Fatigue characteristics and energy evolution analysis of red sandstone under the coupling of freeze–thaw and cyclic loading

•The test of red sandstone under the coupling of freeze–thaw and cyclic loading.•Calculation of freeze–thaw deterioration factor correlations by Pearson's method.•Image integration & least squares methods analyze energy evolution law of rocks.•Energy storage and dissipation of sample under coupling effect follow linear laws.•A conceptual model describes the damage mechanism of rocks under coupling. In order to improve the safety of rock mass engineering in cold regions, this paper discusses the fatigue characteristics and energy evolution of red sandstone under the coupling of freeze–thaw and cyclic loading. Firstly, the correlation between the fatigue life, failure stress, and the number of freeze–thaw cycles of the red sandstone samples was calculated using the Pearson correlation coefficient method. Secondly, the energy evolution of the samples was analyzed using the image integration method and the least squares method. Finally, the damage mechanism of the samples under the coupled effect of freeze–thaw and cyclic loading was discussed using a conceptualized model. The results show that freeze–thaw cycles are negatively correlated with fatigue life and failure stress. The increase in freeze–thaw and fatigue damage leads to an increase in ductility and a decrease in the stiffness of the samples. The total energy density, elastic energy density, and dissipated energy density of the samples all show a quadratic polynomial relationship with the stress level. The energy storage and dissipation coefficients are negatively and positively correlated with the number of freeze–thaw cycles, respectively.