressure testing machine, and the splitting tensile strength and flexural strength were tested in a 1000kN electrohydraulic servo universal testing machine. To obtain the stable descent stage of the stress-strain curve, a rigid auxiliary frame was employed. The load was measured by a force sensor. Fig. 2 is the experimental loading device diagram. According to the Chinese code GB/T 31387-2015 Reactive powder concrete, the loading rates of the compressive strength, splitting tensile strength and flexural strength test were 1.2 MPa/s, 0.08 MPa/s and 0.1 MPa/s, respectively.
3. Results and discussion 3.1. Compressive strength Fig. 3 shows the compressive strength of HPC reinforced with different single fiber or hybrid fiber content. It can be seen from Fig. 3 that when the content of single basalt fiber or polypropylene fiber is low, the addition of fiber cannot improve the compressive strength of HPC, and can even reduce its strength. The compressive strength of the compressive strength of BF0.1PF0 is 0.35% lower than that of BF0PF0 without fiber. The compressive strength of BF0PF0025 is 5.22% lower than that of BF0PF0. A similar result
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5 000 kN test machine
Rigid auxiliary frame Displacement sensor Specimen Force sensor
(a) Loading schematic diagram
(b) Test photo
Fig. 2. Compression stress-strain curve test loading diagram.
The volume fraction of PF is 0 The volume fraction of PF is 0.025%
Compressive strength (MPa)
120 100
The volume fraction of PF is 0.033% The volume fraction of PF is 0.042% 110.07
96.47
98.6 91.43
101.23
96.13 94.67
97.37 98.13 89.57
100.3
103.43 97.33
94.37 88.47
87.13
80 60 40 20 0
0
0.1
0.15
0.2
The volume fraction of BF (%) Fig. 3. Compressive strength of fiber reinforced HPC.
has been reported for the compressive behavior of basalt fiber in high-strength concrete [2]. This similarity may be due to basalt fiber belonging to the high modulus fiber; thus, the load-bearing skeleton cannot form in the matrix when the volume fraction of the fiber is low. The enhancement effect on compressive strength of HPC is smaller than the negative influences of defects caused by the fibers. When the fiber content of single basalt fiber or polypropylene fiber mixtures exceeds a certain scope, the compressive strength of HPC increases with the increase of fiber content. When the volume fraction of basalt fiber is 0.20%, the compressive strength of BF0.2PF0 is 103.43 MPa, which is 7.21% higher than that of BF0PF0, which is 96.47 MPa. The compressive strength of BF0PF0.042 is 101.23 MPa, which is 4.93% higher than that of BF0PF0. Based on the correlation analysis performed in the SPSS software, the correlation coefficient between the basalt fiber volume fraction and compressive strength of HPC is 0.737, and the correlation coefficient between the polypropylene fiber volume fraction and compressive strength of HPC is 0.433. It can be seen that the addition of basalt fiber has a more significant influence on compressive strength of HPC. The diameter of the polypropylene fiber is larger, and the air entraining effect of the fiber increases the pores in the concrete mix, which means that the bonding between the polypropylene fiber and the concrete
matrix is less than that of basalt fiber. Therefore, adding a proper amount of fiber can improve the strength and toughness of HPC, but if the fiber fraction is too low or too high, it will increase its internal defects, which is not conducive to the improvement of strength. For the hybrid fiber HPC, when the volume fraction of the basalt fiber is 0.10% and 0.20%, the compressive strength of HPC decreases with the increase of the polypropylene fiber volume fraction. This may be due to a negative hybrid effect of the two types of fiber. When volume fraction of basalt fiber is small, such as 0.10%, the basalt fiber cannot form a bearing skeleton in the HPC matrix. The low elastic modulus of polypropylene fiber has little contribution to the compressive strength of concrete, and adding polypropylene fiber caused more defects in HPC matrix. When the volume content of basalt fiber reaches 0.20%, the fiber volume fraction is large, so it cannot be dispersed uniformly in HPC. With the addition of polypropylene fiber, wrapped together with the basalt fiber, it is more detrimental to its uniform dispersion and easily agglomerates. Some weak interfaces are formed in HPC, which decrease the strength of the HPC. As seen from Fig. 3, the optimum mixing is achieved when the basalt fiber volume fraction is 0.15%, the volume fraction of polypropylene fiber is 0.033%, and the compressive strength reaches 110.1 MPa, which is 14.10%
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higher than that of HPC without fiber. Under this combination, the fibers can be distributed uniformly in concrete. The two types of fibers can have a complementary effect on the elastic modulus. The elastic modulus of polypropylene fiber is low, which can delay the formation and propagation of microcracks in the early stage of hardening and reduce the number of crack sources. The elastic modulus of basalt fiber is higher and the influence of crack propagation on hardening concrete is better. Therefore, the two fibers can play a role at different levels to improve the compressive strength of HPC.
The test results showed that there was an approximately linear relationship between the flexural strength and the cube compressive strength of the hybrid fiber reinforced HPC. Statistical analyses of the flexural strength and cube compressive strength of the basalt fiber, polypropylene fiber and hybrid fiber HPC were conducted, including the test results in this paper and the results from the previous literatures [21–23]. According to the test data, the relationship between the flexural strength (ff) and the cube compressive strength (fcu) HPC can be expressed as follows, with Fig. 5 acting as a comparison between the fitting curves and test results.
3.2. Flexural strength and splitting tensile strength
f f ¼ 0:118f cu 0:435
f f ¼ ð1 þ 79qBF þ 710qPF 443265qBF qPF Þf f0
12
Flexural strength (MPa)
8
16 14 12
ff=0.118fcu-0.435
10 8 6 4 60
90
120
Fig. 5. The relationship between the flexural strength and cube compressive strength of hybrid fiber reinforced HPC.
The volume fraction of PF is 0.033%
The volume fraction of PF is 0.025%
The volume fraction of PF is 0.042%
10.33 9.74
9.9 10.01
10.47
10.19 9.53
9.36
9.57 8.8
8.39
8.3
8.71
6 4 2 0
0
0.1
150
Cube compressive strength fcu (MPa)
The volume fraction of PF is 0
9.93 9.97
10
18
ð1Þ
where ff and ff0 are the flexural strength of hybrid fiber HPC and matrix HPC, respectively; and qBF and qPF are the basalt fiber volume fraction and polypropylene fiber volume fraction, respectively.
ð2Þ
Fig. 6 shows the test results of the splitting tensile strength, including the single and hybrid fibers. It can be seen from Fig. 6 that the enhancement effect of fiber on the splitting tensile strength is significant. Compared with the splitting tensile strength of HPC without fiber, the splitting tensile strength of HPC reinforced with single basalt fibers increased by 21.90%–38.33%, and the splitting tensile strength of HPC reinforced with single polypropylene fibers increased by 32.86%–44.52%. The results show that the addition of basalt fiber or polypropylene fiber forms
Flexural strength ff (MPa)
Fig. 4 shows the flexural strength of single and hybrid fiber HPC. It can be seen from Fig. 4 that the addition of different types of fiber has different scales of improvement on flexural strength of the HPC. When the volume fraction of basalt fiber increases from 0.01% to 0.15%, to 0.20%, the flexural strength increases by 1.08%, 12.77% and 15.30%, respectively. The addition of basalt fiber can prevent cracks and improve the flexural strength. When the volume fraction of polypropylene fiber is in the range of 0.025% to 0.042%, the strength increases by 19.64% to 24.46%. It can be seen that the flexural strength of the hybrid fiber HPC is higher than that of the single fiber when the basalt fiber volume fraction is 0.15% and the polypropylene fiber volume fraction is 0.025% and 0.033% and when compared with the HPC without fiber, the flexural strength increased by 26.14% and 22.77%, respectively. When the volume fraction of basalt fiber is 0.20%, the flexural strength of HPC is lower than that of the single fiber HPC, but it is still higher than that of the HPC without fiber. This phenomenon may be explained by the fact that the two fibers are intertwined with each other, hindering their uniform dispersion in concrete. The correlation coefficient between the basalt fiber volume fraction and the flexural strength of HPC is 0.895 while that of the polypropylene fiber is 0.975. This indicates that the influence of the polypropylene fiber on the flexural strength is greater than that of the basalt fiber. According to the experimental data, a formula for calculating the flexural strength (ff) of a hybrid fiber HPC is:
0.15
The volume fraction of BF (%) Fig. 4. Flexural strength of fiber reinforced HPC.
0.2
8.33
469
Splitting tensile strength (MPa)
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6
4
5.58
The volume fraction of PF is 0
The volume fraction of PF is 0.033%
The volume fraction of PF is 0.025%
The volume fraction of PF is 0.042%
5.75
6.39 6.24
6.07
5.74
5.59
5.33 5.12 5.19 5.11
5.81
5.6
5.47 5.45
4.2
2
0
0
0.1
0.15
0.2
The volume fraction of BF (%) Fig. 6. Splitting tensile strength of fiber reinforced HPC.
a three-dimensional chaotic distribution in the concrete, which can delay the crack formation and result in an increase in the splitting tensile strength of HPC. The correlation analysis indicated polypropylene fibers with low elastic modulus have a great influence on the splitting tensile strength of HPC. It can be seen that the splitting tensile strength of the hybrid fiber HPC is higher than that of the single-fiber HPC. The splitting tensile strength of the hybrid fiber HPC is 23.57%–52.14% higher than that of HPC without fibers. The splitting tensile strength of BF0.15PF0.025 is the largest with a splitting tension strength of 6.39 MPa, and the splitting tensile strength of BF0.15PF0.025 is 6.24 MPa. It indicates that basalt fiber volume fraction of 0.15% and polypropylene fiber of volume fraction 0.025% are mixed to achieve their respective optimal content. In this mixture, the fibers can be dispersed evenly in the HPC matrix without agglomeration balling. When the fraction of basalt fiber is 0.20%, and the hybrid effect is poor, the splitting tensile strength of the hybrid fiber HPC is lower than that of HPC with single fiber, but it is still higher than that of HPC without fiber. The reason for this phenomenon may be explained by the fact that more fibers are distributed vertically, which cause more cracks and weak interface in the concrete. The relationship between the splitting tensile strength (ft) and flexural strength (ff) of HPC can be expressed as follows: 0:75
f t ¼ 1:027f f
ð3Þ
From the above result it can be seen that the addition of two types of fibers can significantly improve the resisting tension. In the early stage of loading, the tensile stress of HPC is relatively low, and with the formation of microcracks in HPC, the basalt fiber and polypropylene fiber play an increasing role. With an increasing load and microcrack propagation, and the tensile stress transmission is withstood by the basalt fiber and polypropylene fiber. The fibers delay the continued propagation of cracks, slow down the expansion rate, delay the breakage of the HPC specimen, and improve the toughness and tensile strength of the HPC. When the tensile stress exceeds the bond strength between the fibers and HPC matrix, the fibers are pulled out, and the reinforcement action disappears. 3.3. Synergy of BF and PF In the appropriate mixing range, the hybrid fibers in the HPC can play their respective roles to complement each other and
create a positive hybrid effect, which make the improvement of the mechanical properties of HPC more effective than that of single fibers. To analyze the influence of the synergy on the mechanical properties, the synergy effect coefficients are defined as follows:
ax1 ¼
bB - P þ bminðB;PÞ bmaxðB;PÞ þ bminðB;PÞ
ð4Þ
ax2 ¼
bB - P þ bmaxðB;PÞ bmaxðB;PÞ þ bminðB;PÞ
ð5Þ
where, ax1 , ax2 are the synergy effect coefficients, x represents the type of strength, c represents the compressive strength, ac1 and ac2 are the synergy effect coefficients of the compressive strength, f represents the flexural strength, af1 and af2 are the synergy effect coefficients of the flexural strength, s represents the split tensile strength, and as1 and as2 are the synergy effect coefficients of the split tensile strength. In the equation, b is the strength enhancement coefficient due to addition of fiber. b ¼ f x =f x0 , f x and f x0 are the strength of fiber HPC and the strength of HPC without fiber, respectively (compressive strength, flexural strength, split tensile strength), bB - P is the strength enhancement coefficient of hybrid fiber HPC, bmaxðB;PÞ is the maximum enhancement coefficient of single basalt fiber or polypropylene fiber, bminðB;PÞ is the minimum enhancement coefficient of single basalt fiber or polypropylene fiber. When ax1 > 1:0, the two types of fibers have a positive hybrid effect; When ax1 < 1:0, It needs to be judged according to ax2 . If ax2 > 1:0, it is a positive synergy effect; if ax2 < 1:0, it is a negative synergy effect. Table 5 shows the synergy effect coefficient of HPC’s compressive strength, splitting tensile strength and flexural strength. It can be seen from Table 5thatBF0.20PF0.033 and BF0.20PF0.042 with larger fiber volume fractions showed negative synergy effect. The three types of strength synergy effect coefficients of BF0.20PF0.042 were smaller than those of BF0.20PF0.033. It indicated that the fiber volume fraction of the two groups of hybrid fiber HPCs was on the high side. Both BF0.15PF0.025 and BF0.15PF0.033 showed positive synergy effects, which demonstrated that the combination of these fibers has shown the best improvement of the mechanical properties of HPC, and were the best fiber mixes of fiber. It can also be concluded that the basic mechanical properties of HPC can be improved only by adding
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Table 5 HPC strength synergy effect coefficient. Specimen
ac1
ac2
af1
af2
as1
as2
BF0.10PF0.025 BF0.10PF0.033 BF0.10PF0.042 BF0.15PF0.025 BF0.15PF0.033 BF0.15PF0.042 BF0.20PF0.025 BF0.20PF0.033 BF0.20PF0.042
0.992 0.954 0.929 1.004 1.059 0.995 0.969 0.955 0.927
1.017 0.966 0.954 – – 1.015 1.030 0.979 0.938
0.964 0.961 0.914 1.057 1.043 0.976 0.982 0.971 0.948
1.007 1.019 0.999 – – 1.004 1.002 0.976 0.970
0.990 0.996 0.983 1.028 1.011 0.959 0.942 0.936 0.899
1.074 1.082 1.087 – – 1.009 0.961 0.956 0.938
hybrid fibers in certain proportions. Based on the test, it is suggested that the volume fraction of basalt fiber in hybrid fiber HPC should be 0.15%, and volume fraction of polypropylene fiber should be no more than 0.033%.
4. Hybrid fiber HPC compression stress-strain relationship 4.1. Characteristics of compressive stress-strain curves of hybrid fiber HPC According to the test results, the slope of the stress-strain curve changed very little before 50% of the peak load, which shows a approximative linear slop. The proportion limit of the hybrid fiber HPC is higher than that of normal concrete by approximately 30%. The specimen enters a stable stage of development after the proportion limit. As the load steadily increases, several fine vertical cracks appear near the sides, and the slope of the curve begins to decrease. After the peak stress point, the specimen enters the crack instability stage, and the crack begins to widen. The slope of the
curve is negative. There is an inflection point in the descending curve. All the stress-strain curves are similar with ascending and descending curves. Considering that the peak stress and peak strain of HPC with different fiber proportions are different, the normalization is applied in the stress-strain curves. The stress-strain curves are converted into standard curves with x ¼ ec =ec0 and y ¼ rc =f c . f c and ec0 are, respectively, the compressive strength of HPC and the strain corresponding to the peak stress. Fig. 7 shows the typical normalization curve for HPC. A corresponds to the proportion limit point. C corresponds to the peak stress point. At the peak stress, the slope of the curve is 0. D is an inflection point with d2y/dx2 = 0. Table 6 contains the compression characteristic values of hybrid fiber HPC, including the compressive strength, peak strain and elastic modulus of prisms. When the volume fraction of basalt fiber is 0.1%, the axial compressive strength decreased gradually with the increase of polypropylene fiber volume fraction, but the decreasing trend was not obvious. When the volume fraction of basalt fiber was 0.15% and 0.2%, the axial compressive strength first rose and then decreased with the increase of polypropylene fiber volume fraction. When the volume fraction of basalt fiber was 0.15% and polypropylene fiber was 0.033%, the axial compressive strength reached its maximum value, which is 16.7% higher than that of HPC without fiber. The strain of hybrid fiber HPC at peak load ranges from 0.00285 to 0.00335, with an average value of 0.00305, which is slightly lower than that of steel fiber HPC [24]. The relationship between the peak strain ec and the axial compressive strength f c was approximately linear, an equation for describing the relationship were obtained with fitting tests data. As shown in Fig. 8.
ec ¼ ð1120 þ 22:8f c Þ 106
ð6Þ
The elastic modulus of hybrid fiber HPC was between 32.9 GPa and 43 GPa, which is lower than that of steel fiber HPC [24,25]. This could be attributed to the low elastic modulus of basalt fiber and polypropylene fiber. It was found that the elastic modulus of HPC was related to the fabrication of the specimen. In the experiment, the admixture of the two types of fibers will cause cracks in the concrete, which will lead to the change of the elastic modulus of the hybrid fiber HPC, but the difference was not significant. The Poisson ratio of each group was closer, with an average value of 0.19.
y
C (dy/dx=0) 1.0 D (d2y/dx2=0) A
4.2. The equation for compressive stress-strain curve of hybrid HPC
x 0
1.0
According to the above analysis, the compressive stress-strain curve of hybrid HPCs is similar to that of normal concrete (NC). Therefore, the equation form of the stress–strain curve of NC can be applied to hybrid HPC. Presently, numerous mathematical equations for the stress–strain curve of NC have been put forward,
xD
Fig. 7. The typical compressive stress-strain curve of HPC.
Table 6 Characteristic values of compressive stress-strain curves of hybrid fiber HPC. Number
BF volume fraction/%
PF volume fraction/%
Cube compressive strength f cu /MPa
Peak strain
BF0PF0 BF0.10PF0.025 BF0.10PF0.033 BF0.10PF0.042 BF0.15PF0.025 BF0.15PF0.033 BF0.15PF0.042 BF0.20PF0.025 BF0.20PF0.033 BF0.20PF0.042
0 0.10 0.10 0.10 0.15 0.15 0.15 0.20 0.20 0.20
0 0.025 0.033 0.042 0.025 0.033 0.042 0.025 0.033 0.042
86.6 81.9 80.1 79.9 83.2 96.4 88.7 84.3 89.6 75.2
3023 2952 3015 2899 3031 3356 3130 3057 3144 2848
ec /10-6
Elastic modulus E (GPa) – 43.0 32.9 41.5 35.5 40.8 41.3 40.0 42.4 40.9
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D. Wang et al. / Construction and Building Materials 197 (2019) 464–473
sixth-time polynomial equation is used for describing the ascending curve. The equation is as follows:
0.0034
Strain at peak load
Test result Eq.(6)
y ¼ a þ a1 x þ a2 x5 þ a3 x6
The following boundary conditions can be obtained from Fig. 7 ¼ 0. Separately substi(b):①x ¼ 0, y ¼ 0; ②x ¼ 1, y ¼ 1; ③dy dx
0.0032
x¼1
tuting (2) can be obtained the equation:
8 > : a1 þ 5a2 þ 6a3 ¼ 0
0.0030
70
75
80
85
90
95
100
y ¼ a1 x þ ð6 5a1 Þx5 þ ð4a1 5Þx6
Cube compressive strength (MPa) Fig. 8. Relationship between peak strain
dy drc =f c drc =dec jx¼0 Ec ¼ ¼ ¼ dxx¼0 dec =ec0 x¼0 f c =ec0 Ec0
1.2
1.0
1.0
1.0
0.8
0.8
0.8
0.6
0.6
0.6
0.2 0.0 0.0
0.2
0.4
y=σ/fc
1.2
BF0.10PF0.025-1 BF0.10PF0.025-2 BF0.10PF0.025-3 Fitting curve 0.6 0.8 1.0 1.2
0.4
BF0.10PF0.033-1 BF0.10PF0.033-2 BF0.10PF0.033-3 Fitting curve
0.2 1.4
0.0 0.0
1.6
0.2
0.4
0.6
0.8
1.0
0.4
1.2
1.4
0.0 0.0
1.6
(b) BF0.10PF0.033
1.0
1.0
0.8
0.8
0.8
0.6
0.6
0.6
0.4 BF0.15PF0.025-1 BF0.15PF0.025-2 Fitting curve 0.4
0.6
0.8
1.0
y=σ/fc
1.0
y=σ/fc
1.2
0.2
0.4
BF0.15PF0.033-1 BF0.15PF0.033-2 BF0.15PF0.033-3 Fitting curve
0.2 1.2
1.4
0.0 0.0
1.6
0.2
0.4
0.6
(c) BF0.15PF0.025
0.8
1.0
0.4
1.2
1.4
0.0 0.0
1.6
1.0
0.8
0.8
0.8
0.6
0.6
0.6
0.2
0.4
0.6
0.8
1.0
y=σ/fc
1.0
y=σ/fc
1.0
BF0.20PF0.033-1 BF0.20PF0.033-2 BF0.20PF0.033-3 Fitting curve
0.2
1.2
x=ε/εc0
(f) BF0.20PF0.025
1.4
1.6
0.0 0.0
0.2
0.4
0.6
0.8
1.2
1.4
1.6
0.4
0.6
0.8
1.0
1.2
1.4
1.6
(e) BF0.15PF0.042 1.2
0.4
1.0
x=ε/εc0
1.2
0.0 0.0
0.2
(d) BF0.15PF0.033
BF0.20PF0.025-1 BF0.20PF0.025-2 BF0.20PF0.025-3 Fitting curve
0.8
BF0.15PF0.042-1 BF0.15PF0.042-2 BF0.15PF0.042-3 Fitting curve
0.2
1.2
0.2
0.6
x=ε/εc0
x=ε/εc0
0.4
0.4
(c) BF0.10PF0.042
1.2
0.0 0.0
0.2
x=ε/εc0
1.2
0.2
BF0.10PF0.042-1 BF0.10PF0.042-2 Fitting curve
0.2
x=ε/εc0
x=ε/εc0
(a) BF0.10PF0.025
ð10Þ
where E0 is the initial tangential elastic modulus of concrete with units of N/mm2 and Ec is the peak secant modulus with units of N/mm2. Thus, a1 is the ratio of the initial tangential elastic modulus
1.2
y=σ/fc
y=σ/fc
including the unified and segmental equations for ascending and descending curves [26,27]. The equation for the ascending curve is usually polynomial. Because the compressive strength of hybrid HPC is high, and the linear part of the ascending curve is longer, a
0.4
ð9Þ
When x ¼ 0, dy=dx ¼ a1 :
ec and axial compressive strength f c .
a1 ¼
y=σ/fc
ð8Þ
a2 and a3 can be represented by a1 :
0.0028
y=σ/fc
ð7Þ
1.0
0.4
BF0.20PF0.042-1 BF0.20PF0.042-2 BF0.20PF0.042-3 Fitting curve
0.2 1.2
1.4
1.6
0.0 0.0
x=ε/εc0
(g) BF0.20PF0.033 Fig. 9. The experimental curves and fitting curves of stress-strain relationship.
0.2
0.4
0.6
0.8
1.0
1.2
x=ε/εc0
(h) BF0.20PF0.042
1.4
1.6
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D. Wang et al. / Construction and Building Materials 197 (2019) 464–473
to the peak secant modulus of the concrete. According to this con2
dition, when 0 6 x < 1; d y=dx2 6 0, that the range of a1 is 1.0–1.5. The descending curve is described by a rational fraction, and the suggested equation is given by Eq. (11).
y¼
x
ð11Þ
ax2 þ bx þ c
where x ¼ 1, y ¼ 1, dy = 0. Based on this condition the relation equadx tions between c, b and a can be obtained.
c¼a
ð12Þ
b ¼ 1 2a y¼
x
ax2 þ x 2ax þ a
¼
x
ð13Þ
aðx 1Þ2 þ x
x For the descending curve, x P 1, 0 6 y ¼ aðx1Þ 6 1. So 2 þx
aðx 1Þ2 þ x P 0 and aðx 1Þ2 P 0. Therefore, a should satisfy the conditions: a > 0. In this paper, the compressive stress-strain curves of each group are closer. Therefore, a unified mathematical expression is adopted for each group. Through the nonlinear fitting of the measured curve, the parameters a1 and a for each group hybrid fiber HPC are obtained. The stress-strain curve and its fitting for different groups are shown in Fig. 9. It can be seen from Fig. 9 that the value of the parameter is related to the volume fraction of basalt fiber V BF and the volume fraction of polypropylene fiber (V PF ). The variation trend of each group curve can be seen: in the early stage of loading, the curve curvature of each group is larger, and the curve is approximately linear. This finding indicates that the hybrid fiber HPC is in the elastic stage. Some curves will appear concave, which is caused by internal defects in the HPC, but these will not affect the overall trend of the curve. When the stress of the HPC specimen exceeds 50%–60% of the peak stress, the curve begins to deviate from the linear growth trend and the slope decreases. At this point the test curve in the fitting curve fluctuates, but the trend is basically the same. As the stress continues to increase, the fiber tension is increased. The strain continues to increase until the fiber is pulled out or pulled apart. When the internal and external cracks pass through each other, the specimen is destroyed. The relation of parameter (a1 and a) and the fibers volume fraction (V BF and V PF ) were acquired by regressing experimental data of experiment with the least square method.
a1 ¼ 1:417 þ 0:697V BF 6:699V PF ; 0:1% 6 V BF 6 0:2% ;
0:025% 6 V PF 6 0:042%
ð14Þ
a ¼ 5:638 þ 24:01V BF 468:34V PF ; 0:1% 6 V BF 6 0:2% ;
0:025% 6 V PF 6 0:042%
ð15Þ
Table 7 lists the value of each set of experimental parameters and the calculated values of the parameters. The average value of the ratio between the experimental value and calculated value are 1.000 and 1.004 for a1 and a; the mean square errors are 0.041 and 0.197; and the variable coefficients are 0.046 and 0.196, respectively. 5. Conclusions This laboratory study examined the compressive strength, splitting flexural strength and tensile strength with single and hybrid basalt and polypropylene fibers. The hybrid effect of the combined basalt and polypropylene fibers with different volume fractions on the HPC is evaluated. Based on the study, the following conclusions can be drawn: (1) The compressive strength, flexural strength and splitting tensile strength of HPC increased with the increase of the fiber volume fraction of single basalt fiber or polypropylene fiber, but the increase of compressive strength was not significant. When the volume fraction of a single fiber is less than 7.2%, the flexural strength and splitting tensile strength were significantly improved. Compared with HPC without fiber, the flexural strength of HPC reinforced with a single fiber was increased by 1.1%–24.5%, and the splitting tensile strength was increased by 21.9%–44.5%; the effect of polypropylene fiber on the flexural strength and splitting tensile strength of HPC is superior to that of basalt fiber. (2) When the two types of fibers are mixed, there are positive and negative synergy effects. When the volume fraction of basalt fiber was 0.15% and the polypropylene fiber was 0.033%, the synergy effect of hybrid fibers was the best. The compressive strength, flexural strength and splitting strength are increased by 14.1%, 22.8% and 48.6%, respectively, compared with that of HPC without fiber. It was suggested that the volume fraction of basalt fiber in the basalt fiber and polypropylene fiber hybrid fiber concrete be set to 0.15%, and the volume fraction of polypropylene fiber did not exceed 0.033%. (3) Based on the experimental results, a formula for calculating the flexural strength of hybrid fiber HPC is obtained by fitting. The formula was f f ¼ ð1 þ 79qBF þ 710qPF 443265qBF qPF Þf f0 . The conversion relationship between flexural strength and compressive strength was established, which was f f ¼ 0:118f cu 0:435. (4) The sixth-time polynomial and rational fraction are used to fit the ascending and descending sections of the stressstrain curves of the hybrid fiber HPC, and the relationship between the curve parameter (a1 and a) and the fibers volume fraction (V BF and V PF ) is proposed.
Table 7 Comparison of experimental values and calculation value. VBF/(%)
VPF/(%)
0.1 0.1 0.1 0.15 0.15 0.15 0.2 0.2 0.2
0.025 0.033 0.042 0.025 0.033 0.042 0.025 0.033 0.042
a
a1 Experimental value
Calculation value
Ratio
Experimental value
Calculation value
Ratio
1.34 1.297 1.214 1.23 1.32 1.22 1.44 1.38 1.24
1.32 1.27 1.21 1.35 1.30 1.24 1.39 1.34 1.28
1.02 1.02 1.01 0.91 1.02 0.98 1.04 1.03 0.97
12.72 16.24 29.08 15.01 9.92 17.45 15.66 14.67 11.38
14.95 18.69 22.91 13.75 — 21.71 12.54 16.29 —
0.85 0.87 1.27 1.09 — 0.80 1.25 0.90 —
D. Wang et al. / Construction and Building Materials 197 (2019) 464–473
Author contributions Conceptualization, D.H.W.; Data curation, L.B.X.; Investigation, H.S.; Formal analysis, D.H.W.; Project administration, Y.Z.J.; Supervision, J.Z.; Writing—original draft, D.H.W.; Writing—review & editing, D.H.W. and Y.Z.J. Conflict of interest The authors declare that they have no conflict of interest regarding the publication of this paper. Acknowledgements The financial support from National Science Foundation of China (Grant Nos. 51378095 and 51878128) is greatly appreciated. References [1] F.U.A. Shaikh, Review of mechanical properties of short fibre reinforced geopolymer composites, Constr. Build. Mater. 43 (2013) 37–49. [2] A.B. Kizilkanat, N. Kabay, V. Akyüncü, S. Chowdhury, A.H. Akça, Mechanical properties and fracture behavior of basalt and glass fiber reinforced concrete: an experimental study, Constr. Build. Mater. 100 (2015) 218–224. [3] J. Thomas, A. Ramaswamy, Mechanical properties of steel fiber-reinforced concrete, J. Mater. Civ. Eng. 19 (5) (2007) 385–392. [4] M.G. Alberti, A. Enfedaque, J.C. Gálvez, Fibre reinforced concrete with a combination of polyolefin and steel-hooked fibres, Compos. Struct. 171 (2017) 317–325. [5] K. Habel, M. Viviani, E. Denarié, E. Brühwiler, Development of the mechanical properties of an Ultra-High Performance Fiber Reinforced Concrete (UHPFRC), Cem. Concr. Res. 36 (7) (2006) 1362–1370. [6] V. Afroughsabet, L. Biolzi, T. Ozbakkaloglu, High-performance fiber-reinforced concrete: a review, J. Mater. Sci. 51 (14) (2016) 6517–6551. [7] S.F.U. Ahmed, M. Maalej, Tensile strain hardening behaviour of hybrid steelpolyethylene fibre reinforced cementitious composites, Constr. Build. Mater. 23 (1) (2009) 96–106. [8] N. Banthia, F. Majdzadeh, J. Wu, V. Bindiganavile, Fiber synergy in Hybrid Fiber Reinforced Concrete (HyFRC) in flexure and direct shear, Cem. Concr. Compos. 48 (2014) 91–97. [9] C.X. Qian, P. Stroeven, Development of hybrid polypropylene-steel fibrereinforced concrete, Cem. Concr. Res. 30 (1) (2000) 63–69.
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Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Mechanical properties of high performance concrete reinforced with basalt fiber and polypropylene fiber Dehong Wang ⇑, Yanzhong Ju ⇑, Hao Shen, Libin Xu School of Civil Engineering and Architecture, Northeast Electric Power University, Jilin 132012, China
h i g h l i g h t s An experimental study is conducted on hybrid fiber reinforced high performance concrete (HPC). The influence of basalt fiber (BF) and polypropylene fiber (PF) on the mechanical properties of HPC are determined. A formula for calculating the flexural strength of hybrid fiber HPC is developed. The mathematical expression of compressive stress-strain of hybrid fiber reinforced HPC is derived.
a r t i c l e
i n f o
Article history: Received 9 July 2018 Received in revised form 18 October 2018 Accepted 23 November 2018
Keywords: High performance concrete Basalt fiber Polypropylene fiber Mechanical properties Stress-strain relationship
a b s t r a c t The mechanical properties of high performance concrete (HPC) reinforced with basalt fiber and polypropylene fibers were investigated in this study. The influence of single basalt fibers (BFs), single polypropylene fibers (PF) and hybrid fibers with different contents on the compressive strength, flexural strength, splitting tensile strength and stress-strain curve of HPC were investigated. A formula for calculating the flexural strength of hybrid fiber HPC was developed, and a conversion relationship between flexural strength and cube compressive strength was proposed. On the basis of experimental data analysis, the mathematical expression of the compressive stress-strain of hybrid fiber reinforced HPC was derived. Test results indicate that, the strength of HPC reinforced with single doped basalt fibers or polypropylene fibers increases with the increase of the fiber volume fraction. However, the compressive strength increases slightly, while the flexural strength and splitting tensile strength are improved significantly. When the two types of fibers are mixed into HPC simultaneously, there are two kinds of synergy effects (positive and negative synergy effects). When the basalt fiber content is 0.15% and polypropylene fiber content is 0.033%, the synergy effect of fiber mixing is the best. At this time, the compressive strength, flexural strength and splitting tensile strength increased by 14.1%, 22.8% and 48.6%, respectively, when compared with those of HPC without fibers. Ó 2018 Elsevier Ltd. All rights reserved.
1. Introduction Concrete is a widely used material in civil engineering construction. However, normal concrete exhibits poor tensile properties and low ductility [1,2]. The addition of fibers to the concrete mixture can significantly improve the concrete’s mechanical properties, especially for tensile strength [3,4]. High performance concrete (HPC) reinforced with fibers was developed for high strength, toughness, and durability [5,6]. The addition of single fiber can only improve the performance of a single aspect of the concrete, and enhancing the overall performance of concrete, can be achieved by mixing with different fibers [7]. Different types or ⇑ Corresponding authors. E-mail addresses: [email protected] (D. Wang), [email protected] (Y. Ju). https://doi.org/10.1016/j.conbuildmat.2018.11.181 0950-0618/Ó 2018 Elsevier Ltd. All rights reserved.
sizes of fibers are mixed into concrete with a specific admixture to form a hybrid fiber concrete. Different types of fiber can be rationally combined in a concrete matrix, which reinforce the performance of hybrid fiber reinforced concrete at multi-scale [8,9]. Moreover, the cost can be reduced by using cheaper synthetic fibers instead of metal fibers [10]. Walton et al. [11] reported that adding hybrid mixed inorganic fibers and organic fibers into concrete can improve the impact resistance and tensile properties of the concrete matrix. Soroushian et al. [12] investigated the performance of concrete reinforced with two different types of fiber. The experimental results show that the flexural toughness and impact resistance of hybrid fiber concretes are enhanced to some extent, but when compared with plain concrete the compressive strength has slightly decreased. Yew et al. [13] investigated the performances of concrete reinforced with various polypropylene fibers.
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D. Wang et al. / Construction and Building Materials 197 (2019) 464–473
Polypropylene fibers can be used to enhance the tensile and flexural strength and the elasticity modulus of concrete. Moreover, the addition of a 0.5% volume fraction of polypropylene fibers resulted in a 95.8% reduction in the slump. Park et al. [14] investigated the influence of hybrid steel fibers on the tensile behavior of UHPHFRC. The results indicated that the shape of the tensile stress strain curves of UHPHFRC is mainly affected by the type of macro-fiber rather than micro fiber. The utilization of favorably affected the multiple cracking behaviors and strain hardening of UHPHFRC, and. Lawler et al. [15] investigated the flexural toughness, restrained shrinkage and permeability of microfiber and macrofiber hybrid fiber reinforced concrete. The results showed that the microfibers improved the first-crack strength and delayed the development of macrocracks, and thus the strength and crack resistance of the hybrid fiber concrete was better than the resistance of the concrete containing the macrofiber only. Aslani et al. [16] investigated the mechanical properties of hybrid steel fiber and polypropylene fiber. The experimental results showed that the compressive strength and modulus of elasticity of the hybrid fiber reinforced self-compacting concrete of that was 91 days old were higher than those of the steel and polypropylene fiber selfcompacting concrete at the same age. Basalt fiber is a new type of eco-friendly, green and highperformance fiber, it has excellent performance, and has been widely used in many areas [2,17,18]. Basalt fiber can improve the flexural strength, toughness as well as the fracture energy of cement matrix composites [19]. The elastic modulus of basalt fiber can reach 93–115 GPa, which is considerably larger than that of chemical fibers like polypropylene fiber, polyvinyl alcohol fiber and so on. Basalt fiber and polypropylene fiber can form complementary advantages in the concrete matrix, and make up for the defects of each individual fiber, improve the tensile strength of concrete matrix in different scale. Hybrid of basalt fiber and polypropylene fiber instead of steel fiber into HPC matrix have attracted great interests to improve the defect of steel fiber HPC corrosion, which can also reduce the material costs (see Table 3). The research on the mechanical properties of HPC reinforced with basalt fiber and polypropylene fiber is not adequate in the past. The quantitative relationship between mechanical properties of hybrid fiber HPC and fiber content are not clear, and the constitutive relationship of HPC reinforced with basalt fiber and polypropylene fiber has not been investigated. Thus, the main objective of this study is to investigate the mechanical properties of HPC reinforced
with basalt fiber and polypropylene fiber. The interest of this study is to quantify and discuss the effect of basalt fiber and polypropylene fiber and hybrid fibers in enhancing the mechanical properties of HPC, proposed the formulas for predicting the strengths of HPC reinforced with different basalt fiber and polypropylene fiber volume fraction, and established the stress-strain relationship model of hybrid fiber HPC. This research also aims to find the optimum basalt fiber and polypropylene fiber contents that could significantly enhance the mechanical properties of HPC. 2. Experimental program 2.1. Materials Hybrid fiber HPC was prepared by the following ingredients: Grade 42.5 ordinary Portland cement, silica fume, quartz sand, basalt fiber, polypropylene fiber, water reducer and water. The chemical compositions and physical properties and of the cement are shown in Table 1. Silica fume used in this study has a particle size of less than 2 lm, a density of 2.214 kg/m3, and a specific surface area of 143,100 cm2/g. Table 2 summarizes the chemical compositions of the silica fume. The diameter of quartz sand ranges from 0 to 1.25 mm. Table 3 summarizes the main performance indexes and price of basalt fiber and polypropylene fiber, the properties and cost steel fibers are also presented in Table 3 for the purpose of comparing the cost of different types of fiber. Fig. 1 shows the appearance of two types of fibers. Water reducer utilized in this study is a non-naphthalene high-performance water reducer, and the water reduction rate is 29%. 2.2. Mix proportions To study the influence of different contents of the two types of fibers on HPC, 16 different test mixture proportions were designed in this study. The two fibers are nonmetallic fibers, and when the fraction is too large they easily agglomerate. Therefore, the volume fraction of basalt fiber was varied in three groups as 0.10%, 0.15%, 0.20%, and the polypropylene fiber volume fraction was varied in groups as 0.025%, 0.033%, 0.042% [19]. The ratio of water to cement was 0.22, the ratio of silica to cement was 0.3, and the ratio of sand to cement was 1.3 [20]. For the sake of comparative analysis, a mixture of HPC without any fibers, and six mix proportions were
Table 1 The chemical compositions and physical properties of the cement. Mineral compositions (%)
Physical properties
C3S
C2S
C3A
C4AF
f-CaO
f-MgO
Density (g/cm3)
fct,f,3 /MPa
fct,f,28 /MPa
fct,f,3 /MPa
fct,f,28 /MPa
60.5
18.1
7.4
8.9
0.9
1.8
3.18
5.17
9.62
29.2
61.5
Table 2 The chemical compositions of silica fume.
*
Mineral compositions
SiO2
Fe2O3
Al2O3
CaO
MgO
LO.I*
K2O
Na2O
FC
SO3
Content/%
82.22
1.81
0.97
0.36
1.31
1.45
0.84
0.16
0.92
0.27
LO.I = Loss on ignition.
Table 3 The performance indexes of two types of fibers. Fiber type
Density/ gcm3
Elastic modulus/GPa
Tensile strength /MPa
Length /mm
Length-to-diameter ratio
Fibers price (USD/m3-0.042%Vf)
Basalt fiber (BF) Polypropylene fiber (PF) Steel fiber (SF)
2.75 0.91 7.86
80–110 3.5 201
3000–4000 650 2850
12 12 13
1000 600 65
3.00 0.33 9.04
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(a) basalt fiber and (b) polypropylene fiber Fig. 1. The fibers used in the study.
Table 4 The mix proportions of HPC. Specimen
Cement (kg)
Silica fume (kg)
BF0PF0 BF0.10PF0 BF0.15PF0 BF0.20PF0 BF0PF0.025 BF0PF0.033 BF0PF0.042 BF0.10PF0.025 BF0.10PF0.033 BF0.10PF0.042 BF0.15PF0.025 BF0.15PF0.033 BF0.15PF0.042 BF0.20PF0.025 BF0.20PF0.033 BF0.20PF0.042
756.89 756.16 755.80 755.43 756.71 756.65 756.58 755.98 755.92 755.86 755.62 755.56 755.50 755.25 755.19 755.13
227.07 226.85 226.74 226.63 227.01 226.99 226.98 226.79 226.78 226.76 226.68 226.67 226.65 226.58 226.56 226.54
Quartz sand/(kg) 0.63–1.25 (mm)
0.32–0.63 (mm)
0.16–0.32 (mm)
738.12 737.41 737.05 736.70 737.94 737.88 737.82 737.23 737.17 737.11 736.88 736.82 736.76 736.52 736.46 736.40
371.18 370.82 370.64 370.47 371.09 371.06 371.03 370.73 370.70 370.67 370.55 370.52 370.49 370.38 370.35 370.32
169.54 169.38 169.30 169.22 169.50 169.49 169.48 169.34 169.33 169.31 169.26 169.24 169.23 169.18 169.16 169.15
BF (kg)
PF (kg)
Water reducer (kg)
Water (kg)
0.00 2.75 4.13 5.50 0.00 0.00 0.00 2.75 2.75 2.75 4.13 4.13 4.13 5.50 5.50 5.50
0.00 0.00 0.00 0.00 0.23 0.30 0.38 0.23 0.30 0.38 0.23 0.30 0.38 0.23 0.30 0.38
68.12 68.05 68.02 67.99 68.10 68.10 68.09 68.04 68.03 68.03 68.01 68.00 67.99 67.97 67.97 67.96
169.09 168.93 168.85 168.76 169.05 169.03 169.02 168.89 168.87 168.86 168.80 168.79 168.78 168.72 168.71 168.70
[Note] BF = basalt fiber (fraction = 0.1%, 0.15%, 0.2%), PF = polypropylene fiber (fraction = 0.025%, 0.033%, 0.042%).
performed with only one type of fiber. The mix proportions are shown in Table 4, and abbreviations are used for mixtures according to the BF and PF content. BF and PF contents were also given in the abbreviations of mixtures. For instance, BF0.10PF0.025 means that the volume fraction of BF is 0.1% and the volume fraction of PF is 0.025%. 2.3. Fabrication of specimen and loading methods First the quartz sand was mixed for 2–3 min without water in the mixer, then cement and silica fume were added into the mixer and remixed for 3 min. The next step was to add half water and water reducer, and then, the mixture was remixed for approximately 3 min. Subsequently, the remaining half of the water and the fibers were added and remixed for approximately 4 min. Then, the mixture was cast into molds and vibrated on high-frequency vibration table. The specimens were kept in the molds for 24 h under the standard conditions (room temperature of approximately 20 °C and humidity of 95%), then the molds were removed, and specimens were cured in steam of approximately 90 °C for 3 days in the concrete accelerated curing box. The heating rate of the curing box was controlled to increase by no more than 15 °C per hour, and gradually increased to 90 °C. After the steam curing was finished, the specimens were moved into the standard curing room for 24 days. The Chinese code GB/T 31387-2015 Reactive powder Concrete was used to determine the mechanical properties of hybrid fiber HPC. Cube specimens of 100 mm 100 mm 100 mm were used for cube compression and splitting tensile strength tests. Prismatic
specimens of 100 mm 100 mm 300 mm were used for compression stress-strain tests, and prismatic specimens of 100 mm 100 mm 400 mm with a span of 300 mm were used for flexural strength tests. The compression strength test and stress–strain test were loaded by a 5000 kN electro-hydraulic servo pressure testing machine, and the splitting tensile strength and flexural strength were tested in a 1000kN electrohydraulic servo universal testing machine. To obtain the stable descent stage of the stress-strain curve, a rigid auxiliary frame was employed. The load was measured by a force sensor. Fig. 2 is the experimental loading device diagram. According to the Chinese code GB/T 31387-2015 Reactive powder concrete, the loading rates of the compressive strength, splitting tensile strength and flexural strength test were 1.2 MPa/s, 0.08 MPa/s and 0.1 MPa/s, respectively.
3. Results and discussion 3.1. Compressive strength Fig. 3 shows the compressive strength of HPC reinforced with different single fiber or hybrid fiber content. It can be seen from Fig. 3 that when the content of single basalt fiber or polypropylene fiber is low, the addition of fiber cannot improve the compressive strength of HPC, and can even reduce its strength. The compressive strength of the compressive strength of BF0.1PF0 is 0.35% lower than that of BF0PF0 without fiber. The compressive strength of BF0PF0025 is 5.22% lower than that of BF0PF0. A similar result
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5 000 kN test machine
Rigid auxiliary frame Displacement sensor Specimen Force sensor
(a) Loading schematic diagram
(b) Test photo
Fig. 2. Compression stress-strain curve test loading diagram.
The volume fraction of PF is 0 The volume fraction of PF is 0.025%
Compressive strength (MPa)
120 100
The volume fraction of PF is 0.033% The volume fraction of PF is 0.042% 110.07
96.47
98.6 91.43
101.23
96.13 94.67
97.37 98.13 89.57
100.3
103.43 97.33
94.37 88.47
87.13
80 60 40 20 0
0
0.1
0.15
0.2
The volume fraction of BF (%) Fig. 3. Compressive strength of fiber reinforced HPC.
has been reported for the compressive behavior of basalt fiber in high-strength concrete [2]. This similarity may be due to basalt fiber belonging to the high modulus fiber; thus, the load-bearing skeleton cannot form in the matrix when the volume fraction of the fiber is low. The enhancement effect on compressive strength of HPC is smaller than the negative influences of defects caused by the fibers. When the fiber content of single basalt fiber or polypropylene fiber mixtures exceeds a certain scope, the compressive strength of HPC increases with the increase of fiber content. When the volume fraction of basalt fiber is 0.20%, the compressive strength of BF0.2PF0 is 103.43 MPa, which is 7.21% higher than that of BF0PF0, which is 96.47 MPa. The compressive strength of BF0PF0.042 is 101.23 MPa, which is 4.93% higher than that of BF0PF0. Based on the correlation analysis performed in the SPSS software, the correlation coefficient between the basalt fiber volume fraction and compressive strength of HPC is 0.737, and the correlation coefficient between the polypropylene fiber volume fraction and compressive strength of HPC is 0.433. It can be seen that the addition of basalt fiber has a more significant influence on compressive strength of HPC. The diameter of the polypropylene fiber is larger, and the air entraining effect of the fiber increases the pores in the concrete mix, which means that the bonding between the polypropylene fiber and the concrete
matrix is less than that of basalt fiber. Therefore, adding a proper amount of fiber can improve the strength and toughness of HPC, but if the fiber fraction is too low or too high, it will increase its internal defects, which is not conducive to the improvement of strength. For the hybrid fiber HPC, when the volume fraction of the basalt fiber is 0.10% and 0.20%, the compressive strength of HPC decreases with the increase of the polypropylene fiber volume fraction. This may be due to a negative hybrid effect of the two types of fiber. When volume fraction of basalt fiber is small, such as 0.10%, the basalt fiber cannot form a bearing skeleton in the HPC matrix. The low elastic modulus of polypropylene fiber has little contribution to the compressive strength of concrete, and adding polypropylene fiber caused more defects in HPC matrix. When the volume content of basalt fiber reaches 0.20%, the fiber volume fraction is large, so it cannot be dispersed uniformly in HPC. With the addition of polypropylene fiber, wrapped together with the basalt fiber, it is more detrimental to its uniform dispersion and easily agglomerates. Some weak interfaces are formed in HPC, which decrease the strength of the HPC. As seen from Fig. 3, the optimum mixing is achieved when the basalt fiber volume fraction is 0.15%, the volume fraction of polypropylene fiber is 0.033%, and the compressive strength reaches 110.1 MPa, which is 14.10%
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higher than that of HPC without fiber. Under this combination, the fibers can be distributed uniformly in concrete. The two types of fibers can have a complementary effect on the elastic modulus. The elastic modulus of polypropylene fiber is low, which can delay the formation and propagation of microcracks in the early stage of hardening and reduce the number of crack sources. The elastic modulus of basalt fiber is higher and the influence of crack propagation on hardening concrete is better. Therefore, the two fibers can play a role at different levels to improve the compressive strength of HPC.
The test results showed that there was an approximately linear relationship between the flexural strength and the cube compressive strength of the hybrid fiber reinforced HPC. Statistical analyses of the flexural strength and cube compressive strength of the basalt fiber, polypropylene fiber and hybrid fiber HPC were conducted, including the test results in this paper and the results from the previous literatures [21–23]. According to the test data, the relationship between the flexural strength (ff) and the cube compressive strength (fcu) HPC can be expressed as follows, with Fig. 5 acting as a comparison between the fitting curves and test results.
3.2. Flexural strength and splitting tensile strength
f f ¼ 0:118f cu 0:435
f f ¼ ð1 þ 79qBF þ 710qPF 443265qBF qPF Þf f0
12
Flexural strength (MPa)
8
16 14 12
ff=0.118fcu-0.435
10 8 6 4 60
90
120
Fig. 5. The relationship between the flexural strength and cube compressive strength of hybrid fiber reinforced HPC.
The volume fraction of PF is 0.033%
The volume fraction of PF is 0.025%
The volume fraction of PF is 0.042%
10.33 9.74
9.9 10.01
10.47
10.19 9.53
9.36
9.57 8.8
8.39
8.3
8.71
6 4 2 0
0
0.1
150
Cube compressive strength fcu (MPa)
The volume fraction of PF is 0
9.93 9.97
10
18
ð1Þ
where ff and ff0 are the flexural strength of hybrid fiber HPC and matrix HPC, respectively; and qBF and qPF are the basalt fiber volume fraction and polypropylene fiber volume fraction, respectively.
ð2Þ
Fig. 6 shows the test results of the splitting tensile strength, including the single and hybrid fibers. It can be seen from Fig. 6 that the enhancement effect of fiber on the splitting tensile strength is significant. Compared with the splitting tensile strength of HPC without fiber, the splitting tensile strength of HPC reinforced with single basalt fibers increased by 21.90%–38.33%, and the splitting tensile strength of HPC reinforced with single polypropylene fibers increased by 32.86%–44.52%. The results show that the addition of basalt fiber or polypropylene fiber forms
Flexural strength ff (MPa)
Fig. 4 shows the flexural strength of single and hybrid fiber HPC. It can be seen from Fig. 4 that the addition of different types of fiber has different scales of improvement on flexural strength of the HPC. When the volume fraction of basalt fiber increases from 0.01% to 0.15%, to 0.20%, the flexural strength increases by 1.08%, 12.77% and 15.30%, respectively. The addition of basalt fiber can prevent cracks and improve the flexural strength. When the volume fraction of polypropylene fiber is in the range of 0.025% to 0.042%, the strength increases by 19.64% to 24.46%. It can be seen that the flexural strength of the hybrid fiber HPC is higher than that of the single fiber when the basalt fiber volume fraction is 0.15% and the polypropylene fiber volume fraction is 0.025% and 0.033% and when compared with the HPC without fiber, the flexural strength increased by 26.14% and 22.77%, respectively. When the volume fraction of basalt fiber is 0.20%, the flexural strength of HPC is lower than that of the single fiber HPC, but it is still higher than that of the HPC without fiber. This phenomenon may be explained by the fact that the two fibers are intertwined with each other, hindering their uniform dispersion in concrete. The correlation coefficient between the basalt fiber volume fraction and the flexural strength of HPC is 0.895 while that of the polypropylene fiber is 0.975. This indicates that the influence of the polypropylene fiber on the flexural strength is greater than that of the basalt fiber. According to the experimental data, a formula for calculating the flexural strength (ff) of a hybrid fiber HPC is:
0.15
The volume fraction of BF (%) Fig. 4. Flexural strength of fiber reinforced HPC.
0.2
8.33
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D. Wang et al. / Construction and Building Materials 197 (2019) 464–473
6
4
5.58
The volume fraction of PF is 0
The volume fraction of PF is 0.033%
The volume fraction of PF is 0.025%
The volume fraction of PF is 0.042%
5.75
6.39 6.24
6.07
5.74
5.59
5.33 5.12 5.19 5.11
5.81
5.6
5.47 5.45
4.2
2
0
0
0.1
0.15
0.2
The volume fraction of BF (%) Fig. 6. Splitting tensile strength of fiber reinforced HPC.
a three-dimensional chaotic distribution in the concrete, which can delay the crack formation and result in an increase in the splitting tensile strength of HPC. The correlation analysis indicated polypropylene fibers with low elastic modulus have a great influence on the splitting tensile strength of HPC. It can be seen that the splitting tensile strength of the hybrid fiber HPC is higher than that of the single-fiber HPC. The splitting tensile strength of the hybrid fiber HPC is 23.57%–52.14% higher than that of HPC without fibers. The splitting tensile strength of BF0.15PF0.025 is the largest with a splitting tension strength of 6.39 MPa, and the splitting tensile strength of BF0.15PF0.025 is 6.24 MPa. It indicates that basalt fiber volume fraction of 0.15% and polypropylene fiber of volume fraction 0.025% are mixed to achieve their respective optimal content. In this mixture, the fibers can be dispersed evenly in the HPC matrix without agglomeration balling. When the fraction of basalt fiber is 0.20%, and the hybrid effect is poor, the splitting tensile strength of the hybrid fiber HPC is lower than that of HPC with single fiber, but it is still higher than that of HPC without fiber. The reason for this phenomenon may be explained by the fact that more fibers are distributed vertically, which cause more cracks and weak interface in the concrete. The relationship between the splitting tensile strength (ft) and flexural strength (ff) of HPC can be expressed as follows: 0:75
f t ¼ 1:027f f
ð3Þ
From the above result it can be seen that the addition of two types of fibers can significantly improve the resisting tension. In the early stage of loading, the tensile stress of HPC is relatively low, and with the formation of microcracks in HPC, the basalt fiber and polypropylene fiber play an increasing role. With an increasing load and microcrack propagation, and the tensile stress transmission is withstood by the basalt fiber and polypropylene fiber. The fibers delay the continued propagation of cracks, slow down the expansion rate, delay the breakage of the HPC specimen, and improve the toughness and tensile strength of the HPC. When the tensile stress exceeds the bond strength between the fibers and HPC matrix, the fibers are pulled out, and the reinforcement action disappears. 3.3. Synergy of BF and PF In the appropriate mixing range, the hybrid fibers in the HPC can play their respective roles to complement each other and
create a positive hybrid effect, which make the improvement of the mechanical properties of HPC more effective than that of single fibers. To analyze the influence of the synergy on the mechanical properties, the synergy effect coefficients are defined as follows:
ax1 ¼
bB - P þ bminðB;PÞ bmaxðB;PÞ þ bminðB;PÞ
ð4Þ
ax2 ¼
bB - P þ bmaxðB;PÞ bmaxðB;PÞ þ bminðB;PÞ
ð5Þ
where, ax1 , ax2 are the synergy effect coefficients, x represents the type of strength, c represents the compressive strength, ac1 and ac2 are the synergy effect coefficients of the compressive strength, f represents the flexural strength, af1 and af2 are the synergy effect coefficients of the flexural strength, s represents the split tensile strength, and as1 and as2 are the synergy effect coefficients of the split tensile strength. In the equation, b is the strength enhancement coefficient due to addition of fiber. b ¼ f x =f x0 , f x and f x0 are the strength of fiber HPC and the strength of HPC without fiber, respectively (compressive strength, flexural strength, split tensile strength), bB - P is the strength enhancement coefficient of hybrid fiber HPC, bmaxðB;PÞ is the maximum enhancement coefficient of single basalt fiber or polypropylene fiber, bminðB;PÞ is the minimum enhancement coefficient of single basalt fiber or polypropylene fiber. When ax1 > 1:0, the two types of fibers have a positive hybrid effect; When ax1 < 1:0, It needs to be judged according to ax2 . If ax2 > 1:0, it is a positive synergy effect; if ax2 < 1:0, it is a negative synergy effect. Table 5 shows the synergy effect coefficient of HPC’s compressive strength, splitting tensile strength and flexural strength. It can be seen from Table 5thatBF0.20PF0.033 and BF0.20PF0.042 with larger fiber volume fractions showed negative synergy effect. The three types of strength synergy effect coefficients of BF0.20PF0.042 were smaller than those of BF0.20PF0.033. It indicated that the fiber volume fraction of the two groups of hybrid fiber HPCs was on the high side. Both BF0.15PF0.025 and BF0.15PF0.033 showed positive synergy effects, which demonstrated that the combination of these fibers has shown the best improvement of the mechanical properties of HPC, and were the best fiber mixes of fiber. It can also be concluded that the basic mechanical properties of HPC can be improved only by adding
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Table 5 HPC strength synergy effect coefficient. Specimen
ac1
ac2
af1
af2
as1
as2
BF0.10PF0.025 BF0.10PF0.033 BF0.10PF0.042 BF0.15PF0.025 BF0.15PF0.033 BF0.15PF0.042 BF0.20PF0.025 BF0.20PF0.033 BF0.20PF0.042
0.992 0.954 0.929 1.004 1.059 0.995 0.969 0.955 0.927
1.017 0.966 0.954 – – 1.015 1.030 0.979 0.938
0.964 0.961 0.914 1.057 1.043 0.976 0.982 0.971 0.948
1.007 1.019 0.999 – – 1.004 1.002 0.976 0.970
0.990 0.996 0.983 1.028 1.011 0.959 0.942 0.936 0.899
1.074 1.082 1.087 – – 1.009 0.961 0.956 0.938
hybrid fibers in certain proportions. Based on the test, it is suggested that the volume fraction of basalt fiber in hybrid fiber HPC should be 0.15%, and volume fraction of polypropylene fiber should be no more than 0.033%.
4. Hybrid fiber HPC compression stress-strain relationship 4.1. Characteristics of compressive stress-strain curves of hybrid fiber HPC According to the test results, the slope of the stress-strain curve changed very little before 50% of the peak load, which shows a approximative linear slop. The proportion limit of the hybrid fiber HPC is higher than that of normal concrete by approximately 30%. The specimen enters a stable stage of development after the proportion limit. As the load steadily increases, several fine vertical cracks appear near the sides, and the slope of the curve begins to decrease. After the peak stress point, the specimen enters the crack instability stage, and the crack begins to widen. The slope of the
curve is negative. There is an inflection point in the descending curve. All the stress-strain curves are similar with ascending and descending curves. Considering that the peak stress and peak strain of HPC with different fiber proportions are different, the normalization is applied in the stress-strain curves. The stress-strain curves are converted into standard curves with x ¼ ec =ec0 and y ¼ rc =f c . f c and ec0 are, respectively, the compressive strength of HPC and the strain corresponding to the peak stress. Fig. 7 shows the typical normalization curve for HPC. A corresponds to the proportion limit point. C corresponds to the peak stress point. At the peak stress, the slope of the curve is 0. D is an inflection point with d2y/dx2 = 0. Table 6 contains the compression characteristic values of hybrid fiber HPC, including the compressive strength, peak strain and elastic modulus of prisms. When the volume fraction of basalt fiber is 0.1%, the axial compressive strength decreased gradually with the increase of polypropylene fiber volume fraction, but the decreasing trend was not obvious. When the volume fraction of basalt fiber was 0.15% and 0.2%, the axial compressive strength first rose and then decreased with the increase of polypropylene fiber volume fraction. When the volume fraction of basalt fiber was 0.15% and polypropylene fiber was 0.033%, the axial compressive strength reached its maximum value, which is 16.7% higher than that of HPC without fiber. The strain of hybrid fiber HPC at peak load ranges from 0.00285 to 0.00335, with an average value of 0.00305, which is slightly lower than that of steel fiber HPC [24]. The relationship between the peak strain ec and the axial compressive strength f c was approximately linear, an equation for describing the relationship were obtained with fitting tests data. As shown in Fig. 8.
ec ¼ ð1120 þ 22:8f c Þ 106
ð6Þ
The elastic modulus of hybrid fiber HPC was between 32.9 GPa and 43 GPa, which is lower than that of steel fiber HPC [24,25]. This could be attributed to the low elastic modulus of basalt fiber and polypropylene fiber. It was found that the elastic modulus of HPC was related to the fabrication of the specimen. In the experiment, the admixture of the two types of fibers will cause cracks in the concrete, which will lead to the change of the elastic modulus of the hybrid fiber HPC, but the difference was not significant. The Poisson ratio of each group was closer, with an average value of 0.19.
y
C (dy/dx=0) 1.0 D (d2y/dx2=0) A
4.2. The equation for compressive stress-strain curve of hybrid HPC
x 0
1.0
According to the above analysis, the compressive stress-strain curve of hybrid HPCs is similar to that of normal concrete (NC). Therefore, the equation form of the stress–strain curve of NC can be applied to hybrid HPC. Presently, numerous mathematical equations for the stress–strain curve of NC have been put forward,
xD
Fig. 7. The typical compressive stress-strain curve of HPC.
Table 6 Characteristic values of compressive stress-strain curves of hybrid fiber HPC. Number
BF volume fraction/%
PF volume fraction/%
Cube compressive strength f cu /MPa
Peak strain
BF0PF0 BF0.10PF0.025 BF0.10PF0.033 BF0.10PF0.042 BF0.15PF0.025 BF0.15PF0.033 BF0.15PF0.042 BF0.20PF0.025 BF0.20PF0.033 BF0.20PF0.042
0 0.10 0.10 0.10 0.15 0.15 0.15 0.20 0.20 0.20
0 0.025 0.033 0.042 0.025 0.033 0.042 0.025 0.033 0.042
86.6 81.9 80.1 79.9 83.2 96.4 88.7 84.3 89.6 75.2
3023 2952 3015 2899 3031 3356 3130 3057 3144 2848
ec /10-6
Elastic modulus E (GPa) – 43.0 32.9 41.5 35.5 40.8 41.3 40.0 42.4 40.9
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sixth-time polynomial equation is used for describing the ascending curve. The equation is as follows:
0.0034
Strain at peak load
Test result Eq.(6)
y ¼ a þ a1 x þ a2 x5 þ a3 x6
The following boundary conditions can be obtained from Fig. 7 ¼ 0. Separately substi(b):①x ¼ 0, y ¼ 0; ②x ¼ 1, y ¼ 1; ③dy dx
0.0032
x¼1
tuting (2) can be obtained the equation:
8 > : a1 þ 5a2 þ 6a3 ¼ 0
0.0030
70
75
80
85
90
95
100
y ¼ a1 x þ ð6 5a1 Þx5 þ ð4a1 5Þx6
Cube compressive strength (MPa) Fig. 8. Relationship between peak strain
dy drc =f c drc =dec jx¼0 Ec ¼ ¼ ¼ dxx¼0 dec =ec0 x¼0 f c =ec0 Ec0
1.2
1.0
1.0
1.0
0.8
0.8
0.8
0.6
0.6
0.6
0.2 0.0 0.0
0.2
0.4
y=σ/fc
1.2
BF0.10PF0.025-1 BF0.10PF0.025-2 BF0.10PF0.025-3 Fitting curve 0.6 0.8 1.0 1.2
0.4
BF0.10PF0.033-1 BF0.10PF0.033-2 BF0.10PF0.033-3 Fitting curve
0.2 1.4
0.0 0.0
1.6
0.2
0.4
0.6
0.8
1.0
0.4
1.2
1.4
0.0 0.0
1.6
(b) BF0.10PF0.033
1.0
1.0
0.8
0.8
0.8
0.6
0.6
0.6
0.4 BF0.15PF0.025-1 BF0.15PF0.025-2 Fitting curve 0.4
0.6
0.8
1.0
y=σ/fc
1.0
y=σ/fc
1.2
0.2
0.4
BF0.15PF0.033-1 BF0.15PF0.033-2 BF0.15PF0.033-3 Fitting curve
0.2 1.2
1.4
0.0 0.0
1.6
0.2
0.4
0.6
(c) BF0.15PF0.025
0.8
1.0
0.4
1.2
1.4
0.0 0.0
1.6
1.0
0.8
0.8
0.8
0.6
0.6
0.6
0.2
0.4
0.6
0.8
1.0
y=σ/fc
1.0
y=σ/fc
1.0
BF0.20PF0.033-1 BF0.20PF0.033-2 BF0.20PF0.033-3 Fitting curve
0.2
1.2
x=ε/εc0
(f) BF0.20PF0.025
1.4
1.6
0.0 0.0
0.2
0.4
0.6
0.8
1.2
1.4
1.6
0.4
0.6
0.8
1.0
1.2
1.4
1.6
(e) BF0.15PF0.042 1.2
0.4
1.0
x=ε/εc0
1.2
0.0 0.0
0.2
(d) BF0.15PF0.033
BF0.20PF0.025-1 BF0.20PF0.025-2 BF0.20PF0.025-3 Fitting curve
0.8
BF0.15PF0.042-1 BF0.15PF0.042-2 BF0.15PF0.042-3 Fitting curve
0.2
1.2
0.2
0.6
x=ε/εc0
x=ε/εc0
0.4
0.4
(c) BF0.10PF0.042
1.2
0.0 0.0
0.2
x=ε/εc0
1.2
0.2
BF0.10PF0.042-1 BF0.10PF0.042-2 Fitting curve
0.2
x=ε/εc0
x=ε/εc0
(a) BF0.10PF0.025
ð10Þ
where E0 is the initial tangential elastic modulus of concrete with units of N/mm2 and Ec is the peak secant modulus with units of N/mm2. Thus, a1 is the ratio of the initial tangential elastic modulus
1.2
y=σ/fc
y=σ/fc
including the unified and segmental equations for ascending and descending curves [26,27]. The equation for the ascending curve is usually polynomial. Because the compressive strength of hybrid HPC is high, and the linear part of the ascending curve is longer, a
0.4
ð9Þ
When x ¼ 0, dy=dx ¼ a1 :
ec and axial compressive strength f c .
a1 ¼
y=σ/fc
ð8Þ
a2 and a3 can be represented by a1 :
0.0028
y=σ/fc
ð7Þ
1.0
0.4
BF0.20PF0.042-1 BF0.20PF0.042-2 BF0.20PF0.042-3 Fitting curve
0.2 1.2
1.4
1.6
0.0 0.0
x=ε/εc0
(g) BF0.20PF0.033 Fig. 9. The experimental curves and fitting curves of stress-strain relationship.
0.2
0.4
0.6
0.8
1.0
1.2
x=ε/εc0
(h) BF0.20PF0.042
1.4
1.6
472
D. Wang et al. / Construction and Building Materials 197 (2019) 464–473
to the peak secant modulus of the concrete. According to this con2
dition, when 0 6 x < 1; d y=dx2 6 0, that the range of a1 is 1.0–1.5. The descending curve is described by a rational fraction, and the suggested equation is given by Eq. (11).
y¼
x
ð11Þ
ax2 þ bx þ c
where x ¼ 1, y ¼ 1, dy = 0. Based on this condition the relation equadx tions between c, b and a can be obtained.
c¼a
ð12Þ
b ¼ 1 2a y¼
x
ax2 þ x 2ax þ a
¼
x
ð13Þ
aðx 1Þ2 þ x
x For the descending curve, x P 1, 0 6 y ¼ aðx1Þ 6 1. So 2 þx
aðx 1Þ2 þ x P 0 and aðx 1Þ2 P 0. Therefore, a should satisfy the conditions: a > 0. In this paper, the compressive stress-strain curves of each group are closer. Therefore, a unified mathematical expression is adopted for each group. Through the nonlinear fitting of the measured curve, the parameters a1 and a for each group hybrid fiber HPC are obtained. The stress-strain curve and its fitting for different groups are shown in Fig. 9. It can be seen from Fig. 9 that the value of the parameter is related to the volume fraction of basalt fiber V BF and the volume fraction of polypropylene fiber (V PF ). The variation trend of each group curve can be seen: in the early stage of loading, the curve curvature of each group is larger, and the curve is approximately linear. This finding indicates that the hybrid fiber HPC is in the elastic stage. Some curves will appear concave, which is caused by internal defects in the HPC, but these will not affect the overall trend of the curve. When the stress of the HPC specimen exceeds 50%–60% of the peak stress, the curve begins to deviate from the linear growth trend and the slope decreases. At this point the test curve in the fitting curve fluctuates, but the trend is basically the same. As the stress continues to increase, the fiber tension is increased. The strain continues to increase until the fiber is pulled out or pulled apart. When the internal and external cracks pass through each other, the specimen is destroyed. The relation of parameter (a1 and a) and the fibers volume fraction (V BF and V PF ) were acquired by regressing experimental data of experiment with the least square method.
a1 ¼ 1:417 þ 0:697V BF 6:699V PF ; 0:1% 6 V BF 6 0:2% ;
0:025% 6 V PF 6 0:042%
ð14Þ
a ¼ 5:638 þ 24:01V BF 468:34V PF ; 0:1% 6 V BF 6 0:2% ;
0:025% 6 V PF 6 0:042%
ð15Þ
Table 7 lists the value of each set of experimental parameters and the calculated values of the parameters. The average value of the ratio between the experimental value and calculated value are 1.000 and 1.004 for a1 and a; the mean square errors are 0.041 and 0.197; and the variable coefficients are 0.046 and 0.196, respectively. 5. Conclusions This laboratory study examined the compressive strength, splitting flexural strength and tensile strength with single and hybrid basalt and polypropylene fibers. The hybrid effect of the combined basalt and polypropylene fibers with different volume fractions on the HPC is evaluated. Based on the study, the following conclusions can be drawn: (1) The compressive strength, flexural strength and splitting tensile strength of HPC increased with the increase of the fiber volume fraction of single basalt fiber or polypropylene fiber, but the increase of compressive strength was not significant. When the volume fraction of a single fiber is less than 7.2%, the flexural strength and splitting tensile strength were significantly improved. Compared with HPC without fiber, the flexural strength of HPC reinforced with a single fiber was increased by 1.1%–24.5%, and the splitting tensile strength was increased by 21.9%–44.5%; the effect of polypropylene fiber on the flexural strength and splitting tensile strength of HPC is superior to that of basalt fiber. (2) When the two types of fibers are mixed, there are positive and negative synergy effects. When the volume fraction of basalt fiber was 0.15% and the polypropylene fiber was 0.033%, the synergy effect of hybrid fibers was the best. The compressive strength, flexural strength and splitting strength are increased by 14.1%, 22.8% and 48.6%, respectively, compared with that of HPC without fiber. It was suggested that the volume fraction of basalt fiber in the basalt fiber and polypropylene fiber hybrid fiber concrete be set to 0.15%, and the volume fraction of polypropylene fiber did not exceed 0.033%. (3) Based on the experimental results, a formula for calculating the flexural strength of hybrid fiber HPC is obtained by fitting. The formula was f f ¼ ð1 þ 79qBF þ 710qPF 443265qBF qPF Þf f0 . The conversion relationship between flexural strength and compressive strength was established, which was f f ¼ 0:118f cu 0:435. (4) The sixth-time polynomial and rational fraction are used to fit the ascending and descending sections of the stressstrain curves of the hybrid fiber HPC, and the relationship between the curve parameter (a1 and a) and the fibers volume fraction (V BF and V PF ) is proposed.
Table 7 Comparison of experimental values and calculation value. VBF/(%)
VPF/(%)
0.1 0.1 0.1 0.15 0.15 0.15 0.2 0.2 0.2
0.025 0.033 0.042 0.025 0.033 0.042 0.025 0.033 0.042
a
a1 Experimental value
Calculation value
Ratio
Experimental value
Calculation value
Ratio
1.34 1.297 1.214 1.23 1.32 1.22 1.44 1.38 1.24
1.32 1.27 1.21 1.35 1.30 1.24 1.39 1.34 1.28
1.02 1.02 1.01 0.91 1.02 0.98 1.04 1.03 0.97
12.72 16.24 29.08 15.01 9.92 17.45 15.66 14.67 11.38
14.95 18.69 22.91 13.75 — 21.71 12.54 16.29 —
0.85 0.87 1.27 1.09 — 0.80 1.25 0.90 —
D. Wang et al. / Construction and Building Materials 197 (2019) 464–473
Author contributions Conceptualization, D.H.W.; Data curation, L.B.X.; Investigation, H.S.; Formal analysis, D.H.W.; Project administration, Y.Z.J.; Supervision, J.Z.; Writing—original draft, D.H.W.; Writing—review & editing, D.H.W. and Y.Z.J. Conflict of interest The authors declare that they have no conflict of interest regarding the publication of this paper. Acknowledgements The financial support from National Science Foundation of China (Grant Nos. 51378095 and 51878128) is greatly appreciated. References [1] F.U.A. Shaikh, Review of mechanical properties of short fibre reinforced geopolymer composites, Constr. Build. Mater. 43 (2013) 37–49. [2] A.B. Kizilkanat, N. Kabay, V. Akyüncü, S. Chowdhury, A.H. Akça, Mechanical properties and fracture behavior of basalt and glass fiber reinforced concrete: an experimental study, Constr. Build. Mater. 100 (2015) 218–224. [3] J. Thomas, A. Ramaswamy, Mechanical properties of steel fiber-reinforced concrete, J. Mater. Civ. Eng. 19 (5) (2007) 385–392. [4] M.G. Alberti, A. Enfedaque, J.C. Gálvez, Fibre reinforced concrete with a combination of polyolefin and steel-hooked fibres, Compos. Struct. 171 (2017) 317–325. [5] K. Habel, M. Viviani, E. Denarié, E. Brühwiler, Development of the mechanical properties of an Ultra-High Performance Fiber Reinforced Concrete (UHPFRC), Cem. Concr. Res. 36 (7) (2006) 1362–1370. [6] V. Afroughsabet, L. Biolzi, T. Ozbakkaloglu, High-performance fiber-reinforced concrete: a review, J. Mater. Sci. 51 (14) (2016) 6517–6551. [7] S.F.U. Ahmed, M. Maalej, Tensile strain hardening behaviour of hybrid steelpolyethylene fibre reinforced cementitious composites, Constr. Build. Mater. 23 (1) (2009) 96–106. [8] N. Banthia, F. Majdzadeh, J. Wu, V. Bindiganavile, Fiber synergy in Hybrid Fiber Reinforced Concrete (HyFRC) in flexure and direct shear, Cem. Concr. Compos. 48 (2014) 91–97. [9] C.X. Qian, P. Stroeven, Development of hybrid polypropylene-steel fibrereinforced concrete, Cem. Concr. Res. 30 (1) (2000) 63–69.
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