# Effect of Surface Shape and Content of Steel Fiber on Mechanical Properties of Concrete

Authors: Lijuan Zhang; Jun Zhao; Cunyuan Fan; Zhi Wang
Journal: Advances in Civil Engineering
 (2020)

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## Abstract

Steel fiber reinforced concrete (SFRC) has gained popularity in the last decades attributed to the improvement of brittleness and low tensile strength of concrete. This study investigates the effect of three shapes of steel fibers (straight, hooked end, and corrugated) with four contents (0.5%, 1%, 1.5%, and 2%) on the mechanical properties (compression, splitting tension, shear, and flexure) of concrete. Thirteen groups of concrete were prepared and investigated experimentally. Test results indicated that steel fiber had significant reinforcement on mechanical properties of concrete. When the steel fiber content increases from 0.5% to 2.0%, the compressive strengths increase about 4–24%, splitting tensile strengths increase about 33–122%, shear strengths increase about 31–79%, and flexural strengths increase about 25–111%. Corrugated steel fiber has the best reinforced effect on strength of SFRC, hooked end steel fiber takes the second place, and straight steel fiber is the least. Calculated formulas of compressive, splitting tensile, shear, and flexural strengths were established with consideration of the bonding properties between concrete and steel fiber. Influence factors of steel fiberαf and concrete matrix strength αc were put forward and determined by regression analysis of experimental data. Calculated results agree well with the experimental results.


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## Body

## 1. Introduction

Concrete is the largest amount and the most widely used material; its tensile strength is significantly lower than its compressive strength. Synthetic, glass, basalt, carbon, PVA, and steel fiber have been used in concrete to make up for the low tensile strength of concrete [1]. Fiber can notably enhance mechanical performance of concrete [2–4]. Compared with other fibers, steel fiber has many advantages, such as high stiffness and elasticity modulus and tensile strength. Steel fiber reinforced concrete (SFRC) has excellent tensile and flexural property [5, 6], which has been widely used as structural material. In order to improve the reinforced effect of steel fiber, the reinforced mechanism of steel fiber on concrete had been researched widely [7, 8]. Reinforced effect of steel fiber is mainly affected by fiber content, type, geometry, and strength of concrete matrix [9]. When the concrete matrix is fixed, the fiber content, type, and geometry are the main influence factors [10, 11].It is generally acknowledged that the mechanical property of SFRC increases with the rising of steel fiber content. However, some studies suggest that steel fiber does not significantly affect the compressive strength [3]. The axial compressive strength almost keeps unchanged when the volume fraction of steel fiber is larger than 1.0% [12]. Other studies suggest that compressive strength increases by 25% with the volume fraction of steel fiber increasing from 0.5% to 1.5% for the moderately high strength concrete [13]. Some literatures have proved that steel fiber added in concrete increases the compressive strength of concrete by about 4–19% [14, 15]. Steel fiber in concrete significantly increases the split tensile and flexural strength of concrete [12]. Split tensile strength of SFRC is higher about 11–54% than the reference mixture. Besides, flexural strengths of SFRC are higher by 3–81% than reference mixture. In addition, the increase ratio of flexural strength is higher than that of the split tensile and compressive strength [16]. Shear strength increases by 44% for the steel fiber volume fraction of 0.5% and 65% for the volume ratio of 1% [17]. The shear strength of SFRC exhibits a linear increase with the amount of steel fiber crossing the shear crack interface [18]. It can be seen that even if the content of steel fiber is the same, steel fiber still has different reinforced effect on different mechanical property. In a word, the reinforced effect of steel fiber on concrete strength still has not uniform answer.According to manufacturing form, steel fiber is usually classified into three main shapes (straight form, hooked ends form, and corrugated form) [11, 19]. Different steel fiber shapes have different effect on the mechanical performance of concrete due to the different bond property. However, some researchers suggest that steel fiber shape almost has no influence on compressive strength [12] or the compressive performance is insignificantly affected by the length and type of fiber [20]. The compressive strength and the elastic modulus of SFRC were developed with hooked end steel fiber [21]. The compressive strength is improved by twisted steel fiber compared to short straight steel fiber, but the improvement is relatively insignificant compared to what is observed for the tensile and flexural performance [22]. The tensile strength is improved by using the deformed steel fiber, as compared to that with the short straight steel fiber [23]. The specimens with 2% of twisted steel fiber exhibit a tensile strength which is approximately 32% higher than those with 2% of short straight steel fiber. Previous research has showed that corrugated and hooked fiber significantly improved the bond properties by three to seven times when compared to those with straight fiber [24, 25]. It can be concluded that even if the content of steel fiber is the same, the different shape steel fiber has different effect on concrete mechanical property.Although much work has been done about SFRC, there still exists unsolved problem:(i)
Although the reinforced effect of steel fiber on compressive strength is much less than that on tensile strength, shear strength, and flexural strength, the increase ratio of compressive strength still can reach 25% for low or moderately high strength (≤60 MPa) concrete. Some literature studies suggest that steel fiber shape almost has no influence on compressive strength; others indicate that compressive strength can be improved by steel fiber no matter what type steel fiber is. There are still many different conclusions about the reinforced effect of steel fiber on compressive strength, so the reinforced effect of steel fiber with different content and type on compressive strength should be studied further.(ii)
Splitting tensile, flexure, and shear strength of SFRC increase with the rising of steel fiber content; some researchers suggest that concrete strength will no longer increase when steel fiber content exceeds a certain value, which means that there exists the most economical steel fiber content for certain strength. But there is no final word on the most economical content of steel fiber.(iii)
The shape of steel fiber has significantly influence on the enhancement effect of splitting tensile, flexure, and shear strength of SFRC. At the same time, the reinforced effect of different shapes on various mechanical properties of concrete is also different. So, there is the best shape of steel fiber which can achieve the best enhancement effect on one kind of mechanical property of content.How to determine the optimal content and shape of steel fiber is an important problem. This would help improve the utilization rate of steel fiber and reduce the cost of SFRC.In this research, the impact of steel fiber shape and content on the reinforced effect of concrete will be monitored and analyzed through the compressive, splitting tensile, shear, and flexural experiments. Three shapes (straight, hooked end, and corrugated) of steel fiber were used to research the influence on the mechanical performance of concrete with different volume fractions (0, 0.5%, 1%, 1.5%, and 2%). Based on the test result, calculation model of compressive, splitting tensile, shear, and flexural strength of SFRC were put forward.


## 2. Experiment Investigation

### 2.1. Materials

Portland cement (P. O. 42.5) conforming to GB 175 [26] was used in all mixes; properties of the cement are shown in Table 1. The coarse aggregate was crushed limestone with continuous grading of particle sizes from 4.75 mm to 20 mm. Fine aggregate was river sand with a fineness modulus of 2.7. Properties of all aggregates used in the test are shown in Table 2 according to the Chinese Standard GB/T 14685 [27]. Three shapes of steel fiber, namely, straight (ST-F), hooked end (HE-F), and corrugated (CO-F) were used in tests. Geometry and mechanical characteristics of steel fiber are listed in Table 3. Four different volume fractions of steel fiber were developed to cover the majority of practically used fractions range: 0.5%, 1.0%, 1.5%, and 2%.Table 1
Physical and mechanical properties of cement.
TypeSpecific gravity (kg/m3)Surface area (m2/kg) %Standard consistencyStabilitySetting time (min)Compressive strength (MPa)Flexural strength (MPa)InitialFinal3 d28 d3 d28 dP. O. 42.5310035224.7Eligibility17522023.5455.68.5Table 2
Physical properties of the coarse and fine aggregate.
Aggregate typeApparent density (kg/m3)Loose packing density (kg/m3)Dry-rodded density (kg/m3)Water absorption (wt %)Crush index (%)Void ratio (%)Coarse aggregate2814156816301.408.844.3Fine aggregate2556161114860.56——Table 3
Geometry and mechanical characteristics of steel fibers.
ST-FHE-FCO-FFiber shapeStraightHooked endCorrugatedMean length (lf), mm32.3432.1932.27Mean diameter (df), mm1.0360.9931.215Aspect ratio (lf/df)31.2132.4126.56Density (g/cm3)7.97.97.9Elastic modulus (GPa)200200200Tensile strength (MPa)500380500


### 2.2. Mix Proportion

Three shapes of steel fiber and four steel fiber volume fractions (Vf = 0.5%, 1.0%, 1.5%, and 2%) were chosen as test parameters. Steel fiber volume fraction (Vf) was defined as the absolute volume of steel fiber in 1 m3 concrete. Water-cement ratio was taken as 0.55. The mixture proportion design method conformed to the Chinese Standards JGJ 55-2011 [28] and JG/T 472-2015 [29]. The target slump was taken as 180 mm. The sand ratio of plain concrete was taken as 42%. In order to ensure the working performance of concrete, the sand rate increases by 1% when the steel fiber volume fraction increases by 1%. Details of mixture proportion designs are listed in Table 4. PC represents plain concrete for comparison; letters represent the type of steel fiber; numbers represent the steel fiber volume fraction (%), such as ST-F0.5; it means that straight steel fiber and steel fiber volume fraction is 0.5%.Table 4
Mixture proportions (kg/m3).
Mixture numberWaterCementSandStoneSteel fiberPC264480716.5989.50ST-F0.5264480727.8965.839ST-F1264480739.2942.378ST-F1.5264480750.5917.3117ST-F2264480761.9895.1156HE-F0.5264480727.8965.839HE-F1264480739.2942.378HE-F1.5264480750.5917.3117HE-F2264480761.9895.1156CO-F0.5264480727.8965.839CO-F1264480739.2942.378CO-F1.5264480750.5917.3117CO-F2264480761.9895.1156


### 2.3. Test Specimen

The cubic specimens with side length of 150 mm were cast for the compressive strength (fcu, ffcu) and splitting tensile strength (fts, ffts) test, the prism specimens of 100 mm × 100 mm × 300 mm were cast for shear strength (fv, ffv) test, the prism specimens of 100 mm × 100 mm × 400 mm were cast for flexural strength (ftm, fftm) test, and three specimens were prepared for each group. To distinguish the concrete with and without steel fiber, fcu, fts, fv, and ftm are used to represent the mechanical performance indexes of the plain concrete; ffcu, ffts, ffv, and fftm are used to represent the mechanical performance indexes of SFRC.A multifunction mixer was used to prepare the concrete. Mixing process of concrete included three steps: firstly, all aggregate and cement were put into a forced concrete mixer to mix for about 2 minutes; secondly, the water was added and mixed continuously for 2 minutes; finally, steel fiber was sprinkled evenly and then mixed for another 3 minutes. Fresh concrete was put rapidly into the moulds which were brushed oil in advance. Specimens were vibrated for 20 seconds. After 24 hours of curing in air, specimens were carefully demoulded and placed in a curing room at approximately 95% RH and 20°C.


### 2.4. Test Method

All the tests were conducted at the age of 28 days. The compressive strength and splitting tensile strength test were performed according to GB/T50081 [30] and were carried on a servohydraulic closed-loop testing machine with capacity of 3000 kN at the loading rate of 0.6 MPa/s and 0.06 MPa/s, respectively. Test setup of splitting tensile test is shown in Figure 1.Figure 1
Test setup of splitting tensile strength.One steel bearing plate and one plywood bearing strip were placed between specimen and the top and bottom pressure plate, respectively. The section of bearing plate is part of circle radius of 75 mm; thickness is 20 mm. The section of bearing strip is 20 mm × 4 mm. The bearing plate and bearing strip should align with the center line of the top and bottom surface of specimen. The splitting tensile strength of the specimen was calculated as follows:(1)ffts=0.637FA,where ffts is the splitting tensile strength, MPa; F is the maximum applied load indicated by the testing machine, N; A is the area of splitting surface, mm2.The shear test was also carried on a servohydraulic closed-loop testing machine with capacity of 3000 kN at the loading rate of 0.06 MPa/s; the test setup is shown in Figure2.Figure 2
Test setup of shear strength.The load was recorded with a load transducer. The ultimate shear strength was calculated as follows:(2)ffv=F2beffdeff,where ffv is the ultimate shear strength; F is the maximum applied load indicated by the testing machine; beff is the effective width of the specimen (the average value of the width of the two shear sections), and deff is its effective depth (the average value of the depth of the two shear sections).Flexural tests were carried on a MTS810 testing machine with capacity of 500 kN with displacement control at a rate of 0.1 mm/min, according to ASTM C1609 (using beam with third-point loading) [31]. The test setup is shown in Figure 3.Figure 3
Test setup of flexural strength.The specimens were normally rotated an angle of 90° from the casting position to eliminate the eccentricity effect from the roughness of the surface. Calculate the flexural strength of the specimen as follows:(3)fftm=Flbh2,where fftm is flexural strength, MPa; F is the maximum applied load indicated by the testing machine, N; b and h are the average width and height of specimen, mm; l is the span length of test specimen, mm.At least, three specimens in each group were tested and their mean values were taken as the test results. Test results offfcu, ffts, ffv, and fftm are listed in Table 5.Table 5
Test results of mechanics strength (MPa).
Mixture numberffcufftsffvfftmPC34.63.156.854.32ST-F0.5364.199.395.40ST-F138.84.4510.206.25ST-F1.538.14.8911.067.39ST-F240.85.3412.257.95HE-F0.538.24.2810.016.09HE-F138.15.2011.007.26HE-F1.540.35.8112.217.55HE-F241.66.4111.388.68CO-F0.5354.649.806.58CO-F137.75.3010.087.35CO-F1.540.16.5512.018.51CO-F242.97.0011.129.11


## 2.1. Materials

Portland cement (P. O. 42.5) conforming to GB 175 [26] was used in all mixes; properties of the cement are shown in Table 1. The coarse aggregate was crushed limestone with continuous grading of particle sizes from 4.75 mm to 20 mm. Fine aggregate was river sand with a fineness modulus of 2.7. Properties of all aggregates used in the test are shown in Table 2 according to the Chinese Standard GB/T 14685 [27]. Three shapes of steel fiber, namely, straight (ST-F), hooked end (HE-F), and corrugated (CO-F) were used in tests. Geometry and mechanical characteristics of steel fiber are listed in Table 3. Four different volume fractions of steel fiber were developed to cover the majority of practically used fractions range: 0.5%, 1.0%, 1.5%, and 2%.Table 1
Physical and mechanical properties of cement.
TypeSpecific gravity (kg/m3)Surface area (m2/kg) %Standard consistencyStabilitySetting time (min)Compressive strength (MPa)Flexural strength (MPa)InitialFinal3 d28 d3 d28 dP. O. 42.5310035224.7Eligibility17522023.5455.68.5Table 2
Physical properties of the coarse and fine aggregate.
Aggregate typeApparent density (kg/m3)Loose packing density (kg/m3)Dry-rodded density (kg/m3)Water absorption (wt %)Crush index (%)Void ratio (%)Coarse aggregate2814156816301.408.844.3Fine aggregate2556161114860.56——Table 3
Geometry and mechanical characteristics of steel fibers.
ST-FHE-FCO-FFiber shapeStraightHooked endCorrugatedMean length (lf), mm32.3432.1932.27Mean diameter (df), mm1.0360.9931.215Aspect ratio (lf/df)31.2132.4126.56Density (g/cm3)7.97.97.9Elastic modulus (GPa)200200200Tensile strength (MPa)500380500


## 2.2. Mix Proportion

Three shapes of steel fiber and four steel fiber volume fractions (Vf = 0.5%, 1.0%, 1.5%, and 2%) were chosen as test parameters. Steel fiber volume fraction (Vf) was defined as the absolute volume of steel fiber in 1 m3 concrete. Water-cement ratio was taken as 0.55. The mixture proportion design method conformed to the Chinese Standards JGJ 55-2011 [28] and JG/T 472-2015 [29]. The target slump was taken as 180 mm. The sand ratio of plain concrete was taken as 42%. In order to ensure the working performance of concrete, the sand rate increases by 1% when the steel fiber volume fraction increases by 1%. Details of mixture proportion designs are listed in Table 4. PC represents plain concrete for comparison; letters represent the type of steel fiber; numbers represent the steel fiber volume fraction (%), such as ST-F0.5; it means that straight steel fiber and steel fiber volume fraction is 0.5%.Table 4
Mixture proportions (kg/m3).
Mixture numberWaterCementSandStoneSteel fiberPC264480716.5989.50ST-F0.5264480727.8965.839ST-F1264480739.2942.378ST-F1.5264480750.5917.3117ST-F2264480761.9895.1156HE-F0.5264480727.8965.839HE-F1264480739.2942.378HE-F1.5264480750.5917.3117HE-F2264480761.9895.1156CO-F0.5264480727.8965.839CO-F1264480739.2942.378CO-F1.5264480750.5917.3117CO-F2264480761.9895.1156


## 2.3. Test Specimen

The cubic specimens with side length of 150 mm were cast for the compressive strength (fcu, ffcu) and splitting tensile strength (fts, ffts) test, the prism specimens of 100 mm × 100 mm × 300 mm were cast for shear strength (fv, ffv) test, the prism specimens of 100 mm × 100 mm × 400 mm were cast for flexural strength (ftm, fftm) test, and three specimens were prepared for each group. To distinguish the concrete with and without steel fiber, fcu, fts, fv, and ftm are used to represent the mechanical performance indexes of the plain concrete; ffcu, ffts, ffv, and fftm are used to represent the mechanical performance indexes of SFRC.A multifunction mixer was used to prepare the concrete. Mixing process of concrete included three steps: firstly, all aggregate and cement were put into a forced concrete mixer to mix for about 2 minutes; secondly, the water was added and mixed continuously for 2 minutes; finally, steel fiber was sprinkled evenly and then mixed for another 3 minutes. Fresh concrete was put rapidly into the moulds which were brushed oil in advance. Specimens were vibrated for 20 seconds. After 24 hours of curing in air, specimens were carefully demoulded and placed in a curing room at approximately 95% RH and 20°C.


## 2.4. Test Method

All the tests were conducted at the age of 28 days. The compressive strength and splitting tensile strength test were performed according to GB/T50081 [30] and were carried on a servohydraulic closed-loop testing machine with capacity of 3000 kN at the loading rate of 0.6 MPa/s and 0.06 MPa/s, respectively. Test setup of splitting tensile test is shown in Figure 1.Figure 1
Test setup of splitting tensile strength.One steel bearing plate and one plywood bearing strip were placed between specimen and the top and bottom pressure plate, respectively. The section of bearing plate is part of circle radius of 75 mm; thickness is 20 mm. The section of bearing strip is 20 mm × 4 mm. The bearing plate and bearing strip should align with the center line of the top and bottom surface of specimen. The splitting tensile strength of the specimen was calculated as follows:(1)ffts=0.637FA,where ffts is the splitting tensile strength, MPa; F is the maximum applied load indicated by the testing machine, N; A is the area of splitting surface, mm2.The shear test was also carried on a servohydraulic closed-loop testing machine with capacity of 3000 kN at the loading rate of 0.06 MPa/s; the test setup is shown in Figure2.Figure 2
Test setup of shear strength.The load was recorded with a load transducer. The ultimate shear strength was calculated as follows:(2)ffv=F2beffdeff,where ffv is the ultimate shear strength; F is the maximum applied load indicated by the testing machine; beff is the effective width of the specimen (the average value of the width of the two shear sections), and deff is its effective depth (the average value of the depth of the two shear sections).Flexural tests were carried on a MTS810 testing machine with capacity of 500 kN with displacement control at a rate of 0.1 mm/min, according to ASTM C1609 (using beam with third-point loading) [31]. The test setup is shown in Figure 3.Figure 3
Test setup of flexural strength.The specimens were normally rotated an angle of 90° from the casting position to eliminate the eccentricity effect from the roughness of the surface. Calculate the flexural strength of the specimen as follows:(3)fftm=Flbh2,where fftm is flexural strength, MPa; F is the maximum applied load indicated by the testing machine, N; b and h are the average width and height of specimen, mm; l is the span length of test specimen, mm.At least, three specimens in each group were tested and their mean values were taken as the test results. Test results offfcu, ffts, ffv, and fftm are listed in Table 5.Table 5
Test results of mechanics strength (MPa).
Mixture numberffcufftsffvfftmPC34.63.156.854.32ST-F0.5364.199.395.40ST-F138.84.4510.206.25ST-F1.538.14.8911.067.39ST-F240.85.3412.257.95HE-F0.538.24.2810.016.09HE-F138.15.2011.007.26HE-F1.540.35.8112.217.55HE-F241.66.4111.388.68CO-F0.5354.649.806.58CO-F137.75.3010.087.35CO-F1.540.16.5512.018.51CO-F242.97.0011.129.11


## 3. Test Results and Discussion

### 3.1. Compressive Strength

Relationship between compressive strength (ffcu), compressive strength reinforced ratio (ffcu/fcu), and steel fiber volume fraction (Vf) with the different steel fiber shape are shown in Figure 4.Figure 4
Relationship betweenffcu, ffcu/fcu, and Vf.In general,ffcu increased continuously as Vf increased from 0 to 2%. However, the increasing trend has slight difference with the different steel fiber shape. When Vf ≤ 1%, the ffcu/fcu of ST-F and HE-F was slightly bigger than that of CO-F. But, when Vf reached 2%, ffcu/fcu of CO-F reached its maximum value 1.24, which was higher than ffcu/fcu of ST-F and HE-F. It indicated that ST-F and HE-F had better strength reinforcement when Vf was below 1%, while CO-F had better strength reinforcement when Vf was above 1%. Although different steel fiber shape has reinforced effect on compressive strength of concrete, the increment is limited and the maximum value of ffcu/fcu is 1.24.The steel fiber can limit the lateral expansion and restrain the crack propagation of concrete under compressive load, which can delay the damage of concrete and enhance the compressive performance. The reinforced effect is decided by the bonding performance between steel fiber and concrete. The bonding force is affected by the surface shape of steel fiber. So, the different surface shape has the different effect on the compressive strength of concrete.


### 3.2. Tensile Strength

Relationship between splitting tensile strength (ffts), splitting tensile strength reinforced ratio (ffts/fts), and steel fiber volume fraction (Vf) with the different steel fiber shape is shown in Figure 5. ffts increased continuously as Vf increased from 0 to 2%. When Vf ≤ 0.5%, ST-F and HE-F have a similar reinforced effect on concrete; CO-F has a slighter better reinforced effect than them. When Vf ≥ 0.5%, CO-F still has the best reinforced effect and HE-F takes the second place. When Vf = 2%, ffts/fts of CO-F is 2.22, ffts/fts of HE-F is 2.03, and ffts/fts of ST-F is only 1.7. As shown in 3, these three types of steel fibers have similar length and diameter; the only difference is the surface shape. With the same steel fiber content, the reinforced effect can be improved dramatically by changing the surface shape of steel fiber.Figure 5
Relationship betweenffts, ffts/fts, and Vf.Test results proved that CO-F had the best reinforced effect onffts. This is because the surface of CO-F is the shape of corrugate and it can provide higher interface bonding force than ST-F and HE-F. Similarly, HE-F with the hooked form at both ends can provide better interface bonding force than ST-F with straight surface. ST-F has the smallest reinforced effect on ffts because its surface is smooth and can not provide the mechanical occlusive force. It can be seen that because the surface shape of steel fiber has important effect on the interface bonding force between concrete and steel fiber, the surface shape of steel fiber obviously affects the reinforced effect on the splitting tensile strength of concrete. In order to increase the reinforcement of steel fiber on concrete, the rough surface of steel fiber is the best choice.


### 3.3. Shear Strength

Relationship between shear strength (ffv), shear strength reinforced ratio (ffv/fv), and steel fiber volume fraction (Vf) with the different steel fiber shape is shown in Figure 6. When Vf increases from 0 to 0.5%, ffv increases rapidly. When Vf = 0.5%, ffv/fv = 1.37 for ST-F, ffv/fv = 1.46 for HE-F, and ffv/fv = 1.43 for CO-F. Whatever the steel fiber shape is, ffv increases about 40% when Vf increases from 0 to 0.5%. When Vf increases from 0.5 to 1.5%, ffv still increases with the increase of Vf, but the growth ratio is slowing down. When Vf is more than 1.5%, ffv of ST-F continuously increases while ffv decreases with the increase of Vf for HE-F and CO-F.Figure 6
Relationship betweenffv, ffv/fv, and Vf.This result indicates that too much steel fiber can cause shear strength reduction. The reason lies in two aspects. One is that the compressive strength of concrete matrix is not high; it leads steel fiber which is pulled out from concrete matrix before concrete failure because of the low bond force between concrete and steel fiber. And steel fiber cannot give full play when the steel fiber volume fraction is big. Some literature gave a similar result: to improve the shear strength, the first way consists in the increase of the compressive strength of the concrete; the second way is obtained with the addition of fiber [14]. The other reason is that higher Vf may more easily cause the uneven distribution of steel fiber; the uneven distribution of steel fiber leads to the lower bonding force between some steel fiber and concrete and also produces some weakened region. An optimum steel fiber content exists for a given concrete, beyond which the reinforcing effect of steel fiber on the shear strength becomes weakened with increase of steel fiber content. This result is slightly different to many previous literatures which proved that direct shear capacity of SFRC is clearly related to the amount of fiber [15].


### 3.4. Flexural Strength

Relationship between flexural strength (fftm), flexural strength reinforced ratio (fftm/ftm), and steel fiber volume fraction (Vf) with the different steel fiber shape is shown in Figure 7.fftm increased continuously as Vf increased from 0 to 2%. Whatever the shapes of steel fiber are, the three trend lines are nearly straight upward; this indicates that fftm is all nearly a linear function of Vf. However, the slopes of three lines are different, the slope of CO-F is the biggest, and the slope of ST-F is the least. This means that when Vf is fixed, the enhancement effect is different with the different shape of steel fiber. CO-F is the best and HE-F takes the second place. It can be attributed to the bond strength of the matrix and steel fiber. The deformed shape provides better bond property than the straight fiber.Figure 7
Relationship betweenfftm, fftm/ftm, and Vf.WhenVf reaches its maximum value 2%, fftm/ftm of CO-F is 2.11 and fftm/ftm of HE-F is 2.01; this means that fftm of concrete in corrugated and hooked steel fiber doubles the value of plain concrete. fftm/ftm of ST-F is the least, which is 1.84. This proved that steel fiber has excellent enhancement effect on flexural strength. Previous research suggested that the limited volume fraction of HE-F is 1.5% for the economical and efficient use of steel fiber on flexural performance [11]. However, test results of this paper indicated that flexural strength still increased with Vf, even if Vf ≥ 1.5%. This may be because the concrete matrix strength in this test is only about 40 MPa. The flexural failure is attributable mostly to pull-out rather than rupture of the steel fiber. The flexural strength of the SFRC increased with the increase of fiber content, which is closely related to the number of steel fibers that provide a bridging action. Then, steel fiber of deformed shape can play more important role than that with straight shape.


## 3.1. Compressive Strength

Relationship between compressive strength (ffcu), compressive strength reinforced ratio (ffcu/fcu), and steel fiber volume fraction (Vf) with the different steel fiber shape are shown in Figure 4.Figure 4
Relationship betweenffcu, ffcu/fcu, and Vf.In general,ffcu increased continuously as Vf increased from 0 to 2%. However, the increasing trend has slight difference with the different steel fiber shape. When Vf ≤ 1%, the ffcu/fcu of ST-F and HE-F was slightly bigger than that of CO-F. But, when Vf reached 2%, ffcu/fcu of CO-F reached its maximum value 1.24, which was higher than ffcu/fcu of ST-F and HE-F. It indicated that ST-F and HE-F had better strength reinforcement when Vf was below 1%, while CO-F had better strength reinforcement when Vf was above 1%. Although different steel fiber shape has reinforced effect on compressive strength of concrete, the increment is limited and the maximum value of ffcu/fcu is 1.24.The steel fiber can limit the lateral expansion and restrain the crack propagation of concrete under compressive load, which can delay the damage of concrete and enhance the compressive performance. The reinforced effect is decided by the bonding performance between steel fiber and concrete. The bonding force is affected by the surface shape of steel fiber. So, the different surface shape has the different effect on the compressive strength of concrete.


## 3.2. Tensile Strength

Relationship between splitting tensile strength (ffts), splitting tensile strength reinforced ratio (ffts/fts), and steel fiber volume fraction (Vf) with the different steel fiber shape is shown in Figure 5. ffts increased continuously as Vf increased from 0 to 2%. When Vf ≤ 0.5%, ST-F and HE-F have a similar reinforced effect on concrete; CO-F has a slighter better reinforced effect than them. When Vf ≥ 0.5%, CO-F still has the best reinforced effect and HE-F takes the second place. When Vf = 2%, ffts/fts of CO-F is 2.22, ffts/fts of HE-F is 2.03, and ffts/fts of ST-F is only 1.7. As shown in 3, these three types of steel fibers have similar length and diameter; the only difference is the surface shape. With the same steel fiber content, the reinforced effect can be improved dramatically by changing the surface shape of steel fiber.Figure 5
Relationship betweenffts, ffts/fts, and Vf.Test results proved that CO-F had the best reinforced effect onffts. This is because the surface of CO-F is the shape of corrugate and it can provide higher interface bonding force than ST-F and HE-F. Similarly, HE-F with the hooked form at both ends can provide better interface bonding force than ST-F with straight surface. ST-F has the smallest reinforced effect on ffts because its surface is smooth and can not provide the mechanical occlusive force. It can be seen that because the surface shape of steel fiber has important effect on the interface bonding force between concrete and steel fiber, the surface shape of steel fiber obviously affects the reinforced effect on the splitting tensile strength of concrete. In order to increase the reinforcement of steel fiber on concrete, the rough surface of steel fiber is the best choice.


## 3.3. Shear Strength

Relationship between shear strength (ffv), shear strength reinforced ratio (ffv/fv), and steel fiber volume fraction (Vf) with the different steel fiber shape is shown in Figure 6. When Vf increases from 0 to 0.5%, ffv increases rapidly. When Vf = 0.5%, ffv/fv = 1.37 for ST-F, ffv/fv = 1.46 for HE-F, and ffv/fv = 1.43 for CO-F. Whatever the steel fiber shape is, ffv increases about 40% when Vf increases from 0 to 0.5%. When Vf increases from 0.5 to 1.5%, ffv still increases with the increase of Vf, but the growth ratio is slowing down. When Vf is more than 1.5%, ffv of ST-F continuously increases while ffv decreases with the increase of Vf for HE-F and CO-F.Figure 6
Relationship betweenffv, ffv/fv, and Vf.This result indicates that too much steel fiber can cause shear strength reduction. The reason lies in two aspects. One is that the compressive strength of concrete matrix is not high; it leads steel fiber which is pulled out from concrete matrix before concrete failure because of the low bond force between concrete and steel fiber. And steel fiber cannot give full play when the steel fiber volume fraction is big. Some literature gave a similar result: to improve the shear strength, the first way consists in the increase of the compressive strength of the concrete; the second way is obtained with the addition of fiber [14]. The other reason is that higher Vf may more easily cause the uneven distribution of steel fiber; the uneven distribution of steel fiber leads to the lower bonding force between some steel fiber and concrete and also produces some weakened region. An optimum steel fiber content exists for a given concrete, beyond which the reinforcing effect of steel fiber on the shear strength becomes weakened with increase of steel fiber content. This result is slightly different to many previous literatures which proved that direct shear capacity of SFRC is clearly related to the amount of fiber [15].


## 3.4. Flexural Strength

Relationship between flexural strength (fftm), flexural strength reinforced ratio (fftm/ftm), and steel fiber volume fraction (Vf) with the different steel fiber shape is shown in Figure 7.fftm increased continuously as Vf increased from 0 to 2%. Whatever the shapes of steel fiber are, the three trend lines are nearly straight upward; this indicates that fftm is all nearly a linear function of Vf. However, the slopes of three lines are different, the slope of CO-F is the biggest, and the slope of ST-F is the least. This means that when Vf is fixed, the enhancement effect is different with the different shape of steel fiber. CO-F is the best and HE-F takes the second place. It can be attributed to the bond strength of the matrix and steel fiber. The deformed shape provides better bond property than the straight fiber.Figure 7
Relationship betweenfftm, fftm/ftm, and Vf.WhenVf reaches its maximum value 2%, fftm/ftm of CO-F is 2.11 and fftm/ftm of HE-F is 2.01; this means that fftm of concrete in corrugated and hooked steel fiber doubles the value of plain concrete. fftm/ftm of ST-F is the least, which is 1.84. This proved that steel fiber has excellent enhancement effect on flexural strength. Previous research suggested that the limited volume fraction of HE-F is 1.5% for the economical and efficient use of steel fiber on flexural performance [11]. However, test results of this paper indicated that flexural strength still increased with Vf, even if Vf ≥ 1.5%. This may be because the concrete matrix strength in this test is only about 40 MPa. The flexural failure is attributable mostly to pull-out rather than rupture of the steel fiber. The flexural strength of the SFRC increased with the increase of fiber content, which is closely related to the number of steel fibers that provide a bridging action. Then, steel fiber of deformed shape can play more important role than that with straight shape.


## 4. Strength Calculation Model

The above result analysis proved that steel fiber can improveffcu, ffts, ffv, and fftm of concrete obviously with the increasing of Vf. When Vf is fixed, the reinforcement ratio mainly is influenced by the interface bonding force between concrete and steel fiber. The interface bonding force mainly consists of three parts: chemical cementation force, frictional resistance, and mechanical interaction force. Chemical cementation force is mainly influenced by the strength of concrete matrix (fcu). Frictional resistance is mainly affected by surface area and roughness. Mechanical occlusal force is mainly affected by the surface dents of steel fiber. Thus, the important enhancement factors of ffcu, ffts, ffv, and fftm are concrete matrices (fcu), aspect ratio (lf/df), content (Vf), and shape and surface dents of steel fiber.


### 4.1. Effect of Steel Fiber

Based on the above analysis, reinforcement ratio offfcu is influenced by content, aspect ratio, and shape of steel fiber; it can be expressed as follows:(4)ffcufcu=1+αfλf,where ffcu is the compressive strength of SFRC; fcu is the compressive strength of plain concrete; αf is the influence coefficient of steel fiber shape, which is related to the geometric and surface shape of steel fiber; λf is the characteristic coefficient of steel fiber, λf = Vflf/df.αf of these three shapes steel fiber can be obtained through the regression analysis of experiment data in this paper and relative research literature [13, 16, 32–35] based on (4). The relationship between ffcu/fcu and λf is shown in Figure 8.Figure 8
Relationship betweenffcu/fcu and λf (a) ST-F, (b) HE-F, and (c) CO-F.
(a)(b)(c)As shown in Figure8, although the length and aspect ratio of steel fiber from different literature are different, the reinforcement ratio of ffcu had a linear relationship with λf when the surface shape of steel fiber is the same. Value of αf can be obtained through regression analysis: αf = 0.21 for ST-F; αf = 0.27 for HE-F; αf = 0.4 for CO-F. αf of CO-F is the biggest; this is because corrugated surface not only can increase the surface roughness, but also can provide mechanical interaction force. αf of HE-F is in the second place; hooks at the end of steel fiber can increase part of the frictional resistance. Adding surface roughness or uneven of steel fiber can improve its enhancement effect obviously under the condition of keeping content of steel fiber.


### 4.2. Effect of Concrete Matrix

Concrete matrix also plays an important role in bonding strength, so it significantly affects the reinforcement ratio offfts, ffv, and fftm. The reinforcement ratio of ffts, ffv, and fftm can be expressed as follows:(5)Rf=1+αfαcλf,where Rf is strength reinforced ratio of SFRC; it can represent ffts/fts, ffv/fv, or fftm/ftm; αc is the influence coefficient of concrete matrix, which is related to compressive strength of concrete matrix.αc can be obtained through the regression analysis of experiment data in this paper and previous literature [13, 16, 21, 32–36] based on equation (5). According to equation (4), αf is known: αf = 0.21 for ST-F; αf = 0.27 for HE-F; αf = 0.4 for CO-F. The relationship between Rf and αfλf is shown in Figure 9.Figure 9
Relationship betweenRf and αfλf.As shown in Figure9, although the length and aspect ratio of steel fiber from different literature are different and Rf represents different strength reinforcement rates, such as ffts/fts, ffv/fv, or fftm/ftm, Rf showed a linear relationship with αfλf. This indicates that the reinforced effect of concrete matrix on the strength of SFRC is linear when eliminating the effect of steel fiber. As shown in Figure 9, the value of αc can be obtained through linear regression with the experiment data, αc = 4.86 and R2 = 0.87. This shows that the correlation between Rf and αfλf is fairly good. Since the compressive strength of plain concrete in this test is fixed (fcu = 34.6 MPa), the value of αc could change with the changing of fcu. The relationship between fcu and αc should be studied further for high strength concrete.


### 4.3. Formula Validation

Above is the main analysis of the enhancement effect of steel fiber. In order to verify the correctness of the equations (4) and (5) and regression coefficient of αf and αc, the strength calculation method of ffcu, ffts, ffv, and fftm can be put forward based on equations (4) and (5):(6)ffcu=fcu×1+αfλf,(7)ffts=fts×1+αfαcλf,(8)ffv=fv×1+αfαcλf,(9)fftm=ftm×1+αfαcλf,where αf = 0.21 for ST-F; αf = 0.27 for HE-F; αf = 0.4 for CO-F; αc = 4.86; λf = Vflf/df. Putting the test data of fcu in (6), fts in (7), fv in (8), and ftm in (9), the calculated value of ffcu, ffts, ffv, and fftm and the ratio of calculated value to test value are put into Table 6.Table 6
Calculated results and the comparison between calculated results and test results of mechanics strength.
Mixture numberffcufftsffvfftmCal (MPa)C/TCal (MPa)C/TCal (MPa)C/TCal (MPa)C/TPC34.613.151.006.8514.321.00ST-F0.535.70.993.650.877.940.855.010.93ST-F136.90.954.150.939.030.895.700.91ST-F1.538.01.004.660.9510.120.926.380.86ST-F239.10.965.160.9711.210.927.070.89HE-F0.536.10.953.820.898.320.835.240.86HE-F137.60.994.490.869.760.896.160.85HE-F1.539.10.975.160.8911.220.927.080.94HE-F240.70.985.830.9112.681.117.990.92CO-F0.536.41.043.960.858.620.885.440.83CO-F138.31.024.780.9010.391.036.550.89CO-F1.540.11.005.590.8512.161.017.670.90CO-F242.00.986.400.9113.921.258.780.96Note that Cal stands for the calculated result and C/T stands for the ratio of the calculated result with test result.The ratio of calculated value to test value offfcu varies from 0.95 to 1.04; this indicates that calculated value of ffcu coincides with test value quite well. The ratio of calculated value to test value of ffts and fftm varies from 0.85 to 1. Although the calculated value is slightly less than test value, the calculated value is still close to the test value. Except CO-F2, the ratio of calculated value to test value of ffv varies from 0.83 to 1.11; the calculated value is also close to the test value. According to the previous analysis, when Vf is larger than 1.5%, the enhancement effect of steel fiber becomes weak, but in the calculation of equation (8) this can not reflect this character, so when Vf is 2%, the calculated value is larger than the test value. Further research should be taken for SFRC with steel fiber volume fraction that is above 2%.


## 4.1. Effect of Steel Fiber

Based on the above analysis, reinforcement ratio offfcu is influenced by content, aspect ratio, and shape of steel fiber; it can be expressed as follows:(4)ffcufcu=1+αfλf,where ffcu is the compressive strength of SFRC; fcu is the compressive strength of plain concrete; αf is the influence coefficient of steel fiber shape, which is related to the geometric and surface shape of steel fiber; λf is the characteristic coefficient of steel fiber, λf = Vflf/df.αf of these three shapes steel fiber can be obtained through the regression analysis of experiment data in this paper and relative research literature [13, 16, 32–35] based on (4). The relationship between ffcu/fcu and λf is shown in Figure 8.Figure 8
Relationship betweenffcu/fcu and λf (a) ST-F, (b) HE-F, and (c) CO-F.
(a)(b)(c)As shown in Figure8, although the length and aspect ratio of steel fiber from different literature are different, the reinforcement ratio of ffcu had a linear relationship with λf when the surface shape of steel fiber is the same. Value of αf can be obtained through regression analysis: αf = 0.21 for ST-F; αf = 0.27 for HE-F; αf = 0.4 for CO-F. αf of CO-F is the biggest; this is because corrugated surface not only can increase the surface roughness, but also can provide mechanical interaction force. αf of HE-F is in the second place; hooks at the end of steel fiber can increase part of the frictional resistance. Adding surface roughness or uneven of steel fiber can improve its enhancement effect obviously under the condition of keeping content of steel fiber.


## 4.2. Effect of Concrete Matrix

Concrete matrix also plays an important role in bonding strength, so it significantly affects the reinforcement ratio offfts, ffv, and fftm. The reinforcement ratio of ffts, ffv, and fftm can be expressed as follows:(5)Rf=1+αfαcλf,where Rf is strength reinforced ratio of SFRC; it can represent ffts/fts, ffv/fv, or fftm/ftm; αc is the influence coefficient of concrete matrix, which is related to compressive strength of concrete matrix.αc can be obtained through the regression analysis of experiment data in this paper and previous literature [13, 16, 21, 32–36] based on equation (5). According to equation (4), αf is known: αf = 0.21 for ST-F; αf = 0.27 for HE-F; αf = 0.4 for CO-F. The relationship between Rf and αfλf is shown in Figure 9.Figure 9
Relationship betweenRf and αfλf.As shown in Figure9, although the length and aspect ratio of steel fiber from different literature are different and Rf represents different strength reinforcement rates, such as ffts/fts, ffv/fv, or fftm/ftm, Rf showed a linear relationship with αfλf. This indicates that the reinforced effect of concrete matrix on the strength of SFRC is linear when eliminating the effect of steel fiber. As shown in Figure 9, the value of αc can be obtained through linear regression with the experiment data, αc = 4.86 and R2 = 0.87. This shows that the correlation between Rf and αfλf is fairly good. Since the compressive strength of plain concrete in this test is fixed (fcu = 34.6 MPa), the value of αc could change with the changing of fcu. The relationship between fcu and αc should be studied further for high strength concrete.


## 4.3. Formula Validation

Above is the main analysis of the enhancement effect of steel fiber. In order to verify the correctness of the equations (4) and (5) and regression coefficient of αf and αc, the strength calculation method of ffcu, ffts, ffv, and fftm can be put forward based on equations (4) and (5):(6)ffcu=fcu×1+αfλf,(7)ffts=fts×1+αfαcλf,(8)ffv=fv×1+αfαcλf,(9)fftm=ftm×1+αfαcλf,where αf = 0.21 for ST-F; αf = 0.27 for HE-F; αf = 0.4 for CO-F; αc = 4.86; λf = Vflf/df. Putting the test data of fcu in (6), fts in (7), fv in (8), and ftm in (9), the calculated value of ffcu, ffts, ffv, and fftm and the ratio of calculated value to test value are put into Table 6.Table 6
Calculated results and the comparison between calculated results and test results of mechanics strength.
Mixture numberffcufftsffvfftmCal (MPa)C/TCal (MPa)C/TCal (MPa)C/TCal (MPa)C/TPC34.613.151.006.8514.321.00ST-F0.535.70.993.650.877.940.855.010.93ST-F136.90.954.150.939.030.895.700.91ST-F1.538.01.004.660.9510.120.926.380.86ST-F239.10.965.160.9711.210.927.070.89HE-F0.536.10.953.820.898.320.835.240.86HE-F137.60.994.490.869.760.896.160.85HE-F1.539.10.975.160.8911.220.927.080.94HE-F240.70.985.830.9112.681.117.990.92CO-F0.536.41.043.960.858.620.885.440.83CO-F138.31.024.780.9010.391.036.550.89CO-F1.540.11.005.590.8512.161.017.670.90CO-F242.00.986.400.9113.921.258.780.96Note that Cal stands for the calculated result and C/T stands for the ratio of the calculated result with test result.The ratio of calculated value to test value offfcu varies from 0.95 to 1.04; this indicates that calculated value of ffcu coincides with test value quite well. The ratio of calculated value to test value of ffts and fftm varies from 0.85 to 1. Although the calculated value is slightly less than test value, the calculated value is still close to the test value. Except CO-F2, the ratio of calculated value to test value of ffv varies from 0.83 to 1.11; the calculated value is also close to the test value. According to the previous analysis, when Vf is larger than 1.5%, the enhancement effect of steel fiber becomes weak, but in the calculation of equation (8) this can not reflect this character, so when Vf is 2%, the calculated value is larger than the test value. Further research should be taken for SFRC with steel fiber volume fraction that is above 2%.


## 5. Conclusions

The general objective of this research project was to evaluate the effect of steel fiber shape and content on the mechanical property of SFRC and the calculation method of reinforced effect of steel fiber with different shape and content on compressive strength, splitting strength, shear strength, and flexural strength. The main conclusions are as follows:(1)
Expecting that shear strength gets its maximum value at steel fiber volume ratio which is 1.5%, compressive strength, splitting strength, and flexural strength all express linear increase trend with the increasing of steel fiber volume ratio from 0 to 2%.(2
)When the steel fiber content is fixed, CO-F has the best reinforced effect on compressive strength, splitting strength, shear strength, and flexural strength of SFRC; HE-F takes the second place and ST-F is the least.(3)
In order to increase the reinforcement of steel fiber on concrete, the steel fiber has rough surface which is the best choice. At least, interface bonding force should be increased as far as possible.(4)
Two influence factorsαf and αc were put forward and their value was obtained by regression analysis of experiment data. The proposed calculated formulas for compressive strength, splitting tensile strength, shear strength, and flexural strength of SFRC have good agreement with the experimental results.(5)
When steel fiber volume fraction is larger than 2%, the reinforced effect of steel fiber on shear strength needs to be studied further. Relationship betweenfcu and αc should also be researched further for high strength concrete (fcu ≥ 60 MPa).



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*Source: 8834507-2020-07-21.xml*