## 1 Introduction  
Saturated permafrost is primarily composed of a solid soil matrix, unfrozen water, and ice, resulting in significant differences in physical properties compared with conventional soils. The artificial freezing method utilizes refrigeration technology to transform regular soil into permafrost, effectively isolating groundwater from underground structures. This technique has found wide application in the construction of underground passages and tunnels [1; 2; 3]. Simultaneously, numerous infrastructure projects are underway in permanently frozen soil regions [4; 5; 6]. Accidents resulting from insufficient freezing strength have occurred frequently during engineering construction, drawing considerable attention from scholars [7]. Unconfined compressive strength (UCS), as a vital indicator reflecting the physical-mechanical properties of soil in engineering, finds extensive application across various fields [8; 9; 10]. It commonly serves as a basis for studying the reinforcement level of soil after freezing. Numerous scholars have conducted indoor experiments on the unconfined compressive strength of frozen soil. [PERSON] [11] and others studied the variation in the uniaxial compressive strength of remodeled frozen soil under different sand contents and moisture levels, but they overlooked the influence of temperature on strength. [PERSON] et al. [12] conducted experiments on the unconfined compressive strength of different types of in situ frozen soil, considering various soils. [PERSON] et al. [13] investigated the impact of high moisture content on the mechanical properties of frozen silty soil. [PERSON] et al. [14] conducted a series of repetitive unilateral freezing tests on an unsaturated silty clay soil under uniform initial and boundary conditions to reveal changes in temperature, moisture content, and freezing expansion. More researchers have focused on studying the influence of external factors on the unconfined compressive strength of frozen soil. Among these factors, temperature is the most crucial determinant of the unfrozen water content, significantly affecting the degree of soil freezing [15; 16]. [PERSON] [17], based on the experimental results of uniaxial compressive strength of remodeled frozen soil, concluded that the unconfined compressive strength of frozen soil increases with decreasing temperature. However, limited by experimental conditions, more results under different temperatures were not provided. [PERSON] et al. [18] studied the trend of strength changes with different temperatures for saturated frozen clay at different dry densities and constant strain rates, deriving empirical formulas. However, the complexity of the formulas arises from the consideration of different parameters for different soil categories. [PERSON] et al. [19] investigated the strength characteristics of frozen sandy silt under different strain loading rates. [PERSON] et al. [20] further explored the influence of loading rate on the strength of frozen improved soil, taking into account variations in particle size. The strain loading rate also has a significant impact on strength [21; 22], with varying loading rates used in experimental studies by different researchers [23; 24], resulting in noticeable differences in test results. Therefore, it is essential to involve strain rates and other factors collectively in the data analysis process across different studies. In previous studies, numerous empirical formulas for permafrost strength have been derived; however, these formulas are limited to specific experimental soils, and the extrapolation capability of empirical formulas has not been thoroughly investigated. There is a lack of universality in the study of permafrost strength characteristics. The extreme gradient boosting (XGB) algorithm [25], based on gradient boosting trees, is renowned for its high predictive accuracy and strong generalization capabilities. It has been widely applied in various domains, including land subsidence [26; 27], soil strength [28; 29], and slope stability [30; 31].