*3.1. SCB Fatigue Test Results*

The tensile strength of the SFP at different temperature values are shown in Figure 3, which is used as the basis for fatigue test. The variation trend of fatigue life with temperature and stress ratio is shown in Figure 4. Obviously, the properties of the SFP mixture are greatly affected by temperature and stress ratio: The flexural tensile strength decreases with the increase of temperature. When the stress ratio is low, the fatigue life decreases with the increase of temperature, and when the stress ratio is high, the fatigue life first decreases and then increases with the increase of temperature. The fatigue life decreases with the increase of stress ratio. The fitting results of the SFP fatigue prediction model are shown in Table 5. The fatigue prediction model R2 = 0.9937, and the fitting results are good. Compare the fatigue life prediction value calculated by the fatigue prediction model with the actual value obtained from the test, as shown in Figure 5. The analysis of Figure 5 shows that the predicted value of fatigue data is slightly larger than the actual value, but the change trend of the fatigue prediction model is the same. The expression can predict the times of material fatigue failure and judge the change trend of fatigue life under different conditions, which has reference significance in the design of semi-flexible pavement structure.

**Figure 3.** Flexural strength of the SFP.

(**b**) Variation trend of fatigue life with stress ratio.

**Figure 4.** Fatigue life of the SFP mixture.

**Table 5.** Fitting results of fatigue prediction model.


**Figure 5.** Comparison between estimated fatigue life and actual fatigue life.

#### *3.2. Discussion on Fatigue Performance of the SFP Mixture*

Taking the common asphalt mixture AC as the control group, the fatigue performance was measured by using the same test scheme as the above, which was used to evaluate the fatigue resistance of the SFP. Figure 6 shows the fatigue life comparison of the two materials under different environments. The fatigue properties of the two materials are significantly different, and the fatigue life of the SFP is much more sensitive to temperature and stress ratio. At low temperature and a low stress ratio, the fatigue life of the SFP is 4–5 times that of AC, which shows excellent fatigue resistance of the SFP. However, at a low temperature and high stress ratio, the fatigue life of the SFP decreases sharply, which has been significantly less than that of AC under the same conditions. At medium and high temperature, the fatigue life of the SFP is much less than that of AC regardless of the stress ratio. At the same stress ratio, from low temperature to medium temperature, the fatigue life of the SFP is greatly affected by temperature, while from medium temperature to high temperature is less affected by temperature.

(**a**) Variation trend of fatigue life with temperature. (**b**) Variation trend of fatigue life with stress ratio.

**Figure 6.** Fatigue life comparison of AC and SFP.

According to all conditions, the SFP mixture can only have better fatigue resistance under low temperature and low stress ratio, and the fatigue resistance under other conditions is worse than that of asphalt mixture, and the fatigue resistance under high temperature and high stress ratio is far worse than that of asphalt mixture. This is determined by the properties of its constituent materials. The asphalt aggregate ratio of the parent asphalt mixture of the SFP mixture is similar to that of AC mixture used for comparison (4.2% and 5% respectively), but the asphalt binder content of the SFP mixture decreases after grouting. Based on the preliminary analysis of the characteristics of the SFP mixture and the above results, it is considered that the poor fatigue resistance of the SFP mixture is due to the low strength and poor deformation capacity of grouting materials. In the process of fatigue loading, it can be considered that microcracks of different sizes and numbers will be produced in the three materials. The generation time of microcracks and the number and size of microcracks depend on the crack resistance of the material itself. Asphalt has the best deformation ability in the three materials and has self-healing ability. The aggregate has high strength and good crack resistance, it is difficult to produce microcracks, and the fracture energy required for crack propagation is large. The early strength cement used for grouting material has less strength than aggregate, high brittleness, less deformation resistance than asphalt binder, so its crack resistance is the worst. Based on the characteristics of the three materials, the grouting material is most prone to brittle failure during fatigue loading, resulting in stress concentration at the crack tip, which makes the crack expand rapidly in the specimen. In conclusion, the grouting material is easy to crack, resulting in a concentration of stress, which makes the anti-fatigue performance of the SFP poor.

#### *3.3. Digital Image Processing Results*

Count the area share of grouting material in the crack surface of the specimen and take the average value of three parallel specimens as the final result. The trend of the area share of grouting material in the fracture surface with temperature and stress ratio is plotted as shown in Figure 7. Determined by Archimedes method, the connected porosity of parent macroporous asphalt mixture of the SFP mixture in this study is about 18%. Therefore, in the section of the specimen, the area of grouting material should account for about 18%. If the area of grouting material in the fracture surface is relatively small, it can be considered that the crack tends to bypass the grouting material when it occurs and expands. If the area of grouting material accounts for a large proportion, it can be considered that cracks tend to pass through the grouting material when they occur and expand. The analysis of Figure 7 shows that the area of grouting material in the fracture surface of SCB fatigue test accounts for 10–25%.

(**a**) Area share of different stress ratio. (**b**) Area share at different temperature values.

**Figure 7.** Area share of grouting material in the fracture surface.

#### *3.4. Discussion on Cracking Mechanism of the SFP Mixture*

According to Figure 7a, when the stress ratio is less than 0.7, the area proportion of grouting material increases with the increase of stress ratio. Under a fatigue load, with the increase of stress ratio, the grouting material gradually becomes easier to crack than the asphalt phase. The strength of grouting material is higher than that of the asphalt phase. At a low stress ratio, the load has exceeded the fatigue failure stress of asphalt phase. Fatigue cracks begin from the asphalt phase and expand to the whole specimen with the asphalt phase as the main path. Early cracks will also appear in a few grouting materials at stress concentration positions. When the stress ratio increases gradually, the stress of grouting material gradually reaches and exceeds its fatigue failure stress. Due to the large brittleness and poor deformation capacity of the grouting material, the cracks occur earlier than the asphalt phase, and the propagation path of the cracks includes the asphalt phase and the grouting material. When the stress ratio is greater than 0.7, the area proportion of grouting material is close to 18%, which is due to less fatigue times under high stress ratio, and the failure form of material is more similar to single loading failure.

According to Figure 7b, the proportion of grouting material in the area of fracture surface first increases and then decreases with the increase of temperature, which may be due to the fact that the temperature sensitivity of cement grouting material is not as good as that of asphalt mixture. At low temperatures, the stiffness of the asphalt phase and the cement grouting material are both large, and close to brittle failure. However, because the strength of asphalt is lower than that of cement grouting material, its failure time is earlier when the temperature and stress are relatively low, so the area of grouting material in the fracture surface is relatively small. At medium temperature, the strength of asphalt phase and grouting material decreases. Asphalt has higher temperature sensitivity. With the increase of temperature, its deformation capacity improves, and the grouting material is still brittle failure. At the same time, due to the faster decline of modulus of asphalt phase, the grouting material shares a greater proportion of stress, and the cracking time of grouting material is earlier than that of asphalt phase, so the area proportion in the fracture surface increases. At a high temperature, the strength of asphalt decreases obviously, and the proportion of stress shared by grouting material continues to increase after asphalt softening. However, because the decrease of asphalt strength exceeds the increase of stress borne by grouting material, the area proportion of asphalt phase rises somewhat.

In actual use, due to the high strength of aggregate, the loading stress is difficult to cause damage. Asphalt has a self-healing ability.

During fatigue loading, the process of microcrack generation, incomplete self-healing, crack generation and propagation is repeated in the asphalt phase until the material is completely destroyed. The asphalt phase is the main factor controlling the fatigue resistance of asphalt mixture. The difference between the SFP mixture and asphalt mixtures lies in the role of grouting material in the destruction process. The strength of the grouting material is less than that of the aggregate. During the fatigue loading process, microcracks continue to occur in the grouting material, but the grouting material does not have the self-healing ability. At the same time, the stress concentration at the crack tip weakens the self-healing ability of the asphalt phase, and finally leads to the acceleration of the overall failure process of the specimen.

In conclusion, the difference of material properties and temperature sensitivity between the asphalt phase and the grouting material leads to the difference of fracture surface composition of specimens under different conditions. This phenomenon reveals that the poor fatigue resistance of the SFP mixture at medium and high temperature is caused by the brittleness of the grouting material, the difference of modulus between the grouting material and the asphalt, and stress concentration.

#### **4. Conclusions**

The fatigue resistance of the SFP mixture under different temperature values and stress ratio was evaluated by the SCB fatigue test, and the laboratory fatigue prediction model of the SFP mixture is established. The fatigue cracking mechanism of the SFP mixture is analyzed by a digital image processing technology. A fatigue prediction model for SFP structure calculation is derived. The conclusions are as follows:

1. At a low temperature and low stress ratio, the fatigue resistance of the SFP is 2–7 times that of AC. At a medium temperature or high stress, the fatigue resistance of the SFP suddenly drops to 15–45% of AC. Under the condition of high temperature and a high stress ratio, SFP almost loses its anti-fatigue ability.


This study points out that fatigue cracking is one of the main forms of the SFP structural cracking, and proposes a fatigue prediction model for SFP mixtures to provide a reference for structural design and life calculation, and provides research directions for improving the crack resistance of the SFP mixtures from the aspects of material composition and material modification.

There are two main limitations of this study. First, only one mix proportion of the SFP mixture is selected, and the fatigue prediction model has room for further optimization. Secondly, the cracking mechanism of the SFP mixture is analyzed from the surface after fracture, and the observation of fatigue cracking process is lack. In the later research, it is suggested to adjust the mix proportion of the SFP mixture to improve the fatigue prediction model of the SFP. It will be very effective to monitor and analyze the entire process of fatigue cracking of the SFP mixture with the help of real-time computer tomography and digital image correlation technology.

**Author Contributions:** Conceptualization, S.W., X.C and J.H.; methodology, S.W. and H.Z.; software, X.S.; formal analysis, S.W and M.G.; investigation, M.G.; resources, J.H.; data curation, S.W. and H.Z; writing—original draft preparation, S.W.; writing—review and editing, X.C.; visualization, S.W.; supervision, X.C.; project administration, X.C. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by The Open Fund Project of National Key Laboratory of High-Performance Civil Engineering Materials (2016CEM001), the National Natural Science Foundation of China (No. 51778136) and the China Scholarship Council.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data is contained within the article.

**Acknowledgments:** The authors gratefully acknowledge the financial support of Sobute New Materials Co. Ltd.

**Conflicts of Interest:** The authors declare no conflict of interest.
