In order to study the elastic modulus degradation and dynamic characteristics of permafrost at different temperatures

the stress-strain hysteresis curve and fatigue damage life under dynamic load were obtained by cyclic loading and unloading test of frozen soil samples under different below-zero temperature conditions. Fatigue damage parameters of permafrost at different temperatures were determined according to the relationship between fatigue life and stress amplitude. According to the law of elastic modulus degradation of permafrost

the governing equation of dynamic model was proposed and the phenomenological model of fatigue damage of permafrost was established. According to the characteristics of cyclic loading and unloading hysteresis curve measured by permafrost

the method of joint analysis of damping ratio under ideal and non-ideal hysteresis loops was proposed. Based on the Kelvin model

the mathematical relationship between the evolution of the hysteresis loop and the elastic modulus degradation and loading time was established. The study shows that: the phenomenological fatigue damage model

which takes into account the effects of the elastic modulus attenuation

describes the accelerated fatigue damage characteristics of permafrost. Equivalent hysteresis and non-ideal hysteresis damping ratio analysis method is good for taking account of the actual evolutionary characteristics of hysteresis loops. The Kelvin rheological model based on elastic modulus degradation establishes the mathematical relationship between the hysteresis loop and the unloading time.