Effects of Partial Replacement of Cement with Fly Ash on the Mechanical Properties of Fiber-Reinforced Rubberized Concrete Containing Waste Tyre Rubber and Macro-Synthetic Fibers

Abstract

This study investigates the impact of partially replacing cement with fly ash (FA) on the mechanical performance of fiber-reinforced rubberized concrete (FRRC) incorporating waste tyre rubber and recycled macro-synthetic fibers (MSF). FRRC mixtures were prepared with varying fly ash replacement levels (0%, 25%, and 50%), rubber aggregate contents (0%, 10%, and 20% by volume of fine aggregate), and macro-synthetic fiber dosages (0% to 1% by total volume). The fresh properties were evaluated through slump tests, while hardened properties including compressive strength, splitting tensile strength, and flexural strength were systematically assessed. Results demonstrated that fly ash substitution up to 25% improved the interfacial bonding between rubber particles, fibers, and the cementitious matrix, leading to enhanced tensile and flexural performance without significantly compromising compressive strength. However, at 50% replacement, strength reductions were more pronounced due to slower pozzolanic reactions and reduced cement content. The inclusion of MSF effectively mitigated strength loss induced by rubber aggregates, improving post-cracking behavior and toughness. Overall, an optimal balance was achieved at 25% fly ash replacement combined with 10% rubber and 0.5% fiber content, producing a more sustainable composite with favorable mechanical properties while reducing carbon and ecological footprints. These findings highlight the potential of integrating industrial by-products and waste materials to develop eco-friendly, high-performance FRRC for structural applications, supporting circular economy principles and reducing the carbon footprint of concrete infrastructure.

1. Introduction

The construction industry is facing major challenges in reducing its environmental impact due to the heavy consumption of natural resources and the substantial CO₂ emissions associated with conventional materials, particularly cement [1,2,3,4]. In recent decades, the adoption of sustainable construction strategies has gained momentum, with a particular focus on utilizing recycled waste materials to develop eco-friendly substitutes for traditional concrete. One such innovation is fiber-reinforced rubberized concrete (FRRC), a novel composite material that integrates waste tyre rubber particles and synthetic fibers [5,6]. This innovative material not only enhances mechanical properties such as energy absorption and toughness but also directly addresses the global issue of solid waste accumulation. Rubberized concrete is typically generated through partially substituting conventional aggregates with crumb rubber from end-of-life tyres [7,8], which are non-biodegradable and pose serious environmental risks. By 2030, it is projected that over five billion tyres will be discarded globally, generating around 1.2 billion waste tyres annually [9,10,11]. Thus, using discarded rubber in concrete serves as an environmentally friendly waste management approach while also offering functional enhancements. Various studies have indicated that the inclusion of rubber aggregates can boost the material’s resilience, improve energy dissipation, enhance resistance to freeze–thaw cycles and increase deformability [12,13,14]. Despite its benefits, incorporating a high volume of rubber aggregates can significantly reduce concrete’s strengths and the elastic modulus [13,15,16], primarily attributed to weak interfacial bonding between the rubber particles and the cementitious matrix, coupled with the inherently low stiffness of rubber [17,18]. To overcome this challenge, the addition of fibers has been widely studied as an effective reinforcement technique to compensate for the strength loss and improve the post-cracking behavior of the composite [5,6]. Fibers serve as internal reinforcement elements, bridging cracks and improving post-cracking behavior, which contributes to enhanced tensile strength and toughness [19,20]. A variety of fiber types have been investigated in this context, including steel fibers [21,22,23,24], polypropylene fibers [24,25,26], and macro-synthetic fibers produced from recycled plastics [27,28]. When added to rubberized concrete, these fibers significantly enhance flexural strength, fracture energy, and resistance to dynamic loading [17,19,20]. The synergistic interaction between rubber particles and fibers not only compensates for the mechanical drawbacks introduced by rubber but also results in a more ductile and energy-absorbing composite material [29,30]. As a result, FRRC has shown promise in demanding applications such as protective barriers, crash-resistant infrastructure, and pavements, where durability and impact resistance are essential performance criteria [17,31].

Macro-synthetic fibers, typically derived from post-consumer plastics like polypropylene (PP) or polyethylene terephthalate (PET), have garnered significant attention as sustainable reinforcement materials in FRRC, offering both performance enhancement and plastic waste valorization [13,32]. Among them, PP fibers with lengths ranging from 30 to 60 mm with a 0.61 mm² cross-section are currently among the most common steel-wire-like organic fibers used in concrete applications [33]. Their incorporation in FRRC enhances flexural and tensile strength by bridging cracks and compensating mechanical drawbacks caused by rubber particles [28,33,34]. In comparison to traditional steel fibers, they offer several practical advantages such as corrosion resistance, increased toughness, lower density, and improved workability, making them ideal for durable, dynamic-loading applications [13,28,32]. Recent studies have shown that the incorporation of MSF in rubberized concrete significantly improves post-cracking behavior and flexural strength when added in optimal dosages, without causing substantial reductions in workability [8,9]. By repurposing plastic and tyre waste, this FRRC advances circular economy goals and contributes to sustainable, high-performance concrete solutions for infrastructure development.

Despite the advantages of FRRC, it often necessitates a higher cement content than traditional concrete to achieve sufficient bonding among rubber particles, fibers, and the cement matrix. This heavy reliance on cement adversely impacts the environmental benefits of FRRC, as cement manufacturing accounts for approximately 8% of global anthropogenic CO₂ emissions [35,36]. Therefore, minimizing cement content without sacrificing the mechanical and structural performance of FRRC is critical. One of the well-established approaches is the partial substitution of cement with supplementary cementitious materials (SCMs) such as fly ash, metakaolin, silica fume, blast granulated furnace slag, brick powder, concrete powder, etc. Among these SCMs, fly ash has gained widespread acceptance due to its pozzolanic activity. It is an industrial by-product generated from coal combustion in thermal power plants, which improves the long-term strength and durability properties of concrete through its reaction with calcium hydroxide to form additional calcium silicate hydrate (C-S-H) gel [37,38]. The integration of fly ash in concrete not only decreases the carbon footprint but also enhances workability, lowers permeability, and improves durability performance [39,40].

Numerous studies have demonstrated the benefits of fly ash in conventional and fiber-reinforced concrete; however, its effects on FRRC containing MSF remain relatively unexplored. Due to the unique characteristics of rubber and MSF, a detailed investigation of their synergy with fly ash is essential to optimize performance and sustainability. Previous study carried out by Raffoul et al. [18] shows that replacement of coarse rubber content up to 20% resulted in concrete compressive strength higher than 32 MPa which is the minimum required compressive strength for concrete for application in infrastructures specified by Mainroads, Western Australia. Kazmi et al. [41] and Fraternali et al. [42] found that the peak stress, toughness and ductility of concrete increase by up to 1% macro-synthetic fiber. On the contrary, although this study focuses on the maximum utilization of fly ash in replacing cement in concrete; however, the generally recommended replacement rate of using fly ash to replace cement does not exceed 50% [43]. In addition, for low to moderate replacement of Portland cement with fly ash, cement itself acts as an activator for fly ash. However, for a large replacement rate (e.g., beyond 70%) of fly ash, particularly for F class type which has a lower (CaO) than the C class type, an additional activator such as slag is required to obtain early strength of concrete [43]. The binder can affect the bond performance of concrete and reinforcement bars [44].

Based on the aforementioned discussions, this study addresses the knowledge gap by systematically investigating partial cement replacement with fly ash (0%, 25%, 50%) on workability and mechanical properties of FRRC mixtures with varying waste tyre rubber (0%, 10%, 20% by fine aggregate volume) and macro-synthetic fiber contents (0–1% by volume). The impact of fly ash in fiber-rubber-matrix bonding was investigated through workability and mechanical properties such as compressive strength, flexural strength and tensile strength tests. By integrating waste materials and cement replacement, this research aims to promote sustainable concrete development which cannot only enhance FRRC’s structural viability but also reduce environmental impact and support the circular economy in construction.

2. Experimental Program

2.1. Materials

This study employed Portland cement conforming to ASTM C150/C150M [45] standards were used as the primary binder, alongside Class F fly ash as a supplementary cementitious material. The chemical compositions of both Portland cement and fly ash are summarized in Table 1, while their physical properties are detailed in Table 2.

Granite crushed stones with a maximum particle size of 10 mm were used as coarse aggregate. The crushed stones had a specific gravity of 2.69 and met the specifications of ASTM C33 [47]. The fine aggregate utilized was locally available washed sand having a specific gravity of 2.63 and a fineness modulus of 2.6. The recycled waste tyre rubber particles employed in this research were derived from shredded end-of-life tyres. The composition of these rubber particles contained less than 65% polymers and organic material, with carbon black content reaching up to 100%, and had a specific gravity below 1, reflecting their lightweight nature.

The concrete matrix was reinforced using macro-synthetic fibers, marketed under the name ‘eMesh.’ These fibers are produced entirely from recycled plastic materials, exhibiting a specific gravity of 0.92 and containing no moisture. The thickness (diameter) of the fibers is around 0.5 mm and 47 mm long and is known to retain over 98% of its tensile strength when exposed to alkaline conditions [32]. The Modulus of Elasticity is 6 GPa and the minimum tensile strength is 400 MPa. Images of the macro-synthetic fibers and rubber particles used in this study are presented in Figure 1. Potable tap water was used throughout all mixing and curing procedures. The particle distributions of the aggregates are shown in Figure 2.

2.2. Mix Design of Concrete and Preparation of Test Specimens

The concrete mixes were designed to investigate the combined effects of partial cement replacement with fly ash, varying rubber content, and different dosages of macro-synthetic fibers (MSF) on the fresh and mechanical properties of rubberized fiber-reinforced concrete (FRRC). A total of 27 mix proportions were prepared, incorporating three levels of fly ash replacement (0%, 25%, and 50% by weight of binder), two rubber contents (10% and 20% by volume of aggregate), and five fiber dosages (0%, 0.25%, 0.5%, 0.75%, and 1% by total concrete volume). The control mix (C-0-0-0) contained no rubber or fibers, with 100% Portland cement as the binder and was designed with a binder-to-aggregate ratio adjusted to maintain consistency across all mixes. The binder content was maintained constant across all mixes, with cement and fly ash combined to achieve the desired replacement level. The water-cement (W/C) ratio was kept constant for all mixtures at 0.4. The mix proportions for all mixes are summarized in Table 3. Mix codes were structured to reflect the varying parameters; for example, C-0.25-10-25 indicates a mix containing 25% fiber volume fraction, 10% rubber replacement, and 25% cement replacement by fly ash.

The concrete mixing was carried out in accordance with AS1012.2 [48] using a 70 L rotary drum mixer. All materials were prepared in a saturated surface-dry (SSD) condition by soaking for 24 h followed by air drying for another 24 h to maintain a consistent water-to-cement ratio across all mixes. The dry constituents (cement, fly ash, fine aggregate, coarse aggregate, and rubber) were initially dry-mixed for 2 min. Macro-synthetic fibers were then gradually introduced and blended for an additional minute to prevent clumping. Water was subsequently added, followed by another 2 min of mixing to achieve a uniform blend. Slump tests were conducted immediately after mixing completion in accordance with 1012.3.1:2014 [49]. Fresh concrete was cast into standard cylindrical and prismatic molds for compressive, splitting tensile, and flexural strength testing. All specimens were compacted using a vibrating table and demolded after 24 h, then water-cured at 23 ± 2 °C for 28 days. Each test was performed on three identical specimens per mix, and the average value was reported. The concrete mixing process is illustrated in Figure 3.

2.3. Testing Setup

The fresh concrete workability was evaluated using the slump test following the procedures outlined in AS 1012.3.1:2014 [49]. The slump measurements were recorded immediately after mixing to assess the consistency and flowability of each concrete mix. The workability testing of normal and FRRC samples is shown in Figure 4. The density of the concrete was measured using AS 1141.4 [50].

For mechanical characterization, the compressive strength tests were conducted on cylindrical specimens with dimensions of 100 mm × 200 mm, following the guidelines specified in AS 1012.9:2014 [51], using a universal testing machine at 28 days. Flexural strength was determined using prismatic beam specimens of 400 mm × 150 mm × 150 mm, subjected to four-point bending tests in accordance with AS 1012.11-2000 [52]. Splitting tensile strength tests were conducted on cylindrical specimens of 150 mm × 300 mm, using a continuous loading rate of MPa/min until rupture with the compliance of AS 1012.10-2000 [53]. All mechanical tests were carried out after curing the specimens for 28 days in water at 23 ± 2 °C. Each test was conducted on three specimens per mix to ensure repeatability and reliability, with the average value reported. The testing setups for compressive, splitting tensile, and flexural strength tests are shown in Figure 5.

3. Test Results and Discussions

3.1. Effects of Fly Ash on the Slump of FRRC

Figure 6 illustrates the results of the workability of FRRC mixes. The data clearly show that the addition of fly ash consistently enhances the slump values across all mix compositions, indicating improved workability. For instance, the control mix without rubber or fiber (C-0-0-0) exhibited a slump of 140 mm, which increased progressively to 185 mm and 200 mm upon 25% and 50% replacement of cement with fly ash, respectively. This trend was similarly observed in rubberized mixes, where fly ash addition mitigated the reduction in workability caused by rubber particles.

The incorporation of waste tyre rubber generally reduced workability, as evidenced by decreased slump values when comparing mixes with increasing rubber content but no fly ash. For example, FRRC mixes with 0.5% fibers and 10% rubber without fly ash (C-0.5-10-0) showed a slump reduction of 12% compared to the control, highlighting the detrimental effect of rubber on flowability. Wang et al. [13] also reported a reduction of 12% slump for FRRC with 0.5% fibers and 10% rubber. However, Wang, et al. [13] found that the slump of concrete with only 0.5% fibers (without rubber) was higher than concrete with rubber. This reduction can be attributed to the hydrophobic nature and irregular shape of rubber particles, which reduce the flowability of the concrete matrix by disrupting the particle packing and water film continuity [5,54]. However, the addition of fly ash substantially counteracted this reduction, raising the slump to 180 mm and 190 mm for 25% and 50% fly ash replacement levels, respectively. This improvement can be attributed to the spherical morphology of fly ash particles which act as a micro-filler and improve the lubricating effect within the fresh mix, thereby enhancing workability even in the presence of rubber particles [39,40,55].

Fiber content exhibited a pronounced inverse effect on slump, particularly at higher dosages and rubber contents. Increasing macro-synthetic fiber (MSF) content consistently reduced the slump values, with high-fiber, high-rubber mixes (e.g., C-0.50-20-0) showing slumps as low as 60 mm. The physical presence of fibers restricts the movement of aggregates and increases the viscosity of the mix, impairing flowability [32,56]. This negative impact was more pronounced in mixes with greater rubber content, where the combined effect of rubber and fiber further impeded workability. Despite this, fly ash was able to partially mitigate these adverse effects, although its effectiveness diminished at the highest fiber dosages (≥0.75%).

These observations align well with previous studies reported by Wang et al. [13] that rubber particles tend to decrease concrete workability due to their surface properties and size distribution. In addition, the increasing fiber content in rubberized concretes further decreases workability, attributing it to increased internal friction from rubber particles and the limited flow caused by the presence of macro polypropylene fibers. However, supplementary cementitious materials like fly ash can enhance flow characteristics through improved particle packing and lubrication effects of the rubberized concrete, as evident by Bala et al. [39].

When examining the effects of density on the slump of FRRC, it is seen that increasing fly ash reduces concrete density. However, FRRC with lower density increased the slump. This is because concrete with higher density is more compact due to less space for water and air, making it less workable.

3.2. Effects of Fly Ash on the Compressive Strength of FRRC

The compressive strength results of various FRRC mixes are depicted in Figure 7. The control mix (C-0-0-0) exhibited the highest compressive strength of 60.53 MPa. In FRRC mixes without fly ash, adding fiber and rubber decreases their ultimate strength compared to the control specimen. For example, C-0.75-10-0 exhibited a reduction of 25% compressive strength than C-0-0-0. Wang et al. [13] also reported a reduction of 24% of the compressive strength for FRRC with 10% rubber. However, Wang, et al. [13] reported a reduction in only 1.6% of the compressive strength of concrete with only fibers (without rubber). Thus, it is evident that inclusion of rubber is the primary cause of the reduction in the compressive strength of FRRC. The findings also reveal that while the inclusion of fly ash consistently enhanced the workability of the mixes, it generally led to a significant reduction in compressive strength, particularly at higher replacement levels. When 25% and 50% of cement were replaced by fly ash (C-0-0-25 and C-0-0-50), the strength dropped to 41.29 MPa and 29.73 MPa, respectively, indicating a strength reduction of approximately 32% and 51%. In mixes with rubber and fiber, the negative effect of fly ash on compressive strength was more pronounced. For instance, in the C-0.25-10 series, the mix without fly ash (C-0.25-10-0) achieved a compressive strength of 41.87 MPa, which decreased to 39.42 MPa and 15.69 MPa with 25% and 50% fly ash addition, respectively. In mixes with higher rubber content, such as C-0.25-20-50, the compressive strength declined further to 12.46 MPa. The observed strength loss is mainly attributed to the dilution effect, where replacing a portion of cement with less reactive fly ash reduces the early formation of calcium silicate hydrate (C–S–H) gel, a key component responsible for concrete strength [37,57,58]. Moreover, the presence of rubber particles, which are hydrophobic and non-cementitious, further impedes strength development by introducing weak zones and reducing the bond between the aggregate and the cement matrix [59,60]. This effect becomes more critical in high-rubber-content mixtures, for example, in the C-0.75-20-0 mix (without fly ash), the strength was 34.52 MPa, but it dropped sharply to 15.02 MPa when 50% fly ash was used. Incorporation of MSF helped in bridging microcracks and delaying crack propagation; however, this reinforcement benefit could not fully compensate for the strength loss at higher fly ash dosages. For instance, in C-0.50-10-0 (with 0.5% fiber, no fly ash), the strength was 37.38 MPa, dropping to 24.94 MPa and 20.45 MPa at 25% and 50% fly ash levels, respectively.

These findings are consistent with existing literature, which reports that the replacement of cement with fly ash beyond 20–25% typically leads to reduced compressive strength at early curing ages [61,62], especially in concrete incorporating recycled materials. For example, Bala et al. [39] observed similar strength losses in rubberized concrete with fly ash, emphasizing that pozzolanic activity requires extended curing to yield substantial strength gains. While fly ash improves long-term strength and durability due to secondary hydration, such benefits are not fully realized within 28 days of curing, as tested in this study.

3.3. Effects of Fly Ash on the Splitting Tensile Strength of FRRC

The actual splitting tensile strength results for the FRRC mixes and their normalized strength against the compressive strength of concrete (f_c′) are demonstrated in Figure 8a,b, respectively. Generally, all FRRC mixes exhibited a higher splitting tensile strength than the control specimen. However, this contradicts with the observation reported by Wang et al. [13] in which it was reported that FRRC mixes had lower tensile strength than the control specimen. Furthermore, unlike compressive strength trends, splitting tensile strength improved noticeably with the incorporation of fly ash, especially at the 25% replacement level across nearly all mixes. For example, the control mix without fly ash (C-0-0-0) exhibited a splitting tensile strength of 3.01 MPa, whereas the corresponding 25% fly ash mix (C-0-0-25) showed a substantial increase to 7.71 MPa, more than doubling the splitting tensile strength. This enhancement was observed consistently across various rubber and fiber contents, indicating that fly ash plays a significant role in improving tensile properties despite the reductions in compressive strength. The enhancement in splitting tensile strength can be attributed to the pozzolanic reaction of fly ash, which refines the microstructure of the cement matrix, leading to a denser interfacial transition zone (ITZ) and improved bonding between the fibers, rubber particles, and the cementitious matrix [39]. The improved ITZ enhances stress transfer efficiency and crack-bridging capacity of the fibers, which is critical for tensile performance. Moreover, the finer particles of fly ash can fill voids and reduce microcracks, further contributing to splitting tensile strength [38,63]. On the other hand, while increasing fly ash from 25% to 50% generally resulted in a reduction in splitting tensile strength compared to the 25% mixes, these values remained higher than or comparable to the control mixes without fly ash. For instance, the C-0-0-50 mix had a splitting tensile strength of 4.98 MPa, which is lower than C-0-0-25 but still higher than the control. This may be due to the dilution of the cement matrix and reduced early-age reactivity, which weakens the bonding interface between the paste and fibers or rubber particles [37]. Excessive fly ash may also hinder adequate hydration and limit the formation of strong C–S–H gels at early curing stages, ultimately impacting splitting tensile strength. This indicates that moderate fly ash replacement optimizes tensile strength gains, whereas excessive replacement diminishes this benefit due to slower pozzolanic activity and reduced cementitious content [63].

The presence of rubber adversely affects splitting tensile strength due to its low stiffness and poor adhesion to the cement matrix. However, the addition of fly ash mitigates this effect to some extent, especially in mixes with lower fiber content. For example, the splitting tensile strength for C-0.25-10-0 (no fly ash) is 3.34 MPa, which increases to 6.46 MPa with 25% fly ash. Similarly, even at higher rubber and fiber contents, fly ash-enhanced mixes outperform their non-fly ash counterparts in splitting tensile strength. Fiber content also influences tensile strength significantly. Higher fiber contents consistently increased splitting tensile strength, reinforcing the matrix against tensile stresses. However, in high-rubber-content mixes, the effectiveness of fibers is somewhat diminished due to weaker fiber-matrix bonding zones; nevertheless, fly ash inclusion helps improve this bond, as reflected in higher splitting tensile strengths in fly ash mixes compared to their non-fly ash mixes. These findings align with Wang et al. [13], who noted that while rubber weakens tensile strength because of its inadequate adhesion to the cement matrix, the inclusion of PP fibers not only enhances splitting tensile strength to some extent but also significantly contributes to crack control and resistance to crack propagation. Therefore, it can be concluded from the results that 25% fly ash replacement significantly enhances the splitting tensile strength of FRRC by improving matrix densification, ITZ quality, and fiber dispersion, while higher fly ash levels reduce these benefits, especially with increased rubber or fiber content.

3.4. Effects of Fly Ash on the Flexural Strength of FRRC

The actual flexural strength as well as the flexural performance of FRRC mixes normalized against the compressive strength of concrete (f_c′) are presented in Figure 9a,b, respectively. Similarly to tensile strength, generally, all FRCC mixes exhibited a higher flexural strength than the control specimen which also contradicts with the observation reported by Wang et al. [13]. Wang, et al. [13] reported that FRCC mixes had lower flexural strength than the control specimen. It can be seen that the incorporation of fly ash generally reduces flexural strength, although certain trends reveal interactions between rubber, fiber, and fly ash that offer valuable insights. The control concrete mix without rubber, fiber, or fly ash (C-0-0-0) exhibited a flexural strength of 5.26 MPa. Upon the addition of 25% fly ash replacement (C-0-0-25), the flexural strength decreased to 3.92 MPa, further reducing to 3.09 MPa at 50% fly ash (C-0-0-50). This initial reduction suggests that fly ash, when used alone at higher replacement levels, may lower early-age strength due to its slower pozzolanic reaction compared to cement [37]. The presence of fibers mitigated the negative impact of fly ash on flexural strength across all mixes. For example, in mixes with 0.25% fiber and 10% rubber (C-0.25-10), flexural strength decreased from 5.47 MPa without fly ash to 3.15 MPa at 50% fly ash. On the other hand, in mixes with higher (0.75%) fiber contents, C-0.75-10 exhibited a flexural strength of 5.80 MPa without fly ash to 3.64 MPa at 50% fly ash. Similar trends were observed in other fiber and rubber combinations, indicating that fibers help maintain flexural performance by enhancing crack-bridging and improving load transfer during bending, thereby compensating for the reduction in matrix strength caused by partial cement replacement.

The inclusion of rubber generally reduced the flexural strength of FRRC due to its lower stiffness and weak bonding with the cement matrix [64,65]. For instance, mixes without rubber (C-0-0-0) exhibited a flexural strength of 5.26 MPa, whereas mixes with 20% rubber and no fly ash (C-0-0-20) showed noticeably lower values. However, the combined effects of fly ash and fibers helped offset some of this reduction, particularly at moderate fly ash replacement levels. Fly ash’s pozzolanic activity improves the interfacial transition zone (ITZ) by generating additional calcium silicate hydrate (C–S–H) gel [37], enhancing fiber-matrix adhesion and matrix density which are the key factors influencing flexural behavior. This is reflected in mixes like C-0.25-10-25, where flexural strength remained relatively high at 4.26 MPa despite the presence of rubber. Nonetheless, at 50% fly ash replacement, a further decline in flexural strength was observed across nearly all mixes, likely due to the dilution of cementitious material and slower strength development characteristic of high-volume fly ash binders [37,66]. This decrease was especially pronounced in mixes with higher rubber content, where the weak rubber-cement interface amplified the negative effect of reduced binder strength.

These findings align with previous studies performed by Kayali [67] and Barbuta et al. [68] demonstrated that while fly ash enhances flexural toughness in fiber-reinforced concrete through microstructural refinement and improved fiber bonding, excessive fly ash content can reduce overall strength. The results indicate that fly ash affects the flexural strength of FRRC depending on its dosage, with moderate levels (~25%) improving performance by enhancing the matrix and fiber bonding, while higher levels (50%) reduce strength due to cement dilution and slower reaction. Fibers help counteract the adverse effects of rubber and fly ash, highlighting the importance of optimizing fly ash content for balanced mechanical properties in sustainable FRRC.

3.5. Comparisons of the Results with the Existing Literature

A comparative analysis of the compressive strength ranges across different fly ash replacement levels in rubberized concrete from different literature is presented in Table 4. The results consistently demonstrate that increasing fly ash content leads to a decline in compressive strength, regardless of the rubber content used. In the current study, the control mix without fly ash (0% FA) achieved the higher compressive and flexural strength compared to the concrete with different percentages of fly ash. The ranges of the compressive and flexural strength decrease as the fly ash replacement increases, as can be seen from Table 4. This trend is similarly evident in the literature. In the study of Najmi et al. [55], with rubber content varying from 5% to 20%, the compressive strength at 0% fly ash ranged from 10.8 to 22.5 MPa and steadily decreased with higher fly ash content, ranging 9.2–19.4 MPa at 30% replacement. Similarly, the study of Bala et al. [39] which included rubber content (up to 40%) and fly ash replacement levels (0 to 30%), reported compressive strength ranges of 5.33 to 36.47 MPa at 0% fly ash, decreasing to 2.43 to 33.09 MPa at 10% fly ash, and finally 1.20 to 22.43 MPa at 30% fly ash replacement. The reduction in strength with higher fly ash content is primarily attributed to the dilution effect, where the replacement of Portland cement with fly ash reduces the early hydration products necessary for strength development [57]. This delay is further intensified by the inclusion of rubber particles, which tend to form weak interfacial bonds with the cementitious matrix [39,55]. However, interestingly, increasing fly ash replacement up to 25% exhibited the best enhancement of the splitting tensile strength. Najmi, et al. [55] also reported that increasing fly ash up to 25% exhibited an increase in the splitting tensile strength than the specimen with no fly ash. A decrease in the density due to the increase in the fly ash reported in this study in found to be consistent with the observation reported by Najmi, et al. [55], and Bala, et al. [39].

Despite this common trend across studies, the mixes from the current experimental work consistently exhibit higher compressive strengths compared to those reported in the literature at similar fly ash and rubber contents. This superior performance can be attributed to the addition of fibers in the experimental mixes, which likely enhanced crack-bridging capacity and improved post-peak toughness [28,68]. Moreover, the use of a well-optimized mix design fly ash, fibers, and rubber may have contributed to improved matrix integrity and facilitated more efficient pozzolanic reactions of fly ash, especially at moderate replacement levels.

Overall, these results highlight that although fly ash typically reduces compressive strength, especially at higher dosages, this drawback can be effectively countered through fiber reinforcement. The combined use of fly ash and fibers in rubberized concrete not only supports the mechanical performance but also aligns with sustainable construction practices by enabling the beneficial reuse of industrial wastes and by-products.

3.6. Failure Modes of the Specimens

The failure behavior of fiber-reinforced rubberized concrete (FRRC) specimens subjected to axial compression is shown in Figure 9. As shown in Figure 10a, the control specimen (C-0-0-0) experienced a classic shear-type failure characterized by a distinct diagonal crack forming near the mid-height of the specimen, resulting in sudden splitting and fragmentation along the shear plane. This brittle failure mode is aligned with its relatively higher compressive strength (60.5 MPa) but low ductility. The abrupt failure suggests limited energy absorption, typical for plain concrete.

Both fly ash-modified specimens C-0-0-25 and C-0-0-50 (Figure 10b,c) showed failure modes involving angled cracks similar to shear failure; however, the cracks did not form along a precise diagonal plane as in the control. Instead, the cracking was more irregular and dispersed, possibly due to the altered microstructure and increased matrix densification from fly ash’s pozzolanic reaction, which enhances long-term strength and toughness. The presence of fly ash appeared to improve crack distribution, reducing abrupt brittle failure.

Specimens incorporating macro-synthetic fibers and rubber aggregates with varying fly ash contents (Figure 10d–i) exhibited more intricate and distributed failure mechanisms. Unlike the sharp diagonal shear cracks seen in the control mix, these FRRC mixes generally showed multiple microcracks along with distributed cracking across the specimen height. The fibers functioned as internal reinforcement which bridges the cracks and delays their propagation [13], while the rubber particles contributed to increased deformability and energy absorption [56], resulting in more gradual and controlled failure modes. As fiber content increased from 0.25% to 1%, the specimens displayed improved post-peak ductility, with cracks developing in a less defined and more dispersed pattern, deviating from the classical shear failure mode. The addition of 10–20% rubber further promoted ductile deformation by increasing strain capacity and mitigating sudden crack propagation. Higher fly ash replacement levels (25% and 50%) consistently contributed to improved matrix cohesion and crack dispersion, which synergistically worked with the fibers and rubber to produce a complex failure pattern characterized by multiple intersecting cracks, narrower crack widths, and better residual load capacity which is different from the brittle, shear-type failures observed in the control mix.

Figure 11 illustrates the failure mode of the specimens subjected to the tensile splitting test. It can be seen that the tensile failure patterns of all tested specimens predominantly exhibited fracture along the central line, where the tensile stresses were highest. The mode and characteristics of failure, however, varied with mixed composition.

For the C-0-0-25 mix (Figure 11a), the specimen failed abruptly with a sharp, clean crack developing vertically at the mid-span, splitting the specimen into two distinct halves. The absence of fibers led to no crack-bridging mechanism, resulting in rapid crack propagation and brittle failure. The 25% FA replacement slightly improved matrix cohesion but did not significantly affect brittleness. Similarly to this, the specimen of C-0-0-50 mix (no rubber or fiber and 50% FA) failure occurred via a straight fracture along the central plane, as shown in Figure 11b. The higher fly ash content reduced early-age matrix strength and delayed hydration, contributing to a slightly wider and more brittle crack. The lack of fibers allowed immediate crack growth without resistance, causing sudden separation.

On the other hand, for the C-0.5-20-50 mix (containing 0.5% fibers, 20% rubber, and 50% fly ash), the specimen displayed a more tortuous crack path near the center, with visible fiber pull-out and bridging between the fractured surfaces. The MSF enhanced tensile capacity and toughness by bridging cracks, delaying crack opening and propagation. The presence of rubber aggregates improved deformability and energy absorption, allowing the specimen to sustain higher strains before failure, despite the reduced matrix strength from the high fly ash content. For mix C-0.75-10-50 (0.75% fibers, 10% rubber, 50% fly ash), the failure was characterized by multiple micro-cracks and a less-defined fracture path. The higher fiber dosage significantly enhanced ductility and post-cracking toughness through effective crack-bridging, while the moderate rubber content contributed to increased energy dissipation. This combination resulted in delayed and more gradual failure compared to fiber-free mixes, confirming the synergistic effect of fibers and rubber in improving mechanical performance.

Figure 12 illustrates the flexural failure behavior of the tested specimens. Less ductile failure was observed in the C-0-0-25 mix (Figure 11a). The crack rapidly propagated through the tensile zone without significant warning or deformation, resulting in an abrupt loss of load-carrying capacity. This is primarily due to the absence of fiber and rubber aggregates which normally contribute to crack bridging and energy absorption during flexure. In contrast, the specimen of C-1-10-25 mix demonstrated a notably more ductile failure behavior. The presence of macro-synthetic fibers and rubber particles facilitated the development of multiple micro-cracks and crack-bridging mechanisms. The fibers effectively restrained crack opening and delayed fracture propagation, allowing the specimen to sustain higher deflections before failure. This resulted in gradual load reduction post-peak and enhanced toughness compared to the fiber-free mix.

4. Empirical Formulas to Predict the Strength of the FRRC

To facilitate practical applications and performance-based design of FRRC incorporating fly ash as a partial cement replacement, this study develops empirical formulas to calculate the splitting tensile and flexural strengths using a 0.5 power law model. In developing the empirical formulas, the test splitting tensile and flexural strengths of FRRC with fly ash were plotted against $\sqrt{f_c^{\prime }}$, in which $f_c^{\prime }$ is the compressive strength of concrete at 28 days as shown in Figure 13. Based on statistical analysis, a linear relationship is observed.

Finally, the expression to calculate the splitting tensile strength ($f_{ct}$) of concrete at 28 days is derived as follows:

(1)$f_{ct}=1.1686\sqrt{f_c^{\prime }}$

The accuracy of the proposed empirical formula is compared with ACI 318-19 [69], AS 3600-18 [70], and Choi et al. [71] to verify the accuracy of various empirical formulas in predicting the splitting tensile strength of FRRC with fly ash. The empirical formulas for ACI 318-19 [69], AS 3600-18 [70], and Choi, et al. [71] are given in Table 5.

The comparisons of the various empirical formulas to calculate the splitting tensile strength of FRRC with fly ash are compared against the test data in Figure 14. It is seen that the existing empirical formulas significantly underestimate the splitting tensile strength of FRRC with fly ash. On the contrary, the proposed empirical formula provides a close estimation of the splitting tensile strength of FRRC with fly ash obtained from the experimental program carried out in this study. When examining the accuracy of the proposed formula against the test data of FRRC reported by Wang et al. [13], and Alsaif et al. [72], it is observed that the proposed formula significantly overestimates the splitting tensile strength of FRRC. In addition, the splitting tensile strength of FRRC with fly ash obtained from this study is significantly higher than the ones tested by Wang, et al. [13], and Alsaif, et al. [72]. As mentioned earlier, inclusions of fly ash significantly increase the splitting tensile strength of FRRC. It should be noted that the FRRC mixes reported by Wang, et al. [13], and Alsaif, et al. [72] had no fly ash, thus showing a significant deviation from the prediction.

Similarly to tensile strength, based on the statistical analysis, the empirical formula to calculate the flexural strength of FRRC with fly ash is proposed as:

(2)$f_r=0.7856\sqrt{f_c^{\prime }}$

The accuracy of the proposed empirical formula as well as the empirical formulas specified by ACI 318-19 [69], AS 3600-18 [70], Xu et al. [73], and Perumal [74], as summarized in Table 6 are shown in Figure 15. It is observed that although Perumal [74] provides a better estimation of the flexural strength of FRRC with fly ash for compressive strength up to 50 MPa, the flexural strength is significantly overestimated beyond this limit. However, the proposed empirical formula provides the best estimation compared to all empirical formulas. When validating the accuracy of the proposed formula against the test data reported by Wang et al. [13], and Alsaif et al. [72], it is observed that the proposed formula can reasonably predict the flexural strength of FRRC. The inclusion of fly ash decreases the flexural strength of FRRC. The test data reported by Wang, et al. [13], and Alsaif, et al. [72] closely match the data reported in this study. Therefore, there is a good agreement between the prediction and the results reported by Wang, et al. [13], and Alsaif, et al. [72].

5. Carbon Footprint and Land-Saving Implications

There are carbon footprint and land-saving implications with the use of recycled tyres in concrete. The replacement of the best alternative option in terms of structural performance (i.e., 0.5-10-25) can save 14.4% GHG emissions (Figure 16). When using a controlled mix (0-0-0), the GHG emissions are 508 kg CO₂ equivalent (equ-) per m³ of concrete. In the case of the best alternative mix, the GHG emissions can be reduced to 435 kg CO₂ equ- mainly resulting from the replacement of 25% carbon-intensive cement. The recycled tyre does not contribute to GHG savings rather it increases GHG emissions. The emission factor of the recycled tyre (0.65 kg CO₂/kg of recycled tyre) is 51 times more than that of natural aggregates (0.0198 kg CO₂/kg of natural aggregates) [75,76]. This is because of the fact that the shredding of old tyres is a very energy-intensive process (i.e., 1 kWh/kg of shredded tyre) [76]. Since only 10% of natural aggregates were replaced with the recycled car tyre and one-quarter of carbon-intensive cement was replaced with fly ash, the overall GHG saving was achieved from the use of 0.5-10-25 mix. Nevertheless, the use of recycled tyre can offer significant land saving benefits as discussed below.

The amount of land saved associated with the diversion of recycled tyre waste from landfill to concrete batching plants has been determined. The estimation is based on the amount of land saved in quarries of the natural aggregates and the amount of landfill saved due to the diversion of recycled tyre waste. Around 140,000 tonnes of tyre waste are generated each in Western Australia [79]. It was estimated that what would be the amount of land that could be saved if these wastes were recycled into concrete aggregates.

About 0.55 m² of land is required to produce 1 tonne of gravel [80]. This value was multiplied by the amount of natural aggregates that can be replaced by the recycled tyre per year to calculate the amount of land that can be saved in the quarry area (A_q). The value of A_q was thus estimated to be 77 hectares.

In the case of landfill area saving, Equation (3) published by Paul et al. [81] was used. In this case, the shape of the landfill was considered to be a conical frustum and its volume (V) was calculated as,

(3)$V={\displaystyle \frac{1}{3}}\pi h[{\left({\displaystyle \frac{d}{2}}\right)}^2+{\left({\displaystyle \frac{D}{2}}\right)}^2+{\displaystyle \frac{dD}{2}}]$

where ‘D’ and ‘d’ are the top and bottom diameters, respectively. ‘d’ is equal to (D/2)-75 and h = 25 m.

The amount of recycled tyre in tonnes (140,000 tonnes) was converted to volume (116,667 m³) by multiplying by the density of the tyres. Once the value of ‘V’ in Equation (3) was obtained, the values for ‘d’ and ‘D’ were determined by using the ‘goal seek’ optimization tool in Excel. The following formula was used to calculate the amount of landfill area saved (A_lf), which is 1.5 Ha, due to the diversion of recycled tyre wastes for use in concrete (Equation (4)).

(4)$A_{lf}={\pi \left({\displaystyle \frac{D}{2}}\right)}^2$

Therefore, the total amount of land that can be saved both in quarry and landfill locations was calculated as, 77 Ha + 1.5 Ha = 79.5 Ha. As the population is increasing, the tyre wastes will increase proportionately. The use of these recycled car tyres in concrete can thus reduce a significant amount of ecological footprints resulting from human activities in the near future.

6. Conclusions

This study investigated the effects of partial cement replacement with fly ash on the mechanical performance and workability of fiber-reinforced rubberized concrete (FRRC) containing different percentages of waste tyre rubber aggregates and recycled macro-synthetic fibers. The key findings are summarized as follows:

Fly ash significantly improves workability across all the mixes, increasing slump from 140 mm (control) up to 200 mm at 50% replacement, even mitigating the flowability loss caused by rubber particles. However, increasing fiber content consistently reduced workability due to the physical obstruction of fibers, with the lowest slump recorded at 60 mm in high-rubber, high-fiber mixes.

Compressive strength was adversely affected by fly ash replacement, showing a decline from 60.53 MPa in the control to 29.73 MPa at 50% fly ash. Rubber further reduced compressive strength by introducing weak interfaces, with high-rubber mixes dropping to 12.46 MPa at 50% fly ash. Although fibers bridged microcracks and enhanced toughness, they could not fully offset strength loss caused by high fly ash and rubber content.

In contrast, tensile strength improved notably with 25% fly ash replacement, more than doubling from 3.01 MPa (control) to 7.71 MPa, attributed to improved matrix densification and enhanced fiber-matrix bonding. Increasing fly ash beyond 25% reduced tensile gains but still maintained values above the control. Rubber reduced tensile capacity due to poor bonding, yet fly ash partially mitigated this, while fibers consistently improved tensile resistance.

Flexural strength showed a decreasing trend with increasing FA content, falling from 5.26 MPa in the control to 3.09 MPa at 50% FA due to slower pozzolanic reaction of FA. However, fibers contributed significantly to maintaining flexural performance by enhancing crack bridging, especially at moderate fly ash levels, while rubber content weakened the matrix stiffness and bonding. The combined presence of fly ash and fibers helped offset rubber’s negative influence on flexural strength, highlighting the importance of a balanced mix design.

The developed empirical formulas for predicting tensile and flexural strengths of FRRC with fly ash showed superior accuracy compared to existing models, closely matching experimental data and enabling reliable performance-based design for sustainable FRRC applications.

The use of waste tyres in concrete can reduce around 14% of GHG emissions while maintaining structural integrity. This substitution also has a significant bearing in reducing ecological bearings. A gross estimate for Western Australia shows that about 80 hectares of land can be avoided through this recycling activity.

In conclusion, fly ash serves as a valuable SCM in FRRC by enhancing workability and tensile performance, while presenting challenges in compressive and flexural strength at high replacement levels. The synergistic use of fibers helps alleviate some mechanical drawbacks, highlighting the importance of optimizing mix proportions for sustainable and durable concrete. Future research should focus on long-term durability assessments, such as resistance to environmental degradation and extended curing effects to examine the long-term pozzolanic benefits of fly ash, as well as the exploration of alternative fibers and rubber particle treatments to improve composite bonding and mechanical resilience. In addition, the combinations of slag or silica fume with fly ash in the mechanical and durability of FRRC should be further studied.

Author Contributions

Conceptualization, M.A., W.B.; Methodology, M.A.,W.B.; Validation, M.A., W.B.; Formal analysis, M.A., W.B., N.J.M.; Investigation, M.A., W.B., N.J.M.; Data curation, M.A., N.J.M., W.B.; Writing—original draft, M.A., N.J.M., W.B.; Writing—review and editing, F.S., X.Z., V.I.P.; Visualization, W.B., F.S., X.Z., V.I.P.; Project administration, M.A., W.B. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.

Acknowledgments

The authors acknowledge the support provided by Flexiroc Australia by supplying shredded rubber and concrete mix design. The support from Enviromesh, formerly Fibercon is also acknowledged for supplying eMesh fibers used in this study.

Conflicts of Interest

The authors declare no conflicts of interest.

Footnotes

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Figures and Tables

Figure 1 MSF and rubber used in this study.

Figure 2 Particle distributions of aggregates as well as MSF and rubber used in this study.

Figure 3 Preparation of tested samples.

Figure 4 Slumps of normal and FRRC samples.

Figure 5 Setting up of tested samples under different loading conditions. (unit in mm).

Figure 6 Slump of tested samples. (Note: Blue represents density while orange represents slump).

Figure 7 Compressive strength of tested samples.

Figure 8 Splitting tensile strength of tested samples (a) actual strength (b) normalized strength.

Figure 9 Flexural strength of tested samples (a) actual strength (b) normalized strength.

Figure 10 Typical failure patterns of tested specimens under compression test.

Figure 11 Typical failure patterns of tested specimens under splitting tensile strength test.

Figure 12 Typical failure patterns of tested specimens under flexure test.

Figure 13 Relationships between compressive strength against splitting tensile strength and flexural strengths of FRRC.

Figure 14 Validating the accuracy of the proposed empirical formulas to predict the tensile strength of FRRC with fly ash with the test data reported in this study and reported by Wang et al. [13], and Alsaif, et al. [72].

Figure 15 Validating the accuracy of the proposed empirical formulas to predict the flexural strength of FRRC with fly ash with the test data reported in this study and reported by Wang et al. [13], and Alsaif, et al. [72].

Figure 16 Carbon footprints of controlled (0-0-0) and recycled tyre concrete (0.5-10-25) mixes. [Emission factors of these inpits were sourced from Grant [75], Loo et al. [76], Biswas et al. [77], Simms et al. [78]].

Table 1

Chemical composition of Portland cement and fly ash (by weight%) [46].

Component	Portland Cement	Fly Ash
CaO	64	0.9
SiO2	20.2	65.1
Al2O3	5.3	24.5
Fe2O3	2.7	4
MgO	1.4	0.6
MnO	-	0.07
K2O	-	1.17
Na2O	0.6	0.39
P2O5	-	0.4
TiO2	-	1.1
Cl	0.01	-
SO3		0.1
Others	0.25	0.37
Loss on ignition (LOI)	2.3	1.3

Table 2

Physical properties of Portland cement and fly ash.

Properties	Portland Cement	Fly Ash
Specific Gravity	2.5–3.2	2.35–2.40
Melting Point	>1200 °C	>1400 °C
Particle size	10–30% of Particles are ≤7 µm	40% of particles are ≤7 µm
Odor	Odorless	Odorless

Table 3

Normalized weight of materials relative to the weight of the cement for casting of 1 m³ volume of concrete and their measured density.

Sample	Rubber (%)	Fiber(%)	Cement	Fly Ash	Fine Aggregate	Coarse Aggregate	Rubber	MSF
C-0-0-0	0	0	1	0	1.96	2.04	0.00	0
C-0-0-25			0.75	0.25
C-0-0-50			0.5	0.5
C-0.25-10-0	10	0.25	1	0	1.96	1.86	0.07	0.0051
C-0.25-10-25			0.75	0.25
C-0.25-10-50			0.5	0.5
C-0.25-20-0	20		1	0	1.96	1.66	0.15
C-0.25-20-25			0.75	0.25
C-0.25-20-50			0.5	0.5
C-0.50-10-0	10	0.5	1	0	1.96	1.86	0.07	0.0102
C-0.50-10-25			0.75	0.25
C-0.50-10-50			0.5	0.5
C-0.50-20-0	20		1	0	1.96	1.66	0.15
C-0.50-20-25			0.75	0.25
C-0.50-20-50			0.5	0.5
C-0.75-10-0	10	0.75	1	0	1.96	1.86	0.07	0.0153
C-0.75-10-25			0.75	0.25
C-0.75-10-50			0.5	0.5
C-0.75-20-0	20		1	0	1.96	1.66	0.15
C-0.75-20-25			0.75	0.25
C-0.75-20-50			0.5	0.5
C-1-10-0	10	1	1	0	1.96	1.86	0.07	0.0204
C-1-10-25			0.75	0.25
C-1-10-50			0.5	0.5
C-1-20-0	20		1	0	1.96	1.66	0.15
C-1-20-25			0.75	0.25
C-1-20-50			0.5	0.5

Table 4

Comparison of compressive strength of rubberized concrete with varying fly ash content: experimental results vs. literature data.

Fly Ash (%)	Rubber Content(%)			Rubber Content (%)		Rubber Content(%)		Rubber Content(%)
	10–20	5–20	0–40	10–20	5–20	10–20	5–20	0–20	5–20	0–40
	Compressive Strength Range (MPa)			Splitting Tensile Strength Range (MPa)		Splitting Tensile Strength Range (MPa)	Flexural Strength Range (MPa)	Density (kg/m3)
	This Study	Study by Najmi et al. [55]	Study by Bala et al. [39]	This Study	Study by Najmi et al. [55]	This Study	Study by Najmi et al. [55]	This Study	Study by Najmi et al. [55]	Study by Bala et al. [39]
0	31.57–41.87	10.8–22.5	5.33–36.47	2.64–3.88	1.57–2.46	4.87–5.80	2.54–3.83	2183–2300	2030–2217	1611–2241
10	-	11.2–25.4	2.43–33.09	-	1.62–2.72	-	2.37–3.87	-	2077–2237	1696–2265
20	-	10.4–21.8	1.42–24.62	-	1.41–2.50	-	2.52–3.35	-	2051–2225	1786–2249
25	20.13–39.42	-	-	5.67–6.95	-	2.52–5.11	-	2177–2299	-	-
30	-	9.2–19.4	1.20–22.43	-	1.18–2.33	-	2.09–3.24	-	2011–2186	1769–2279
40	-	-	-	-	-	-	-	-	-	-
50	12.46–24.94	-	-	4.44–5.86	-	3.15–5.12	-	2170–2287	-	-

Table 5

Existing empirical formulas specified to calculate tensile strength.

Model	Equation
ACI 318-19 [69]	$f_{ct,ACI}=0.62\sqrt{f_c^{\prime }}$
AS 3600-18 [70]	$f_{ct,AS3600}=0.6\sqrt{f_c^{\prime }}$
Choi et al. [71]	$f_{ct,Choi}=0.55\sqrt{f_c^{\prime }}$

Table 6

Existing empirical formulas specified to calculate flexural strength.

Model	Equation
ACI 318-19 [69]	$f_{r,ACI}=0.62\sqrt{f_c^{\prime }}$
AS 3600-18 [70]	$f_{r,AS3600}=0.6\sqrt{f_c^{\prime }}$
Xu et al. [73]	$f_{r,Xu}=0.39{(f_c^{\prime })}^{0.59}$
Perumal [74]	$f_{r,Perumal}=0.259{(f_c^{\prime })}^{0.843}$

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