Abstract
As modern civil engineering places increasing demands on concrete materials for high performance and environmental sustainability, the limitations of ordinary concrete in terms of resource consumption and performance enhancement have become increasingly apparent. Currently, the mix design of composite systems incorporating graphite tailings (GT), nanosilica (NS), and steel fibers relies heavily on empirical methods, lacks systematic quantitative optimization, and the mechanisms of synergy among these factors remain unclear, thereby limiting the engineering application of modified eco-concrete. This study employs a Box-Behnken design to systematically investigate the effects of GT, NS, and steel fibers on the 28-day compressive, split tensile, and flexural strengths of concrete. Combined with scanning electron microscopy (SEM) characterization to reveal the microstructural mechanisms, the study verifies the optimal mix proportions through model optimization. The results indicate that the effects of all three factors on the mechanical properties of concrete follow a quadratic nonlinear pattern. The strength of the main effects varies: for compressive strength, NS > steel fibers > GT; for split tensile and flexural strengths, steel fibers > NS > GT. Among these, steel fibers were the core dominant factor in enhancing the tensile and flexural properties of concrete (F-values of 1285.31 and 410.88, respectively). At the same time, NS was the dominant factor in improving compressive strength (F = 447.43), and the optimal replacement rate for graphite tailings was approximately 20%. Interaction analysis revealed significant synergistic effects between GT and NS for compressive strength, between NS and steel fibers for split tensile strength, and between GT and NS as well as NS and steel fibers for flexural strength (interaction terms P < 0.05). The comprehensive optimal mix ratio obtained through response surface model optimization was GT 21.79%, NS 1.48%, and steel fibers 1.49%. The measured 28-day compressive, split tensile, and flexural strengths reached 58.43 MPa, 6.74 MPa, and 10.82 MPa, respectively. Compared to the reference group, these values increased by 38.43%, 39.54%, and 44.65%, respectively, with the relative errors between the measured values and the model predictions all controlled within 5%. SEM characterization revealed that the cement matrix in the GNS4 and GNS18 groups exhibited significantly higher densification than the reference group. The transition zone at the interface between the steel fibers and the matrix exhibited tight bonding, providing reliable mechanical interlocking and chemical bonding that effectively suppressed crack initiation and propagation.
1 Introduction
With the rapid rise of global industries such as new energy, electronics, and information technology, as well as high-end composite materials, graphene—a novel nanomaterial with outstanding physical, chemical, and mechanical properties—is seeing its applications expand, and market demand steadily rise (Ma et al., 2025). This trend has directly driven the large-scale mining and processing of high-purity graphite raw materials, leading to an explosive increase in the generation of graphite tailings (GT). As an unavoidable byproduct of graphite ore extraction, GT are characterized by high volumes, complex composition, difficulty in disposal, and low rates of comprehensive utilization (Zhang et al., 2025; Yi et al., 2024; ). The vast majority of GT are disposed of through open-air stockpiling or landfilling, which not only occupies a large amount of valuable land resources but also poses multiple serious threats to the surrounding ecological environment. Among these, heavy metal pollution is particularly prominent and has become a key hidden hazard, constraining regional ecological and environmental safety (; ). Relevant studies have confirmed that GT themselves constitute a significant source of severe heavy metal pollution, with cadmium (Cd) and mercury (Hg) as the primary pollutants. In some regions, toxic and hazardous heavy metals such as lead (Pb) and chromium (Cr) have also been detected in GT, with concentrations far exceeding soil environmental quality standards.
Using graphite tailings as a substitute for natural river sand in the production of eco-concrete can achieve environmental protection and sustainability benefits in three areas: solid waste disposal, conservation of natural aggregates, and low-carbon emissions reduction. First, the large-scale utilization of tailings can completely resolve ecological risks—such as heavy metal leaching, dust emissions, and soil erosion—associated with open-air stockpiling. It prevents tailings from occupying land and polluting surrounding soil and water bodies, thereby eliminating environmental hazards posed by solid waste from the graphite mining industry at the source and achieving the safe disposal of industrial tailings. Second, replacing natural river sand with fine tailings aggregate reduces river sand extraction activities, alleviating ecological damage caused by sand mining—such as riverbed destruction, river siltation, and degradation of riparian vegetation—while conserving scarce natural sand and gravel resources and easing the industry-wide bottleneck of aggregate supply shortages in the building materials sector. From the perspective of the “Dual Carbon” goals and the circular economy, graphite tailings require no additional calcination or processing; they can be incorporated into concrete production after simple screening. Compared to artificial manufactured sand, this significantly reduces energy consumption in crushing and grinding processes, thereby lowering carbon emissions during production. At the same time, the resource recovery of solid waste aligns with policies on the recycling of industrial solid waste, extends the closed-loop resource cycle of the graphite industry chain, and reduces the overall production cost of concrete. The long-term promotion of this graphite tailings-modified concrete can facilitate the implementation of synergistic solid waste utilization models in the building materials industry, support carbon reduction and emissions cuts in the construction sector, and align with the development goals of green building materials, sustainable infrastructure, and the “Dual Carbon” targets.
During long-term open-air storage of GT, natural processes such as rainfall, surface runoff, and soil infiltration gradually cause heavy metals in the tailings to migrate and spread into the surrounding soil. This results in severe soil contamination around the storage sites, with contamination levels in deeper soil layers being significantly higher than in surface soil. Such contamination not only degrades the physical and chemical properties of the soil and inhibits crop growth but also accumulates through the food chain, ultimately posing a threat to human health (). Furthermore, long-term stockpiling of GT may also trigger secondary environmental issues, such as dust pollution and soil erosion, exacerbating the burden on the ecological environment. Therefore, achieving large-scale, high-value-added resource utilization of GT is not only an urgent necessity for resolving the problem of industrial solid waste accumulation and alleviating environmental pressure, but also a key measure for promoting the green and sustainable development of the graphene industry, implementing the “dual carbon” goals, and fostering the coordinated advancement of ecological conservation and industrial development ().
In the field of civil engineering, concrete has become the most widely used and highest-volume construction material globally due to its numerous advantages, including the availability of raw materials, high strength, excellent durability, and ease of construction. It is widely used in various infrastructure projects, including residential buildings, roads and bridges, water conservancy projects, and underground engineering, resulting in extremely high demand for natural aggregates (especially natural sand) (). However, due to long-term rapid development of the construction industry, the overexploitation of natural sand has become increasingly severe. This has not only led to a series of ecological and environmental issues—such as river siltation, riverbed destruction, and vegetation degradation—but has also caused natural sand reserves to diminish steadily. The problem of resource scarcity has become increasingly prominent, with some regions even facing the dilemma of “no sand available.” Consequently, the shortage of natural aggregate resources has become a major bottleneck constraining the high-quality and sustainable development of China’s construction industry. Against this backdrop, the search for green, environmentally friendly, and cost-effective alternatives to natural sand has become a research hotspot in the field of green building materials and an inevitable trend in industry development (Sun et al., 2025; Zhang et al., 2023). The use of industrial solid waste as a substitute aggregate in concrete not only facilitates large-scale utilization of this material and alleviates environmental pressure from its stockpiling but also reduces concrete production costs and decreases reliance on natural resources. This approach achieves the goal of resource recovery by “turning waste into treasure,” aligning with the principles of green building and sustainable development. GT, as a potential substitute for natural sand in fine aggregate, consist primarily of silicon dioxide (SiO2) and aluminum oxide (Al2O3). Their chemical composition is highly similar to that of natural sand, meeting the basic requirements for use as fine aggregate in concrete. Furthermore, GT consist of fine particles with a relatively uniform particle-size distribution. When incorporated into concrete, they effectively fill the voids between the cement paste and aggregates, optimizing the concrete’s internal structure, increasing the density of the concrete matrix, and thereby improving certain mechanical properties.
In line with the need to recycle solid waste from the building materials industry, GT can be used as a substitute for natural sand and gravel in concrete production. Currently, many experiments are being conducted in this area. Quan et al. (2024) used mining solid waste materials, such as GT and coal gangue, as aggregates, combined with steel slag, blast furnace slag, and fly ash, to prepare alkali-activated concrete with high tailings content. Through microstructural testing, they revealed the evolution of strength and hydration mechanisms, elucidating the effects of aggregate type, tailings content, and steel slag blending on mechanical properties, failure characteristics, and microstructural products. Liu et al. (2024) sought to address the high cost and significant ecological impact of river sand aggregates in ultra-high-performance concrete (UHPC). They prepared UHPC by replacing river sand with 0%–100% GT. At a 50% replacement rate, the 28-day compressive strength increased by 7.33%, while carbon emissions were reduced by up to 6.96% and production costs by 20%. used 0%–100% GT to replace river sand and, by combining macro- and micro-scale failure characteristics, revealed the mechanical evolution patterns. Concrete strength initially increased, then decreased as the tailings content increased; mechanical properties were excellent at 10%–60% replacement rates, with 30% as the optimal replacement rate, while replacement rates exceeding 70% exacerbated interface defects and crack propagation. Liu et al. (2022a) prepared eco-friendly steel fiber concrete by partially replacing fine aggregate with GT and co-mixing with steel fibers, investigating the compressive and flexural properties of the concrete at tailings replacement rates of 0%, 10%, and 20%. The study indicates that the bulk density of GT is higher than that of river sand; reasonable incorporation can optimize the interfacial structure and suppress crack propagation. A 10% incorporation rate is more conducive to the uniform distribution of steel fibers, whereas excessive incorporation can degrade the concrete’s internal structure.
Although using GT sand to replace natural sand in the production of green, ecological concrete achieves the dual goals of solid waste disposal and resource conservation, the modified concrete still suffers from issues such as uneven pore distribution and insufficient interfacial bond strength at the microstructural level. Meeting the stringent requirements for mechanical performance and long-term durability in high-end infrastructure is difficult. Against this backdrop, the application of nanomaterials offers an effective means to improve concrete performance. Among these, nano-silica (NS), with its unique advantages of small particle size, large specific surface area, and high chemical reactivity, has gradually become a research focus in driving the development of solid waste-based concrete toward high performance and high added value. replaced cement in concrete with 0.5%–2.0% nano-silica and conducted tests on compressive, tensile, and flexural strengths, impermeability, and microstructure at different ages. They noted that an appropriate amount of NS can enhance the mechanical strength of concrete; while the impermeability of concrete decreases with age, early-age compressive strength is significantly improved. The greatest decline in impermeability occurred at a 1.5% replacement rate, whereas a slight recovery in impermeability was observed at a 2% replacement rate, due to nanoparticle agglomeration. incorporated 2% by weight of NS into high-strength concrete, employing a research methodology that combined contact angle and water absorption tests with physical, mechanical, and electrochemical experiments. They investigated its effects on the concrete’s compressive, tensile, and elastic moduli, Poisson’s ratio, and corrosion resistance. The results indicated that NS accelerates hydration and improves concrete density and physical-mechanical properties; however, both hydrophobic and standard NS reduce the concrete’s corrosion resistance and directly influence corrosion behavior. Nigam and Verma (2023) incorporated NS at levels ranging from 0.0% to 3.0% (in 0.5% increments) into ordinary concrete, tested its setting time, workability, and compressive, split tensile, and flexural mechanical properties, and fitted correlation equations. The results showed that as the nano-silica content increased, the mechanical properties of the concrete gradually improved, while workability decreased; a relationship between flexural and compressive strengths was also established. See Table 1 for a comparison of the relevant experiments.
TABLE 1
| Authors | Combination | Year | Limitations of the study |
|---|---|---|---|
| Quan et al. (2024) | GT,Slag | 2024 | Alkali-activated systems are costly, fail to address the brittleness of concrete, and lack interfacial modification of nanofillers |
| Liu et al. (2024) | GT | 2024 | Due to the lack of toughening components, the improvement in tensile and flexural strength is limited; there are no nanofillers to optimize the interfacial transition zone |
| Liu et al. (2022a) | GT,steel fibers | 2022 | Only a binary mixture was used; no nano-SiO2 was introduced. There was no quantification of multifactorial interactions, no response surface optimization, and the microscopic mechanisms underlying the synergy among the three components were not elucidated |
| NS | 2023 | Using only nano-silica as a single additive, without combining solid waste aggregates and steel fibers, makes it impossible to achieve both the resource recovery of solid waste and the toughening of the material |
Overview of Previous relevant studies.
In line with the trend of using GT to replace natural sand in the production of eco-concrete, the microscopic properties of nano-silica can effectively address the performance shortcomings of GT-based concrete, thereby achieving the dual objectives of “resource recovery from solid waste and high-performance concrete.” Unlike traditional modified materials, which can optimize performance in only one dimension, NS, with its nanoscale particle size, can fill the microscopic pores between GT particles and cement hydration products, further refining the internal pore structure of the concrete. Simultaneously, the high reactivity of NS allows it to undergo a pozzolanic reaction with calcium hydroxide generated during cement hydration, producing a greater amount of dense calcium silicate hydrate (C-S-H) gel (; Su et al., 2025; Zhang et al., 2024). Song et al. (2021) prepared cement-stabilized soil specimens with varying proportions of tailings and NS, and conducted unconfined compressive strength and scanning electron microscopy tests. They found that an appropriate amount of tailings can enhance the strength of cement-stabilized soil, with an optimal blending ratio of 20%. NS can significantly improve the mechanical properties of iron tailings cement-stabilized soil. It achieves this by promoting cement hydration, cementing clay particles, and filling internal voids, thereby optimizing the soil’s microstructure and enhancing its density.
In practical engineering applications, ordinary concrete exhibits poor tensile and flexural strengths and is highly brittle (; Yu et al., 2024; Yi et al., 2024). During loading, it is prone to developing microcracks that propagate rapidly, reducing structural load-bearing capacity and durability and severely affecting the service life, safety, and stability of engineering structures. Steel fibers, as concrete reinforcement and modification materials, are widely used in concrete modification research due to their high strength and toughness. When steel fibers are uniformly incorporated into the concrete matrix, their random distribution effectively bridges microcracks, suppressing crack initiation and propagation while simultaneously bearing a portion of the tensile stress. This significantly enhances the concrete’s tensile, flexural, and bending strengths as well as its toughness (Rashidi et al., 2024; Peng et al., 2023; ). conducted research on steel fiber-reinforced concrete using uniaxial compression tests combined with imaging and acoustic emission monitoring, finding that the optimal fiber content is 0.4%–0.6%. Furthermore, the addition of steel fibers significantly improves the concrete’s compressive energy absorption, toughness, and crack resistance. TA Mehmandari et al. (Mehmandari et al., 2024) prepared hybrid fiber concrete by co-blending recycled steel fibers from waste tires with industrial steel fibers. They investigated its flexural mechanics and ductility using three-point bending tests, digital image correlation, CT scanning, and SEM. They noted that the blended steel fibers balance mechanical enhancement with green, low-carbon benefits; recycled steel fibers can suppress microcracks and reduce the pull-out rate of commercial steel fibers; and the blended system significantly improves the concrete’s flexural toughness, ductility, and bond strength at the interface. conducted flexural tests on steel fiber-reinforced recycled aggregate concrete beams. Using water-cement ratio, recycled coarse aggregate replacement rate, and steel fiber volume content as study parameters, they proposed a reasonable range of bond coefficients applicable to this type of beam.
Based on the above studies, is the performance optimization of concrete modified by the composite addition of GT, NS, and steel fibers an effective approach to achieving high-value utilization of GT and enhancing concrete performance? Are its mechanical properties influenced by a combination of factors such as the GT replacement rate, NS dosage, and steel fibers dosage? Given that the relationship among these factors is not a simple linear superposition, do complex interactive effects exist? Current research in this field predominantly employs single-variable or orthogonal experimental designs. While these methods can preliminarily identify the influence trends and optimal ranges of individual factors, they cannot systematically quantify the coupled effects of interactions among multiple factors on concrete performance. It is also difficult to accurately establish quantitative relationship models between the influencing factors and the target concrete performance, let alone efficiently identify the optimal mix design parameters that balance solid waste incorporation, concrete performance, and project economics.
Against this backdrop, Response Surface Methodology (RSM)—a multifactorial experimental research method that integrates experimental design, regression analysis, and optimization analysis—has been widely applied in fields such as concrete mix design optimization and the performance regulation of solid waste-based materials (; ; Myers et al., 1989). This is due to its unique advantages, including high experimental efficiency, the ability to accurately reveal factor interactions, and the capability to establish quantitative regression models and optimize parameters. Compared to traditional experimental methods, RSM eliminates the need for extensive repetitive testing. Through rational experimental design, it can obtain comprehensive experimental data with fewer test groups. Subsequently, regression analysis is used to establish relationships between influencing factors and response values, clarifying the influence patterns of individual factors and their interactions on the response values. Finally, model optimization determines the optimal combination of experimental parameters, providing scientific and precise theoretical support for engineering practice (; ). employed response surface modeling to investigate the impact resistance of micro-steel fiber concrete incorporating nano-silica; they concluded that the combined addition of micro-steel fibers and nano-SiO2 significantly enhances the concrete’s impact resistance, though high dosages of both reduce the ductility coefficient. All specimens exhibited similar failure modes, and the response surface prediction model demonstrated good correlation. Mosaberpanah et al. (2019) conducted experimental tests on the compressive strength and rheological properties of high-performance concrete. They set the nano-silica content at 0%–5% and replaced cement with waste glass powder (maximum particle size of 63 μm) at 0%–20%. Using a centered composite factorial (CFC) design, response surface methodology (RSM) for modeling, and analysis of variance (ANOVA) for model validation. Under the premise of reducing the cement content in UHPC, the study confirmed that both the individual additions of nano-silica fume and waste glass powder, as well as their interaction, can significantly enhance the mechanical and rheological properties of ultra-high-performance concrete. Based on this, to address the issues of unclear multifactorial interaction effects and difficulty in determining optimal mix proportions, this paper introduces the response surface method to conduct relevant experimental studies. The primary influencing factors are the GT replacement rate, the NS dosage, and the steel fiber volume content. Using 28-day compressive, splitting, and flexural strengths as core response variables, a response surface experimental design was formulated (Figure 1). A quadratic regression model was established by fitting the experimental data, and the model’s validity and goodness of fit were verified. The mechanisms by which each factor and its interactions influence the mechanical properties of concrete were systematically analyzed, providing a theoretical basis and technical support for the large-scale, high-value utilization of GT and the engineering application of high-performance eco-concrete.
2 Materials and methods
2.1 Materials
In this experiment, GT, NS, and steel fibers were selected as concrete admixtures and incorporated into the matrix; the selected materials are shown in Figure 2. The particle size distributions of GT, NS, and medium-grade sand are shown in Figure 3. Portland Ordinary Portland Cement (P.O) Grade 42.5 was selected as the cementitious material. Its major chemical components were determined using X-ray fluorescence (XRF) spectroscopy, and the test results are presented in Table 2. The key performance indicators of this cement are shown in Table 3. Crushed stone was used as the coarse aggregate; its performance parameters are detailed in Table 4. Medium-grade sand was used as the fine aggregate, and its main performance indicators are listed in Table 5. A powdered, high-efficiency polyhydroxy acid-based water-reducing agent was used, with a water-reduction rate of at least 25% (Table 6). The specific performance indicators of the barbed steel fibers are shown in Table 7. The NS used in the experiment was a white powdery solid with a particle size of 20 nm and a purity of 99%.
FIGURE 1
FIGURE 2
FIGURE 3
TABLE 2
| CaO | SiO2 | Al2O3 | Fe2O3 | SO3 | MgO | K2O | TiO2 | Na2O | MnO2 | Others |
|---|---|---|---|---|---|---|---|---|---|---|
| 47.2 | 27.5 | 9.6 | 6.4 | 3.9 | 1.6 | 1.2 | 1 | 0.9 | 0.4 | 0.3 |
Material: XRF analysis results of cement/%.
TABLE 3
| Type of cement | Stability | Incipient condensation time/min | Compressive strength/MPa | Flexural strength/MPa | |||
|---|---|---|---|---|---|---|---|
| Initial setting time | Final setting | 3d | 28d | 3d | 28d | ||
| P.O 42.5 | Eligible | 280 | 335 | 24.2 | 46.3 | 5.0 | 6.7 |
Cement performance indicators.
TABLE 4
| Coarse aggregate | Crushing index /% | Apparent density (kg·m-3) | Particle size/mm | Packing density/(kg·m-3) | Fines content/% |
|---|---|---|---|---|---|
| Crushed stone | 5.4 | 2771 | 25∼37.5 | 1360 | 0.7 |
Coarse aggregate performance indicators.
TABLE 5
| Type of sand | Fineness modulus | Apparent density(kg·m-3) | Mud lump content/% | Packing density (kg·m-3) | Porosity(%) | Fines content(%) |
|---|---|---|---|---|---|---|
| Medium | 2.2 | 2620 | 0 | 1460 | 44 | 1.6 |
Physical properties of sand.
TABLE 6
| Sample name | Appearance | Moisture content (%) | pH | Cement slurry flowability (mm) | Water reduction rate of mortar (%) | Concrete tax reduction rate (%) | Air content in concrete (%) |
|---|---|---|---|---|---|---|---|
| Water-reducing agent | Grayish-white | 1.81 | 7 | 280 | 19 | 32 | 1.7 |
Water-reducing agent specifications.
TABLE 7
| Geometry | Tensile strength/MPa | Lengths/mm | Equivalent diameter/mm | Aspect ratio |
|---|---|---|---|---|
| End Hook Type | 1000 | 35 | 1 | 35 |
Performance indicators of steel fibers.
Specifically, the GT was sourced from Wukong Group Graphite Industry Co., Ltd. in Luobei County, Hegang City. The polyhydroxy acid-based high-efficiency water-reducing agent was purchased from Shanghai Chenqi Chemical Technology Co., Ltd. The cement was sourced from Yatai Cement Plant. The NS was purchased from Bisley New Materials (Suzhou) Co., Ltd. The steel fibers were purchased from Nai Zhu (Henan) New Materials Technology Co., Ltd. The crushed stone is artificially crushed and was purchased from Henan Shanjin Mining Co., Ltd.
2.2 Introduction to response surface methodology
This study employed Response Surface Methodology (RSM) to optimize the mix designs and properties of GT-, NS-, and steel fibers-modified concrete. This method is an experimental optimization technique that combines mathematics and statistics. It fits quadratic polynomial regression models using a limited number of experimental data points to quantify the relationship between input factors (independent variables) and response values (dependent variables). It analyzes main effects and interaction effects of factors and efficiently identifies optimal parameter combinations, effectively replacing the traditional trial-and-error method to improve experimental efficiency and optimization accuracy.
The experiments employed a Box-Behnken design (BBD), selecting GT, NS, and steel fibers as key influencing factors. Based on preliminary experiments and relevant literature, reasonable ranges and three levels for each factor were determined to design multiple experimental groups. Concrete specimens were cast according to the design plan, with experimental variables strictly controlled; target response values were measured after standard curing.
A regression model relating the factors to the response variable was established using a quadratic polynomial. The significance of the model was tested using the P-value and the P-value of the misfit term. At the same time, goodness-of-fit was evaluated using the coefficient of determination (R2), the adjusted R2, and the predicted R2. The model was required to meet the criteria of P < 0.05 (significant) and a P-value for the misfit term >0.05 (no misfit). The influence of each factor and its interactions on the response values was analyzed using main effect and interaction plots. Optimal parameter combinations were identified using the fitted model, and the predicted values were experimentally validated to assess the model’s reliability and the practicality of the optimization results.
It should be noted that the primary reason this study selected BBD rather than CCD for the response surface design was the significant difference between the two approaches in terms of experimental scale and suitability for variable boundaries. In a three-factor experiment, the CCD requires more test groups, whereas the BBD requires only 17 groups. This reduces the material and time costs associated with concrete pouring, 28-day curing, and microstructural testing. At the same time, the CCD includes axial points that exceed the specified admixture dosage range, whereas GT, NS, and steel fibers all have reasonable upper limits for engineering dosages; excessive dosages can lead to problems such as gradation deterioration, nano-agglomeration, and fiber clumping.
2.3 Preparation of modified concrete
The factor level parameters for the modified concrete specimens are shown in Table 8, and the specific mix proportions are detailed in Table 9. The water-cement ratio was set at 0.4, with a water content of 160 kg/m3; the dosage of polyhydroxy acid-based high-performance water-reducing admixture was 1% of the cement content, and the sand content was controlled at 36%. This experiment was divided into two phases: optimization and screening. In the second phase, comparative tests were conducted on the final optimized mix design to evaluate performance differences.
TABLE 8
| Category | Name | Units | Typology | Low | High |
|---|---|---|---|---|---|
| A | GT | % | factor | 10 | 30 |
| B | NS | % | factor | 0.5 | 1.5 |
| C | steel fibers | % | factor | 0.5 | 1.5 |
| R1 | Compressive strength | MPa | response value | ||
| R2 | Splitting tensile strength | MPa | response value | ||
| R3 | Flexural strength | MPa | response value |
Factor level table for modified concrete.
TABLE 9
| Category | Number | GT (%) | NS (%) | Steel fibers (%) | R1 MPa | R2 MPa | R3 MPa |
|---|---|---|---|---|---|---|---|
| Control group | GNS0 | 0 | 0 | 0 | 42.21 | 4.83 | 7.48 |
| Optimization Group | GNS1 | 20 | 0.5 | 0.5 | 51.27 | 4.98 | 7.23 |
| GNS2 | 30 | 1 | 1.5 | 49.38 | 6.32 | 10.38 | |
| GNS3 | 30 | 1 | 0.5 | 46.19 | 4.97 | 7.27 | |
| GNS4 | 20 | 1.5 | 1.5 | 60.41 | 7.08 | 10.88 | |
| GNS5 | 20 | 1 | 1 | 56.22 | 6.11 | 9.93 | |
| GNS6 | 10 | 1.5 | 1 | 52.46 | 5.67 | 9.64 | |
| GNS7 | 30 | 0.5 | 1 | 44.17 | 4.86 | 8.03 | |
| GNS8 | 20 | 0.5 | 1.5 | 53.54 | 6.02 | 10.52 | |
| GNS9 | 10 | 1 | 1.5 | 50.53 | 6.18 | 10.99 | |
| GNS10 | 20 | 1 | 1 | 55.87 | 6.15 | 10.39 | |
| GNS11 | 20 | 1 | 1 | 56.12 | 6.07 | 10.27 | |
| GNS12 | 10 | 0.5 | 1 | 46.82 | 4.92 | 9.12 | |
| GNS13 | 20 | 1.5 | 0.5 | 58.76 | 5.56 | 8.87 | |
| GNS14 | 20 | 1 | 1 | 55.76 | 6.12 | 10.35 | |
| GNS15 | 20 | 1 | 1 | 56.72 | 6.08 | 10.31 | |
| GNS16 | 10 | 1 | 0.5 | 48.34 | 4.78 | 7.73 | |
| GNS17 | 30 | 1.5 | 1 | 54.21 | 5.77 | 9.78 | |
| Optimal Group | GNS18 | 21.79 | 1.48 | 1.49 | 58.43 | 6.74 | 10.82 |
Modified concrete mix proportions.
GT, represents the percentage by mass of the river sand substitute, NS, represents the percentage by mass of the cement substitute, and steel fibers represents the volume fraction.
The modified concrete was prepared using the dry-mixing method, following the procedure below: First, coarse aggregate, fine aggregate, nano-admixture, water-reducing agent and steel fibers were precisely weighed according to the design quantities, then placed in wa mixer for 3 min of dry mixing. Subsequently, the specified amount of water was added, and mixing continued for 2 min until the mixture was homogeneous. The homogenized mixture was poured into pre-set molds, and the formed specimens were placed in a constant-temperature, humidity-curing chamber (20 °C ± 2 °C, 95% relative humidity) and cured to the specified age in accordance with test requirements.
2.4 Instruments for testing mechanical properties
Mechanical property tests on the specimens were conducted after 28 days of curing. In accordance with the technical specifications of the National Standard of the People’s Republic of China GB/T 50,081–2019 “Standard Test Methods for Physical and Mechanical Properties of Concrete,” standard cubic specimens measuring 100 mm × 100 mm × 100 mm were tested for compressive strength and splitting tensile strength, while non-standard prismatic specimens measuring 100 mm × 100 mm × 400 mm were tested for flexural strength. The equipment used for these tests was the CSS-WAW1000 universal testing machine manufactured by Jinan Zhongluchang Testing Machine Manufacturing Co., Ltd. To ensure test data reliability and accuracy, three parallel specimens were used in each test series, and the final test results were evaluated as the arithmetic mean of the three specimens’ values.
2.5 Microscopic physical examination of test specimens
After the compressive strength test, irregular fragments were selected from the compressed and failed specimens for testing. First, the samples were immersed in anhydrous ethanol for 24 h to halt the hydration reaction; they were then placed in an oven and dried to a constant mass before undergoing subsequent microscopic analysis. Before microscopic examination, each specimen was gold-plated under vacuum to enhance surface conductivity and thereby improve scanning image quality. A scanning electron microscope (SEM) was used to observe the specimens from each group, capturing images of the microstructural characteristics of multiple fragments.
3 Results and discussion
3.1 Macro-scale failure modes in concrete
Figure 4 shows the macroscopic failure modes of the reference group (GNS0) and the modified group (GNS4) in the cube compression test. The reference group (GNS0) exhibited brittle failure, as shown in Figure 4a. After reaching the ultimate load, the specimen failed abruptly, with extensive conical spalling occurring at the corners and edges. The concrete disintegrated into fragments, the original cube edges disappeared, and the failure process showed no obvious warning signs. This failure mode stems from the rapid, unimpeded propagation of microcracks in ordinary concrete under axial loading. When the main crack penetrates the specimen, the internally stored elastic strain energy is released instantly, causing the concrete matrix to fracture as a whole.
FIGURE 4
The failure mode of the modified group GNS4 exhibits ductile failure characteristics, as shown in Figure 4b. After reaching the ultimate load, the specimen did not undergo sudden disintegration; the overall cubic shape remained intact, with only one or several through-cracks extending from the bottom to the top appearing on the sides. There was no significant concrete spalling, and the specimen was generally well preserved. The failure process was distinctly gradual, with the load decreasing slowly, demonstrating excellent energy dissipation capacity. This may be attributed to the three-dimensional bridging and crack-stopping effect of the steel fibers. When internal microcracks initiated and propagated, the steel fibers effectively bridged the cracks to transfer stress, preventing rapid crack propagation and matrix spalling, and forcing the cracks to detour around the fibers while dissipating significant fracture energy. Concurrently, the strengthening effect of nano-silica on the interface transition zone and the optimization of aggregate gradation by GT further enhance the matrix’s integrity and crack resistance.
3.2 Strength prediction model for modified concrete
Response surface methodology is a multi-factor, multi-level optimization method that integrates experimental design, mathematical statistics, and regression modeling. It enables a systematic investigation of the effects of multiple independent variables, interactions between factors, and quadratic terms on the target response. The Box-Behnken Design (BBD) is a classic, widely used three-level experimental design within response surface methodology. It requires no extreme corner points, involves fewer experimental groups, is cost-effective, and offers high fitting accuracy, making it suitable for multi-factor formulation and process optimization studies. After scientifically arranging experimental points based on BBD, a second-order polynomial surface model is fitted using response surface methodology to analyze the significance of each factor’s influence and the trends in response changes. Rapid optimization determines the optimal material formulation and process parameters, and accurately predicts performance outcomes across different parameter combinations. This approach significantly reduces the number of experiments, shortens the R&D cycle, and lowers experimental costs, making it widely applicable in research scenarios such as concrete modification, building material formulation, and the optimization of engineering process parameters (). employed the response surface method to investigate the effects of 0%–30% calcium carbide residue (CCR) as a cement substitute and 0%–4% nano-silica (NS) content on multiple concrete properties, and conducted multi-objective mix design optimization. They concluded that CCR content within 15% and NS content within 3% can significantly improve concrete mechanical properties and water absorption performance. The RSM prediction model demonstrated excellent correlation, with the optimal mix ratio being 10.6% CCR replacing cement and 1.95% NS added to the cementitious materials. Based on the aforementioned experimental data, this study coupled the response surface method with the Box-Behnken experimental design (RSM-BBD) to perform regression analysis of the results in Table 9, thereby establishing the regression equations listed below (Equations 1–3).
The results of the analysis of variance (ANOVA) for modified concrete are presented in Tables 10–12. The three quadratic polynomial regression models constructed for compressive strength, split tensile strength, and flexural strength all demonstrated excellent reliability. Overall, the models were highly significant (P < 0.0001), the misfit terms were not significant (P > 0.05), and the adjusted coefficients of determination (Adj R2) reached 0.9883, 0.9934, and 0.9734, respectively. The coefficients of variation (C.V.) were all below 3%, and the Adequate Precision was well above 4. This indicates that the models exhibit a high degree of fit with the experimental data and good repeatability, accurately reflect the quantitative relationships among the various factors and the strength indices, and demonstrate reliable predictive capabilities.
TABLE 10
| Source | Sum of squares | df | Mean square | F value | Prob > F | Significance determination |
|---|---|---|---|---|---|---|
| Model | 343.56 | 9 | 38.17 | 151.42 | <0.0001 | significant |
| A-GT | 2.20 | 1 | 2.20 | 8.75 | 0.0212 | * |
| B-NS | 112.80 | 1 | 112.80 | 447.43 | <0.0001 | ** |
| C-steel fibers | 10.81 | 1 | 10.81 | 42.88 | 0.0003 | ** |
| AB | 4.84 | 1 | 4.84 | 19.20 | 0.0032 | ** |
| AC | 0.25 | 1 | 0.25 | 0.99 | 0.3525 | - |
| BC | 0.096 | 1 | 0.096 | 0.38 | 0.5565 | - |
| A2 | 209.51 | 1 | 209.51 | 831.05 | <0.0001 | ** |
| B2 | 0.46 | 1 | 0.46 | 1.83 | 0.2182 | - |
| C2 | 0.95 | 1 | 0.95 | 3.75 | 0.0939 | - |
| Residual | 1.76 | 7 | 0.25 | |||
| Lack of Fit | 1.20 | 3 | 0.40 | 2.86 | 0.1677 | not significant |
| Pure Error | 0.56 | 4 | 0.14 | |||
| Cor Total | 345.33 | 16 |
Analysis of compressive strength regression models.
“**” indicates extreme significance (P < 0.01). “*” indicates significance (P < 0.05). Adj R-Squared = 0.9883, Pred R-Squared = 0.9417, C.V., 0.95%, Adequate Precision = 43.425.
TABLE 11
| Source | Sum of squares | df | Mean square | F value | Prob > F | Significance determination |
|---|---|---|---|---|---|---|
| Model | 6.64 | 9 | 0.74 | 268.87 | <0.0001 | significant |
| A-GT | 0.017 | 1 | 0.017 | 6.24 | 0.0411 | * |
| B-NS | 1.36 | 1 | 1.36 | 496.42 | <0.0001 | ** |
| C-steel fibers | 3.52 | 1 | 3.52 | 1285.31 | <0.0001 | ** |
| AB | 6.400E-003 | 1 | 6.400E-003 | 2.33 | 0.1704 | - |
| AC | 6.250E-004 | 1 | 6.250E-004 | 0.23 | 0.6476 | - |
| BC | 0.058 | 1 | 0.058 | 21.01 | 0.0025 | ** |
| A2 | 1.39 | 1 | 1.39 | 506.35 | <0.0001 | ** |
| B2 | 0.22 | 1 | 0.22 | 78.95 | <0.0001 | ** |
| C2 | 3.981E-003 | 1 | 3.981E-003 | 1.45 | 0.2674 | - |
| Residual | 0.019 | 7 | 2.742E-003 | |||
| Lack of Fit | 0.015 | 3 | 5.025E-003 | 4.88 | 0.0799 | not significant |
| Pure Error | 4.120E-003 | 4 | 1.030E-003 | |||
| Cor Total | 6.65 | 16 |
Analysis of splitting tensile strength regression models.
“**” indicates extreme significance (P < 0.01). “*” indicates significance (P < 0.05). Adj R-Squared = 0.9934, Pred R-Squared = 0.9628, C.V., 0.91%, Adequate Precision = 56.427.
TABLE 12
| Source | Sum of squares | df | Mean square | F value | Prob > F | Significance determination |
|---|---|---|---|---|---|---|
| Model | 24.65 | 9 | 2.74 | 66.12 | <0.0001 | significant |
| A-GT | 0.51 | 1 | 0.51 | 12.31 | 0.0099 | ** |
| B-NS | 2.28 | 1 | 2.28 | 55.01 | 0.0001 | ** |
| C-steel fibers | 17.02 | 1 | 17.02 | 410.88 | <0.0001 | ** |
| AB | 0.38 | 1 | 0.38 | 9.13 | 0.0193 | * |
| AC | 5.625E-003 | 1 | 5.625E-003 | 0.14 | 0.7234 | - |
| BC | 0.41 | 1 | 0.41 | 9.89 | 0.0163 | * |
| A2 | 2.03 | 1 | 2.03 | 49.09 | 0.0002 | ** |
| B2 | 0.72 | 1 | 0.72 | 17.29 | 0.0043 | ** |
| C2 | 0.90 | 1 | 0.90 | 21.74 | 0.0023 | ** |
| Residual | 0.29 | 7 | 0.041 | |||
| Lack of Fit | 0.15 | 3 | 0.051 | 1.51 | 0.3408 | not significant |
| Pure Error | 0.14 | 4 | 0.034 | |||
| Cor Total | 24.94 | 16 |
Analysis of flexural strength regression models.
“**” indicates extreme significance (P < 0.01). “*” indicates significance (P < 0.05). Adj R-Squared = 0.9734, Pred R-Squared = 0.8927, C.V., 2.14%, Adequate Precision = 25.526.
Analysis of main effects revealed the patterns of differential contributions of each factor to strength. GT, NS, and steel fibers all had significant effects on all three strength measures (P < 0.05). Among these, the F-value for steel fibers was significantly higher than those of the other factors in the split tensile strength (F = 1285.31) and flexural strength (F = 410.88) models, making it the dominant factor in enhancing the tensile and flexural performance of concrete. The pozzolanic activity and matrix densification effects of NS were most pronounced in compressive strength (F = 447.43).
Analysis of interaction and quadratic terms further validated the synergistic and nonlinear effects among factors. Only some interactions (e.g., GT and NS in the compressive strength model; NS and steel fibers in the split tensile model; GT and NS, and NS and steel fibers in the flexural strength model) reached the significance level. Among the quadratic terms, the quadratic effect of GT was highly significant in all three strength models. In contrast, the quadratic effect of NS was significant in split tensile and flexural strengths, further clarifying the nonlinear regulatory patterns of these factors on strength. The quadratic effect of steel fibers was significant in flexural strength. GT exhibited a significant quadratic nonlinear effect, consistent with its mechanism of action: “compaction at low admixture levels and gradation deterioration at high admixture levels” ().
3.3 Analysis and diagnosis of response surface models for modified concrete
To quantitatively evaluate the predictive performance of the model, this paper conducts a multidimensional error analysis as shown in Figures 5a–i, systematically presenting three key sets of results: the variation characteristics of residuals with respect to the model’s predicted values, the distribution patterns of residuals relative to the experimentally measured values, and the deviation characteristics between the predicted and measured concrete strengths. Zhang et al. (2021) noted that model simulation outputs and visual analysis diagrams can effectively assess model stability and quantify prediction accuracy, while also providing a scientific basis for optimizing experimental protocols and process parameters.
FIGURE 5
Figure 5 uses a color gradient to classify response levels: blue indicates a low response level, green corresponds to a moderate response level, and red represents a high response level. The error analysis results show that the measured concrete strength data is highly correlated with the model predictions, and the residuals for all test samples are within the preset error tolerance range, fully demonstrating the model’s excellent predictive accuracy and reliable overall confidence level.
3.4 Analysis of the mechanical strength of modified concrete
Figure 6 visually illustrates the regulatory mechanisms of GT, NS, steel fibers, and their interactions on the 28-day compressive strength of concrete through response surface and contour plots. This is attributed to its high pozzolanic activity and the filling effect of microfillers, which not only consume Ca(OH)2 generated from cement hydration to form additional C-S-H gel but also refine pores and reduce matrix porosity, thereby significantly improving density (). Increasing the steel fibers content also increases overall strength. Its crack-bridging effect bridges microcracks during compression, delays crack propagation and penetration, and suppresses brittle failure of the specimens, thereby improving the concrete’s compressive load-bearing capacity (Thomas and Ramaswamy, 2007). In contrast, the GT content exhibits a quadratic effect on compressive strength, initially increasing and then decreasing: at low dosages (10%–20%), tailings sand particles can fill voids in the mortar, optimize aggregate gradation, and improve matrix density. When the dosage exceeds 20%, excess tailings sand results in a degraded aggregate gradation, leading to a decrease in strength (Liu et al., 2022b).
FIGURE 6
The interaction effects among various factors differ significantly. Notably, the effects of GT and NS on compressive strength are significant, with a clear synergistic effect: an appropriate dosage of NS improves the transition zone between the tailings sand and the mortar, allowing the micro-aggregate filling effect of GT to be fully utilized. The interaction between GT and steel fibers, however, has a weaker effect, showing no clear synergistic or antagonistic action. Based on the response surface patterns and contour line distributions, the mechanisms of action of the various modifying materials align closely with the model results, validating the rationality and reliability of the regression model; moreover, the optimal GT dosage consistently remains stable at around 20%.
Furthermore, the substitution rate of graphite tailings follows a double-parabolic pattern—rising initially and then declining—with the optimal substitution ratio stabilizing at around 20%. This variation may result from the combined effects of aggregate gradation filling and the evolution of interfacial defects. When the substitution rate of graphite tailings is below 20%, the matrix lacks sufficient fine particles, resulting in a large number of micron-scale interconnected pores within the mortar. Graphite tailings particles are fine in size and have a chemical composition similar to that of natural sand. When added in appropriate amounts, they can fill the voids between coarse and fine aggregates and cement hydration products, optimize the continuous aggregate gradation, and improve the density of the matrix. At the same time, the reactive silico-aluminate components in the tailings can weakly participate in pozzolanic reactions, generating a small amount of C-S-H gel, which further optimizes the transition zone at the mortar-aggregate interface. Macroscopically, this manifests as a sustained improvement in all mechanical strengths of the concrete. When the substitution rate exceeds 20%, the proportion of fine aggregates in the matrix becomes too high, causing an imbalance in the overall aggregate gradation. As a result, the mortar cannot fully encapsulate the tailings particles, leading to the formation of a large number of weak interfaces within the matrix. Graphite tailings particles have smooth surfaces with few sharp edges, resulting in weaker mechanical interlock with the cement paste compared to natural river sand; excessive incorporation significantly increases the number of interface defects.
Based on the response surface analysis results and considering the cost factor of NS, an optimal mix design for compressive strength was obtained through separate optimization; the results are shown in Table 13.
TABLE 13
| Optimal blending ratio group | GT(%) | NS(%) | Steel fibers(%) | Predicted compressive strength | Notes |
|---|---|---|---|---|---|
| 1 | 18.3466 | 1.49836 | 1.48665 | 60.414 | Optimal compressive strength |
| 2 | 19.0291 | 0.5 | 1.5 | 53.6245 | NS is used the least |
Optimal dosage of modified concrete.
3.5 Analysis of the tensile strength of modified concrete under splitting loads
Figure 7 shows the response surface and contour plots of the 28-day splitting tensile strength of concrete under the two-way interaction of GT, NS, and steel fibers, illustrating the regulatory patterns of each factor and their interaction effects on splitting tensile performance. Overall, an increase in the steel fibers content had the most significant enhancing effect on the split tensile strength; the response surface showed a steep upward trend with increasing steel fibers content, reflecting the dominant role of the steel fiber’s bridging and crack-stopping effect on the concrete’s tensile performance. The strengthening effect of NS is equally pronounced; as the dosage increases, the matrix density improves, providing a stronger anchoring interface for the steel fibers and indirectly amplifying the fibers’ toughening effect. GT, on the other hand, exhibits a typical quadratic nonlinear effect, with strength first increasing and then decreasing with dosage, peaking at around 20%.
FIGURE 7
The interaction effects among the factors showed significant differences, with the synergistic toughening effect of NS and steel fibers being the most prominent. The contour lines exhibited a distinct arched distribution, corresponding to a significant BC interaction term in the analysis of variance (P < 0.05). The synergistic mechanism between the two is as follows: the pozzolanic reaction and pore refinement effect of NS significantly improved the matrix density, providing a stronger anchoring interface for the steel fibers. Meanwhile, the crack-bridging and crack-inhibiting effect of steel fibers effectively suppresses the initiation and propagation of microcracks in the dense matrix. Under the coupled action of these two factors, the improvement in tensile strength far exceeds that achieved by single-additive reinforcement. The interactions between GT and NS, as well as between GT and steel fibers, were not significant, showing no obvious synergistic or antagonistic effects.
The morphological characteristics of the response surface and contour lines closely align with the mechanisms of action of each modifying material, further validating the regression model’s reliability. The bridging crack-inhibiting effect of steel fibers is the core mechanism for enhancing splitting tensile strength; the synergistic toughening between NS and steel fibers is the key interaction; and the contribution of GT is primarily manifested in the micro-aggregate filling aspect at an appropriate dosage (Xue et al., 2021; Tadayon et al., 2010). Based on the response surface analysis results and the cost factor of NS, the optimal mix design was obtained with the sole objective of optimizing splitting tensile strength; the optimization results are shown in Table 14.
TABLE 14
| Optimal blending ratio group | GT(%) | NS(%) | Steel fibers(%) | Prediction of splitting tensile strength | Objective |
|---|---|---|---|---|---|
| 1 | 20.8396 | 1.48695 | 1.49707 | 7.0992 | Optimal splitting tensile strength |
| 2 | 20.0396 | 0.631696 | 1.5 | 6.28532 | NS is used the least |
Optimal dosage of modified concrete.
3.6 Analysis of the flexural strength of modified concrete
Figure 8 shows the response surface and contour plots of the 28-day flexural strength of concrete under the two-way interaction of GT, NS, and steel fibers, providing a visual representation of how these factors and their interactions influence flexural performance. Overall, an increase in the steel fibers content has the most significant enhancing effect on flexural strength; the response surface shows a steep upward trend as the steel fibers content increases, reflecting the dominant role of the steel fiber’s crack-bridging effect on the concrete’s flexural performance. The matrix reinforcement effect of NS significantly improves flexural strength; its pozzolanic activity and pore refinement optimize the interfacial transition zone, providing a stronger anchoring interface for the steel fibers. GT, on the other hand, exhibits a typical quadratic nonlinear effect, with strength first increasing and then decreasing with dosage, peaking at around 20% (; ; ).
FIGURE 8
The interaction effects among the various factors show distinct differences and are highly consistent with the material modification mechanisms. The interactions between GT and NS, as well as between steel fibers and NS, are both significant, with contour lines exhibiting a distinct arched distribution; this corresponds to significant AB and BC interaction terms in the analysis of variance (P < 0.05). The synergistic mechanism between GT and NS is as follows: the pozzolanic activity of NS and the micro-aggregate filling effect improve the transition zone at the tailings sand–slurry interface, reduce interfacial defects, and broaden the optimal dosage range of GT. The synergistic mechanism between steel fibers and NS manifests as follows: the matrix densified by NS provides a stronger anchoring interface for the steel fibers, while the crack-bridging effect of the steel fibers further inhibits crack propagation in the dense matrix; the coupled action of these two factors significantly enhances the concrete’s flexural strength. The interaction between GT and steel fibers was not significant, showing no obvious synergistic or antagonistic effects.
The morphological characteristics of the response surface and contour lines further validated the reliability of the regression model and the mechanisms of action of each factor. The crack-bridging effect of steel fibers F is the core mechanism for enhancing flexural strength, determining the crack propagation path and failure mode of the specimens under bending loads; the matrix densification effect of NS is a key auxiliary factor, which indirectly amplifies the fiber’s toughening effect by optimizing the interface; The secondary effect of GT defines its optimal dosage range, which should be controlled around 20% to achieve the best filling effect. Based on the results of the response surface analysis and considering the cost factor of NS, the optimal mix design was obtained with the sole objective of optimizing flexural strength; the optimization results are shown in Table 15.
TABLE 15
| Optimal blending ratio group | GT(%) | NS(%) | Steel fibers(%) | Predicted flexural strength | Objective |
|---|---|---|---|---|---|
| 1 | 16.9769 | 1.13496 | 1.41307 | 11.1792 | Optimal flexural strength |
| 2 | 15.7022 | 0.5 | 1.5 | 10.7484 | NS |
Optimal dosage of modified concrete.
3.7 Accuracy analysis of modified concrete models
Based on the data obtained from the concrete tests in Table 8, this study strictly limited the dosage of GT, NS, and steel fibers to the predefined range established for the experiments. Compressive strength, flexural strength, and splitting tensile strength were selected as performance response indicators. Using the response surface method (RSM), a multi-factor performance optimization analysis was conducted. The specific design scheme is shown in Table 16, and the optimal composite dosage ratios for GT, NS, and steel fibers were ultimately determined through fitting and solution. The test results indicate that the concrete achieves optimal comprehensive mechanical properties when the admixture contents of GT, NS, and steel fibers are 21.79%, 1.48%, and 1.49%, respectively. Compared to the control group, the concrete’s compressive strength, split tensile strength, and flexural strength increased by 38.43%, 39.54%, and 44.65%, respectively. Since the optimization predictions from response surface models often deviate somewhat from actual engineering conditions, a set of parallel validation tests was conducted using the same admixture ratios to verify further verify the applicability and reliability of this optimal mix design. Among these, the compressive, splitting tensile, and flexural strengths of the optimized values differed from the actual measured strengths by 3.45%, 4.94%, and 2.08%, respectively. The test results show that the relative errors for all mechanical strength indices of the concrete were controlled within 5%. See Table 17 for details.
TABLE 16
| Factors | Goals | Lower limit | Upper limit |
|---|---|---|---|
| A | in range | 10 | 30 |
| B | in range | 0.5 | 1.5 |
| C | in range | 0.5 | 1.5 |
| R1 | maximize | 44.17 | 60.41 |
| R2 | maximize | 4.78 | 7.06 |
| R3 | maximize | 7.23 | 10.99 |
Optimization objectives for modified concrete.
TABLE 17
| Typology | Dosage | Strength/MPa | Error and improvement rate/% | ||||||
|---|---|---|---|---|---|---|---|---|---|
| GT | NT | Steel fibers | R1 | R2 | R3 | R1 | R2 | R3 | |
| Control group | 0 | 0 | 0 | 42.21 | 4.83 | 7.48 | - | - | - |
| Optimal value | 21.79 | 1.48 | 1.49 | 60.52 | 7.09 | 11.05 | - | - | - |
| Actual measurement | 21.79 | 1.48 | 1.49 | 58.43 | 6.74 | 10.82 | 38.43 | 39.54 | 44.65 |
Predicted results and errors for modified concrete.
ound the result to two decimal places.
3.8 Microstructure of modified concrete
Figure 9 shows the microstructural characterization of concrete specimens cured for 28 days, as observed by SEM. Figure 9a presents the high-magnification microstructure of the control group (GNS0), which exhibits the typical characteristics of hydration products in ordinary Portland cement. The cement paste matrix surface shows numerous microcracks and nanoscale pores, and the hydration products are distributed relatively uniformly. Since no modifying materials were introduced in this group, there was no significant obstruction to crack propagation, and the specimen exhibited the brittle failure characteristics inherent to ordinary concrete. Figure 9b shows the low-magnification morphology of the modified group GNS4, where steel fibers are uniformly dispersed within the matrix and form a three-dimensional interlaced network with the aggregate. Hydration products adhere to the fiber surfaces, creating a well-bonded interface transition zone with the matrix. Compared to the reference group, the number of microcracks in the matrix is significantly reduced, and their propagation paths are deflected; cracks are bridged and blocked at the fibers and are forced to detour, consuming a large amount of fracture energy, in conjunction with the hydration-promoting effect of nano-silica and the aggregate-filling effect of GT.
FIGURE 9
Figure 9c shows the microstructure of the optimal GNS18 group obtained via response surface optimization, which represents a systematic refinement compared to the reference group. The steel fibers exhibit no significant agglomeration and are tightly enveloped by a dense C-S-H gel. The interface transition zone between the fibers, matrix, and aggregate matrix has been improved, resulting in a significant increase in interfacial bond strength. This may be attributed to the fact that NS fills micro-pores and undergoes secondary hydration reactions with Ca(OH)2, generating more C-S-H gel and thereby achieving matrix densification and interface strengthening (Yunchao et al., 2021; ). GT optimizes the aggregate gradation and increases the system’s bulk density. steel fibers, through its crack-bridging and stress-transfer functions, effectively suppresses the initiation and propagation of macro-cracks (Nis, 2018).
Based on the SEM-EDS elemental mapping (Figures 10, 11), energy-dispersive X-ray spectroscopy (EDS) spectra (Figure 12), and quantitative elemental analysis results (Table 18), it can be seen that. Figure 10 shows localized enrichment of Si in the reference group (GNS0), with Ca distributed over a large area in the matrix. Figure 11 shows that Si is uniformly dispersed throughout the optimal group (GNS18), overlapping extensively with Ca and O; simultaneously, uniformly distributed Fe and Mn can be detected, confirming the tight interlocking of the steel fibers with the modified cement matrix. Combined with the quantitative comparison of normalized elemental mass fractions in Table 18, it is evident that, compared to GNS0, the mass fraction of Si in GNS18 increased from 7.40% to 10.44%, while the mass fraction of Ca decreased from 34.21% to 28.56%. This quantitatively demonstrates that NS exhibits pozzolanic activity, continuously consuming Ca(OH)2 within the system and generating more dense C-S-H gel with a low calcium-to-silicon ratio, thereby achieving densification and strengthening at the fiber-matrix interface at the compositional level.
FIGURE 10
FIGURE 11
FIGURE 12
TABLE 18
| Experimental group | Elements | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| O | Ca | Si | Al | S | C | Fe | Mn | K | |
| GNS0 | 47.99 | 34.21 | 7.40 | 1.30 | 0.28 | 8.82 | 0 | 0 | 0 |
| GNS18 | 46.80 | 28.56 | 10.44 | 2.01 | 0.36 | 7.24 | 2.34 | 0.58 | 1.67 |
Normalized mass of elements (%).
Combining the results of microstructural and elemental characterization, a synergistic reinforcement effect between NS and steel fibers is observed. On the one hand, NS fills the capillary pores in the matrix and consumes the calcium hydroxide enriched at the interface, thereby improving the loose defects at the fiber-matrix interface and forming a continuous, dense hydration bonding layer, which significantly enhances the chemical bonding strength and mechanical anchoring force of the steel fibers. On the other hand, the matrix modified by NS densification can stably anchor the steel fibers. The randomly distributed steel fibers form a three-dimensional crack-retardation network that, under load, continuously bridges microcracks and transfers tensile stress, forcing cracks to propagate in a meandering manner and dissipating a significant amount of fracture energy.
4 Conclusion
This study focuses on optimizing the mechanical properties of concrete modified by a composite blend of GT, NS, and steel fibers. Through a systematic investigation involving macroscopic failure tests, response surface modeling, multifactorial effect analysis, and microstructural characterization, the study elucidated the synergistic modification mechanism of this ternary composite system and produced high-performance modified concrete. The main conclusions and findings are as follows.
A quadratic polynomial response surface model constructed based on a Box-Behnken design accurately describes the influence of GT, NS, and steel fibers on the 28-day compressive, split tensile, and flexural strengths of concrete. All three strength models achieved a highly significant level (P < 0.01), with no significant outliers (P > 0.05). The adjusted coefficient of determination (Adj R2) reached 0.9883, 0.9934, and 0.9734, respectively, and the coefficient of variation (C.V.) was consistently below 3%. and the Adequate Precision (Adequate Precision) was well above 4. This indicates that the models exhibit high fit, good reproducibility, and strong predictive capability, effectively quantifying the relationships between each factor and concrete’s mechanical properties.
For all three factors, there are clear optimal dosage thresholds affecting the mechanical properties of concrete. The overall ranking of main effects on compressive strength is NS > steel fibers > GT, while for split tensile strength and flexural strength, the ranking is steel fibers > NS > GT. Among these, steel fibers serves as the core regulatory factor, with changes in its dosage having the greatest impact on split tensile and flexural strengths (F-values of 1285.31 and 410.88, respectively); within the experimental range, strength generally increases with increasing steel fibers content. NS primarily enhances compressive strength through pozzolanic activity and the filling effect of microfine aggregates (F = 447.43). GT exhibited a “quadratic parabolic” variation pattern for all strength properties, with an optimal replacement rate of approximately 20%. At low dosages, optimizing aggregate gradation and improving matrix density led to strength gains; at high dosages, strength decreased due to internal defects introduced by gradation deterioration.
Multi-objective optimization was performed to maximize compressive, split tensile, and flexural strengths, yielding an optimal mix ratio of 21.79% GT, 1.48% NS, and 1.49% steel fibers. The measured 28-day compressive, split tensile, and flexural strengths reached 58.43 MPa, 6.74 MPa, and 10.82 MPa, respectively, representing increases of 38.43%, 39.54%, and 44.65% compared to the reference group. Validation test results showed that the relative errors between measured and model-predicted values for all strength indicators were controlled within 5% (3.45%, 4.94%, and 2.08%, respectively).
Macro-scale failure modes and microstructural analysis indicate that the reference group exhibited typical brittle failure characteristics, with sudden disintegration occurring upon reaching the ultimate load. In contrast, the modified groups exhibited ductile failure, with the specimens remaining largely intact and showing only a few through-cracks; the failure process was distinctly progressive. At the microstructural level, the multi-level filling effect and hydration regulation of GT and NS resulted in a more uniform distribution and denser structure of the C-S-H gel. Simultaneously, steel fibers formed a tight bond in the interface transition zone with the cement paste matrix, creating reliable mechanical interlocking and chemical bonding. This effectively suppressed crack initiation and propagation, providing a solid microstructural foundation for improving macroscopic mechanical properties.
In terms of large-scale application at construction sites, the GT, NS silica, and steel fibers used in this study are all materials with a stable commercial supply. The processes for concrete mixing, pouring, vibrating, and curing are consistent with those for ordinary structural concrete, requiring no additional specialized construction equipment. The construction process is simple and highly adaptable, meeting the basic conditions for large-scale project implementation. At the same time, the application of this mix design still faces certain practical challenges: graphite tailings are limited by their source locations, and long-distance transportation increases construction costs. NS powder is prone to agglomeration, requiring standardized dosing methods during on-site construction. The steel fiber composite system reduces the workability of the mix, demanding higher precision in on-site quality control. In terms of performance and cost comparison, compared to conventional concrete, the optimized mix exhibits significant improvements in compressive, tensile, and flexural strengths, with crack resistance and structural ductility markedly superior to those of conventional concrete. The resourceful use of graphite tailings as a substitute for natural river sand effectively reduces the procurement costs of natural aggregates, offsetting the incremental material costs associated with nano-silica and steel fibers; as a result, the overall construction cost is lower when the material is used locally within the mining area.
This study mainly investigates the mechanical properties and microstructural mechanisms of the optimized ternary modified concrete at 28 days, and there are still insufficient explorations on its long-term durability performance under complex service environments, which is a limitation of this study. To further improve the performance evaluation system and engineering application basis of graphite tailings modified concrete, future research will focus on systematic long-term durability tests. Specifically, relevant tests including water absorption, chloride penetration resistance, freeze-thaw resistance, and sulfate attack resistance will be carried out to explore the long-term performance attenuation law and internal durability degradation mechanism of the modified concrete.
Statements
Data availability statement
The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.
Author contributions
KL: Writing – original draft. GF: Writing – review and editing.
Funding
The author(s) declared that financial support was received for this work and/or its publication. This work was supported by the Key Research Project of Higher Education Institutions in Henan Province (16B560006).
Conflict of interest
The author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
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Summary
Keywords
graphite tailings sand, mechanical properties, microstructure, nanoscale silica, steel fibers
Citation
Li K and Fa G (2026) Optimization of the mechanical properties of concrete using graphite tailings, steel fibers, and nano-silica based on RSM-BBD. Front. Mater. 13:1887801. doi: 10.3389/fmats.2026.1887801
Received
21 May 2026
Revised
06 July 2026
Accepted
09 July 2026
Published
05 August 2026
Volume
13 - 2026
Edited by
Xiaojian Gao, Harbin Institute of Technology, China
Reviewed by
Saeed B. Nia, Iowa State University of Science and Technology Iowa State Online, United States
Yuvaperiyasamy M, Saveetha University, India
Updates
Copyright
© 2026 Li and Fa.
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*Correspondence: Ke Li, ny_like@163.com
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