# Experimental Test and Prediction Model of Soil Thermal Conductivity in Pernafrost Regions
## 3 Testing Scheme
### Cluster Analysis of Different Soils' Thermal Conductivity  
The probability distribution of thermal conductivity of 12 types of unfrozen soil (\(\lambda_{u}\)) is shown in Figure 5. It can be seen in Figure 5a that the thermal conductivity of clay and silty clay soil is significantly smaller than that of other soil types in the high probability interval. Comparatively, the thermal conductivity of clay and silty clay soil in their main distribution range (probability greater than 10%) is between 1.1\(\sim\)1.7 \(\mathrm{W}/(\mathrm{m}\cdot\mathrm{K})\), while the thermal conductivity of weathered mudstone varies in the range of 1.3\(\sim\)1.9 \(\mathrm{W}/(\mathrm{m}\cdot\mathrm{K})\). The average thermal conductivity values of two clay soils and weathered mudstone are 1.415 and 1.513 \(\mathrm{W}/(\mathrm{m}\cdot\mathrm{K})\), respectively. It also shows in Figure 5b that the main probability distributions of thermal conductivity of medium fine sand, gravel sand, boulder, breccia and gravel are all at the intervals of 1.5\(\sim\)2.3 \(\mathrm{W}/(\mathrm{m}\cdot\mathrm{K})\), which is larger than that of the silty sand. Moreover, according to the comparative results of Figure 5a,b, it can be concluded that silt, silty sand, weathered mudstone, weathered phyllite and weathered slate have similar thermal conductivity probability distribution patterns. This indicates that particle size and intrinsic heat-conducting capacity of the soil skeleton have a significant effect on soil thermal conductivity. As the particle size of soil tends to be finer, the average heat transfer cross-section area reduces and the thermal resistance increases, which results in decreasing soil thermal conductivity. Meanwhile, as the thermal conductivity of soil's mineral skeleton increases, the heat-transfer efficiency along the heat-transfer path improves either, which results in the increasing of soil thermal conductivity. Therefore, compared to gravel soil or sandy soil, the thermal conductivity of clay soil is usually relatively small due to its fine particle size and lower soil skeleton thermal conductivity.  
Figure 6 shows the thermal conductivity probability distribution of 12 types of frozen soil (\(\lambda_{f}\)). It can be seen that the main thermal conductivity distribution intervals of frozen silt, silty sand, weathered mudstone, weathered phyllite and weathered slate are basically between 1.7 and 2.5 \(\mathrm{W}/(\mathrm{m}\cdot\mathrm{K})\) (Figure 6a), which confirms the reasonableness of the above classification. Likewise, the thermal conductivity distribution law of frozen clay soil (clay and silty clay) or sand-gravel soil (medium fine sand, gravel sand, boulder, breccia and gravel in Figure 6b) can also be classified into one cluster for analysis.  
Figure 5: Probability distribution of thermal conductivity of 12 types of unfrozen soil. (**a**) Fine grained soil, (**b**) Coarse grained soil.  
Furthermore, considering the difference of soil water holding capacity, the above 12 types of frozen soil can also be approximately classified into different types. For instance, clay soil has small particles and strong water-binding ability. Hence, it belongs to high water-holding capacity soil (HWHCS). The gravel soil and sand, by contrast, have more coarse particles and readily lose moisture. Therefore, it can be distinguished as low water-holding capacity soil (LWHCS). The water-holding capacity of silt and fully weathered rock is mediocre, which can be marked as medium water holding capacity soil (MWHCS). Therefore, to obtain the variation features and prediction models of soil thermal conductivity, the typical specimens in the QTEC are classified as three clusters according to their thermal conductivity probability distribution and water-holding capacity (as shown in Table 2).