Effect of Disturbance Frequency on Cyclic Hardening Behavior and Energy Dissipation of Coal under Cyclic Loads

The fatigue response of rock under cyclic loading is a key scientific issue in geotechnical engineering, and its fatigue strength is usually significantly lower than that under monotonic loading. Underground coal mining is often affected by various anthropogenic and natural disturbances. This paper investigates the effects of cyclic loading frequency and applied stress level on the fatigue life of coal through uniaxial compression tests. The tests employed an equal-amplitude, stepwise cyclic loading and unloading path to simulate the disturbance of the rock mass around actual cavities, increasing the number of cycles at each stress level to 5000 to significantly amplify the influence of disturbance parameters on the strength and damage evolution of coal samples. By analyzing parameters such as peak stress, Young's modulus, elastic energy ratio, and cumulative dissipated energy, the results show that the disturbance frequency is closely related to the cyclic hardening behavior and damage accumulation of the specimen. Specifically, at low stress levels, increasing the frequency reduces the growth rate of Young's modulus, i.e., it slows down cyclic hardening. At high stress levels, increasing the frequency accelerates hardening. At intermediate stress levels, a transitional state appears where the trend of Young's modulus with frequency reverses, reflecting the competitive transition between two mechanisms: damage dominance and rate-effect strengthening dominance. Energy analysis indicates that, as frequency increases, the specimens generally exhibit a decrease in the elastic energy ratio and an increase in the growth rate of cumulative dissipated energy. This frequency effect is particularly significant at low stress levels. As the stress level increases, its regulatory capacity on the distribution of elastic energy gradually weakens, and the specimen tends toward a purely elastic response. This paper reveals the synergistic influence mechanism of loading frequency and stress level on the mechanical behavior of coal, providing a theoretical basis for understanding the long-term stability of underground coal pillars and surrounding rock.