## 1 Introduction  
Vertical [1] and inclined shafts [2] constructed in coal mines in the western provinces of China, such as Shaanxi and Inner Mongolia, encounter the situation of crossing the water-rich Luohe Formation sandstone strata. When ordinary drilling methods cannot be successfully used, an artificial freezing method is needed [3]. The mechanical behaviours of various rocks subjected to freezing have been previously investigated. The general rule is that the lower the freezing temperature, the greater the compressive strength and the cracking stress of rock [4, 5], which is essential for the safe excavation of a mining shaft after artificial freezing. However, when the fissure water of a rock mass freezes after freezing of the mining shaft, the volume expansion of joint filling is constrained by the surrounding rock mass, resulting in a frost-heaving force [6]. The temperature of the frozen walls changes with time and space in the process of wellbore construction [7, 8, 9]. The decrease in temperature will increase the frost-heaving pressure [10], resulting in irreversible damage, such as an increase of rock porosity [11]. With the increase in the excavation depth of the mining shaft, the high confining pressure makes the frost-heaving damage of water-rich sandstone more severe [12]. The fissure tip produces stress concentration when the ice volume expands. Once the stress exceeds the tensile strength of the rock mass, various mesoscopic and macroscopic cracks initiate, expand and penetrate [13; 14; 15; 16]. Therefore, after the artificial frozen wall is thawed, during the period when the surrounding rock is melted without grouting or the grouting is basically without strength, the structure of the surrounding rock is seriously damaged, and its mechanical properties are significantly reduced. Rock cracks are more likely to fracture and fail, leading to wellbore damage and causing accidents, such as water seepage and well flooding [17]. Therefore, it is also necessary to explore the mechanical properties of frozen rock after thawing. Because performing a uniaxial compression test is relatively easy, most previous research has focused on the mechanical behaviour of samples under uniaxial compression. The following conditions have mainly been considered: freeze-thaw times [18; 19; 20], moisture content [21; 22], the geometric distribution of prefabricated or natural fissures [23; 24; 25; 26], and loading patterns, such as cyclic loading and static-dynamic loading [27; 28; 29; 30; 31]. In the test process, computed tomography scanning can be used to observe better the micropropagation law of the cracks in frozen-thawed rock [32; 33]. A nuclear magnetic resonance test can be used to analyse the change of rock porosity caused by freezing-thawing and load [34; 35]. Acoustic emission monitoring can be used to analyse the initiation position and macroscopic propagation law of cracks [36; 37; 38]. However, most rock strata encountered in practical engineering are subjected to confining pressure, so the mechanical properties of rock under triaxial compression at a normal temperature have also been studied. For example, [PERSON] et al. [39; 40] analysed the effects of ambient pressure and the dip angle of rock bridges on the crack development and fracture of quasi-rock prefabricated double fissures. [PERSON] et al. [41] compared the influence of triaxial and uniaxial load patterns on the compressive resistance, deformation evolution, and static elastic modulus of rock. Only a few scholars have performed triaxial compression tests of frozen-thawed rock and analysed the following influencing factors: the geometric distribution of prefabricated fissures [42] and the loading mode [43]. In addition to experimental research, some researchers have also theoretically analysed and established a constitutive model of freeze-thaw damage for rock and analysed its damage evolution law [44]. Some scholars have combined the macroscopic static elastic modulus and microscopic element strength of rock [45].