*2.3. Analysis Methodology*

2.3.1. Fatigue Prediction Model of Materials in Laboratory

The establishment of the SFP fatigue prediction model draws lessons from the establishment method of asphalt mixture fatigue prediction model, such as the SHRP model, Asphalt Institute (AI model), shell model, and the multivariable and multi parameter fatigue prediction model established by Tongji University and South China University of Technology. The main idea of fatigue prediction model is to establish the relationship between material stress or strain and fatigue action times, introduce the influence of temperature, consider the modulus of asphalt mixture, asphalt aggregate ratio and other factors to improve it. Based on the data of SCB fatigue test, a fatigue prediction model suitable for SFP can be established. The variables of the fatigue prediction model mainly include the stress of the material, the dynamic modulus of the SFP mixture, and the ambient temperature. Referring to the fatigue prediction model of asphalt mixture mentioned above, the stress and modulus are the base in the formula, and the other influencing factors are constant parameters and the index of e (base of natural logarithm). The basic form of the final SFP mixture fatigue prediction model is as follows:

$$N\_f = k \varepsilon^{k\_1(N-T)} \sigma^{k\_2(N-T) + k\_3} |E\_0|^{k\_4} \tag{2}$$

*Nf* is fatigue life, times; *T* is temperature of test piece and environment, ◦C; *σ* is tensile stress, MPa; |*E*0| is dynamic modulus at 20 ◦C, MPa. *N*, *k*1, *k*2, *k*<sup>3</sup> and *k*<sup>4</sup> can be obtained by fitting the test results. In this study, only one mix proportion of the SFP is adopted, so *k*<sup>4</sup> is taken as 0.

The fatigue prediction model can be used to predict the fatigue life of materials in the laboratory and can be used to calculate the fatigue life of structures in engineering after modification.

#### 2.3.2. Analysis Method of Fracture Surface in SCB Fatigue Test

As shown in Figure 1 the fracture surface of the SFP mixture consists of aggregate, grouting material, asphalt and its interface with other materials (hereinafter referred to as asphalt phase). The color of aggregate and grouting material is gray white, which is quite different from that of asphalt phase, and the asphalt phase is pure black. The color of aggregate and grouting material is similar, so it is difficult to distinguish them in digital image processing. However, the aggregate is mainly distributed in the cutting seam in the cross-section, and hardly distributed in the fracture surface, which can be ignored in image processing. Therefore, it is only necessary to distinguish the two colors in the image to achieve the purpose of statistical distribution of grouting material and the asphalt phase in the fracture surface.

**Figure 1.** Fracture surface of the SCB fatigue test.

The original image was rotated and cut to get the fracture surface area, then it was binary processed by MATLAB [33]. Black pixels and white pixels represent the asphalt phase and grouting material, respectively, and their proportion in the total image pixels was calculated. The calculated results can be used to analyze the similarities and differences of the SFP fatigue failure process under different conditions, so as to further analyze the fatigue failure mechanism of the SFP.

The fracture surface image was randomly selected to determine the binarization threshold. As shown in Figure 2, the best effect was achieved by selecting the calculation result of gray thresh function of MATLAB plus 0.15 as the threshold. This threshold calculation method can reduce the errors caused by material reflection, camera aperture size, exposure time and so on.

(**c**) 0.5. (**d**) AI calculation results +0.15.
