## 2 Materials and Methods
### Establishment of Permatfrost Subgrade Model in ABAQUS  
As the subgrade is a strip structure and can be considered as an infinite extension along the longitudinal direction, the influence of the spacing effect can be ignored, and a two-dimensional model can be used for simulation. This model consists of a natural  
Figure 4: The layout of observation sensors in the K67+300 subgrade section.  
foundation and embankment. Considering the influence of subgrade construction on underground frozen soil, the width of the natural foundation is 50 m, and the depth is 15 m. The width of the embankment is 12.75 m, the height is 3 m, and the slope is 1:1.5. The subgrade filling materials are mainly sand gravel, and rubble. The sand gravel layer is 2.5 m thick, and the rubble layer is 0.5 m thick. From 0 m to 0.5 m below the ground is silty clay, and from 0.5 m to 15 m is gravelly soil.  
ABAQUS was used to establish the finite element model of the permafrost subgrade in the forest region. The grid was divided into 3342 units in total, and the size of each unit was 0.5 m. The boundary conditions of the model include temperature boundary, moisture boundary, and displacement boundary. For temperature boundary conditions, the upper boundary of the model adopted the average land surface temperature measured in the field during the observation period, including two parts with and without vegetation cover, as shown in Figure 5. The left and right boundaries were set as thermal insulation. According to the engineering geological survey report, the temperature below 10 m underground is constant at \(-1\)\({}^{\circ}\)C in this area, so the temperature of the lower boundary of the model was set to \(-1\)\({}^{\circ}\)C. For the water boundary condition, it was assumed that the two sides and the bottom of the model were impermeable boundaries, and the upper boundary was an open boundary. The influence of groundwater recharge on the water separation field within the calculation scope was not considered. For displacement boundary conditions, the displacement in the x direction was fixed on both sides of the model, the displacement in the x and y directions was fixed on the lower boundary, and the upper boundary was free.  
The material parameters in the model were obtained through field and laboratory tests [28; 29], as shown in Tables 1 and 2. The materials consisted of gravel, rubble, clay, and gravel soil. A linear elastic model was adopted for subgrade filling materials and underlying rock and soil mass. To simplify the calculation, the thermal conductivity, specific heat capacity, and elastic modulus only considered the freeze-thaw state in this simulation process.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Material** & \(\rho_{d}\) **(kg/m\({}^{3}\))** & \(\theta_{u}\) **(\%)** & \(k\) **(m/s)** & \(\mu\) & \(E_{u}\) **(Mpa)** & \(E_{f}\) **(Mpa)** \\ \hline Gravel & 2010 & 17 & \(7.2\times 10^{-4}\) & 0.29 & 2.35 & 90 \\ Rubble & 2400 & 10 & \(1.1\times 10^{-2}\) & 0.30 & 2.65 & 130 \\ Clay & 1700 & 23 & \(1.5\times 10^{-8}\) & 0.23 & 2.05 & 58 \\ Gravel soil & 1950 & 15 & \(6.9\times 10^{-3}\) & 0.25 & 2.20 & 70 \\ \hline \hline \end{tabular} Note: \(\rho_{d}\) = density; \(\theta_{u}\) = volumetric water content; \(k\) = hydraulic conductivity; \(\mu\) = Poisson’s ratio; \(E_{u}\) = elastic modulus of unfrozen soil; \(E_{f}\) = elastic modulus of frozen soil.  
\end{table}
Table 1: Physical parameters in the permafrost subgrade model.  
Figure 5: Monthly average land surface temperature.