## 1 Introduction  
Coal resources make up a large proportion of the world's energy supply. Currently, coal accounts for 27% of the primary energy consumption worldwide [1]. Some countries around the world have an increasing demand for energy resources [2, 3], while coal resources cannot be substituted by alternative sources of energy. The extraction of shallow coal reserves has been insufficient to satisfy the rising demand, and consequently, there has been a gradual increase in the excavation depths of mines worldwide [4, 5]. With the increase in the depth of mining, the geological conditions are becoming more complex, landslide disasters caused by various reasons are prone to occur [6, 7, 8, 9], and the mining environment is becoming increasingly unfavorable [10]. So far, artificial ground freezing has become the way to prevent water intrusion and well gusing in the process of shaft sinking in deep alluvium and fractured rock strata [11, 12, 13]. The artificially chilled brine passes through the freezing pipe, and consequently, the frozen wall is formed around the shaft. The frozen wall is a useful protective screen for resisting earth pressure and preventing groundwater infiltration into the well. The construction complexity of the frozen wall inevitably increases with soil thickness and depth of freezing, resulting in more frequent disasters caused by the freezing and melting process of soil [14, 15]. Therefore, it is imperative to study the mechanical properties and damage progression of deeply frozen soil. From the perspective of damage mechanics, the failure of soil resulting from the application of external loading is a transition from primary to secondary soil structure. The evolution of damage can be seen as a blend of undisturbed soil and soil that is wholly damaged [16; 17; 18]. [PERSON] et al. [19] first proposed the concept of damage mechanics in the study of creep fracture and cited the concept of the 'continuity factor'. [PERSON] [20] pointed out that, when the external loading is applied to the soil, the soil can be regarded as the superposition of the undisturbed soil and the damaged soil, and he introduced the concept of a damage ratio and established the damage constitutive model of structural clay. [PERSON] et al. [21] used cement to improve the soil, studied the damage evolution of the improved soil, and established the damage constitutive model of cement-improved soil under uniaxial compression, based on the study of the evolution law. [PERSON] et al. [22] used Weibull distribution to simulate the whole process of damage evolution, coupled stress field, temperature field, and water field and fitted the stress-strain curves of frozen sand at different temperatures to obtain the model. [PERSON] et al. [23] conducted the rapid loading test, consolidation test, and triaxial compressive strength test of the natural sedimentary structural clay in Lianyungang and studied the relationship between the damage variable and disturbance degree of soil. [PERSON] et al. [24] proposed the damage variable considering the cutting effect of the ice lenses and established the corresponding elastoplastic damage constitutive model of the frozen soil. [PERSON] et al. [25] proposed an elastoplastic damage constitutive model based on super/sub-loading yield surface and verified the model by observing the mechanical behavior of frozen soil and frozen saline soil through the triaxial compression test. [PERSON] et al. [26] established a new composite structure fractional constitutive model by establishing the creep relationship between the bonding unit and the friction unit based on the microscopic damage mechanism of frozen soil. The above research shows that scholars have limited research on the damage evolution of soil to only from a single direction, and there is almost no research on deep soil. Therefore, in this paper, deep expansive clay was studied, and the damage evolution of soil under the combined action of loading and freeze-thaw cycles was studied in more depth.