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.

中文翻译：

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冻融与循环加载耦合下红砂岩疲劳特征及能量演化分析

为了提高寒冷地区岩体工程的安全性，本文探讨了冻融与循环荷载耦合作用下红砂岩的疲劳特性和能量演化。首先，采用皮尔逊相关系数法计算了红砂岩样品的疲劳寿命、破坏应力与冻融循环次数之间的相关性。其次，利用图像积分法和最小二乘法对样品的能量演化进行了分析。最后，利用概念化模型讨论了冻融和循环加载耦合作用下样品的损伤机制。结果表明，冻融循环与疲劳寿命和失效应力呈负相关。冻融和疲劳损伤的增加导致样品的延展性增加和刚度降低。样品的总能量密度、弹性能量密度和耗散能量密度均与应力水平呈二次多项式关系。能量储存和耗散系数分别与冻融循环次数呈负相关和正相关。