# Middle Rock Pillar Stability Criteria for a Bifurcated Small Clear-Distance Tunnel
## 6 Discussion
However, if any of the \(S1\) and \(C\) values exceeded the corresponding limit values, the MRP was considered unstable. The main advantage of using these criteria was the ability to dynamically adjust the target of evaluation, connecting it to the deformation and stress of the MRP with respect to the construction process. This enabled the control of MRP stability. Furthermore, by reflecting the fundamental principles of deformation and stress between the tunnel and the MRP, the criteria avoided the influence of construction methods, excavation progress, and other factors, making it more aligned with actual requirements. This study focused on examining the displacement, stress, and plastic zone criteria to determine the stability of intermediate rocks. In the construction process, it was essential to assess intermediate rock inclusions. This can be achieved by synthesizing three evaluation angles, as depicted in Figure 23, to establish comprehensive criteria. To apply these criteria effectively, it is necessary to determine the net distance between the rock and clarify the width-span ratio. Furthermore, \(H\), \(V\), \(S\), and \(C\) values must be obtained based on the stress criteria formula and plastic zone criteria formula, taking into account the width-span ratio. Additionally, deformation data were determined by analyzing the settlement of the arch roof and the convergence of the horizontal clearance of the two tunnels. If the fracture rock mass parameters required for stability analysis were proximate to the initial parameters of the surrounding rock (as illustrated in Table 4 and if one of the indicators, such as displacement, stress, or the plastic zone, exceeded the corresponding limit value, the MRP was considered unstable. In cases where the grade of the MRP exceeded grade III, the cohesion force corresponding to the limit state increased, as did the stress value at the central position of the MRP. Consequently, when assessing the stability of the MRP, the dominant parameters to consider were \(H\), \(V\), and \(C\) derived from the displacement criteria and the plastic zone criteria, whereas the stress criterion \(S\) serves as a secondary parameter. If the \(H\), \(V\), and \(C\) values exceed their respective limit values, this indicates instability in the MRP. Alternatively, if the grade of the MRP was lower than grade III, the cohesive force and elastic modulus corresponding to the limit state decreased. This results in increased vertical displacement in the upper region of the MRP and increased horizontal displacement in the middle region. Furthermore, the stress at the central position of the MRP decreased. In such cases, when assessing the stability of this type of MRP, the main parameters to consider were \(S\) and \(C\) derived from the stress criteria and the plastic zone criteria, whereas the displacement criteria \(H\) and \(V\) serve as secondary parameters. Judging the instability of the MRP solely on the basis of \(H\) and \(V\) values exceeding the limit value was not possible. However, if either the \(S\) or \(C\) value exceeds the corresponding limit value, it indicates instability in the MRP. On the whole, the use of these criteria was subject to dynamic change and can be attributed to the deformation and stress of the MRP as a result of the construction process. It was used to ensure the stability of the MRP by monitoring the deformations of the two tunnels. Additionally, by reflecting the fundamental laws of deformation and stress between the tunnel and the MRP, it can also account for factors such as construction schemes and excavation methods. Therefore, the criteria were better suited to practical requirements. The proposed criteria were derived from a concrete engineering case study, with the methodology applicable to future tunnel projects. When extending this approach, tunnel sections should be selected based on lithological variations, structural layout, and  
Figure 23: Comprehensive criteria for stability of the MRP.