## 1 Introduction  
Mining tremors are highly common dynamic phenomena in mining operations, which are essentially the release of locally accumulated elastic energy during rock fractures. The intensity of mining tremors is determined by the fracture scale, mechanical properties of the rock materials, stress conditions of the seismic source, fracture model, and many other factors [1, 2]. Similar to earthquakes, strong tremors cause the violent shaking of ground buildings [3, 4], the collapse of underground cavities, gas outbursts [5], and rockbursts [6]. In particular, at larger depths of mining operations, underground openings are under conditions of high geo-stress and the disturbance of strong mining tremor, which can easily cause surrounding-rock fracture, disintegration, and caving to the goaf; it can even induce dynamic disasters. In recent decades, scholars have conducted a lot of research on the stress distribution and failure mechanism of underground roadways [7, 8, 9, 10, 11]. In 1898, [PERSON] [8] obtained the analytical formula of the stress field around the circular cavity for the first time based on the assumption of the plane strain. In 1952, [PERSON] [9] analyzed the influence of the hole shape on the stress concentration of the surrounding rock. Then, the stress field distribution of a non-circular roadway is obtained through the complex function method [12, 13, 14]. [PERSON] et al. [15] studied the mechanism of the progressive failure of three-dimensional roadways, indicating that the surrounding rock of the roadway would fail in spalling when the tangential stress exceeds its compressive strength. From this research, it can be found that most of the studies on the stress concentration around the cavity mainly focus on the static and quasi-static conditions and rarely consider the impact of dynamic disturbances. Mine tremors mainly radiate energy in the form of stress waves. When a stress wave arrives at underground openings, it transmits and bends along the hole and generates diffraction owing to the difference in wave impedance between the rock and air. This causes the stress at the edge of the hole to be significantly higher than that in other areas. [PERSON] and [PERSON] [16] pointed out that when stress waves caused by an explosion reach the tunnel boundary, they will be reflected and converted into tensile stress waves, resulting in the failure of the surrounding rock (i.e., spall failure). Similarly, the literature [17; 18; 19; 20] also focuses on the influence of rock tensile strength and stress wave incident strength on spalling. However, the spall failure is only a part of the reason for roadway failure induced by stress waves. As a whole structure, the stress distribution of the surrounding rock differs greatly in different regions of roadways under the disturbance of stress waves, rather than only tensile stress. Compression caused by stress wave incidence is also an important cause of hole failure [21; 22; 23]. Therefore, the stress evolution process of the whole structure of the hole generated by stress wave incidence has drawn attention. [PERSON] and [PERSON] [23] elaborated on the method for solving dynamic stress concentration, which lay the foundation for the following research in the field. Then, the dynamic stress distribution of the surrounding rock under more complex incident waves and irregular roadway shapes is studied through the indirect boundary integration equation method and the wave function expansion method [24; 25; 26; 27; 28]. However, these studies only focus on the stress change around the roadway at the moment of incident stress waves, ignoring the influence of the rock's mechanical strength on the stability of the surrounding rock, and lack in-depth investigations into the failure process of the surrounding rock. The particle flow code (PFC) has been widely used to study the mechanical properties and micro-failure mechanism of rocks.