Strength Analysis and Ratio Optimization of New Sealing Materials With Response Surface Method

The inuence of the interaction among water-cement ratio, content of expansion agent, water reducing agent, and retarder on the compressive strength of new sealing material was studied. The Design-Expert software was used to design experiments, establish a quadratic polynomial regression model, draw response surface, and optimize parameters. The microstructure morphology of the sample is explored by scanning electron microscope (Hereinafter referred to as SEM). The research results show that the interaction between water-cement ratio and expansion agent content is the most crucial factor affecting the compressive strength of the new sealing material. Under the optimal condition of 0.4% water reducing agent, 0.04% retarder, 0.8 water-cement ratio, and 8% expansion agent, the compressive strength of the sealing material cured for 3 d and 7 d is 39.247 MPa and 41.044 MPa, with the maximum absolute error of 1.71% and 2.81%, which proves the high accuracy of the model. The main hydration products of the new sealing material are ettringite and C-S-H gel, interlacing each other to form a dense structure, which contributes to the high strength of the new sealing material. MPa, and the maximum is 39.918 Mpa; After 7d curing (the curing conditions are the same), the minimum compressive strength is 27.012 MPa and the maximum is 42.197 MPa. These results show that the new sealing material has good mechanical properties.


Introduction
China is currently faced with the most severe gas disaster in coal mines in the world (Yuan 2016;Zhang et al. 2019a; Xue and Yuan 2017). Gas pre-drainage is effective for coal mine gas control, and the the performance of sealing material is the key to ensuring drainage e ciency.
The coal mine gas drilling sealing material can be divided into inorganic grouting material and organic grouting material. Inorganic sealing materials are mainly cement mortar low-cost but easy to shrink and crack (Guo et Sui et al. 2015). In recent years, scholars have studied composite sealing materials for coal mines. Some researchers have developed a CF expansion sealing material with cement, the base material, and metal Al powder, gypsum, and other inorganic additives with good expansibility (Li et al. 2018a; Zhang et al. 2019b). Glass ber would reduce the uidity of pure cement paste, and the higher the content of glass ber, the more pronounced the effect (Wang et al. 2018). Carbon nano bers can effectively increase the shrinkage and crack resistance of ultra-ne cement while keeping the hardness unchanged (Hogancamp et al. 2017). Fly ash were using as a base material and adding water-retaining agent, expansion agent. This material, with a certain degree of expansion, is not easy to shrink and adheres tightly to coal, and could signi cantly improve the mechanical properties of grouting materials (Zhai et  The optimization of sealing materials has not been extensively studied using multiple nonlinear regression analysis. This paper investigates the performance of composite sealing materials from the perspective of macromechanics and microstructure with the quadratic polynomial regression model. The results reveal that the interaction between the water-cement ratio, retarder, expansion agent, and water reducing agent in the composite sealing material system signi cantly affects the compressive strength of the sealing material cured for 3d and 7d. The optimal ratio is determined by the veri cation test, and the mechanism of action of the new sealing material is revealed by SEM analysis.

Materials
The base material used in the experiment is ultra ne Portland cement. The measured value of D90 and D50 are 12.6 µm and 5µm, respectively, which can be effectively injected into micro-cracks below 0.1 mm. The seaweed powder with a white appearance, which is easily soluble in water, is used as the retarder. The solution is a colorless and transparent viscous liquid, which can advance the setting time and improve the strength of cement materials (DU et al. 2019). After being added, PCE (Polycarboxylic acid water-reducing agent), a white powder, which is easily soluble in water, can disperse cement particles with the water-reduction rate of 20-35% (Shui et al. 2016;Zhang and Kong 2015). The compound expansive agent of calcium oxide and calcium sulfate (HCSA), with a gray-white appearance, promotes a good spatial structure of cement hydration products (Feng et al. 2012;Pan et al. 2020). The composition of ultra ne cement and expansion agent used in the experiment is shown in Table 1.

Method
A total of 29 sets of experiments with four factors and three levels was designed by Design-Expert 8.0.5 software ( Table 2). The four factors are water-cement ratio, retarder content, water reducing agent content, expansion agent content, as shown in Table 2. The materials were mixed, then water was added, and the mixture was poured into the triple mold (7.07 cm × 7.07 cm × 7.07 cm). The mold surface was scraped at and put into the curing box. After curing the mixture for one day, the mold was removed, and then the stone body was cured for 3d and 7d.
The compressive strength of stones of different ages was tested by the RMT uniaxial press (Fig. 2).   According to the experimental results in Table 3, the water-cement ratio, retarder, water reducing agent, and expansion agent were set as independent variables A, B, C, D, and the compressive strength of the samples cured for 3d and 7d were used as the objective function for multiple nonlinear regression tting.

Model establishment
The quadratic equation model is the best tting model, according to Design-Expert 8.0.5 software. The multinomial regression equations of 3d compressive strength (Y3d) and 7d compressive strength (Y7d) related to independent variables A, B, C, and D were:  (2) The positive and negative coe cients indicate the increase and decrease of the response value caused by the change of the independent variable.

Model variance analysis and signi cance test
As shown in Table 4, the P values of the two models are both less than 0.0001, indicating a small experimental error (Bao 2019). It can be seen from the signi cance test that the signi cance order of each factor in the regression equation of the sample cured for 3d is as follows: A (water-cement ratio) > D (expansion agent) > C (water reducing agent) > B (retarder); Interaction of different factors: AD (watercement ratio, expansion agent) > AC (water-cement ratio, water-reducing agent) > AB (water-cement ratio, retarder) > CD (water-cement ratio, expansion agent) > BD (retarder, expansion agent) > BC (retarder, water reducing agent). The P value of A and D is less than 0.0001, indicating extremely signi cant in uence. The P value of B and C is greater than 0.05, showing the insigni cant impact; The P value of AD and AC is less than 0.05, suggesting a signi cant effect. The P value of AB, BC, BD, and CD is greater than 0.05, indicating insigni cant in uence. The P value of the BC is 0.8102, meaning the least signi cant impact.
The order of the signi cance of each factor in the regression equation of specimen cured for 7 days is as follows: A (water-cement ratio) > D (expansion agent) > C (water reducing agent) > B (retarder); Interaction of different factors: AD (water-cement ratio, expansion agent) > AC (water-cement ratio, water-reducing agent) > AB (water-cement ratio, retarder) > CD (water-cement ratio, expansion agent) > BD (retarder, expansion agent) > BC (retarder, water reducing agent). The P value of A and D is less than 0.0001, indicating extremely signi cant in uence. The P value of B and C is greater than 0.05, indicating an insigni cant impact. The P value of AD is less than 0.05, indicating signi cant interaction. The P value of the AC changes from 0.0432 to 0.3482, suggesting that the interaction between A and C has a more signi cant impact on the sample cured for three days, and the longer the sample is cured, the less signi cant the effect. The P value of BC is 0.9413, indicating the least signi cant interaction effect. As the items (F value, R2.) of conformity degree comparison were relatively abstract, it was necessary to verify the selected model in other ways. The studentized residual was used to compare the predicted residual value and the actual value (Fig. 3). The points were mostly concentrated in the center of the map in terms of the abscissas and was distributed approximately on a straight line, indicating that the model was reliable.   The smoother response surface in Fig. 4 (e) and (f) indicates less signi cant in uence of the interaction of the retarder and watercement ratio on the compressive strength. When the water-cement ratio remains unchanged, the compressive strength of the sample increases rst and then decreases with the increase of retarder content. When the content of the retarder is constant, the compressive strength of the sample increases rapidly with the decrease of the water-cement ratio, and the steep response surface shows that the retarder has little effect on the compressive strength.

Response surface analysis
As shown in Fig. 4 (g) and (h), when the content of the expansion agent is constant, the compressive strength increases with the increase of the water reducing agent, indicating that the expansion agent has less in uence on the uidity. When the value of the water reducing agent reaches the upper limit, and the value of the expansion agent reaches the lower limit, the response surface is steep, indicating that the interaction of the two factors has the greatest impact on the compressive strength.  Table 4. When the content of the expansion agent remains constant, the compressive strength increases and then decreases with the increase of the content of the retarder. When the content of the retarder remains unchanged, the compressive strength of the sample decreases rapidly with the increase of the content of the expansion agent, indicating that the effect of the water-cement ratio on the response value is more signi cant than that of the retarder. The response surface is relatively at on the whole, indicating that the in uence of the interaction between the retarder and the expansive agent is small.
As shown in Fig. 4 (k) and (l), when the retarder interacts with the expansion agent, the response surface is relatively smooth, indicating that the in uence of the interaction on the compressive strength is the least signi cant, which is consistent with the results of the variance analysis.

Response surface optimization prediction and veri cation
The experimental results were further analyzed by taking the compressive strength of the sample as the optimization index. The optimized experimental scheme was obtained by the Design-Expert software where the content of water reducing agent is 0.4%, the content of retarder is 0.04%, the water-cement ratio is 0.8, and the content of expansion agent is 8%. The scheme was then veri ed. Due to limited space, the results were shown in Table 5 without being described in detail. It can be seen that the compressive strength of the specimen cured for 3 d and 7 d under the optimal condition are 39.247 MPa and 41.044 MPa, with the maximum absolute error between the predicted value and actual value of compressive strength as 1.71% and 2.81%, respectively, indicating that the model is relatively reliable.

Microscopic Characterization Of Sealing Material
It can be seen from Fig. 5 (a), (b) that the connection between the hydration products of the ordinary cement material during curing is loose, resulting in a lower compressive strength. When cured for three days, the cement clinker is encapsulated by C-S-H gel with obvious pore structure and large pore volume; After 7-day curing, the surface area of the C-S-H gel gradually increases, the volume gradually expands, and the pore becomes smaller. With the hydration reaction, the number of C-S-H gels increases, and some needle-shaped AFt crystals appear.
It can be seen from Fig. 5 (c), (d) that the gel particles of the new sealing material are interconnected compactly, which increases the strength of the material. After 3d curing, C-S-H gel with dense structure and fewer pores were formed, which were wrapped with cement clinker; After 7d curing, a large number of ettringite crystals were formed, indicating that the admixture can promote cement hydration reaction, and AFt crystals were generated with expansion effect. The C-S-H gel and AFt were densely and uniformly cross-

Conclusions
The results obtained in this study made it possible to draw the following conclusions.
(1) An orthogonal experiment, taking the compressive strength as the response value, was designed using Design-Expert software. The quadratic model about the compressive strength and test factors (water-cement ratio, water reducing agent, retarder, expansion agent) was established and optimized.
(2) Through variance analysis and the signi cance test, the signi cance order of the in uence of each component on the compressive strength were obtained as follows: Water cement ratio expansion agent water reducing agent retarder. According to the response surface drawn by the regression equation, the interaction between water-cement ratio and expansion agent has the most signi cant effect on the compressive strength, and the interaction between retarder and water reducing agent has the least signi cant effect on the compressive strengt.
(3) The optimal experimental condition was obtained by response surface analysis: water reducing agent content of 0.4%, retarder content of 0.04%, the water-cement ratio of 0.8, and expansion agent content of 8%. The compressive strength of the new sealing material cured for 3d and 7d were 39.247 MPa and 41.044 MPa, with the maximum absolute error of 1.71% and 2.81%, respectively. The predicted value was highly consistent with the measured value.
(4) Compared with ordinary cement materials, the new sealing material has a denser overall structure and fewer pores. The hydration products C-S-H gel, AFt, and other cementing materials, which are uniformly cross-bonded together, increase the uniformity and compactness of the material, thus improving the strength of the material. Figure 1 Raw materials of the sealing material Figure 2 Compressive strength test Three-dimensional response curve of compressive strength