## 4 Engineering Application and Analysis  
### Project Overview  
The Wu Fengshan Tunnel, located on Binhai Avenue in Chunhu Town, Fenghua District, Ningbo City, serves as a primary thoroughflare. It is designed for a first-class road with a speed limit of 80 km/h and spans a total length of 1350 m, with the maximum burial depth reaching approximately 140 m, classifying it as a long, deep, mountain-crossing tunnel. The geological formation at the tunnel site predominantly consists of tuff from the Upper Jurassic Xitou Mountain Group, with local outcrops of intrusive granite near the tunnel portals. The surface is covered by a thin layer of colluvial silty clay and slope alluvial clayy gravel.  
The fault zone of the tunnel, ranging from pile numbers K25 + 826 to K25 + 886, is selected for detailed analysis. The surrounding rock in this section is predominantly slightly weathered tuff, with an average depth of approximately 110 m and classified as level IV. The study section is traversed by fault Fw2, characterized by a more fragmented rock mass with well-developed joints, leading to relatively poor integrity and stability of the surrounding rock. The geological conditions are notably complex in this area. The parameters of the surrounding rock for the study section are summarized in Table 1.  
Figure 8: Relationship among ratio of inner radius to outer radius, reserved deformation, and maximum compressive stress.  
Based on the correlation between \(BQ\) and \(GSI\) values as defined in Equation (8), the \(GSI\) for the surrounding rock in the study section is determined to be 24.63. The surrounding rock of the study section is a micro-weathering tuff, and the rock is relatively hard, so the value [33] of \(m_{\text{i}}\) is taken as 18. By substituting the \(GSI\), \(D\), and \(m_{\text{i}}\) values into Equations (2)-(4), the rock parameters \(m_{\text{b}}\), \(s\), and \(a\) for the study section are calculated as 0.76, 0, and 0.53, respectively. Utilizing Equation (9) and the modulus of elasticity \(E_{0}\) of the rock in the study section, the equivalent deformation modulus \(E\) of the surrounding rock is determined to be 1.02 Gpa. Consequently, according to Equations (11)-(13), the maximum radius \(R_{\text{p}}\) of the plastic zone in the study section is 8.98 m. Furthermore, Equation (16) indicates that the maximum displacement of the tunnel wall in the study section is 26.9 mm. A summary of the calculated deformation results for the surrounding rock in the study section is presented in Table 2.  
The S4-3 type lining is implemented in the tunnel study section, with an excavation volume of 146.90 m\({}^{3}\) per linear meter. Calculations reveal an equivalent radius [34] of 7.18 m, a lining thickness of 74 cm, and an inner radius \(R_{\text{a}}\) of 6.44 m. This lining is constructed using C35 concrete. In accordance with the Code for Design of Reinforced Concrete Thin Shell Structures (JGJ22-2012) [35], the elastic modulus of the concrete lining is determined based on the entire cross-section of homogeneous concrete, without accounting for the steel reinforcement's transformed area or excluding the volume of prestressed reinforcement channels. The elastic modulus of the lining is calculated to be 31.5 Gpa, with a Poisson's ratio of 0.2. The pertinent parameters for the S4-3 type lining are detailed In Table 3.