## 3 Test Results and Analysis
### Temperature Distribution of Pavement Model Test  
In this section, K-type thermocouples were utilized to acquire temperature data from the pavement model during the heating process. Based on the collected data, the temperature distribution characteristics of the carbon fiber-heated pavement were analyzed.  
Figure 4a,b show the warming trends in TC\({}_{\text{A}}\) and TC\({}_{\text{B}}\) with heating time at different depths of the pavement, respectively. The TC\({}_{\text{A}}\) and TC\({}_{\text{B}}\) warming trends for the same depth case can be divided into two stages: the first for the start of heating to 2 h and the second for heating 2 h to 6 h. The temperature rose faster in the first stage, then progressively slowed down in the second. Taking the 5 cm depth pavement as an example, the first-stage TC\({}_{\text{A}}\) temperature rose from \(-3\)\({}^{\circ}\)C to 5\({}^{\circ}\)C with a heating rate of 4 \({}^{\circ}\)C/h, and the TC\({}_{\text{B}}\) temperature rose from \(-3\)\({}^{\circ}\)C to 4\({}^{\circ}\)C with a heating rate of 4.75 \({}^{\circ}\)C/h; the second-stage TC\({}_{\text{A}}\) temperature rose from 5\({}^{\circ}\)C to 10 \({}^{\circ}\)C with a heating rate of 1.25 \({}^{\circ}\)C/h, and the TC\({}_{\text{B}}\) temperature rose from 4 \({}^{\circ}\)C to 8 \({}^{\circ}\)C with a heating rate of 1 \({}^{\circ}\)C/h. The temperature of the first-stage TC\({}_{\text{A}}\) rose from \(-3\)\({}^{\circ}\)C to 5\({}^{\circ}\)C at a pace of 4 \({}^{\circ}\)C/h, whereas the temperature of the second-stage TC\({}_{\text{B}}\) climbed from \(-3\)\({}^{\circ}\)C to 4\({}^{\circ}\)C at a rate of 4.75 \({}^{\circ}\)C/h. According to [PERSON]'s law, the greater the temperature difference, the greater the heat flow density and thus the faster the heating rate, whereas in the second stage, as the temperature difference between the carbon fiber heating wire and the road surface decreased, the heat flow density and thus the heating rate decreased.  
Figure 3: Distribution of data acquisition layers and data point numbers.  
Figure 4c shows the horizontal temperature uniformity at various pavement depths, particularly the temperature difference in the horizontal direction between \(\mathrm{TC_{A}}\) and \(\mathrm{TC_{B}}\). For instance, the maximum temperature difference was 2 \({}^{\circ}\)C between depths of 5 cm and 15 cm, while it was 0.3 \({}^{\circ}\)C between depths of 15 cm and 5 cm. The results indicated that the pavement temperature became more uniform with increasing depth. During heating, temperature gradients existed in both the horizontal and vertical directions of the pavement.  
Figure 5a,b illustrate how the temperature gradient evolved over time in the horizontal and vertical directions, respectively. In the horizontal direction, the temperature gradient at depths of 2 cm, 5 cm, and 10 cm all demonstrated a trend of initially rapidly increasing followed by slowing down, as shown in Figure 5a. However, the temperature differential in the horizontal direction exhibited steady linear growth at a depth of 15 cm. These trends indicated that the horizontal temperature gradient increased at a slower rate with distance away from the carbon fiber heating wire. In the vertical direction, the temperature gradients of both \(\mathrm{TC_{A}}\) and \(\mathrm{TC_{B}}\) evolved similarly--growing rapidly initially and then stabilizing after 2 h of heating, as depicted in Figure 5b. The vertical temperature gradient reached its maximum value after 2 h. This showed that the vertical temperature gradient was greater closer to the carbon fiber heating wire. According to the design specifications for highway cement concrete pavement, the temperature gradient of carbon fiber-heated pavement was much greater than the value provided in the design specification.  
Figure 4: The temperature distribution properties of carbon fiber\(-\)heated pavement at various depths.