# Nonlinear Stability Analysis of Shallow-Buried Bias Tunnel Based on Failure Mode Improvement
## 7 Conclusions  
1. When conducting the support design calculations for the surrounding rock in the circular arc failure mode of shallow-buried tunnels in slope sections, the upper-bound limit analysis method demonstrates significant advantages. Compared with the code-based method and the limit equilibrium method, the upper-bound limit analysis method yields the smallest value of surrounding rock pressure. Additionally, it effectively reduces the design requirements and engineering costs of the support structure, thereby achieving higher economic benefits. 2. The enclosed rock pressure under the circular damage mode of shallow-buried tunnel in the sloping section increases with the increasing value of the geotechnical nonlinear coefficient \(m\). When the value of \(m\) is larger, the effect on the enclosing rock pressure is more significant; the nonlinear damage criterion cannot be crudely simplified to a linear criterion; otherwise, it will underestimate the upper limit value of the enclosing rock pressure, and decreasing the ratio of the horizontal support force to the vertical support force \(K\) will cause a significant increase in the enclosing rock pressure. 3. The increase in slope crest load and the enlargement of the burial depth ratio have a significantly greater impact on the soil on the shallow-buried side than on the deep-buried side. This can easily cause the circular arc failure mode of the shallow-buried tunnel to shift towards the shallow-buried side, while also increasing the stress concentration in the surrounding rock on the shallow-buried side and reducing the overall stability of the tunnel. In the actual project, for special geological conditions such as loess sedimentation areas, reinforcement measures can be taken in advance for the rock and soil body on the shallow side to prevent engineering accidents caused by the offset. 4. An increase in axial tensile stress and a decrease in cohesion will cause the damage surface to extend outward and the area of shear zone to increase. The increase in axial tensile stress will cause the surrounding rock pressure to increase, while the increase in cohesive force will lead the surrounding rock pressure to decrease. When the surrounding rock conditions are poor, the surrounding rock of the tunnel is prone to forming a large plastic zone, which may pose safety hazards. By employing numerical simulation and based on the surrounding rock conditions and the monitoring of data obtained during the construction phase, measures such as shotcrete-anchorage support and grouting reinforcement can be implemented to enhance the stability of shallow-buried, eccentrically loaded tunnels. 5. The current study on the nonlinear stability analysis of shallow-buried, eccentrically loaded tunnels in circular arc failure mode is limited to the scenario of simple eccentric loading. Future research will extend to the stability analysis of tunnels under coupled hydrological actions and the reinforcement of tunnel stability under the influence of multiple complex factors. Additionally, in-depth explorations will be conducted in conjunction with practical engineering cases. Conceptualization, W.L. ; methodology, W.L. and G.X. ; software, Z.T. ; validation, W.L. and G.X. ; formal analysis, G.X. and Z.T. ; investigation, X.L. and H.W. ; resources, W.L. and J.C.; data curation, X.L. and H.W. ; writing--original draft preparation, G.X. and Z.T. ; writing--review and editing, G.X. ; visualization, Z.T. ; supervision, W.L. and X.L. ; project administration, J.C.; funding acquisition, W.L. and J.C. All authors have read and agreed to the published version of the manuscript.