## 3 Numerical Modeling of the Deformation Control of Tunnel Surrounding Rock  
### Model Building  
In response to the specific conditions at the Xiaoyuan Tunnel site, a detailed 3D model was developed, reflecting the actual conditions of the surrounding rock and the distribution of ground stress. Using ABAQUS finite element simulation software, the construction of the surrounding rock section from ZK2985+195 to ZK2985+555 was numerically simulated and analyzed. To minimize the influence of the tunnel model boundary on computational data, distances greater than three times the tunnel excavation span were chosen as the left and right boundaries of the model, in accordance with [PERSON]'s principle. The scope of the tunnel model area was determined based on the principle that the zone of influence from tunnel excavation ranges from 3 to 5 times the diameter of the excavation [39]. The model is established based on the following assumptions. (1) Regardless of the stratification of the surrounding rock mass, it is regarded as a continuous, single, and isotropic ideal elastoplastic medium. (2) Tunnel excavation proceeds in a step-by-step manner, and the construction of support structures is promptly carried out after each excavation stage. (3) The influence of groundwater on the excavation process is ignored. To accurately represent geostress, the vertical direction of the model was set to the \(z\)-axis and the horizontal direction to the \(x\)-axis. The 3D mesh distribution of the model is shown  
Figure 1: Longitudinal section of the Xiaoyuan Tunnel.  
in Figure 2. The model uses eight-node linear hexahedral elements for simulation, with reduced integration, and adopts the Mohr-Coulomb criterion. Accordingly, the horizontal dimensions of the surrounding rock were set to 120 m, the vertical to 120 m, and the \(y\)-axis (the tunnel direction) to 20 m. The shallow buried side was set to 70 m, with 50 m for the left and right offsets. To simulate the stress state before tunnel excavation in the actual geological environment, this paper achieves a stable state of the model by applying gravity loads prior to the tunnel excavation simulation. The geostress equilibrium contour map has been added to the revised manuscript as Figure 3. The stress boundary conditions at the excavation boundary of the tunnel model are set as free boundaries, with constraints in the \(x\)-direction applied to the left and right directions, and constraints in the \(y\)-direction applied to the front and back directions. The top surface of the model is set as an unconstrained free surface, while the bottom surface of the model and the ends of the anchor rods are set with fixed constraints. The simulation of the contact interface between the lining and the surrounding rock is achieved by setting up a Contact Pair.  
As the first four-lane super large section highway tunnel in Jiangxi Province, the Xiaoyuan Tunnel has a net height of 5 m, a net width of 18.25 m, a maximum buried depth of 76 m, a maximum excavated section area of 275.7 square meters, and a maximum excavated width of 22.38 m. The detailed structural parameters are shown in Figure 4. The model includes a variety of excavation methods, such as the CRD method, three-benching seven-step method, and the double-side drift method. The structural grid cells chosen resulted in a model grid divided into 31,914 nodes and 27,568 cells. The model components, such as surrounding rock and lining, were represented as C3D  
Figure 3: Contour map of the geostress equilibrium (unit: Pa).  
Figure 2: Mesh diagram of the finite element 3D model.  
anchors were modeled as B31 beam cells. Parameters for the surrounding rock and support structures required for the simulation were derived from site design and investigative data.