## 3 Numerical Simulation of Tunnel Excavation without Grouting  
### The Selection of the Tunnel Section and Establishment of Numerical Model  
In order to prove the feasibility of tunnel construction in grouted reinforced engineering spoil, the numerical simulation of Yujingshan tunnel is conducted in FLAC\({}^{\text{3D}}\). Due to the complicated geology conditions of Yujingshan tunnel, the mechanical response of a single tunnel section cannot truly reflect the mechanical response of tunnel infrastructure. Therefore, the tunnel sections are generally divided into two types according to the positional relationship between the karst cave and tunnel infrastructure. A typical section of the first kind is similar to the section of mileage number D3K279 + 888 (I-type); the karst cave is on the single side of the tunnel infrastructure, which leads to large asymmetrical load on the tunnel lining. The other kind is similar to D3K279 + 938 (II-type). Although the tunnel infrastructure is surrounded by the karst cave except for the crown of the tunnel, the large width of the karst cave may cause large deformations of the tunnel basement. Figure 4 shows the numerical model of the tunnel with two sections. The model dimensions of mileage number D3k279 + 888 and D3k279 + 938 are 120 m \(\times\) 50 m \(\times\) 140 m and 140 m \(\times\) 50 m \(\times\) 140 m, respectively. The dimensions of tunnel infrastructure are 17.22 m \(\times\) 25.21 m. The mechanical response of surrounding rock under a three-step excavation method is analyzed by [PERSON] et al. (2020), the results show that the small stress is induced in the second lining, the stability of surrounding rock can meet the requirement of safety. [PERSON] et al. (2022) proposed a countermeasure against the complicated tunnel with inclined shafts, connecting air ducts and main tunnel excavation in limestone region with low bearing capacity ([PERSON] et al., 2022). The settlement of complex tunnel vault is controlled by flexibly converting the excavation method. Compared with the literature, the three-step excavation method was suitable for tunneling in a limestone region and was adopted during the simulated analysis. According to the geological survey report of Yujingshan tunnel, the physical and mechanical parameters of strata in the giant karst cave region are listed in Table 1. The mechanics properties of the V-level surrounding rock are adopted to the engineering spoil. The Mohr-Coulomb failure criterion is adopted in the surrounding rock, the second lining is considered to the elastic model. Figure 3: Hydrological profile of karst cave hall. The grounded bolt, anchor mesh shotcrete and steel arch compound support are adopted to the first lining, and the mechanical properties of support are listed in Table 2. The primary lining and bolt are simulated by shell and cable structure element, respectively. The steel mesh and steel arch convert to the strength of the primary lining according to the equivalent strength principle, that is,  
\[E_{c}=E_{0}+\frac{A_{s}E_{s}}{A_{c}} \tag{1}\]  
where \(E_{c}\) and \(E_{0}\) are the converting elasticity modulus and origin elasticity modulus of concrete, respectively. \(E_{s}\) is the elasticity modulus of steel, and \(A_{s}\) and \(A_{c}\) are the sectional area of steel arch and concrete, respectively. The elasticity modulus and Poisson ratio of bolt are 210 Gpa and 0.3, respectively. When the tunnel is excavated to the karst region, the karst cave is backfilled with engineering spoil. In this case, the karst cave is not disturbed by external forces and remains stable. Therefore, the karst cave wall should not be directly connected with engineering spoil. In this paper, the interface elements between the karst cave wall and engineering spoil are established. The mechanical properties of interface elements can be calculated by