## 1 Introduction
[23] established a new model similar to the [PERSON] model which simulates the relationship between various soil textures and their water contents and effective thermal conductivities. [PERSON] et al. [24] compared and evaluated eight soil thermal conductivity models through actual measurements and proposed an improved thermal conductivity prediction model that considers particle size distribution parameters. [PERSON] et al. [25] expanded [PERSON]'s model and developed a thermal conductivity calculation model that is applicable to more soil conditions. Compared with traditional empirical fitting methods, machine learning methods can achieve more accurate estimations through training with a large amount of data, and they have also been widely used for the prediction of frozen soil thermal conductivity [26; 27; 28]. For instance, [PERSON] et al. [29] analyzed the factors affecting the thermal conductivity of soil during the freeze-thaw process and established a prediction model for thermal conductivity using artificial neural network technology. [PERSON] et al. [30] combined the firefly algorithm with the extreme learning machine method to establish a model for predicting the thermal conductivity of unsaturated soil. In recent years, researchers have also studied measurement methods and predictive models of the soil thermal conductivity in the near-phase-transition zone. For example, [PERSON] et al. [31] combined the steady-state method with the transient method and proposed a method for measuring the thermal conductivity of frozen soil near 0 \({}^{\circ}\)C. After an analysis of various models for estimating characteristic soil freezing curves, [PERSON] et al. [32] proposed a new method for predicting the thermal conductivity of frozen soil based on the geometric mean model. This model can effectively predict the thermal conductivity of frozen soil and how it varies in the temperature range of \(-20\)\({}^{\circ}\)C to 0 \({}^{\circ}\)C. [PERSON] et al. [33] used the steady-state method to measure the thermal conductivity of frozen and thawed lime soil and found that the phase change in the soil mainly occurs between \(-3\) and \(-2\)\({}^{\circ}\)C. [PERSON] et al. [34; 35] proposed an artificial neural network prediction model based on the internal and external factors of the soil, which can effectively predict the thermal conductivity of sandy soil at temperatures ranging from \(-7\)\({}^{\circ}\)C to 4 \({}^{\circ}\)C. Although extensive research has been conducted on the thermal conductivity of various types of frozen soil [36], studies on the thermal conductivity characteristics of frozen soil in the near-phase-transition zone are relatively scarce. Existing thermal conductivity data of frozen soil were mostly measured at low temperatures (e.g., \(T<-4\)\({}^{\circ}\)C), and there is a lack of test data near the phase change point [37; 38]. Furthermore, current models for predicting the thermal conductivity of frozen soil in the near-phase-transition zone have limitations in terms of accuracy and applicability [39; 40]. To address this, in the present work, a method for testing the thermal conductivity of fine sandy soil in the near-phase-transition zone is proposed. This method involves measuring thermal conductivity using the transient plane heat source method and determining the volumetric specific heat capacity via weighing the unfrozen water content. The unfrozen water content of sand specimens in the near-phase-transition zone was determined using nuclear magnetic resonance (NMR) technology, and corresponding empirical fitting formulas were established. Based on the test results, the temperature variation characteristics and parameter influence laws of thermal conductivity in the near-phase-transition zone were investigated. Additionally, thermal conductivity prediction models based on multiple regression (MR) and a radial basis function neural network (RBFNN) were established.