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

State Key Laboratory of Mountain Bridge and Tunnel Engineering, Chongqing Jiaotong University, Chongqing 400074, China School of Civil Engineering, Chongqing Jiaotong University, Chongqing 400074, China Hunan Branch of Chongqing Luwei Civil Engineering Design Co., Ltd.,, Chongqing 410000, Hunan, China Chongqing Communications Planning Survey & Design Institute, Chongqing 401121, China Inner Mongolia Transportation Design & Research Institute Co. Ltd.,, Huhhot 010010, China


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: where K c I is the stress intensity factor of the concrete matrix under σ; K 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. is 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][3][4]. In recent years, microsteel fibers have been used in high performance concrete [5][6][7][8][9], usually with the diameter about 0.2 mm, which have shown that [10][11][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. erefore, 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.
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][22][23]. Additionally, such the microcracks can be self-healed under certain exposure conditions [24][25][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]. e 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  Advances in Civil Engineering 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 fullsection design, namely, steel fibers usually used in total section. erefore, 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.

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 ε 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 ε tu of the lower MSFRC reaches the cracking strain earlier. When h f reaches the critical depth, ε tc and ε tu simultaneously reach the cracking strain, respectively. In the critical state, taking ε tc and ε tu as known quantities into equation (2), the critical depth of the MSFRC layer h fcr can be obtained. If h f < h fcr , the strain of the normal concrete at cracking ε tc is known, while ε tu is variable; then the relationship between the depth of the MSFRC layer h f and the cracking moment of the beam M cr can be obtained by taking the cracking strain ε tc into (2). If h f > h fcr , the relationship between h f and M cr also can be obtained by taking ε tu as a known quantity into the following equation: Here, in the critical state of cracking, x is the compression zone depth of the composite beam; h, b, h f , and a  Advances in Civil Engineering are the section depth, the section width, the MSFRC layer depth, and the concrete cover depth of the beam; ε tu and ε s are the tensile strain of MSFRC and the reinforcement, while σ tu and σ s are the corresponding stress; ε tc and ε c are, respectively, the tensile and compressive strain of the normal concrete, while σ tc and σ c are the corresponding stress; M cr represents the cracking moment of the partially reinforced beam due to bending. eoretically, 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. e relationship trend between the cracking moment M 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. erefore, based on the results of MSFRC, the partially reinforced RC beam with the MSFRC was designed to study its flexural behavior further.

Raw Materials.
Ordinary Portland cement denoted as Grade P.O. 42.5 was used in this study, and its main properties are given in Table 1. Fly-ash met the requirements of Grade I of the Chinese standard GB1596-2005, and its main properties are shown in Table 2. e size range of continuously graded coarse aggregate (limestone gravel) used was 5-20 mm, and the fineness modulus of fine aggregate (medium-coarse sand) was 2.8; the properties of aggregates are shown in Table 3. e superplasticizer used was a polycarboxylic water-reducer with water reducing efficiency of 26.6%. Two kinds of microsteel fibers, with the same aspect-ratio of 65 and different volume fraction, were used. Table 4 gives the main properties of microsteel fibers.

Mixture Proportions.
e proportions of MSFRC are summarized in Table 5, where the water-to-binder ratio was maintained unchanged at 0.38, and the replacement ratio of cement with fly ash in mass at 0.30. For RC, the reference mixture, the slump flow reaches up to 600 mm. In Table 5, NC stands for concrete without fibers, SFRC-P stands for a series of MSFRC with Type I microsteel fiber, and SFRC-J means with Type II.

Test Method.
According to Chinese standard test method for fiber reinforced concrete CECS13:2009 and standard for test method of mechanical properties on ordinary concrete GB/T 50081-2002, totally 108 specimens were made and tested, which were involved with tests of strength, elastic modulus, and flexural toughness.
Displacement control mode was firstly adopted as the loading method to test 28 d compressive strengths of MSFRC cube of 100 mm size and prism of 400 mm × 100 mm × 100 mm size. Load was unloaded till the load dropped to 90% of the ultimate load, then the compressive strength of concrete cube (f cc ) and the compressive strength of concrete prism (f cp ) were calculated according to the ultimate load. After unloading, force control mode was used to test residual compressive strength of the tested specimens till they failed completely; then we can get the residual compressive strength of concrete cube (f cc ′ ) and the residual compressive strength of prism (f cp ′ ). Prism specimens with size 300 mm × 100 mm × 100 mm are employed to test modulus of elasticity of MSFRC under compression (E c ).
As for the test of bending strength and modulus, specimens with MSFRC in total section shown in Figure 7 are firstly designed to test their 28 d bending strengths (f ct ); meanwhile, the flexural elastic modulus (E t ) of MSFRC in total section was computed according to the relationship of stress to strain of the bending specimen. e strain gauges were placed on the bottom of the pure bending zone of specimens shown in Figure 8. When loading, values of load and strain are acquired synchronously; then E t is calculated by linear regression treatment of the load-strain relationship curve before cracking, which is determined according to observed mutant strain or a visible crack.
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 ε tu , σ tu , ε tc , and σ tc were approximately evaluated according to the bending test, σ c and ε 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. e time interval between the two castings is controlled within 20 minutes.       Advances in Civil Engineering e 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: where f k � L/150 (L is the clear span of tested specimens), mm; P cr is the first cracking load of MSFRC, N; Ω k is the area under the load-displacement curve with a midspan deflection of L/150, Nmm.

Test
Results. e hardened properties of the MSFRC mixes, including the compressive strength, the flexural strength, the elastic modulus, and the flexural toughness ratio, are listed in Table 6. f cc and f cc ′ are the average value of the compressive strength and the residual compressive strength of concrete cube, respectively, while f cp and f cp ′ are of concrete prism. f ct is the average value of the bending strength. E c and E t are the average value of the modulus of elasticity under compression and bending, respectively. R e is the flexural toughness ratio of MSFRC.

Strength and Elastics Modulus of MSFRC in Total
Section. Compared with the reference group of NC in Table 6, with the addition of microsteel fiber content from 1.5% to 3.0%, the cubic compressive strength of MSFRC is increased by 5.0% to 21.0%, the prismatic compressive

Bending Toughness of MSFRC in Total Section.
According to Figure 9, for the reference normal concrete, when crack occurs, then the specimen suddenly collapses, which is characterized with obvious brittle failure. e first cracking load P cr determined from the load-deflection curve is equivalent to the ultimate load, while, as to MSFRC, the addition of microsteel fiber increases the first cracking load and ultimate load, and the descending portion of the loaddeflection curve is gentle, which show that MSFRC is characterized with good bearing capacity and deformability. Table 6 shows, in case of equivalent fiber volume content, the flexural toughness ratio R e of the MSFRC with Type I fiber is 69% to 77% higher than that with Type II; under the same fiber type, R e increases with fiber volume content, while Type I fiber has more significant effect on R e than Type II.     Table 6 shows that in case of the equivalent fiber volume content, the bending strength of partial MSFRC specimens involved with Type I fiber is slightly better than that with Type II; the bending strength of MSFRC in partial section is only 3.9% to 8.4% lower than that in full section, while fiber consumption is saved by two-thirds, which show a high costperformance ratio.

Design of the RC Beam Partially Reinforced with MSFRC.
Materials study has found that MSFRC, involved with Type I fiber, has better strengthening and toughening effect than that with Type II, and MSFRC partially employed in tension zone is a cost-effective method. According to stress-strain field characteristics of beam structures, the pure bending state of the four-point bending RC beam can be simplified as a plane stress issue shown in Figure 10. e effect of a steel rebar in RC beam is to generate a pair of opposing concentrated forces shown in Figure 10(a), which act on the edge crack surface to prevent crack propagation [33][34][35], while, in the RC beam partially reinforced with MSFRC, due to crack-retarding and toughening effect of MSFRC, the edge crack becomes an internal eccentric crack shown in Figure 10(b), and the concentrated forces produced by the rebar provide crack closure forces partially. But, in RC beams, due to large aspect ratio and strong orientation of steel rebar, the rebar's volume fraction is very small. erefore, the rebar mainly plays the role of bridging discrete macroscopic cracks, while its bridging effect on microcracks is limited; thus, the crack resistance of RC beam mainly depends on concrete matrix itself, namely, the tensile strength of concrete matrix. In this paper, by arranging MSFRC in partial tension zone of RC beam shown as Figure 10(b), which is involved with Type I fiber, a composite beam partially reinforced with MSFRC is put forward. e quantity of microsteel fiber per cubic meter of concrete mix is inversely proportional to the square of the diameter; therefore, in the case of constant fiber volume content, compared with larger diameter steel fiber, there are more fibers per cubic meter of MSFRC, which can bridge a large number of microdefects or macrocracks in the material under load. en, mechanical properties of the material are greatly improved; meanwhile, in the beam, the previous edge crack of an ordinary concrete beam shown in Figure 10(a) becomes a central crack in the RC beam partially reinforced with MSFRC shown in Figure 10(b). Other things being equal, the edge crack is easier to propagate than the center crack; thus, the crack resistance and serviceability of the RC beam partially reinforced with MSFRC will be improved greatly. erefore, the RC beam partially reinforced with MSFRC under four-point loading, involved without hangers, stirrups, and bent bars in the pure bending region, was designed as shown in Figure 11. HRB 335 deformed bars were employed as the longitudinal reinforcement and hanger, while HPB300 plain bars were used as stirrups and bent bars. In the region of the partially reinforced beam subjected to shear force and bending moment, the stirrup spacing is 50 mm, and bent-bar spacing is 150 mm. e yield strength, ultimate strength, elastic modulus, and percentage contraction of cross-sectional area at fracture of the longitudinal reinforcement are 392.5 MPa, 505.0 MPa, 210 GPa, and 26.5%, respectively. e mix proportions and properties of the normal concrete and MSFRC are shown in Tables 5 and  6.
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.

Load-Displacement Curves.
Load-midspan displacement curves are shown in Figure 13, which take the load P b as ordinate and the midspan displacement D b as abscissa. Compared with the RC beam, the first cracking load, yield load, and ultimate load of the PSFRC beam are increased by 119%, 21%, and 12%, respectively. e ratio of the first cracking load to the yield load is about 0.22 for the RC beam but is 0.44 for the PSFRC beam. So, the partially reinforced beam is characterized with excellent crack resistance.

Crack Development and Failure Mode.
e first crack that occurred in PSFRC beam was significantly later than that in RC beam, and the height and width of the initial crack were much smaller under the same loading condition, which mean that the crack resistance of the RC beam partially reinforced with MSFRC was improved remarkably. After cracking, the height and width of cracks in PSFRC beam developed more slowly, and cracks reached the steady state later, where the number and height of cracks were kept stable. e height and width of the main crack varying with load are shown in Figures 14 and 15，which take the load P b as ordinate and the main crack width w and the height h as abscissa. Results show that, under the control of same crack width, the bearing capacity of PSFRC beam is improved by about 50% or more than that of RC beam, which contributes to the application of high-strength rebar in RC structures; for the RC beam, the steady state occurs at about 50% of the ultimate load and 70% for the PSFRC beam. e 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 8 Advances in Civil Engineering   Advances in Civil Engineering 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. e bending failure model of the PSFRC beam is a typical ductile failure as shown in Figure 13.

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, σ 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]. e cracking moment M cr is related to the influence coefficient of plastic section modulus c m , the standard tensile strength of concrete matrix f 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 cr and then obtain c m according to the following: Assuming that c m is the function of the reinforcement ratio ρ and the fiber volume content V f , the linear fitting method is used to obtain the calculation formula of cracking moment M cr , which is shown in the following: where the influence factor of reinforcement ratio k(ρ) reflects the influence of ρ on c 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). erefore, k(ρ) is specified to be zero and needs to be explored in the next research.
After the cracking moment M cr is calculated according to (5), then the calculated cracking load P b cr,j of the beam under four-point loading can be obtained.  Figure 17; then the calculation formula of ultimate moment M u is obtained as follows 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 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 ftu is calculated according to the following: where f tk is the standard tensile strength of concrete matrix in RC beam partially reinforced with MSFRC, β tu is the influence coefficient of steel fiber on tensile behavior of MSFRC in the tensile zone of the partially reinforced beam, η f is the characteristic value of steel fiber in the partially reinforced beam, V f is the fiber volume fraction in MSFRC,    Table 7. In Table 7, P b cr,j and P b cr,t , respectively, represent the calculated and experimental results of the cracking load, and P b u,j and P b cr,t are of the ultimate load, which are in good agreement.

Conclusion
rough 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 Figure 17: Ultimate moment calculation diagram of normal section. toughness of MSFRC with Type I microsteel fiber has increased by 69% to 77% compared to Type II. (4) e 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 costeffective. 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) e 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. e calculation of bearing capacity is also in good agreement with the experimental results.

Data Availability
e data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that they have no conflicts of interest.