## 2 Materials and Methods
### Research Data  
#### 2.2.1 Permafrost Prior Data  
Permafrost has special subgrade conditions that need to be considered in road engineering. In the route selection and design stage of the road project, it is necessary to determine the geological conditions of the road route through drilling, geophysical prospecting, and geological exploration in combination with prior data.  
In this study, the permafrost prior data consists of borehole data from road surveys, field investigation data, and special ground features, in which the borehole data from the road survey are the main data (Figure 2a). Although most data are located on the road line and the spatial position is not random enough, the survey data cover a variety of terrain, and the altitude is widely distributed. It is scattered on the line with a total length of 80 km and is representative.  
The provincial highway 308 (S308) of the Inner Mongolia Autonomous Region is located in the study area. The geological investigation report of S308 includes 431 boreholes altogether, from which 201 borehole data with permafrost information were selected (92 non-permafrost boreholes and 109 permafrost boreholes; the report was obtained in July 2017). Because of costs, temperature measurements were not conducted in the boreholes. These boreholes are mainly distributed along the design line of the road, with an interval ranging from 500 m to 1 km between each other. In special sections, the interval is shortened to  
Figure 2: Permafrost prior data. (**a**) is the schematic diagram of the zoomed out prior data; (**b**,**c**) refers to the cities and towns, and lakes that are artificially designated as non-permafrost areas; (**d**–**f**) are the permafrost prior data constructed by the borehole data of S308; and (**g**) is the permafrost ice layer taken during the investigation in the study area.  
40 m. A few boreholes are located on both sides of the line. The depth of boreholes mainly ranges from 15 m to 35 m, and some special positions, such as where the permafrost layer is thick, increase to 40 m. Because the boreholes serve the road survey, most of the boreholes are located at the flat position or at the foot of the slope, some of the boreholes are located on the gentle slope, and a few of the boreholes are located on the steep slope.  
Borehole data were mainly used to construct the permafrost prior data. The principle of construction is to take each permafrost borehole and non-permafrost borehole as the center of the circle and build the buffer zone with a certain radius (Figure 2d-f). It is believed that the presence of permafrost at the center of the circle can represent the presence of permafrost in the buffer zone. Based on the observation and experience of the geological investigation of S308, this radius was taken as 50 m in the study area.  
The main rock of Arxan is basalt. Some towns have existed for decades and the buildings in the towns have not subsided. Therefore, these towns are generally considered to be free of permafrost. In addition, the mountain lakes in Arxan are mainly evolved from former volcanoes [32]. It is believed that no permafrost exists below. These towns and lakes were also added to the permafrost prior data as non-permafrost areas (Figure 2b,c). In order to avoid affecting the boundaries of towns and lakes, the selected samples were located inside the towns and lakes and kept at a distance from their boundaries. In addition, during the field investigation, some locations with permafrost were found by the high-density resistivity method (Figure 2g).  
Based on the above principles, a total of 2.292 km\({}^{2}\) of permafrost samples (1.225 km\({}^{2}\) based on boreholes and 1.067 km\({}^{2}\) based on field investigations) and 1.9706 km\({}^{2}\) of non-permafrost samples (0.9257 km\({}^{2}\) based on boreholes and 1.0449 km\({}^{2}\) from towns and lakes) were obtained in the total area of 7420.02 km\({}^{2}\) in Arxan.