To investigate the influence of steel fiber in ultra-high performance concrete mix that was cured at natural environmental conditions in five specimen groups categorized by differences in fiber volume ratio (Vf) from the initial specimen group of 1% fiber volume ratio up to the last specimen group of 3% with 0.5% volume rate increment for steel fibers from the first up to the last specimen group. Conducting laboratory UHPC with steel fiber volume ratio (Vf) beyond 3% experimental evaluations poses a challenge on controlling the flowability of fresh concrete [25] because steel fibers significantly reduces fluidity of fresh concrete [26] .

The primary ingredients were special reactive powder concrete, steel fiber, and water. Special reactive powder concrete is a new construction engineering material used to make UHPC in China. It is special because all necessary fine aggregates, including silica fume, binders, and other reactive admixtures, are already mixed during manufacturing, making it easy for application in the construction industry since primary aggregates are already mixed at respective optimum ratios. UHPC copper-coated micro steel fiber was mixed in the five specimen groups at different fiber volume percentages of 1%, 1.5%, 2%, 2.5%, and 3%, respectively. Table 1 illustrates the characteristics of steel fiber specified according to manufacturer’s standards, and Figure 1 shows the materials used in the mix design. The water-to-cement ratio w/c was 0.2 which is according to the design mix of UHPC standards.

Casting design mix

At first, a UHPC horizontal mix rotating drum was used to mix the three components. The UHPC horizontal mix rotating drum’s main advantage is that it evenly distributes micro steel fibers along the horizontal length, positively influencing fiber orientation during mixing as an agglomeration of fiber will be avoided. The long, curved blades make it more convenient to evenly spread the steel fiber within the drum, as shown in Figure 2 . I firstly poured reactive powder concrete into the drum and rotated it for about a minute then slowly added water periodically after every forty-five seconds rotation to make sure the powder was evenly mixed with water until all the w/c of 0.2 was fully mixed then later carefully added the steel fiber according to respective specimen volume ratios in small portions each moment until all the steel fiber was fully blended. Each load took about six and a half minutes to fully mix until ready to be cast into respective molds for curing.

Test specimens in this experimental program were cured in natural environmental conditions in open weather. October (end of spring) in Changchun, China, ranges from an average temperature of 5 degrees Celsius in the early morning to 22 degrees Celsius in the afternoon. The cast specimens were de-molded after 7 days of casting, then later put in an laboratory store room and were regularly water sprayed at room temperature water on the surface until 28 days of curing were complete, as shown in Figure 3 , then tested for uniaxial compressive strength and flexural strength under four-point beam load conditions at a later stage.

This section examines the mechanical performance of concrete prism specimens reinforced with a hybrid mix of 13 mm micro-steel fibers and 20 mm recycled steel fibers (1:1 ratio) at 2.5%, 3%, and 3.5% volume fractions which portrayed best flexural performance in previous tests. Numerical simulations assess their behavior under four-point bending test. Increasing length of steel fibers has no significant improvement towards compressive strength of UHPC [27] [28] but long steel fibers exhibit higher flexural strength than short fibers [29] therefore this part only focused on flexural test evaluations. Previous tests using only micro-steel fibers showed superior results but high cost, whereas recycled fibers offer a cost-effective alternative (10 times cheaper) [30] . The hybrid approach balances performance and affordability in (UHPC). Key fiber parameters are provided in Table 2 .

After 28 days of curing, both compressive and flexural tests were conducted. 100mm cubes were tested for compression, while the 1000 mm × 100 mm × 300 mm prism specimens for all five groups were tested for flexure at Jilin Jianzhu University engineering simulation and research laboratory (as illustrated in Figure 4 ). YAR 2000 is the type of hydraulic jack that can administer loads up to 2000 KN, and it was used to perform both tests for all five specimen groups.

Firstly, the compressive load was applied at a rate of 1 MPa/s and gave excellent results, but after realizing that the rate was too fast as the test was performed in under a minute, the compressive load rate was later reduced to 0.5 MPa/s for the rest of the compressive tests. The flexural strength was loaded at a rate of 0.1 MPa/s. The beam was subjected to two equally concentrated loads at 50 mm from the mid-span via a four-point loading method. A single hydraulically actuated jack was used to supply the monotonically increasing load through a displacement control method. Figure 5 shows the actual test setup for (a) the compression test and (b) the four-point loading test, which was the actual setup for all specimens tested.

This study used Finite Element Analysis (FEA) in ABAQUS to analyze steel fiber-reinforced ultra-high-performance concrete under uniaxial compression and four-point bending. The Concrete Damaged Plasticity model simulated concrete’s nonlinear behavior, with material properties derived from lab tests (Young’s Modulus: 39,100 MPa, Poisson’s ratio: 0.2). Python scripting automated modeling, while steel fibers were represented as line elements. Nine specimen groups with steel fiber volumes ranging from 1% to 5% (in 0.5% increments) were tested. For compression, 100 mm cubes were used, and 100 × 100 × 300 mm prisms were tested in bending. A 1 MPa load rate was applied along the y-axis, with the bottom surface fully constrained. Frictional contact (μ = 0.3) was set for bending tests. Specimen loading configurations are illustrated in Figure 6 .

Both specimen samples were globally meshed within the meshing range parameters prescribed in the simulation software. When dividing the mesh of the specimen model, the size of the mesh defines the degree of accuracy of the results and the period for analysis; therefore, observing the density of mesh divisions is essential in the finite element analysis process. Adopting a reasonable mesh size division [31] [32] improves the convergence of simulation results. Figure 7 shows meshed samples of (a) a concrete cube and (b) a prism specimen with a global mesh size of 10.

Resistance forces of sections subjected to flexure are calculated from a linear strain

diagram that is bounded by compression strain limit corresponding to UHPC crushing and reinforcing steel limits that correspond to rupture of reinforcing steel, but members that do not have steel reinforcing bars or pre-stressed strands, the strains are limited to strain at peak tensile strength of UHPC [33] . UHPC is a material that is still being researched. Hence, there is a lack of abundant data that can be referred to come up with a factor of factored flexural resistance, but the LRFD guidelines that propose flexural resistance $M_r$ = resistance factor for flexural moment ${Ø}_f$ multiplied by nominal flexure moment $M_n$. The resistance factor ${Ø}_f$ calculations are well elaborated in AASHTO LRFD BDS [34] .

The ductility factors of a structure are the maximum deformation or ultimate load divided by the corresponding deformation or load at yield. It is a useful non-dimensional index of inelastic deformation. µ = θ ultimate/θ yield where µ is ductility index, θ ultimate is max load or deformation, and θ yield is yield load or deformation [35] . The ductility of concrete beams can be quantified using the ductility index expressed by the deflection ductility index, curvature ductility index, or rotational ductility index. After a flexural test on a concrete beam, mid-span deflection can be used to get the ductility index where the above equation will be adjusted to ѳ ultimate being mid-span deflection at ultimate load and ѳ yield as mid-span deflection at yield load [36] . This paper used the deflection ductility index to calculate ductility. The curvature ductility ratio uses the bending moment at the ultimate load divided by the bending moment at the yield load. If the curvature ductility ratio > 2.0, the flexural resistance of the member is taken equal to the moment at a yield of reinforcement, but if the curvature ductility ratio < 2.0, then the flexural resistance of the member must be taken as max of 0.5 of the moment or flexural resistance calculated without considering the contribution of steel fibers [38] . Flexural strength was calculated as given by the equation according to GB50081-2019 as follows:

$f=\frac{Fl}{b{h}^2}$ (2-1)

In Equation (2-1), F is the load applied at failure, l is the length of the span, b is the width of the specimen, and h is the height of the specimen.

The deflection ductility index was used to calculate the ductility of the beams.

$\mu =\frac{\Delta u}{\Delta y}$ (2-2)

In Equation (2-2), ∆u is the deflection at the ultimate load, while ∆y is the deflection at the yield load [36] .

In reality, reinforced concrete beams crack (micro-cracks within the specimen) before they even reach the yielding point, which is also known as the point of the first crack. Calculating the service stiffness of a reinforced concrete section according to the load and resistance factors specified in reinforced concrete design codes is essential. Service stiffness is approximately 60% to 70% of the ultimate load [38] . In this experimental setup, 10% before and after the standard gave a more realistic solution; hence, 50% to 80% was considered. Post-peak stiffness is a mechanical behavior of a material after it has reached its ultimate strength and begins to soften or degrade, which quantifies the rate of decline in resistance (stress) with respect to deformation (strain) in the post-peak regime of the stress-strain curve. Calculating post-peak stiffness is also a reliable way to check for the ductility of the beam under a four-point loading test. It is obtained by calculating a slope on the load-deflection curve at points between 90% and 70% of the ultimate load, which is the descending part of the curve just before failure, also regarded as the softening phase.

To analyze the elasticity of a beam under a point loading test other than just relying on the visual analytics of the load-deflection curve, post-elastic strength [39] can be calculated as follows

$1-\left[\frac{F\left(\max \right)-F\left(\text{yield}\right)}{F\left(\text{yield}\right)}\right]$ (2-3)

In Equation (2-3), F(max) is the maximum load (peak state load), and F(yield) is the load at the yield point. The results are a numeration between 0 and 1. Post-elastic strength component 0 is a highly inelastic phase, while 1 is a perfectly elastic phase.

Compression test

Ultra-high-performance concrete reinforced with steel fibers relies on the fiber-matrix composite for compressive strength. Ultimate stress increases with the steel fiber volume ratio. Figure 8 shows failure specimens, with 1% fiber content (c) exhibiting larger cracks compared to minimal cracks in (a). Higher fiber ratios (2.5% and 3%) resulted in more ductile failure, reducing disintegration compared to the 1% specimen. Table 3 and Table 4 shows calculated results for compression test results for both laboratory experimental results and numerical simulation model results.

Flexural test

The 100 × 100 × 300 mm prism specimens from all five groups underwent flexural testing under a linearly increasing load controlled by a 2000 KN hydraulic actuator. The first crack formation was accompanied by an audible sound, followed by visible micro-cracks at the beam’s bottom surface between the loading points. As the load increased, multiple micro-cracks developed until a dominant mid-section crack formed, widening as it propagated upward, absorbing smaller cracks along its path. The 1% steel fiber specimen exhibited two cracks—a primary crack near the left bearing (widest at the bottom) and a minor, narrower crack extending vertically. The 1.5% fiber specimen developed a single crack near the right bearing, extending toward the compression zone, while the 2% fiber specimen showed a similar pattern but with less fiber pull-out. The 2.5% fiber specimen behaved comparably to the 2% group. In contrast, the 3% fiber specimen displayed a more expansive crack originating near the mid-left, curving upward with minimal fiber pull-out and fewer powdery particles. Figure 9 illustrates the failure patterns for each specimen group (a-f). Calculated four point loading evaluations are well outlined in Table 5 .

The concrete specimens exhibited varying responses to Von Mises stress, visualized through a color spectrum: red indicated high-stress vulnerability, amber/ yellow moderate susceptibility, and green/blue zones with minimal deformation. Specimens with lower steel fiber ratios (e.g., 1%) showed limited stress resistance, evidenced by dominant blue surfaces ( Figure 10 ). Higher fiber ratios (1.5% - 2.5%) displayed gradual improvements, with lighter blue tops indicating marginally better absorption. Notably, ratios of 3% - 3.5% demonstrated visibly enhanced stress absorption, while 4% - 5% ratios achieved peak performance, though no significant gain occurred beyond 4% (constant spectra). Such delicate observation corresponds well with other laboratory experimental evaluations where the compressive strength was 5.06% and 7.6% lower than that of 3% volume fiber at 4% and 5% volume fiber [4] . Another laboratory experimental study revealed that adding steel fibers from 3% to 45% resulted in reduction of compressive strength from 207 MPa to 158 MPa [40] meaning that fiber volume ratio beyond 3.5% had no significant influence on the compressive strength. Steel fibers predominantly absorbed stresses, exhibiting red spectra at peak failure, confirming their role in transferring internal stresses and boosting compressive strength. This underscores steel fibers’ critical contribution to UHPC’s stress-resistant capacity.

(g) 4% steel fiber volume ratio

Flexural strength test (Four-point bending load)

Steel fibers increase concrete beams’ flexural resistance under bending. Figures 11(a)-(j) shows prisms after testing, with stress absorption rising with fiber content (1% - 5%). More fibers led to higher load-bearing capacity, proving their effectiveness in enhancing flexural performance.

(g) 4% steel fiber volume ratio

The hybrid recycled industrial and microfibers in concrete prisms reduced ductility under flexural loading. A ductility index ≥ 2 indicates high ductility, while values slightly below suggest semi-ductility; lower values denote brittleness, leading to sudden failure. Steel fibers typically enhance ductility, but the 2.5% hybrid mix showed the highest index (1.7145), with 3% and 3.5% mixes scoring lower (1.429 and 1.4628), confirming reduced ductility. The 3.5% specimen had the lowest flexural strength (11.8017 MPa) despite its high peak load, indicating that excess recycled fibers diminished flexural performance and stiffness. Spectral analysis ( Figure 12 ) revealed failure at low-stress levels, with fibers absorbing less stress than the concrete matrix in previous tests, resulting in inadequate resistance to flexural stresses. Table 6 shows calculated evaluations for hybrid fiber tests.

The modulus of elasticity (E), representing the slope of the linear elastic region in the stress-strain curve, was determined between 0.3 and 0.5 of the peak stress to minimize the influence of early-stage micro cracking and plastic deformation, thereby providing a more reliable reflection of the material’s elastic behavior [25] . Experimental results demonstrated a direct correlation between compressive strength and (E) at lower steel fiber volume ratio (Vf), The optimal E in laboratory tests occurred at fiber volume ratio (Vf) = 2.5%, with negligible variation below this threshold, suggesting a limit to fiber efficacy in enhancing elastic stiffness. Prior studies attributes this plateau effect to increased porosity from fiber clustering in (UHPFRC) [25] . ABAQUS simulations produced systematically higher E values, likely due to idealized material assumptions (e.g., perfect fiber-matrix bonding). While (E) was low at fiber volume ratio (Vf) = 1 − 1.5%, it peaked sharply at 3.5%, and became unstable beyond this point, with a notable dip at 4% before recovering at 5%. Although the highest simulated E occurred at fiber volume ratio (Vf) = 5%, the 3.5% mix seemed optimal due to its stability, whereas experiments identified 2.5% as the most effective. This divergence underscores the limitations of homogenized numerical models in capturing real-world complexities such as fiber dispersion and defect-induced softening, particularly at higher fiber volume ratio (Vf) where material heterogeneity dominates. The experimental plateau in E beyond = 2.5% and fiber volume ratio (Vf) = 3.5% for ABAQUS simulations further indicates a saturation point for fiber reinforcement in elastic deformation resistance, a critical insight for optimizing UHPFRC design. Figure 13 shows the comparison of modulus of elasticity. Other studies reveals that modulus of elasticity increases with an increase in steel fiber volume (Vf) [41] , however, modulus of elasticity reduces at 4% fiber volume [40] . This signifies that increase in steel fiber volume (Vf) up to 3.5% has a positive influence on the mechanical properties of concrete but fiber volume beyond that deteorates the UHPC mechanical performance due to agglomeration of fiber [4] leading to more pores and internal defects with unfavourably insufficient density of hardened UHPFRC and large void ratio [25] .

The flexural behavior of steel fiber-reinforced concrete prisms was first investigated through laboratory experiments, revealing a direct correlation between fiber content and flexural strength. The minimum strength of 5.2 MPa was recorded at 1% steel fibers, while the maximum of 10.68 MPa was achieved at 3%. Beyond this threshold, a slight reduction in strength was observed, suggesting an optimal fiber reinforcement ratio for maximizing flexural capacity. Complementing these findings, ABAQUS simulations demonstrated a similar trend, with flexural strength increasing sharply between 2% and 2.5% before reaching an optimum of 13.405 MPa at 3%. Beyond this point, a marginal decline occurred, reinforcing the experimental conclusion that steel fibers exhibit peak effectiveness up to 3%. Figure 14 compares the flexural strength from laboratory experiments and ABAQUS simulation results.

The simulations further highlighted load-bearing performance, with the minimum peak load at 55.44 kN (1%) and the maximum at 186.37 N (5%), confirming that incremental fiber volume ratio (Vf) enhances structural resistance. Additionally, ductility improved consistently with fiber content, mitigating brittle failure. However, post-peak stiffness diminished beyond 3.5%, indicating reduced fiber efficiency in the post-cracking phase. Both experimental and numerical analyses exhibited a linear load-deflection relationship in the elastic stage, while the softening phase in simulations showed increased deflection tolerance at higher fiber ratios, underscoring steel fibers’ role in enhancing deformation capacity.

However, the introduction of a hybrid fiber mix (recycled industrial and microfibers) introduced trade-offs. The 3.5% hybrid specimen displayed the lowest flexural strength (11.80 MPa) despite achieving the highest peak load, suggesting compromised stiffness. Ductility was also affected, as the highest index (1.7145 at 2.5%) declined at higher ratios (1.429 at 3%, 1.4628 at 3.5%). This indicates that hybrid fibers, while improving load capacity, may not sustain ductility as effectively as pure steel fibers. Figure 15 shows the ductility performance, with hybrid fiber specimens exhibiting the lowest ductility index.

These findings emphasize optimizing fiber content within the 2.5% - 3.5% range to balance strength, ductility, and post-cracking performance. A 3% steel fiber content emerged as the most effective for flexural enhancement, while hybrid mixes require further refinement to mitigate ductility reductions.

In laboratory experiments, UHPC prism specimens with higher steel fiber ratios demonstrated superior resistance to deformation, as reflected in their service stiffness—a key engineering parameter for pre-crack deformation resistance. The minimum service stiffness was 15.57 kN/mm at a 1% steel fiber volume ratio, while a 1.5% ratio doubled this value. At 2%, service stiffness peaked at 107.7 kN/mm, marking a 3.5-fold increase over the 1.5% ratio and representing the most effective enhancement. Further increments (2.5% to 3%) yielded diminishing returns, improving stiffness by only 1.06 times.

ABAQUS simulations showed that service stiffness reached optimal stability at a 3.5% steel fiber ratio, beyond which performance became erratic. Figure 16 illustrates the relationship between service stiffness and fiber volume ratio.

In lab tests, post-peak stiffness increased steadily with fiber content, peaking at 2.5%. In contrast, simulations and hybrid fiber specimens achieved optimum post-peak stiffness at 3.5%. However, hybrid mixes underperformed compared to pure micro steel fiber specimens, indicating the need for further research to optimize hybrid ratios (combining micro and recycled steel fibers) for improved post-peak behavior. Figure 17 compares post-peak stiffness across different steel fiber volume ratios.

A cutting-edge review study on fiber utilization in UHPC analyzed steel fiber performance data from a broad spectrum of 213 studies, concluding that the optimal steel fiber volume ratio should not exceed 3% [42] . This finding aligns with the evaluations presented in this paper, which identify an optimal steel fiber ratio between 3% and 3.5%, as illustrated in Table 7 .