## 1 Introduction  
Over 70% of China's permafrost is distributed in the Qinghai-Tibet Plateau, which is also the region with the highest altitude and the most extensive permafrost distribution in the middle and low latitudes of the world [1; 2; 3]. Various large-scale engineering structures widely distributed in the plateau's permafrost regions significantly affect heat transfer in the soil, ultimately changing the thermal balance and temperature field of the permafrost [4; 5; 6]. This has led to noticeable permafrost degradation, presenting new problems and challenges to the construction and operation of large-scale linear engineering projects in this region [7; 8; 9; 10]. In terms of practical engineering, the thermal conductivity of permafrost in negative temperature areas, which is close to the initial freezing temperature point (defined as the \"near-phase-transition zone\"), is the key physical parameter affecting the thermal stability of engineering structures. However, measuring the thermal conductivity of permafrost in the near-phase-transition zone requires temperature control and heat flow monitoring with an extremely high precision, which is limited by cost and complexity. To date, there are no well-established methods for testing the thermal conductivity of permafrost in the near-phase-transition zone, which is crucial for describing the distribution of the permafrost temperature field and ensuring project safety. Recent investigations into soil thermal conductivity have led to significant progress in various aspects. Researchers have carried out a large number of studies on thermal conductivity test methods. For instance, [PERSON] et al. [11] utilized the calorimeter method, the heat flow meter method, and the probe method to measure the thermal conductivity of various frozen soils and established a series of widely used thermal parameter tables for frozen soil. [PERSON] et al. [12] conducted laboratory testing using single- and dual-probe methods to determine the thermal conductivity of loam and found that the test results of the dual-probe method were more accurate than those of the single-probe method. [PERSON] et al. [13] and [PERSON] et al. [14] also carried out a series of experimental studies on the thermal conductivity of aeolian sandy soil, clay, and silty clay using the transient hot wire method. With advancements in theoretical understanding and technological capabilities, numerous scholars have further improved and proposed new thermal conductivity testing techniques. For example, [PERSON] et al. [15] incorporated a heat jacket into the frozen soil thermal conductivity testing apparatus used in the steady-state comparative method, significantly reducing the radial heat loss of the device and enhancing measurement accuracy. [PERSON] et al. [16] designed an innovative dual-probe thermal pulse sensor for the measurement of the thermal properties of frozen soil. To avoid costly and time-consuming experimental procedures and to facilitate engineering applications, researchers have conducted statistical analyses on a large amount of frozen soil thermal conductivity test data and proposed many data-driven empirical formulas [17; 18]. Based on the results of testing 19 soil types, [PERSON] [19] established initial empirical formulas for thermal conductivity using water content and dry density. [PERSON] [20] proposed an interpolation calculation model of soil thermal conductivity using normalized coefficients and soil saturation. [PERSON] et al. [21] developed a general model for calculating the thermal conductivity of frozen soil which is based on the liquid water content, frost heave, porosity, and initial water content. [PERSON] et al. [22] established an empirical model of the relationship between thermal conductivity and porosity based on data from 28 partially frozen soils. Scholars have also made many improvements to classic thermal conductivity empirical models to broaden their applicability and increase their prediction accuracy. For example, [PERSON] et al.