Study on the Damage Characteristics and Internal Variable Modeling of Single-Fracture Sandstone under the Coupling Effect of Freeze–Thaw and Fatigue Load

The fractured rock mass in the western cold region is affected by freezing and thawing disasters and is prone to local damage and fracture along the fissures’ ends. The fatigue damage induced by repeated frost heave and traffic loads seriously endangers the stability of cold region roadbed. This paper selects sandstone as the research object. Firstly, 20 freeze–thaw cycles were performed on fractured sandstone samples with different inclination angles of 30°, 45°, 60°, and 90°. Subsequently, triaxial compression and triaxial fatigue loading tests were conducted to explore the mechanical properties and fracture morphology evolution mechanism during the compression process of freeze–thaw fractured sandstone. Nuclear magnetic resonance technology (NMR) was used to measure the H-containing fluid inside rock pores. The microscopic damage characteristics inside the rock were analyzed from the NMR T2 relaxation spectrum signal and pore size distribution characteristics. Based on the internal variable theory of continuum mechanics, a fatigue model of freeze–thaw fractured sandstone with different inclination angles was established. The results show that sandstone strength was negatively correlated with the fracture dip angle, and the axial deformation and shear failure angle were positively correlated with the fracture dip angle. The mechanical properties of the sandstone were deteriorated by fatigue loading. When the crack angle was 90°, the fatigue failure strength of the rock sample was the lowest. The T2 spectrum distribution of the fractured sandstone mainly had three peaks and the pore size was mainly medium and small pores. There was a small leftward shift after freeze–thaw cycles and fatigue loading. The T2 spectrum area was significantly affected by fatigue loading, with the highest rate of change at a crack angle of 30°. Through the fine correspondence between the axial residual deformation and the deformation modulus, a fatigue model with different crack inclination angles was established using the axial residual deformation as the internal variable, and the rationality of the model was verified by fatigue loading tests.