## 3 Asymmetric Failure Characteristics of Roadway Under Dynamic Pressure in the Floor  
### Stress Distribution Pattern on the Floor  
By establishing the mechanical model of the stress distribution on the working face floor, it is known that the expressions of the mining-induced stress \(\sigma_{x}\) and \(\sigma_{y}\) on the floor, the lateral pressure coefficient \(\lambda\), and the angle of the principal stress \(\alpha\) are as shown in Equations (3)-(5). In the equations, the detailed parameters of \(A_{1}\) to \(A_{7}\) are presented in Table 1.  
\[\left\{ \begin{array}{l}\sigma_{xi}=-\dfrac{2q}{\pi}\int_{\varepsilon_{i}}^{ \varepsilon_{i+1}}k_{i+1}\dfrac{qx^{3}\mathrm{d}\epsilon}{\left[x^{2}+\left(y -\epsilon\right)^{2}\right]^{2}}\\ \\ \sigma_{yi}=-\dfrac{2}{\pi}\int_{\varepsilon_{i}}^{\varepsilon_{i+1}}k_{i+1} \dfrac{qx(y-\epsilon)^{2}\mathrm{d}\epsilon}{\left[x^{2}+\left(y-\epsilon \right)^{2}\right]^{2}}\end{array} \right. \tag{3}\]  
\[\left\{ \begin{array}{l}\sigma_{x}=\dfrac{-2 qx^{3}}{\pi}\sum\limits_{i=1}^{3} k_{i+1}\biggl{(}\dfrac{A_{1}+\arctan A_{5}}{2x^{3}}-\dfrac{A_{2}-\arctan A_{7}}{2x^{3}} \biggr{)}\\ \\ \sigma_{y}=-\dfrac{2 qx}{\pi}\sum\limits_{i=1}^{3}k_{i+1}\biggl{[}\dfrac{1}{2 }\Bigl{(}A_{3}+\dfrac{\arctan A_{5}}{x}\Bigr{)}+\dfrac{1}{2}\Bigl{(}-A_{4}+ \dfrac{\arctan A_{6}}{x}\Bigr{)}\biggr{]}\end{array} \right. \tag{4}\]  
\[\left\{ \begin{array}{l}\lambda=\dfrac{q^{4}}{\pi}\sum\limits_{i=1}^{3}k_{i+1 }\sqrt{\begin{bmatrix}A_{1}-A_{2}+\arctan A_{5}+\arctan A_{7}\bigr{]}^{2}+\\ \left[x(A_{3}-A_{4})+\arctan A_{5}+\arctan A_{6}\right]^{2}\\ \\ \alpha=\sum\limits_{i=1}^{3}k_{i+1}\arctan\biggl{[}\dfrac{A_{1}-A_{2}+\arctan A _{5}+\arctan A_{7}}{A_{3}x-A_{4}x+\arctan A_{5}+\arctan A_{6}}\biggr{]}\end{array}  \right. \tag{5}\]  
Field measurements of the advanced abutment pressure have shown [29] that the peak position of the advanced abutment pressure in the working face is typically 4 to 8 m away from the coal wall, the influence range is 40 to 60 m, and the stress concentration factor is 2.5 to 3.0. Therefore, the relevant coefficients of the advanced abutment pressure \begin{table}
\begin{tabular}{c c c c c c c} \hline \(A_{1}\) & \(A_{2}\) & \(A_{3}\) & \(A_{4}\) & \(A_{5}\) & \(A_{6}\) & \(A_{7}\) \\ \hline \(\frac{x(\varepsilon_{i+1}-y)}{x^{2}+(\varepsilon_{i+1}-y)^{2}}\) & \(\frac{x(-y-\varepsilon_{i})}{x^{2}+(y+\varepsilon_{i})^{2}}\) & \(\frac{y-\varepsilon_{i+1}}{x^{2}+(\varepsilon_{i+1}-y)^{2}}\) & \(\frac{y+\varepsilon_{i+1}}{x^{2}+(y+\varepsilon_{i})^{2}}\) & \(\frac{\varepsilon_{i+1}}{x}\) & \(\frac{y+\varepsilon_{i+1}}{x}\) & \(\frac{y+\varepsilon_{i}}{x}\) \\ \hline \end{tabular}
\end{table} 
Table 1: The detailed parameters of \(A_{1}\) to \(A_{7}\). Figure 3: Mechanical model of the underlying roadway in the floor of the working face. are determined as follows: \(\epsilon_{1}\) = 10 m, \(\epsilon_{2}\) = 30 m, \(\epsilon_{3}\) = 200 m, \(k_{1}\) = 1.5, \(k_{2}\) = 0.5, \(k_{3}\) = 0, \(\gamma\) = 25 kN/m\({}^{3}\), and \(H\) = 400 m.  
Substituting the relevant parameters, the three-dimensional surfaces of the vertical mining-induced stress \(\sigma_{x}\) of the working face floor, the horizontal mining-induced stress \(\sigma_{y}\) of the floor, the angle of the principal stress \(\alpha\), and the lateral pressure coefficient \(\lambda\) of the floor are plotted as shown in Figure 4.  
From the analysis in Figure 4, the following can be seen:  
1. Distribution characteristics of the mining stress of the floor: 1. The mining stress of the floor is all compressive stress (\(\sigma_{x}\) < 0 MPa, \(\sigma_{y}\) < 0 MPa), and the absolute value of the mining stress continuously decreases with the increase in the horizontal distance \(y\) and the vertical distance \(x\).