# Study of the Failure Mechanism of Soft Rock Mining Roadways Based on Limit Analysis Theory
## 4 Conclusions  
1. Based on the limit analysis theory of plastic mechanics, a rigid sliding block system model of the failure of the rock surrounding a soft rock roadway under dynamic pressure is constructed. The formulas for calculating the self-weight power of the slider in the velocity discontinuity line of the rock surrounding the roadway, the power of the surrounding rock pressure, and the energy dissipation rate of the velocity discontinuity line are derived, and the upper limit objective function of the height of the velocity discontinuity line is obtained.
2. With adoption of the return airway of the 1506 working face in Anyang Coal Mine as the engineering background, the failure height \(h\) of the roadway roof under different overburden loads \(\sigma_{\rm s}\) is calculated in Origin. The results show that when the overburden load \(\sigma_{\rm s}\) < 3.54 MPa, the velocity discontinuity line is mainly distributed in the coal wall. When 3.54 MPa < \(\sigma_{\rm s}\) < 3.77 MPa, the velocity discontinuity line extends from the coal side to the direct roof and the maximum failure height is 4.3 m. When the overburden load \(\sigma_{\rm s}\) > 3.77 MPa, the velocity discontinuity line penetrates the interface between the direct roof and the basic roof and extends upward. When \(\sigma_{\rm s}\) = 9.0 MPa, the failure height is 15.62 m.
3. By building a physical similarity model of the 1506 return airway, the failure mode of the roadway and the failure height of the roof are obtained by applying different overburden loads \(\sigma_{\rm s}\). The results show that the failure mode of the roadway and the failure height of the roof in the physical similarity simulation are basically consistent with the theoretical analysis. Shear failure first occurs on the side of the roadway. The fractures expand along the blind support area and low-strength support area above the syncline of the roadway bottom angle. Finally, arc-shaped shear slip cracks are formed. At the same time, the support strength of the angled anchor cable and bolt in the roadway shoulder is weakened. When the fracture passes through the interface between the direct roof and the basic roof, a shear slip zone is formed. Under the action of self-weight and roof pressure, the rock mass in the shear slip zone is unstable and deforms.  
Methodology, S.G. and T.Y.; data curation, Y.H. and J.W.; manuscript writing, S.G.; similar simulation experiments S.G., Y.H. and H.W.; writing--review and correction, J.Z. All authors have read and agreed to the published version of the manuscript.  
This study was supported by the National Natural Science Foundation of China project (51774229, 52004200), the order of sponsors is [PERSON], [PERSON]. Thank you very much for the support of the National Natural Science Foundation project.  
Not applicable.  
The relevant data in this manuscript were obtained from field measurement and tests, which are real and effective.  
Thank you to [PERSON] from Shaanxi Branch of China United Network Communications Co., Ltd.; [PERSON] from Shaanxi Mineral Resources Survey and Evaluation Center; [PERSON] from China Coal Xi'an Design Engineering Co., Ltd.; and Anyang Coal Mine, for their convenience and support in writing this manuscript.  
The authors declare that there are no conflicts of interest in the publication of this paper.