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To measure the electromagnetic properties of steel fiber-reinforced concrete (SFRC) in the X-band, 1-port measurements were performed using a lens horn antenna in a free-space measurement system. Free-space 1-port calibration with translations of the position of the reflector regarding the characteristics of the focused beam lens horn antenna was applied. The intrinsic impedance and complex permittivity of the SFRC were obtained from the measured reflection characteristics. The steel fiber content increased and the electromagnetic properties of the SFRC gradually changed from a dielectric to a conductor, even in very low frequencies compared to the plasma frequencies of general metal, which are optical frequencies. This is considered to be the plasmon effect of the metallic structure formed by the steel fiber. This result is applicable for analyses of the electromagnetic phenomenon of large structures with fiber content.
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Adding fibers is highly effective to enhance the deflection and ductility of fiber-reinforced polymer (FRP)-reinforced beams. In this study, the stress and strain conditions of FRP-reinforced lightweight aggregate concrete (LWC) beams with and without fibers at ultimate load level were specified. Based on the sectional analyses, alternative equations to predict the balanced reinforcement ratio and flexural capacity for beams failed by balanced failure and concrete crushing were established. A rational equation for estimating the short-term stiffness of FRPâ»LWC beams at service-load levels was suggested based on Zhu's model. In addition, the contribution of the steel fibers on the short-term stiffness was quantified incorporating the effects of FRP reinforcement ratio. The proposed short-term stiffness model was validated with measured deflections from an experimental database for fiber-reinforced normal weight concrete (FNWC) beams reinforced with FRP bars. Furthermore, six glass fiber-reinforced polymer (GFRP)-reinforced LWC beams with and without steel fibers were tested under four-point bending. Based on the test results, the proposed models and procedures according to current design codes ACI 440.1R, ISIS-M03, GB 50608, and CSA S806 were linked together by comparing their predictions. The results showed that increasing the reinforcement ratio and adding steel fibers decreased the strain of the FRP bars. The flexural capacity of the LWC beams with and without steel fibers was generally underestimated by the design codes, while the proposed model provided accurate ultimate moment predictions. Moreover, the proposed short-term stiffness model yielded reasonable estimations of deflection for both steel fiber-reinforced lightweight aggregate concrete (SFLWC) and FNWC beams.
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With the advantages of high tensile, bending, and shear strength, steel fiber concrete structures have been widely used in civil engineering. The health monitoring of concrete structures, including steel fiber concrete structures, receives increasing attention, and the Electromechanical Impedance (EMI)-based method is commonly used. Structures are often subject to changing axial load and ignoring the effect of axial forces may introduce error to Structural Health Monitoring (SHM), including the EMI-based method. However, many of the concrete structure monitoring algorithms do not consider the effects of axial loading. To investigate the influence of axial load on the EMI of a steel fiber concrete structure, concrete specimens with different steel fiber content (0, 30, 60, 90, 120) (kg/m³) were casted and the Lead Zirconate Titanate (PZT)-based Smart Aggregate (SA) was used as the EMI sensor. During tests, the step-by-step loading procedure was applied on different steel fiber content specimens, and the electromechanical impedance values were measured. The Normalized root-mean-square deviation Index (NI) was developed to analyze the EMI information and evaluate the test results. The results show that the normalized root-mean-square deviation index increases with the increase of the axial load, which clearly demonstrates the influence of axial load on the EMI values for steel fiber concrete and this influence should be considered during a monitoring or damage detection procedure if the axial load changes. In addition, testing results clearly reveal that the steel fiber content, often at low mass and volume percentage, has no obvious influence on the PZT's EMI values. Furthermore, experiments to test the repeatability of the proposed method were conducted. The repeating test results show that the EMI-based indices are repeatable and there is a great linearity between the NI and the applied loading.
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This study examined the electrical and self-sensing capacities of ultra-high-performance fiber-reinforced concrete (UHPFRC) with and without carbon nanotubes (CNTs). For this, the effects of steel fiber content, orientation, and pore water content on the electrical and piezoresistive properties of UHPFRC without CNTs were first evaluated. Then, the effect of CNT content on the self-sensing capacities of UHPFRC under compression and flexure was investigated. Test results indicated that higher steel fiber content, better fiber orientation, and higher amount of pore water led to higher electrical conductivity of UHPFRC. The effects of fiber orientation and drying condition on the electrical conductivity became minor as sufficiently high amount of steel fibers, 3% by volume, was added. Including only steel fibers did not impart UHPFRC with piezoresistive properties. Addition of CNTs substantially improved the electrical conductivity of UHPFRC. Under compression, UHPFRC with a CNT content of 0.3% or greater had a self-sensing ability that was activated by the formation of cracks, and better sensing capacity was achieved by including greater amount of CNTs. Furthermore, the pre-peak flexural behavior of UHPFRC was precisely simulated with a fractional change in resistivity when 0.3% CNTs were incorporated. The pre-cracking self-sensing capacity of UHPFRC with CNTs was more effective under tensile stress state than under compressive stress state.
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Factory made steel fiber and steel fiber derived from worn tires was used to develop cement concrete, which was subjected to torsional forces. A dedicated stand for torsion tests, allowing for the measurement of force, deflection, and torsion angle, was used. The test results showed that both the factory-made fiber and the waste steel fiber significantly improved torsional properties of the concrete matrix. The test results of specimens made with waste fiber were characterized by slightly worse results compared to factory-made fibers, but there was a significant improvement in torsional properties compared to samples without fibers. Taking into account the financial and environmental benefits, the application of waste steel fiber recovered from car tires could be an interesting alternative to using commercially sold steel fiber applied for the production of construction elements subjected to torsional forces.
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Herein, a practical ultra-high-performance concrete (UHPC) was created by adding two different shapes of steel fibers and curing them at ambient temperature using palygorskite-nanofiber (PN) as the modifier. The compressive strength, flexural strength, water absorption capacity, and porosity were analyzed to determine the effects of the steel fibers and PNs on the UHPC mechanical and physical properties. The steel fibers and PNs were found to improve these properties. The UHPC mechanical properties were outstanding at 1.5% fiber dosage, while physical properties were excellent at 1.0% fiber dosage. The mechanical and physical characteristics of UHPC were preferably at a PN dosage of 0.2% and the fiber dosage of 1.0%. The compressive and flexural strengths of straight-steel-fiber UHPC were 145.57 and 19.67 MPa, respectively, i.e., 42.0 and 109.4% higher than those of the reference specimens (i.e., those without fibers or PNs); the water absorption capacity and porosity decreased by 50.1 and 60.7%, respectively. The compressive and flexural strengths of hooked-end-steel-fiber UHPC were 18.3 and 96.0% higher than those of the reference specimens, respectively, and the water absorption capacity and porosity decreased by 43.2 and 29.8%, respectively. These results could provide vital information for the promotion and practical application of UHPC.
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With diminishing natural aggregate resources and increasing environmental protection efforts, the use of recycled fine aggregate is a more sustainable approach, although challenges persist in achieving comparable mechanical properties. Exploration into the incorporation of steel fibers with recycled aggregate has led to the development of steel-fiber-reinforced recycled aggregate concrete. This study investigates the shrinkage performance and compressive constitutive relationship of steel fiber recycled concrete with different steel fibers and recycled aggregate dosages. Initially, based on different replacement rates of recycled coarse aggregate and different volume contents of steel fiber, experimental results demonstrate that as the replacement rate of recycled coarse aggregate increases, shrinkage also increases, while the addition of steel fiber can mitigate this effect. An empirical shrinkage model for steel fiber recycled concrete under natural curing conditions is also proposed. Subsequently, based on the uniaxial compression test, findings indicate that with an increasing replacement rate of recycled fine aggregate, the peak stress and elastic modulus of concrete decrease, accompanied by an increase in peak strain, and the addition of steel fiber limits concrete crack development and enhances its brittleness while the peak stress and strain of recycled fine aggregate concrete are enhanced. However, the steel fiber volume percentage has a negligible effect on the elastic modulus. A constitutive relationship for concrete considering the effects of recycled fine aggregate and steel fiber is also proposed. This finding provides foundational support for the influence patterns of steel fiber dosage and recycled aggregate ratio on the mechanical properties of steel fiber recycled concrete.
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This paper investigates the effects of steel fiber and PVA fiber hybrid blending on the compressive strength (fcc), splitting tensile strength (fts), compression energy (W1.0), and shrinkage properties of concrete. It also establishes a multi-factor crack resistance index evaluation model based on the Analytic Hierarchy Process (AHP) to comprehensively evaluate the crack resistance of concrete. The results show that the steel-PVA hybrid fiber (S-PVA HF) further enhances fcc, fts, the compression energy, and the shrinkage suppression properties of the concrete. The crack resistance of the steel-PVA hybrid fiber concrete (S-PVA HFRC) is the best when the proportion of steel fiber is 1.0% and that of the PVA fiber is 0.2%, and it increases up to 143% compared to the baseline concrete. The established concrete crack resistance evaluation model has a certain reliability.
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The associated effects of temperature and steel fiber content on the energy absorption properties of concrete were examined using quasi-static uniaxial compression tests of concrete materials with varied steel fiber contents (0%, 0.5%, 1%, and 1.5%) at various temperatures (20 °C, 200 °C, 400 °C, and 520 °C). The experimental findings demonstrate that steel fibers can greatly boost concrete's ability to absorb energy and that the toughness index rises with steel fiber concentration. The energy absorption capacity of concrete under high-temperature conditions also significantly decreases as temperature rises, and the energy absorption ability of steel fiber concrete under the same temperature is superior to that of plain concrete. The coupled influence factor K of temperature-steel fiber percentage characterizing the energy-absorbing ability of concrete was determined, and the coupled influence law of temperature and steel fiber content on the energy-absorbing capacity of concrete materials was summarized and analyzed on the basis of the experimental data of high-temperature compression. Equivalent equations for steel fiber reinforcing and temperature weakening effects when they are comparable (K = 1) are developed and equivalent parameters for concrete materials are given.
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Recycling rubber and/or steel fiber components of waste tires in construction applications is a venue for maximizing the recycling rate of these items. Additionally, it supports the move towards producing sustainable construction materials and conserving natural resources. Previous research explored the viability of employing recycled waste rubber particles as an alternative for natural aggregate. Despite the adverse effect of rubber on the mechanical properties of concrete (e.g., lower compressive strength), it produces several advantages, including excellent dynamic and ductility properties, which can be utilized in structural members critical to dynamic loads, e.g., blasts, earthquakes, and impacts. In an effort to expand the adoption of waste rubber in concrete beams and to eliminate key concerns associated with the degradation of their flexural behavior, the functionally graded (FG) beams concept was utilized. The present investigation comprised the testing of five beams using a four-point bending configuration. Plain concrete, rubberized concrete (RuC), and steel-fiber reinforced rubberized concrete (SFRRuC) beams were cast along with FG beams arranged in two layers. The top layer of the FG beams comprised plain concrete, while the bottom layer consisted of RuC or SFRRuC. Experimental findings indicated that the flexural behavior of the FG beam with layers of SFRRuC and plain concrete exceeded the flexural strength, displacement ductility ratio, and toughness performances of the plain concrete beam by 9.9%, 12.9%, and 24.4%, respectively. The moment-curvature relationship was also predicted for the tested beam and showed an excellent match with the experimentally measured relationship.
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Structural health monitoring (SHM) is crucial for maintaining concrete infrastructure. The data collected by these sensors are processed and analyzed using various analysis tools under different loadings and exposure to external conditions. Sensor-based investigation on concrete has been carried out for technologies used for designing structural health monitoring sensors. A Sensor-Infused Structural Analysis such as interfacial bond-slip model, corroded steel bar, fiber-optic sensors, carbon black and polypropylene fiber, concrete cracks, concrete carbonation, strain transfer model, and vibrational-based monitor. The compressive strength (CS) and split tensile strength (STS) values of the analyzed material fall within a range from 26 to 36 MPa and from 2 to 3 MPa, respectively. The material being studied has a range of flexural strength (FS) and density values that fall between 4.5 and 7 MPa and between 2250 and 2550 kg/m3. The average squared difference between the predicted and actual compressive strength values was found to be 4.405. With cement ratios of 0.3, 0.4, and 0.5, the shear strength value ranged from 4.4 to 5.6 MPa. The maximum shear strength was observed for a water-cement ratio of 0.4, with 5.5 MPa, followed by a water-cement ratio of 0.3, with 5 MPa. Optimizing the water-cement ratio achieves robust concrete (at 0.50), while a lower ratio may hinder strength (at 0.30). PZT sensors and stress-wave measurements aid in the precise structural monitoring, enhanced by steel fibers and carbon black, for improved sensitivity and mechanical properties. These findings incorporate a wide range of applications, including crack detection; strain and deformation analysis; and monitoring of temperature, moisture, and corrosion. This review pioneers sensor technology for concrete monitoring (Goal 9), urban safety (Goal 11), climate resilience (Goal 13), coastal preservation (Goal 14), and habitat protection (Goal 15) of the United Nations' Sustainable Development Goals.
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Ultra-high-performance concrete (UHPC) is an advanced cement-based material with excellent mechanical properties and durability. However, with the improvement of UHPC's compressive properties, its insufficient tensile properties have gradually attracted attention. This paper reviews the tensile properties of steel fibers in UHPC. The purpose is to summarize the existing research and to provide guidance for future research. The relevant papers were retrieved through three commonly used experimental methods for UHPC tensile properties (the direct tensile test, flexural test, and splitting test), and classified according to the content, length, type, and combination of the steel fibers. The results show that the direct tensile test can better reflect the true tensile strength of UHPC materials. The tensile properties of UHPC are not only related to the content, shape, length, and hybrids of the steel fibers, but also to the composition of the UHPC matrix, the orientation of the fibers, and the geometric dimensions of the specimen. The improvement of the tensile properties of the steel fiber combinations depends on the effectiveness of the synergy between the fibers. Additionally, digital image correlation (DIC) technology is mainly used for crack propagation in UHPC. The analysis of the post-crack phase of UHPC is facilitated. Theoretical models and empirical formulas for tensile properties can further deepen the understanding of UHPC tensile properties and provide suggestions for future research.
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This study proposes a novel approach by adding Portland limestone cement (PLC) to preplaced aggregate steel fiber reinforced concrete (PASFRC) to create a sustainable concrete that minimizes CO2 emissions and cement manufacturing energy usage. The method involves injected a flowable grout after premixing and preplacing steel-fibers and aggregates in the formwork. This study evaluates the mechanical properties of a novel sustainable concrete that uses PLC and steel fibers. To achieve the intended objective, long and short end-hooked steel fibers of 1%, 2%, 3%, and 6% were incorporated in PASFRC. Also, Analysis of variance (ANOVA) was used to examine the data. Results indicated that PLC and higher fiber doses increased the mechanical properties of PAC. At 90 days, PASFRC mixtures containing 6% long steel fibers demonstrated superior compressive, tensile, and flexural strengths, registering the highest values of 49.8 MPa, 7.7 MPa, and 10.9 MPa, respectively and differed by 188%, 166%, and 290%, respectively from fiberless PAC. The study confirmed the suitability and effectiveness of using PLC with steel fibers in PAC which significantly improved the mechanical properties of PASFRC. This was verified through analytical analysis and new empirical equations were proposed to predict the mechanical properties of PASFRC.
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In cold areas, the steel fiber reinforced rubber concrete (SFRRC) pavement is exposed to natural environment and experiences varying degrees of damage from freezing and thawing. This can have a serious impact on the normal usage and safe operation of the pavement structure. This research examines the impact of varying rubber concentrations on multiple variables, such as the rate of mass reduction, relative dynamic modulus of elasticity, compressive strength, and thickness of the damage layer (Hf) during freeze-thaw (F-T) durability testing conducted on SFRRC. Furthermore, an analysis is conducted to determine the degradation pattern exhibited by SFRRC. The internal structure evolution and pore structure characteristics of SFRRC were examined using scanning electron microscopy and mercury intrusion porosimetry techniques, which revealed the underlying damage mechanism in SFRRC during F-T cycles. The results suggest that the addition of an appropriate amount of rubber can effectively enhance the frost resistance of SFRRC in water. A gradual improvement in the frost resistance of SFRRC is observed when increasing the rubber content from 0 to 10%. The optimal frost resistance is observed in SFRRC with 10% rubber content. However, when the rubber content reaches 15%, SFRRC exhibits significant degradation and lower level of resistance to freezing compared to SFRRC without rubber. Microcracks form within SFRRC due to the freezing-thawing forces experienced during the experiment, resulting in the development of a damage layer that extends from the surface to the interior. The compressive strength of the damaged layer significantly decreases as Hf increases. The addition of appropriate rubber in SFRRC improves its pore structure, leading to an increased proportion of harmless or less harmful pores and a reduction in average pore size, thereby significantly enhancing its frost resistance.
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Fiber concrete exhibits superior performance in various aspects compared to plain concrete and has been widely researched and applied worldwide. However, many industrially made fibers are expensive, and their cost has to be considered before use; thus, it would be economically valuable to find inexpensive fibers with excellent properties to make fiber concrete. Rural areas have many rich straw resources to be disposed of; at the same time, the rapid development of the automobile industry has introduced a large number of used tires containing steel wire with a very low reuse rate. These two low-cost materials can be processed to make fibers, making the study of mechanical properties regarding their incorporation into concrete practically significant for reducing the cost of fiber concrete. Based on this, a three-factor, three-level orthogonal test was conducted to investigate the effects of different dosages of corn straw fibers and scrap steel fibers, as well as the water-cement ratio, on the mechanical properties of concrete. The optimum level of each factor for blended straw-waste-steel-fiber concrete with different mechanical properties was obtained using the polar and ANOVA methods. It was found that the compressive strength, splitting tensile strength, flexural strength, and impact resistance of the specimens after fiber dosing were better than those of plain concrete specimens with the same water-cement ratio. The maximum improvement was 14.96% in cubic compressive strength, 42.90% in tensile strength, and 16.30% in flexural strength, while the maximum improvement in impact energy consumption at the final crack was 228.03%. Combined with SEM microanalysis, the two fibers formed a stronger whole with the C-S-H gel. When the specimen was subjected to load, the two fibers were able to withstand part of the load, thus enhancing the load-bearing capacity. Finally, the optimal mix ratio of blended straw-scrap-steel-fiber concrete was determined to be 0.8% corn straw fibers by volume, 0.6% scrap steel fibers by volume, and a 0.45 water-cement ratio by combining the weights of the levels of each factor under its four different mechanical properties through hierarchical analysis. This analysis of mechanical properties provides a reference for practical applications in future projects.
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In the current investigation, the effect of recycled steel fibers recovered from waste tires on the pull-out response of ribbed steel bars from carbon nanotube (CNT)-modified ultrahigh performance fiber reinforced concrete (UHPFRC) was considered using the multiscale finite element method (MSFEM). The MSFEM is based on three phases to simulate CNT-modified UHPC, recycled steel fibers (RSFs), and ribbed steel bars. For the first time, a bar ribbed has been simulated to make more realistic assumptions, and RSFs have been distributed in the form of curved cylinders of different lengths and with a random distribution within a concrete matrix. The interaction of the steel bar and the RSFs with the concrete is applied by the cohesive zone model (CZM). After confirming the simulation outcomes with the experimental results, the steel bar pull-out response is investigated using load-slip curves. The impact of the CNT content, RSFs and their aspect ratio on the bond strength of steel bars and CNT-modified UHPFRC was assessed. The results show that using RSFs with a lower aspect ratio (steel microfibers) significantly improves the pull-out characteristics of steel bars from concrete. Accordingly, the proposed MSFEM is considered for simulating the effects of different parameters on the pull-out response of ribbed steel bars from concrete without causing complex, time-consuming, or costly experiments. The results indicated that waste fiber or RSF can be used as a toughening component in CNT-modified ultrahigh-performance concrete and as a replacement for industrial steel fibers.
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Brittle shear failure of beam-column joints, especially during seismic events poses a significant threat to structural integrity. This study investigates the potential of steel fiber reinforced concrete (SFRC) in the joint core to enhance ductility and overcome construction challenges associated with traditional reinforcement. A non-linear finite element analysis (NLFEA) using ABAQUS software was conducted to simulate the behavior of SFRC beam-column joints subjected to cyclic loading. Ten simulated specimens were analyzed to discern the impact of varying steel fiber volume fraction and aspect ratio on joint performance. Key findings reveal that a 2% volume fraction of steel fibers in the joint core significantly improves post-cracking behavior by promoting ductile shear failure, thereby increasing joint toughness. While aspect ratio variations showed minimal impact on load capacity, long and thin steel fibers effectively bridge cracks, delaying their propagation. Furthermore, increasing steel fiber content resulted in higher peak-to-peak stiffness. This research suggests that strategically incorporating SFRC in the joint core can promote ductile shear failure, enhance joint toughness, and reduce construction complexities by eliminating the need for congested hoops. Overall, the developed NLFEA model proves to be a valuable tool for investigating design parameters in SFRC beam-column joints under cyclic loading.
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The study and utilization of fully recycled aggregate concrete (FRAC), in which coarse and fine aggregates are completely replaced by recycled aggregates, are of great significance in improving the recycling rate of construction waste, reducing the carbon emission of construction materials, and alleviating the ecological degradation problems currently faced. In this paper, investigations were carried out to study the effects of steel fiber (0.5%, 1.0%, and 1.5%) and polypropylene fiber (0.9 kg/m3, 1.2 kg/m3 and 1.5 kg/m3) on the properties of FRAC, including compressive strength, splitting tensile strength, the splitting tensile load-displacement curve, the tensile toughness index, flexural strength, the load-deflection curve, and the flexural toughness index. The results show that the compressive strength, splitting tensile strength, and flexural strength of fiber-reinforced FRAC were remarkably enhanced compared with those of ordinary FRAC, and the maximum increase was 56.9%, 113.3%, and 217.0%, respectively. Overall, the enhancement effect of hybrid steel-polypropylene fiber is more significant than single-mixed fiber. Moreover, the enhancement of the crack resistance, tensile toughness, and flexural toughness obtained by adding steel fiber to the FRAC is more significant than that obtained by adding polypropylene fiber. Furthermore, adding polypropylene fiber alone and mixing it with steel fiber showed different FRAC splitting tensile and flexural properties.
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A high strain rate occurs when the strain rate exceeds 100 s-1. The mechanical behavior of materials at a high strain rate is different from that at middle and low strain rates. In order to study the dynamic compressive mechanical properties of ultra-high-performance steel-fiber-reinforced concrete (UHPSFRC) at high strain rates, an electro-hydraulic servo universal testing machine and a separate Hopkinson pressure bar (SHPB) with a diameter of 120 mm were used, respectively. A quasi-static compression test (strain rate 0.001 s-1) and impact compression test with a strain rate range of 90~200 s-1 were carried out to study the failure process, failure mode, and stress-strain curve characteristics of UHPSFRC at different strain rates and quantify the strain rate strengthening effect and fiber toughening effect. Based on the statistical damage theory and energy conversion principle, a dynamic damage constitutive model considering the effects of strain rate and fiber content was constructed. The results showed that the rate correlation of UHPSFRC and the fiber toughening properties showed a certain coupling competition mechanism. When the fiber content was less than 1.5%, with an increase in the steel fiber content, the crack initiation and propagation time of the specimen was extended, and the strain rate sensitivity gradually decreased. When the fiber content was 2%, the impact compressive strength of the specimen was optimal. Compared with UHPC, the dynamic increase factor (DIF) of UHPSFRC was significantly lower. The dynamic damage constitutive model established in this paper, considering the influence of strain rate and fiber content, has a good applicability and can describe the mechanical behavior of UHPSFRC at a high strain rate.
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In this paper, permeable geopolymer concrete with high compressive strength and permeability is prepared using alkali-activated metakaolin as a slurry, and its mechanical properties are reinforced by adding steel fibers. The influencing factors of the strength, porosity and permeability coefficient of the fiber-reinforced permeable geopolymer concrete, as well as its microstructure and curing mechanism, are determined by conducting an unconfined compressive strength test, scanning electron microscopy, energy-dispersive spectroscopy and X-ray diffraction. The test results show that, under the water permeability required to meet the specification conditions, when the alkali activator modulus is 1.4 and the activation-to-solid ratio is 0.9, the effect of metakaolin activation is the most obvious, and the unconfined compressive strength of the permeable geopolymer concrete is the highest. Moreover, the paste formed via the alkali activation of metakaolin contains a large number of silica-oxygen and aluminum-oxygen bonds with a dense and crack-free structure, which enables the paste to tightly combine with the aggregates; the strength of the permeable geopolymer concrete is early strength, and its strength at a curing age of 3 days is the highest. The strength at a curing age of 3 days can reach 43.62% of the 28-day strength; the admixture of steel fiber can effectively improve the strength of the permeable concrete, and with an increase in the amount of admixture, the strength of the fiber shows a trend of increasing, and then decreasing. Under the conditions of this test, a volume of steel fiber of 0.3% enables the optimum unconfined compressive strength to be reached.