The Flexural Behavior and Mechanical Properties of Super High-Performance Concrete (SHPC) Reinforced Using the Hybridization of Micro Polypropylene and Macro Steel Fibers

: There is a need to investigate the flexural behavior and mechanical properties of super high-performance concrete (SHPC) for a better understanding of its response to compression, tension, and bending. Super-high-performance concrete (SHPC) lies between high-performance concrete (HPC) and ultra-high-performance concrete (UHPC) in strength, durability, and workability and is suitable for sustainable buildings. This paper presents an extensive experimental and analytical study to investigate the effect of the hybridization of micro-polypropylene and macro-steel fibers on the flexural behavior and mechanical properties of super-high-performance concrete (SHPC). The hybridization of both micro-PP fibers and macro-hooked-end ST fibers gathers the benefits of their advantages and offsets their disadvantages. Three types of fibers (micro polypropylene fibers (PP), macro hooked-end steel fiber (ST), and hybrid fiber (PP + ST)) with different fiber content up to 2% were tested to study their effect on the following: (a) the workability of fresh concrete, (b) concrete compressive strength, (c) splitting tensile strength, (d) flexural behavior, including flexural tensile strength and toughness, and (e) the optimum percentage of each of the two fibers, PP and ST, in the hybrid to get the maximum structural and economic benefits of hybridization. Based upon the experimental results and using a statistical program, formulae to calculate both the tensile splitting strength ( f sp ) and the flexural tensile strength in the form of the modulus of rupture ( f ctr ) were obtained. These formulae were able to predict accurately both the splitting tensile strength and modulus of rupture for SHPC with each of the three types of fibers used in this research. Also, they were in very good agreement with the values corresponding to different experimental results of other research, which means the ability to use these equations more generally. In addition, the prediction of the additional ultimate moment provided for all fibers was investigated. This research confirms the structural and the economical efficiency of hybridization in the behavior of SHPC. It was found that the optimum percentage of the fiber volume content for the hybrid of ST and PP is 1%; 0.5% for each of the two kinds.


Introduction
According to the Nevada Department of Transportation, super high-performance concrete (SHPC) is defined as a self-consolidating concrete (SCC) that has, after 28-days, a minimum compressive strength and modulus of rupture of 68.9 MPa and 6.89 MPa, respectively, while its 28-day toughness is calculated using ASTM C1609.It is typically reinforced with 1.5-2% of the volume using steel fibers.Silica fume is also typically present, and a high fine-to-coarse aggregate ratio is used to improve particle packing.SHPC provides an alternative to ultra-high-performance concrete (UHPC) in applications where high-performance concrete (HPC) is not enough.UHPC requires high shear mixing and cannot be produced in drum-type mixers like ready-mixed trucks.SHPC, on the other hand, is cheaper, stronger, and more crack-resistant than HPC and compatible with a drum mixer [1].
Generally, codes and standards [2][3][4] do not provide analytical formulae to calculate the effect of fibers on the structural behavior of concrete structures.However, ACI 318-19 [5] introduced some new rules with reference to minimum shear reinforcement.Also, fib Model Code 2010 [6] provided information on the effect of fibers on the structural behavior (i.e., flexure, shear, and punching) of concrete structures.In addition, several guidelines for designing fiber-reinforced concrete (FRC) have been developed [7][8][9][10][11].ACI 544.4R-18 [11] determined that 0.3-mm-diameter is the limit between micro-fibers and macro-fibers.
Fibers are made of different materials, such as steel, glass, and synthetics such as acrylic, aramid, carbon, nylon, polyester, polyethylene, and polypropylene [12,13].Fibers can increase the capacity of a concrete section either in tension or flexure, depending on their type, dosage, and geometry.As a result, fiber-reinforced concrete (FRC) is widely used due to its excellent mechanical performance, while fibers significantly affect its fresh properties, workability, and may affect its long-term properties [14,15].
The hybridization of micro-PP fibers and macro-hooked-end ST fibers gathers the benefits of their advantages and offsets their disadvantages.ST fibers have very high values for modulus of elasticity, bond stresses, and fiber crack bridging compared with other fibers.PP fibers have excellent properties in terms of plastic shrinkage, durability, and fire resistance, adding to their availability and very low price.On the other hand, ST fibers are expensive, can be corroded by rust, and have low fire resistance.PP fibers are short with a low modulus of elasticity and density, resulting in balling and, hence, much more voids.So, it is required to determine the optimum percentage of each of the two fibers in the hybrid to get the maximum structural and economic benefits of hybridization.Qiana and Stroeven (2000) [50] tested hybrid polypropylene-steel fiber concrete with low fiber content to determine the optimal fiber size, fiber content, and fly ash content.It was concluded that steel fiber sizes affected mechanical properties differently.After nearly fifteen years of aging, the mechanical behavior of three types of high-performance fiber-reinforced concrete (HPFRC) was experimentally studied by Di Nunzio et al. (2018) [51].The mixtures were cast in 2003 using mixtures of steel and polypropylene fibers.It was found that flexural tensile strength increased for all mixtures.The same trend is still present.Özbay et al. (2021) [52] prepared nine concrete batches with polypropylene (PP), steel, macro-synthetic, and hybrid forms of fibers to study fiber-reinforced concrete's compressive and flexural strength.It was found that the polypropylene-steel-macro-synthetic-fiber hybrid had the highest flexural strength.Prabath and Ramadoss (2022) [53] conducted an experimental study on the influence of fiber volume fractions of single and hybrid fibers on the mechanical and ductility performance of high-performance concrete (HPC) with water-binder (w/b) ratios of 0.28 and 0.38.Stress-stain behavior showed that high-performance steel-fiber reinforced concrete (HPSFRC) improved the [54] compressive toughness and ductility considerably.In high-performance hybrid-fiber reinforced concrete (HP-HyFRC), this improvement is high due to the synergetic effect between both the fibers.Ali et al. (2023) [54] used six highperformance concrete mixtures reinforced with a 2.5% fiber volume fraction to examine the impact of both fiber type and fiber hybridization on the repeated impact strength.The results showed that specimens with pure long steel fiber had the highest impact numbers for both cracking (N cr ) and failure (N f ).
Di Prisco et al. ( 2013) [55] carefully discussed and presented simplified composite models in the material section of fib Model Code 2010 [6] to evaluate the uniaxial tension residual strength, mainly fiber pull-out.Their reliability and limitations are indicated with reference to several FRC materials characterized by different matrixes, steel fibers, and fiber contents.The design rules are derived from a unified classification of FRC composites based on a three-point bending test, already accepted as a European standard.
Based on a database that contained 69 results from three-point notched SFRC beam bending tests, Moraes Neto et al. (2014) [56] presented equations to forecast the values of f R1 and f R3 .According to database analysis, the fiber-reinforcement index (V f × l f /d f ) greatly impacts the f Ri values.This database is limited to tests for concrete reinforced with hooked-end steel fibers, with a volume percentage ranging from 0.13 to 1.25 percent and a fiber aspect ratio from 50 to 80.

Research Significance
Studying the structural behavior of super high-performance concrete (SHPC) provided with hybrid fibers of micro polypropylene (PP) and macro steel fiber (ST), especially with equal content, is promising and unique.This research studies the effect of hybrid fibers on both the mechanical properties and flexural behavior of SHPC through extensive experimental and analytical work.Three types of fibers (PP only, ST only, and hybrid of both PP + ST) with different fiber contents, up to 2%, were tested to study their effects on: (a) the workability of fresh concrete, (b) concrete compressive strength, (c) splitting tensile strength, (d) flexural behavior, including flexural tensile strength and toughness.(e) the optimum percentage of each of the two fibers, PP and ST, in the hybrid to get the maximum structural and economic benefits of hybridization.
In addition, this research aims to get an accurate prediction for both the splitting tensile strength and modulus of rupture for SHPC with each of the three types of fibers mentioned before.

Experimental Program
The mechanical properties of SHPC for different types and amounts of fibers were investigated through ten mixtures using different sizes of standard cubes and cylinders that are allowed by the Egyptian code ECP 203-2020 [2].In addition, the flexural behavior was investigated using standard notched beams accepted by the fib-model code 2010 [6].
The extensive experimental work consisted of ten mixtures: three with micro-PP fibers, three with macro-hooked-end ST fibers, three with hybrid (PP + ST) fibers, and a reference mixture without fibers.Three percentages for the fiber volume content were used for each fiber type: 0.5%, 1%, and 2%.For the reference mixture (without fibers) and for each percentage of the fiber volume content mixture, twenty-seven specimens were tested: six cubes 150 mm × 150 mm × 150 mm (compression), six cubes 100 mm × 100 mm × 100 mm (compression), six cylinders 150 mm-diameter × 300 mm-height (compression), three cylinders 150 mm-diameter × 300 mm-height (splitting), three cylinders 100 mm-diameter × 200 mm-height (splitting), and three notched beams 150 mm × 150 mm × 500 mm (flexure).The total number of specimens was 270.The results of each number of specimens for the same purpose were averaged, and the average value was used in the research.

Materials of SHPC
Locally produced ordinary Portland cement CEM I 42.5N, crushed limestone with a maximum nominal size of 20 mm, natural siliceous sand with a maximum size of 4.75 mm, and a finesse modulus of 2.64 were used to produce the SHPC mixture.Figure 1 shows the grading of both the sand and crushed limestone used in the SHPC mixtures.The water used for casting and curing was potable water with a pH of 7. Also, the mixture is normally based on polycarboxylate and was used and manufactured to conform to ASTM C494 specification type F. A low water-to-cement ratio (W/C) necessitates the use of super-plasticizer (SP) for super-high-performance composites to provide high workability and cover the effect of adding fibers.
The extensive experimental work consisted of ten mixtures: three with micro-P bers, three with macro-hooked-end ST fibers, three with hybrid (PP + ST) fibers, a reference mixture without fibers.Three percentages for the fiber volume content w used for each fiber type: 0.5%, 1%, and 2%.For the reference mixture (without fibers) for each percentage of the fiber volume content mixture, twenty-seven specimens w tested: six cubes 150 mm × 150 mm × 150 mm (compression), six cubes 100 mm × 100 × 100 mm (compression), six cylinders 150 mm-diameter × 300 mm-height (compress three cylinders 150 mm-diameter × 300 mm-height (splitting), three cylinders 100 diameter × 200 mm-height (splitting), and three notched beams 150 mm × 150 mm × mm (flexure).The total number of specimens was 270.The results of each number of s imens for the same purpose were averaged, and the average value was used in th search.

Materials of SHPC
Locally produced ordinary Portland cement CEM I 42.5N, crushed limestone w maximum nominal size of 20 mm, natural siliceous sand with a maximum size of mm, and a finesse modulus of 2.64 were used to produce the SHPC mixture.Figu shows the grading of both the sand and crushed limestone used in the SHPC mixt The water used for casting and curing was potable water with a pH of 7. Also, the mix is normally based on polycarboxylate and was used and manufactured to conform ASTM C494 specification type F. A low water-to-cement ratio (W/C) necessitates the of super-plasticizer (SP) for super-high-performance composites to provide high wo bility and cover the effect of adding fibers.Two different types of fibers were utilized: micro polypropylene (PP) and macro hooked-end steel (ST) fibers, as shown in Figure 2. Micro (PP) fibers had a length of 12 mm and an aspect ratio (L f /d f ) of 400 (where L f and d f stand for the fiber's length and diameter, respectively).On the other hand, (ST) fibers had an aspect ratio (L f /d f ) of 50 and were compatible with ASTM A820 criteria.mm and an aspect ratio (Lf/df) of 400 (where Lf and df stand for the fiber's length and diameter, respectively).On the other hand, (ST) fibers had an aspect ratio (Lf/df) of 50 and were compatible with ASTM A820 criteria.Table 1 presents the properties of the two types of fibers used in this research.

Mixtures Proportions and Studied Variables
Ten mixtures were created to examine the mechanical characteristics and flexural behavior of SHPC with various types and dosages of fibers.The reference mix was created as self-compacted high-performance concrete (SCHPC) to examine various kinds of impacts on workability.The other nine mixes are divided into three groups according to the type of fiber used.The compositions for each of these mixes are listed in Table 2.

Mixtures Proportions and Studied Variables
Ten mixtures were created to examine the mechanical characteristics and flexural behavior of SHPC with various types and dosages of fibers.The reference mix was created as self-compacted high-performance concrete (SCHPC) to examine various kinds of impacts on workability.The other nine mixes are divided into three groups according to the type of fiber used.The compositions for each of these mixes are listed in Table 2.The ratio between weight of water and the total weight of binder (cement).

Group 1: Effect of micro-Polypropylene fibers (PP)
In addition to the reference mixture without fiber (B0.0), three mixtures are included in this group: B0.5, B1.0, and B2.0 containing polypropylene fibers with 0.5, 1.0, and 2.0% of volume, respectively.Adding to their positive effect on fire resistance and durability, PP fibers would be useful in preventing steel corrosion.

Group 2: Effect of Macro End Hooked Steel Fibers (ST)
In addition to the reference mixture without fiber (B0.0), three mixtures are included in this group: S0.5, S1.0, and S2.0 containing ST fibers with 0.5, 1.0, and 2.0% of volume, respectively.Numerous studies have demonstrated the superior performance of macro-ST fibers on the structural behavior of HPC.

Group 3: Effect of Hybrid Polypropylene and steel fibers (PP + ST)
In addition to the reference mixture without fiber (B0.0), three mixtures are included in this group: H0.5, H1.0, and H2.0 containing hybrids of PP + ST fibers with 0.5, 1.0, and 2.0% of volume, respectively.The volumes of PP and ST fibers are equal in each of these mixtures.The selection of this hybrid was based on the benefits of each of the two types of fibers.

Mixture Casting and Test Specimens
Coarse aggregates (crushed limestone) and sand were first combined for one minute.Then, the cement and 3/4 of the water were added and mixed for two minutes.After that, the mixture is diluted with a quarter of water and mixed for three minutes.Finally, fibers were added slowly by hand while mixing to ensure a uniform distribution.The specimens were then cast in accordance with EN 12390-2 [63].The samples were kept in a mold for twenty-four hours.They were cured for 28 days using burlap saturated in water.
For each HPC mixture, the flexural tensile strength (limit of proportionality (LOP), residual) was determined by performing three point-bending tests on three notched prismatic specimens of Length × Width × Height = 550 × 150 × 150 mm in accordance with EN14651 [64] and fib model code 2010 [6].A notch with dimensions of Depth × Wide = 25 mm × 5 mm was cut in the mid-length of the specimen.The distance between supports was 500 mm. Figure 3 shows the dimensions of the notched prismatic specimens accepted by fib model code 2010, whereas Figure 4 shows the wooden mold of the notched beam before its casting.

Testing Methods
First, the slump flow test was performed on fresh SCHPC mixtures, which is the same test used for plain self-compacted concrete (SCC) (ASTM C 1611/C 1611M; EN 12350-8) [61].The slump flow test is used to evaluate the free horizontal flow of SCC.The total horizontal spread, or diameter of the slump flow, was measured.EN 206-9, ACI 237R [57], and Egyptian specifications provide acceptable ranges for the slump-flow diameter and recommended values for particular applications.The flow rate of SCC, a measure of its viscosity, can be derived from slump flow experiments by measuring the time taken for the concrete to spread to a 500 mm diameter, commonly designated as T50.The workability of traditional vibrated HPC mixtures is typically evaluated using the slump test (ASTM C143/C143M, EN 12350-2, and ECP 203-2020) as a simple field test, according to ACI. 455.2R-17 [61].
To assess the compressive strength, a compression test was conducted for the cubes and cylinders mentioned before after 28 days using compression test equipment with a capacity of 2000 kN in accordance with ECP203-2020 [2] and EN 12390-3 [63].The cylinders of the splitting tensile test were loaded horizontally in the compression test machine to evaluate the tensile splitting strength after 28 days under EN 12390-6 and ECP203-2020 standards.

Testing Methods
First, the slump flow test was performed on fresh SCHPC mixtures, which is the same test used for plain self-compacted concrete (SCC) (ASTM C 1611/C 1611M; EN 12350-8) [61].The slump flow test is used to evaluate the free horizontal flow of SCC.The total horizontal spread, or diameter of the slump flow, was measured.EN 206-9, ACI 237R [57], and Egyptian specifications provide acceptable ranges for the slump-flow diameter and recommended values for particular applications.The flow rate of SCC, a measure of its viscosity, can be derived from slump flow experiments by measuring the time taken for the concrete to spread to a 500 mm diameter, commonly designated as T 50 .The workability of traditional vibrated HPC mixtures is typically evaluated using the slump test (ASTM C143/C143M, EN 12350-2, and ECP 203-2020) as a simple field test, according to ACI. 455.2R-17 [61].
To assess the compressive strength, a compression test was conducted for the cubes and cylinders mentioned before after 28 days using compression test equipment with a capacity of 2000 kN in accordance with ECP203-2020 [2] and EN 12390-3 [63].The cylinders of the splitting tensile test were loaded horizontally in the compression test machine to evaluate the tensile splitting strength after 28 days under EN 12390-6 and ECP203-2020 standards.
The flexural tensile strength was calculated through a three-point bending test on the notched beam of Figure 3 according to EN 14,651 [64].When drawing the forcedeformation curve, the deformation is defined as the crack mouth opening displacement (CMOD), the opening of the notch in the bottom face of the tested beam.According to the lack of clip gauges, a pi-shape displacement transducer (PI-Gauge with Gauge Length 100 mm and Sensitivity (×10 −6 strain/mm)) was used and put at 10 mm above the bottom fiber.Midspan deflections were measured using linear variable differential transformers (LVDT) with 0.001 mm precision at each loading level.Figure 5 shows the setup of the test and the locations of the instruments.
Buildings 2024, 14, x FOR PEER REVIEW 8 of 37 The flexural tensile strength was calculated through a three-point bending test on the notched beam of Figure 3 according to EN 14,651 [64].When drawing the force-deformation curve, the deformation is defined as the crack mouth opening displacement (CMOD), the opening of the notch in the bottom face of the tested beam.According to the lack of clip gauges, a pi-shape displacement transducer (PI-Gauge with Gauge Length 100 mm and Sensitivity (×10 −6 strain/mm)) was used and put at 10 mm above the bottom fiber.Midspan deflections were measured using linear variable differential transformers (LVDT) with 0.001 mm precision at each loading level.Figure 5 shows the setup of the test and the locations of the instruments.

Workability
According to EN 206:2013 [63], SHPC is classified with respect to consistence into three classes (SF1, SF2, and SF3) concerning slump-flow classes, whereas HPC is classified into five classes (S1, S2, S3, S4, and S5). Figure 6 shows the relationship between slump and fiber volume content for all the mixtures in this research, including the reference one.Mixtures of Group 3 (PP + ST fibers); H0.5 has a slump flow of 560 mm and T50 equal to 10 s, which is classified as SHPC in the SF1 class.H1.0 and H2.0 have slumps of 165 and 25 mm, respectively.They are classified as HPCs in classes S4 and S1, respectively.The results showed that adding (PP + ST) fibers beyond 0.5% (0.25% for each) changed the classification from SHPC to HPC.To explain the previous behavior, it is important to define both "Balling" and "Fiber Count".When fibers entangle into large clumps or balls in a mixture, this is called "balling".On the other hand, "fiber count" is the number of fibers in a unit volume of concrete matrix.As the PP-fiber count was higher than that of ST fibers, the balling of micro-PP fibers occurred more than that of macro-ST fibers.This is the reason that the workability of the mixture with PP fibers is much less than that with ST fibers.Hence, the presence of micro-PP fibers in the mixture with hybrid (PP + ST) fibers made its workability less than that of the mixture with macro-ST fibers, while the presence of macro-ST fibers made the workability of the mixture with hybrid (PP + ST) fibers better than that of the mixture with micro-PP fibers, especially for fiber content less than 1%.Mixtures of Group 1 (PP fibers): B0.5, B1.0, and B2.0 have slumps of 175, 145, and 15 mm, respectively.This means that adding PP fibers changed the group from SHPC to HPC, and increasing its content caused the slump class to change from SF2 to S4, S3, S2, and S1, respectively.
Mixtures of Group 2 (ST fibers); S0.5 and S1.0 have slump flows of 610 and 570 mm, respectively, while the slump of S2.0 equals 143 mm.Mixtures S0.5 and S1.0 are classified as SHPC of the SF1 class with T 50 of 9 and 12 s, respectively.However, S2.0 is classified as HPC in the S3 class.The results showed that adding ST fibers beyond 1.0% changed the classification from SHPC to HPC.
Mixtures of Group 3 (PP + ST fibers); H0.5 has a slump flow of 560 mm and T 50 equal to 10 s, which is classified as SHPC in the SF1 class.H1.0 and H2.0 have slumps of 165 and 25 mm, respectively.They are classified as HPCs in classes S4 and S1, respectively.The results showed that adding (PP + ST) fibers beyond 0.5% (0.25% for each) changed the classification from SHPC to HPC.To explain the previous behavior, it is important to define both "Balling" and "Fiber Count".When fibers entangle into large clumps or balls in a mixture, this is called "balling".On the other hand, "fiber count" is the number of fibers in a unit volume of concrete matrix.As the PP-fiber count was higher than that of ST fibers, the balling of micro-PP fibers occurred more than that of macro-ST fibers.This is the reason that the workability of the mixture with PP fibers is much less than that with ST fibers.Hence, the presence of micro-PP fibers in the mixture with hybrid (PP + ST) fibers made its workability less than that of the mixture with macro-ST fibers, while the presence of macro-ST fibers made the workability of the mixture with hybrid (PP + ST) fibers better than that of the mixture with micro-PP fibers, especially for fiber content less than 1%.
in a unit volume of concrete matrix.As the PP-fiber count was higher than that of ST fibers, the balling of micro-PP fibers occurred more than that of macro-ST fibers.This is the reason that the workability of the mixture with PP fibers is much less than that with ST fibers.Hence, the presence of micro-PP fibers in the mixture with hybrid (PP + ST) fibers made its workability less than that of the mixture with macro-ST fibers, while the presence of macro-ST fibers made the workability of the mixture with hybrid (PP + ST) fibers better than that of the mixture with micro-PP fibers, especially for fiber content less than 1%.

Compressive Strength
Table 3 includes the results of the compressive strength, tensile splitting strength, and modulus of rupture tests for all the specimens in this research.Figure 8 shows the relation between the percentage of fiber volume content and the cube compressive strengths after 28 days for all the specimens, including the reference one, using two sizes of cubes: 150 × 150 × 150 mm and 100 × 100 × 100 mm. Figure 9 shows the relationship between the percentage of fiber volume content and the ratio between the compressive strength of the cube 150 × 150 × 150 mm (fcu) for the three groups and that for the reference mixture B0.0 (fcu,B0.0).

Compressive Strength
Table 3 includes the results of the compressive strength, tensile splitting strength, and modulus of rupture tests for all the specimens in this research.Figure 8 shows the relation between the percentage of fiber volume content and the cube compressive strengths after 28 days for all the specimens, including the reference one, using two sizes of cubes: 150 × 150 × 150 mm and 100 × 100 × 100 mm. Figure 9 shows the relationship between the percentage of fiber volume content and the ratio between the compressive strength of the cube 150 × 150 × 150 mm (f cu ) for the three groups and that for the reference mixture B0.0 (f cu,B0.0 ).increase, compared with the reference one, was conservative: 2.6%, 3.9%, and 9% for PP, hybrid, and ST fiber mixtures, respectively.Increasing the fiber volume content of all the specimens to 2.0% led to a decrease in compressive strength.The compressive strengths for the 2%-ST mixture were greater than those of the reference mixture by 6.9%.On the other hand, the 2%-fiber-mixture compressive strengths with PP and hybrid (PP + ST) fibers were less than those of the reference mixture by 6 and 4%, respectively.Also, the results indicated that the ratio between the compressive strength of cube 100 × 100 × 100 (fcu100) and that of cube 150 × 150 × 150 (fcu) was 1.03 to 1.05, which is very close to the value proposed by ECP203-2020.The previous results show that the compressive strengths of the studied fiber mixtures fluctuate close to those of plain concrete (the reference mixture).This may be related to the voids and microscopic cracks that fibers produce, which cause localized stress.On the one hand, fibers slow down the spread of cracks through the bridging effect, thus limiting lateral expansion macroscopically.Buildings 2024, 14, x FOR PEER REVIEW 11 of 37 increase, compared with the reference one, was conservative: 2.6%, 3.9%, and 9% for PP, hybrid, and ST fiber mixtures, respectively.Increasing the fiber volume content of all the specimens to 2.0% led to a decrease in compressive strength.The compressive strengths for the 2%-ST mixture were greater than those of the reference mixture by 6.9%.On the other hand, the 2%-fiber-mixture compressive strengths with PP and hybrid (PP + ST) fibers were less than those of the reference mixture by 6 and 4%, respectively.Also, the results indicated that the ratio between the compressive strength of cube 100 × 100 × 100 (fcu100) and that of cube 150 × 150 × 150 (fcu) was 1.03 to 1.05, which is very close to the value proposed by ECP203-2020.The previous results show that the compressive strengths of the studied fiber mixtures fluctuate close to those of plain concrete (the reference mixture).This may be related to the voids and microscopic cracks that fibers produce, which cause localized stress.On the one hand, fibers slow down the spread of cracks through the bridging effect, thus limiting lateral expansion macroscopically.The results of Group 2, ST fibers, show that the hooked-end shape significantly impacts crack bridging and introduces dowel action that resists shear cracks and increases All fiber mixtures with (PP, ST, PP + ST) show almost similar behavior.The compressive strength increased with increasing the percentage of fiber volume content to 1%.This increase, compared with the reference one, was conservative: 2.6%, 3.9%, and 9% for PP, hybrid, and ST fiber mixtures, respectively.Increasing the fiber volume content of all the specimens to 2.0% led to a decrease in compressive strength.The compressive strengths for the 2%-ST mixture were greater than those of the reference mixture by 6.9%.On the other hand, the 2%-fiber-mixture compressive strengths with PP and hybrid (PP + ST) fibers were less than those of the reference mixture by 6 and 4%, respectively.Also, the results indicated that the ratio between the compressive strength of cube 100 × 100 × 100 (f cu100 ) and that of cube 150 × 150 × 150 (f cu ) was 1.03 to 1.05, which is very close to the value proposed by ECP203-2020.The previous results show that the compressive strengths of the studied fiber mixtures fluctuate close to those of plain concrete (the reference mixture).This may be related to the voids and microscopic cracks that fibers produce, which cause localized stress.On the one hand, fibers slow down the spread of cracks through the bridging effect, thus limiting lateral expansion macroscopically.
The results of Group 2, ST fibers, show that the hooked-end shape significantly impacts crack bridging and introduces dowel action that resists shear cracks and increases confinement.On the other hand, mixtures of Group 1 PP fibers demonstrated the least impact on compressive strength, whereas mixtures of Group 3 (with hybrid PP + ST fibers) produced results that fell in between those of Groups 1 and 2, due to the hybridization of micro-PP and macro-ST fibers.
Figure 10 shows the relationship between the percentage of fiber volume content and the compressive strength of both cubes (150 × 150 × 150) and cylinders (150 × 300) for all mixtures.Both cubes and cylinders behaved the same way.The ratio between cylinder compressive strength ( fc ) and cube compressive strength (f cu ) ranged from 0.90 to 0.93, as shown in Table 3.Finally, Figure 11 shows the crack pattern for the cubes of mixtures B0.5, S0.5, H0.5, H1.0, and S2.0.
Buildings 2024, 14, x FOR PEER REVIEW 12 of 37 confinement.On the other hand, mixtures of Group 1 PP fibers demonstrated the least impact on compressive strength, whereas mixtures of Group 3 (with hybrid PP + ST fibers) produced results that fell in between those of Groups 1 and 2, due to the hybridization of micro-PP and macro-ST fibers.
Figure 10 shows the relationship between the percentage of fiber volume content and the compressive strength of both cubes (150 × 150 × 150) and cylinders (150 × 300) for all mixtures.Both cubes and cylinders behaved the same way.The ratio between cylinder compressive strength ( ) and cube compressive strength (fcu) ranged from 0.90 to 0.93, as shown in Table 3.Finally, Figure 11 shows the crack pattern for the cubes of mixtures B0.5, S0.5, H0.5, H1.0, and S2.0.

Tensile Splitting Strength
Figure 11 shows the crack pattern of the cylinders splitting for mixtures B0.5, S0.5, H0.5, H1.0, and S2.0. Figure 12 and Table 3 show the relationship between the percentage of fiber volume content and the tensile splitting strengths for cylinders 150 × 300 and 100 × 200 for all mixtures after 28 days.Generally, adding fibers, regardless of the type and volume fraction, improved the tensile splitting strength compared to the reference mixture B0.0 (without fibers).The tensile splitting strengths of HPC mixtures with fibers ranged from 5.66 MPa to 9.20 MPa, higher than the 3.82 MPa of the reference mixture B0.0

Tensile Splitting Strength
Figure 11 shows the crack pattern of the cylinders splitting for mixtures B0.5, S0.5, H0.5, H1.0, and S2.0. Figure 12 and Table 3 show the relationship between the percentage of fiber volume content and the tensile splitting strengths for cylinders 150 × 300 and 100 × 200 for all mixtures after 28 days.Generally, adding fibers, regardless of the type and volume fraction, improved the tensile splitting strength compared to the reference mixture B0.0 (without fibers).The tensile splitting strengths of HPC mixtures with fibers ranged from 5.66 MPa to 9.20 MPa, higher than the 3.82 MPa of the reference mixture B0.0 (without fibers).Also, the tensile splitting strengths of cylinders 100 × 200 (f sp,100 ) were higher than those of cylinders 150 × 300 (f sp ) in the range from 1.03 to 1.07.(without fibers).Also, the tensile splitting strengths of cylinders 100 × 200 (fsp,100) were higher than those of cylinders 150 × 300 (fsp) in the range from 1.03 to 1.07.Figure 13 shows the ratio between the concrete tensile splitting strength of all cylinders 150 × 300 (fsp) for all mixtures and that of the reference mixture B0.0 (fsp,B0.0)(without fibers).Figure 13 shows the ratio between the concrete tensile splitting strength of all cylinders 150 × 300 (f sp ) for all mixtures and that of the reference mixture B0.0 (f sp,B0.0 ) (without fibers).Figure 13 shows the ratio between the concrete tensile splitting strength of all cylinders 150 × 300 (fsp) for all mixtures and that of the reference mixture B0.0 (fsp,B0.0)(without fibers).For Group 1, PP fiber content of 0.5, 1.0, and 2.0% led to tensile splitting strengths of 6.23, 6.86, and 5.66 MPa, respectively, which were higher than those of the reference mixture (without fibers = 3.82 MPa) by 63, 80, and 48%, respectively.This result indicated that For Group 1, PP fiber content of 0.5, 1.0, and 2.0% led to tensile splitting strengths of 6.23, 6.86, and 5.66 MPa, respectively, which were higher than those of the reference mixture (without fibers = 3.82 MPa) by 63, 80, and 48%, respectively.This result indicated that the optimum percentage of PP fibers is 1%, after which the tensile splitting strength decreases with increasing PP fibers.This may be related to the increase in voids due to the increasing balling effect of PP fibers.
For Group 2, ST fiber content of 0.5, 1.0, and 2.0% led to tensile splitting strengths of 6.94, 8.49, and 9.20 MPa, respectively, which were higher than those of the reference mixture (without fibers) by 81, 122, and 141%, respectively.These results indicated that increasing the percentage of ST fibers increases the tensile splitting strength.This is due to the high modulus of elasticity and bond stresses of hooked-end ST fibers adding to their crack bridging.
For Group 3, hybrid PP + ST fiber content of 0.5, 1.0, and 2.0% led to tensile splitting strengths of 6.51, 7.78, and 6.51 MPa, respectively, which were higher than those of the reference mixture (without fibers) by 70, 104, and 70%, respectively.These results indicated that the optimum percentage of hybrid PP + ST fibers is 1%, after which the tensile splitting strength decreases with increasing hybrid fibers.This may be related to the increase in voids due to the increasing balling effect of PP fibers.However, due to both the high modulus of elasticity and bond stresses of hooked-end ST fibers adding to their crack bridging, using hybrid fibers of micro-PP and macro-ST fibers equally increased the tensile splitting strength to a value in between using either ST or PP fibers only.
Figure 14 shows the relationship between the ratio f sp / f cu and the percentage of fiber volume content for the three groups.
high modulus of elasticity and bond stresses of hooked-end ST fibers adding to their crack bridging, using hybrid fibers of micro-PP and macro-ST fibers equally increased the tensile splitting strength to a value in between using either ST or PP fibers only.
Figure 14 shows the relationship between the ratio   ⁄ and the percentage of fiber volume content for the three groups.According to the available experimental data in this research and using a statistical analysis program, it is possible to predict the tensile splitting strength as a function of the fiber volume fraction and the square root of the concrete compressive strength by a polynomial 2nd order relationship as follows: For PP fibers with Vf up to 2%: For ST fibers with Vf up to 2%: For hybrid PP + ST fibers with Vf up to 2%, distributed equally: According to the available experimental data in this research and using a statistical analysis program, it is possible to predict the tensile splitting strength as a function of the fiber volume fraction and the square root of the concrete compressive strength by a polynomial 2nd order relationship as follows: For PP fibers with V f up to 2%: For ST fibers with V f up to 2%: For hybrid PP + ST fibers with V f up to 2%, distributed equally: where: f sp is the tensile splitting strength of a cylinder 150 × 300 mm (N/mm 2 ), f cu is the concrete compressive strength of a cube 150 × 150 × 150 mm (N/mm 2 ), V f is the fiber volume content (%), RI is the fiber reinforcement index, l f is the fiber length (mm), d f is the fiber equivalent diameter (mm), E s is the module of elasticity for steel fibers (N/mm 2 ), E f is the modulus of elasticity for fiber material (N/mm 2 ), K is the bond factor (0.5 for round straight fibers, 0.75 for crimped or corrugated fiber, and 1.0 for end-hook fibers), I 1 is the ratio of the content of PP fiber to the total content of hybrid fiber, RI 1 is the fiber reinforcement index for PP fiber, I 2 is the ratio of the content of ST fiber to the total content of hybrid fiber, and RI 2 is the fiber reinforcement index for ST fiber.
The values of the theoretical splitting strength (f sp,th ) and the experimental splitting strength (f sp,exp ) are shown in Table 4 and Figure 15.To examine the accuracy of these equational predictions, two statistical coefficients were calculated and evaluated: the coefficient of variation (COV) and the coefficient of determination (R 2 ).COV measures the variation of the model predictions concerning the mean value, while R 2 is a tool to evaluate the ability of the formula to predict the splitting strength.It should be emphasized that the analytical model's predictions are more precise the lower the COV value.Also, if the R 2 value is close to 1, it indicates that the analytical model can accurately forecast the splitting strength and represent the complete range of input data.Table 4 includes the values of COV and R 2 for the tested groups in this research.
The collected findings showed that the average value of f sp,th /f sp,exp for the three equations was 0.99.The COV ranged between 0.52% and 3.38%, whereas the R 2 ranged between 0.98 and 1.0.These values demonstrate that the three proposed equations can accurately predict the tensile splitting strength.Figure 16 shows a comparison between previous results of He et al. (2022) [24], Altalabani et al. (2020) [41], and Islam and Gupta (2016) [39] with the corresponding results calculated using the equations of this research, from Equation (1) to Equation (4).The results show a very good agreement that allows the use of these equations more generally.To examine the accuracy of these equational predictions, two statistical coefficients were calculated and evaluated: the coefficient of variation (COV) and the coefficient of determination (R 2 ).COV measures the variation of the model predictions concerning the mean value, while R 2 is a tool to evaluate the ability of the formula to predict the splitting strength.It should be emphasized that the analytical model's predictions are more precise the lower the COV value.Also, if the R 2 value is close to 1, it indicates that the analytical model can accurately forecast the splitting strength and represent the complete range of input data.Table 4 includes the values of COV and R 2 for the tested groups in this research.
The collected findings showed that the average value of fsp,th/fsp,exp for the three equations was 0.99.The COV ranged between 0.52% and 3.38%, whereas the R 2 ranged between 0.98 and 1.0.These values demonstrate that the three proposed equations can accurately predict the tensile splitting strength.Figure 16 shows a comparison between previous results of He et al. (2022) [24], Altalabani et al. (2020) [41], and Islam and Gupta (2016) [39] with the corresponding results calculated using the equations of this research, from Equation (1) to Equation (4).The results show a very good agreement that allows the use of these equations more generally.

The Flexural Behavior
In this part, the flexural behavior of each specimen was analyzed by determining the flexure tensile strength or modulus of rupture (fctr), the load-CMOD curve, and the residual flexural strength.In addition, toughness will be examined, which reflects the energyabsorbing capacity of concrete under load and may be calculated using the area beneath the load-displacement curve.The modulus of rapture (fctr) is the greatest flexural tensile strength that can be resisted by a beam section, which may be calculated using Equation (5).

The Flexural Behavior
In this part, the flexural behavior of each specimen was analyzed by determining the flexure tensile strength or modulus of rupture (f ctr ), the load-CMOD curve, and the residual flexural strength.In addition, toughness will be examined, which reflects the energy-absorbing capacity of concrete under load and may be calculated using the area beneath the load-displacement curve.

The Modulus of Rupture (f ctr )
The modulus of rapture (f ctr ) is the greatest flexural tensile strength that can be resisted by a beam section, which may be calculated using Equation (5).
where: F max is the maximum applied flexure load (N), L is the span of the beam (mm), b is the width of the beam (mm), and h sp is the height of the beam, excluding the height of the notch (mm).
The associations between flexural tensile strength, f ctr , and fiber volume content (V f ) for the three research groups are shown in Figure 17.The values of the flexural tensile strength f ctr for the three groups are presented in Table 3. Figure 18 shows the ratio of the flexural tensile strength f ctr to that of the reference one f ctr,B0 .0 versus the percentage of fiber volume content for the research groups.For Group 1, PP fiber content of 0.5, 1.0, and 2.0% resulted in flexural tensile strengths of 5.69, 6.14, and 6.72 MPa, respectively, which were greater than those of the reference mixture (without fibers = 5.63 MPa) by 1, 9, and 19%, respectively.This modest increase is due to PP's small values of tensile strength, modulus of elasticity, and density.Also, the short length of PP fibers may be another reason.For Group 2, ST fiber content of 0.5, 1.0, and 2.0% resulted in flexural tensile strengths of 9.42, 11.88, and 14.51 MPa, respectively, which were greater than those of the reference For Group 1, PP fiber content of 0.5, 1.0, and 2.0% resulted in flexural tensile strengths of 5.69, 6.14, and 6.72 MPa, respectively, which were greater than those of the reference mixture (without fibers = 5.63 MPa) by 1, 9, and 19%, respectively.This modest increase is due to PP's small values of tensile strength, modulus of elasticity, and density.Also, the short length of PP fibers may be another reason.For Group 2, ST fiber content of 0.5, 1.0, and 2.0% resulted in flexural tensile strengths of 9.42, 11.88, and 14.51 MPa, respectively, which were greater than those of the reference mixture (without fibers) by 67, 111, and 158%, respectively.This huge increase is due to ST's high values of modulus of elasticity and bond stresses.Also, the end hook shape results in very effective crack-bridging.
For Group 3, hybrid PP + ST fiber content of 0.

Figure 18.
The ratio f ctr /f ctr,B0.0versus the percentage of fiber volume content.
For Group 1, PP fiber content of 0.5, 1.0, and 2.0% resulted in flexural tensile strengths of 5.69, 6.14, and 6.72 MPa, respectively, which were greater than those of the reference mixture (without fibers = 5.63 MPa) by 1, 9, and 19%, respectively.This modest increase is due to PP's small values of tensile strength, modulus of elasticity, and density.Also, the short length of PP fibers may be another reason.
For Group 2, ST fiber content of 0.5, 1.0, and 2.0% resulted in flexural tensile strengths of 9.42, 11.88, and 14.51 MPa, respectively, which were greater than those of the reference mixture (without fibers) by 67, 111, and 158%, respectively.This huge increase is due to ST's high values of modulus of elasticity and bond stresses.Also, the end hook shape results in very effective crack-bridging.
For Group 3, hybrid PP + ST fiber content of 0.5, 1.0, and 2.0% resulted in flexural tensile strengths of 6.58, 7.62, and 7.77 MPa, respectively, which were greater than those of the reference mixture (without fibers) by 17, 35, and 38%, respectively.These results are higher than those of PP fibers and much lower than those of ST fibers.This means that the disadvantages of PP fibers break down the advantages of end-hook ST fibers.Also, after a hybrid fiber content of 1%, the flexural tensile strength remained nearly unchanged.All of these may be attributed to the increased voids caused by the balling action of PP fibers and to their short length.
Figure 19 shows the relationship between the percentage of fiber volume content and the ratio between the tensile splitting strength (f sp ) and the flexural tensile strength (f ctr ).ECP 203-2020 states that the ratio f sp /f ctr is approximately 0.7.
ildings 2024, 14, x FOR PEER REVIEW 19 of 37 higher than those of PP fibers and much lower than those of ST fibers.This means that the disadvantages of PP fibers break down the advantages of end-hook ST fibers.Also, after a hybrid fiber content of 1%, the flexural tensile strength remained nearly unchanged.All of these may be attributed to the increased voids caused by the balling action of PP fibers and to their short length.
Figure 19 shows the relationship between the percentage of fiber volume content and the ratio between the tensile splitting strength (fsp) and the flexural tensile strength (fctr).ECP 203-2020 states that the ratio fsp/fctr is approximately 0.7.
For Group 1 (PP fibers), fsp/fctr is in the range of 0.84 to 1.12.This means that PP fibers, which were effective in increasing the splitting tensile strength to a fiber volume content of 1%, were modest in increasing the modulus of rapture.
For Group 2 (ST fibers), fsp/fctr is in the range of 0.63 to 0.73, which is near the value recommended by ECP 203-2020.This means that ST fibers are the most effective in increasing the modulus of rapture.
For Group 3 (hybrid PP + ST fibers), fsp/fctr is in the range of 0.84 to 1.0, which is so close to that of the PP fibers (group 1), indicating the same behavior.For Group 1 (PP fibers), f sp /f ctr is in the range of 0.84 to 1.12.This means that PP fibers, which were effective in increasing the splitting tensile strength to a fiber volume content of 1%, were modest in increasing the modulus of rapture.
For Group 2 (ST fibers), f sp /f ctr is in the range of 0.63 to 0.73, which is near the value recommended by ECP 203-2020.This means that ST fibers are the most effective in increasing the modulus of rapture.
For Group 3 (hybrid PP + ST fibers), f sp /f ctr is in the range of 0.84 to 1.0, which is so close to that of the PP fibers (group 1), indicating the same behavior.
Figure 20 shows the relationship between the ratio f ctr / f cu and the percentage of fiber volume content for all the studied groups.According to the available experimental data and using a statistical analysis program, a prediction for the flexural tensile strength as a function of the fiber volume fraction and the square root of the concrete compressive strength may be given by a polynomial 2nd order relationship as follows: For PP fibers with Vf up to 2%: For ST fibers with Vf up to 2%: For hybrid PP + ST fibers with Vf up to 2%, distributed equally: The values of the splitting strength, either theoretical (fctr,th) or experimental (fctr,exp) are shown in Table 4 and Figure 21.The collected findings showed that the average value of fctr,th/fctr,exp for the three equations was 0.99.The COV ranged between 1.1% and 1.86%, whereas the R 2 ranged between 0.99 and 1.0.These values demonstrate that the three proposed equations can accurately predict the flexural tensile strength.Figure 22 shows a comparison between the previous results of Prabath and Ramadoss (2022) [53] and Hussain et al. (2020) [42] with the corresponding results calculated using the equations of this research: Equations ( 6)- (8).The results show a very good agreement that allows the use of these equations more generally.According to the available experimental data and using a statistical analysis program, a prediction for the flexural tensile strength as a function of the fiber volume fraction and the square root of the concrete compressive strength may be given by a polynomial 2nd order relationship as follows: For PP fibers with V f up to 2%: For ST fibers with V f up to 2%: For hybrid PP + ST fibers with V f up to 2%, distributed equally: The values of the splitting strength, either theoretical (f ctr,th ) or experimental (f ctr,exp ) are shown in Table 4 and Figure 21.The collected findings showed that the average value of f ctr,th /f ctr,exp for the three equations was 0.99.The COV ranged between 1.1% and 1.86%, whereas the R 2 ranged between 0.99 and 1.0.These values demonstrate that the three proposed equations can accurately predict the flexural tensile strength.Figure 22 shows a comparison between the previous results of Prabath and Ramadoss (2022) [53] and Hussain et al. (2020) [42] with the corresponding results calculated using the equations of this research: Equations ( 6)- (8).The results show a very good agreement that allows the use of these equations more generally.

Load-CMOD Curve and the Residual Flexural Strength
Figure 23 shows the load-CMOD curves for all the specimens.It is obvious that all the added fibers, whatever the type and amount, enhance the flexural behavior and alter the flexural load-CMOD curve's appearance.For the reference beam with mixture B0.0 (without fiber), the behavior is linear until the maximum flexural load.After that, a sharp fall occurred, indicating a brittle failure.

Load-CMOD Curve and the Residual Flexural Strength
Figure 23 shows the load-CMOD curves for all the specimens.It is obvious that all the added fibers, whatever the type and amount, enhance the flexural behavior and alter the flexural load-CMOD curve's appearance.For the reference beam with mixture B0.0 (without fiber), the behavior is linear until the maximum flexural load.After that, a sharp fall occurred, indicating a brittle failure.

Load-CMOD Curve and the Residual Flexural Strength
Figure 23 shows the load-CMOD curves for all the specimens.It is obvious that all the added fibers, whatever the type and amount, enhance the flexural behavior and alter the flexural load-CMOD curve's appearance.For the reference beam with mixture B0.0 (without fiber), the behavior is linear until the maximum flexural load.After that, a sharp fall occurred, indicating a brittle failure.For Group 1 (PP fibers): For PP fiber content up to 1.0%, the flexural load increased almost linearly until the maximum flexural load, which was nearly equal to that of the reference beam.After that, it displayed nearly flawless plastic behavior, with barely any hardening until failure.However, the PP fiber content was 2.0%, and after the quasi-linear part, it led to a nonlinear behavior up to the peak load.Following the peak, the reinforced materials (fibers) displayed softening behavior, with decreased loading levels and increased CMOD, which indicates the occurrence of the initial cracking.After that, a pseudo-CMOD hardening occurred until CMOD ≈ 2 mm, followed by another softening.This hesitating behavior represented the uncertainty for the mixture with 2% PP fiber content in resisting flexure.
For Group 2 (ST fibers), a nonlinear behavior was developed before the peak load, demonstrating a pseudo-CMOD hardening behavior with an increase in the load after the beginning of the initial microcracking.It is likely a result of the strong bond between the fibers and matrix, resulting in proper load transfer by the fibers at the onset of crack propagation.After the point of maximum load, softening occurred due to crack bridging by fibers, which resulted in a more significant global bending deformation and a corresponding increase in post-peak residual flexural strength.
For Group 3 (PP + ST fibers), the overall behavior is similar to that of Group 2 (ST fibers) due to the effect of ST fibers.However, Group 3 underwent loading much less than that of Group 2 due to voids and balling by PP fibers.
Briefly, micro-PP fibers (Group 1) led to the least flexural behavior, whereas ST fibers (Group 2) demonstrated the best flexural behavior.Hybrid fibers (Group 3) exhibited behavior resembling ST fibers (Group 2) but had values near those of PP fibers (Group 1), demonstrating the efficacy of the hybridization process.Crack patterns of notched beams during the flexure test are shown in Figure 24.For Group 1 (PP fibers): For PP fiber content up to 1.0%, the flexural load increased almost linearly until the maximum flexural load, which was nearly equal to that of the reference beam.After that, it displayed nearly flawless behavior, with barely until However, the PP fiber content was 2.0%, and after the quasilinear part, it led to a nonlinear behavior up to the peak load.Following the peak, the reinforced materials (fibers) displayed softening behavior, with decreased loading levels and increased CMOD, which indicates the occurrence of the initial cracking.After that, a pseudo-CMOD hardening occurred until CMOD ≈ 2 mm, followed by another softening.This hesitating behavior represented the uncertainty for the mixture with 2% PP fiber content in resisting flexure.
For Group 2 (ST fibers), a nonlinear behavior was developed before the peak load, demonstrating a pseudo-CMOD hardening behavior with an increase in the load after the beginning of the initial microcracking.It is likely a result of the strong bond between the fibers and matrix, resulting in proper load transfer by the fibers at the onset of crack propagation.After the point of maximum load, softening occurred due to crack bridging by fibers, which resulted in a more significant global bending deformation and a corresponding increase in post-peak residual flexural strength.
For Group 3 (PP + ST fibers), the overall behavior is similar to that of Group 2 (ST fibers) due to the effect of ST fibers.However, Group 3 underwent loading much less than that of Group 2 due to voids and balling by PP fibers.
Briefly, micro-PP fibers (Group 1) led to the least flexural behavior, whereas ST fibers (Group 2) demonstrated the best flexural behavior.Hybrid fibers (Group 3) exhibited behavior resembling ST fibers (Group 2) but had values near those of PP fibers (Group 1), demonstrating the efficacy of the hybridization process.Crack patterns of notched beams during the flexure test are shown in Figure 24.
Residual flexural strength is useful for determining fibers' contribution to concrete performance after cracking.The residual flexural strength was examined in accordance with EN 14651:2005 + A1:2007.The limit of proportionality (LOP or f L ) is the stress at the notch tip, which is considered to act in an uncracked midspan section with a linear stress distribution of a specimen exposed to a center-point load.Conventionally, the LOP corresponds to the maximum force for CMOD values less than 0.05 mm.f L , f R1 , f R2 , f R3 , and f R4 are the flexural strengths corresponding to flexural loads F L , F R1 , F R2 , F R3 , and F R4 , at CMOD values of 0.05, 0.5, 1.5, 2.5, and 3.5 mm, respectively (see Figure 23).The experimental data for the limit of proportionality and residual flexural strength are presented in Table 5.To determine the residual strength and LOP, apply Equation ( 9).
where f i is the flexural strength corresponding to the flexural load F i .Residual flexural strength is useful for determining fibers' contribution to concrete performance after cracking.The residual flexural strength was examined in accordance with EN 14651:2005 + A1:2007.The limit of proportionality (LOP or is the stress at the notch which is considered to act in an uncracked midspan section with a linear stress distribution of a specimen exposed to a center-point load.Conventionally, the LOP corresponds to the maximum force for CMOD values less than 0.05 mm.fL, fR1, fR2, fR3, and fR4 are the flexural strengths corresponding to flexural loads FL, FR1, FR2, FR3, and FR4, at CMOD values of 0.05, 0.5, 1.5, 2.5, and 3.5 mm, respectively (see Figure 23).The experimental data  The flexural residual strength-CMOD curves are identical to the flexural load-CMOD curves in Figure 23.The significance of computed residual strength for the structural design and classification of FRC in accordance with fib Code 2010 will be examined in this section.
f R1 and f R3 are the characteristic flexural residual strength values for serviceability and ultimate conditions, respectively.According to fib Code 2010, it is possible to categorize the post-cracking strength of FRC using two parameters: a number and a letter.The number represents the minimum interval value of f R1 in MPa, whereas the letter represents the f R3 /f R1 ratio as follows: 1.
The data demonstrate that the limit of proportionality f L for beams with micro-PP fibers in Group 1 is nearly equivalent to the flexural strength of reference beam B0.0 (without fiber).In addition, the residual strength f R1 for beams B0.5 and B1.0 was roughly equivalent to the flexural strength of the reference beam; however, f R1 for beam B2.0 was 22 percent greater than the reference beam.The ratio of f R3 /f R1 had a nearly constant value of 1.0 for beams B0.5 and B1.0 but decreased to 0.53 for beam B2.0.The categorization of beams in Group 1 was 5c, 5c, and 6a for beams B0.5, B1.0, and B2.0, respectively, indicating that all fiber beams in Group 1 might be useful in structural design, with the best performance in this group being reached with 1% micro-PP fiber content, according to Table 5.
The limit of proportionality f L for Group 2 macro-ST fiber beams was almost equal and showed an increase of about 67% over reference beam B0.0's flexural strength (without fiber).Additionally, compared to the flexural strength of the reference beam, the residual strength f R1 for beams S0.5, S1.0, and S2.0 increased by 65, 110, and 156 percent, respectively.f R3 /f R1 values were 0.88, 0.99, and 0.93 for beams S0.5, S1.0, and S2.0, which are classified as 9b, 11c, and 14c, respectively.This means that all of the macro-ST fiber beams in Group 2 could be very effective in the structural design, and the best performance was achieved for fiber content of 2.0%.Also, the categorization of beams increases as the ST fiber content increases.
For beams containing hybrid fibers in Group 3, the limit of proportionality f L increased as the fiber content increased, exhibiting an average increase of around 31% above the flexural strength of the reference beam B0.0 (without fiber).In addition, the residual strength f R1 for beams H0.5, H1.0, and H2.0 was higher than the flexural strength of the reference beam B0.0 by 14, 32, and 26%, respectively.The ratio of f R3 /f R1 was nearly steady at 0.88 for beams H0.5 and H1.0, but increased to 1.0 for beam H2.0.The categorization of beams in Group 3 was 6b, 7b, and 7c for beams H0.5, H1.0, and H2.0, respectively, indicating that all hybrid fiber beams in Group 3 may be used effectively in structural design, and the best performance was achieved at a hybrid fiber content of 2.0%.Also, the categorization of beams increases as hybrid fiber content increases.

Toughness and Ductility
Toughness denotes the ability of the material/member to absorb energy when loaded, which can be determined by calculating the area beneath the load-displacement curve (Figure 25). Figure 26 and Table 6 show the values of toughness at the peak load (T p ), proposed by He et al. (2022) [24], and at a deflection of 3.0 mm (T 3.0 ).strength fR1 for beams H0.5, H1.0, and H2.0 was higher than the flexural strength of th reference beam B0.0 by 14, 32, and 26%, respectively.The ratio of fR3/fR1 was nearly stead at 0.88 for beams H0.5 and H1.0, but increased to 1.0 for beam H2.0.The categorization o beams in Group 3 was 6b, 7b, and 7c for beams H0.5, H1.0, and H2.0, respectively, ind cating that all hybrid fiber beams in Group 3 may be used effectively in structural desig and the best performance was achieved at a hybrid fiber content of 2.0%.Also, the catego rization of beams increases as hybrid fiber content increases.

Toughness and Ductility
Toughness denotes the ability of the material/member to absorb energy when loaded which can be determined by calculating the area beneath the load-displacement curv (Figure 25). Figure 26 and Table 6 show the values of toughness at the peak load (Tp proposed by He et al. (2022) [24], and at a deflection of 3.0 mm (T3.0).
Increasing fiber volume content increases the fracture toughness of beams made o both ST and hybrid fibers.The same behavior occurred for beams with PP fiber conten up to 1%.However, increasing its content to 2.0% decreased the fracture toughness.
ST fibers led to the highest T3.0.Group 3 (with hybrid fibers) had a higher T3.0 tha that with PP fibers, and both were lower than specimens with ST fibers.In specimen S2. the highest effect on toughness T3.0 is visible.For all specimens, Tp was less than T3.0.The maximum value of Tp was in specimens S2.0 and S1.0 with ST fiber contents of 2% and 1%, respectively.On the other hand, specimen B2.0 with a PP fiber content of 2% has a high value of Tp, which is 74 and 77 times higher than those of specimens B1.0 and B0.5, respectively.This result of specimen B2.0 may be considered a leap that occurred due to its large number of fibers and small value of modulus of elasticity, which led to a high value of Δp at peak load and hence a very high value of Tp.As a conclusion, Tp, which is calculated at a very early stage of behavior, cannot be considered an index for comparison between different types of fibers.Only T3.0  Increasing fiber volume content increases the fracture toughness of beams made of both ST and hybrid fibers.The same behavior occurred for beams with PP fiber content up to 1%.However, increasing its content to 2.0% decreased the fracture toughness.
ST fibers led to the highest T 3.0 .Group 3 (with hybrid fibers) had a higher T 3.0 than that with PP fibers, and both were lower than specimens with ST fibers.In specimen S2.0, the highest effect on toughness T 3.0 is visible.
For all specimens, T p was less than T 3.0 .The maximum value of T p was in specimens S2.0 and S1.0 with ST fiber contents of 2% and 1%, respectively.On the other hand, specimen B2.0 with PP fiber content of 2% has a high value of T p , which is 74 and 77 times higher than those of specimens B1.0 and B0.5, respectively.This result of specimen B2.0 may be considered a leap that occurred due to its large number of fibers and small value of modulus of elasticity, which led to a high value of ∆ p at peak load and hence a very high value of T p .As a conclusion, T p , which is calculated at a very early stage of behavior, cannot be considered an index for comparison between different types of fibers.Only T 3.0 is the right index for this comparison.
Generally, fiber-reinforced concrete exhibited higher global bending deformation.In this study, LOP is considered the load that causes the first crack to appear.Except for plain concrete (reference beam), the peak load for concrete mixtures is larger than LOP, demonstrating the materials' ductility.Ductility will be measured using the ductility index (DI), defined by the following relation: where ∆ p is the deflection at the peak load and ∆ L is the deflection at LOP.The higher ductility index indicates higher ductility before the peak load.The values of DI are detailed in Figure 27.
In specimens B0.0, B0.5, B1.0, S0.5, H0.5, and H1.0, the ductility index DI equals one, which means that the maximum load of each is equal to its LOP load.DI for specimen B2.0 with PP fiber content of 2% is the maximum due to its large number of fibers and small value of modulus of elasticity, which led to a small value of ∆ L at LOP and high values of ∆ p at peak load.However, specimens with ST fibers are more effective than others since their behavior is permanent, not a leap like specimen B2.0.
which means that the maximum load of each is equal to its LOP load.DI for specimen B2.0 with PP fiber content of 2% is the maximum due to its large number of fibers and small value of modulus of elasticity, which led to a small value of ΔL at LOP and high values of Δp at peak load.However, specimens with ST fibers are more effective than others since their behavior is permanent, not a leap like specimen B2.0.

Prediction of the Effect of Fibers on the Ultimate Flexure Moment
The residual strength should be considered the primary criterion because it is influenced by the type and quantity of fibers used as well as the characteristics of the concrete.The engineer can use a performance-based calculation and specification to guarantee proper performance from FRC as a composite material.Fibers in a fractured concrete section bridge the gaps and prevent them from widening, giving post-crack load-carrying capacity under tension, bending, and shear.
Standard beam tests, as detailed in a previous section, are used to measure material qualities such as residual strength.In order to calculate the FRC's performance and the accompanying load-carrying capacity, these properties are then introduced into the equations as they are described in this section.In order to determine the proper design strength, test programs need to be carried out in a certain way.It considers the appropriateness of allowing for the uncertainties covered by the partial safety factors in conventional design.
Since plain concrete's tensile strength is negligible, the conventional design does not account for it.The effective tensile strength of FRC is employed in the design process because the post-cracking tensile strength of concrete can be increased by adding steel or synthetic macrofibers.As previously stated, it is challenging to do a proper tension test.Hence, flexural tests are used instead.The measured residual flexural strength is then used to calculate the residual tensile strength using conversion factors.ACI.544.8R contains more information about the tensile stress-strain response of FRC and its relationship with the results of the flexural strength test.
According to numerous studies, the flexural residual strength of FRC in a cracked section is typically 2.5 to 3 times greater than the tensile residual strength.The flexural residual strength from a beam test should be used to compute the tensile residual strength for design reasons.Such computations must adhere to the FRC design approach's rules,

Prediction of the Effect of Fibers on the Ultimate Flexure Moment
The residual strength should be considered the primary criterion because it is influenced by the type and quantity of fibers used as well as the characteristics of the concrete.The engineer can use a performance-based calculation and specification to guarantee proper performance from FRC as a composite material.Fibers in a fractured concrete section bridge the gaps and prevent them from widening, giving post-crack load-carrying capacity under tension, bending, and shear.
Standard beam tests, as detailed in a previous section, are used to measure material qualities such as residual strength.In order to calculate the FRC's performance and the accompanying load-carrying capacity, these properties are then introduced into the equations as they are described in this section.In order to determine the proper design strength, test programs need to be carried out in a certain way.It considers the appropriateness of allowing for the uncertainties covered by the partial safety factors in conventional design.
Since plain concrete's tensile strength is negligible, the conventional design does not account for it.The effective tensile strength of FRC is employed in the design process because the post-cracking tensile strength of concrete can be increased by adding steel or synthetic macrofibers.As previously stated, it is challenging to do a proper tension test.Hence, flexural tests are used instead.The measured residual flexural strength is then used to calculate the residual tensile strength using conversion factors.ACI.544.8R contains more information about the tensile stress-strain response of FRC and its relationship with the results of the flexural strength test.
According to numerous studies, the flexural residual strength of FRC in a cracked section is typically 2.5 to 3 times greater than the tensile residual strength.The flexural residual strength from a beam test should be used to compute the tensile residual strength for design reasons.Such computations must adhere to the FRC design approach's rules, and in reality, the conversion factor is commonly chosen between 0.4 and 0.33.Such correlations have been confirmed by numerical research and tests (Mobasher et al., 2014) [11].
For FRC, there are typically two design levels that can be taken into account: (1) the serviceability limit state (SLS) at smaller deflections, which corresponds to smaller crack widths in the range of 0.4 to 1 mm, and (2) the ultimate limit state (ULS) at more considerable deflections, which corresponds to larger crack widths in the range of 2.0 to 3.5 mm.Higher residual strength values are required for SLS since smaller crack widths must be maintained.As a result, the desired limit state is used to establish the specified residual strength for FRC.
In Europe and some other countries, the BS EN-l4651:2007 [64] test method and design parameters f R1 , f R2 , f R3 , and f R4 are more common.The implementation of these parameters in the design process will be explained later.
The moment crack width relationship from the BS EN 14651:2007 test on notched beams can be used to execute the FRC design utilizing the fib Model Code 2010 design principles, which are briefly discussed here.According to Equations ( 11) through ( 16), the nominal moment for an FRC section, M n-FRC , is determined from the force equilibrium in the cross-section, as shown in Figure 28.A FRC beam section reinforced with fibers is shown schematically in Figure 28a; the distribution of flexural stresses is shown in Figure 28b; and the simplified distribution of normal stresses in the fractured section is shown in Figure 28c.For ultimate state design, the tensile residual strength f Ftu is set to a constant value.Two models are suggested for determining FRC's post-crack tensile strength.The ultimate tensile strength of FRC, f Ftu-FRC , is taken as a constant value of one-third times the flexural residual strength of FRC, f R3, that is measured from the BS EN 14651:2005 beam test in the first model, referred to as simplified rigid-plastic.Tensile strength and nominal bending moment equations are provided in Equations ( 11) and ( 12), respectively.strength for FRC.
In Europe and some other countries, the BS EN-l4651:2007 [64] test method and d sign parameters fR1, fR2, fR3, and fR4 are more common.The implementation of these param eters in the design process will be explained later.
The moment crack width relationship from the BS EN 14651:2007 test on notche beams can be used to execute the FRC design utilizing the fib Model Code 2010 desig principles, which are briefly discussed here.According to Equations ( 11) through (16), th nominal moment for an FRC section, Mn-FRC, is determined from the force equilibrium the cross-section, as shown in Figure 28.A FRC beam section reinforced with fibers shown schematically in Figure 28a; the distribution of flexural stresses is shown in Figu 28b; and the simplified distribution of normal stresses in the fractured section is shown Figure 28c.For ultimate state design, the tensile residual strength fFtu is set to a consta value.Two models are suggested for determining FRC's post-crack tensile strength.Th ultimate tensile strength of FRC, fFtu-FRC, is taken as a constant value of one-third times th flexural residual strength of FRC, fR3, that is measured from the BS EN 14651:2005 bea test in the first model, referred to as simplified rigid-plastic.Tensile strength and nomin bending moment equations are provided in Equations ( 11) and ( 12), respectively.For serviceability and the ultimate limit design of an FRC section, the second mod (of fib Code 2010) presupposes a linear connection between residual strength and fractu width.Tensile strength and nominal bending moment calculation equations are presente in Equations ( 13)-( 16), respectively.Note that Equations ( 15) and ( 16) are to calculate th bending moment corresponding to the presence of fibers in service and ultimate lim states, respectively.When selecting the appropriate equations, care should be taken consider the state of design: serviceability limit state (SLS) versus ultimate limit sta (ULS).It should be emphasized that fiber materials that are not considerably influence by time, temperature, or both are covered for design per the fib Model Code 2010.Add tionally, minimal specifications must be met, such as fR1/fL > 0.4 and fR3/fR1 > 0.5, where fl the limit of proportionality (LOP) determined using Equation (9).The fib Model Cod 2010's standards are mainly based on the knowledge of steel fiber-reinforced concrete.
Using the rigid-plastic model (for ULS only): For serviceability and the ultimate limit design of an FRC section, the second model (of fib Code 2010) presupposes a linear connection between residual strength and fracture width.Tensile strength and nominal bending moment calculation equations are presented in Equations ( 13)-( 16), respectively.Note that Equations ( 15) and ( 16) are to calculate the bending moment corresponding to the presence of fibers in service and ultimate limit states, respectively.When selecting the appropriate equations, care should be taken to consider the state of design: serviceability limit state (SLS) versus ultimate limit state (ULS).It should be emphasized that fiber materials that are not considerably influenced by time, temperature, or both are covered for design per the fib Model Code 2010.Additionally, minimal specifications must be met, such as f R1 /f L > 0.4 and f R3 /f R1 > 0.5, where f l is the limit of proportionality (LOP) determined using Equation (9).The fib Model Code 2010's standards are mainly based on the knowledge of steel fiber-reinforced concrete.
Using the rigid-plastic model (for ULS only): Using the linear model (for SLS and ULS): For all beams, the ultimate moment of the FRC section, M nu-FRC , was calculated and presented in Figure 29.According to the fib model code 2010, the figure demonstrates that all specimens containing fibers had residual flexural strengths that were sufficient to create the ultimate moment, M nu-FRC .The M nu-FRC value for the beams made of micro-PP fibers in Group 1 was the lowest of all the investigated groups at 2.13, 2.28, and 1.4 kN•m for beams B0.5, B1.0, and B2.0, respectively.According to these findings, of all the beams in this group, beam B1.0 with a PP fiber content of 1% displayed the best M nu-FRC value.The highest M nu-FRC values were found in Group 2 beams with macro-ST fibers, with values of 3.15, 4.56, and 5.25 kN•m for beams S0.5, S1.0, and S2.0, respectively.According to these findings, beam S2.0 with an ST fiber content of 2% had the highest M nu-FRC value of any beam in this group, proving that M nu-FRC rises as ST fiber content increases.M nu-FRC values for Group 3 hybrid fiber beams ranged from 2.2 to 2.8 kN•m.These values were greater than those for Group 1 with micro-PP fiber beams and lower than those for Group 2 with macro-ST fiber beams (Group 2).Additionally, the results of the hybrid fiber Group 3 beams show that M nu-FRC increases as hybrid fiber content does.

𝑀
=   • ℎ 6 For all beams, the ultimate moment of the FRC section, Mnu-FRC, was calculated and presented in Figure 29.According to the fib model code 2010, the figure demonstrates that all specimens containing fibers had residual flexural strengths that were sufficient to create the ultimate moment, Mnu-FRC.The Mnu-FRC value for the beams made of micro-PP fibers in Group 1 was the lowest of all the investigated groups at 2.13, 2.28, and 1.4 kN.m for beams B0.5, B1.0, and B2.0, respectively.According to these findings, of all the beams in this group, beam B1.0 with a PP fiber content of 1% displayed the best Mnu-FRC value.The highest Mnu-FRC values were found in Group 2 beams with macro-ST fibers, with values of 3.15, 4.56, and 5.25 kN.m for beams S0.5, S1.0, and S2.0, respectively.According to these findings, beam S2.0 with an ST fiber content of 2% had the highest Mnu-FRC value of any beam in this group, proving that Mnu-FRC rises as ST fiber content increases.Mnu-FRC values for Group 3 hybrid fiber beams ranged from 2.2 to 2.8 kN.m.These values were greater than those for Group 1 with micro-PP fiber beams and lower than those for Group 2 with macro-ST fiber beams (Group 2).Additionally, the results of the hybrid fiber Group 3 beams show that Mnu-FRC increases as hybrid fiber content does.According to Equation ( 17), the nominal bending moment for a typical reinforced concrete section made without fibers, M n-RC , is computed from the force equilibrium in the cross-section shown in Figure 30.Figure 30a is a schematic illustration of a portion of an RC beam without fibers.In contrast, Figure 30b depicts the actual distribution of normal stresses.The simplified distribution of normal stresses in the cracked section is shown in Figure 30c. where, For the design and construction of concrete members with high reinforcement and steel congestion, hybrid reinforcement (consisting of bars and fibers) could be a suitable solution.As illustrated in Figure 31, the moment capacity of a hybrid FRC section is computed considering the contribution of both steel bars and fibers.Figure 31a is a beam section reinforced with bars and fibers, while Figure 31b shows the distribution of normal stresses in a cracked section.
According to Equation ( 17), the nominal bending moment for a typical reinforced concrete section made without fibers, Mn-RC, is computed from the force equilibrium in the cross-section shown in Figure 30.Figure 30a is a schematic illustration of a portion of an RC beam without fibers.In contrast, Figure 30b depicts the actual distribution of normal stresses.The simplified distribution of normal stresses in the cracked section is shown in Figure 30c. where, For the design and construction of concrete members with high reinforcement and steel congestion, hybrid reinforcement (consisting of bars and fibers) could be a suitable solution.As illustrated in Figure 31, the moment capacity of a hybrid FRC section is computed considering the contribution of both steel bars and fibers.Figure 31a is a beam section reinforced with bars and fibers, while Figure 31b shows the distribution of normal stresses in a cracked section.The concrete carries the compressive stresses, while the hybrid action of bars and fibers carries the tensile stresses/forces.These calculations can be performed for the serviceability limit state (SLS) and ultimate limit state (ULS) using the general guidelines outlined in the preceding section.Equation ( 19) depicts a member's usual form of nominal moment capacity with hybrid reinforcement (Mn-HFRC).Various hybrid reinforcement designs are feasible; further details can be found in fib Model Code 2010 and ACI.544.4R-18.

𝑀
=  + where, For the design and construction of concrete members with high reinforcement and steel congestion, hybrid reinforcement (consisting of bars and fibers) could be a suitable solution.As illustrated in Figure 31, the moment capacity of a hybrid FRC section is computed considering the contribution of both steel bars and fibers.Figure 31a is a beam section reinforced with bars and fibers, while Figure 31b shows the distribution of normal stresses in a cracked section.The concrete carries the compressive stresses, while the hybrid action of bars and fibers carries the tensile stresses/forces.These calculations can be performed for the serviceability limit state (SLS) and ultimate limit state (ULS) using the general guidelines outlined in the preceding section.Equation ( 19) depicts a member's usual form of nominal moment capacity with hybrid reinforcement (Mn-HFRC).Various hybrid reinforcement designs are feasible; further details can be found in fib Model Code 2010 and ACI.544.4R-18.The concrete carries the compressive stresses, while the hybrid action of bars and fibers carries the tensile stresses/forces.These calculations can be performed for the serviceability limit state (SLS) and ultimate limit state (ULS) using the general guidelines outlined in the preceding section.Equation ( 19) depicts a member's usual form of nominal moment capacity with hybrid reinforcement (M n-HFRC ).Various hybrid reinforcement designs are feasible; further details can be found in fib Model Code 2010 and ACI.544.4R-18.

𝑀 = 𝑀 + 𝑀
6.The Economic Impact of Using Fiber Reinforcement for Beams

Cost Analysis
The cost of 1 m 3 of each mix was calculated as given in Table 7, where the final cost of mixtures (EGP/m 3 ) is the sum of materials' costs and the cost of mixing, transporting, and placing concrete.A cost analysis shows that using fiber reinforcement drastically increases the cost of concrete production.Steel fiber influenced the final cost of concrete more negatively among all fibers.The cost of SHPC rises by 59%, 119%, and 237% due to the inclusion of 0.5, 1.0, and 2.0% steel fibers, respectively.This is mainly due to the high mass of steel fibers that are required at a 1% volume fraction (78 kg/m 3 ) compared to that of polypropylene fibers (9 kg/m 3 ).The difference in the fiber material density caused huge differences in the costs of fiber-reinforced concrete mixtures.

Cost to Benefit Analysis
Although fiber reinforcements are expensive, their potential benefits, such as improved mechanical properties and the requirement of lesser design dimensions, cannot be ignored in the economic analysis.This study used a beam with a cross-sectional dimensions of 200 × 600 mm and reinforced with 4T16 to calculate the ultimate moment for all the mixtures to study the effect of fibers on the improvement in the flexural strength.For ST fibers, the ultimate moment increased by about 58, 83, and 96% for ST fiber content of 0.5, 1.0, and 2.0%, respectively.On the other hand, for PP fibers, the ultimate moment increased by about 39, 42, and 26% for PP fiber content of 0.5, 1.0, and 2.0%, respectively.Meanwhile, for hybrid fibers, the ultimate moment increased by about 39, 42, and 26% for hybrid fiber content of 0.5, 1.0, and 2.0%, respectively (see Table 8).Using fibers in RC beams leads to smaller section dimensions or minimized reinforcement.Therefore, a cost-to-benefit analysis for each mixture should be performed.Now, it is required to consider that all the beams in Table 9 have the same flexural capacity or maximum moment.Hence, the change in the fiber type and its volume content will lead to a change in the reinforcement compared with that of the reference beam, and the cost of each RC beam per unit length was calculated.The results of Table 9 indicate that the selection of fiber reinforcement required to upgrade the flexural strength of the beam of a certain mixture significantly depends upon the type of fiber and its volume content.Beam S2.0 with ST fiber of 2% volume content is the most expensive among other beams, indicating that steel fiber is not an economical choice to upgrade flexural strength.
Steel fiber mixtures produced the highest flexural strength in the case of SHPC and, at the same time, the highest cost among other fibers.On the other hand, polypropylene and hybrid fiber-reinforced mixtures show noticeably lower cost values despite showing less flexural strength than steel fiber mixtures.Furthermore, polypropylene and hybrid fiber-reinforced mixtures are economical based on their relative costs compared with the reference one without fibers.Results from both Tables 8 and 9 show that hybrid fibers and polypropylene fibers can help reduce the cost as well as the dimensions and reinforcement of the beams.For SHPC, both polypropylene and hybrid fiber-reinforced mixtures are more economical than ST fiber-reinforced mixtures.

Conclusions
This paper investigates the mechanical properties and flexural behavior of super highperformance concrete (SHPC) experimentally and analytically.The effect of hybridization of both micro polypropylene (PP) and macro-end-hooked steel (ST) fibers upon the flexural behavior and mechanical properties of SHPC was studied.
The experimental work was extensive and consisted of ten mixtures: three with micro-PP fibers, three with macro-hooked-end ST fibers, three with hybrid (PP + ST) fibers, and a reference mixture without fibers.The total number of specimens was 270.
The results of the experimental work were used to obtain the effects of both fiber type and its percentage of volume content on the following: (a) the workability of fresh concrete, (b) concrete compressive strength, (c) splitting tensile strength, (d) flexural behavior, including flexural tensile strength and toughness, and (e) the optimum percentage of each of the two fibers, PP and ST, in the hybrid to get the maximum structural and economic benefits of hybridization.
In addition, these experimental results were used, through a statistical program, to obtain accurate formulae that could predict both the splitting tensile strength ( f sp ) and modulus of rupture ( f ctr ) for SHPC with each of the three types of fibers mentioned before.Also, these formulae were used to calculate splitting tensile strength and modulus of rupture, corresponding to the experimental results of other researchers, to examine their validity and accuracy.
Also, the prediction of the additional ultimate moment due to the presence of fibers (M nu-FRC ) for all the beams was investigated.
Finally, cost-benefit analysis was conducted on the beams of all the mixtures to determine the economic feasibility of each.
The following can be concluded from the results of this experimental and analytical investigation: 1.
Both the tensile splitting strength ( f sp ) and the flexural tensile strength in the form of the modulus of rupture ( f ctr ) can be predicted as a function of the volume fraction of PP, ST, and hybrid fibers and the square root of the concrete compressive strength by a polynomial with a 2nd order relationship using a statistical analysis program.

2.
The obtained formulae were able to predict accurately both the splitting tensile strength and modulus of rupture for SHPC with each of the three types of fibers used in this research.Also, they were in very good agreement with the values corresponding to different experimental results of other research, which means the ability to use these equations more generally.

3.
Nominal additional ultimate bending moment (M nu-FRC ), due to the presence of fibers, increases with increasing the percentage of fiber volume content, either ST or hybrid (ST + PP) fibers.It is not the case for PP fibers with 2% volume content.ST fibers led to the highest M nu-FRC values.M nu-FRC values for Group 3 (hybrid fiber) beams ranged from 2.2 to 2.8 kN•m.These values were greater than those for Group 1 (micro-PP fiber) beams and lower than those for Group 2 (macro-ST fiber) beams.

4.
For all mixtures, reference and fibered ones, the cylinder compressive strength ( fc ) showed the same behavior as the cube compressive strength ( f cu ), and the ratio ( fc / f cu ) ranged from 0.9 to 0.93.

5.
Hybrid fiber content up to 0.5% demonstrated a conservative change in consistency, but when the hybrid fiber content increased from 1.0 to 2.0 percent, the mix consistency changed from SHPC to HPC with slump classes S4 and S2, respectively.6.
For mixtures of hybrid fiber, the compressive strengths typically fluctuate in a range close to those of plain concrete.It may be related to the voids and microscopic cracks that fibers produce, which, on the one hand, cause localized stress concentrations and, on the other hand, slow down the spread of cracks (the bridging effect).7.
Increasing the amount of hybrid fibers up to 1% increased the tensile splitting strength in this group.However, increasing the amount of hybrid fibers to 2% decreased tensile splitting strength.This was due to the balling effect of the high-volume content of PP fibers, which led to more voids in mix H2.0, and may be due to their short length.8.
Due to the higher modulus of elasticity, bond stresses, and fiber crack bridging of hooked-end ST fibers, the flexural tensile strength increased much more with macro ST fibers than with micro-PP fibers.However, when using hybrid fibers of micro-PP fibers and macro-ST fibers with equal volume content, the flexural tensile strength increased but was still close to that of Group 1 (PP fibers).9.
According to the Load-CMOD curves, micro-PP fibers (Group 1) showed the least flexural behavior, whereas ST fibers (Group 2) demonstrated the most flexural behavior compared to other fibers.The hybrid fibers (Group 3) exhibited behavior resembling ST fibers (Group 2) but had values near PP fibers (Group 1).10.For hybrid fibers (Group 3), the ratio of f R3 /f R1 was nearly steady at 0.88 for beams H0.5 and H1.0 but increased to 1.0 for beam H2.0.The categorization of beams according to fib model code 2010 in Group 3 was 6b for beams H0.5, 7b for beams H1.0, and 7c for beams H2.0, indicating that all hybrid fiber beams in Group 3 may be used effectively in structural design, with the best performance reached in this group with a hybrid fiber content of 2.0%.11.Increasing the fiber volume content demonstrated an increase in fracture toughness for ST and hybrid fibers.On the other hand, increasing the volume content of PP fibers up to 1.0% increased the fracture toughness T 3.0 , while increasing from 1.0 to 2.0% revealed a decrease in the fracture toughness T 3.0 .12.For all specimens, T p was less than T 3.0 .However, according to the experimental results, T p , which is calculated at a very early stage of behavior, cannot be considered an index for comparison between different types of fibers.Only T 3.0 is the right index for this comparison.13.Both hybrid and polypropylene fibers can help reduce the cost as well as the dimensions and reinforcement of RC sections.For SHPC, both polypropylene and hybrid fiber-reinforced mixtures are much more economical than ST fiber-reinforced mixtures.14.Finally, the optimum percentage for the fiber volume content for the hybrid of ST and PP is 1%; 0.5% for each of the two kinds.

Figure 1 .Figure 1 .
Figure 1.Grading of sand and crushed limestone used in the SHPC mixes.Two different types of fibers were utilized: micro polypropylene (PP) and m hooked-end steel (ST) fibers, as shown in Figure 2. Micro (PP) fibers had a length o

Figure 4 .
Figure 4.The wooden mold of the notched beam before casting.

Figure 4 .
Figure 4.The wooden mold of the notched beam before casting.

Buildings 2024 , 37 Figure 6 .
Figure 6.The relationships between the slump and fiber volume content.Mixtures of Group 2 (ST fibers); S0.5 and S1.0 have slump flows of 610 and 570 mm, respectively, while the slump of S2.0 equals 143 mm.Mixtures S0.5 and S1.0 are classified as SHPC of the SF1 class with T50 of 9 and 12 s, respectively.However, S2.0 is classified as HPC in the S3 class.The results showed that adding ST fibers beyond 1.0% changed the classification from SHPC to HPC.Mixtures of Group 3 (PP + ST fibers); H0.5 has a slump flow of 560 mm and T50 equal to 10 s, which is classified as SHPC in the SF1 class.H1.0 and H2.0 have slumps of 165 and 25 mm, respectively.They are classified as HPCs in classes S4 and S1, respectively.The results showed that adding (PP + ST) fibers beyond 0.5% (0.25% for each) changed the classification from SHPC to HPC.To explain the previous behavior, it is important to define both "Balling" and "Fiber Count".When fibers entangle into large clumps or balls in a mixture, this is called "balling".On the other hand, "fiber count" is the number of fibers in a unit volume of concrete matrix.As the PP-fiber count was higher than that of ST fibers, the balling of micro-PP fibers occurred more than that of macro-ST fibers.This is the reason that the workability of the mixture with PP fibers is much less than that with ST fibers.Hence, the presence of micro-PP fibers in the mixture with hybrid (PP + ST) fibers made its workability less than that of the mixture with macro-ST fibers, while the presence of macro-ST fibers made the workability of the mixture with hybrid (PP + ST) fibers better than that of the mixture with micro-PP fibers, especially for fiber content less than 1%.

Figure 6 .
Figure 6.The relationships between the slump and fiber volume content.

Figure 7
Figure 7 displays the slump flow of mixtures B0.0 and H0.5 as well as the slump test for mixtures B0.5, B2.0, and H2.0.With a slump flow of 680 mm and a T 50 of 7 s, the reference SHPC mixture B0.0 was classified as SF2 class.Mixtures of Group 1 (PP fibers): B0.5, B1.0, and B2.0 have slumps of 175, 145, and 15 mm, respectively.This means that adding PP fibers changed the group from SHPC to HPC, and increasing its content caused the slump class to change from SF2 to S4, S3, S2, and S1, respectively.Mixtures of Group 2 (ST fibers); S0.5 and S1.0 have slump flows of 610 and 570 mm, respectively, while the slump of S2.0 equals 143 mm.Mixtures S0.5 and S1.0 are classified as SHPC of the SF1 class with T 50 of 9 and 12 s, respectively.However, S2.0 is classified as HPC in the S3 class.The results showed that adding ST fibers beyond 1.0% changed the classification from SHPC to HPC.Mixtures of Group 3 (PP + ST fibers); H0.5 has a slump flow of 560 mm and T 50 equal to 10 s, which is classified as SHPC in the SF1 class.H1.0 and H2.0 have slumps of 165 and 25 mm, respectively.They are classified as HPCs in classes S4 and S1, respectively.The results showed that adding (PP + ST) fibers beyond 0.5% (0.25% for each) changed the classification from SHPC to HPC.To explain the previous behavior, it is important to define both "Balling" and "Fiber Count".When fibers entangle into large clumps or balls in a mixture, this is called "balling".On the other hand, "fiber count" is the number of fibers in a unit volume of concrete matrix.As the PP-fiber count was higher than that of ST fibers, the balling of micro-PP fibers occurred more than that of macro-ST fibers.This is the reason that the workability of the mixture with PP fibers is much less than that with ST fibers.Hence, the presence of micro-PP fibers in the mixture with hybrid (PP + ST) fibers made its workability less than that of the mixture with macro-ST fibers, while the presence of macro-ST fibers made the workability of the mixture with hybrid (PP + ST) fibers better than that of the mixture with micro-PP fibers, especially for fiber content less than 1%.

Figure 8 .
Figure 8.The relationships between the cube compressive strength with different dimensions and fiber volume content for the three groups in this study.

Figure 8 .
Figure 8.The relationships between the cube compressive strength with different dimensions and fiber volume content for the three groups in this study.

Figure 8 .
Figure 8.The relationships between the cube compressive strength with different dimensions and fiber volume content for the three groups in this study.

Figure 9 .
Figure 9.The relationship between f cu /f cu,B0.0,and percentage of fiber volume content.

Figure 10 .
Figure 10.Cube/cylinder compressive strength versus the percentage of fiber volume content.

Figure 10 .
Figure 10.Cube/cylinder compressive strength versus the percentage of fiber volume content.

Figure 10 .
Figure 10.Cube/cylinder compressive strength versus the percentage of fiber volume content.

Figure 12 .
Figure 12.Tensile splitting strength versus percentage of fiber volume content.

Figure 12 .
Figure 12.Tensile splitting strength versus percentage of fiber volume content.

Figure 12 .
Figure 12.Tensile splitting strength versus percentage of fiber volume content.

Figure 13 .
Figure 13.The relationship between f sp /f sp,B0.0,and percentage of fiber volume content.

Figure 14 .
Figure 14.Ratio of   ⁄ versus the percentage of fiber volume content.

Figure 15 .
Figure 15.Experimental and predicted tensile splitting strength versus the percentage of fiber volume content.

Figure 15 . 37 Figure 16 .
Figure 15.Experimental and predicted tensile splitting strength versus the percentage of fiber volume content.ldings 2024, 14, x FOR PEER REVIEW 17 of 37

Figure 16 .
Figure 16.Predicted tensile splitting strength versus experimental results of other researchers.

Figure 17 . 37 Figure 17 .
Figure 17.Flexural tensile strength f ctr versus the percentage of fiber volume content.

Figure 19 .
Figure 19.Ratio fsp/fctr versus the percentage of fiber volume content.

Figure 20
Figure20shows the relationship between the ratio   ⁄ and the percentage of fiber volume content for all the studied groups.

Figure 19 .
Figure 19.Ratio f sp /f ctr versus the percentage of fiber volume content.

Figure 20 .
Figure 20.Ratio f ctr / f cu versus the percentage of fiber volume content.

Figure 21 .
Figure 21.Experimental and predicted flexural tensile strength versus the percentage of fiber volume content.

Figure 22 .
Figure 22.Predicted flexural tensile strength versus experimental results of other researchers.

Figure 21 .
Figure 21.Experimental and predicted flexural tensile strength versus the percentage of fiber volume content.

Figure 22 .
Figure 22.Predicted flexural tensile strength versus experimental results of other researchers.

Figure 23 .
Figure 23.Applied load (in kN) versus CMOD in (mm) for all specimens.

Figure 23 .
Figure 23.Applied load (in kN) versus CMOD in (mm) for all specimens.

Figure 25 .
Figure 25.The applied load and deflection relationships for all specimens.

Figure 25 . 37 Figure 26 .
Figure 25.The applied load and deflection relationships for all specimens.

Figure 26 .
Figure 26.Toughness T p and T 3.0 for all specimens.

Figure 28 .
Figure 28.Schematics of stress block for a cracked FRC flexural member: (a) FRC beam section width b and height h; (b) distribution of flexural stresses; and (c) simplified distribution of norm stresses [11].

Figure 28 .
Figure 28.Schematics of stress block for a cracked FRC flexural member: (a) FRC beam section of width b and height h; (b) distribution of flexural stresses; and (c) simplified distribution of normal stresses [11].

Figure 30 .
Figure 30.Schematics of stress block for a cracked reinforced concrete flexural member without fibers: (a) reinforced concrete beam section; (b) actual distribution of normal stresses; and (c) simplified distribution of normal stresses [11]. =  •  •  −  2

Figure 31 .
Figure 31.Stress block diagram for a cracked flexural member with hybrid reinforcing: (a) beam section; and (b) distribution of normal stresses and forces from fibers and reinforcing bar [11].

Figure 30 .
Figure 30.Schematics of stress block for a cracked reinforced concrete flexural member without fibers: (a) reinforced concrete beam section; (b) actual distribution of normal stresses; and (c) simplified distribution of normal stresses [11].

Figure 30 .
Figure 30.Schematics of stress block for a cracked reinforced concrete flexural member without fibers: (a) reinforced concrete beam section; (b) actual distribution of normal stresses; and (c) simplified distribution of normal stresses [11]. =  •  •  −  2

Figure 31 .
Figure 31.Stress block diagram for a cracked flexural member with hybrid reinforcing: (a) beam section; and (b) distribution of normal stresses and forces from fibers and reinforcing bar [11].

Figure 31 .
Figure 31.Stress block diagram for a cracked flexural member with hybrid reinforcing: (a) beam section; and (b) distribution of normal stresses and forces from fibers and reinforcing bar [11].
Table 1 presents the properties of the two types of fibers used in this research.

Table 2 .
Mix proportions for HPC and SHPC.

Table 2 .
Mix proportions for HPC and SHPC.
* V f %: percentage of the fiber volume content, PP: polypropylene fiber, and ST: end-hook steel fiber.** W/B:

Table 3 .
Compressive strength, tensile splitting strength, and modulus of rupture for all mixtures.

Table 3 .
Compressive strength, tensile splitting strength, and modulus of rupture for all mixtures.

Table 4 .
Experimental and theoretical results for both splitting tensile strength and flexural tensile strength.

Table 5 .
Experimental results for both the limit of proportionality and the residual flexural strength.

Table 6 .
Experimental results for the toughness and the ductility index.

Table 7 .
Final cost of concrete mixes, incl.cost of mixing, transportation, and placing.

Table 8 .
Moment capacity for beams of each mixture.

Table 9 .
Final cost of the unit length of the RC bream.