## 3 Asymmetric Failure Characteristics of Roadway Under Dynamic Pressure in the Floor
### Asymmetric Failure Characteristics of Underlying Roadway  
With the advancement of the working face, the stress distribution of the underlying roadway changes significantly. Moreover, due to the continuous changes in the lateral pressure \(P_{3}\) of the surrounding rock and the angle of the principal stress \(\alpha\), the shape and size of the plastic zone of the surrounding rock keep changing, posing a serious threat to the stability of the roadway. To study the dynamic failure situation of the underlying roadway of the floor, in this paper, the relevant parameters of Equation (9) are assumed as follows: cohesion \(c=4.0\) MPa, internal friction angle \(\varphi=30^{\circ}\), roadway radius \(r=2.5\) m, and surrounding rock radius \(R=3.5\) m. Using the \"Mathematica 14\" software, based on the different vertical distances (x = 15 m, 17.5 m, 20 m, 27.5 m, and 35 m) between the working face and the roadway, the \(f\) curves during the advancement process of the working face (y = 60\(\sim\)5 m) were calculated and plotted. Taking the maximum value of the \(f\) equation as the research object and combining the built-in \"Max\" function of the program, the variation patterns of the maximum value of the \(f\) equation and the angle \(\beta\) between it and the horizontal axis were studied. The \(f\) curves are presented in Figures 5-9. \begin{table}
\begin{tabular}{c c c} \hline
**Parameter** & **Expression** & **Parameter** & **Expression** \\ \hline \(A_{8}\) & \(\frac{x(y+z_{1})}{z^{2}(y+z_{2})^{2}+\arctan\left(\frac{y+z_{1}}{x}\right)}+ \arctan\left(\frac{z_{2}-y}{x}\right)\) & \(A_{13}\) & \(\frac{y-z_{3}}{x^{2}+(y-z_{3})^{2}}+\frac{\arctan\left(\left(z_{3}-y\right)/x \right]}{x}\) \\ \(A_{9}\) & \(\frac{x(y+z_{1})}{z^{2}(y+z_{2})^{2}+\arctan\left(\frac{y-z_{1}}{x}\right)^{2} +\arctan\left(\frac{y-z_{2}}{x}\right)}+\arctan\left(\frac{z_{3}-z}{x}\right)\) & \(A_{14}\) & \(\frac{\arctan\left(\left(y+z_{3}\right)/x\right]}{x}-\frac{y+z_{3}}{x^{2}+(y+z _{2})^{2}}\) \\ \(A_{10}\) & \(\frac{y}{x^{2}+y^{2}}+\frac{y-z_{3}}{x^{2}+(y-z_{3})^{2}}+\frac{2\pi\pi\pi}{2 \pi\pi}\) & \(A_{15}\) & \(\sin[2\theta-2\arctan(B_{1}/B_{2})]^{2}\) \\ \(A_{11}\) & \(\frac{y+z_{1}}{z^{2}(y+z_{1})^{2}+\frac{y-z_{2}}{x^{2}+(y-z_{2})^{2}}+\frac{ \arctan\left(\left(z_{3}+z_{1}\right)/x\right]}{2\pi}}+\frac{\arctan\left( \left(z_{3}-z\right)/x\right]}{2\pi}\) & \(A_{16}\) & \((H+x)\gamma\) \\ \(A_{12}\) & \(\frac{y}{x^{2}+y^{2}+\frac{z_{1}(x-y)}{x^{2}+(y-z_{1})^{2}}+\arctan\left( \left(z_{1}-y\right)/x\right)+\arctan\left(y/x\right)}\) & / & / \\ \(B_{1}\) & \(-2A_{10}Hk_{1}x\gamma-2A_{11}Hk_{2}^{22}\gamma-(A_{13}+A_{14})Hx\gamma/\pi\) & \(B_{2}\) & \(2A_{9}Hx^{3}\gamma-2A_{12}Hk_{1}x^{3}\gamma-2A_{8}Hk_{2}x^{3}\gamma\) \\ \(C_{1}\) & \(1+\sqrt{B_{1}^{2}+B_{2}^{2}}/[(H+x)\gamma]\) & \(C_{3}\) & \(1-\sqrt{B_{1}^{2}+B_{2}^{2}}/[(H+x)\gamma]\) \\ \(C_{2}\) & \(-1+\sqrt{B_{1}^{2}+B_{2}^{2}}/[(H+x)\gamma]\) & \(C_{4}\) & \(\frac{3^{4}\cos[2\theta-2\arctan(B_{1}/B_{2})]}{R^{4}}\) \\ \hline \end{tabular}
\end{table} 
Table 2: Relevant parameters of Mohr-Coulomb criterion \(f\). Figure 5: The \(f\) curve of the surrounding rock of the roadway with vertical distance \(x=5\) m.  
Figure 6: The \(f\) curve of the surrounding rock of the roadway with vertical distance \(x=12.5\) m.  
Figure 7: The \(f\) curve of the surrounding rock of the roadway with vertical distance \(x=20\) m.  
The following can be derived from the analysis of Figures 5-9:  
1. As the horizontal distance \(y\) decreases, the criterion \(f\) of the surrounding rock of the roadway transitions from \"circular\" through \"rectangular\" and finally transforms into \"butterfly-like\".