# Study on Cold Resistance Performance of Composite Subgrade Structure in Seasonal Frozen Regions
## 3 Results and Discussion
### Temperature Distribution of Subgrade during Monitoring Period  
A temperature distribution map was drawn to evaluate the cold resistance performance of the composite subgrade. Linear interpolation was used to deduce the distribution. Due to the symmetry of the subgrade model, it was equivalent to monitoring the temperature data of 10 control points, with subsequent interpolation along the width and depth. The transverse axis refers to the monitoring process and the longitudinal axis refers to subgrade depth, as demonstrated in Figures 4 and 5.  
Figure 4: Temperature distribution map of the subgrade without a cold resistance layer.  
Figure 3: Diagram of air temperature variation during the monitoring period.  
It can be seen clearly from Figures 4 and 5 that setting the XPS plates had a significant impact on temperature distribution inside the subgrade.  
For the subgrade without a cold resistance layer, the 0 \({}^{\circ}\)C isotherm extended rapidly from top to bottom and reached the bottom of the subgrade on the 22 nd day with a decrease in ambient temperature. The whole subgrade was in a completely negative temperature condition which was maintained until the monitoring process ended, and the temperature distribution inside the subgrade was fully controlled by ambient temperature.  
However, the temperature distribution map of the subgrade with a cold resistance layer was totally different. The temperature distribution above the XPS plates was mainly controlled by ambient temperature, and the 0 \({}^{\circ}\)C isotherm extended more slowly. Compared to the case without a cold resistance layer, the 0 \({}^{\circ}\)C isotherm tended to be basically stable, and it was completely above the XPS plates in the whole monitoring period. The temperature distribution under XPS plates attenuated downward, and its attenuation amplitude was smaller based on the color variation. The temperature distribution of most areas was demonstrated in red and yellow, which means that the temperature was positive. In particular, for the region 15-20 cm near the bottom of the XPS plates, the temperature stayed red in the whole monitoring period. On the 34 th day, the phenomenon of negative temperature appeared at the bottom of the subgrade, and the 0 \({}^{\circ}\)C isotherm extended upward slowly until 18 cm away (the 80 th day) from the bottom of the subgrade. Then, the 0 \({}^{\circ}\)C isotherm stopped rising. There are two possible causes for this phenomenon. Firstly, the effective range of the thermal insulation of XPS plates was limited and soil beyond the range would freeze. Secondly, the size of the XPS plates buried in the subgrade model was not big enough and the temperature distribution at the bottom of the model was invaded by negative temperature energy from the ambient soil, as shown in Figure 6.  
It is well illustrated in Figure 6 that negative temperature energy spread downward along the direction of subgrade depth and bypassed the XPS plates, while an obvious phenomenon of thermal accumulation was formed at the bottom of the XPS plates. The subgrade soil beneath the XPS plates was invaded in the most marginal area by the negative temperature energy of the ambient soil. The degree and the range of energy invasion were controlled by the boundary conditions of the subgrade model, which was the air temperature input. As can be seen from Figure 5, up to 18-cm-deep soil was attacked by negative temperature energy, and the temperature dropped below 0 \({}^{\circ}\)C. It can be estimated that when the XPS plates were big enough to ensure that the subgrade soil in key parts (such as the subgrade soil beneath the carriageway) was not attacked by negative temperature energy, the cold resistance effect would be very prominent.  
Figure 5: Temperature distribution map of the subgrade with a cold resistance layer.