## 2 Materials and Experimental Methods
### Experimental Methods
#### 2.3.3 Four-Point Bending Fatigue Test  
The 15 mm thickness of the CNFPUC material was poured on the bottom of treated concrete beams. According to the industry standard of China \"JTG E20-2011 Standard Test Methods of Bitumen and Bituminous Mixtures for Highway Engineering\" and the four-point bending fatigue dimension based on \"T 0739-2011 Four-point Bending Fatigue Life Test of Bituminous Mixtures\", the size of the specimen after pouring CNFPUC was 380 mm \(\times\) 50 mm \(\times\) 63.5 mm. At the same time, a 10-mesh copper mesh electrode with a size of 25 mm \(\times\) 40 mm was embedded in the specimen. The electrode position is shown in Figure 4b. The resistance changes during fatigue loading were measured by using the UT61E digital multimeter, and the resistivity between the two electrodes was calculated by the formula \(\rho=RS\)/L [28]. Three resistance strain gauges were pasted equally at the middle of a pure curved section of the beam bottom span. The dynamic stress-strain test and analysis system of DH5921 were used to test the bending tensile strain variation of CNFPUC during the fatigue process, as shown in Figure 4a.  
Using a four-point bending fatigue fixture with a UTM-30 test system, the loading frequency was 10 Hz, and the constant strain control mode of continuous partial sine loading was adopted. Based on the constant strain controlled mode of continuous partial sine loading, the fatigue stress levels at corresponding ambient temperatures were determined to be 0.6, 0.7, and 0.8, respectively, by the bending test results. The loading waveform was a half sine wave; the test termination condition was the number of loading cycles in which the bending stiffness modulus was reduced to 50% of the initial bending stiffness modulus, and the stress ratio was 0.1. The maximum fatigue strain, fatigue cycle number, load size, specimen displacement, and maximum tensile stress on the bottom of the specimen were recorded in real time and then calculated. The maximum tensile stress was determined according to formula:  
\[\sigma_{t}=\frac{L\times P}{w\times h^{2}}\]  
\(\sigma_{t}\)--Maximum tension stress (Pa);  
Figure 4: Four-point bending fatigue test. (**a**) Fatigue test device; (**b**) two electrode position diagram (mm).  
\(L\)--Beam span, i.e., the distance between two clamps at the outer end (m);  
\(P\)--Peak load (N);  
\(w\)--Beam breadth (m);  
\(h\)--Beam depth (m).  
The maximum tensile strain formula is:  
\[\varepsilon_{t}=\frac{12\times\delta\times h}{3\times L^{2}-4\times a^{2}}\]  
\(\varepsilon_{t}\)--Maximum tensile strain (m/m);  
\(\delta\)--Beam center maximum displacement (m);  
\(a\)--Adjacent chuck center spacing.  
Bending stiffness modulus: \(S=\frac{\sigma_{t}}{\varepsilon_{t}}\).  
The relationship between the macroscopic phenomenon of the specimen at each fatigue stage was observed in detail, especially the formation and the propagation of the macro crack, the complete failure of the specimen, the number of cycles, the stress levels, and the temperatures of the specimens. Six parallel tests were carried out under the same test conditions, and when the difference between one of the measured values and the average value of a group of specimens was more than 1.82-times greater than the standard deviation, the test data were rejected. At the same time, there should have been no less than six valid specimens in each set of tests.