## 1 Introduction  
Grouting reinforcement is commonly employed in engineering to enhance the mechanical properties of fissured rock bodies [1]. However, freeze-thaw cycles in the seasonal freezing zone cause the fissure structure to continue developing, which negatively impacts the effectiveness of grouting and leaves the grouted bodies vulnerable to significant geologic hazards [2]. Therefore, studying the evolution of the mechanical properties of freeze-thaw grouted fissured rock bodies in complex environments is crucial for the theoretical development of stability control in rock engineering within the seasonal freezing zone. Currently, research on the mechanical properties of fractured rock masses under freeze-thaw cycles mainly focuses on the characteristics of different fractures [3; 4; 5; 6; 7]. [PERSON] et al. [8] found, through triaxial compression tests, that the degradation mode of single-fracture sandstone gradually transitioned from brittle shear failure to ductile crushing failure as the number of freeze-thaw cycles increased. Moreover, the fracture penetration rate exhibits a nonlinear relationship with the number of freeze-thaw cycles. [PERSON] et al. [9], based on uniaxial freeze-thaw tests of open fracture specimens, further pointed out that the freezing method and fracture inclination angle significantly affected the threshold of fracture-induced freezing expansion by altering the ice expansion stress distribution. When the fracture inclination angle is between 60\({}^{\circ}\) and 90\({}^{\circ}\), the path of freezing-induced cracks leads to a reduction in the uniaxial strength of the rock mass. [PERSON] et al. [10], in their study of slate, demonstrated that the bedding dip had a selective effect on freeze-thaw damage. When the bedding direction aligns with the freeze-thaw stress direction, the elastic modulus can decrease by as much as 32%. [PERSON] et al. [11] revealed, through triaxial tests, that the fracture trace length was more sensitive to the strength degradation of the rock mass than the fracture width and that temperature variations had a more significant weakening effect on the peak strength of fractured rock masses under low confining pressures. Although these studies clarify the influence of single factors, most of them have not quantified the nonlinear cumulative effect of multiple factors interacting. For example, the damage model established by [PERSON] et al. [12] only considers the linear superposition of freeze-thaw cycles and fracture inclination, while the experiments of [PERSON] et al. [13] showed that when the number of freeze-thaw cycles exceeds 20, the contribution of the joint filling material type to strength loss increases from 15% to 40%, suggesting that the interaction between freeze-thaw cycles and other factors may exhibit temporal dependence. Regarding the study of the mechanical properties of fractured rock masses under grouting reinforcement, [PERSON] et al. [14] found, through triaxial tests, that the peak deviatoric stress of the grouted body was positively correlated with the roughness, thickness, and quantity of grout veins. [PERSON] et al. [15], through direct shear tests, further demonstrated that the strength model of the grouted body must simultaneously consider the synergistic effect of grout permeability and confining pressure. [PERSON] et al. [16] conducted normal and tangential mechanical loading tests on grouted rock mass fracture specimens, concluding that grouting reinforcement increases the overall strength and stability of the rock mass by improving the mechanical properties of the fracture surfaces. [PERSON] et al. [17] revealed the marginal effects of grout material types: when the confining pressure exceeds 10 MPa, the strength difference between chemical grout and cement-based grout decreases from 25% to 8%, indicating that environmental stresses may alter the material performance advantage. [PERSON] et al.