# Middle Rock Pillar Stability Criteria for a Bifurcated Small Clear-Distance Tunnel
## 7 Conclusions  
This study focused on the bifurcation small clear-distance tunnel of the Xiamen Haicang Shugang evacuation channel under the underground interchange tunnel. The stability criteria of the MRP during the design and construction phases were analyzed through numerical simulation. The main conclusions are as follows:  
1. By varying the cohesion of the surrounding rock while keeping the other parameters constant, the stability state of a small clear-distance tunnel was investigated. It was observed that increasing the cohesion of the surrounding rock resulted in a longer distance of stable tunnel excavation. When the cohesion exceeded 1.4 MPa, the small clear-distance tunnel remained stable even with increasing clear distance. The minimum cohesion at convergence of the small-clearance tunnel excavation model increased as the density and modulus of elasticity of the surrounding rock increased. Therefore, this study proposes an initial determination of small-clearance tunnel stability on the basis of the parameters of the surrounding rock density, modulus of elasticity, and cohesion during the design stage. 2. By analyzing displacement data from monitoring points obtained through simulation, the relationships between horizontal clearance convergence and vertical displacement of the main line tunnel and ramp tunnel and between horizontal displacement and vertical displacement of the MRP were examined. This analysis led to the establishment of horizontal and vertical displacement criteria for the MRP. 3. This study analyzes the relationship between the convergence of horizontal clearance and the vertical displacement of the main line tunnel and ramp tunnel, as well as the stress of the MRP. The stress criteria for ensuring the stability of the MRP were determined via the linear regression method. 4. By analyzing the distribution and changes in the plastic zone of the MRP during excavation, it was determined that the plastic zone was initially distributed in the inner wall and center of the tunnel after the main tunnel and ramp were excavated. It was important to carefully consider construction speed and support measures to ensure construction safety and rock mass quality. 5. To assess the stability of the MRP, a plasticity zone index called \(C\) was introduced. By examining the correlation between \(C\) and the convergence of the horizontal headroom and the vertical displacement of the vault in small-clearance tunnels, the plasticity criteria for the stability of the MRP were proposed. 6. In the construction of a bifurcated small-clearance tunnel, the stability of the MRP can be dynamically determined and controlled by considering the displacement, stress, and plasticity zone. 7. The proposed criteria, derived from a concrete engineering case study, can be extended to other similar projects with comparable frameworks. The threshold values and variables should be determined based on project-specific characteristics, such as clear-distance range, geological complexity, and data availability. **Author Contributions:** Conceptualization, [PERSON], T.C., Y.G. and X.L. ; methodology, [PERSON], Y.L. and T.C. ; software, Y.L. and T.C. ; validation, [PERSON], Y.L., T.C., A.C., H.L. and X.L. ; formal analysis, [PERSON], Y.L., T.C. and A.C.; investigation, J.W., T.C. and X.L. ; resources, J.W. and X.L. ; data curation, Y.L., T.C., A.C. and H.L. ; writing--original draft preparation, [PERSON], Y.L. and A.C.; writing--review and editing, [PERSON], Y.L., X.L. and Y.G. ; visualization, [PERSON] and Y.L. ; supervision, [PERSON]; project administration, [PERSON], T.C., L.L. and X.L. ; funding acquisition, [PERSON] All authors have read and agreed to the published version of the manuscript. **Funding:** This research was funded by the Sinohyro Bureau No.