## 4 Conclusions  
Given the limited research on the physical and mechanical properties of grouting reinforcement bodies in cold regions, coupled with the challenges and high costs associated with in-situ testing of fractured rock masses, this study focuses on fractured sandstone grouting reinforcement bodies. It utilizes a combination of wave velocity testing, nuclear magnetic resonance (NMR) analysis, triaxial compression tests, and other laboratory techniques. A series of investigations into the physical and mechanical properties of fractured sandstone grouting reinforcement bodies subjected to freeze-thaw cycles have been conducted, leading to the following key conclusions:  
* As the number of freeze-thaw cycles increases, both the mass and wave velocity of the grouting reinforcement body decrease, while the mass loss rate and wave velocity loss rate increase. After 30 freeze-thaw cycles, the maximum mass loss rate of the sample is 1.25%, and the wave velocity loss rate exceeds 25%. Under the same number of freeze-thaw cycles, the mass loss rate increases with the increase in crack dip angle. * The NMR T\({}_{2}\) spectra curve of the grouting reinforcement body shifts to the right as the number of freeze-thaw cycles increases, indicating that the freeze-thaw process promotes the continuous initiation, development, and expansion of internal pores within the grouting reinforcement body. In the initial stages of the freeze-thaw cycle, pore size evolution progresses from micropores to mesopores and macropores. In the later stages of the freeze-thaw cycle, the evolution is primarily from mesopores to macropores. * The freeze-thaw cycle weakens the mechanical properties of the grouting reinforcement body. As the number of freeze-thaw cycles increases, both the peak strength and elastic modulus of the grouting reinforcement body decline, following a negative exponential function under varying confining pressures. Cohesion and the internal friction angle progressively decrease with increasing freeze-thaw cycles. Under the same number of freeze-thaw cycles, the peak strength and elastic modulus of the grouting reinforcement body decrease as the crack dip angle increases but increases with higher confining pressures. The relationship between peak strength and confining pressure adheres to the Coulomb linear strength criterion. * The crack dip angle and confining pressure significantly influence the failure mode of the grouting reinforcement body. Plastic flow is observed after the peak of the stress-strain curve for grouting reinforcement bodies subjected to high confining pressures with crack dip angles of \(0^{\circ}\), \(30^{\circ}\), or \(45^{\circ}\), leading to a marked enhancement in ductility. In contrast, the stress-strain curves of grouting reinforcement bodies with a45\({}^{\circ}\) crack dip angle under low confining pressure and a 60\({}^{\circ}\) crack dip angle exhibit a substantial decline after reaching the peak. This decline is primarily attributed to the stress exceeding the shear strength of the slurry-rock interface layer, resulting in shear slip along the fracture planes. All authors contributed to the study's conception and design. S.L. : formal analysis, investigations, and writing-original draft; J.Z. ([PERSON]): funding acquisition, supervision, and writing-review; Z.Y. : methodology, investigation, experiment; T.Z. : writing-review and editing; [PERSON]. ([PERSON]): assisting writing-review. All authors have read and agreed to the published version of the manuscript. All data, models, or codes that support the findings of this study are available from the corresponding author upon reasonable request. This research is jointly supported by the National Natural Science Foundation of China (Grant No. 51804157), Bingtuan Financial Science and Technology Project (Grant No. 2023 AB016-02) and Shaanxi Province key research and development Project (Grant No. 2024 GX-YBXM-479).