## 4 Stress Distribution Characteristics of Roadway Surrounding Rock
### Influence of Aspect Ratios on Stress Distribution for Surrounding Rock in Rectangular Roadways  
In order to study the laws on the influence of different aspect ratios on the stress distribution in surrounding rock of rectangular roadways, tangential stresses in a total of five roadway models were calculated when the vertical force was \(P_{0}\) and the side-pressure coefficients \(\lambda\) were 0, 0.5, 1, 1.5 and 2. Figure 6 shows tangential stress distribution curves of roadway surrounding rock with different aspect ratios. The stress distribution for \begin{table}
\begin{tabular}{c c c c c c} \hline \hline _b/h_ & \(k\) & \(R\) & _c_\({}_{1}\) & _c_\({}_{3}\) & _c_\({}_{5}\) \\ \hline
7 & 0.1209 & 9.7724 & 0.7251 & \(-\)0.0790 & \(-\)0.0344 \\
8 & 0.1140 & 10.9083 & 0.7544 & \(-\)0.0718 & \(-\)0.0325 \\
9 & 0.1081 & 12.0419 & 0.7781 & \(-\)0.0658 & \(-\)0.0307 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._  
Figure 5: Stress distribution of \(\sigma_{\theta}\) in polar coordinate system with different aspect ratios. surrounding rock in rectangular roadways is displayed under nine different changing conditions of side-pressure coefficients, where roadway aspect ratios \(b/h\) were from 1 to 9. As shown in Figure 6, displaying tangential stress distribution curves of roadway surrounding rock with different aspect ratios, when \(b/h\) was smaller than 2, the stress distribution was relatively smooth; when \(b/h\) was larger than 2 but smaller than 4, the stress distribution along surrounding rock was relatively steep and suddenly reached the maximum value at the corner; when \(b/h\) was larger than 4, the stress upon rock surrounding the roadway increased sharply from both the two sides and the roof near the corner of the roadway towards its angular point, and then reached the maximum value, and most of the roadway roof remained in a stable range; when \(b/h\) was equal to 1, stress values in the side wall centers were 0.67 \(P_{0}\), the stress value in the roof center was 0.67 \(P_{0}\), and the stress value at the angular point was 6 \(P_{0}\), 8.96 times the value in the side wall center and 8.96 times the value in the roof center; then, when \(b/h\) was equal to 4, stress values in the side wall centers were 1.74 \(P_{0}\), the stress value in the roof center was 0.29 \(P_{0}\), and the stress  
Figure 6: Tangential stress distribution curves of roadway surrounding rock with different aspect ratios. value at the angular point was 8.25 \(P_{0}\), 4.74 times of the value at the side wall center and 28.44 times of the value in the roof center; it can be seen that with the increase in aspect ratio, the smaller the tangential stress upon the roadway roof, the larger the tangential stresses upon both side walls, and the smaller its difference from the maximum stress upon the angular point. The stress on surrounding rock at the roadway corner varies significantly, and the stress distributions along the roof, the base plate and the two side walls of the roadway are relatively flat. The stresses upon both side walls of the roadway increase with the increase in aspect ratio while the stress upon the roof is the opposite situation. The increase in side-pressure coefficient has a particularly prominent influence on side walls of the roadway, and the pressure of surrounding rock will accumulate in the roadway corner. The larger the aspect ratio, the flatter the stress transition on both side walls, and the more intense the stress transition on the roof. The stress concentration at the roadway corner was more obvious when \(b/h\) was larger than 4, and shear failure was more likely to break out in this case, resulting in the roof caving and then instability in the surrounding rock of roadway. Therefore, when a roadway with super-large sections and a \(b/h\) larger than 4 is under construction, a reinforced support to the roadway corner will be necessary [41].