To investigate the pore structure evolution characteristics and damage mechanism of sandstone subjected to treatment with freeze–thaw cycles, quantitative analyses were conducted on the longitudinal wave velocity (LWV) and T₂ spectrum of sandstone before and after 10, 20, 30, and 40 freeze–thaw cycles, using longitudinal wave velocity testing, low-field nuclear magnetic resonance (NMR) testing, and fractal theory. The results show that, with the increase in the number of freeze–thaw cycles, the LWV of sandstone gradually decreases, the amplitude of the saturated T₂ spectrum gradually increases, the amplitude of the centrifugal T₂ spectrum gradually decreases, the total porosity and effective porosity increase, and the residual porosity decreases. After undergoing freeze–thaw cycles, sandstone exhibits obvious fractal characteristics in both the total porosity NMR fractal dimension and the effective porosity NMR fractal dimension, and the growth rates of both decrease exponentially with the increase in the number of freeze–thaw cycles. The magnitude of the fractal dimensions reflects the complexity of the pore structure, with smaller fractal dimensions indicating better pore connectivity. In summary, the damage evolution mechanism of sandstone under freeze–thaw cycles is characterized by the gradual expansion and interconnection of internal closed micro-pores (cracks), along with increased total porosity and effective porosity, leading to enhanced freeze–thaw damage.

The study of the constitutive model under stress loading for rock after undergoing freeze-thaw weathering cycles (FTWCs) treatment has important theoretical significance for the site operation and numerical calculation of rock mass engineering in cold regions. In this work, a series of FTWCs treatment tests of sandstone were carried out, and the evolution characteristics of the T₂ spectrum distribution curve for sandstone before and after FTWCs treatment were analyzed utilizing nuclear magnetic resonance (NMR) technology. The schematic diagram of freeze-thaw damage evolution for sandstone was drawn, and the damage evolution mechanism was analyzed. Evolution laws of the stress-strain curves, peak and residual strength, peak and residual strain, and Young's modulus of sandstone under different FTWCs and confining pressures were analyzed by conventional triaxial compression tests. A piecewise constitutive model under triaxial stress loading for sandstone after undergoing FTWCs treatment was established, and the model considered the significant influence of FTWCs on the nonlinear deformation in the compaction stage and residual strength. By introducing error analysis indexes, the proposed model and published models were compared with the experimental data, it was found that the proposed model's performance is better than the published models, which indicated that the proposed model has good performance and strong universality.