Mechanical Properties of Microsteel Fiber Reinforced Concrete and Its Gradient Design in the Partially Reinforced RC Beam

Abstract

Effects of two kinds of microsteel fibers were employed in reinforced concrete (RC) with different fiber volumes fraction. The RC beam was partially reinforced by microsteel fiber reinforced concrete (MSFRC) based on the idea of gradient design. Flexural performances were specially investigated. Results show that microsteel fiber highly strengthened and toughened the concrete matrix. With the same fiber volume content, the concrete reinforced by Type I fiber was generally better in strength compared with that of Type II, while the bending toughness was substantially improved. The bending strength of the concrete reinforced by microsteel fiber in partial section of tensile region was comparable to that in whole section. Based on the traditional strength theory, the critical MSFRC layer depth of in the partially reinforced RC beam was about 0.3 times of the beam depth, which possessed the same crack resistance ability with the beam composed of MSFRC in the whole section. Compared with that of the reference beam, the cracking load of the partially reinforced beam was enhanced by 119%, and the ratio of the cracking moment to ultimate moment improved by 91%. Moreover, the width and height of the cracks in the partially reinforced beam developed much slower than those in the reference beam, and the steady state in which all cracks emerged appeared later; meanwhile, the crack spacing in the pure bending region was smaller, and the number of cracks in the bending-shear region was less, which means that the partially reinforced beam is of excellent properties to resist cracking and bending. Finally, the calculation formula of the bearing capacity of the partially reinforced beam was proposed, which was in good agreement with experimental results.

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. Introduction

Mixing of randomly distributed steel fibers into fresh concrete can prevent initiation and propagation of cracks in hardened concrete and thus improve strength and toughness of the material. Taking a central Mode I crack of length 2a in an infinitely wide concrete plate subjected to the far-field uniform normal stress σ as example (Figure 1), fibers in concrete can be assumed to perpendicular to the crack line (the effects of oblique fibers with crack can be also decomposed into effects of perpendicular and horizontal to crack line) and the separation interfaces between fibers and concrete to be very small; thus, the effect of a fiber can be equivalent to a concentrated force P acting on the crack surface (Figure 2). When the crack spans n fibers, the stress intensity factor K at the crack tip is as follows:$$\begin{array}{}\text{(1)}& K=K_I^c-K_I^f=\sigma \sqrt{\pi a}-{\displaystyle \sum _{i=1}^n\frac{P_i}{\sqrt{\pi a}}\sqrt{\frac{2a-b_i}{b_i}}},\end{array}$$where $K_I^c$is the stress intensity factor of the concrete matrix under σ; $K_I^f$ is the stress intensity factor generated by fibers, $P_i$ is the concentrated force generated by the fiber i, $b_i$ is the distance from the fiber i to the crack tip, and a is the length of half crack.

[figure omitted; refer to PDF]

According to equation (1), when $b_i⟶0$, that is, the crack tip is just approaching the fiber $b_i$ infinitely, $K_I^f⟶\infty$, which means fibers will generate huge reverse stress intensity factor to prevent crack propagation; all other things being equal, the more the number of fibers per unit volume concrete, the more remarkable crack-retarding effect. If the fiber diameter is reduced by half, while the length remains the same; then the original one fiber is equivalent to the current four microfibers in volume; the bonding area between fiber and concrete matrix is doubled consequently, the fiber pull-out force is double that of the original in the case of the same bonding strength and detaching zone between concrete and fiber; under the circumstance of the same fiber pull-out force, the bonding detachment zone would be reduced, and the closure force provided by fibers, namely, the concentration force P, is closer to the crack face; thus, the crack-retarding effect is better. This shows that the crack-retarding and toughening effect of microsteel fiber will be more promising.

Compared with conventional concrete, steel fibers reinforced concrete (SFRC) has excellent mechanical properties and durability [1]. However, in a large number of related studies on SFRC, the typical steel fiber employed in concrete matrix is generally 0.5 to 0.8 mm in diameter or equivalent diameter, 30 to 60 mm in length, and 0.5% to 3.0% in the fiber volume fraction [2–4]. In recent years, microsteel fibers have been used in high performance concrete [5–9], usually with the diameter about 0.2 mm, which have shown that [10–12] the crack-retarding and toughening effect of the Type I microsteel fiber (usually smooth cold-drawn wire with about 0.2 mm in diameter) in SFRC are better than those of the larger diameter steel fiber, while the effect of the Type II micro steel fiber (deformed cut sheet) remains to be studied. Therefore, the first step, two kinds of microsteel fibers (Type I, the smooth cold-drawn wire, and Type II, deformed cut sheet) with a diameter or equivalent diameter of 0.2 mm and length of 13 mm are employed to study their crack-retarding and toughening effects, which are shown in Figures 3 and 4.

[figure omitted; refer to PDF]

Due to good properties of SFRC, in the 1970s, Swamy used SFRC to enhance the flexural behavior of RC beams and found that the strengthening effect of SFRC, which is in the total section of the beam or tension zone or as a tensile skin, is almost identical. In the 1980s, Sri Ravindrarajah and Al-Noori [13] studied the effect of steel fiber distribution on the ultimate strength of concrete beams and revealed that the fiber in the compression zone does not significantly improve the beam strength, while partially reinforced beams are composed of fibers in the bottom layer even about 25% more than that for the fully reinforced beams [14]. In 1998, Yi and Shen proposed the concept of partially high percentage fiber reinforced concrete (PHPFRC), and full load-deflection curves of flexural PHPFRC specimens indicated that the crack resistance, bearing capacity, and stiffness were enhanced significantly [15, 16]. In 2001, based on experimental tests of RC beam partially with SFRC, Zhao et al. got the anticracking capacity formulation of the normal section of the beam [17]. In 2002, researches on cement-based functionally graded material showed that fibers should be distributed according to the stress field characteristics of materials [18]. Based on the research of engineered cementitious composites (ECC), Qin et al. put the concept of ultrahigh toughness cementitious composites (UHTCC) obtaining functionally graded composite beam by using UHTCC to replace part of the concrete, which surrounds the main longitudinal reinforcement, and studied its bending properties [19, 20]. ECC is a kind of highly ductile fiber reinforced concrete; it shows a special strain-hardening behavior under tensile loadings; meanwhile, along with developing multiple microcracks on specimens, as a result, its tensile strain capacity is several hundred times of convention concrete [21–23]. Additionally, such the microcracks can be self-healed under certain exposure conditions [24–26]. Due to the above unique characteristics, ECC is expected to improve the structural performance of infrastructures [27, 28]. In recent years, partially reinforced beams with fiber also have been involved in concrete composite structures composed of ECC and FRP bars [29, 30]. The strength and durability of conventional concrete are dominated by the low tensile strength at the interfacial transition zone between mortar matrix and aggregates, where cracks tend to appear and propagate. For steel fiber reinforced concrete, the high tensile strength and bridging capability between fibers and matrix can resist the crack initiation and propagation, leading to high load-carrying capability, ductility, and durability [31, 32]. According to the above studies, partially reinforced beam with fibers can fully utilize the crack-retarding and toughening effects of fiber reinforced concrete and is characterized with good cost-effectiveness. But, due to design theory, construction technology, and some other factors, a large number of research and application of SFRC members usually adopt full-section design, namely, steel fibers usually used in total section.

Therefore, based on the MSFRC research and the characteristics of the stress field of the beam structure, the critical thickness of MSFRC layer in RC beam partially reinforced by MSFRC was obtained based on the traditional strength theory, and the bending capacity of the partially reinforced beam was studied further.

2. Critical Depth of MSFRC Layer of the Partially Reinforced Beam Based on Strength Theory

According to the characteristics of the stress field of the beam structure due to bending and the idea of gradient design, the partially reinforced concrete beam was obtained by using MSFRC to replace part of normal concrete in the bottom layer of tension zone. For simplicity, taking a rectangular section as an example, it is assumed that the strain distribution of the normal section of the partially reinforced beam conforms to the plane section in the critical state of cracking, and the stress and strain distribution of the beam are shown in Figure 5. When the MSFRC layer $h_f$ is relatively thin, the strain ${\epsilon }_{\text{tc}}$ of the upper concrete of the interface between the normal concrete layer and the MSFRC layer reaches the cracking strain earlier. When the MSFRC layer $h_f$ is relatively thick, the strain ${\epsilon }_{tu}$ of the lower MSFRC reaches the cracking strain earlier. When $h_f$ reaches the critical depth, ${\epsilon }_{\text{tc}}$ and ${\epsilon }_{\text{tu}}$ simultaneously reach the cracking strain, respectively. In the critical state, taking ${\epsilon }_{\text{tc}}$ and ${\epsilon }_{\text{tu}}$ as known quantities into equation (2), the critical depth of the MSFRC layer $h_{\text{fcr}}$ can be obtained. If $h_f<h_{\text{fcr}}$, the strain of the normal concrete at cracking ${\epsilon }_{\text{tc}}$ is known, while ${\epsilon }_{\text{tu}}$ is variable; then the relationship between the depth of the MSFRC layer $h_f$ and the cracking moment of the beam $M_{\text{cr}}$ can be obtained by taking the cracking strain ${\epsilon }_{\text{tc}}$ into (2). If $h_f>h_{\text{fcr}}$, the relationship between $h_f$ and $M_{\text{cr}}$ also can be obtained by taking ${\epsilon }_{tu}$ as a known quantity into the following equation:

[figure omitted; refer to PDF]

Here, in the critical state of cracking, $x$ is the compression zone depth of the composite beam; $h$, $b$, $h_f$, and $a$ are the section depth, the section width, the MSFRC layer depth, and the concrete cover depth of the beam; ${\epsilon }_{\text{tu}}$ and ${\epsilon }_s$ are the tensile strain of MSFRC and the reinforcement, while ${\sigma }_{\text{tu}}$ and ${\sigma }_s$ are the corresponding stress; ${\epsilon }_{tc}$ and ${\epsilon }_c$ are, respectively, the tensile and compressive strain of the normal concrete, while ${\sigma }_{\text{tc}}$ and ${\sigma }_c$ are the corresponding stress; $M_{\text{cr}}$ represents the cracking moment of the partially reinforced beam due to bending.

Theoretically, the cracking capacity of the partially reinforced beam with MSFRC increases with the depth of the MSFRC layer until the critical depth and then tends to stabilize, which mainly depends on mechanical properties of MSFRC and the normal concrete. The relationship trend between the cracking moment $M_{\text{cr}}$ and the ratio of the MSFRC depth to the beam depth hf/h could be obtained as shown in Figure 6. In the critical state of $h_f$, the MSFRC layer and the normal concrete layer simultaneously crack and the two materials are utilized most efficiently. Therefore, based on the results of MSFRC, the partially reinforced RC beam with the MSFRC was designed to study its flexural behavior further.$$\begin{array}{}\text{(2)}& \begin{array}{c}\frac{{\epsilon }_c}{x}=\frac{{\epsilon }_{tc}}{h-h_f-x}=\frac{{\epsilon }_{tu}}{h-x}=\frac{{\epsilon }_s}{h-x-a},\\ {\sigma }_c=f{\epsilon }_c;{\sigma }_{tc}=f{\epsilon }_{tc};{\sigma }_{tu}=f{\epsilon }_{tu};{\sigma }_s=f{\epsilon }_s,\\ \frac{1}{2}{\sigma }_{c}xb=\frac{1}{2}{\sigma }_{tc}h-h_f-xb+{\sigma }_{tu}{h}_{f}b+{\sigma }_s{A}_s,\\ M_{cr}=\frac{1}{2}{\sigma }_{tc}bh-h_f-x\frac{2}{3}h-h_f-x+\frac{2}{3}x+\frac{1}{3}{\sigma }_{tu}hbh-\frac{h_f}{2}-\frac{x}{3}+{\sigma }_s{A}_{s}h-a-\frac{x}{3},\end{array}\end{array}$$

[figure omitted; refer to PDF]

When the properties of MSFRC in total section were obtained, the critical depth of MSFRC layer of the partially reinforced specimen without the reinforcement rebar was estimated to be about one-third of the specimen section depth according to (2), varied with the fiber content, where ${\epsilon }_{\text{tu}}$, ${\sigma }_{\text{tu}}$, ${\epsilon }_{\text{tc}}$, and ${\sigma }_{\text{tc}}$ were approximately evaluated according to the bending test, ${\sigma }_c$ and ${\epsilon }_c$ took design standard values of corresponding strength level concrete of Chinese code for design of concrete structures GB 50010-2010. Specimens with MSFRC in partial section are formed by the two-stage casting method. Firstly, the vibrated MSFRC in the tension zone is casted; then, the upper vibration-free ordinary concrete is casted. The time interval between the two castings is controlled within 20 minutes.

The three-point bending flexural test was employed to evaluate the bending toughness of MSFRC prism specimens with size 400 mm × 100 mm × 100 mm as shown in Figure 9. According to load-displacement curves at midspan of MSFRC specimens, the flexural toughness ratio (R_e) was got by (3) suggested in Chinese standard CECS13:2009. Figure 9 shows that when the volume fraction of the microsteel fiber reaches 3.0%, the load-deflection curves were characterized with a deflection hardening characteristic, which was nondistinctive:$$\begin{array}{}\text{(3)}& R_e=\frac{{\Omega }_k}{P_{\text{cr}}{f}_k},\end{array}$$where $f_k=L/150$ (L is the clear span of tested specimens), mm; $P_{\text{cr}}$ is the first cracking load of MSFRC, N; ${\mathrm{\Omega }}_k$ is the area under the load-displacement curve with a midspan deflection of $L/150$, Nmm.

[figure omitted; refer to PDF]

Two different kinds of sections were employed in the bending test, one of which identified as RC beam is the normal concrete in full section, and the other is MSFRC in partial section involved with Type I microsteel fiber at the ratio of 1.5% volume fraction, identified as PSFRC beam. Based on the above conclusion and according to (2), the critical ratio of is about 0.3, in which case the reinforcing effect of the beam partially reinforced by MSFRC is approximately equivalent to the beam with MSFRC in full section. Strain and deflection gauges were arranged according to Chinese standard for test method of concrete structures GB/T 50152-2012 shown in Figure 12.

[figure omitted; refer to PDF]

The typical crack distribution diagrams of the test beams are shown in Figure 16. Compared with the pure bending region of the RC beam, the number of cracks in the PSFRC beam increases by 100%; thus, the crack spacing is much smaller; meanwhile, some microcracks with small height occur during the loading, which mean that the stress distribution of steel bars is more uniform, and the bearing capacity of the PSFRC beam has been improved. In the bending-shear region, the number of cracks in the PSFRC beam is less than that of RC beam, so the RC beam partially reinforced with MSFRC can also improve the shear resistance. The bending failure model of the PSFRC beam is a typical ductile failure as shown in Figure 13.

[figure omitted; refer to PDF]

4.3. Bearing Capacity Calculation

4.3.1. Cracking Load

According to the cracking load calculation diagram of normal section of the RC beam partially reinforced by MSFRC as shown in Figure 5, ${\sigma }_{\text{tu}}$ in (2) should be determined by the tensile stress-strain relationship curve of MSFRC or is 0.5 to 0.6 times the bending strength of the material, which varies with the fiber content [36]. The cracking moment $M_{\text{cr}}$ is related to the influence coefficient of plastic section modulus ${\gamma }_m$, the standard tensile strength of concrete matrix $f_{\text{tk}}$, and elastic section modulus $w_0$, which is listed as (4). According to Code for Design of Concrete Structures GB50010, for C40 concrete, $f_{tk}$ is 2.39 MPa and $w_0$ is calculated by the principle of the equivalent elastic modulus. Equation (2) is employed to calculate $M_{\text{cr}}$ and then obtain ${\gamma }_m$ according to the following:$$\begin{array}{}\text{(4)}& {\gamma }_m=\frac{M_{\text{cr}}}{f_{\text{tk}}{w}_0}.\end{array}$$

Assuming that ${\gamma }_m$ is the function of the reinforcement ratio $\rho$ and the fiber volume content $V_f$, the linear fitting method is used to obtain the calculation formula of cracking moment $M_{\text{cr}}$, which is shown in the following:$$\begin{array}{}\text{(5)}& \begin{array}{c}{\gamma }_m=1.132+4.5V_f+k\rho ,\\ M_{cr}={\gamma }_m{f}_{tk}{w}_0,\end{array}\end{array}$$where the influence factor of reinforcement ratio $k\rho$ reflects the influence of $\rho$ on ${\gamma }_m$.

In the test of the RC beam partially reinforced with MSFRC, the reinforcement ratio is constant; that is, the variable of reinforcement ratio is not involved in (5). Therefore, $k\rho$ is specified to be zero and needs to be explored in the next research.

After the cracking moment $M_{\text{cr}}$ is calculated according to (5), then the calculated cracking load $P_{\text{cr},j}^b$ of the beam under four-point loading can be obtained.

4.3.2. Ultimate Load

According to Code for Design of Concrete Structures GB50010 and Technical Specification for Fiber Reinforced Concrete Structures CECS38:2004, the calculation diagram of the ultimate moment of normal section of the RC beam partially reinforced with MSFRC $M_u$ is shown as Figure 17; then the calculation formula of ultimate moment $M_u$ is obtained as follows$$\begin{array}{}\text{(6)}& \begin{array}{c}{f}_{c}bx=f_y{A}_s+f_{ftu}b{x}_t,\\ M_u=f_{c}bx{h}_0-\frac{x}{2}-f_{ftu}b{x}_t\frac{x_t}{2}-a,\end{array}\end{array}$$where $f_c$ is the compressive strength of concrete in compression zone, $f_y$ is the standard tensile strength of steel rebar, $x$ is the compression zone height, $x_t$ is the height of equivalent rectangular stress block of MSFRC in the tension zone, $f_{\text{ftu}}$ is the tensile strength of the equivalent rectangular stress block, $h_0$ is the effective section height of the composite beam, and $a$ is the concrete cover depth. $f_{\text{ftu}}$ is calculated according to the following:$$\begin{array}{}\text{(7)}& \begin{array}{c}{f}_{ftu}=f_{tk}{\beta }_{tu}{\eta }_f,\\ {\eta }_f=V_f\lambda ,\end{array}\end{array}$$where $f_{\text{tk}}$ is the standard tensile strength of concrete matrix in RC beam partially reinforced with MSFRC, ${\beta }_{\text{tu}}$ is the influence coefficient of steel fiber on tensile behavior of MSFRC in the tensile zone of the partially reinforced beam, ${\eta }_f$ is the characteristic value of steel fiber in the partially reinforced beam, $V_f$ is the fiber volume fraction in MSFRC, and $\lambda$ is the aspect ratio of steel fiber. In (7), $f_{tk}$ is 2.39 MPa according to GB50010, and ${\beta }_{\text{tu}}$ is 1.3 for bending member according to CESS 38:2004.

[figure omitted; refer to PDF]

4.3.3. Comparative Analysis of the Calculated and Experimental Results

The calculation of the cracking load and ultimate load of the test beam and the experimental results are shown in Table 7. In Table 7, $P_{\text{cr},j}^b$ and $P_{\text{cr},t}^b$, respectively, represent the calculated and experimental results of the cracking load, and $P_{u,j}^b$ and $P_{\text{cr},t}^b$ are of the ultimate load, which are in good agreement.

Table 7

Calculated and experimental results of the cracking load and ultimate load.

Group	$P_{\text{cr},j}^b$ (kN)	$P_{\text{cr},t}^b$ (kN)	$P_{u,j}^b$ (kN)	$P_{u,t}^b$ (kN)
RC beam	14.4	16.8	61.2	73.8
PSFRC beam	32.5	36.8	75.0	83.0

5. Conclusion

Through the experimental study on microsteel fiber reinforced concrete (MSFRC) and the RC beam partially reinforced with MSFRC, the following conclusions can be drawn:

(1) Compared with the reference group of the normal concrete, the compressive strength of the cubic and prismatic specimen for MSFRC is increased by 5.0% to 21.0% and 9.9% to 25.0%, respectively, the bending strength is increased by 94.9% to 156.4%, the compressive elastic modulus is increased by 0.9% to 4.7.%, and the bending modulus is increased by 8.6% to 43.8%, which indicate that the bending properties of MSFRC are significantly improved; the ratio of prismatic compressive strength and the bending strength of MSFRC to the cubic compressive strength is 0.69 to 0.80 and 0.12 to 0.16, respectively, which are improved in varying degrees. Under the same conditions, the strength and modulus of MSFRC involved with Type I microsteel fiber are generally better than that with Type II, especially for bending properties.

(2) The residual compressive strength of the cubic and prismatic specimen for MSFRC is 65.3% to 81.6% and 62.6% to 77.0% of their primary loading strength, respectively, which are characterized with good ductility. In the same case, the residual strength of MSFRC involved with Type I micro steel fiber is also superior to that with Type II.

(3) Compared with the reference group of the normal concrete, the bending toughness of MSFRC is greatly enhanced. In the identical conditions, the bending toughness of MSFRC with Type I microsteel fiber has increased by 69% to 77% compared to Type II.

(4) The bending strength of the specimen partially reinforced with MSFRC is only 3.9% to 8.4% lower than that with MSFRC in the full section, but the steel fiber consumption is saved by two-thirds, which is cost-effective. In the identical circumstances, the bending strength of concrete partially reinforced with MSFRC involved with s Type II is superior to that with Type II.

(5) The critical depth of MSFRC layer in the RC beam partially reinforced with MSFRC is about 0.3 times the beam height, the crack-retarding, and strengthening effect of which is equivalent to the beam with MSFRC in full section. In the gradient design, the MSFRC layer and the normal concrete layer are simultaneously cracked, the roles of which can be fully utilized. Compared with the normal RC beam, the cracking load and the ultimate load of the partially reinforced beam were increased by 119% and 21%, respectively; the crack width and height were developed more slowly, and cracks reached the steady state later. And when cracks tended to be steady, the number of cracks in the partially reinforced beam is more than that in the RC beam; thus, the crack spacing is much smaller, and meanwhile the number of cracks in the bending-shear region is less than that of RC beam, which revealed the superior crack-control capacity and bending resistance of the partially reinforced beam. The calculation of bearing capacity is also in good agreement with the experimental results.

Acknowledgments

The authors sincerely thank the Natural Science Foundation of Chongqing (no. cstc2019jcyj-msxmX0744), China, Scientific and Technological Research Program of Chongqing Municipal Education Commission (no. KJ1500512), Foundation of State Key Laboratory of Mountain Bridge and Tunnel Engineering (CQSLBF-2015-12), and Science Foundation of Chongqing Jiaotong University (20JDKJC-B006) for financial support.

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