Flexural capacity of fiber reinforced concrete with a ...

Construction and Building Materials 138 (2017) 222–231

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Flexural capacity of fiber reinforced concrete with a consideration of concrete strength and fiber content Jong-Han Lee a, Baiksoon Cho b,⇑, Eunsoo Choi c a

Department of Civil Engineering, Daegu University, Gyeongsan, Republic of Korea Department of Civil Engineering, Inje University, Gimhae, Republic of Korea c Department of Civil Engineering, Hongik University, Seoul, Republic of Korea b

h i g h l i g h t s Flexural capacity of SFRC with variance in concrete strength and fiber content were evaluated. First peak and post-cracking strength, and energy absorption capacity were discussed. Effects of concrete strength and fiber content in equivalent strength ratio were evaluated. Ultimate capacity of floor slabs was evaluated considering concrete strength and fiber content.

a r t i c l e

i n f o

Article history: Received 15 September 2016 Received in revised form 26 December 2016 Accepted 25 January 2017 Available online 16 February 2017 Keywords: Fiber-reinforced concrete Concrete strength Fiber volume fraction Cracking strength Energy absorption capacity Equivalent flexural strength ratio

a b s t r a c t An experimental study was performed to examine the effects of concrete strength and fiber content ratio on the flexural capacity of steel fiber-reinforced concrete. Three fiber volume fractions, 0.25, 0.375, and 0.5%, and three concrete compressive strengths, 25, 35, and 45 MPa, were designed for the experiments. The stress and deflection relationship, first peak and post-cracking strength, and energy absorption capacity were evaluated with respect to the variance in the fiber volume fraction and concrete strength. The results showed that the equivalent flexural strength ratio, which is determined from the first peak strength and energy absorption capacity, increased with the increase in the fiber volume fraction but decreased with the increase in the concrete strength. Furthermore, the effects of the concrete strength and fiber content ratio are discussed in a steel fiber-reinforced concrete floor slab. The ultimate flexural capacity also required a consideration of the influence of the content ratio of steel fiber as well as the strength of cement composite matrix. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction Cement is an essential material for construction, but it is very vulnerable to tensile forces. Therefore, cement-based materials undergo cracking when subjected to a tensile load. The application of short-length fibers can enhance the ability to resist tensile cracks and improve the energy absorption of concrete. With the ability to enhance the ductility of concrete, steel fiber-reinforced concrete (SFRC) has been developed since the 1960s [1]. Studies of SFRC have mainly focused on the effects of the geometric types, volume fraction, and strength of steel fibers on the flexural behavior of cementitious composites [2–10]. The use of steel fibers in concrete was expanded to the application of various fibers, such ⇑ Corresponding author. E-mail addresses: [email protected] (J.-H. Lee), [email protected] (B. Cho), [email protected] (E. Choi). http://dx.doi.org/10.1016/j.conbuildmat.2017.01.096 0950-0618/Ó 2017 Elsevier Ltd. All rights reserved.

as synthetic fibers, glass and carbon fibers, and natural fibers. In particular, steel and synthetic fibers were used to assess the properties and performance of concrete [11–14]. The influence of the combination of steel and synthetic fibers on the flexural loadcarrying capacity and toughness of concrete were also investigated with respect to the shape, length, and dosage of the steel and synthetic fibers. In addition, several studies [15–17] examined the influence of steel fibers in combination with steel bar reinforced concrete beams. Most studies attempted to evaluate the amount of steel bar reinforcement in FRC members as well as the enhancement of flexural capacity associated with the types and contents of steel fibers. SFRC are used most widely and reliably in the practical fields, particularly for tunnel shotcrete and precast tunnel segments [4,15,17–19], as well as in industrial pavements and slabs [20–22]. In the design of these structures, an equivalent flexural strength ratio is used to account for the improvement of flexural

J.-H. Lee et al. / Construction and Building Materials 138 (2017) 222–231

tensile performance of SFRC. The equivalent flexural strength ratio, which is determined from the energy absorption capacity and the first peak strength measured from the beam tests, is strongly dependent on the content ratio of fibers in concrete. Therefore, as described previously, most of the previous studies evaluated the effect of the fiber geometric types and content on the flexural strength and toughness of fiber-reinforced concrete. That is, given a type of fiber, the equivalent flexural strength ratio is determined according to the fiber content. On the other hand, the equivalent flexural strength ratio can be affected by the strength of the cementitious composite matrix. A few researchers [6,11,23] conducted experimental studies to assess the influence of fibers on the flexural performance of high-strength SFRC. Kim and Naaman [6] examined the effects of the geometric types of steel fibers in high-strength fiber-reinforced cementitious materials, and Banthia and Gupta [11] assessed the properties and performance of fiberreinforced concrete in a high strength matrix. Mansur et al. [23] derived the stress and strain curve for high-strength fiberreinforced concrete. These studies focused on the effects of the types and geometries of steel fibers in high-strength concrete. However, few studies have shown the effect of the strength of the cementitious composite matrix in combination with the fiber contents on the both the flexural strength and energy absorption of fiber-reinforced concrete. Therefore, this study evaluated the effects of the concrete strength and fiber content ratio on the flexural strength, energy absorption, and equivalent flexural strength ratio of concrete reinforced with steel fiber. For this purpose, this study conducted flexural tests on SFRC beams with three concrete strengths, 25, 35, and 45 MPa, and three fiber volume fractions, 0.25, 0.375, and 0.50%. According to the stress and deflection relationship obtained from the flexural tests, the cracking and post-cracking strengths and energy absorption capacity were evaluated with respect to the concrete strength and fiber volume fraction. In the design of SFRC structures, the tensile performance is commonly measured using the equivalent flexural strength ratio. Therefore, this study analyzed the correlations of the flexural strength, energy absorption, and equivalent flexural strength ratio with the concrete strength and fiber content ratio. Furthermore, this study examined the effects of the concrete strength and fiber content ratio on the flexural capacity of SFRC floor slab, which is one of the most widely applied structures in practice. 2. Experimental program 2.1. Test variables To assess the effects of the strength of concrete combined with the content of steel fibers on the flexural strength of SFRC, three different concrete strengths, 25, 35, and 45 MPa, and three different fiber volume fractions, 0.25, 0.375, and 0.50%, were designed.

Table 1 Test variables and specimens. Name of the specimens

Compressive strength of concrete (MPa)

Fiber volume fraction (%)

C25-250 C25-375 C25-500

25

0.250 0.375 0.500

C35-250 C35-375 C35-500

35

0.250 0.375 0.500

C45-250 C45-375 C45-500

45

0.250 0.375 0.500

223

Table 1 lists the SFRC specimens according to the experimental variables of the concrete strength and fiber volume fraction. The steel fiber involved in this study was a hooked-end type that is commonly used in the field. Table 2 presents the geometry and material properties of the steel fiber. 2.2. Manufacturing of specimen To evaluate the flexural tensile performance, SFRC beams were manufactured according to ASTM C 1609 [24]. Cement was first mixed with sand, gravel, silica fume, and steel fibers, and then water containing high performance super-plasticizer were added to mix until the steel fibers were uniformly distributed in the concrete matrix. The design strength of the concrete was controlled by adjusting the proportion of cement, water, and super-plasticizer with constant amount of gravel and sand. All the mix proportions were also designed to satisfy a slump value more than 12 cm, which is commonly used in the construction field. Table 3 lists the mix proportions for each of the designed concrete strength. The SFRC mixture was poured into a steel mold of 150 mm high, 150 mm wide, and 500 mm long. The specimens were covered with a vinyl sheet and cured for twenty-four hours. Subsequently, the fiber-reinforced concrete beam specimens were cured in a water tank at 23 ± 1 °C before the flexural tests. A total of 54 SFRC beam specimens, six beams per type of variable, were manufactured to ensure the reliability of the experimental results. Three cylinders per test variable were manufactured to evaluate the influence of the fiber-reinforced concrete strength. That is, three cylinder tests were carried out for the test variable of C25-250. Thus, the compressive strength for the C25-250 was determined as the mean of the three cylinder tests. Table 4 summarizes the compressive strengths of the SFRC measured from the cylinder tests. For the designed compressive strength of 25, 35, and 45 MPa, the measured compressive strength, which is the mean of a total of nine cylinder tests per design strength, was 26.4, 36.4, and 47.9 MPa, respectively. Therefore, the measured compressive strength of the SFRC agrees well with the designed values. 2.3. Test set-up and measurement The beam specimen was installed as a simply-supported condition with a length of 450 mm between the supports. To generate the pure flexural moment in the beam, two-point loads, 150 mm apart, were simultaneously applied to the specimen. To prevent local cracking at the loading points and distribute the applied load along the width of the beam, rubber strips were used at each loading point. In addition, another rubber strip was used at the supports to induce a uniform distribution of reaction forces at the supports. Fig. 1 presents the four point flexural test of a SFRC beam specimen based on the ASTM C 1609 standard [24]. The vertical load was applied at a rate of 0.2 mm/min. and continued until the deflection of the beam at mid-span was 3 mm, or 1/150 of the beam span. The vertical displacement was measured using two linear variable differential transducers (LVDTs) installed on the front and back sides of the beam at the mid-span. According to Gopalaratnam et al. [25], the vertical deflection measured at the mid-span can be approximately double that of the real deflection at the cracking strength of concrete. This is because additional deflection occurs due to the elastic and inelastic behaviors of the load-applying device and the sliding of the specimen. Therefore, to exclude the influence of the additional deflection in this measurement, a deflection measurement device proposed by ASTM C 1609 [24] was manufactured and instrumented, as shown in Fig. 1.

224


Table 2 Geometric and material properties of the steel fiber. Types of steel fibers

Tensile strength (MPa)

Aspect ratio

Length (mm)

Diameter (mm)

Hooked-end

1200

67

60

0.90

Table 3 Mix proportion of the concrete (Units: kg/m3). Name of Specimens

Strength (MPa)

Steel fiber

Cement

Water

Gravel

Sand

Silica fume

Super-plasticizer

C25-250 C25-375 C25-500

25

20 30 40

400

242

1065

663

40

0

C35-250 C35-375 C35-500

35

20 30 40

400

198

1065

663

40

0

C45-250 C45-375 C45-500

45

20 30 40

400

165

1065

663

40

4.4

Table 4 Compressive strength of concrete from the cylinder tests. Name of the specimens

Design strength (f ck ; MPa)

f ck

Mean

C25-250 C25-375 C25-500

25

26.1 (0.80) 26.2 (0.70) 27.0 (0.48)

26.4

C35-250 C35-375 C35-500

35

34.6 (2.90) 37.4 (4.20) 37.3 (3.11)

36.4

C45-250 C45-375 C45-500

45

46.7 (3.45) 48.7 (3.43) 48.2 (3.38)

47.9

Measured strength (MPa)

*

Values in the parentheses represent the standard deviation.

Fig. 1. Photograph of the ASTM C 1609 flexural test for the SFRC beam specimen.

3. Experimental results and discussion

3.2. Ultimate flexural strength and energy absorption capacity

3.1. Stress and deflection relationship The stress and deflection curves obtained from the four point bending tests of the SFRC beams are shown in Fig. 2. The deflection was calculated as the average of the vertical displacements measured from two LVDTs on both sides of the beam at the midspan. The stress, f, was calculated from the applied vertical load, P, using the following equation [24]:

f ¼

PL bd

2

:

where L, b, and d are the span, width, and depth of the beam specimen, respectively. The stress and deflection curves show elastic behavior up to the cracking of concrete. The stress at the first cracking of concrete was defined to be the cracking strength of the SFRC, which coincides with the first peak strength, f 1 , defined in the ASTM C 1609 standard [24]. The cracking strength showed a tendency to increase with the increase in the fiber volume fraction and concrete strength, as shown in Fig. 2. Immediately after concrete cracking occurs, the stress of the fiber-reinforced concrete beam suddenly dropped, particularly for the fiber volume fraction of 0.25%. The decrease in the stress is also dependent on the content ratio of the steel fiber and the strength of concrete. That is, the magnitude of the decrease in the stress decreases with the increase in the fiber volume fraction and concrete strength. Subsequently, post-cracking stress also showed a tendency to increase with increasing fiber volume fraction and concrete strength. In particular, for the fiber volume fractions of 0.375% and 0.50%, the SFRC beams show deflection-hardening behavior, in which the maximum postcracking strength is larger than the cracking strength. The influence of concrete strength on the post-cracking strength is prominent in the early deflection of the beam. As the deflection increases, the difference of the post-cracking strength was insignificant between the concrete strengths of 25 and 35 MPa. On the other hand, the SFRC beams with the strength of 45 MPa exhibited a relatively rapid decrease in the post-cracking strength as the deflection increased and the cracks grew, as shown in Fig. 2. Therefore, in the case of higher strength concrete reinforced with steel fibers, the energy absorption capacity could be lower than that of the SFRC with normal-strength concrete. As a result, the strength of SFRC can affect the magnitude of its cracking and maximum strength as well as the post-cracking behavior, which is related to the energy absorption capacity of concrete.

ð1Þ

The experimental results of the SFRC beams are summarized in Table 5. The first peak strength, f 1 , initiates tensile cracking in the fiber-reinforced concrete beams, at which the elastic region finishes and the initial slope of the stress and deflection curve abruptly changes. The ultimate strength, f u , is defined as the maximum stress observed from the flexural test of the fiber-reinforced beam. When the maximum stresses observed after concrete cracking are lower than the f 1 , the ultimate strength is the same as the f 1 . According to the flexural test results for a total of 54 fiberreinforced beam specimens, the cracking and ultimate strengths

225


The steel fiber and concrete matrix are combined to resist external loads before concrete cracking occurs. The behavior of the fiber-reinforced concrete beam can be defined as elastic because the component materials are within the elastic region before concrete cracking. After concrete cracks, the steel fibers mixed in the concrete have a significant effect on impeding the growth of tensile cracks in concrete. The energy absorption capacity, which is the level of flexural performance after concrete cracking occurs, is an important factor that can be used to assess the effect of the fiber on the flexural performance of the fiber-reinforced concrete beam. Therefore, this study evaluated the energy absorption capacity of T D600 and T D150 , which are the energy absorption capacity of SFRC up to the 0.75 mm (1/600 of beam span) and 3 mm (1/150 of beam span) deflections of the reinforced beam, respectively, as illustrated in Fig. 3. Similar to the cracking and ultimate strengths, the value of T D600 tended to increase with the increase in the fiber volume fraction and concrete strength. The energy absorption of T D150 also increased as the fiber volume fraction increased. However, with the same fiber volume fraction, the T D150 in the 35 MPa concrete strength was somewhat larger than that in the 25 MPa concrete strength. The difference between the 25 MPa and 35 MPa concrete strengths was negligibly small. In contrast, the fiberreinforced concrete beam with the strength of 45 MPa exhibited a decreased in the energy absorption of T D150 . This indicates that as discussed previously in the stress and deflection relationship, the high-strength concrete reinforced with steel fibers, which showed a relatively rapid decrease in post-cracking strength, can decrease the energy absorption capacity compared to the normal-strength concrete reinforced with steel fibers. The flexural tensile performance of SFRC is commonly evaluated using the equivalent flexural strength ratio, Re;3 , which is determined from the energy absorption capacity up to a deflection of 1/150 of the beam span and the first peak load. Therefore, from the load and deflection curves obtained from the measurements, the value of Re;3 can be calculated by [26,27]:

Fig. 2. Stress and deflection curves measured from the SFRC beam tests with the change in the strength of concrete for fiber volume fractions of (a) 0.25%, (b) 0.375%, and (c) 0.50%.

tended to increase with the increase in the fiber content ratio and concrete strength. In particular, the ultimate strength was larger than the cracking strength for the fiber volume fractions of 0.375% and 0.50%.

Fig. 3. Definition of the first peak load and energy absorption capacity from a typical load and deflection curve.

Table 5 Summary of the experimental results. Specimens

V f (%)

f ck (MPa)

f 1 (MPa)

f p (MPa)

TD 600 (MPa)

TD 150 (MPa)

Re;3

C25-250 C35-250 C45-250

0.250

25 35 45

3.43 4.74 4.81

3.43 4.74 4.81

14.9 18.4 18.2

55.3 59.7 41.0

0.731 (0.092) 0.565 (0.116) 0.379 (0.049)

C25-375 C35-375 C45-375

0.375

25 35 45

3.29 4.07 5.51

3.69 4.32 5.66

18.1 20.7 25.1

75.8 78.9 66.1

1.161 (0.315) 0.870 (0.094) 0.540 (0.109)

C25-500 C35-500 C45-500

0.500

25 35 45

3.55 4.16 5.33

4.76 4.80 6.81

21.9 22.1 32.0

95.6 103.0 96.3

1.195 (0.157) 1.155 (0.199) 0.762 (0.114)

226

Re;3 ¼


T D150 P1 dL=150

ð2Þ

where T DL=150 is the energy absorption capacity up to a deflection of dL=150 , dL=150 is the deflection corresponding to the 1/150 of the beam span (=3 mm), and P1 is the first peak load. According to the flexural test results for a total of 54 fiber-reinforced beam specimens, as shown in Table 5, the Re;3 value associated with the cracking strength and energy absorption showed a tendency to increase with increasing fiber volume fraction but decreased with increasing concrete strength. 4. Analytical evaluation and discussion 4.1. Correlation analysis In the design of structures, such as tunnel shotcrete, precast tunnel segment, and slabs, using SFRC, the flexural tensile performance is evaluated using the equivalent flexural strength ratio, Re;3 . The experimental results of this study revealed that the Re;3 is dependent on the fiber content fraction and the concrete strength. Therefore, correlation analysis was first performed to evaluate the associations of the concrete strength and fiber content ratio with the Re;3 , which is a function of the energy absorption and first peak strength, as described in Eq. (2). Fig. 4 shows the correlation coefficients of the cracking strength (f 1 ), residual strength (f 150 ), energy absorption (T D150 ), and equivalent flexural strength ratio (Re;3 ). The correlation coefficient between f 1 and the concrete strength, and T D150 and the fiber volume fraction was similar, approximately 0.849 and 0.867, respectively. Therefore, the f 1 in the region of the elastic behavior is strongly dependent on the

concrete strength. The energy absorption of T D150 , which is related to the post-cracking strength of the SFRC, showed a strong relationship with the fiber content. This suggests that the Re;3 , which is determined based on the values of both f 1 and T D150 , should be evaluated by taking the strength of the concrete and the content ratio of steel fibers into consideration. The correlation coefficient of Re;3 with the concrete strength and fiber content ratio was approximately 0.592 and 0.604, respectively. That is, the Re;3 is almost equally correlated with both the concrete strength and fiber content ratio. Furthermore, the variance in Re;3 follows in the same direction with the change in fiber volume fraction but in the opposite direction with the change in concrete strength. Similarly, the stress, f 150 , was also correlated with both the concrete strength and fiber content ratio because it included the influence of its post-cracking behavior. The correlation coefficient with the concrete strength and fiber content ratio was approximately 0.59 and 0.60, respectively.

4.2. Influence of the fiber volume fraction and concrete strength on the first peak strength and energy absorption To evaluate the effects of the fiber volume fraction on the Re;3 of SFRC, the average values of f 1 and T D150 obtained from the flexural tests were plotted as a function of the change in the fiber volume fraction for three concrete strengths, as shown in Fig. 5. The lines shown in Fig. 5 were obtained from linear regression analysis for each concrete strength. Based on the linear regression lines, the first peak strength, f 1 , is hardly related to the change in the fiber volume fraction, as shown in Fig. 5(a). On the other hand, the linear regression lines of T D150 , shown in Fig. 5(b), exhibited a linear

Fig. 4. Correlation coefficients of the (a) f 1 , (b) f 150 , (c) T D150 , and (d) Re;3 of the SFRC with the concrete strength and fiber volume fraction.

227


(a)

(a) f

= 25 MPa

f

= 35 MPa

f

= 45 MPa

ck

First peak strength, f1 (MPa)

ck ck

6

First peak strength, f1 (MPa)

6

5

4

5

4

V = 0.25 % f

3

3

V = 0.375 % f

V = 0.50 % f

0.25

0.375

25

0.5

ck

f

= 25 MPa

f

= 35 MPa

f

= 45 MPa

ck

D

ck

Energy absorption, T 150 (Joules)

f

ck

D

(MPa)

(b) 120

(b) 120 Energy absorption, T 150 (Joules)

45

Concrete strength, f

Fier volume fraction, V (%)

100

35

80

60

40

100

80

60

V = 0.25 %

40

f

V = 0.375 % f

V = 0.50 % f

20

20 0.25

0.375

0.5

25

35

45

Concrete strength, f

Fier volume fraction, V (%)

ck

f

(MPa)

Fig. 5. Relationship between the fiber volume fraction and the (a) f 1 and (b) T D150 .

Fig. 6. Relationship between the concrete strength and the (a) f 1 and (b) T D150 .

relationship with the fiber volume fraction. A slight difference

of T D150 is strongly dependent on the fiber content ratio. With no dif-

the fiber volume fraction and concrete strength. As shown in Fig. 7(a), Re;3 increases as the content ratio of steel fibers increases. Therefore, the tensile performance of the SFRC is commonly controlled by the amount of steel fibers inserted in the concrete. That is, the values of Re;3 for the concrete strengths of 25, 35, and 45 MPa have similar increasing rates with the increase in the fiber volume fraction and relatively constant differences at each volume fraction. The Re;3 increases by an average of approximately 0.19 with the increase in the fiber volume fraction by 0.1%. Fig. 7(a) also shows a difference between concrete strengths, which indicates the influence of the concrete strength in Re;3 . The change in the Re;3 as a function of the concrete strength is plotted in Fig. 7(b). The value of Re;3 shows a tendency to decrease with the increase in the concrete strength. With the similar differences according to the change in the fiber volume fraction, Re;3 decreases by approximately 0.23 with every 10 MPa increase in concrete strength.

ference between the concrete strengths, the T D150 increases by approximately 18.5 Nmm with a 0.1% increase in the fiber volume fraction.

5. Design of the flexural capacity of SFRC floor slab considering the variations in concrete strength and fiber content fraction

among the concrete strengths was observed in terms of the

T D150 .

In addition, the change in the f 1 and T D150 was evaluated with the change in the concrete strength, as shown in Fig. 6. According to linear regression lines, the f 1 is strongly dependent on the concrete strength and increases almost linearly by approximately 0.90 MPa with a 10 MPa increase in concrete strength. Little differences among the fiber volume fractions were observed, as expected from the previous section. On the other hand, the energy capacity of T D150 hardly differs with the change in the concrete strength, but there is a difference between the fiber volume fraction, as shown in Fig. 6(b). Therefore, the strength of f 1 can neglect the influence of the content ratio of steel fibers in concrete while the energy capacity

4.3. Evaluation of the equivalent flexural strength ratio with the fiber volume fraction and concrete strength Fig. 7 shows the relationship between the equivalent flexural strength ratio, Re;3 , determined from the values of f 1 and T D150 , and

5.1. Design method Since the SFRC has been actively applied to floor slabs, the effects of the concrete strength and fiber content ratio in the design of the flexural capacity of SFRC floor slabs were evaluated. The

228


Pu ¼

1

Pu ¼

> :

4pðMp þM n Þ a 13l

Pu ¼

0.5

fck = 35 MPa

0

0.25

0.375

ð4Þ

8 pðMp þMn Þ > þ 2M n > 2
> : pðMp þMn2aÞþ4Mn

for a=l P 0:2

8 2M n > < > :

fck = 25 MPa

0.25

a=l ¼ 0

for a=l P 0:2

1 3l

0.75

4M n 1al

for

a=l ¼ 0 ð5Þ

a=l ¼ 0 ð6Þ

for a=l P 0:2

Eqs. (4)–(6) are provided for the ultimate load capacity of the floor slab at the internal, edge, and corner locations, respectively. In the equations, the term, a, is the equivalent radius of the contact area of load, and l is the radius of relative stiffness, which is mainly determined by the stiffness of the slab concrete and the modulus of subgrade reaction. For the values of a=l between 0 and 0.2, TR-34 [26] suggests that a liner interpolation can be used to determine the ultimate load capacity.

fck = 45 MPa

0.5

Fier volume fraction, Vf (%)

(b) 1.5 Equivalent flexural strength ratio, Re

8 2pðMp þ M n Þ for >