# Experimental Test and Prediction Model of Soil Thermal Conductivity in Pernafrost Regions
## 1 Introduction  
A rammed soil foundation is a widely utilized construction and building foundation type in permafrost regions and its thermal response to external heat disturbance determines the stability and sustainability of engineering applications to a certain extent [1; 2]. Due to the temperature sensitivity of frozen soil, the mechanical properties differ greatly before and after freezing and thawing, which tends to induce various engineering diseases characterized by thaw settlement and frost heave [3]. Thermal conductivity is one of the most important parameters of frozen soil, which is also a prime influencing factor of engineering structural damage caused by thaw settlement and frost heave [4; 5]. As a complex multi-phase composition, previous research indicates that the thermal conductivity of frozen soil is associated with many factors [6; 7; 8]: inherent mineralogical skeleton, particle size, spatialpore arrangement, porosity, dry density, water content and temperature, etc. Thus, investigation of the variation features and parameter influence mechanism of soil thermal conductivity is of great importance and contributes to the promotion of stability and sustainability of engineering applications in cold regions. In past decades, a number of experimental measurements and calculation models were utilized to obtain the thermal conductivity of soil [4; 5; 6; 7; 8; 9; 10]. The experimental measurement method can be roughly divided into two categories: steady state method and transient method [4; 6; 9; 10]. The corresponding methods includes steady-state heat flow meter, steady-state comparison, steady-state flat plate, transient spherical probe, transient hot wire, transient heat pulse and transient plane source (TPS) methods etc. [11; 12; 13; 14]. For instance, [PERSON] et al. [15] measured the thermal conductivity of the frozen and unfrozen soils using the steady state comparative method, and proposed some widely used empirical formulas between thermal conductivity and influencing factors' parameters (e.g., dry density and water content). [PERSON] et al. [16] designed an improved steady state apparatus for measuring soil thermal conductivity, and a thermal jacket was utilized in the experiment to minimize the radial heat loss. [PERSON] et al. [17], [PERSON] et al. [18], and [PERSON] et al. [19] conducted a series of laboratory test using the transient hot wire method to investigate aeolian sand, frozen clay, and silty clay, respectively. [PERSON] et al. [20] measured the thermal properties of partially frozen soil with a dual probe heat-pulse sensor, and a numerical solution for radial heat conduction was developed to determine the thermal parameters accurately and simultaneously. Furthermore, due to high cost, time-consuming and usually limited conditions of experimental measurement, many researchers also summarized a considerable number of calculation models of soil thermal conductivity with different methods [7; 8]. [PERSON] [21] presented a semi-empirical predictive model for moist soils and testified that soil thermal conductivity could be estimated reasonably using its dry density and water content. [PERSON] et al. [22] developed a theoretical model to predict the thermal conductivity of heterogeneous solid mixtures assuming the parabolic distribution of discontinuous phase volume fraction. [PERSON] [23] proposed a normalized thermal conductivity conception (Ke, which was the function of thermal conductivity of soils, dry soils and saturated soils) and given the relationship between Ke and saturation level (Sr) for soil thermal conductivity interpolated calculation. Recently, based on a large number of experimental results, [PERSON] et al. [24] established an empirical formula of relative porosity, saturation degree, dry density and water content to predict thermal conductivity. [PERSON] et al. [25] and [PERSON] et al. [26] further studied the thermal conductivity of soils and established a new Ke-Sr relationship incorporating variables of soil type and porosity separately. [PERSON] et al.