## 4 Stress Distribution Characteristics of Roadway Surrounding Rock
### Analysis on Safe Side-Pressure Coefficient Range for Roadway with Different Aspect Ratios  
Due to the stress redistribution along surrounding rocks after roadway excavation, surrounding rocks on the two side walls bulge inward and trigger large deformation. An unsupported roof area exists before any support to surrounding rock in the roadway. The larger the unsupported roof span, the more susceptible the lower part of the roof will be to gravity stress, thus generating a downward tensile stress and triggering bed separation and cracking. The large space below broken stratum can cause the rock beam to break and collapse easily [43]. As the tensile strength of rock is generally 1/20 to 1/10 of its compressive strength, the roof of a roadway with super-large sections is extremely unstable under tensile stress and prone to roof caving and other similar disasters. Therefore, avoidance of tensile stress upon the surrounding rock surface of a roadway is a key factor to improve the stability in roadway surrounding rocks, and particular attention should be paid to preventing a fracture in the roadway roof center.  
Figure 7: Tangential stress distribution curve of roadway surrounding rock under different side-pressure coefficients.  
Threshold values \(\lambda_{\rm up}\) and \(\lambda_{\rm down}\), between which there is no tensile stress upon the roadway boundary, were calculated via Equation (23). When \(\lambda\) is larger than \(\lambda_{\rm up}\), tensile stresses take place on both side walls of the roadway; when \(\lambda\) is smaller than \(\lambda_{\rm down}\), tensile stress takes place on the roof; when \(\lambda\) is larger than \(\lambda_{\rm up}\) but smaller than \(\lambda_{\rm down}\), compressive stresses take place on all roadway boundaries. According to Figure 8, as the roadway aspect ratio increased from 1 to 9, its \(\lambda_{\rm up}\) increased from 1.823 to 5.865 and its \(\lambda_{\rm down}\) increased from 0.549 to 0.888. When these side-pressure coefficients of the environment where the roadway is located exceed these threshold values, tensile stress takes place on the roadway boundary, triggers tensile failure and thereby causes instability in a roadway with super-large sections.  
The following results were obtained by fitting the calculated results in Figure 8:  
\[\lambda_{up}:y_{1}=1.3892+0.4108x_{1}+0.0098x_{1}^{2},R^{2}=0.99 \tag{24}\]  
\[\lambda_{down}:y_{2}=0.4739+0.0985x_{2}-0.0599x_{2}^{2},R^{2}=0.98 \tag{25}\]  
It can be seen from Figure 8 that when \(\lambda\) is larger than 1.823, the aspect ratio increased by the side-pressure coefficient can improve the stress condition of surrounding rock and avoid side wall failure due to excessive horizontal stress. When \(\lambda\) is smaller than 0.888, a reduced aspect ratio can avoid the influence of tensile stress upon the roadway roof. These conclusions conform to the analysis results concerning the influence of the aspect ratio upon the stress distribution along surrounding rock, as given in Sections 4.1 and 4.2 in this paper.  
The limiting side-pressure fitting curve was obtained from Equations (24) and (25). As can be seen from the comparison in Table 3, both calculated results and fitting results in this paper are within the scope of the literature. Therefore, the range of side-pressure coefficient subject to no tensile stress can be calculated through the calculation method or the fitting formula in this paper during the actual excavation, and the results can serve as a theoretical reference for roadway design and surrounding rock stability analysis.  
Figure 8: The limit side-pressure coefficient range where no tensile stress occurs at the roadway boundary.