## 1 Introduction
### Analysis of Influencing Factors on Mechanical Characteristics of Gas-Containing Coal  
(1) Effect of confining pressure on mechanical properties of gas-containing coal  
Relevant scholars [37] have made linear fittings between compressive strength and the confining pressure of gas-containing coal under different confining pressure conditions, and they observed that there is an obvious linear relationship between compressive strength and confining pressure. With an increase in confining pressure, the compressive strength of gas-containing coal increases gradually, and its bearing capacity also increases continuously. (2) The effect of porosity on mechanical properties of gas-containing coal  
The macroscopic method is usually adopted to describe the porosity of gas-containing coal, which is defined as the percentage of the pore volume in the material to the total volume of the material in the natural state:  
\[n=\frac{v_{p}}{v}\times 100\%=\frac{v-v_{s}}{v}\times 100\% \tag{1}\]  
where \(n\) is the porosity of the gas-containing coal, which is dimensionless; \(v_{p}\) is the volume occupied by pores and cracks in gas-containing coal; \(v_{s}\) is the solid volume of gas-containing coal. According to the above equation, when the porosity of coal changes, the volume deformation of coal will be caused, and the larger the porosity, the more obvious the deformation of gas-containing coal [38]. (3) Influence of seepage on mechanical properties of gas-containing coal  
According to the basic theory of coal and rock mass deformation and gas seepage, coupled with the interaction between gas and deformation of coal, a mathematical equation of gas-solid coupling in the fracture process of gas-containing coal can be established [39]. Consistent with the linear permeation law, the gas motion equation is established as follows:  
\[q_{i}=-\lambda_{ij}\frac{dP}{dn} \tag{2}\]  
where \(q_{i}\) is the gas seepage velocity component (I = 1, 2, 3... ) (m/d); \(\lambda_{ij}\) is the component of the permeability coefficient tensor (\(i\), \(j\) = 1, 2, 3,... ) (m\({}^{2}\)/(MPa\({}^{2}\)-d)); \(P\) is the square of the coal seam's gas pressure (MPa\({}^{2}\)). According to the gas content coefficient method, the gas content equation can be expressed as follows:  
\[X=A\sqrt{p} \tag{3}\]where \(X\) is the gas content in coal rock (m\({}^{3}\)/t); \(A\) is the gas content coefficient of coal seam (m\({}^{3}\)/(m\({}^{3}\)-MPa\({}^{1/2}\))); \(P\) is coal seam gas pressure (MPa). At the same time, seepage tests under triaxial compression show the following [40]: There is a negative exponential relationship between the effective volumetric stress and permeability before the peak point of gas-containing coal samples. After the peak point, there is still an exponential relationship between effective volumetric stress and permeability, but the coefficient changes, which is different from that before the peak point. The permeability of coal samples containing gas changes in the opposite direction to the effective volumetric stress, that is, when the effective volumetric stress increases, permeability decreases, and vice versa. Effect of gas pressure on mechanical properties of gas-containing coal  
Under the condition of certain axial and confining pressures, the increase in gas pressure has two effects on outburst coal samples: one is that its mechanical effect leads to the increase in coal pores; the other is that its adsorption effect leads to a decrease in coal pores. There is a critical gas pressure that is less than the critical gas pressure range, and an increase in gas pressure caused by pore expansions is smaller than the adsorption of gas caused by pore contraction, resulting in a reduction in permeable pores and gas permeability and a decrease in the permeability coefficient.