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To study rock damage characteristics under long-term freeze-thaw cycles and loads, rock freeze-thaw and creep damage factors were defined based on nuclear magnetic resonance porosity and volume strain, respectively. The damage factor is introduced into the basic rheological element, and the non-linear creep damage constitutive model and freeze-thaw rock equation are established to describe non-linear creep characteristics under a constant load. Simultaneously, the creep test of freeze-thaw rock under step loading is performed. Based on the test data, the applicability and accuracy of the creep damage freeze-thaw rock model are analyzed and verified. The results show that freeze-thaw cycles result in continuous rock pore structure damage and deterioration, and nuclear magnetic resonance porosity enhancement. The constant load induces increasing rock plastic deformation, volume, and creep aging damage. As the loading stress increases, the instantaneous rock elastic parameters increase, and the rheological elastic and viscosity parameters decrease. Furthermore, the damage degradation of freeze-thaw cycles weakens the rock viscoplasticity, resulting in a rapid decrease in the viscosity parameter with an increase in freeze-thaw cycles. Generally, the continuous damage of the rock is degraded, and the long-term strength decreases continuously.

In order to study the creep mechanical properties of sandstone subjected to graded loading under the condition of freeze-thaw cycles, 15 freeze-thaw cycles were conducted with four groups of rock samples. The porosity variation of sandstone before and after the freeze-thaw cycles were obtained by using the nuclear magnetic resonance (NMR) technique. The results show that under the action of freeze-thaw cycles, the cohesion between particles inside the rock decreases, the pore structure deteriorates continuously, and the porosity of the rocks increases. During the graded loading creep test, the rock underwent macroscopic failure under low-level loading. Moreover, the fracture morphology showed tensile-shear failure characteristics, which caused obvious decreases in the long-term strength of the rock. The comprehensive analysis of the experimental data to establish the creep model and constitutive equation under the condition of the freeze-thaw cycle, and discuss the relationship between creep model parameters and freeze-thaw factors. The nonlinear creep mode can effectively reflect the graded loading creep law of frozen and thawed sandstone.

To study the evolutionary characteristics of mesostructural damage to saturated limestone under different loading and unloading paths, three types of loading and unloading tests involving three different loading rates and initial peak stresses were performed. Nuclear magnetic resonance technology and scanning electron microscopy were used to investigate the evolutionary characteristics of pore water during the loading and unloading of the limestone. The results indicated that, with an increase in the initial peak stress, the rock viscoplasticity gradually decreased, and the variation of pore radius and the reduction of bound water decreased. With an increasing loading rate, the mesostructure evolution law under disturbance-increasing amplitude (DIA) cycling was opposite to those under increasing amplitude (IA) and repeated-increasing amplitude (RIA) cycling. With the increasing loading stress level, the porosity decreased and then increased. Under increasing amplitude cycling, a larger initial porosity resulted in higher pore compaction and expansion limits. Reducing the initial peak stress inhibited the pore expansion, whereas it had the opposite effect under RIA and DIA cycling. During loading and unloading, bound water exists in pores of organic matter and mesopores, and free water exists in macropores of intergranular and transgranular fractures. These changes indicate certain laws under different loading and unloading paths. The results of this study indicate that the mesostructure characteristics of rock depend on the loading and unloading paths.

To reveal the energy-dissipation mechanism of the rock deformation and destruction process under the influence of freeze–thaw cycles and investigate the essence of rock freeze–thaw damage, the evolution characteristics of the total strain energy, elastic energy, and dissipated energy in the sandstone failure process are analysed according to the energy principle, number of freeze-thaw cycles, and uniaxial compression. The results reveal that: (1) the evolution behaviours of the total strain energy, elastic energy, and dissipative energy of sandstone under different numbers of freeze–thaw cycles are similar; that is, the total strain energy and elastic energy gradually increase with the increasing strain, and the elastic energy decreases sharply after reaching the peak limit. The dissipative energy gradually increases and thereafter remains stable; finally, it rapidly increases. (2) With increasing freeze–thaw cycles, the growth rates of the total strain energy, elastic energy, and dissipated energy gradually decrease, whereas the energy value at the peak first increases and then decreases. The energy distribution during rock loading is affected by the number of freeze-thaw cycles (defined as N). When N is