4.1. Test Results of Response Metrics for the RSM
A total of 27 modified grouting material samples were prepared according to different designs of the RSM model, labeled sequentially from X-1 to X-27. Following the experimental procedure outlined above, the fluidities, compressive strengths, and fracture energies of all 27 samples were tested and calculated.
The fluidities of different samples are displayed in
Figure 5. It can be seen that all the fluidity values range from 12 to 18 s and the fluidities of samples X5, X6, X9, X10, X21, and X22 are much higher than those of other samples. As shown in
Figure 5, a mixing speed of 1000 rpm was used for the preparation of these samples. It is speculated that a low mixing speed was not sufficient to disperse the polymer additives in the grouting materials homogeneously, which increased the viscosities of the grouting material samples. Moreover, the added water-soluble polymer and asphalt emulsion would adsorb on the cement particles. The formation of polymer film and membrane would prevent the interaction between cement particles/admixture and water. Therefore, the flowability of the grouting slurry decreased. Thus, higher mixing speeds (e.g., 2000 rpm and 3000 rpm) should be selected for the preparation of polymer-modified grouting slurries.
The compressive strengths of all 27 samples are shown in
Table 9. By comparing samples with lower polymer content and those with high polymer content (X2 vs. X4, X15 vs. X16, X21 vs. X22, X23 vs. X24), it is shown that the addition of higher polymer contents lowers the compressive strength of the grouting material, which can be attributed to the low stiffness of the polymer and entrained air produced during mixing. It was found that adding defoamer increased the compressive strengths of the modified grouting materials (X5 vs. X6, X14 vs. X16, X17 vs. X19). As observed from the prepared samples shown in
Figure 6, there were more tiny bubbles in the grouting slurries with higher polymer content when insufficient defoamer was blended in. As these bubbles would lower the strength of the samples, the defoamer was used to eliminate those bubbles; therefore, the strengths of grouting materials with high defoamer content were higher.
Of special interest, the fracture energies of different samples determined from the flexural test were analyzed and are displayed in
Figure 7. Unlike in the fluidity and compressive strength data, different grouting materials exhibit distinct fracture energy values. Notably, the coefficient of variation in fracture energy is relatively the highest among all the test results.
To investigate the influences of different parameters on the anti-cracking abilities of grouting materials, the fracture energy data and force–displacement curves of different samples were compared as shown in
Figure 8. Even though each sample has different contents of additives, it is obvious from
Figure 8a that a higher mixing speed promotes an increase in the fracture energy of the grouting material. The homogeneously distributed polymer and grouting material contributes to a denser and more refined microstructure. It is interesting to see that the polymer content and w/e ratio only have slight influences on the fracture energies of the eight selected modified grouting materials, although the strengths of the samples were found to decrease after blending with the polymer. However, the dosage of defoamer significantly influenced the fracture energies of the grouting materials. For those samples with relatively low w/e content, the existence of emulsified asphalt promoted the emergence of air bubbles during the preparation process at high mixing speed. If the air does not escape during the formation process of the polymer film, polymer balloons will form, causing voids in the cement matrix that will lower the fracture energy of grouting material samples. The defoamer eliminates these bubbles. As the microstructures of cured grouting material samples become denser, their fracture energies increase. It is worth noting that different groups of the compared samples exhibit similar pre-peak and post-peak slopes in their force–displacement curves except for samples X-13 and X-14. Increasing the polymer content makes the grouting material’s pre-peak curve less steep, while not changing its post-peak slope. It is concluded that the modification mechanism of different additives is quite distinct.
4.2. Response Analysis of the Factors in the RSM
Based on the results of the modified grouting material performance tests, a central composite response surface mathematical model was constructed using Minitab software. The model incorporates full quadratic terms, which include linear, squared, and interaction terms. The fitted model equations (Z1, Z2, and Z3) correspond to the predicted response values for fluidity, compressive strength, and fracture energy, respectively. The parameters A, B, C, and D represent the actual factor levels of w/e ratio, polymer content, defoamer content, and mixing speed, respectively.
ANOVA was used to test the significance of the regression coefficients and verify the RSM model’s goodness of fit. The analysis result is shown in
Table 10. Parameters with a
p-value lower than 0.05 are considered to have a significant influence on the properties of grouting materials, while those with a
p-value higher than 0.05 are not. For convenience, “***”, “**” and “*” are used to represent extremely significant, very significant, and significant, respectively.
As shown in
Table 10, the
p-values for all response models are less than 0.05. This indicates that the probability of the response values derived due to error is less than 0.05, which shows extremely significant statistical differences. Therefore, the mathematical fitting model can be considered highly accurate with a good fit. To further explore the influence trends of factors A, B, C, and D on the response indicators, a thorough analysis of the Z
1 to Z
3 response models is conducted in the following subsections.
4.2.1. Analysis of Fluidity Response
Based on the fluidity response model, the w/e ratio, polymer content, and defoamer content are all found to be insignificant factors. Therefore, these three factors are excluded from the model. As shown in
Table 10, the
p-value of the fitting equation between mixing speed and fluidity is less than 0.001. It is concluded that the mixing speed has an extremely significant impact on the fluidity of the grouting slurry.
Figure 9 illustrates the fitted relationship between mixing speed and fluidity. It can be observed that within a certain range, the fluidity of the grouting material decreases rapidly as the mixing speed increases. This phenomenon is attributed to the fact that higher mixing speeds may introduce excessive air bubbles into the slurry, which reduce its viscosity and consequently increases the flowability. Additionally, the shear force within the slurry continuously escalates as the mixing speed increases, potentially weakening the cohesive forces between the water-based epoxy resin/emulsified asphalt and the cementitious slurry. This manifests macroscopically as an improvement in the flowability of the cementitious slurry. However, once the mixing speed exceeds a specific threshold, the fluidity of the slurry begins to go up slightly while no obvious increase in the flowability of the grouting slurry can be observed. This indicates that the mixing speed of 2000 rpm is efficient for mixing modified grouting slurry homogeneously.
4.2.2. Analysis of Compressive Strength Response
Based on the fitted compressive strength response model, polymer content and mixing speed are found to be insignificant factors. In this regard, they are excluded from the model. The compressive strength response surface model is shown in
Figure 10.
As the w/e ratio increases, the compressive strength initially increases and then decreases. This proves that an increase in epoxy resin content within a certain range is beneficial for improving the compressive strength of the grouting material. This can be explained as that water-based epoxy resin can increase the density of the cementitious slurry. However, as the proportion of water-based epoxy resin continues to increase, the compressive strength of the cement slurry begins to significantly decrease when the w/e ratio exceeds 0.7. This can be attributed to the existence of excessive epoxy resin groups surrounding the cement particles. The low stiffness of polymer additives would lower the strength of the grouting material.
With an increase in defoamer content, the compressive strength initially increases and then decreases. This can be explained by the defoamer being able to rapidly reduce the surface tension of the grouting material and spread over the surface of the bubbles formed due to high-speed mixing. This effect lowers the surface strength, elasticity, and viscosity of the liquid film. Within a certain range of defoamer content, this helps accelerate the removal of air bubbles, making the grouting material denser. However, when the content of defoamer is too high, excessive particles disperse and embed within the grouting material, forming micro-defects (as shown in
Figure 11). When the grouting material is subjected to external loads, cracks tend to initiate from these micro-defects. The compressive strength of the sample would be reduced thereby.
4.2.3. Analysis of Fracture Energy Response
The RSM of fracture energy is illustrated in
Figure 12. As demonstrated by the model, the fracture energy exhibits a strong correlation with three key factors: the w/e ratio, polymer dosage, and mixing speed. As the values of these three parameters change, the fracture energy increases initially and then decreases subsequently.
As the w/e ratio increases, the fracture energy of the cement-based grouting materials exhibits a fluctuating trend. Notably, from 0.5 to 0.7, the fracture energy is relatively high. Conversely, when the ratio is either too low or too high, the fracture energy of the sample stays at a low level. This indicates a significant influence of the w/e ratio on the fracture energy of the slurry. As shown in
Figure 12, the most appropriate w/e ratio facilitates the optimization of the cement slurry’s microstructure. The resilience and crack resistance of the samples is enhanced, which corresponds to higher fracture energies. However, an excessively high proportion of epoxy resin/asphalt emulsion leads to increased brittleness of the cementitious slurry, which consequently reduces its fracture energy.
As shown in
Figure 12, the polymer content significantly influences the fracture energy of the slurry. When the polymer content is 3% to 5%, the fracture energy increases notably with an increase in the polymer content. Proper amounts of polymer effectively increase the internal resilience of the cement slurry and improve its microstructural compactness, thereby increasing the fracture energy of the grouting material. However, when the polymer content is excessively high, the excessive organic materials surrounding the cement particles may impede the hydration process of the cement, resulting in a decrease in the internal density of the slurry.
Mixing speed also has a significant influence on the fracture energy of cementitious grouting material, as demonstrated in
Figure 12. The peak value of fracture energy is observed within the mixing speed range of 1500 rpm to 2000 rpm. An appropriate mixing speed facilitates the uniform distribution of different components. The structural stability of the slurry is enhanced and the fracture energy is consequently improved. However, an excessively low mixing speed may result in a non-uniform distribution of additives, thereby degrading the mechanical properties of the hardened cementitious slurry. Notably, an excessively high mixing speed may introduce more voids in the grouting material samples, which may lower its fracture energy.
4.2.4. Optimal Solutions for the RSM Model
Utilizing the response surface optimization module in Minitab software, compressive strength and fracture energy were set as “maximize-type” response indexes, while fluidity was set as a “target-type” response index. Fixing the optimal levels of each parameter as hold values allows the generation of predicted response values. The optimal mix proportions for the composite toughened grouting material were determined to be a w/e ratio of 0.64, polymer content of 3.3%, and defoamer content of 0.2%. In addition, the optimal mixing speed was chosen to be 2000 rpm. To validate the model’s prediction accuracy, actual measurements were conducted according to the aforementioned experimental scheme. The predicted and measured results are listed in
Table 11. It can be seen that all errors between the predicted response values and the actual measured values are within 5%, with the maximum error being 3.2%. Based on this, the model is considered valid and has good prediction accuracy.
4.3. Analysis of Micromorphology
According to
Section 4.2.4, four kinds of grouting materials were prepared, namely commercial grouting material, grouting material modified with 3.3% water-based epoxy resin, grouting material modified with 3.3% emulsified asphalt, and the optimally designed grouting material from
Table 11. All the grouting slurries were prepared with a mixing speed of 2000 rpm. The SEM micromorphologies of all the grouting materials are shown in
Figure 13. The amorphous C-S-H gels and numerous needlelike ettringites (Aft) were found in the samples. As observed, the micro-morphological comparison between the optimally designed grouting material and the compared groups reveals distinct differences in their microstructural characteristics. The commercial grouting material exhibits poor internal compactness with the presence of microcracks, which are responsible for its inadequate toughness. When water-based epoxy resin was added to the commercial grouting material, the epoxy group in the epoxy resin and the amino group in the curing agent underwent dehydration condensation and then cross-linking to form a huge interpenetration polymer network. The gaps between hydrated products were also filled by polymer particles.
In contrast, the addition of emulsified asphalt to the commercial grouting material resulted in a reduction in the size of microcracks as seen in
Figure 13c, which contributed to a moderate improvement in toughness. However, the most notable enhancement was observed in the optimally designed grouting material, as evidenced in
Figure 13d. This material demonstrated a significant increase in density, with a marked reduction in both the number and size of microcracks. The integration of water-based epoxy resin and emulsified asphalt into the cement-based grouting material formed a three-dimensional spatial network structure. In this network, cement hydration products served as the continuous phase and emulsified asphalt and epoxy resin act as the modified dispersed phase. The formed three-dimensional network structure was beneficial to enhancing the flexural performance of grouting material. The hardened polymer films acted like microfibers, inhibiting the formation and development of cracks. This structural configuration not only improved the material’s resistance to drying shrinkage stress but also enhanced its durability and long-term performance.
4.4. Evaluation of the Anti-Cracking Ability of SFP Mixture
For convenience, semi-flexible pavement mixtures fabricated using commercial grouting material, water-based epoxy resin-modified grouting material, emulsified asphalt-modified grouting material, and optimized grouting material were designated as Samples 1, 2, 3, and 4. The force–displacement curves of all the mixtures are shown in
Figure 14. It can be seen that adding water-based epoxy resin into the grouting material does not lower the peak force of the SFP material. Notably, the force–displacement curve of Sample 3 demonstrated the lowest peak force value among all the samples. As shown in
Table 12, the fracture energies of the SFP samples increased slightly by using polymer-modified grouting materials. It is worth noting that Sample 4 has the highest FI value, showing the best anti-cracking ability. In
Figure 15, the grouting material–asphalt mastic interfacial failures are marked as red areas. The cement side of the failed interface can be clearly seen in the marked area of one fractured sample. The asphalt side of the failed interface can be found in the symmetric site of the other fractured sample. It is observed that Sample 2 has the largest areas of interfacial failures, which corresponds to the lowest FI value among all the mixtures. Qualitatively, Sample 4 displays more adhesive failures than the other samples, while Sample 1 shows more brittle cementitious failures. This phenomenon indicates that the stress may distributed more evenly in Sample 4 due to the enhancement in the grouting material’s toughness and interfacial bonding.