Fatigue fracture behaviour and constitutive model of freeze-thaw sandstone under multilevel fatigue loads

The fatigue fracture behaviour and a constitutive model of the freeze-thaw (F-T) sandstone are studied to investigate the failure mechanism of engineering rock in cold regions. First, the fatigue properties of the samples are analysed in terms of stress-strain, deformation characteristics, and pore structure. Second, the types of hysteresis curves are analysed using the load-unload response ratio (LURR) method. Scanning electron microscopy (SEM) and acoustic emission (AE) techniques are then used to investigate the structural damage, crack evolution, and spectral characteristics of the samples. Based on the Lemaitre strain equivalence hypothesis, the improved Harris distribution is used to propose a new constitutive model of rock that underwent F-T cycles under multilevel fatigue loading. Finally, based on the strain difference model, the nonlinear stage of the model is corrected by defining new compaction coefficients using the Weibull distribution. Research shows that the deformation modulus of the F-T rock mass under fatigue loading has degradation behaviour and F-T cycles enhance the fatigue softening of samples. The dominant frequency range of samples under coupling is 70–330 kHz, showing multiband coexistence. As fatigue loading progresses, the hysteresis curve changes from stress hysteresis to strain hysteresis, and the frequency band gradually widens and develops towards low frequencies. The occurrence of a 0 kHz dominant frequency or LURR = 1 can be used as an early warning index of rock fatigue failure. As the number of F-T cycles progresses, the porosity composition curve shifts to the right, and the distribution of AE counts and the dominant frequency shift to the early loading stage.