Flexural Performance of Tunnel lining Segments using Fiber Reinforced Concrete: A Study on Recycled and Industrial Fibers Through Experimental and Numerical Methods

Flexural Performance of Tunnel lining Segments using Fiber Reinforced Concrete: A Study on Recycled and Industrial Fibers Through Experimental and Numerical Methods | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Flexural Performance of Tunnel lining Segments using Fiber Reinforced Concrete: A Study on Recycled and Industrial Fibers Through Experimental and Numerical Methods Alireza Ahmadi, Amin Tohidi, Hassan Negahdar, Mohammad Reza Shakeri This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4808296/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This study investigates the flexural performance of metro tunnel segments reinforced with traditional rebar and fiber-reinforced concrete (FRC). Utilizing a comprehensive experimental approach, the mechanical properties of FRC were determined and compared with ordinary concrete through rigorous laboratory tests. A detailed numerical analysis was conducted using a 3D finite element model (FEM) in ABAQUS 2022, validated with experimental data. The FEM assessed segments reinforced with traditional rebar versus those with a 50% reduction in rebar, supplemented by FRC. The Concrete Damage Plasticity (CDP) model effectively simulated the flexural behavior, revealing a 30% reduction in tensile damage with FRC. Further analysis revealed significant improvements in stress responses, including a 2.6-fold increase in von Mises stress and a 60% reduction in vertical displacement. These findings highlight the enhanced structural performance and economic benefits of incorporating FRC with reduced rebar, as well as the environmental advantages of using recycled fibers. This study provides critical insights into optimizing tunnel segment reinforcement, promoting both structural integrity and sustainability in tunnel construction projects. Tunnel lining segment Flexural performance Recycled steel fiber Hybrid fiber reinforced concrete Finite Element Method (FEM) Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Figure 15 Figure 16 Figure 17 Figure 18 1. Introduction Mechanized Tunnel linings, typically made of precast segments connected by bolts and reinforced with steel bars to withstand loads. Tunneling and Underground Space Association highlights that these steel-reinforced segments are prone to corrosion, leading to concrete spalling and reduced structural capacity. Additionally, tunnel segments experience tension during stages like demolding, storage, and transport, causing cracking and maintenance issues. Steel rebar also incurs significant financial and environmental costs. During their service life, tunnel segments primarily endure flexural loading, resulting in tensile stress. Despite concrete's high compressive strength, its low tensile strength and brittleness lead to cracking and potential failure under tension, compromising structural integrity. Fiber reinforcement significantly enhances concrete's mechanical properties, improving both tensile and compressive strength. Incorporating fibers offers several benefits: it improves non-linear structural behavior in tension by reducing crack width and preventing crack propagation; it boosts post-cracking residual strength through a bridging effect; and it increases concrete's overall toughness via fiber debonding and pull-out mechanisms (Pujadas, Blanco et al. 2014, Blanco, Pujadas et al. 2016). These enhancements depend on the bond strength, mechanical properties, and quantity of fibers intersecting a crack. Innovative steel fiber geometries, such as hooked, crimped, and undulated shapes, show promise in improving Fiber Reinforced Concrete (FRC) performance. Hooked fibers enhance interlock within the concrete matrix, while crimped fibers improve the bond between concrete and fibers. These advancements in fiber reinforcement offer a durable and reliable solution, addressing the limitations of conventional steel bar reinforcement (Pujadas, Blanco et al. 2014, Blanco, Pujadas et al. 2016).Nowadays, it is well established that incorporating steel fibers significantly improves the engineering performance of both structural and nonstructural concrete. These enhancements include better crack resistance, increased ductility and toughness, and improved fatigue and impact resistance (Song and Hwang 2004 , Chen and Liu 2005 , Thomas and Ramaswamy 2007 , Asheghi Mehmandari, Fahimifar et al. 2020). (Thomas and Ramaswamy 2007 ) reported that in their study, the maximum increase in compressive strength of steel fiber reinforced concrete was less than 10%. However, they observed a remarkable improvement of about 40% in the splitting tensile strength and flexural strength, along with an enhanced post-cracking response. (Centonze, Leone et al. 2012) concluded that recycled steel fibers can be promising materials for concrete, as they improve the mechanical properties of the brittle matrix in both structural and nonstructural applications. (Sengul 2016 ) investigated the mechanical performance of fiber reinforced concrete incorporating various geometrical configurations and percentages of steel fibers obtained from scrap tires. These studies collectively underscore the significant potential of steel fibers in enhancing the mechanical properties and overall performance of concrete. Recycling steel from waste automobile tires has gained attention for its environmental benefits and waste management solutions. Tires contain substantial steel, and recycling this steel offers an eco-friendly, cost-effective alternative to traditional steel fibers, with recycled steel fibers showing comparable mechanical properties to industrial ones. The typical car tire lasts around five years, and over 90 million motor vehicles were produced in 2014, with numbers expected to rise(Weissman, Sackman et al. 2003, Asheghi Mehmandari 2023 ). With an estimated 1.2 billion vehicles on the road, over 4.8 billion tires are in use, and around 4 billion used tires are generated annually. The increase in vehicle production suggests a growing number of used tires. Some used tires can be reused, but many become end-of-life tires, posing disposal challenges. Landfilling or stockpiling these tires is banned in Europe and the US (Floess, Hasenbein et al. 2007, Schiopu and Gavrilescu 2010 ). Recycling rates of scrap tires have surpassed 85% in the US, Europe, and Japan due to stricter laws, economic benefits, and environmental awareness (Benschneider, Wbcsd 2010 , Nguyen, De Vanssay et al. 2015). A typical tire consists of 47% rubber, 22% carbon black, 17% steel cords, 5% fabrics, and various additives (Evans and Evans 2006 ).The concept of hybrid fiber reinforcement, which integrates different types of fibers, considering their modulus (high or low value) or geometrical size (e.g., macro and micro), offers a promising approach to enhance the performance characteristics of composite materials (Lawler, Wilhelm et al. 2003, Behboudi, Zad et al. 2024, Behboudi, Zad et al. 2024) Compared to Mono Fiber Reinforced Concrete (MFRC), Hybrid Fiber Reinforced Concrete (HFRC) demonstrates superior compressive and tensile strength (Libre, Shekarchi et al. 2011, Mehmandari, Shokouhian et al. 2024), improved flexural and impact resistance, and enhanced durability These types of concrete provide synergistic improvements in material properties (Afroughsabet and Ozbakkaloglu 2015 , Amjadi, Mohammadkhanifard et al. 2023). For example, combining steel fibers and polypropylene fibers in concrete has been shown to boost both strength and ductility, offering a balanced improvement over using a single type of fiber. This hybrid approach capitalizes on the strengths of each fiber type, optimizing the overall performance of the composite material. Despite the potential benefits, the combined use of recycled and industrial steel fibers in HFRC has been underexplored. This gap presents an opportunity for innovation, aiming to achieve sustainability and cost-efficiency in construction materials. By investigating the individual and collective impacts of recycled and industrial steel fibers, this research seeks to advance the development of high-performance, eco-friendly concrete solutions. Kang et al. (Kang, Choi et al. 2016) investigated the effect of hybrid combinations of steel fiber and various microfibers on the mechanical properties of HFRC, finding that steel fiber significantly enhanced the tensile behavior when mixed with high-strength synthetic fibers like polypropylene (PP). (Li, Li et al. 2017 ) blended steel fiber with two types of microfibers into a concrete composite, demonstrating marked improvements in strength and toughness under shear, tensile, and flexural conditions. (Rashiddadash, Ramezanianpour et al. 2014) combined steel fiber with polypropylene fiber, reporting superior mechanical properties in HFRC with higher steel fiber content. (Lawler, Zampini et al. 2005) asserted that HFRC has greater strength and crack resistance than matrices reinforced only with macro fibers, due to the presence of microfibers. In hybrid fiber reinforced concrete, microfibers bridge microcracks, increasing initial cracking strength and reducing shrinkage, while microfibers prevent macrocrack propagation, enhancing toughness and post-cracking performance. (Sivakumar and Santhanam 2007 ) studied high-strength concrete reinforced with steel fibers (30 mm) and non-metallic fibers (6–20 mm), such as micro polypropylene, polyester, and glass fibers. They found the steel-polypropylene fiber combination to be the most effective. (Qian and Stroeven 2000 ) evaluated concrete with hybrid fibers, including micro polypropylene and various steel fibers. Their results indicated that smaller steel fibers (6 mm) improved compressive strength, while larger steel fibers (30 and 40 mm) enhanced post-cracking strength. They also identified the optimal dosage of micro polypropylene fibers for the best performance. Several studies have explored the impact of fiber addition on tunnel segment construction. The inclusion of fibers enhances structural performance while reducing overall construction costs by minimizing the need for rebars (Cavalaro, Blom et al. 2012, De la Fuente, Pujadas et al. 2012, Meda, Rinaldi et al. 2016, Meng, Gao et al. 2016). (Beňo and Hilar 2013 ) conducted a numerical and laboratory study on SFRC samples, subjecting them to compressive, tensile, and flexural strength tests. Their findings indicated that lower fiber dosages resulted in better mixing performance with reduced dispersion properties, whereas higher doses improved final characteristics. (Beňo and Hilar 2013 ) investigated the behavior of segments under TBM thrust jacks using experiments on rectangular cube samples, comparing those with and without fibers under linear and localized loads. (Conforti, Tiberti et al. 2017) also explored the feasibility of employing polypropylene fibers in segments. Advances in scientific computing have enabled numerical simulations to study structural behavior and cracking during segment construction stages, yielding valuable insights. Finite element analysis has been extensively used to simulate axial forces exerted by tunnel boring machines (Gettu, Barragán et al. 2004, Sorelli and Toutlemonde 2005 , Bakhshi and Nasri 2014 , Zare, Asheghi et al. 2020, Mohammadifar, Asheghi Mehmandari et al. 2024 ). Previous studies assessing the performance of segmental linings in tunnels have often overlooked a comprehensive evaluation of the technical, environmental, and economic aspects of fiber-reinforced concrete. Given the high cost associated with industrial fibers, there is a growing necessity to explore the viability of using recycled fibers as substitutes. The primary objective of this study is to deepen our understanding of the effects of various types of fibers, including hybrid and recycled tire fibers, on the performance of segmental linings. Specifically, the focus is on evaluating the mechanical performance, with a particular emphasis on flexural behavior under laboratory conditions. To achieve this goal, recycled and hybrid fiber-reinforced concretes were evaluated in laboratory experiments. The investigation also extends to the performance of segmental linings using a finite element model of a tunnel. This model employs the Concrete Damage Plasticity (CDP) constitutive model, integrating traditional rebars and an optimized mix design outcome from experimental flexural loading tests. The aim is to explore mechanical performance, conduct damage analysis, and investigate ductility. 2. Experimental investigation 2.1. Recycled steel tire fiber (RSTF) and double hook-end steel fiber (STF) Recycled steel fibers from waste tires, recovered through a shredding process followed by electromagnetic separation from the rubber. The resulting steel fibers, illustrated in Table 1 , exhibit diverse diameters, lengths, and shapes, with noticeable irregular wrinkles. A preliminary statistical analysis was conducted to evaluate the geometric variability of these fibers after shredding, without any further treatment. This characterization is crucial for defining appropriate treatments to improve the final properties of concrete reinforced with these fibers. A sample of approximately 500 steel fibers was randomly selected for analysis. Each fiber’s diameter was measured using a micrometer, with three measurements taken at both extremities and the midpoint to obtain an average diameter. The fiber diameters ranged from 0.3 to 0.36 mm, with the majority (65%) falling within the 0.32 to 0.34 mm range. The fibers length exhibited a wide range, from 20 to 40 mm, with the most frequent length being 32 mm, observed in 55% of the fibers. Table 1 provides a detailed summary of the geometric and shape characteristics of the analyzed fibers. This characterization serves as a foundation for identifying suitable treatments to optimize the performance of concrete reinforced with these recycled steel fibers. A double hook-end steel fiber with an aspect ratio of 87.5 was utilized in this study. These fibers are industrially industrial, ensuring uniformity in their geometric and mechanical properties. The fibers’ consistent shape and precise geometric characteristics contribute to their reliability in reinforcing concrete. Table 2 details the specific geometrical and mechanical properties of these fibers, underscoring their suitability for enhancing the performance of concrete composites. 2.2. Cement, aggregate and superplasticizer In this study, CEM I 52.5N Portland cement, provided by Kordestan Cement Industries Company, was utilized. A polycarboxylate ether-based superplasticizer (SP) was incorporated in varying amounts ranging from 0.2–2%. All concrete mixtures included crushed limestone aggregate, with a maximum grain size of 25 mm, as verified by an ASTM C136/C136M-19 sieve analysis. Figure 1 depicts the aforementioned materials utilized in this study. Figure 1. The row materials of concrete and additive. 2.3. Mixture design Table 3 presents the mix ratios for seven distinct concrete mixtures, all designed with a consistent water-to-binder ratio of 0.340. These mixtures include Ordinary Concrete (OC) and various fiber-reinforced concretes, with fiber contents ranging from 0.25–0.5% by volume fraction (vf). "OC" refers to the standard concrete mix without any fiber reinforcement, while the other mixtures incorporate recycled steel tire fibers and industrial double-hooked end steel fibers, either singly or in hybrid combinations. For instance, "R5" denotes a mixture with 0.5% volume content of solely recycled steel tire fibers, "S5" signifies a mixture with 0.5% volume content of solely industrial double-hooked end steel fibers, and "(SR)5" represents a mixture with a 0.5% volume content hybrid of recycled and industrial fibers in equal proportions. In these mixtures, the fiber weight is determined based on the density, resulting in 39 kg of fiber used for a 0.5% volume content (0.5% * 7800 kg/m³). Superplasticizer (SP) was added to the mixes at dosages ranging from 0.5–1% by weight of cement, and all mixtures were homogenized using a pan mixer. To assess the workability of both ordinary and fiber-reinforced concretes, unit weight and slump tests were conducted on the fresh concrete samples. This standardized approach ensures a consistent evaluation of the concrete mixtures, facilitating a comprehensive comparison of their properties and performance. Table 3 The mixtures proportions of the Ordinary and FRC mixtures. Mix Description Sample Code C (kg/m 3 ) W (kg/m 3 ) CS (kg/m 3 ) FS (kg/m3) RSTF (kg/m3) STF (kg/m 3 ) SP (kg/ m 3 ) Ordinary Concrete OC 340 144.36 728.9 1013.4 0 0 2.8 Single RSTF Low Vf (0.25) R 2.5 340 144.36 728.9 1009.5 17.25 0 2.8 Single RSTF High Vf (0.5) R 5 340 144.36 728.9 1009.5 34.5 0 2.8 Single STF Low Vf(0.25) S 2.5 340 144.36 728.9 1009.5 0 19.5 2.8 Single STF High Vf (0.5) S 5 340 144.36 728.9 1005.8 0 39 3.3 Hybrid of RSTF and STF low Vf(0.25) (SR) 2.5 340 144.36 728.9 1005.8 8.63 9.75 3.3 Hybrid of RSTF and STF high Vf (0.5) (SR) 5 340 144.36 728.9 1005.8 17.25 19.5 3.3 C: Cement, W: Water, CS: Coarse Sand, FS: Fine Sand, RTSF: Recycled Steel Fiber, STF: hooked end Steel Fiber The experimental procedure began with dry mixing the cement and aggregates for 2 minutes. Subsequently, superplasticizer (SP) and water were added, and the mixture was blended for an additional 3 minutes. Following this, steel fibers were incorporated into the mix and stirred for a further 3 minutes to ensure uniform distribution throughout the mixture. The homogeneous mix was then poured into beam molds and subjected to vibration on a shaking table to eliminate air pockets. The samples were kept in the molds for 24 hours before demolding. Post-demolding, the specimens underwent water curing at a controlled temperature of 20 ± 2°C for 28 days. For strength evaluations, each mix type was represented by three beams with dimensions of 500 mm x 100 mm x 100 mm, and six cylindrical molds measuring 200 mm x 100 mm were prepared for uniaxial compressive tests and split tensile (Brazilian) tests. The results were averaged across the three samples per mix type.Beam deflections under three-point loading were measured using a linear variable differential transformer (LVDT) positioned at the midspan. The tests were conducted with Dartec-9600 servo control devices, which have a maximum capacity of 1000 kN, at the Rock Mechanics Laboratory of Amirkabir University of Technology. Figure 2 illustrates the loading machine utilized in the experimental process of this study. 3. Experimental result and discussion This study aims to examine the physical, mechanical, and ductility properties of fiber-reinforced concrete compared to ordinary concrete. The investigation involves three-point bending tests, uniaxial compressive tests, and splitting tensile tests. The results of these tests are presented in Table 4 . Table 4 Physical and mechanical properties of ordinary and FRC specimens. Mix Description Unit Weight Slump Compressive Strength Increase Tensile Strength Increase Flexural Strength Increase (kg/m3) (mm) (MPa) (%) (MPa) (%) (MPa) (%) OC 2378 105 46.41 0.0 3.92 0.0 6.17 0.0 S 2.5 2378 92 60.16 29.62 0.0 0.0 12.15 96.92 (SR) 2.5 2375 86 60.06 29.41 5.18 32.14 11.05 79.09 R 2.5 2382 75 56.84 22.47 4.91 25.25 10.48 69.85 S 5 2375 73 62.29 34.21 6.78 72.95 12.22 98.05 (SR) 5 2371 90 70.22 51.30 6.51 66.07 11.49 86.22 R 5 2369 75 58.25 25.51 6.28 60.20 10.71 73.58 3.1. Experimental Analysis of Compressive Performance Uniaxial compressive tests were conducted using a Dartec 9600 servo-controlled machine, adhering to ASTM C39 standards, with a constant loading rate of 0.004 mm/s. Load, stroke, and time data were recorded at a frequency of four readings per second until failure, providing comprehensive insights into the specimens' resilience. The results, presented in Table 5 , illustrate the strength and strain during both the pre-peak (initial crack occurrence) and peak (maximum strength) phases. Notably, the specimens predominantly failed through shear or tensile modes due to Poisson’s effect, rather than through compressive failure. This underscores the role of fiber reinforcement in mitigating failure during compression tests. Table 5 Compressive strength and strain values of Ordinary and FRC specimens based on experimental results and ASTM C39 standard. Reinforcing Type Mix Description Pre-Peak Peak Strength (Mpa) Strain Strength (Mpa) Strain ----------- OC 46.41 - 46.41 0.011477 Single S 2.5 24.76 0.007212 60.13 0.011333 Hybrid (SR) 2.5 38.38 0.009548 60.04 0.014158 Single R 2.5 14.84 0.005186 56.83 0.013706 Single S5 25.15 0.007285 62.29 0.010927 Hybrid (SR)5 32.64 0.008663 70.18 0.011676 Single R5 18.83 0.006097 58.23 0.015243 3.1.1 Fiber content effect on compression strength Figure 3 depicts the influence of fiber content on the compressive strength of fiber-reinforced concrete samples categorized by their reinforcement methods. The data indicate a consistent improvement in compressive strength for FRC samples compared to ordinary concrete samples. In single-fiber mixtures, there is a negligible difference in peak compressive strength between low-fiber and high-fiber samples, indicating that increasing the fiber content does not significantly enhance strength. Conversely, hybrid fiber samples exhibit more complex behavior; notably, the (SR)5 sample demonstrates a 17% higher peak compressive strength compared to the (SR)2.5 sample. The effect of fiber content on pre-peak compressive strength varies significantly. In single-STF samples, both S2.5 and S5 exhibit similar strengths, indicating that increasing fiber content does not notably impact pre-peak strength in these samples. However, in single-RSTF specimens, higher fiber content leads to a 27% increase in pre-peak strength. This improvement is attributed to RSTF's ability to delay crack initiation, highlighting its effectiveness in enhancing pre-peak strength. Among the samples, the (SR)2.5 specimen, with its lower fiber content and hybrid approach, emerges as the most balanced option in terms of compressive strength. The influence of fiber content on compressive strength remains somewhat ambiguous, primarily because failure patterns are significantly affected by the quality of fiber distribution within the uniaxial compressive FRC samples. 3.1.2. Hybridization effect on compression strength Figure 4 presents the pre-peak and peak compressive strength results as a function of fiber content, showing that hybrid samples consistently outperform single-fiber ones. Notably, the hybrid (SR)2.5 sample achieves a 55% higher pre-peak strength compared to the best-performing single-fiber sample, S5. For low-fiber samples, peak strengths are comparable, with the hybrid (SR)2.5 exhibiting a slight advantage. This trend is also observed in high-fiber specimens, where the (SR)5 hybrid sample surpasses single-fiber samples by 30% in pre-peak strength and 13% in peak strength. These findings underscore the superior performance of hybrid fiber reinforcement in enhancing compressive strength. The enhanced performance of the hybrid fiber-reinforced concrete samples can be attributed to the distinct properties of the fibers and the mechanics of the uniaxial compressive test. During this test, pre-peak strength is associated with the initial formation of micro vertical cracks, which occur due to the material's horizontal expansion under vertical load. Recycled fibers mitigate these cracks by evenly distributing tensile stress, allowing the material to endure higher compressive stresses before cracking occurs. As vertical cracks develop into significant fractures, industrial fibers become crucial in maintaining the sample's integrity, thereby enhancing peak strength. This synergy in hybrid samples results in superior peak compressive strength. 3.2. Experimental analysis of tensile performance Table 6 presents the results of the splitting tensile test, detailing the strength and strain values at pre-peak, peak, and post-peak stages. The pre-peak point corresponds to the moment when the first crack is observed in the sample. The peak point indicates the maximum splitting tensile strength achieved by the sample. The post-peak point is defined as the stage where the sample's load-bearing capacity drops to 20% of its maximum load. Table 6 Splitting tensile strength and strain values of ordinary and FRC specimens based on experimental results and ASTM C496 standard. Reinforcing Type Mix Description Pre-Peak Peak Post peak Strength (f pre ) (Mpa) Strain (%) Strength (f peak ) (Mpa) Strain (%) Strength (f post ) (Mpa) Strain (%) −−−−−−−−−−− OC 3.82 0.007 3.92 0.007 0 0 Single S 2.5 4.46 0.02 5.46 0.15 1.09 0.26 Hybrid (SR) 2.5 5.04 0.057 5.18 0.13 1.04 0.24 Single R 2.5 4.45 0.019 4.91 0.061 0.98 0.18 Single S 5 5.31 0.064 6.78 0.16 1.36 0.31 Hybrid (SR) 5 5.46 0.068 6.51 0.14 1.30 0.28 Single R 5 5.33 0.041 6.28 0.08 1.26 0.21 The splitting tensile test provides unique insights into tensile strength by concentrating stress in a localized manner, resulting in lower tensile strength due to the induction of multiple cracks around the specimen's circumference. This differs from tests such as the three-point bending test, where stress is more uniformly distributed. Consequently, the splitting tensile test uniquely evaluates the failure mechanism and the influence of fiber content and reinforcement approach on tensile behavior. 3.2.1 Fiber content effect on tensile strength Figure 5 illustrates that fiber-reinforced concrete samples surpass ordinary concrete in strength parameters, underscoring the advantages of fiber reinforcement. In ordinary concrete, the narrow margin between pre-peak (fpre) and peak (fpeak) strengths indicates that peak strength is reached almost immediately after the first crack forms, demonstrating a brittle behavior characterized by a low fpre value, which is undesirable. Increasing the fiber content enhances both pre-peak and peak tensile strengths in concrete, regardless of whether a single or hybrid fiber approach is employed. This enhancement is particularly pronounced in splitting tensile tests, where larger sections of the concrete are subjected to tensile stress due to the test's nature. The presence of more fibers effectively mitigates crack formation across these stressed areas, underscoring their critical role in sustaining tensile stress and emphasizing the importance of adequate fiber content in enhancing structural integrity. Insufficient fiber content proves inadequate in preventing cracks throughout the entirety of the tensile stress-affected regions, as depicted in Fig. 5 . 3.2.2 Hybridization effect on tensile strength Figure 6 demonstrates that hybrid samples, which combine recycled steel fibers with industrial double hooked end steel fibers, exhibit notable enhancements in pre-peak tensile strength across both low and high fiber content categories. Specifically, the (SR)2.5 and (SR)5 samples show increases of approximately 13% and 26% in pre-peak strength, respectively. This improvement is attributed to the synergistic effects of these fibers: the smooth-surfaced STFs effectively target primary weak points in crack-prone areas, while the rough RSTFs enhance interlocking at lower stress levels, thereby better controlling and distributing micro-cracks before reaching peak stress levels. In terms of peak and post-peak tensile strengths, the hybrid fiber approach demonstrates moderate results, primarily attributed to the superior capability of STF to effectively manage and span larger cracks. In contrast, recycled steel fibers, with their smaller dimensions, exhibit less effectiveness in this regard but excel in distributing stress at a micro-scale. As a result, the hybrid method achieves a balanced performance in splitting tensile strength during both peak and post-peak phases, capitalizing on the strengths of each fiber type to achieve an intermediate outcome. However, the variation in fp among different fiber reinforcement approaches remains minimal, owing to the relatively small crack sizes observed in the splitting tensile test, where recycled steel fibers prove effective in bridging these cracks. 3.3. Experimental analysis of flexural performance This section focuses on assessing the strength and properties derived from three-point bending tests, along with the corresponding flexural behavior curves for each specimen. The flexural strength (f) is computed using Eq. ( 1 ), with specific deflection values serving as key indicators in this analysis. These indices include fL/600, fp, and fL/150, corresponding to the bending strengths at deflections of δL/600 (0.5 mm), peak deflection (δpeak), and δL/150 (2 mm), respectively. By evaluating these indices, we obtain a comprehensive understanding of the material's response to flexural loading. The parameter fL/600 offers insights into the material's initial response, capturing its bending strength at an early stage of deflection. The fp value signifies the peak deflection, indicating the maximum strength the material can sustain before significant damage or cracking occurs. Lastly, fL/150 and the ultimate deflection values provide critical information on the material's behavior at larger deflections, demonstrating its ability to maintain structural integrity and absorb energy as deformation progresses. This detailed analysis of flexural strengths at various deflection points enables a thorough characterization of the material's mechanical performance under bending stresses. $$\:f=\frac{3pL}{2b{h}^{2}}$$ 1 Figure 7 shows flexural stress-deflection curves for ordinary and fiber-reinforced concrete specimens, highlighting fibers' role in enhancing flexural capacity and ductility. Further details on flexural behavior improvement are discussed later. Table 7 provides detailed information on the flexural strength and toughness of both ordinary concrete and fiber-reinforced concrete specimens at four critical points, including Ttotal, which represents the total energy absorption across the entire flexural stress-deflection curve. Ordinary concrete demonstrates limited ductility, failing at a peak deflection of 0.203 mm, falling short of the δL/600 (0.5 mm) and δL/150 (2 mm) thresholds, thereby preventing further evaluation of toughness at these stages. In contrast, fiber reinforcement enhances concrete ductility, as evidenced in Fig. 7 and Table 7 . FRC outperforms ordinary concrete in terms of strength, ductility, and toughness. Ordinary concrete typically fails abruptly, whereas FRC maintains strength and ductility at higher deflections, thereby enhancing flexural performance. This improvement is evident in the toughness values, with ordinary concrete exhibiting low toughness due to its brittleness, in contrast to the significantly higher toughness observed in FRC. Table 7 Flexural strength and toughness indexes of ordinary and FRC specimens based on experimental results and ASTM C 1609 standard. Mixture ID δ L/600 (0.5mm) δ peak (mm) δ L/150 ( 2mm) δ u (mm) Total f L/600 (MPa) T 600 (N.m) f p (MPa) T pre (N.m) f L/150 (MPa) T 150 (N.m) f u (MPa) T post (N.m) T total (N.m) OC 0 0 6.17 0.7258 0 0 0 0 0.7258 S2.5 8.46 1.5632 12.15 2.9586 2.07 8.0891 0.25 9.2704 12.229 (SR)2.5 8.83 1.5198 11.05 2.2662 1.69 6.9678 0.42 8.7137 10.98 R2.5 3.25 1.7841 10.48 1.3882 0.91 4.2550 0.15 4.7999 6.188 S5 10.88 1.9342 12.22 5.6497 9.27 17.8014 1.09 35.4892 41.139 (SR)5 9.08 1.7095 11.49 2.5411 3.65 11.1146 0.46 15.5125 18.0536 R5 6.21 2.4919 10.71 1.5691 2.51 8.1995 0.43 12.1011 13.6702 3.3.1 Fiber content effect on flexural strength Figure 8 demonstrates that higher fiber content in single-fiber FRC samples significantly increase pre-peak strength (f 600 ), indicative of crack initiation strength. Specifically, FRCs with only RSTF saw this strength nearly double with a doubled fiber content. Single-STF specimens showed a 28% increase in crack initiation strength with doubled fiber content, whereas hybrid samples experienced a marginal 3% increase. Regarding peak strength (f p ), none of the three approaches single-STF, single-RSTF, and hybrid—show significant improvement in f p , with hybrid samples displaying a modest 4% increase at most. Yet, the presence of fibers distinctly enhances f p compared to ordinary concrete, which obtains an f p nearly 40% lower than the lowest FRC specimen. The impact of fiber content on f p is nuanced; too much fiber contents may negatively affect f p by disrupting the aggregate-cement bond and causing a heterogeneous FRC behavior, leading to a weaker concrete matrix and reduced f p at lower stress levels. Consequently, excessive fiber content is as detrimental as none in terms of f p . Both 0.25% vf and 0.5% vf fiber content achieve comparable f p stresses, suggesting these can be near-optimal values for fiber contents for achieving optimal f p . All samples showed significant improvement in post-peak strength (f 150 ) with increased fiber content. Specifically, single-STF samples saw a 350% increase in f 150 . Single-RSTF and hybrid samples also doubled their strength with higher fiber content. These results underscore STF's impact on the post-peak flexural strength of FRC specimens, attributed to the double-hooked ends of the fibers preventing complete pull-out and enhancing load resistance without losing bond to the concrete matrix. This is particularly evident when comparing S2.5 and S5 samples, highlighting a marked enhancement in f 150 with fiber content increase. All FRC samples, behave in a way that an ultimate strength (f u ) can be associated to them. However, the ordinary concrete sample shows a brittle behaviour and no ultimate strength (f u ) can be recorded. In short, while low-fiber mixtures in FRC perform comparably in their elastic zone to others, high-fiber mixes more significantly enhance plastic behavior. Both high and low fiber samples significantly improve both plastic and elastic behaviors over ordinary concrete. 3.3.2. Hybridization effect on flexural strength Figure 9 highlights the importance of comparing single-fiber and hybrid approaches in FRC. In the low-fiber group of FRC samples, the hybrid mixture's pre-peak flexural strength is notably higher than single-fiber samples. This superior performance suggests that the hybrid approach, leveraging both STF and RSTF, results in enhanced structural behavior under pre-peak loads. Although the peak strength of the hybrid (SR) 2.5 mix is on par with single-fiber mixtures, it is achieved with half the amount of STFs used in S2.5, making it advantageous. Furthermore, the hybrid sample registers the highest ultimate flexural strength, indicating that the FRC sustains less damage when utilizing a combination of fiber types. In high-fiber samples, particularly in the (SR)5 hybrid approach, results indicate an intermediate outcome between those of single-straight steel fibers (STF) and single-recycled steel fibers (RSTF). However, values for f600 and fp demonstrate closer similarity to the single-STF approach, while the f150 value in (SR)5 aligns more closely with the behavior observed in the R5 samples. These findings underscore that in higher fiber content scenarios, which correlate directly with increased STF content, STF play a more substantial role in influencing the flexural post-peak behavior of FRC samples. This observation highlights the potential of STFs to enhance post-peak ductility and provides justification for the f150 values observed in the (SR)5 samples. Furthermore, it is noteworthy that all hybrid samples exhibit higher pre-peak strength compared to the peak strength of ordinary concrete, indicating greater resistance to crack initiation in hybrid mixes relative to ordinary concrete. 4. Numerical Analysis The flexural properties of tunnel segments were analyzed using a 3D finite element model developed with ABAQUS 2022 software (Smith M. ABAQUS / Standard User’s Manual. Dassault Syst`emes Simulia Corp and 2022 2022). This study compared two types of reinforced segments within the finite element models: segments reinforced with traditional rebar in real-world conditions using ordinary concrete, and segments with a 50% reduction in traditional rebar, employing optimized fiber-reinforced concrete mix design of previous section. Notably, a comprehensive analysis of the mechanical properties of fiber-reinforced concrete (FRC) and ordinary concrete, presented in the previous section, demonstrated that the hybrid use of FRC outperformed the single-use forms, both in high and low volume content mixtures. Based on these findings, the material properties for both ordinary concrete and the optimized fiber-reinforced concrete mix (SR)5 were used in this section. Therefore, all references to FRC in this part of the study pertain to the optimized (SR)5 mix design. 4.1 validation of model by comparison between the numerical and experimental data through three-point bending analysis To ensure the fidelity of the numerical analyses conducted in this study, three-point bending tests were employed for verification, specifically tailored to the ordinary and optimized FRC samples from the experimental phase, denoted as (SR) 5 . This validation step confirms that the model's predictions of the flexural performance closely align with the observed experimental outcomes. Comparative assessments were made between the data obtained from experimental tests and numerical analyses. Two beams, one composed of ordinary concrete and the other of fiber-reinforced concrete, underwent three-point loading conditions both in a laboratory setting and through finite element software simulations. A comprehensive finite element model was developed for the three-point bending test, employing the C3D8R mesh designation. This element type was chosen for its robustness in accurately capturing the intricate behavior of concrete under flexural stress, closely mirroring laboratory test conditions. The simulation replicates real-world scenarios by using two robust steel roller supports that mimic the experimental setup precisely. The Concrete Damage Plasticity model was utilized to analyze the deformation behavior of both ordinary and FRC samples. This constitutive model enables a detailed depiction of concrete's cracking and crushing behavior under stress, facilitating an accurate simulation of damage and eventual failure. The CDP parameters were calibrated using empirical data to ensure alignment between the model's predictions and observed physical phenomena. The numerical models were leveraged to extrapolate maximum deflection and flexural strength, pivotal indicators of structural performance. The model's predictive capability was validated by comparing its computational outputs with empirical data collected from physical experiments, demonstrating enhanced simulation accuracy. Figure 10 illustrates the numerical model of the three-point bending test, while Table 8 provides an in-depth comparison between experimental results and data obtained from finite element studies. It is noteworthy that "δpeak" denotes the peak deflection, representing the maximum displacement experienced by the beam during the three-point bending test, while "Mr" signifies flexural strength, a measure of the material's resistance to bending or flexural loads. These parameters are instrumental in evaluating structural performance under bending loads. The comparison reveals a satisfactory level of agreement across all studied parameters. Figure 10. Verification of numerical and experimental Model of 3PB test. Table 8 comparison between the results of experimental and finite elements methods. Ordinary Concrete Fiber reinforced concrete δ peak Numerical = 0.210mm Experimental = 0.225 mm Difference ratio = 7.1% Numerical = 0.84mm Experimental = 0.88 mm Difference ratio = 5% M r Numerical = 5.81 MPa Experimental = 6.17 MPa Difference ratio = 6.1% Numerical = 11.03 MPa Experimental = 11.49 MPa Difference ratio = 4.2% 4.2. Three-dimensional modeling procedure Figure 11 displays the 3D finite element model, including the geometry of the segment and its rebar, which contains 35,216 elements. The model's boundary was fixed in three directions, while the side boundaries were kept free to displace vertically. The Concrete Damage Plasticity constitutive model was adopted for the concrete segments to simulate the inelastic behaviour of concrete by incorporating isotropic-damaged elasticity alongside tensile and compressive plasticity. After a thorough review of existing literature, it was determined that no dedicated model exists specifically for comprehensively modelling FRC materials. However, previous studies provide insights into modelling FRC materials using the CDP approach. The flexibility of the CDP model allows for adjustments to its material property descriptors to better suit the characteristics of FRC. In this study, laboratory analyses of FRC, detailed in the experimental section, served as the foundation for calibrating our model. Additionally, through validation against data obtained from three-point bending tests, rigorous efforts were made to enhance the accuracy of the CDP model in simulating the performance of FRC. Figure 12 illustrates the response of concrete-based materials under compressive and tensile stresses, factors considered within the CDP model. Figure 13 and Fig. 14 provides essential data required to characterize the behavior of primary support in the Concrete Damage Plasticity model for tunnel construction. These data were obtained through laboratory tests detailed in previous sections of this paper. Empirical relationships and back-calculation procedures, following the guidelines outlined in ACI 544.8R-16, were employed to determine the tensile parameters. To establish the tension parameters, a closed-form solution of the moment-curvature response and a load-deflection calculation specific to fiber-reinforced concrete (FRC) were utilized. These methods, proposed by (Soranakom and Mobasher 2007 )and (Soranakom, Yekani-Fard et al. 2008), link the simplified stress-strain tensile model to flexural test results. Additionally, the data presented in Table 9, along with other material characteristics such as dilation angle, eccentricity, the ratio of biaxial to uniaxial compression (Kc), and viscosity, were defined within the CDP model. Figure 13. (a) Compressive and (b) Tensile behavioral curve in ordinary and optimum FRC sample Figure 14. (a) Compressive and (b) Tensile damage parameter curve in ordinary and optimum FRS sample. 5. Numerical results 5.1. Tensile damage under flexural stresses Figure 15 illustrates the DAMAGET contours for the final linings of metro tunnels, comparing scenarios using Traditional Rebar with Ordinary Concrete and 50% Traditional Rebar with Fiber-Reinforced Concrete. DAMAGET represents the level of tensile damage in concrete, ranging from 0 (no damage) to 1 (complete failure). Using 50% Traditional Rebar with FRC resulted in approximately a 30% reduction in DAMAGET compared to the scenario with Traditional Rebar and Ordinary Concrete. Additionally, the damaged zone area notably decreased when using FRC compared to ordinary shotcrete. These findings underscore the effectiveness of fiber-reinforced concrete in enhancing the performance and safety of tunnel support structures. Notably, the tensile damage in FRC and its dynamic behavior under earthquake loading are interconnected. The inclusion of fibers in FRC enhances its tensile strength and ductility, mitigating the risk of cracking or rupture under seismic conditions. Figure 15. DAMAGET contour for different tunnel lining support. 5.2. Principal stress mobilizes on segment Figure 16 and Fig. 17 meticulously depict the stress responses when comparing the use of Traditional Rebar with Ordinary Concrete against employing 50% Traditional Rebar with Fiber-Reinforced Concrete for metro tunnel segments. These visual representations offer a comprehensive analysis, showcasing von Mises stress contours alongside principal stresses in the vertical dimension (S, S33). Such detailed illustrations are instrumental in understanding the nuanced stress behaviors exhibited by different materials, a crucial aspect in engineering evaluations. Von Mises stress, a pivotal parameter for predicting material yield under diverse loading conditions, holds particular significance in tunnel construction. Notably, with the adoption of 50% Traditional Rebar with FRC, substantial improvements in stress responses are evident. Figure 16 underscores this improvement, revealing a significant 2.6-fold increase in von Mises stress. Moreover, notable disparities emerge in the comprehensive analysis of major stresses, as showcased in Fig. 16 and Fig. 17. For instance, the stress in the y-direction (S33) escalates from 1.8e6 Pa in ordinary concrete to 3.22e6 Pa in FRC. These findings not only underscore the effectiveness of combining traditional rebar with FRC in stress management but also offer valuable insights for engineering applications in tunnel construction. Furthermore, our FRC samples contain recycled fibers, which are environmentally friendly and cost-saving. The use of recycled fibers significantly reduces the environmental footprint of construction materials by diverting waste from landfills and decreasing the demand for virgin materials. This sustainable approach not only benefits the environment but also results in substantial cost savings. The reduction in material costs, combined with a 50% decrease in rebar usage, translates into significant financial benefits for the project. This not only lowers overall expenses but also streamlines construction processes, making the project more economically viable and efficient in the long run Fig. 16 and Fig. 17 meticulously depict the stress responses when comparing the utilization of Traditional Rebar with Ordinary Concrete against employing 50% Traditional Rebar with FRC for metro tunnel segments. These visual representations offer a comprehensive analysis, showcasing von Mises stress contours alongside principal stresses on the vertical dimension (S, S33). Such detailed illustrations are instrumental in understanding the nuanced stress behaviors exhibited by different materials, a crucial aspect in engineering evaluations. Von Mises stress, a pivotal parameter for predicting material yield under diverse loading conditions, holds particular significance in tunnel construction. Notably, with the adoption of 50% Traditional Rebar with Fiber-Reinforced Concrete, substantial improvements in stress responses are evident. Figure 16 underscores this improvement, revealing a significant 2.6 times increase in von Mises stress. Moreover, notable disparities emerge in the comprehensive analysis of major stresses, as showcased in Fig. 16 and Fig. 17.. For instance, the stress in the y-direction (S33) escalates from 1.8e6 Pa in ordinary concrete to 3.22e6 Pa in FRC. These findings not only underscore the effectiveness of combining traditional rebar with FRC in stress management but also offer valuable insights for engineering applications in tunnel construction. It's worth emphasizing that this conclusion is underpinned by a substantial 50% reduction in rebar usage, yielding significant financial benefits for the project. This reduction not only translates into cost savings but also streamlines construction processes, making the project more economically viable and efficient in the long run. Figure 16. Mises stress for a segment with different material. Figure 17. Stresses in Y direction (S33) for a segment with different material. 5.3. Vertical displacement under flexural loading In the U3 analysis, which focuses on vertical displacement, the comparison between using Ordinary Concrete and employing 50% Traditional Rebar with Fiber-Reinforced Concrete for metro tunnel segments reveals significant findings. As illustrated in Fig. 18 vertical displacement experiences a remarkable reduction of 60% when utilizing the FRC sample compared to Ordinary Concrete. This reduction is immensely important for the performance of concrete segments. Decreased vertical displacement signifies enhanced stability and structural integrity, crucial factors in tunnel construction where maintaining dimensional stability is paramount.The utilization of fiber-reinforced concrete plays a pivotal role in achieving this reduction. Fibers, such as steel or synthetic fibers, are incorporated into the concrete mix to improve ductility and enhance the material's ability to withstand tensile stresses. In the context of tunnel segments, where the concrete is subjected to various loading conditions and potential deformations, the introduction of fibers significantly enhances the material's capacity to resist cracking and deformation, ultimately leading to reduced vertical displacement. Moreover, the reduction in displacement not only ensures the structural stability of the tunnel segments but also contributes to the overall safety and longevity of the infrastructure. By employing FRC, engineers can achieve an optimal balance between structural strength and flexibility, mitigating the risk of excessive deformation while maintaining the integrity of the tunnel structure over time. The observed decrease in vertical displacement highlights the effectiveness of utilizing fiber-reinforced concrete as a means of vastly improving the performance and durability of concrete segments in metro tunnel construction. Additionally, the use of recycled fibers in FRC further amplifies its benefits. These environmentally friendly fibers reduce the environmental footprint by minimizing waste and decreasing the reliance on virgin materials. This sustainable approach not only promotes environmental stewardship but also results in substantial cost savings. The combined benefits of reduced material costs and a significant decrease in rebar usage translate into considerable financial advantages, making the project more economically viable and efficient in the long run. Figure 18 . displacement in Y direction (U33) for a segment with different material. 6. Conclusion This study extensively evaluated the flexural performance of metro tunnel segments reinforced with traditional rebar and fiber-reinforced concrete. Through experimental and numerical analyses, the efficacy of FRC in enhancing structural integrity, stress management, and reducing displacement was demonstrated. Additionally, the use of recycled fibers provided significant economic and environmental benefits. The validated finite element model using the Concrete Damage Plasticity approach proved to be a reliable tool for simulating concrete behavior under stress. The conclusions of this study are categorized below: Enhanced structural performance : Incorporating FRC with a 50% reduction in traditional rebar significantly improved the flexural strength and reduced tensile damage in tunnel segments, as confirmed by both experimental and numerical analyses. Effective stress management : The 3D finite element model revealed substantial improvements in stress responses, with a 2.6-fold increase in von Mises stress and significant escalation in principal stresses (S33) from 1.8e6 Pa in ordinary concrete to 3.22e6 Pa in FRC. Reduction in vertical displacement : Vertical displacement analysis showed a remarkable 60% reduction when utilizing FRC compared to ordinary concrete, indicating enhanced stability and dimensional integrity of the tunnel segments. Economic and environmental benefits : Using recycled fibers in FRC not only improved structural performance but also provided cost savings and environmental benefits by reducing the demand for virgin materials and overall material costs. Superior flexural behavior : Experimental results quantitatively demonstrated that FRC beams exhibited a 25% increase in flexural load-carrying capacity and a 20% improvement in deflection performance compared to ordinary concrete beams, showcasing its potential for resisting cracking, enhancing durability, and managing higher load capacities in tunnel applications. Improved tensile and compressive performances : Experimental results quantitatively demonstrated that FRC exhibited a 25% increase in tensile strength and a 15% increase in compressive strength compared to ordinary concrete, showcasing its potential for resisting cracking, enhancing durability, and managing higher load capacities in tunnel applications. Declarations Author Contributions: Alireza Ahmadi : Writing- Original draft, Methodology, Investigation. Amin Tohidi : Supervision, Conceptualization, Methodology, Investigation. Hassan Negahdar : Data curation, Writing- Original draft preparation. 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"End-of-life tires: a framework for effective management systems." World Business Council for Sustainable Development. Full report . Weissman, S. L., et al. (2003). "Extending the lifespan of tires." Sympletic Engineering Corporation. Institute for Transportation Studies. University of California at Berkeley . Zare, P., et al. (2020). Experimental Assessment of Damage and Crack Propagation Mechanism in Heterogeneous Rocks . 5th International Conference on Applied Research in Science and Engineering. University of Amsterdam, Netherlands. Table 1 and 2 Table 1 and 2 are available in the Supplementary Files section. Additional Declarations No competing interests reported. Supplementary Files Table1and2.docx Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4808296","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":342865257,"identity":"cfa045f4-386e-405e-bd37-abcc5d524064","order_by":0,"name":"Alireza Ahmadi","email":"","orcid":"","institution":"Azad Islamic University","correspondingAuthor":false,"prefix":"","firstName":"Alireza","middleName":"","lastName":"Ahmadi","suffix":""},{"id":342865258,"identity":"ce7f82b6-2372-425b-9d93-7bdf94301905","order_by":1,"name":"Amin 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approach.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-4808296/v1/c8f57b9ad0bbcc72297b1209.png"},{"id":63029899,"identity":"ff6ad0ba-67ec-418e-8c34-066fbf1f2339","added_by":"auto","created_at":"2024-08-22 09:11:13","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":50702,"visible":true,"origin":"","legend":"\u003cp\u003eCompressive strength of samples, grouped by fiber content.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-4808296/v1/ffc609252a042f4a60bfcf2e.png"},{"id":63031326,"identity":"763df698-e8ed-4626-93e1-0fb7af15d2b7","added_by":"auto","created_at":"2024-08-22 09:27:12","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":58798,"visible":true,"origin":"","legend":"\u003cp\u003eSplitting tensile strength of samples, grouped by mixture approach.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-4808296/v1/6e76a7f1a6ecb388542de979.png"},{"id":63030639,"identity":"6b7f7874-d1d1-4834-9024-3aeb6e0d2184","added_by":"auto","created_at":"2024-08-22 09:19:11","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":57620,"visible":true,"origin":"","legend":"\u003cp\u003eSplitting tensile strength of samples, grouped by fiber content.\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-4808296/v1/0f34bf93080d9d9fe7e25b82.png"},{"id":63030640,"identity":"4d9070cf-0a7b-438f-9679-e04bac1108ed","added_by":"auto","created_at":"2024-08-22 09:19:11","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":213585,"visible":true,"origin":"","legend":"\u003cp\u003eFlexural stress-deflection curves of ordinary and FRC specimens.\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-4808296/v1/e34b04b0dbd2bcf7bc5d3aaa.png"},{"id":63029888,"identity":"3002a246-cb37-4f23-aeb3-c7c35649f553","added_by":"auto","created_at":"2024-08-22 09:11:11","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":48421,"visible":true,"origin":"","legend":"\u003cp\u003eFlexural strength of samples, grouped by mixture approach.\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-4808296/v1/3bc316768853c00d349dbbc3.png"},{"id":63029889,"identity":"5e62bb34-7655-49c1-a64e-9ae6f621910e","added_by":"auto","created_at":"2024-08-22 09:11:11","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":48607,"visible":true,"origin":"","legend":"\u003cp\u003eFlexural strength of samples, grouped by fiber content.\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-4808296/v1/ea57a51718f699320a8602dc.png"},{"id":63029896,"identity":"6f027f3d-db30-4a9f-adfe-5b61fd258eca","added_by":"auto","created_at":"2024-08-22 09:11:12","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":1808368,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eVerification of \u003c/strong\u003enumerical and experimental Model of 3PB test.\u003c/p\u003e","description":"","filename":"10.png","url":"https://assets-eu.researchsquare.com/files/rs-4808296/v1/f1a36d76cac0e0684ff9a84b.png"},{"id":63029885,"identity":"2d6b11cb-aadc-43ee-babb-31f9f7b33593","added_by":"auto","created_at":"2024-08-22 09:11:11","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":498343,"visible":true,"origin":"","legend":"\u003cp\u003eThe 3D finite element model\u003c/p\u003e","description":"","filename":"11.png","url":"https://assets-eu.researchsquare.com/files/rs-4808296/v1/5f3294969fbb7ad95bf30f1f.png"},{"id":63030646,"identity":"5e70df95-d7a7-4486-a9b3-4aba48750f55","added_by":"auto","created_at":"2024-08-22 09:19:12","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":181196,"visible":true,"origin":"","legend":"\u003cp\u003eResponse of concrete-based material to (a) compressive, and (b) tensile stresses.\u003c/p\u003e","description":"","filename":"12.png","url":"https://assets-eu.researchsquare.com/files/rs-4808296/v1/8781e4a14a90c649d2201288.png"},{"id":63030643,"identity":"f7111fbd-4d2c-4bbb-8b5f-cd38e8a6e1ee","added_by":"auto","created_at":"2024-08-22 09:19:11","extension":"png","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":124877,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Compressive and (b) Tensile behavioral curve in ordinary and optimum FRC sample\u003c/p\u003e","description":"","filename":"13.png","url":"https://assets-eu.researchsquare.com/files/rs-4808296/v1/374fe987655181f67ee8017d.png"},{"id":63030644,"identity":"8a180be7-5af2-4370-8465-79fb0829a0d3","added_by":"auto","created_at":"2024-08-22 09:19:12","extension":"png","order_by":14,"title":"Figure 14","display":"","copyAsset":false,"role":"figure","size":105815,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Compressive and (b) Tensile damage parameter curve in ordinary and optimum FRS sample.\u003c/p\u003e","description":"","filename":"14.png","url":"https://assets-eu.researchsquare.com/files/rs-4808296/v1/b3ea1690a4528008ba1b4373.png"},{"id":63029898,"identity":"6e9ac022-38d1-43ee-8ed0-9dca5469a075","added_by":"auto","created_at":"2024-08-22 09:11:13","extension":"png","order_by":15,"title":"Figure 15","display":"","copyAsset":false,"role":"figure","size":474957,"visible":true,"origin":"","legend":"\u003cp\u003eDAMAGET contour for different tunnel lining support.\u003c/p\u003e","description":"","filename":"15.png","url":"https://assets-eu.researchsquare.com/files/rs-4808296/v1/dca1d2219e208ebd2efe8bf9.png"},{"id":63030642,"identity":"b354f530-7dc2-4ef0-bbae-e809d8d6e991","added_by":"auto","created_at":"2024-08-22 09:19:11","extension":"png","order_by":16,"title":"Figure 16","display":"","copyAsset":false,"role":"figure","size":549285,"visible":true,"origin":"","legend":"\u003cp\u003eMises stress for a segment with different material.\u003c/p\u003e","description":"","filename":"16.png","url":"https://assets-eu.researchsquare.com/files/rs-4808296/v1/24fe0dc5033c0a1fd48dae2b.png"},{"id":63029894,"identity":"c506e549-d4a0-4cec-8521-6f47e04e8e22","added_by":"auto","created_at":"2024-08-22 09:11:12","extension":"png","order_by":17,"title":"Figure 17","display":"","copyAsset":false,"role":"figure","size":582615,"visible":true,"origin":"","legend":"\u003cp\u003eStresses in Y direction (S33) for a segment with different material.\u003c/p\u003e","description":"","filename":"17.png","url":"https://assets-eu.researchsquare.com/files/rs-4808296/v1/acab36a28bcb3c9adad3920c.png"},{"id":63029891,"identity":"d5054d9a-a1e1-4600-bee4-9a2abee20d98","added_by":"auto","created_at":"2024-08-22 09:11:12","extension":"png","order_by":18,"title":"Figure 18","display":"","copyAsset":false,"role":"figure","size":507982,"visible":true,"origin":"","legend":"\u003cp\u003edisplacement in Y direction (U33) for a segment with different material.\u003c/p\u003e","description":"","filename":"18.png","url":"https://assets-eu.researchsquare.com/files/rs-4808296/v1/dc171cf4842ea5a2aa4b28fc.png"},{"id":66674927,"identity":"e800bb61-fd84-4564-b92a-562a3bb33eb5","added_by":"auto","created_at":"2024-10-15 11:02:53","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":10708083,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4808296/v1/d615ad29-0801-463e-836f-f65f5bc54ff2.pdf"},{"id":63029880,"identity":"d4351a8a-e2ee-4dc6-b146-11090312072a","added_by":"auto","created_at":"2024-08-22 09:11:11","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":67911,"visible":true,"origin":"","legend":"","description":"","filename":"Table1and2.docx","url":"https://assets-eu.researchsquare.com/files/rs-4808296/v1/178419d69df1e17f6fb96260.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Flexural Performance of Tunnel lining Segments using Fiber Reinforced Concrete: A Study on Recycled and Industrial Fibers Through Experimental and Numerical Methods","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eMechanized Tunnel linings, typically made of precast segments connected by bolts and reinforced with steel bars to withstand loads. Tunneling and Underground Space Association highlights that these steel-reinforced segments are prone to corrosion, leading to concrete spalling and reduced structural capacity. Additionally, tunnel segments experience tension during stages like demolding, storage, and transport, causing cracking and maintenance issues. Steel rebar also incurs significant financial and environmental costs. During their service life, tunnel segments primarily endure flexural loading, resulting in tensile stress. Despite concrete's high compressive strength, its low tensile strength and brittleness lead to cracking and potential failure under tension, compromising structural integrity. Fiber reinforcement significantly enhances concrete's mechanical properties, improving both tensile and compressive strength. Incorporating fibers offers several benefits: it improves non-linear structural behavior in tension by reducing crack width and preventing crack propagation; it boosts post-cracking residual strength through a bridging effect; and it increases concrete's overall toughness via fiber debonding and pull-out mechanisms (Pujadas, Blanco et al. 2014, Blanco, Pujadas et al. 2016). These enhancements depend on the bond strength, mechanical properties, and quantity of fibers intersecting a crack. Innovative steel fiber geometries, such as hooked, crimped, and undulated shapes, show promise in improving Fiber Reinforced Concrete (FRC) performance. Hooked fibers enhance interlock within the concrete matrix, while crimped fibers improve the bond between concrete and fibers. These advancements in fiber reinforcement offer a durable and reliable solution, addressing the limitations of conventional steel bar reinforcement (Pujadas, Blanco et al. 2014, Blanco, Pujadas et al. 2016).Nowadays, it is well established that incorporating steel fibers significantly improves the engineering performance of both structural and nonstructural concrete. These enhancements include better crack resistance, increased ductility and toughness, and improved fatigue and impact resistance (Song and Hwang \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2004\u003c/span\u003e, Chen and Liu \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2005\u003c/span\u003e, Thomas and Ramaswamy \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2007\u003c/span\u003e, Asheghi Mehmandari, Fahimifar et al. 2020). (Thomas and Ramaswamy \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2007\u003c/span\u003e) reported that in their study, the maximum increase in compressive strength of steel fiber reinforced concrete was less than 10%. However, they observed a remarkable improvement of about 40% in the splitting tensile strength and flexural strength, along with an enhanced post-cracking response. (Centonze, Leone et al. 2012) concluded that recycled steel fibers can be promising materials for concrete, as they improve the mechanical properties of the brittle matrix in both structural and nonstructural applications. (Sengul \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2016\u003c/span\u003e) investigated the mechanical performance of fiber reinforced concrete incorporating various geometrical configurations and percentages of steel fibers obtained from scrap tires. These studies collectively underscore the significant potential of steel fibers in enhancing the mechanical properties and overall performance of concrete. Recycling steel from waste automobile tires has gained attention for its environmental benefits and waste management solutions. Tires contain substantial steel, and recycling this steel offers an eco-friendly, cost-effective alternative to traditional steel fibers, with recycled steel fibers showing comparable mechanical properties to industrial ones. The typical car tire lasts around five years, and over 90\u0026nbsp;million motor vehicles were produced in 2014, with numbers expected to rise(Weissman, Sackman et al. 2003, Asheghi Mehmandari \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). With an estimated 1.2\u0026nbsp;billion vehicles on the road, over 4.8\u0026nbsp;billion tires are in use, and around 4\u0026nbsp;billion used tires are generated annually. The increase in vehicle production suggests a growing number of used tires. Some used tires can be reused, but many become end-of-life tires, posing disposal challenges. Landfilling or stockpiling these tires is banned in Europe and the US (Floess, Hasenbein et al. 2007, Schiopu and Gavrilescu \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2010\u003c/span\u003e). Recycling rates of scrap tires have surpassed 85% in the US, Europe, and Japan due to stricter laws, economic benefits, and environmental awareness (Benschneider, Wbcsd \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2010\u003c/span\u003e, Nguyen, De Vanssay et al. 2015). A typical tire consists of 47% rubber, 22% carbon black, 17% steel cords, 5% fabrics, and various additives (Evans and Evans \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2006\u003c/span\u003e).The concept of hybrid fiber reinforcement, which integrates different types of fibers, considering their modulus (high or low value) or geometrical size (e.g., macro and micro), offers a promising approach to enhance the performance characteristics of composite materials (Lawler, Wilhelm et al. 2003, Behboudi, Zad et al. 2024, Behboudi, Zad et al. 2024) Compared to Mono Fiber Reinforced Concrete (MFRC), Hybrid Fiber Reinforced Concrete (HFRC) demonstrates superior compressive and tensile strength (Libre, Shekarchi et al. 2011, Mehmandari, Shokouhian et al. 2024), improved flexural and impact resistance, and enhanced durability These types of concrete provide synergistic improvements in material properties (Afroughsabet and Ozbakkaloglu \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2015\u003c/span\u003e, Amjadi, Mohammadkhanifard et al. 2023). For example, combining steel fibers and polypropylene fibers in concrete has been shown to boost both strength and ductility, offering a balanced improvement over using a single type of fiber. This hybrid approach capitalizes on the strengths of each fiber type, optimizing the overall performance of the composite material. Despite the potential benefits, the combined use of recycled and industrial steel fibers in HFRC has been underexplored. This gap presents an opportunity for innovation, aiming to achieve sustainability and cost-efficiency in construction materials. By investigating the individual and collective impacts of recycled and industrial steel fibers, this research seeks to advance the development of high-performance, eco-friendly concrete solutions.\u003c/p\u003e \u003cp\u003eKang et al. (Kang, Choi et al. 2016) investigated the effect of hybrid combinations of steel fiber and various microfibers on the mechanical properties of HFRC, finding that steel fiber significantly enhanced the tensile behavior when mixed with high-strength synthetic fibers like polypropylene (PP). (Li, Li et al. \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2017\u003c/span\u003e) blended steel fiber with two types of microfibers into a concrete composite, demonstrating marked improvements in strength and toughness under shear, tensile, and flexural conditions. (Rashiddadash, Ramezanianpour et al. 2014) combined steel fiber with polypropylene fiber, reporting superior mechanical properties in HFRC with higher steel fiber content. (Lawler, Zampini et al. 2005) asserted that HFRC has greater strength and crack resistance than matrices reinforced only with macro fibers, due to the presence of microfibers. In hybrid fiber reinforced concrete, microfibers bridge microcracks, increasing initial cracking strength and reducing shrinkage, while microfibers prevent macrocrack propagation, enhancing toughness and post-cracking performance. (Sivakumar and Santhanam \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2007\u003c/span\u003e) studied high-strength concrete reinforced with steel fibers (30 mm) and non-metallic fibers (6\u0026ndash;20 mm), such as micro polypropylene, polyester, and glass fibers. They found the steel-polypropylene fiber combination to be the most effective. (Qian and Stroeven \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2000\u003c/span\u003e) evaluated concrete with hybrid fibers, including micro polypropylene and various steel fibers. Their results indicated that smaller steel fibers (6 mm) improved compressive strength, while larger steel fibers (30 and 40 mm) enhanced post-cracking strength. They also identified the optimal dosage of micro polypropylene fibers for the best performance. Several studies have explored the impact of fiber addition on tunnel segment construction. The inclusion of fibers enhances structural performance while reducing overall construction costs by minimizing the need for rebars (Cavalaro, Blom et al. 2012, De la Fuente, Pujadas et al. 2012, Meda, Rinaldi et al. 2016, Meng, Gao et al. 2016). (Beňo and Hilar \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2013\u003c/span\u003e) conducted a numerical and laboratory study on SFRC samples, subjecting them to compressive, tensile, and flexural strength tests. Their findings indicated that lower fiber dosages resulted in better mixing performance with reduced dispersion properties, whereas higher doses improved final characteristics. (Beňo and Hilar \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2013\u003c/span\u003e) investigated the behavior of segments under TBM thrust jacks using experiments on rectangular cube samples, comparing those with and without fibers under linear and localized loads. (Conforti, Tiberti et al. 2017) also explored the feasibility of employing polypropylene fibers in segments. Advances in scientific computing have enabled numerical simulations to study structural behavior and cracking during segment construction stages, yielding valuable insights. Finite element analysis has been extensively used to simulate axial forces exerted by tunnel boring machines (Gettu, Barrag\u0026aacute;n et al. 2004, Sorelli and Toutlemonde \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2005\u003c/span\u003e, Bakhshi and Nasri \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2014\u003c/span\u003e, Zare, Asheghi et al. 2020, Mohammadifar, Asheghi Mehmandari et al. \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). Previous studies assessing the performance of segmental linings in tunnels have often overlooked a comprehensive evaluation of the technical, environmental, and economic aspects of fiber-reinforced concrete. Given the high cost associated with industrial fibers, there is a growing necessity to explore the viability of using recycled fibers as substitutes. The primary objective of this study is to deepen our understanding of the effects of various types of fibers, including hybrid and recycled tire fibers, on the performance of segmental linings. Specifically, the focus is on evaluating the mechanical performance, with a particular emphasis on flexural behavior under laboratory conditions. To achieve this goal, recycled and hybrid fiber-reinforced concretes were evaluated in laboratory experiments. The investigation also extends to the performance of segmental linings using a finite element model of a tunnel. This model employs the Concrete Damage Plasticity (CDP) constitutive model, integrating traditional rebars and an optimized mix design outcome from experimental flexural loading tests. The aim is to explore mechanical performance, conduct damage analysis, and investigate ductility.\u003c/p\u003e"},{"header":"2. Experimental investigation","content":"\u003cdiv id=\"Sec3\"\u003e\n \u003ch2\u003e2.1. Recycled steel tire fiber (RSTF) and double hook-end steel fiber (STF)\u003c/h2\u003e\n \u003cp\u003eRecycled steel fibers from waste tires, recovered through a shredding process followed by electromagnetic separation from the rubber. The resulting steel fibers, illustrated in Table\u0026nbsp;\u003cspan\u003e1\u003c/span\u003e, exhibit diverse diameters, lengths, and shapes, with noticeable irregular wrinkles. A preliminary statistical analysis was conducted to evaluate the geometric variability of these fibers after shredding, without any further treatment. This characterization is crucial for defining appropriate treatments to improve the final properties of concrete reinforced with these fibers. A sample of approximately 500 steel fibers was randomly selected for analysis. Each fiber\u0026rsquo;s diameter was measured using a micrometer, with three measurements taken at both extremities and the midpoint to obtain an average diameter. The fiber diameters ranged from 0.3 to 0.36 mm, with the majority (65%) falling within the 0.32 to 0.34 mm range.\u003c/p\u003e\n \u003cp\u003eThe fibers length exhibited a wide range, from 20 to 40 mm, with the most frequent length being 32 mm, observed in 55% of the fibers. Table \u003cspan\u003e1\u003c/span\u003e provides a detailed summary of the geometric and shape characteristics of the analyzed fibers. This characterization serves as a foundation for identifying suitable treatments to optimize the performance of concrete reinforced with these recycled steel fibers.\u003c/p\u003e\n \u003cdiv\u003eA double hook-end steel fiber with an aspect ratio of 87.5 was utilized in this study. These fibers are industrially industrial, ensuring uniformity in their geometric and mechanical properties. The fibers\u0026rsquo; consistent shape and precise geometric characteristics contribute to their reliability in reinforcing concrete. Table \u003cspan\u003e2\u003c/span\u003e details the specific geometrical and mechanical properties of these fibers, underscoring their suitability for enhancing the performance of concrete composites.\u003c/div\u003e\n \u003cdiv\u003e\u003cbr\u003e\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec4\"\u003e\n \u003ch2\u003e2.2. Cement, aggregate and superplasticizer\u003c/h2\u003e\n \u003cp\u003eIn this study, CEM I 52.5N Portland cement, provided by Kordestan Cement Industries Company, was utilized. A polycarboxylate ether-based superplasticizer (SP) was incorporated in varying amounts ranging from 0.2\u0026ndash;2%. All concrete mixtures included crushed limestone aggregate, with a maximum grain size of 25 mm, as verified by an ASTM C136/C136M-19 sieve analysis. Figure\u0026nbsp;1 depicts the aforementioned materials utilized in this study.\u003c/p\u003e\n \u003cdiv\u003e\u003cbr\u003e\u003c/div\u003e\n \u003cp\u003e\u003cstrong\u003eFigure\u0026nbsp;1.\u003c/strong\u003e The row materials of concrete and additive.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec5\"\u003e\n \u003ch2\u003e2.3. Mixture design\u003c/h2\u003e\n \u003cp\u003eTable\u0026nbsp;\u003cspan\u003e3\u003c/span\u003e presents the mix ratios for seven distinct concrete mixtures, all designed with a consistent water-to-binder ratio of 0.340. These mixtures include Ordinary Concrete (OC) and various fiber-reinforced concretes, with fiber contents ranging from 0.25\u0026ndash;0.5% by volume fraction (vf). \u0026quot;OC\u0026quot; refers to the standard concrete mix without any fiber reinforcement, while the other mixtures incorporate recycled steel tire fibers and industrial double-hooked end steel fibers, either singly or in hybrid combinations. For instance, \u0026quot;R5\u0026quot; denotes a mixture with 0.5% volume content of solely recycled steel tire fibers, \u0026quot;S5\u0026quot; signifies a mixture with 0.5% volume content of solely industrial double-hooked end steel fibers, and \u0026quot;(SR)5\u0026quot; represents a mixture with a 0.5% volume content hybrid of recycled and industrial fibers in equal proportions. In these mixtures, the fiber weight is determined based on the density, resulting in 39 kg of fiber used for a 0.5% volume content (0.5% * 7800 kg/m\u0026sup3;).\u003c/p\u003e\n \u003cp\u003eSuperplasticizer (SP) was added to the mixes at dosages ranging from 0.5\u0026ndash;1% by weight of cement, and all mixtures were homogenized using a pan mixer. To assess the workability of both ordinary and fiber-reinforced concretes, unit weight and slump tests were conducted on the fresh concrete samples. This standardized approach ensures a consistent evaluation of the concrete mixtures, facilitating a comprehensive comparison of their properties and performance.\u003c/p\u003e\n \u003cdiv\u003e\n \u003ctable id=\"Tab3\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv\u003eTable 3\u003c/div\u003e\n \u003cdiv\u003e\n \u003cp\u003eThe mixtures proportions of the Ordinary and FRC mixtures.\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eMix\u003c/p\u003e\n \u003cp\u003eDescription\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"8\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSample\u003c/p\u003e\n \u003cp\u003eCode\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"8\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eC\u003c/p\u003e\n \u003cp\u003e(kg/m\u003csup\u003e3\u003c/sup\u003e)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"8\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eW\u003c/p\u003e\n \u003cp\u003e(kg/m\u003csup\u003e3\u003c/sup\u003e)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"8\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eCS\u003c/p\u003e\n \u003cp\u003e(kg/m\u003csup\u003e3\u003c/sup\u003e)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"8\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eFS\u003c/p\u003e\n \u003cp\u003e(kg/m3)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"8\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eRSTF\u003c/p\u003e\n \u003cp\u003e(kg/m3)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"8\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSTF\u003c/p\u003e\n \u003cp\u003e(kg/m\u003csup\u003e3\u003c/sup\u003e)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\" rowspan=\"8\"\u003e\u0026nbsp;\u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSP\u003c/p\u003e\n \u003cp\u003e(kg/ m\u003csup\u003e3\u003c/sup\u003e)\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eOrdinary Concrete\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eOC\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e340\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e144.36\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e728.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1013.4\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.8\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSingle RSTF Low Vf (0.25)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eR\u003csub\u003e2.5\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e340\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e144.36\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e728.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1009.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e17.25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.8\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSingle RSTF High Vf (0.5)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eR\u003csub\u003e5\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e340\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e144.36\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e728.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1009.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e34.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.8\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSingle STF Low Vf(0.25)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eS\u003csub\u003e2.5\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e340\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e144.36\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e728.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1009.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e19.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e2.8\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eSingle STF High Vf (0.5)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eS\u003csub\u003e5\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e340\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e144.36\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e728.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1005.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e0\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e39\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.3\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eHybrid of RSTF and STF low Vf(0.25)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e(SR)\u003csub\u003e2.5\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e340\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e144.36\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e728.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1005.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e8.63\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e9.75\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.3\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eHybrid of RSTF and STF high Vf (0.5)\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e(SR)\u003csub\u003e5\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e340\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e144.36\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e728.9\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e1005.8\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e17.25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e19.5\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e3.3\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003ctfoot\u003e\n \u003ctr\u003e\n \u003ctd colspan=\"17\"\u003e\u003cstrong\u003eC: Cement, W: Water, CS: Coarse Sand, FS: Fine Sand, RTSF: Recycled Steel Fiber, STF: hooked end Steel Fiber\u003c/strong\u003e\u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tfoot\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n \u003cp\u003eThe experimental procedure began with dry mixing the cement and aggregates for 2 minutes. Subsequently, superplasticizer (SP) and water were added, and the mixture was blended for an additional 3 minutes. Following this, steel fibers were incorporated into the mix and stirred for a further 3 minutes to ensure uniform distribution throughout the mixture. The homogeneous mix was then poured into beam molds and subjected to vibration on a shaking table to eliminate air pockets. The samples were kept in the molds for 24 hours before demolding. Post-demolding, the specimens underwent water curing at a controlled temperature of 20\u0026thinsp;\u0026plusmn;\u0026thinsp;2\u0026deg;C for 28 days. For strength evaluations, each mix type was represented by three beams with dimensions of 500 mm x 100 mm x 100 mm, and six cylindrical molds measuring 200 mm x 100 mm were prepared for uniaxial compressive tests and split tensile (Brazilian) tests. The results were averaged across the three samples per mix type.Beam deflections under three-point loading were measured using a linear variable differential transformer (LVDT) positioned at the midspan. The tests were conducted with Dartec-9600 servo control devices, which have a maximum capacity of 1000 kN, at the Rock Mechanics Laboratory of Amirkabir University of Technology. Figure \u003cspan\u003e2\u003c/span\u003e illustrates the loading machine utilized in the experimental process of this study.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"3. Experimental result and discussion","content":"\u003cp\u003eThis study aims to examine the physical, mechanical, and ductility properties of fiber-reinforced concrete compared to ordinary concrete. The investigation involves three-point bending tests, uniaxial compressive tests, and splitting tensile tests. The results of these tests are presented in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003ePhysical and mechanical properties of ordinary and FRC specimens.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"14\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c12\" colnum=\"12\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c13\" colnum=\"13\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c14\" colnum=\"14\"\u003e\u003c/div\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eMix Description\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\" morerows=\"8\" rowspan=\"9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eUnit Weight\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\" morerows=\"8\" rowspan=\"9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eSlump\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\" morerows=\"8\" rowspan=\"9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eCompressive Strength\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eIncrease\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\" morerows=\"8\" rowspan=\"9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003eTensile\u003c/p\u003e \u003cp\u003eStrength\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003eIncrease\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\" morerows=\"8\" rowspan=\"9\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003eFlexural\u003c/p\u003e \u003cp\u003eStrength\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003eIncrease\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e(kg/m3)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e(mm)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e(MPa)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e(%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e(MPa)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e(%)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e(MPa)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e(%)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2378\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e105\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e46.41\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e3.92\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e6.17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e0.0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eS\u003csub\u003e2.5\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2378\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e92\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e60.16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e29.62\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e12.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e96.92\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e(SR)\u003csub\u003e2.5\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2375\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e86\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e60.06\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e29.41\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e5.18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e32.14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e11.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e79.09\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eR\u003csub\u003e2.5\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2382\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e75\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e56.84\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e22.47\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e4.91\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e25.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e10.48\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e69.85\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eS\u003csub\u003e5\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2375\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e73\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e62.29\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e34.21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e6.78\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e72.95\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e12.22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e98.05\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e(SR)\u003csub\u003e5\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2371\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e70.22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e51.30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e6.51\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e66.07\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e11.49\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e86.22\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eR\u003csub\u003e5\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2369\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e75\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e58.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e25.51\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e6.28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e60.20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e10.71\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c14\"\u003e \u003cp\u003e73.58\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e3.1. Experimental Analysis of Compressive Performance\u003c/h2\u003e \u003cp\u003eUniaxial compressive tests were conducted using a Dartec 9600 servo-controlled machine, adhering to ASTM C39 standards, with a constant loading rate of 0.004 mm/s. Load, stroke, and time data were recorded at a frequency of four readings per second until failure, providing comprehensive insights into the specimens' resilience. The results, presented in Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e, illustrate the strength and strain during both the pre-peak (initial crack occurrence) and peak (maximum strength) phases. Notably, the specimens predominantly failed through shear or tensile modes due to Poisson\u0026rsquo;s effect, rather than through compressive failure. This underscores the role of fiber reinforcement in mitigating failure during compression tests.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eCompressive strength and strain values of Ordinary and FRC specimens based on experimental results and ASTM C39 standard.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"9\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eReinforcing Type\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eMix\u003c/p\u003e \u003cp\u003eDescription\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c5\" namest=\"c3\"\u003e \u003cp\u003ePre-Peak\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c9\" namest=\"c7\"\u003e \u003cp\u003ePeak\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eStrength\u003c/p\u003e \u003cp\u003e(Mpa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eStrain\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eStrength\u003c/p\u003e \u003cp\u003e(Mpa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003eStrain\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e-----------\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eOC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e46.41\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e46.41\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.011477\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSingle\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eS\u003csub\u003e2.5\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e24.76\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.007212\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e60.13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.011333\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHybrid\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(SR)\u003csub\u003e2.5\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e38.38\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.009548\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e60.04\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.014158\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSingle\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eR\u003csub\u003e2.5\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e14.84\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.005186\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e56.83\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.013706\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSingle\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eS5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e25.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.007285\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e62.29\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.010927\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHybrid\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(SR)5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e32.64\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.008663\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e70.18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.011676\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSingle\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eR5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e18.83\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.006097\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e58.23\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.015243\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cdiv id=\"Sec8\" class=\"Section3\"\u003e \u003ch2\u003e3.1.1 Fiber content effect on compression strength\u003c/h2\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e3\u003c/span\u003e depicts the influence of fiber content on the compressive strength of fiber-reinforced concrete samples categorized by their reinforcement methods. The data indicate a consistent improvement in compressive strength for FRC samples compared to ordinary concrete samples. In single-fiber mixtures, there is a negligible difference in peak compressive strength between low-fiber and high-fiber samples, indicating that increasing the fiber content does not significantly enhance strength. Conversely, hybrid fiber samples exhibit more complex behavior; notably, the (SR)5 sample demonstrates a 17% higher peak compressive strength compared to the (SR)2.5 sample.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe effect of fiber content on pre-peak compressive strength varies significantly. In single-STF samples, both S2.5 and S5 exhibit similar strengths, indicating that increasing fiber content does not notably impact pre-peak strength in these samples. However, in single-RSTF specimens, higher fiber content leads to a 27% increase in pre-peak strength. This improvement is attributed to RSTF's ability to delay crack initiation, highlighting its effectiveness in enhancing pre-peak strength. Among the samples, the (SR)2.5 specimen, with its lower fiber content and hybrid approach, emerges as the most balanced option in terms of compressive strength. The influence of fiber content on compressive strength remains somewhat ambiguous, primarily because failure patterns are significantly affected by the quality of fiber distribution within the uniaxial compressive FRC samples.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section3\"\u003e \u003ch2\u003e3.1.2. Hybridization effect on compression strength\u003c/h2\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e4\u003c/span\u003e presents the pre-peak and peak compressive strength results as a function of fiber content, showing that hybrid samples consistently outperform single-fiber ones. Notably, the hybrid (SR)2.5 sample achieves a 55% higher pre-peak strength compared to the best-performing single-fiber sample, S5. For low-fiber samples, peak strengths are comparable, with the hybrid (SR)2.5 exhibiting a slight advantage. This trend is also observed in high-fiber specimens, where the (SR)5 hybrid sample surpasses single-fiber samples by 30% in pre-peak strength and 13% in peak strength. These findings underscore the superior performance of hybrid fiber reinforcement in enhancing compressive strength.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe enhanced performance of the hybrid fiber-reinforced concrete samples can be attributed to the distinct properties of the fibers and the mechanics of the uniaxial compressive test. During this test, pre-peak strength is associated with the initial formation of micro vertical cracks, which occur due to the material's horizontal expansion under vertical load. Recycled fibers mitigate these cracks by evenly distributing tensile stress, allowing the material to endure higher compressive stresses before cracking occurs. As vertical cracks develop into significant fractures, industrial fibers become crucial in maintaining the sample's integrity, thereby enhancing peak strength. This synergy in hybrid samples results in superior peak compressive strength.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e3.2. Experimental analysis of tensile performance\u003c/h2\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e presents the results of the splitting tensile test, detailing the strength and strain values at pre-peak, peak, and post-peak stages. The pre-peak point corresponds to the moment when the first crack is observed in the sample. The peak point indicates the maximum splitting tensile strength achieved by the sample. The post-peak point is defined as the stage where the sample's load-bearing capacity drops to 20% of its maximum load.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eSplitting tensile strength and strain values of ordinary and FRC specimens based on experimental results and ASTM C496 standard.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"13\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c12\" colnum=\"12\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c13\" colnum=\"13\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eReinforcing Type\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eMix Description\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c5\" namest=\"c3\"\u003e \u003cp\u003ePre-Peak\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c9\" namest=\"c7\"\u003e \u003cp\u003ePeak\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colspan=\"3\" nameend=\"c13\" namest=\"c11\"\u003e \u003cp\u003ePost peak\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eStrength (f\u003csub\u003epre\u003c/sub\u003e) (Mpa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eStrain\u003c/p\u003e \u003cp\u003e(%)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eStrength (f\u003csub\u003epeak\u003c/sub\u003e)\u003c/p\u003e \u003cp\u003e(Mpa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003eStrain\u003c/p\u003e \u003cp\u003e(%)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c12\"\u003e \u003cp\u003eStrength (f\u003csub\u003epost\u003c/sub\u003e)\u003c/p\u003e \u003cp\u003e(Mpa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c13\"\u003e \u003cp\u003eStrain\u003c/p\u003e \u003cp\u003e(%)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003csub\u003e\u0026minus;\u0026minus;\u0026minus;\u0026minus;\u0026minus;\u0026minus;\u0026minus;\u0026minus;\u0026minus;\u0026minus;\u0026minus;\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eOC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3.82\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.007\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e3.92\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.007\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSingle\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eS\u003csub\u003e2.5\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e4.46\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e5.46\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e1.09\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0.26\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHybrid\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(SR)\u003csub\u003e2.5\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e5.04\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.057\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e5.18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e1.04\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0.24\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSingle\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eR\u003csub\u003e2.5\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e4.45\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.019\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e4.91\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.061\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e0.98\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0.18\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSingle\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eS\u003csub\u003e5\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e5.31\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.064\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e6.78\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e1.36\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0.31\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHybrid\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(SR)\u003csub\u003e5\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e5.46\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.068\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e6.51\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e1.30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0.28\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSingle\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eR\u003csub\u003e5\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e5.33\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.041\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e6.28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.08\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e1.26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c13\"\u003e \u003cp\u003e0.21\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe splitting tensile test provides unique insights into tensile strength by concentrating stress in a localized manner, resulting in lower tensile strength due to the induction of multiple cracks around the specimen's circumference. This differs from tests such as the three-point bending test, where stress is more uniformly distributed. Consequently, the splitting tensile test uniquely evaluates the failure mechanism and the influence of fiber content and reinforcement approach on tensile behavior.\u003c/p\u003e \u003cdiv id=\"Sec11\" class=\"Section3\"\u003e \u003ch2\u003e3.2.1 Fiber content effect on tensile strength\u003c/h2\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e5\u003c/span\u003e illustrates that fiber-reinforced concrete samples surpass ordinary concrete in strength parameters, underscoring the advantages of fiber reinforcement. In ordinary concrete, the narrow margin between pre-peak (fpre) and peak (fpeak) strengths indicates that peak strength is reached almost immediately after the first crack forms, demonstrating a brittle behavior characterized by a low fpre value, which is undesirable.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIncreasing the fiber content enhances both pre-peak and peak tensile strengths in concrete, regardless of whether a single or hybrid fiber approach is employed. This enhancement is particularly pronounced in splitting tensile tests, where larger sections of the concrete are subjected to tensile stress due to the test's nature. The presence of more fibers effectively mitigates crack formation across these stressed areas, underscoring their critical role in sustaining tensile stress and emphasizing the importance of adequate fiber content in enhancing structural integrity. Insufficient fiber content proves inadequate in preventing cracks throughout the entirety of the tensile stress-affected regions, as depicted in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e5\u003c/span\u003e.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section3\"\u003e \u003ch2\u003e3.2.2 Hybridization effect on tensile strength\u003c/h2\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e6\u003c/span\u003e demonstrates that hybrid samples, which combine recycled steel fibers with industrial double hooked end steel fibers, exhibit notable enhancements in pre-peak tensile strength across both low and high fiber content categories. Specifically, the (SR)2.5 and (SR)5 samples show increases of approximately 13% and 26% in pre-peak strength, respectively. This improvement is attributed to the synergistic effects of these fibers: the smooth-surfaced STFs effectively target primary weak points in crack-prone areas, while the rough RSTFs enhance interlocking at lower stress levels, thereby better controlling and distributing micro-cracks before reaching peak stress levels.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn terms of peak and post-peak tensile strengths, the hybrid fiber approach demonstrates moderate results, primarily attributed to the superior capability of STF to effectively manage and span larger cracks. In contrast, recycled steel fibers, with their smaller dimensions, exhibit less effectiveness in this regard but excel in distributing stress at a micro-scale. As a result, the hybrid method achieves a balanced performance in splitting tensile strength during both peak and post-peak phases, capitalizing on the strengths of each fiber type to achieve an intermediate outcome. However, the variation in fp among different fiber reinforcement approaches remains minimal, owing to the relatively small crack sizes observed in the splitting tensile test, where recycled steel fibers prove effective in bridging these cracks.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003e3.3. Experimental analysis of flexural performance\u003c/h2\u003e \u003cp\u003eThis section focuses on assessing the strength and properties derived from three-point bending tests, along with the corresponding flexural behavior curves for each specimen. The flexural strength (f) is computed using Eq.\u0026nbsp;(\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e), with specific deflection values serving as key indicators in this analysis. These indices include fL/600, fp, and fL/150, corresponding to the bending strengths at deflections of δL/600 (0.5 mm), peak deflection (δpeak), and δL/150 (2 mm), respectively. By evaluating these indices, we obtain a comprehensive understanding of the material's response to flexural loading. The parameter fL/600 offers insights into the material's initial response, capturing its bending strength at an early stage of deflection. The fp value signifies the peak deflection, indicating the maximum strength the material can sustain before significant damage or cracking occurs. Lastly, fL/150 and the ultimate deflection values provide critical information on the material's behavior at larger deflections, demonstrating its ability to maintain structural integrity and absorb energy as deformation progresses. This detailed analysis of flexural strengths at various deflection points enables a thorough characterization of the material's mechanical performance under bending stresses.\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:f=\\frac{3pL}{2b{h}^{2}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e7\u003c/span\u003e shows flexural stress-deflection curves for ordinary and fiber-reinforced concrete specimens, highlighting fibers' role in enhancing flexural capacity and ductility. Further details on flexural behavior improvement are discussed later.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab7\" class=\"InternalRef\"\u003e7\u003c/span\u003e provides detailed information on the flexural strength and toughness of both ordinary concrete and fiber-reinforced concrete specimens at four critical points, including Ttotal, which represents the total energy absorption across the entire flexural stress-deflection curve. Ordinary concrete demonstrates limited ductility, failing at a peak deflection of 0.203 mm, falling short of the δL/600 (0.5 mm) and δL/150 (2 mm) thresholds, thereby preventing further evaluation of toughness at these stages. In contrast, fiber reinforcement enhances concrete ductility, as evidenced in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e7\u003c/span\u003e and Table\u0026nbsp;\u003cspan refid=\"Tab7\" class=\"InternalRef\"\u003e7\u003c/span\u003e. FRC outperforms ordinary concrete in terms of strength, ductility, and toughness. Ordinary concrete typically fails abruptly, whereas FRC maintains strength and ductility at higher deflections, thereby enhancing flexural performance. This improvement is evident in the toughness values, with ordinary concrete exhibiting low toughness due to its brittleness, in contrast to the significantly higher toughness observed in FRC.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab7\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 7\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eFlexural strength and toughness indexes of ordinary and FRC specimens based on experimental results and ASTM C 1609 standard.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"13\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c12\" colnum=\"12\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c13\" colnum=\"13\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eMixture ID\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003eδ\u003csub\u003eL/600\u003c/sub\u003e (0.5mm)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e \u003cp\u003eδ\u003csub\u003epeak\u003c/sub\u003e (mm)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c9\" namest=\"c8\"\u003e \u003cp\u003eδ\u003csub\u003eL/150 (\u003c/sub\u003e2mm)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c12\" namest=\"c11\"\u003e \u003cp\u003eδ\u003csub\u003eu\u003c/sub\u003e(mm)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c13\"\u003e \u003cp\u003eTotal\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003ef\u003csub\u003eL/600\u003c/sub\u003e (MPa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eT\u003csub\u003e600\u003c/sub\u003e (N.m)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003ef\u003csub\u003ep\u003c/sub\u003e (MPa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eT\u003csub\u003epre\u003c/sub\u003e (N.m)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003ef\u003csub\u003eL/150\u003c/sub\u003e (MPa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003eT\u003csub\u003e150\u003c/sub\u003e (N.m)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c11\"\u003e \u003cp\u003ef\u003csub\u003eu\u003c/sub\u003e (MPa)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c12\"\u003e \u003cp\u003eT\u003csub\u003epost\u003c/sub\u003e (N.m)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c13\"\u003e \u003cp\u003eT\u003csub\u003etotal\u003c/sub\u003e\u003c/p\u003e \u003cp\u003e(N.m)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eOC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e6.17\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.7258\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c13\"\u003e \u003cp\u003e0.7258\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eS2.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e8.46\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.5632\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e12.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e2.9586\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e2.07\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e8.0891\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e9.2704\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c13\"\u003e \u003cp\u003e12.229\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e(SR)2.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e8.83\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.5198\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e11.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e2.2662\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1.69\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e6.9678\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0.42\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e8.7137\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c13\"\u003e \u003cp\u003e10.98\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eR2.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3.25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.7841\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e10.48\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1.3882\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.91\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e4.2550\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e4.7999\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c13\"\u003e \u003cp\u003e6.188\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eS5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e10.88\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.9342\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e12.22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e5.6497\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e9.27\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e17.8014\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e1.09\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e35.4892\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c13\"\u003e \u003cp\u003e41.139\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e(SR)5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e9.08\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.7095\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e11.49\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e2.5411\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e3.65\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e11.1146\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0.46\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e15.5125\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c13\"\u003e \u003cp\u003e18.0536\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eR5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e6.21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.4919\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e10.71\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1.5691\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e2.51\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e8.1995\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e0.43\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e12.1011\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c13\"\u003e \u003cp\u003e13.6702\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cdiv id=\"Sec14\" class=\"Section3\"\u003e \u003ch2\u003e3.3.1 Fiber content effect on flexural strength\u003c/h2\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e8\u003c/span\u003e demonstrates that higher fiber content in single-fiber FRC samples significantly increase pre-peak strength (f\u003csub\u003e600\u003c/sub\u003e), indicative of crack initiation strength. Specifically, FRCs with only RSTF saw this strength nearly double with a doubled fiber content. Single-STF specimens showed a 28% increase in crack initiation strength with doubled fiber content, whereas hybrid samples experienced a marginal 3% increase.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eRegarding peak strength (f\u003csub\u003ep\u003c/sub\u003e), none of the three approaches single-STF, single-RSTF, and hybrid\u0026mdash;show significant improvement in f\u003csub\u003ep\u003c/sub\u003e, with hybrid samples displaying a modest 4% increase at most. Yet, the presence of fibers distinctly enhances f\u003csub\u003ep\u003c/sub\u003e compared to ordinary concrete, which obtains an f\u003csub\u003ep\u003c/sub\u003e nearly 40% lower than the lowest FRC specimen. The impact of fiber content on f\u003csub\u003ep\u003c/sub\u003e is nuanced; too much fiber contents may negatively affect f\u003csub\u003ep\u003c/sub\u003e by disrupting the aggregate-cement bond and causing a heterogeneous FRC behavior, leading to a weaker concrete matrix and reduced f\u003csub\u003ep\u003c/sub\u003e at lower stress levels. Consequently, excessive fiber content is as detrimental as none in terms of f\u003csub\u003ep\u003c/sub\u003e. Both 0.25% vf and 0.5% vf fiber content achieve comparable f\u003csub\u003ep\u003c/sub\u003e stresses, suggesting these can be near-optimal values for fiber contents for achieving optimal f\u003csub\u003ep\u003c/sub\u003e. All samples showed significant improvement in post-peak strength (f\u003csub\u003e150\u003c/sub\u003e) with increased fiber content. Specifically, single-STF samples saw a 350% increase in f\u003csub\u003e150\u003c/sub\u003e. Single-RSTF and hybrid samples also doubled their strength with higher fiber content. These results underscore STF's impact on the post-peak flexural strength of FRC specimens, attributed to the double-hooked ends of the fibers preventing complete pull-out and enhancing load resistance without losing bond to the concrete matrix. This is particularly evident when comparing S2.5 and S5 samples, highlighting a marked enhancement in f\u003csub\u003e150\u003c/sub\u003e with fiber content increase. All FRC samples, behave in a way that an ultimate strength (f\u003csub\u003eu\u003c/sub\u003e) can be associated to them. However, the ordinary concrete sample shows a brittle behaviour and no ultimate strength (f\u003csub\u003eu\u003c/sub\u003e) can be recorded. In short, while low-fiber mixtures in FRC perform comparably in their elastic zone to others, high-fiber mixes more significantly enhance plastic behavior. Both high and low fiber samples significantly improve both plastic and elastic behaviors over ordinary concrete.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec15\" class=\"Section3\"\u003e \u003ch2\u003e3.3.2. Hybridization effect on flexural strength\u003c/h2\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e9\u003c/span\u003e highlights the importance of comparing single-fiber and hybrid approaches in FRC. In the low-fiber group of FRC samples, the hybrid mixture's pre-peak flexural strength is notably higher than single-fiber samples. This superior performance suggests that the hybrid approach, leveraging both STF and RSTF, results in enhanced structural behavior under pre-peak loads. Although the peak strength of the hybrid (SR)\u003csub\u003e2.5\u003c/sub\u003e mix is on par with single-fiber mixtures, it is achieved with half the amount of STFs used in S2.5, making it advantageous. Furthermore, the hybrid sample registers the highest ultimate flexural strength, indicating that the FRC sustains less damage when utilizing a combination of fiber types.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn high-fiber samples, particularly in the (SR)5 hybrid approach, results indicate an intermediate outcome between those of single-straight steel fibers (STF) and single-recycled steel fibers (RSTF). However, values for f600 and fp demonstrate closer similarity to the single-STF approach, while the f150 value in (SR)5 aligns more closely with the behavior observed in the R5 samples. These findings underscore that in higher fiber content scenarios, which correlate directly with increased STF content, STF play a more substantial role in influencing the flexural post-peak behavior of FRC samples. This observation highlights the potential of STFs to enhance post-peak ductility and provides justification for the f150 values observed in the (SR)5 samples. Furthermore, it is noteworthy that all hybrid samples exhibit higher pre-peak strength compared to the peak strength of ordinary concrete, indicating greater resistance to crack initiation in hybrid mixes relative to ordinary concrete.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"4. Numerical Analysis","content":"\u003cp\u003eThe flexural properties of tunnel segments were analyzed using a 3D finite element model developed with ABAQUS 2022 software (Smith M. ABAQUS / Standard User\u0026rsquo;s Manual. Dassault Syst`emes Simulia Corp and 2022 2022). This study compared two types of reinforced segments within the finite element models: segments reinforced with traditional rebar in real-world conditions using ordinary concrete, and segments with a 50% reduction in traditional rebar, employing optimized fiber-reinforced concrete mix design of previous section. Notably, a comprehensive analysis of the mechanical properties of fiber-reinforced concrete (FRC) and ordinary concrete, presented in the previous section, demonstrated that the hybrid use of FRC outperformed the single-use forms, both in high and low volume content mixtures. Based on these findings, the material properties for both ordinary concrete and the optimized fiber-reinforced concrete mix (SR)5 were used in this section. Therefore, all references to FRC in this part of the study pertain to the optimized (SR)5 mix design.\u003c/p\u003e\n\u003cdiv id=\"Sec17\"\u003e\n \u003ch2\u003e\u003cstrong\u003e4.1 validation of model by comparison between the numerical and experimental data through three-point bending analysis\u003c/strong\u003e\u003c/h2\u003e\n \u003cp\u003eTo ensure the fidelity of the numerical analyses conducted in this study, three-point bending tests were employed for verification, specifically tailored to the ordinary and optimized FRC samples from the experimental phase, denoted as (SR)\u003csub\u003e5\u003c/sub\u003e. This validation step confirms that the model\u0026apos;s predictions of the flexural performance closely align with the observed experimental outcomes. Comparative assessments were made between the data obtained from experimental tests and numerical analyses. Two beams, one composed of ordinary concrete and the other of fiber-reinforced concrete, underwent three-point loading conditions both in a laboratory setting and through finite element software simulations. A comprehensive finite element model was developed for the three-point bending test, employing the C3D8R mesh designation. This element type was chosen for its robustness in accurately capturing the intricate behavior of concrete under flexural stress, closely mirroring laboratory test conditions. The simulation replicates real-world scenarios by using two robust steel roller supports that mimic the experimental setup precisely. The Concrete Damage Plasticity model was utilized to analyze the deformation behavior of both ordinary and FRC samples. This constitutive model enables a detailed depiction of concrete\u0026apos;s cracking and crushing behavior under stress, facilitating an accurate simulation of damage and eventual failure. The CDP parameters were calibrated using empirical data to ensure alignment between the model\u0026apos;s predictions and observed physical phenomena. The numerical models were leveraged to extrapolate maximum deflection and flexural strength, pivotal indicators of structural performance. The model\u0026apos;s predictive capability was validated by comparing its computational outputs with empirical data collected from physical experiments, demonstrating enhanced simulation accuracy. Figure\u0026nbsp;10 illustrates the numerical model of the three-point bending test, while Table\u0026nbsp;\u003cspan\u003e8\u003c/span\u003e provides an in-depth comparison between experimental results and data obtained from finite element studies. It is noteworthy that \u0026quot;\u0026delta;peak\u0026quot; denotes the peak deflection, representing the maximum displacement experienced by the beam during the three-point bending test, while \u0026quot;Mr\u0026quot; signifies flexural strength, a measure of the material\u0026apos;s resistance to bending or flexural loads. These parameters are instrumental in evaluating structural performance under bending loads. The comparison reveals a satisfactory level of agreement across all studied parameters.\u003c/p\u003e\n \u003cdiv\u003e\u003cbr\u003e\u003c/div\u003e\n \u003cp\u003e\u003cstrong\u003eFigure\u0026nbsp;10. Verification of\u003c/strong\u003e numerical and experimental Model of 3PB test.\u003c/p\u003e\n \u003cdiv\u003e\n \u003ctable id=\"Tab8\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv\u003eTable 8\u003c/div\u003e\n \u003cdiv\u003e\n \u003cp\u003ecomparison between the results of experimental and finite elements methods.\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\u0026nbsp;\u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eOrdinary Concrete\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003eFiber reinforced concrete\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u0026delta;\u003csub\u003epeak\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNumerical\u0026thinsp;=\u0026thinsp;0.210mm\u003c/p\u003e\n \u003cp\u003eExperimental\u0026thinsp;=\u0026thinsp;0.225 mm\u003c/p\u003e\n \u003cp\u003eDifference ratio\u0026thinsp;=\u0026thinsp;7.1%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNumerical\u0026thinsp;=\u0026thinsp;0.84mm\u003c/p\u003e\n \u003cp\u003eExperimental\u0026thinsp;=\u0026thinsp;0.88 mm\u003c/p\u003e\n \u003cp\u003eDifference ratio\u0026thinsp;=\u0026thinsp;5%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eM\u003csub\u003er\u003c/sub\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNumerical\u0026thinsp;=\u0026thinsp;5.81 MPa\u003c/p\u003e\n \u003cp\u003eExperimental\u0026thinsp;=\u0026thinsp;6.17 MPa\u003c/p\u003e\n \u003cp\u003eDifference ratio\u0026thinsp;=\u0026thinsp;6.1%\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eNumerical\u0026thinsp;=\u0026thinsp;11.03 MPa\u003c/p\u003e\n \u003cp\u003eExperimental\u0026thinsp;=\u0026thinsp;11.49 MPa\u003c/p\u003e\n \u003cp\u003eDifference ratio\u0026thinsp;=\u0026thinsp;4.2%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n \u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec18\"\u003e\n \u003ch2\u003e4.2. Three-dimensional modeling procedure\u003c/h2\u003e\n \u003cp\u003eFigure\u0026nbsp;\u003cspan\u003e11\u003c/span\u003e displays the 3D finite element model, including the geometry of the segment and its rebar, which contains 35,216 elements. The model\u0026apos;s boundary was fixed in three directions, while the side boundaries were kept free to displace vertically.\u003c/p\u003e\n \u003cp\u003eThe Concrete Damage Plasticity constitutive model was adopted for the concrete segments to simulate the inelastic behaviour of concrete by incorporating isotropic-damaged elasticity alongside tensile and compressive plasticity. After a thorough review of existing literature, it was determined that no dedicated model exists specifically for comprehensively modelling FRC materials. However, previous studies provide insights into modelling FRC materials using the CDP approach. The flexibility of the CDP model allows for adjustments to its material property descriptors to better suit the characteristics of FRC. In this study, laboratory analyses of FRC, detailed in the experimental section, served as the foundation for calibrating our model. Additionally, through validation against data obtained from three-point bending tests, rigorous efforts were made to enhance the accuracy of the CDP model in simulating the performance of FRC. Figure\u0026nbsp;\u003cspan\u003e12\u003c/span\u003e illustrates the response of concrete-based materials under compressive and tensile stresses, factors considered within the CDP model.\u003c/p\u003e\n \u003cp\u003eFigure 13 and Fig. 14 provides essential data required to characterize the behavior of primary support in the Concrete Damage Plasticity model for tunnel construction. These data were obtained through laboratory tests detailed in previous sections of this paper. Empirical relationships and back-calculation procedures, following the guidelines outlined in ACI 544.8R-16, were employed to determine the tensile parameters. To establish the tension parameters, a closed-form solution of the moment-curvature response and a load-deflection calculation specific to fiber-reinforced concrete (FRC) were utilized. These methods, proposed by (Soranakom and Mobasher \u003cspan\u003e2007\u003c/span\u003e)and (Soranakom, Yekani-Fard et al. 2008), link the simplified stress-strain tensile model to flexural test results. Additionally, the data presented in Table\u0026nbsp;9, along with other material characteristics such as dilation angle, eccentricity, the ratio of biaxial to uniaxial compression (Kc), and viscosity, were defined within the CDP model.\u003c/p\u003e\n \u003cdiv\u003e\u003cstrong\u003eFigure\u0026nbsp;13.\u003c/strong\u003e (a) Compressive and (b) Tensile behavioral curve in ordinary and optimum FRC sample\u003c/div\u003e\n \u003cdiv\u003e\u003cstrong\u003eFigure\u0026nbsp;14.\u003c/strong\u003e (a) Compressive and (b) Tensile damage parameter curve in ordinary and optimum FRS sample.\u003c/div\u003e\n\u003c/div\u003e"},{"header":"5. Numerical results","content":"\u003cdiv id=\"Sec20\"\u003e\n \u003ch2\u003e5.1. Tensile damage under flexural stresses\u003c/h2\u003e\n \u003cp\u003eFigure\u0026nbsp;15 illustrates the DAMAGET contours for the final linings of metro tunnels, comparing scenarios using Traditional Rebar with Ordinary Concrete and 50% Traditional Rebar with Fiber-Reinforced Concrete. DAMAGET represents the level of tensile damage in concrete, ranging from 0 (no damage) to 1 (complete failure). Using 50% Traditional Rebar with FRC resulted in approximately a 30% reduction in DAMAGET compared to the scenario with Traditional Rebar and Ordinary Concrete. Additionally, the damaged zone area notably decreased when using FRC compared to ordinary shotcrete. These findings underscore the effectiveness of fiber-reinforced concrete in enhancing the performance and safety of tunnel support structures. Notably, the tensile damage in FRC and its dynamic behavior under earthquake loading are interconnected. The inclusion of fibers in FRC enhances its tensile strength and ductility, mitigating the risk of cracking or rupture under seismic conditions.\u003c/p\u003e\n \u003cdiv\u003e\u003cstrong\u003eFigure\u0026nbsp;15.\u003c/strong\u003e DAMAGET contour for different tunnel lining support.\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec21\"\u003e\n \u003ch2\u003e5.2. Principal stress mobilizes on segment\u003c/h2\u003e\n \u003cp\u003eFigure\u0026nbsp;16 and Fig.\u0026nbsp;17 meticulously depict the stress responses when comparing the use of Traditional Rebar with Ordinary Concrete against employing 50% Traditional Rebar with Fiber-Reinforced Concrete for metro tunnel segments. These visual representations offer a comprehensive analysis, showcasing von Mises stress contours alongside principal stresses in the vertical dimension (S, S33). Such detailed illustrations are instrumental in understanding the nuanced stress behaviors exhibited by different materials, a crucial aspect in engineering evaluations. Von Mises stress, a pivotal parameter for predicting material yield under diverse loading conditions, holds particular significance in tunnel construction. Notably, with the adoption of 50% Traditional Rebar with FRC, substantial improvements in stress responses are evident. Figure\u0026nbsp;16 underscores this improvement, revealing a significant 2.6-fold increase in von Mises stress. Moreover, notable disparities emerge in the comprehensive analysis of major stresses, as showcased in Fig.\u0026nbsp;16 and Fig.\u0026nbsp;17. For instance, the stress in the y-direction (S33) escalates from 1.8e6 Pa in ordinary concrete to 3.22e6 Pa in FRC. These findings not only underscore the effectiveness of combining traditional rebar with FRC in stress management but also offer valuable insights for engineering applications in tunnel construction. Furthermore, our FRC samples contain recycled fibers, which are environmentally friendly and cost-saving. The use of recycled fibers significantly reduces the environmental footprint of construction materials by diverting waste from landfills and decreasing the demand for virgin materials. This sustainable approach not only benefits the environment but also results in substantial cost savings. The reduction in material costs, combined with a 50% decrease in rebar usage, translates into significant financial benefits for the project. This not only lowers overall expenses but also streamlines construction processes, making the project more economically viable and efficient in the long run Fig.\u0026nbsp;16 and Fig.\u0026nbsp;17 meticulously depict the stress responses when comparing the utilization of Traditional Rebar with Ordinary Concrete against employing 50% Traditional Rebar with FRC for metro tunnel segments. These visual representations offer a comprehensive analysis, showcasing von Mises stress contours alongside principal stresses on the vertical dimension (S, S33). Such detailed illustrations are instrumental in understanding the nuanced stress behaviors exhibited by different materials, a crucial aspect in engineering evaluations. Von Mises stress, a pivotal parameter for predicting material yield under diverse loading conditions, holds particular significance in tunnel construction. Notably, with the adoption of 50% Traditional Rebar with Fiber-Reinforced Concrete, substantial improvements in stress responses are evident. Figure\u0026nbsp;16 underscores this improvement, revealing a significant 2.6 times increase in von Mises stress. Moreover, notable disparities emerge in the comprehensive analysis of major stresses, as showcased in Fig.\u0026nbsp;16 and Fig.\u0026nbsp;17.. For instance, the stress in the y-direction (S33) escalates from 1.8e6 Pa in ordinary concrete to 3.22e6 Pa in FRC. These findings not only underscore the effectiveness of combining traditional rebar with FRC in stress management but also offer valuable insights for engineering applications in tunnel construction. It\u0026apos;s worth emphasizing that this conclusion is underpinned by a substantial 50% reduction in rebar usage, yielding significant financial benefits for the project. This reduction not only translates into cost savings but also streamlines construction processes, making the project more economically viable and efficient in the long run.\u003c/p\u003e\n \u003cdiv\u003e\u003cstrong\u003eFigure\u0026nbsp;16.\u003c/strong\u003e Mises stress for a segment with different material.\u003c/div\u003e\n \u003cdiv\u003e\u003cstrong\u003eFigure\u0026nbsp;17.\u003c/strong\u003e Stresses in Y direction (S33) for a segment with different material.\u003c/div\u003e\n\u003c/div\u003e\n\u003cdiv id=\"Sec22\"\u003e\n \u003ch2\u003e5.3. Vertical displacement under flexural loading\u003c/h2\u003e\n \u003cp\u003eIn the U3 analysis, which focuses on vertical displacement, the comparison between using Ordinary Concrete and employing 50% Traditional Rebar with Fiber-Reinforced Concrete for metro tunnel segments reveals significant findings. As illustrated in Fig.\u0026nbsp;18 vertical displacement experiences a remarkable reduction of 60% when utilizing the FRC sample compared to Ordinary Concrete. This reduction is immensely important for the performance of concrete segments. Decreased vertical displacement signifies enhanced stability and structural integrity, crucial factors in tunnel construction where maintaining dimensional stability is paramount.The utilization of fiber-reinforced concrete plays a pivotal role in achieving this reduction. Fibers, such as steel or synthetic fibers, are incorporated into the concrete mix to improve ductility and enhance the material\u0026apos;s ability to withstand tensile stresses. In the context of tunnel segments, where the concrete is subjected to various loading conditions and potential deformations, the introduction of fibers significantly enhances the material\u0026apos;s capacity to resist cracking and deformation, ultimately leading to reduced vertical displacement. Moreover, the reduction in displacement not only ensures the structural stability of the tunnel segments but also contributes to the overall safety and longevity of the infrastructure. By employing FRC, engineers can achieve an optimal balance between structural strength and flexibility, mitigating the risk of excessive deformation while maintaining the integrity of the tunnel structure over time. The observed decrease in vertical displacement highlights the effectiveness of utilizing fiber-reinforced concrete as a means of vastly improving the performance and durability of concrete segments in metro tunnel construction. Additionally, the use of recycled fibers in FRC further amplifies its benefits. These environmentally friendly fibers reduce the environmental footprint by minimizing waste and decreasing the reliance on virgin materials. This sustainable approach not only promotes environmental stewardship but also results in substantial cost savings. The combined benefits of reduced material costs and a significant decrease in rebar usage translate into considerable financial advantages, making the project more economically viable and efficient in the long run.\u003c/p\u003e\n \u003cdiv\u003e\u003cstrong\u003eFigure\u0026nbsp;18\u003c/strong\u003e. displacement in Y direction (U33) for a segment with different material.\u003c/div\u003e\n\u003c/div\u003e"},{"header":"6. Conclusion","content":"\u003cp\u003eThis study extensively evaluated the flexural performance of metro tunnel segments reinforced with traditional rebar and fiber-reinforced concrete. Through experimental and numerical analyses, the efficacy of FRC in enhancing structural integrity, stress management, and reducing displacement was demonstrated. Additionally, the use of recycled fibers provided significant economic and environmental benefits. The validated finite element model using the Concrete Damage Plasticity approach proved to be a reliable tool for simulating concrete behavior under stress. The conclusions of this study are categorized below:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eEnhanced structural performance\u003c/b\u003e: Incorporating FRC with a 50% reduction in traditional rebar significantly improved the flexural strength and reduced tensile damage in tunnel segments, as confirmed by both experimental and numerical analyses.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eEffective stress management\u003c/b\u003e: The 3D finite element model revealed substantial improvements in stress responses, with a 2.6-fold increase in von Mises stress and significant escalation in principal stresses (S33) from 1.8e6 Pa in ordinary concrete to 3.22e6 Pa in FRC.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eReduction in vertical displacement\u003c/b\u003e: Vertical displacement analysis showed a remarkable 60% reduction when utilizing FRC compared to ordinary concrete, indicating enhanced stability and dimensional integrity of the tunnel segments.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eEconomic and environmental benefits\u003c/b\u003e: Using recycled fibers in FRC not only improved structural performance but also provided cost savings and environmental benefits by reducing the demand for virgin materials and overall material costs.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eSuperior flexural behavior\u003c/b\u003e: Experimental results quantitatively demonstrated that FRC beams exhibited a 25% increase in flexural load-carrying capacity and a 20% improvement in deflection performance compared to ordinary concrete beams, showcasing its potential for resisting cracking, enhancing durability, and managing higher load capacities in tunnel applications.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003e \u003cb\u003eImproved tensile and compressive performances\u003c/b\u003e: Experimental results quantitatively demonstrated that FRC exhibited a 25% increase in tensile strength and a 15% increase in compressive strength compared to ordinary concrete, showcasing its potential for resisting cracking, enhancing durability, and managing higher load capacities in tunnel applications.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAuthor Contributions:\u003c/strong\u003e \u003cstrong\u003e\u003cem\u003eAlireza Ahmadi\u003c/em\u003e\u003c/strong\u003e: Writing- Original draft, Methodology, Investigation. \u003cstrong\u003e\u003cem\u003eAmin Tohidi\u003c/em\u003e\u003c/strong\u003e: Supervision, Conceptualization, Methodology, Investigation. \u003cstrong\u003e\u003cem\u003eHassan Negahdar\u003c/em\u003e\u003c/strong\u003e: Data curation, Writing- Original draft preparation. \u003cstrong\u003e\u003cem\u003eMohammad Reza Shakeri\u003c/em\u003e\u003c/strong\u003e: preparation, Methodology. All authors reviewed the manuscript.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u0026nbsp; \u003cstrong\u003eDeclarations Competing Interests\u003c/strong\u003e: The authors declare no competing interests\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eAfroughsabet, V. and T. Ozbakkaloglu (2015). \u0026quot;Mechanical and durability properties of high-strength concrete containing steel and polypropylene fibers.\u0026quot; \u003cu\u003eConstruction and Building Materials\u003c/u\u003e\u003cstrong\u003e94\u003c/strong\u003e: 73-82.\u003c/li\u003e\n \u003cli\u003eAmjadi, M., et al. (2023). \u0026quot;Comparing pull-out capacity of expandable anchors using discrete/coupled Eulerian element methods versus finite element technique.\u0026quot; \u003cu\u003eMarine Georesources \u0026amp; Geotechnology\u003c/u\u003e: 1-16.\u003c/li\u003e\n \u003cli\u003eAsheghi Mehmandari, T. 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University of Amsterdam, Netherlands.\u003c/li\u003e\n\u003c/ol\u003e"},{"header":"Table 1 and 2","content":"\u003cp\u003eTable 1 and 2 are available in the Supplementary Files section.\u003c/p\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Tunnel lining segment, Flexural performance, Recycled steel fiber, Hybrid fiber reinforced concrete, Finite Element Method (FEM)","lastPublishedDoi":"10.21203/rs.3.rs-4808296/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4808296/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study investigates the flexural performance of metro tunnel segments reinforced with traditional rebar and fiber-reinforced concrete (FRC). Utilizing a comprehensive experimental approach, the mechanical properties of FRC were determined and compared with ordinary concrete through rigorous laboratory tests. A detailed numerical analysis was conducted using a 3D finite element model (FEM) in ABAQUS 2022, validated with experimental data. The FEM assessed segments reinforced with traditional rebar versus those with a 50% reduction in rebar, supplemented by FRC. The Concrete Damage Plasticity (CDP) model effectively simulated the flexural behavior, revealing a 30% reduction in tensile damage with FRC. Further analysis revealed significant improvements in stress responses, including a 2.6-fold increase in von Mises stress and a 60% reduction in vertical displacement. These findings highlight the enhanced structural performance and economic benefits of incorporating FRC with reduced rebar, as well as the environmental advantages of using recycled fibers. This study provides critical insights into optimizing tunnel segment reinforcement, promoting both structural integrity and sustainability in tunnel construction projects.\u003c/p\u003e","manuscriptTitle":"Flexural Performance of Tunnel lining Segments using Fiber Reinforced Concrete: A Study on Recycled and Industrial Fibers Through Experimental and Numerical Methods","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-08-22 09:11:04","doi":"10.21203/rs.3.rs-4808296/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"ecb4cf39-d969-476b-9765-2cf45ecc4b74","owner":[],"postedDate":"August 22nd, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-10-15T10:54:28+00:00","versionOfRecord":[],"versionCreatedAt":"2024-08-22 09:11:04","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4808296","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4808296","identity":"rs-4808296","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}