Mixture ratio optimization of basalt fiber recycled aggregate concrete based on RSM

In this paper, the effects of W/B ratio, recycled aggregate (RA) content and basalt fiber (BF) dosage on the compressive strength, splitting tensile strength and slump of concrete were investigated and a regression model was developed for analysis and prediction, and the regression model was validated using ANOVA and confidence analysis. Statistical analysis revealed that W/B ratio, RA content and BF dosage had significant effects on all properties of concrete. The established regression model fits the experimental data well and can accurately predict the properties of concrete. It was also found that there was a significant interaction between W/B ratio and BF dosage, as well as RA content and BF dosage, which suggests that the combination of these factors should be considered in the design of concrete mixture ratio to achieve optimum performance. The predicted values of compressive strength, split tensile strength and slump of concrete under optimum proportioning were in good agreement with the experimental values. Therefore, optimizing the concrete proportion by response surface methodology can improve the testing efficiency and obtain basalt fiber recycled aggregate concrete that meets the design requirements and has better overall performance.


Introduction
With the acceleration of urbanization, a large number of old buildings will be demolished, which will inevitably produce a large amount of construction waste [1][2][3].Construction waste mainly includes waste concrete and waste bricks.Using waste concrete to partially or completely replace natural aggregate to prepare recycled aggregate concrete can not only solve the problem of construction waste dumping and landfill, but also save natural resources and protect the environment [4,5].However, due to the defects of recycled aggregate such as rough surface, large porosity, low strength and high water absorption, its engineering application is limited [6].In order to expand the scope of application of recycled aggregate concrete, a comprehensive and systematic study of its performance is needed, and the mixture ratio design directly determines the working performance, mechanical properties and durability of recycled aggregate concrete, which is a prerequisite for the performance study [7,8].
As a high-performance fiber material, basalt fiber exhibits excellent mechanical properties and durability, which can reduce the shrinkage and cracking of concrete during the stress process, and also maintain the stability of concrete under complex environmental conditions [9].During the process of replacing natural aggregates with recycled aggregates, there may be certain differences in their physical and chemical properties, which may lead to fluctuations in the performance of concrete.The incorporation of basalt fiber is expected to make up the defects of recycled aggregates and improve the mechanical properties of concrete, making the performance of concrete more stable and reliable.Additionally, with the increasing awareness of environmental protection, recycled aggregate concrete, as a green building material, is increasingly widely used in the construction industry.The addition of basalt fiber can not only enhance the performance of recycled aggregate concrete but also contribute to promoting the concept of green buildings and sustainable development.
At present, most of the scholars refer to the ordinary concrete proportion design specification for recycled aggregate concrete proportion design, and use orthogonal test to seek the optimal proportion [10][11][12].However, when using orthogonal tests to seek the optimal proportion, the consideration of the interaction between factors will lead to a large amount of workload, and it is not possible to obtain a clear functional relationship between the factors and the response values in the specified area [13,14].Response surface method is a product of the combination of mathematics and statistics, which can use a small amount of experimental data to establish a mathematical model between multiple factors and one or more response values, and evaluate the effect of the interaction between factors on the response values to determine the optimal response values, and has the advantages of fewer tests, lower cost, and higher accuracy compared with orthogonal tests.
In recent years, the response surface method has begun to be applied to the optimization of cement mortar and concrete proportion in the field of construction materials.Zhang et al [15] obtained the optimal aggregate gradation and additive dosage of recycled aggregate pervious concrete by BBD mode design of response surface method.Luo et al [9] used the response surface method for multi-objective optimization of basalt fiber concrete proportion by taking water -cement ratio, sand ratio and basalt fiber dosage as factors to achieve toughening of concrete and to obtain a concrete proportion that meets the expected requirements.The above studies show that basalt fibers can be used to optimize the mechanical properties of concrete, and the application of the response surface method to the optimization of construction material fits has significant advantages, but there are fewer studies related to the application of the response surface method for the optimization of basalt fiber recycled aggregate concrete.
Current research on basalt fiber recycled aggregate concrete mostly focuses on the influence of single factors on concrete properties and lacks a systematic study under the combined effect of multiple factors.Therefore, in this study, basalt fiber recycled aggregate concrete was taken as the research object, and 20 sets of ratios were designed to test the slump, compressive strength, and splitting tensile strength of the concrete by using the central composite design method with the comprehensive consideration of W/B ratio, RA content and BF dosage.The response surface models of slump, compressive strength and splitting tensile strength were established, and the mixture ratio optimization was carried out by the aspired function, and finally the optimal mixture ratio of basalt fiber recycled aggregate concrete was obtained.This study not only enriches the performance optimization theory of basalt fiber recycled aggregate concrete, but also provides an important theoretical basis and practical guidance for the selection and application of concrete materials in actual projects.

Materials
The cement is Qinling brand ordinary silicate cement with strength grade of 42.5.The fine aggregate is river sand with fineness modulus of 2.8.The particle size of coarse aggregate is 5∼12.5 mm, including natural coarse aggregate and recycled coarse aggregate with original strength grade of C40, whose apparent morphology and performance indexes are shown in figure 1 and table 1, respectively, where the natural coarse aggregate is continuous graded gravel, and the recycled coarse aggregate is produced by Shaanxi Jianxin Environmental Protection Technology Development Co.The superplasticizer (SP) was produced by Jinan Yao Sen Biochemical Co., Ltd and its water reduction rate, specific gravity and solid content were 25%, 1.06 and 28%, respectively.Basalt fiber was produced by Shanghai Yingjia Industrial Development Co., Ltd and its physical properties are shown in table 2.

Mixture ratios
The design method adopted is the central composite design, it boasts the advantage of dividing each design variable into several levels that are symmetric relative to the center of the design space within the given range of design parameters.Through composite design, it can comprehensively cover the entire design space with a relatively small number of experimental schemes.Furthermore, this experimental design method exhibits excellent fitting effects when fitting the response surface.This method divides the design groups into factorial groups, axial groups, and central groups.Among them, the main function of the factorial groups is to estimate the first-order terms and interaction terms, that is, to investigate the individual impact of each factor on the response variable as well as the interaction between factors.The axial groups are used to estimate the curvature of the response surface, thereby determining whether there is a nonlinear relationship between the factors and the response.The central group represents the intermediate level combination of all factors, and multiple repetitions of the central point experiment are required to estimate the experimental error more effectively, thus enhancing the accuracy and reliability of the model.
The aim of this paper is to investigate the effects of water-binder ratio, recycled aggregate and basalt fiber on compressive strength, split tensile strength and slump of concrete.The experimental water consumption was fixed, and the water-binder ratio (Factor A, levels 0.36, 0.39, 0.43, 0.47 and 0.50), recycled aggregate content (Factor B, levels 0, 20%, 50%, 80% and 100%), and basalt fiber dosage (Factor C, levels 0, 0.08%, 0.20%, 0.32% and 0.40%) were selected.The three-factor with five-level test was designed and the experimental data were processed using the central composite design method in the Design-expert software, and the test factors and levels as well as the concrete mixture ratios are shown in table 3.

Concrete preparation and testing methods
Firstly, the concrete mixer was slurried.After the concrete is well mixed, its slump is tested and recorded, then it is poured into a pre-lubricated test mold and vibrated using a vibrating table.Over-vibration and leakage of vibration should be avoided to prevent segregation of the concrete and to reduce the bonding strength of the fibers to the substrate.Subsequently, the specimens were smoothed with a spatula and labeled on the specimen molds, which were demolded after 24 h.Finally, the specimens were placed in the curing pool for 28 d.Compressive strength and splitting tensile strength tests were conducted according to GB/T 50081 [16] and the specimens were cubes with a side length of 150 mm, and the loading equipment was a TYA-2000 electrohydraulic pressure tester.4. The parameters of the statistical model are shown in table 5, in which p-value is a statistical measure that helps determine the strength of evidence against the null hypothesis in a hypothesis test.It represents the probability of observing a test statistic as extreme as, or more extreme than, the observed sample statistic, assuming that the null hypothesis is true.In practical terms, the p-value is used to make decisions about whether to reject or fail to reject the null hypothesis.If the p-value is smaller than the chosen level of significance (often set at 0.05), it suggests that the observed data is unlikely to have occurred by chance alone, and the null hypothesis is rejected in favor of the alternative hypothesis.On the other hand, if the p-value is larger than the chosen level of significance, it suggests that the observed data could reasonably occur by chance, and there is not enough evidence to reject the null hypothesis.

Experimental results and discussions
According to the P-value, it can be seen that W/B ratio (A), RA content (B) and BF dosage (C) have significant effects on all responses, in addition, AC, A 2 and B 2 have significant effects on compressive

. The variance of the models
The above regression models were subjected to ANOVA and credibility analysis, and the results are shown in table 6, respectively.In this paper, the F-test evaluates the model significance, and the coefficient of determination R 2 , the adjusted coefficient of determination R 2 a and the predicted coefficient of determination R 2 p are used to comprehensively evaluate the model credibility.The coefficient of determination is a statistical measure used to assess the degree of fit of the regression model to the data, which ranges from 0 to 1.The closer the value is to 1, the higher the degree of fit of the model to the data.The adjusted coefficient of determination is a modification of the coefficient of determination that takes into account the number of independent variables in the model, aiming to provide a more accurate assessment of the model's fit.It introduces a penalty term to balance the number of independent variables and the degree of fit, providing a more reliable measure of the model's fit.The predicted coefficient of determination is a statistical measure used to assess the predictive power of additional independent variables added to a model.It is commonly used in cross-validation and model improvement to evaluate the contribution of new variables to the model's predictive ability.In summary, the coefficient of determination is used to evaluate the fit of a regression model, the adjusted coefficient of determination is a modification that considers the number of variables, and the predicted coefficient of determination is used to assess the predictive power of additional variables.
As can be seen from table 6, the F-value of the compressive strength regression model is 70.61, which indicates that the significance of the regression model is high; at the same time, R 2 , R 2 a and R 2 p are 0.994, 0.982 and 0.956 respectively, which indicates that the regression model has a high reliability.The F-value the split tensile strength regression model is 141.77, which indicates that the regression model is highly significant; at the same time, R 2 , R 2 a and R 2 p are 0.998, 0.991 and 0.972, respectively, which indicates that the regression model has high reliability.The analytical results of the slump regression model are consistent with the results of the first two models, which also have high reliability.

The residual of the models
Studentized residuals are the values obtained by dividing the residuals by the standard deviation, which are used to visually determine whether the residuals follow a normal distribution [17][18][19].The studentized residuals can be derived from the ordinary residuals, which plays a very important role in the diagnosis of regression model [20,21].The ANOVA function of Design-expert software can be used to derive the studentized residuals of compressive strength, split tensile strength and slump regression models, and the results are shown in figure 2. It can be seen that the studentized residuals of all regression models are randomly distributed and the absolute value is less than 2. The studentized residuals of compressive strength and slump are in the interval of [−2, 2], and the studentized residuals of split tensile strength are in the interval of [−1.5, 2], which indicates that the residuals are relatively small, and the fitting effect of the model is satisfactory.The normal probability distributions of the studentized residuals of compressive strength, split tensile strength and slump were plotted in figure 3. The standard deviations of compressive strength, split tensile strength and slump are 1.04, 0.73 and 0.96, respectively, indicating that the studentized residuals of slump, compressive strength and split tensile strength conform to normal distribution.Therefore, it is effective to use the proposed model to explain and predict the compressive strength, split tensile strength and slump.Scatter plots of experimental and predicted values of compressive strength, split tensile strength and slump were plotted as shown in figure 4. It can be seen that the predicted and experimental values of all models are in close agreement and the scatter points are clustered around the y = x line, indicating that the response surface model can predict the compressive strength, splitting tensile strength and slump of concrete with high accuracy.

Analysis and discussion of BFRAC properties based on RSM models 3.2.1. Compressive strength
The response trajectories of compressive strength under the influence of different factors are shown in figure 5, and it can be seen that the compressive strength tends to decrease with the increase of water-binder ratio and recycled aggregate content.Interestingly, the concrete compressive strength increases and then decreases with the increase in basalt fiber dosage.This may because when the concrete subjected to external pressure, the fibers can effectively absorb and disperse the energy and delay the generation and expansion of cracks, which is beneficial to improving the compressive strength of concrete [22][23][24].Therefore, an increase in the basalt fiber dosage at the initial stage leads to an increase in the compressive strength of concrete.However, when the fiber dosage is too high, the interlacing between the fibers will be strengthened to form fiber clusters, which may lead to an increase in the voids inside the concrete, thereby weakening the mechanical properties of the concrete.A 3D response surface plot of compressive strength was drawn according to the regression model to visualize and analyze the effect of the interaction of the two factors on the compressive strength of recycled aggregate concrete, and the results are shown in figure 6. Observing the surface and the projected trajectory shows that there is a significant interaction between the water-binder ratio and basalt fiber dosage, indicating that the effect of water-binder ratio and basalt fiber dosage on the compressive strength of concrete is not a simple linear superposition effect.This is because a lower water-binder ratio leads to better filling and bonding of cement particles and improves the densification of the concrete, however, a low water-binder ratio makes the concrete more viscous and makes it difficult to disperse the fibers adequately.This may lead to fibers bunching together, resulting in the fact that fiber dispersion may be somewhat compromised at low water-binder ratios using the same basalt fiber dosage [25,26].An appropriate amount of fiber dosage can effectively prevent crack extension and improve the toughness and crack resistance of concrete.However, at too high fiber dosage, the interlacing between fibers is enhanced, which may lead to fiber clustering and agglomeration, which will weaken the dispersion effect of fibers and may reduce the densification of the hydrocolloid gel [27].In summary, the choice of water-binder ratio can affect the dispersion of fibers, while the fiber dosage will affect the densification of hydrocolloid gel, therefore, the effect of water-binder ratio and basalt fiber dosage on concrete properties is not a simple linear cumulative effect, but there is an interactive effect.Comprehensive consideration and optimal design of water-binder ratio and basalt fiber dosage are required to achieve the best performance of concrete.

Split tensile strength
The response trajectories of splitting tensile strength under the influence of different factors are shown in figure 7, which shows that the splitting tensile strength tends to decrease with the increase of water-binder ratio and recycled aggregate content.With the increase of basalt fiber dosage, the concrete splitting tensile strength gradually increases, which is different from the trend of compressive strength.Different from the compressive strength, the increase in splitting tensile strength is mainly due to the tensile properties and dispersion effect of basalt fibers, and the addition of fibers can form a fiber network structure, effectively preventing the expansion of cracks and improving the splitting tensile strength of concrete by absorbing and dispersing stress.With the increase of basalt fiber dosage, the tensile properties and dispersing effect of fibers are gradually enhanced, which leads to the monotonous increase of splitting tensile strength [28][29][30].In conclusion, the incorporation of basalt fibers can improve the cohesion and strength of concrete and fill microcracks, thus increasing the compressive strength of concrete.However, too high fiber dosage may lead to increased fiber clustering and porosity,  reducing the compressive strength of concrete [9].The enhanced tensile properties and dispersion of fibers help to increase the splitting tensile strength of concrete.Therefore, in concrete design and construction, the amount of fibers incorporated need to be considered comprehensively to balance the requirements of compressive strength and splitting tensile strength of concrete.
The three-dimensional response surface plots of split tensile strength were plotted according to the regression model, and the results are shown in figure 8. Observing the surface and the projected trajectory shows that there is an obvious interaction between water-binder ratio and basalt fiber dosage as well as recycled aggregate content and basalt fiber dosage.That's because the recycled aggregate content can fill the pore voids in the concrete and form a more compact structure between the cementite particles to improve the strength of the concrete.When the water-gel ratio is high, the incorporation of recycled aggregates can fill more pore spaces, thus further increasing the splitting tensile strength of concrete.However, when the water-binder ratio is low, the effect of recycled aggregate incorporation on the enhancement of split tensile strength of concrete will be weakened because the concrete itself already has a high degree of compactness.When the recycled aggregate  content is higher, its pore-filling effect can form a synergistic effect with basalt fibers to improve the splitting tensile strength of concrete.However, as the recycled aggregate content continues to increase, the excessive particle content may negatively affect the mechanical properties of the concrete, leading to a decrease in the splitting tensile strength.

Slump
The response trajectory of slump under the influence of different factors is shown in figure 9, which make it clear that the slump shows a decreasing trend with the increase of recycled aggregate content and basalt fiber dosage, and the slump of concrete increases gradually with the increase of water-binder ratio.The higher surface roughness of recycled aggregate adsorbs some water, further reducing the free water content in the concrete system, resulting in weakened fluidity and lower slump [31].The addition of basalt fibers enhances the cohesion and internal cohesion of concrete.Specifically, the fibers form a network structure within the concrete, increasing its viscosity, making it more difficult for the concrete to disperse and collapse during the slump test.And with the increase of water-binder ratio, the water content in concrete is relatively high, and the higher water-binder ratio will make the water in concrete dispersed between cement particles, making concrete more fluid.In summary, the increase in the amount of recycled aggregate and basalt fiber dosage decreases the slump  of concrete, while the increase in water-binder ratio increases the slump of concrete.This is due to the filling effect and hindering effect of recycled aggregates and fibers, as well as the effect of water-binder ratio on the fluidity of concrete.In the actual project, it is necessary to select the appropriate amount of recycled aggregate, fiber dosage and water-binder ratio according to the construction requirements and the needs of concrete properties to obtain the concrete slump that meets the requirements.
The three-dimensional response surface of slump is plotted according to the regression model and the results are shown in figure 10.Observing the surface and the projected trajectory shows that, similar to the splitting tensile strength, there is a significant interaction between the water-binder ratio and basalt fiber dosage as well as the recycled aggregate content and basalt fiber dosage.That's because when the water-binder ratio is low, the filling effect of recycled aggregate is more obvious and has a greater effect on the slump of concrete.And when the water gel ratio is higher, the concrete itself already has a higher fluidity, the filling effect of recycled aggregate is weaker, so the effect on the slump is smaller.The appropriate amount of recycled aggregate can fill the pore void and increase the densification of concrete, while the inclusion of basalt fibers can form a fiber network structure, effectively preventing the expansion of cracks and improving the toughness and crack resistance of concrete [32].When the content of recycled aggregate is low, the enhancement effect of basalt fiber is more significant, and has a greater impact on the slump of concrete.When the dosage of recycled aggregate is higher, the filling effect of recycled aggregate and the reinforcing effect of basalt fiber synergize with each other to improve the slump of concrete, and the interaction between them is more obvious.In summary, the interaction between the water-binder ratio and recycled aggregate is mainly due to the fact that the water-binder ratio determines the water content and fluidity in concrete, while the recycled aggregate content affects the aggregate filling performance.The interaction of recycled aggregate content and basalt fibers is mainly due to the filling effect of recycled aggregate and the reinforcing effect of basalt fibers synergize with each other and affect the slump of concrete accordingly.The optimum values of factors for basalt fiber recycled aggregate concrete are 0.398 for W/B ratio, 100% for RA content and 0.152% for BF dosage.In summary, this optimal mixture ratio is derived by comprehensively considering the W/B ratio, RA content, and BF dosage while ensuring the strength of the concrete.It not only reflects the optimization of concrete performance but also contributes to saving natural resources, reducing environmental burden, and embodying the concepts of sustainable development and green building.

Validation of the optimal models
To further validate the accuracy of the model, the mixture ratios in section 3.3.1 were verified experimentally, and the test values of strength and slump were compared with the predicted values, and the results are shown in table 8, which were verified using the absolute value of relative error, calculated by the formula in equation (7).As can be seen from table 8, with the optimal mixture ratio, the absolute values of relative errors between the test values and the predicted values of compressive strength, split tensile strength and slump are 3.6%, 0.7% and −4.0%, respectively, which are all less than 5%, indicating that the prediction accuracy of the regression model is high.Therefore, optimizing the concrete mixture ratio by response surface can improve the efficiency of the test, so as to obtain basalt fiber recycled aggregate concrete that meets the design objectives and has better comprehensive performance.

Conclusions
In this paper, experimental studies and multi-objective optimization of basalt fibers recycled aggregate concrete have been investigated and the following conclusions can be drawn: (1) The factors W/B ratio, RA content and BF dosage have significant effects on the compressive strength, splitting tensile strength, and slump of concrete.In concrete mixture ratio design, careful consideration and optimization of these factors are necessary to achieve the desired concrete properties.
(2) The regression models for compressive strength, splitting tensile strength, and slump have high reliability, and the R 2 for all three models are close to 1, indicating a strong fit to the data, which suggests that the regression models can accurately predict the concrete properties based on the given factors.
(3) The scatter plots of the experimental and predicted values show that they are very close to each other, indicating that the error between the regression model and the data is very small and can effectively explain and predict the concrete properties, which further proves the accuracy of the regression model in predicting the concrete properties.
(4) The interaction between the factors W/B ratio and BF dosage, as well as RA content and BF dosage, has a significant impact on the compressive strength, splitting tensile strength, and slump of concrete.This suggests that the effects of these factors on the concrete properties are not simply additive but rather exhibit interactive effects.Therefore, it is important to carefully consider the combination of these factors in concrete mixture ratio design to achieve optimal performance.The optimal mixture ratio of basalt fiber recycled aggregate concrete with strength of 40 MPa is 0.398 for W/B ratio, 100% for RA content and 0.152% for BF dosage.

3. 1 .
Establishment and statistical analysis of the RSM models 3.1.1.Establishment of the RSM models The measured values of compressive strength, splitting tensile strength and slump of concrete are shown in table

Figure 2 .
Figure 2. The predicted values against the externally studentized residuals.

Figure 4 .
Figure 4.The predicted against actual values.

Figure 5 .
Figure 5.The responses trace for compressive strength.

Figure 6 .
Figure 6.Influence of W/B ratio and BF dosage on compressive strength.

Figure 7 .
Figure 7.The responses trace for split tensile strength.

Figure 8 .
Figure 8. Response surface plot of split tensile strength.

Figure 9 .
Figure 9.The responses trace for slump.

3. 3 .
Application of the RSM models 3.3.1.Optimization of the mixture ratio Multi-objective optimization of recycled aggregate concrete with basalt fibers was carried out based on the regression model combined with the desire function (equations (4) ∼ (6).The optimization objective is to seek

Table 1 .
Properties of coarse aggregates.

Table 2 .
Properties of basalt fiber.

Table 5 .
Parameters of the models.), and AB, BC, A 2 and B 2 have significant effects on splitting tensile strength (R 2 ) and slump (R 3 ).The regression fitting analysis of the test data in table 4 was carried out using Design-expert software to obtain the response surface fitting equations R 1 , R 2 and R 3 for compressive strength, split tensile strength and slump as shown in equation (1), Equations (2) and (3), respectively.

Table 6 .
ANOVA for the models.

Table 7 .
Optimization target of DSC.
the optimal recycled aggregate substitution rate (Factor B) and basalt fiber dosage (Factor C) under different water-binder ratios (Factor A) to obtain the maximum values of concrete splitting tensile strength and slump under a specific compressive strength design objective (set at 40 MPa in this paper).The optimized design objectives are shown in table7.Based on the desire function, the basalt fiber recycled aggregate concrete proportion is optimized using the optimization numerical module of Design Expert software.The desirability contour is shown in figure 11.The desirability of 0.94160 shows that the optimization results are satisfactory.
ARD is the absolute relative deviation; E t is the test result; and M p is the predicted result model.