# Experimental Test and Prediction Model of Soil Thermal Conductivity in Pernafrost Regions
## 3 Testing Scheme
### Experimental Methods  
A Hot Disk 1500s Thermal Conductivity Analyzer (Hot Disk Co. Ltd., Uppsala, Sweden) was used to measure the thermal conductivities of all specimens (Figure 3a). The analyzer's measurement accuracy is \(\pm 3\%\), which is based on the transient plane source (TPS) testing method. The isotropic hypothesis was utilized in the thermal conductivity measurement. During the test, the analyzer obtained temperature variation values (\(\Delta\overline{T}(\tau)\)) and the dimensionless time constant (\(D(\tau)\)) by monitoring the change of film sensor resistance, then drew the corresponding relationship curve, and finally calculated soil thermal conductivity (\(\lambda\)) by the slope value of \(\Delta\overline{T}(\tau)\) and \(D(\tau)\) line equations:  
\[\Delta\overline{T}(\tau)=\frac{P_{0}}{\pi^{3/2}r\lambda}D(\tau) \tag{1}\]  
where \(P_{0}\) is the total output of power and \(r\) is the radius of the film sensor.  
In order to make the specimen as large as possible, the No. 4922 Kapton film probe was used in the experiment (radius is 29.4 mm). The specimens were formed into two columns with 80 mm in diameter and 30 mm in height. The dry density and water content of specimens were determined by the field measurement data, which was tested by the suspending weigh method and oven drying method, respectively. The corresponding test soil was taken from sample library (Figure 3b). After drying, milling and sieving, the specimen was sampled by the statistic pressure method. Furthermore, for the high water content and icy specimens, the crushed smoothie was used for specimen making.  
In the test, the Kapton probe was fixed on the stainless steel sample holder, and two sample columns were placed on both sides of the probe (Figure 3c). To ensure the probe was in close contact with the sample, two plastic film-covered specimens were compacted with a sample holder's clamp. As the measurement of unfrozen soil thermal conductivity finished, the specimens were placed in a freezing cabinet (Figure 3d) and frozen for 24 h (\(T<-10\)\({}^{\circ}\)C). Then the specimens were placed into the stainless steel sample holder and continued to freeze in the cabinet for 2 h again (to avoid the environment thermal disturbance). The thermal conductivity analyzer needs to define appropriate test time and power parameters to obtain reasonable test results. For every specimen, the thermal conductivity measurement was conducted twice and took the average of the two test results as the experimental result. When the measuring error was larger than 5% due to improper parameter settings,  
Figure 2: Statistic numbers of test samples for certain soil type.  
multiple experiments were conducted to obtain reasonable test results. The main test procedures are listed in Figure 4. In addition, the flatness of the pre-frozen soil sample measuring surface was necessarily checked before the testing of frozen soil. The roughness surface needed to be polished by scraper and placed in the cabinet until the temperature fluctuation was eliminated.  
Figure 4: Flow diagram of thermal conductivity test.  
Figure 3: Schematic of thermal conductivity test system. (**a**) Thermal conductivity analyzer; (**b**) soil sample library; (**c**) specimen and Kapton probe; (**d**) freezing cabinet.  
Distribution Characteristics and Cluster Analysis of Frozen and Unfrozen Soil Thermal Conductivities