Optimizing fluidity and tensile strength of magnetically driven epoxy-cement repair materials based on response surface

Underwater crack repair is challenging due to drainage and exhaust, slurry retention at fixed points, and other issues. Magnetically driven epoxy resin cement slurry was developed, which can perform directional movement and fixed-point retention of slurry under the effect of an applied magnetic field. This paper focuses on slurry fluidity and tensile properties. Firstly, in the preliminary pre-study, the main influencing factors of the ratios were determined. Then, the optimum range of each factor is determined by a single-factor experiment. Furthermore, the response surface method (RSM) is applied to obtain an optimal ratio. Finally, the slurry is characterized by micro. Results showed that the evaluation index F proposed in this paper can well evaluate the interaction between fluidity (X) and tensile strength (Y). The 2FI regression model and the quadratic regression model are developed with fluidity and tensile strength as the response values and Epoxy Resin (ER) content, water-cement ratio, Fe3O4 content and sulphoaluminate cement (SAC) content as the influencing factors, and have reasonable fit and reliability. The relationship between the degree of influence of the influencing factors on the response value X and the response value Y in ascending order was: ER content > water-cement ratio > SAC content > Fe3O4 content. The magnetically driven slurry made by the optimal ratio can reach a fluidity rate of 223.31 mm and a tensile strength of 2.47 MPa. This is with relative errors of 0.36% and 1.65% from the model predicted values. Microscopic analysis showed that the magnetically driven epoxy resin cement slurry had a favorable crystalline phase, surface morphology, and structural composition.

With the rapid growth of the global construction industry, a large number of infrastructures are being planned and being constructed. Many underwater concrete structures in service are susceptible to cracks and holes due to freeze-thaw cycles 1-3 , dry-wet cycles 4,5 , sulfate and chloride erosion 4,6,7 , resulting in significant deterioration of their performance 8 . Although, repair materials in the building field, polymer-modified cementitious materials have been widely applied 9,10 . However, the repair and reinforcement of underwater concrete structures must face the problems of construction drainage and exhaust, upward sloping cracks and defects, low filling rate of tiny fissures, and difficult slurry retention under moving water conditions, which makes this repair work still challenging 11 .
At present, conventional pressure grouting methods cannot solve the problems of ventilation, drainage, and slurry retention at fixed points. Inspired by magnetic fluids, we are developing a magnetically driven epoxy resin cement slurry. This will achieve directional movement and fixed-point retention under an applied magnetic field, as shown in Fig. 1. This work is based on the principle that Fe 3 O 4 can be "target-driven" under a magnetic field 12 . The magnetically driven slurry with fresh properties of the slurry possessed the capacity to fill, move and resist segregation [13][14][15] , which can overcome gravity to repair upward sloping cracks and defects 16 . Liu et al. 16 developed a magnetic epoxy resin cement grouting anchor material with anti-gravity self convergence, guided flow, and real-time controllable slurry viscosity under the action of magnetic field, and explored the mechanism of slurry hardening and microscopic pore change law under the action of magnetic field, without involving the Experimental Raw materials. Commercial waterborne epoxy resin was produced from Shenyang Dongyan Tuyan Decoration Co., Ltd. (Shenyang, China), the relevant indicators are shown in Table 1. Fe 3 O 4 with a density of 5.17 g/ cm 3 , a specific surface area of 50 m 2 /g, and a purity of 99.9% with a powder diameter of 45 μm was provided by Hebei Casting & Research Alloy Materials Co., Ltd (Shijiazhuang, China) to improve the magnetic attraction of aqueous magnetically driven epoxy resin cement slurry. Hydroxyethyl methyl cellulose (also known as flocculant) was produced by Zhengzhou An Anankang Food Chemical Co., Ltd. (Zhengzhou, China) to enhance the dispersion resistance of the slurry. SiKa ViscoCrete-540P was used as a magnetically driven epoxy resin cement slurry water reducer, and the silicone antifoaming agent (also known as defoamer) was both used in this study.  www.nature.com/scientificreports/ Type P·O 52.5 ordinary Portland cement (OPC), SAC and silica fume (SF) were used as binders. The partial replacement of OPC with SAC is to shorten the coagulation time of the slurry forming the stone body. In addition, the partial replacement of OPC with SF is to improve the impermeability of the stone body 23 . The specific surface area of OPC, SAC and SF was 0.382 m 2 /g, 0.402 m 2 /g and 19.8 m 2 /g respectively, and their corresponding chemical compositions are shown in Table 2.
Preparation of magnetically driven epoxy resin cement slurry. Emulsion type epoxy resin was obtained by mixing the epoxy resin composite with the waterborne hardener (hardener: pure epoxy resin at 0.85:1). magnetically driven epoxy resin cement slurrys were then prepared with a constant epoxy resin content (5% by mass of the total cement). The SAC:OPC ratio by mass was 10%:90%, and SF-to-cement was 0.05. For basic proportions, a fixed Fe 3 O 4 -to-cement ratio, water-to-cement and flocculant-to-cement ratios were applied, which were 1:5, 0.5 and 0.01 respectively. The defoamer (1 wt% of the epoxy resin aqueous solution) and the superplasticizer (denoted as SP with a fixed ratio of 1 wt% of the total cement) were also used for minimising bubbles introduced by the addition of epoxy resin and for improving the workability of the slurry, respectively. In order to show the relative contents of different components clearly, basic proportions are shown in Table 3.
For the specimens, SF, SAC, and OPC were mixed for 30 s at low speed. Then Fe 3 O 4 and flocculant were added into the mixing bowl. This dry mixture was mixed for 60 s. The defoamer, superplasticizer, water, epoxy resin and hardener were fully mixed for three minutes at the same speed before casting. The above aqueous solution must be prepared within 20 min prior to its addition into the dry powder system. This is in order to prevent its early hardening after the hardener has been was cast into dumbbell moulds. After 24 h, specimens were demoulded and cured in standard curing conditions (temperature = 20 ± 1 °C, relative humidity ≥ 95%) for six days. Forming and curing regimes were based on Chinese standards SL/T 807-2021 and DL/T 5126-2001, used for testing epoxy resin grout for hydraulic structures and polymer-modified cement mortar, respectively.
In order to study the effect of OPC replacement with SF, the fluidity and tensile tests of the reference group (0 of SF content) of "the basic proportions of magnetically driven epoxy resin cement slurry" were conducted. The fluidity of the basic proportions and reference groups was 237 mm and 234 mm, respectively. The tensile strengths were 1.36 MPa and 1.38 MPa, respectively. The results showed that replacement of OPC with 5% SF had no effect on the fluidity and tensile strength of the magnetically driven epoxy-resin cement slurry.
Experimental design. Single factor experimental design. According to the previous experiments, ER content, water-cement ratio, Fe 3 O 4 content and SAC content were determined as the main experimental influencing factors. On the premise of other conditions remaining unchanged, the ER content, water-cement ratio, Fe 3 O 4 content and SAC content were changed in turn, and their effects on fluidity and tensile strength were studied to determine the optimal range of each factor.
Response surface optimization experimental design. The three-level, four-factorial Central-Composite experimental design with a categoric factor of 0 was employed to optimize the mix proportion based on the response values X and Y. The design was composed of three levels (high, medium and low, being coded as + 1, 0 and − 1) and a total of 30 runs were carried out in duplicate to optimize the level of chosen variables, such as ER content, water-cement ratio, Fe 3 O 4 content and SAC content. For the purpose of statistical computations, the four independent variables were denoted as A 1 , A 2 , A 3 and A 4 , respectively. According to the preliminary experiments, the range and levels used in the experiments are selected and listed in Table 4.
The experimental design matrix of the Central-Composite Design is tabulated in Table 5, and corresponding experiments were performed. The results were analyzed by applying the coefficient of determination (R 2 ), analysis of variance (ANOVA), contour lines, and response surface.
Characterisation of magnetically driven epoxy resin cement slurry. Tensile strength test. Tensile strength test, in accordance with the Chinese standard (SL/T 807-2021) was carried out on dumbbell-shaped www.nature.com/scientificreports/ samples with the moulds specifically designed to fabricate the samples required for testing using an electronic universal testing machine, as shown in Fig. 2. The moulds were internally coated with some debonding agent in order to avoid the adhesion of the slurry to the mould during the curing process. For the tensile strength test, three samples were used and the average value was considered as the final result, and the measurements were performed at a speed rate of 0.5 mm/min.
Fluidity. The fluidity of magnetically driven epoxy resin cement slurry was assessed using a truncated cone fluidity test. The fluidity was obtained by averaging the diameters (mm) measured in three directions in accordance with the Chinese standard GB/T 50448-2015.
Microscopic analysis. The prepared specimens of optimal mix proportions were cured under standard curing conditions for 28 days. The crystal phase of solidification was determined by a Japan SmartLab diffractometer.

Single factor experimental results
Effect of ER content. It can be seen in Figs. 3 and 4 that with the increase of ER content, the value of degree of fluidity gradually decreases, while the value of tensile strength gradually increases. The greater the degree of ER content, the higher the viscosity, and the higher the viscosity, the smaller the fluidity 24 . This indirectly explains the uniform dispersion of ER in the magnetically driven epoxy resin cement slurry. As long as ER is cured, it can be used as a binder to bond the hydrated inorganic crystalline products to the cement paste. It can be seen from the SEM that the complexes are covered on the surface of the hydrated products or adsorbed on the inorganic surface. In some cases, it enhances the bonding ability of cement slurry solidification, thereby improving its tensile strength 19 . A common evaluation index F such as Eq. (1) was introduced to evaluate the interaction effect of ER content on the value of degree of fluidity and the value of tensile strength of magnetically driven epoxy resin cement slurry.
The evaluation index F under different ER content is shown in Fig. 5. As shown in Fig. 5, the evaluation index F increases and then decreases as the ER content increases, and the evaluation index F is maximum when the ER content is 7%.
Effect of water-cement ratio. It can be seen in Figs. 3 and 4 that with the increase of water-cement ratio, the value of degree of fluidity gradually increases, while the value of tensile strength gradually decreases. At higher water-cement ratio, slurry has less consistency, poor cohesion and water retention, and in the same ER content, fluidity increases with the increase in water-cement ratio. In the same ER content, with the increase of water-cement ratio, resulting in more water, the pore space of the slurry increases, the structure is more loose, and the tensile strength is reduced.    Fig. 5. It can be seen from Fig. 5 that as the water-cement ratio increases, the evaluation index F first decreases slightly, then increases and then decreases slowly, and the evaluation index F is maximum when the water-cement ratio is 0.5.  Water-cement ratio, A 2

Effect of
Fluidity (mm) Figure 3. Effect of different factors on fluidity. Water-cement ratio,  Effect of SAC content. It can be seen in Figs. 3 and 4 that as the SAC content increases, the value of degree of fluidity gradually decreases. In contrast, the value of tensile strength decreases rapidly and then slowly. Under the same conditions of water-cement ratio, the flow of slurry is mainly related to the fineness of cement particles. The finer the particle size and the larger the surface area, the more water is required and the smaller the fluidity 26 . The particle fineness of SAC is larger than that of OPC, and as the SAC content increases, the fluidity decreases. Tensile strength is related to the setting time of magnetically driven epoxy resin cement slurry. As the SAC content increases, the CA 3 S content increases. The magnetically driven epoxy resin cement slurry hydrates faster and has a shorter setting time. Since the main hydration products are coarse crystals and cannot be evenly distributed over time, internal micro-cracks result in weak points, resulting in reduced tensile strength 27 .
Equation (1) is applied to calculate the evaluation index F under different SAC content, and the results are shown in Fig. 5. It can be seen from Fig. 5 that with the increase of SAC content, the evaluation index F gradually decreases. The SAC content of 5% is selected as the optimum considering the contribution to the shortening of the setting time.

Response surface optimization analysis
For RSM, the most commonly used second-order polynomial equation and 2FI equation developed for regression fitting experimental data and determining the relevant model terms can be written respectively as: where X and Y represent the predicted response, i.e. the fluidity (mm) and tensile strength (MPa) by the mix proportion optimization, α 0 and β 0 the constant coefficients, α i and β i , the ith linear coefficient of the input factor A i , α ii and β ii , the ith quadratic coefficient of input factor A i , α ij and β ij , the different interaction coefficients between input factors A i and A j (i = 1-4, j = 1-4 and i ≠ j), ε X and ε Y , the error of the model.
The equation expresses the relationship between the predicted response and independent variables in coded values according to Tables 4 and 5 Table 5. The second-order polynomial equation and 2FI equation for predicting the optimum point were obtained according to the Central-Composite design and input variables 28 , and then the empirical relationship between the response and the independent variables in the coded units was presented on the basis of the experimental results as follows: Water-cement ratio, A 2  Table 5, and the model ANOVA results for the response values X are obtained as shown in Table 6. As can be seen from Table 6, P r > F < 0.000 1 is very significant, indicating that the model can be well optimized mix proportion. The lack of fit (P r > F = 0.0691 > 0.05) is not significant, indicating that the model is significantly reliable. The F-test shows that the magnitude of the influence factor on the response value X is A 2 > A 1 > A 4 > A 3 . A 1 A 2 and A 1 A 3 (P r > F < 0.01) had a highly significant effect, A 1 A 4 and A 3 A 4 (P r > F < 0.05) had a significant effect, while A 2 A 3 and A 2 A 4 (P r > F > 0.05) had a non-significant effect. Figure 6a,b respectively show the residual positive distribution of response value X and the distribution of actual and predicted values. As can be seen from the Fig. 6a, positive residual distribution, actual value and predicted value all present linear distribution. And the uniform distribution on the y = x line in Fig. 6b, which indicates that this model can be well predicted. R 2 adj = 0.9375, which explains 93.75% of the variation with small errors. R 2 = 0.9590 and C V = 1.72%, indicating that the experiment is credible and accurate. Therefore, model (4) can be used to analyze and predict the response value X. Table 6. Variance analysis results of the response value X. S S is sum of squares, D F is degrees of freedom, M S is mean square, Pr > F is probability without significant, Pr > F ≤ 0.01 is extremely significant(**), Pr > F ≤ 0.05 is significant(*).   Table 5, and the model ANOVA results for the response values Y are obtained as shown in Table 7.
As can be seen from Table 7, P r > F < 0.000 1 is very significant, indicating that the model can be well optimized for the mix proportion. The lack of fit (P r > F = 0.1223 > 0.05) is not significant, indicating that the model is significantly reliable. The F-test shows that the magnitude of the influence factor on the response value Y is 1, A2 2, A2 3 and A2 4 (P r > F < 0.01) had a highly significant effect, A 3 A 4 (P r > F < 0.05) had a significant effect, while A 1 A 2 and A 1 A 4 (P r > F > 0.05) had a non-significant effect. Figure 7a,b respectively show the positive residual distribution of response value Y and the distribution of actual and predicted values. As the same as the response value X, the positive residual distribution, actual value and predicted value of response value Y all present linear distribution, and also the actual and predicted values are evenly distributed along the y = x line. The correlation coefficient R 2 adj is 0.9262, which explains 92.62% of the variation with small errors. R 2 = 0.9618 and C V = 7.17%, indicating that the experiment is credible and accurate. Therefore, model (5) can be used to analyze and predict the response value Y.
Contour and response surface analysis. Contour    www.nature.com/scientificreports/ fluence of the interaction of the other two factors on the response value X when two of the four factors take a certain level. Figure 8 illustrates the interaction effects of ER content, and water-cement ratio on the response value X, when Fe 3 O 4 content and SAC content are located at the central level (A 3 = 15%, A 4 = 5%)). Figure 8a shows that the response value X increases as A 2 increases when A 1 is certain. When A 1 = 7%, the response value X tends to change most significantly, increasing from 225.00 mm to about 250.00 mm. It can be seen from Fig. 8b that the response surface shows an overall upward trend, as A 1 decreases and A 2 trends up. Figure 9 shows the interaction effects of ER content, and Fe 3 O 4 content on the response value X, when the water-cement ratio and SAC content are located at the central level (A 2 = 0.5, A 4 = 5%). It can be seen in Fig. 9a shows that the response value X decreases as A 3 increases when A 1 is certain. When A 1 = 5%, the trend of the response value X decreasing with A 3 is not significant. In contrast, the trend of the response value X changing from A 1 = 6-9% is significant. When A 1 = 9%, the response value X drops from about 240.00 mm to 220.00 mm. It can be seen from Fig. 9b that the response surface shows a downward trend with the increase of A 1 and A 3 . Figure 10 displays the interaction effects of ER content, and SAC content on the response value X, when the water-cement ratio and Fe 3 O 4 content are located at the central level (A 2 = 0.5, A 3 = 15%). As shown in Fig. 10a shows that the response value X decreases as A 4 increases when A 1 is certain. When A 1 = 9%, the trend of the response value X decreasing with A 4 is not significant. In contrast, the trend of the response value X changes more significantly when A 1 = 5-8%. It can be seen in Fig. 10b that the response surface shows a downward trend with the increase of A 1 and A 4 , but the trend is weaker than the interaction effect between A 1 and A 3 .
The interaction effects of water-cement ratio and Fe 3 O 4 content on the response value X, when ER content, and SAC content are located at the central level (A 1 = 7%, A 4 = 5%) is shown in Fig. 11. It can be seen in Fig. 11a shows that the response value X decreases as A 3 increases when A 2 is certain, but not by much. As seen in Fig. 11b that the response surface shows a slow upward trend with the increase of A 2 and A 3 .
The Fig. 12 demonstrates the interaction effects of water-cement ratio and SAC content on the response value X, when ER content, and Fe 3 O 4 content are located at the central level (A 1 = 7%, A 3 = 15%). The Fig. 12a shows     www.nature.com/scientificreports/ that the response value X decreases as A 4 increases when A 2 is certain, but not by much. It can be seen in Fig. 12b that the response surface shows a slow upward trend with the increase of A 2 and A 4 . This change trend is similar to the interaction effect between A 2 and A 3 . Figure 13 shows the interaction effects of SAC content and Fe 3 O 4 content on the response value X, when ER content, and water-cement ratio are located at the central level (A 1 = 7%, A 2 = 0.5). It can be seen from Fig. 13a shows that the response value X decreases as A 4 increases when A 3 is certain. When A 3 = 10%, the response value X tends to change more significantly, decreasing from about 245.00 mm to 230.00 mm. While A 3 = 20%, the response value X tends to change insignificantly with A 4 . As shown in Fig. 13b shows that the response surface shows an overall increasing trend with the increase of A 3 and A 4 .
As shown in Figs. 8, 9, 10, 11, 12 and 13, a comprehensive comparison of the factors' interactions on the response value X reveals no significant interaction between A 2 and A 3 , or A 2 and A 4 . However, the interaction between A 1 and A 3 , and A 1 and A 2 are more significant than the interaction between A 1 and A 4 , and A 3 and A 4 . Combined with Table 6, it can be seen that the degree of interaction between the factors on the response value X in the ascending order of Contour and response surface analysis of the response value Y. The contours and response surfaces between ER content (A 1 ), water-cement ratio (A 2 ), Fe 3 O 4 content (A 3 ), SAC content (A 4 ) and the response value Y are shown in Fig. 14, 15, 16, 17, 18 and 19. Figure 14 shows the interaction effects of ER content, and water-cement ratio on the response value Y, when Fe 3 O 4 content and SAC content are located at the central level (A 3 = 15%, A 4 = 5%). It can be seen from Fig. 14a that the shape of the contours is circular 29 . This indicates that the interaction between A 1 and A 2 is not significant, which is consistent with the results in Table 7. It can be seen in Fig. 14b shows that the slope of the response surface is very gentle in the direction of A 1 and A 2 changes. Basically no surface changes can be found, indicating that A 1 and A 2 have limited influence on the response value Y. Figure 15 illustrates the interaction effects of ER content, and Fe 3 O 4 content on the response value Y, when the water-cement ratio and SAC content are located at the central level (A 2 = 0.5, A 4 = 5%). As seen in Fig. 15a,       www.nature.com/scientificreports/ the shape of the contours is elliptical 29 , indicating that the interaction between A 1 and A 3 is significant, which is consistent with the results in Table 7. It can be seen in Fig. 15b that with an increase in A 1 and A 3 , the response surface shows a tendency to rise and then fall, exhibiting an upward convex spherical surface. Figure 16 demonstrates the interaction effects of ER content, and SAC content on the response value Y, when the water-cement ratio and Fe 3 O 4 content are located at the central level (A 2 = 0.5, A 3 = 15%). As seen in Fig. 16a that the contours exhibit elliptical characteristics, indicating a significant interaction between A 1 and A 4 . It can be seen in Fig. 16b shows that the slope of the response surface is gentler in the direction of change of A 1 and A 4 This indicates that A 1 and A 4 have some influence on the response value Y. However, this influence is not very significant, which is consistent with the results in Table 7. Figure 17 displays the interaction effects of water-cement ratio and Fe 3 O 4 content on the response value Y, when ER content, and SAC content are located at the central level (A 1 = 7%, A 4 = 5%). As seen in Fig. 17a that the response value Y decreases as A 3 increases when A 2 is certain. When A 2 = 0.55, the trend of the response value Y does not change significantly. However, the trend of the response value Y changes significantly when A 2 = 0.45, decreasing from about 2.15 to 1.90 MPa. It can be seen from Fig. 17b that the response surface shows a downward trend, as A 2 falls and A 3 increases. Figure 18 shows the interaction effects of water-cement ratio and SAC content on the response value Y, when ER content, and Fe 3 O 4 content are located at the central level (A 1 = 7%, A 3 = 15%). It can be seen in Fig. 18a that when A 2 is certain, the response value Y decreases with the increase of A 4 . When A 2 = 0.55, the trend of change in the response value Y is not significant. However, the trend of the response value Y changes significantly when A 2 = 0.45 ~ 0.50, and decreases from 2.20 MPa to about 1.80 MPa when A 2 = 0.45. It can be seen from Fig. 18b that the response surface shows a downward trend with the increases of A 2 and A 4 . Figure 19 shows the interaction effects of SAC content and Fe 3 O 4 content on the response value Y, when ER content, and water-cement ratio are located at the central level (A 1 = 7%, A 2 = 0.5). As seen in Fig. 19a, the shape of the contours is elliptical, indicating that the interaction between A 3 and A 4 is significant, which is consistent with the results in Table 7. It can be seen in Fig. 19b that with an increase in A 3 and A 4 , the response surface shows a tendency to rise and then fall, exhibiting an upward convex spherical surface.    A 1 and A 2 , or A 1 and A 4 . However, the interaction between A 2 and A 3 , and A 2 and A 4 are more significant than the interaction betweenA 1 and A 3 , and A 3 and A 4 . Combined with Table 7, it can be seen that the degree of interaction between the factors on the response value Y in the ascending order of Optimal mix proportion and model verification. The optimal combination of factors obtained by Design Expert optimization analysis is: 8.78% ER content, 0.45water-cement ratio, 10% Fe 3 O 4 content, 2.96% SAC content. The predicted values of the X and Y are 223.31 mm and 2.47 MPa, respectively, and the corresponding evaluation index F is 551.58. In order to facilitate the experimental operation, the optimal mix proportions were adjusted as follows: 8.8% ER content, 0.45 water-cement ratio, 10% Fe 3 O 4 content, 3.0% SAC content, and other conditions are the same as the basic mix proportions.
To verify the reliability of the model, the above optimal fit magnetically driven epoxy resin cement slurry was formulated and the results are shown in Table 8. It can be seen from Table 8 that the correlation between the predicted value and the actual value is high. The X, Y and F are 222.50 mm, 2.43 MPa and 540.68 respectively. The relative error is only 0.36%, 1.65% and 2.02%.

Microscopic characterization of optimal mix proportion
Phase composition. Figure 20 displays the XRD test results of solidification. As can be seen in Fig. 20, the strongest diffraction peak of ettringite is 2θ = 9.1°, the strongest diffraction peak of iron oxide is 2θ = 35.5°, the strongest diffraction peak of hydrated calcium silicate is 2θ = 29.5°, the strongest diffraction peak of tricalcium silicate is 2θ = 32.2°, the strongest diffraction peak of Ca(OH) 2 is 2θ = 18.0°, and the strongest diffraction peak of SiO 2 is 2θ = 26.6°. The cement in solidification is fully hydrated, and a large amount of C-S-H gel and ettringite are formed.
Phase characteristics. In Fig. 21, the physical phase characteristics of solidification can be seen. As seen in Fig. 21, the solidification has the flat and compact morphology of a typical complex. The epoxy resin cured material interacts ionically with Ca 2+ in AFt and Ca(OH) 2 to form complexes, and a large amount of crystalline material is generated 13 . The characteristic peak of epoxy resin is present at 830 cm −130 . 1509 cm −1 is the peak of C=C bond stretching vibration in the benzene ring 31 , which is the characteristic peak of ER. There is no epoxy group vibration peak at 913 cm −1 , indicating that ER can open the ring smoothly in the cement base and complete the curing process 30,31 . The area range 1250-600 cm −1 is the region of Si-O characteristic peaks 32 , which are the relevant characteristic peaks of hydrated calcium silicate (C-S-H) products. 3641 cm −1 is the Ca-OH

Conclusion
1. This paper proposes to evaluate the index F, which can effectively evaluate the interaction between the fluidity and tensile strength of the slurry. 2. The 2FI regression model and the quadratic regression model are developed with fluidity and tensile strength as response values. In addition, ER content, water-cement ratio, Fe 3 O 4 content and SAC content are considered influencing factors. ANOVA and model fit tests validated the models, and the 2 regression models have reasonable fit and reliability. 3. According to the ANOVA, the relationship between the degree of influence of the influencing factors on response value fluidity (X) and tensile strength (Y) in ascending order is: ER content > water-cement ratio > SAC content > Fe 3 O 4 content. 4. When the 8.8% ER content, 0.45 water-cement ratio, 10% Fe 3 O 4 content, and 3.0% SAC content, the response value X is 223.31 mm, the response value Y is 2.47 MPa, and the corresponding evaluation index F is 551.58, with relative errors of only 0.36%, 1.65%, and 2.02% respectively, indicating that the regression model fits well and the parameters are reliable. 5. The XRD, SEM and FTIR analyses show that the magnetically driven epoxy resin cement slurry is well hydrated, generating a large number of C-S-H gels and calcium alumina generation, and ER can be cured smoothly with the flat and compact morphology of a typical complex.