# Energy Behaviour of Coal Failure under Uniaxial Cyclic Loading/Unloading
###### Abstract  
Cool failure is often the precursor of dynamic disaster. The energy evolution behaviour at different stress values was analysed under the gradation of equal amplitude cyclic loading/unloading. Based on the energy dissipation behaviour, the energy evolution model of the coal specimen was established. The multi-parameter energy behaviour predicting model was proposed. Then, the energy storage factor criterion, the energy tangent factor criterion, the energy dissipation growth factor criterion and the energy damage factor criterion of the coal specimen were proposed during the coal fracture process. The energy density and the energy storage status showed different evolution patterns under cyclic loading/unloading. The energy behaviours and status were different in fracture stages of coal specimens, and the dissipated energy behaviour had a sudden response during the failure process. The energy storage and energy dissipation mechanism were related to their respective limits. The energy storage mechanism showed a growth pattern of \"low energy promotion, high energy suppression and dissipation promotion, cumulative suppression\". The damage evolution equation and the energy behaviour evolution criterion were established under the cyclic loading/unloading. cyclic loading/unloading; energy behaviour; energy evolution model; predicting criterion +
Footnote †: journal: Applied Sciences  
a given energy condition, rocks yield more easily at low frequencies and amplitudes than at high frequencies and amplitudes [24; 25]. Therefore, many researchers have investigated the damage of rock materials under cyclic loading. For example, the damage evolution pattern of rocks was analysed in multi-valued amplitude cyclic loading tests at different confining pressures [26; 27; 28]. After this, the energy dissipation characteristics of coal specimens were used to describe the propagation of crack growth behaviour under layered cyclic loading [29; 30]. In particular, the peak stress of cyclic loading has a strong influence on the fatigue behaviour of coal specimens and the degree of damage increases with increasing energy dissipation density [31; 32]. Up to now, it has been shown that the damage pattern of specimens under cyclic loading is different from the damage pattern under static loading, and some studies have also advanced the constitutive relations and damage behaviour aspects of rocks under quasi-dynamic loading. However, the dynamic damage of rocks from an energy perspective remains unclear, especially in cyclic loading condition. The results of the exploration of the relationship between energy transformation and coal damage showed that the energy behaviour was different at different stages of deformation [33; 34; 35; 36]. Therefore, the energy density of rock materials increased nonlinearly under different loading/unloading rates; it is also worth noting that the loading and unloading speed has a considerable effect on the dissipated energy density [37; 38; 39]. In actual projects, rock materials are usually loaded/unloaded repeatedly, such as in coal mining, tunnel excavation and roadway support [40]. The strength and deformability are closely related to the stress state and loading history. It was widely accepted that the damage evolution was driven by energy, and different stress paths had different mechanical behaviour and energy conversion characteristics. This is also a feasible way to reveal the phenomenon of energy release and stress dissipation during rock destruction from the perspective of energy [41; 42; 43; 44]. The damage variable of the coal materials was defined by different parameters under cyclic loading/unloading, but the description of other mechanical behaviours of rock samples was ignored. Moreover, it was not comprehensive to describe the failure characteristics of rocks only using the damage variable, which is defined by dissipative energy. It also ignored the influence of other energy behaviours on their failure state under the cyclic loading/unloading process.