## 1 Introduction  
In deep underground coal mines, the strata and coal seams are always subjected to both static geo-stress and dynamic stress disturbance. Therefore, coal burst hazards usually result from the superposition of dynamic and static loads [1, 2]. The quasi-static and dynamic mechanical behaviors of rock mass and coal have been investigated in a large number of theoretical and experimental studies [3, 4]. It is well known that the mechanical behaviors of rock mass and coal under dynamic loading conditions are quite different from those under quasi-static conditions due to the strain rate effect. Materials with higher strain rates are more likely to show greater strength during mechanical tests, while their mechanical behaviors become more complex when the static and dynamic loading are both considered. The burst threshold and energy evolution of the coal body may vary from case to case, because it depends on the couple static and dynamic loading conditions. Therefore, the coupled effect of static and dynamic loads is expected to be considered in practical engineering, especially for dynamic disasters. As an ideal and reliable mechanical test apparatus to study the dynamical mechanical behaviors of rock, the split Hopkinson pressure bar (SHPB) system has been widely used to determine the dynamic response and instability characteristics of rock mass and coal under high strain rates [5, 6, 7, 8]. To study the mechanical behaviors of rock mass under coupled static-dynamic loads, [PERSON] et al. [9] developed an improved SHPB system which allows the specimen to be subjected to coupled axial static pre-stress and axial impact loading. Based on the coupled static-dynamic SHPB test method, great progress has been made in terms of the study of the mechanical behaviors of rock mass in complex stress conditions. [PERSON] et al. [10] revealed that for a given static pre-stress, rock strength rises with the increase in dynamic loads. Moreover, the increase in pre-stress may change the failure patterns and results in more shear cracks. [PERSON] et al. [11] conducted a series of coupled static and dynamic loading tests of rock specimen with a hole and investigated the dynamic failure characteristics of rock specimens at different pre-stress levels. The result shows that static pre-stress strongly affects the failure intensity and the primary fractures are caused by the combination of both static and dynamic stress. [PERSON] et al. [12] experimentally investigated the mechanical behaviors of rock specimens containing two non-coplanar fissures. [PERSON] et al. [13] reveal that the effect of confining stress on the dynamic strength of coal may be greater than that of axial pre-stress. Their results show that the specimens' mechanical properties are highly dependent on the dynamic strain rate when the static pre-stress keeps constant in some cases. The coupled static and dynamic mechanical behaviors of rock mass in non-coal underground mines have been extensively investigated in many studies, as mentioned above. Compared to the rock mass, coal is always characterized by lower strength and less bump proneness [14]. Nevertheless, with the increase in mining depth, coal mining may be associated with coal burst hazards as the coal body is generally highly stressed in deep coalmines. As a result, more and more coal bump hazards are happening in many coal mining countries including the USA, China, Poland and Australia [15; 16; 17]. However, studies on dynamical-mechanical response characteristics of coal under coupled static and dynamic stress conditions remain insufficient. More studies are expected to improve the understanding of the mechanical behaviors and instability mechanism of coal under coupled static and dynamic stress conditions. Compared with laboratory experiments, numerical simulations are able to exactly record the stress and energy states and failure evolution, which is helpful in the determination of specimens' mechanical behavior and their failure mechanism.