# Study on Cold Resistance Performance of Composite Subgrade Structure in Seasonal Frozen Regions
## 2 Materials and Methods  
### XPS Plates  
XPS plates are a kind of foam with a perfect honeycomb structure, which is rigid and closed-cell. Because of its excellent engineering characteristics of low thermal conductivity, good thermal insulation performance, and high compressive strength, XPS plates are suitable for road engineering. The compressive strength of XPS plates adopted in this study was 400 kPa. According to the relevant literature ([PERSON] et al., 2018), the load of traffic and structure weight transferred to the top surface of the subgrade through the pavement structure was 50-100 kPa, which is far less than the compressive strength of an XPS plate. The basic parameters of XPS plates used in this paper are shown in Table 1.  
It can be easily figured out that the thickness of XPS plates is the main factor affecting the thermal insulation effect of the cold resistance layer ([PERSON] et al., 2018; [PERSON] et al., 2018; [PERSON] et al., 2018; [PERSON] et al., 2018). In consideration of preventing negative temperature energy from entering, a thicker XPS should result in a better cold resistance effect. However, there is not a linear relationship between the cold resistance effect and the thickness of the XPS plates. As the thickness of the XPS plate increases, the degree of the cold resistance effect decreases gradually. Additionally, it is also economically unreasonable if the XPS plates are too thick. Therefore, the thickness of XPS plates can be obtained according to the thermal resistance equivalence and specific parameters. The calculation process is as described below. According to some studies ([PERSON] et al., 2018; [PERSON] et al., 2018; [PERSON] et al., 2018) and engineering data, it can be concluded that the range of road freezing depth in Changchun is 150-250 cm. The typical pavement structure in the northeast area was adopted, which consists of asphalt concrete (18 cm), cement stabilized macadam (54 cm), and graded macadam (20 cm). To effectively maintain the cold resistance effect, the thermal resistance of XPS plates and the pavement structure above should be equivalent to the thermal resistance of 250 cm of silty clay. Before calculating, the thickness of the pavement structure should be converted to the \begin{table}
\begin{tabular}{c c c c c} \hline
**Apparent Density** & **Compressive Strength** & **Volume Water Absorption** & **Thermal Conductivity (W/m-\({}^{\circ}\)C)** \\ \hline
0.04 g/cm\({}^{3}\) & 410 kPa & 0.39\% & 0.0245 (20 \({}^{\circ}\)C) & 0.0243 (\(-\)18 \({}^{\circ}\)C) \\ \hline \end{tabular}
\end{table} 
Table 1: Parameters of the extruded polystyrene (XPS) plates. thickness of silty clay according to the thermal resistance equivalence. Then, the thickness of XPS plates can be calculated using Equation (1). \[\frac{\mathrm{d_{x}}}{\mathrm{k_{x}}}=\frac{\mathrm{d_{s}}}{\mathrm{k_{s}}}, \tag{1}\]  
where dx and ds are the thicknesses of XPS plates and the equivalent soil, respectively, while \(\mathrm{k_{x}}\) and \(\mathrm{k_{s}}\) are the thermal conductivities of XPS plates and the equivalent soil, respectively. The values of the thermal conductivity of the road structure layers are shown in Table 2.  
(1) Equivalent thickness of silty clay above XPS plates  
According to Equation (1), the equivalent thicknesses of silty clay for 18-cm-thick asphalt concrete, 54-cm-thick cement-stabilized macadam, and 20-cm-thick graded macadam are 9.8 cm, 38.5 cm, and 39.8 cm, respectively. Thus, the equivalent thickness of silty clay above the XPS plates was 87.7 cm by adding up the values above. (2) Thickness of XPS plates  
According to the data on freezing depth in Changchun and the calculation result above, the equivalent thickness of silty clay is in the range of 62.3 cm to 162.3 cm. The thickness of XPS plates was calculated as a range of 1.3 cm to 3.4 cm. The safety factor was used to modify the theoretically calculated thickness value in order to ensure that the XPS plates could indeed block the negative temperature energy.