# Research on the Laws of Overlying Rock Fracture and Energy Release under Different Mining Speeds
## 2 Influence of Working Face Advancing Speed on Energy Release of Overlying Strata  
Observations and analyses of mine pressure indicate that a working face advancing at high speed tends to facilitate the breaking of the overlying rock structure in the higher rock strata, leading to the formation of a masonry beam structure [38]. The destruction of this stable masonry beam structure releases significant energy that is transmitted to the working face of the mining area. Consequently, investigating the breaking mechanism of mining speed on the rock mass masonry beam structure above the mining face is crucial for preventing rock burst disasters. As the working face advances, the rotary subsidence of the masonry beam structure diminishes with the increased height of the overlying rock. Figure 1a illustrates the breaking form of the masonry beam in the key layer of the overlying rock at the working face. The rock block situated above the gangue that does not come into contact with the lower part is referred to as an untouched gangue fracture, depicted in Figure 1b. In contrast, a touching gangue fracture occurs when the rock block breaks upon touching the lower gangue, as shown in Figure 1c. Due to the proximity of the unfractured gangue in the low voussoir beam to the coal seam, studying the energy release law during a fracture is essential, given the significant impact of the disaster that can result from this. To streamline the application of mechanical theory in calculations, rock block A is conceptualized as a simplified beam structure from which a mechanical model is derived, as shown below in Figure 2.  
In accordance with the stability theory of broken overburden rock [39], the load \(R\) exerted by broken rock block B on unbroken rock block A is represented as follows:  
\[R=\frac{4h_{0}-3\sin\theta}{2(2h_{0}-\sin\theta)}qL \tag{1}\]  
In Equation (1), \(h_{0}=\frac{h}{L}\) represents the ratio of the thickness to the length of the rock block, \(\theta\) denotes the rotation angle of rock block B, \(c\) signifies the uniform distribution load, \(h\) represents the thickness of rock mass, and \(L\) denotes the length of the rock block. Under the combined influence of the concentrated load \(R\) and uniform load \(q\), the maximum deflection value of the structural beam is observed at the end structure position. The expression for deflection \(\omega\) is given as follows:  
\[\omega=\frac{22h_{0}-15\sin\theta}{24(2h_{0}-\sin\theta)}\frac{qL^{4}}{EI} \tag{2}\]  
Figure 1: The figure shows the fracture types of a voussoir beam. Figure 2: The figure shows a simplified mechanical model of rock block A.  
where \(I\) represents the moment of inertia of the rock section, and \(E\) denotes the elastic modulus of the rock mass. The maximum stress value \(\sigma\) of the single-sided fixed beam structure is located at the fixed end, and its expression is provided as follows:  
\[\sigma=\frac{3h-2L\sin\theta}{2h-L\sin\theta}\frac{6\mu L^{2}}{h^{2}}\leq R_{t} \tag{3}\]  
where \(R_{t}\) represents the tensile strength of the rock beam structure. The relationship between the rotation angle \(\theta\) and the breaking interval of the low voussoir beam structure is expressed as follows:  
\[\sin\theta=\frac{2R_{t}h^{3}-18 hqL^{2}}{R_{t}h^{2}L-12 qL^{3}} \tag{4}\]  
The relationship between the rotation angle and the released energy during fracture is as follows:  
\[U=\frac{q^{2}L^{5}}{20 EI}+\frac{4h_{0}-3\sin\theta}{(2h_{0}-\sin\theta)}\frac{ q^{2}L^{5}}{8 EI}+\left(\frac{4h_{0}-3\sin\theta}{(2h_{0}-\sin\theta)}\right)^{2} \frac{q^{2}L^{5}}{12 EI} \tag{5}\]  
Formulas (4) and (5) clearly show that both the breaking distance and the energy released during the fracturing of the masonry beam structure depend on the rotation angle. With an increase in the rotation angle, there is a corresponding rise in both the breaking distance and the energy released.