## 4 Case Study
### Design of the Number of Preset Seams
#### 4.3.1 Lateral Pressure Coefficient Less than One  
To investigate the optimal number of preset seams when the lateral pressure coefficient is less than 1, this section establishes a two-dimensional numerical model for the lateral pressure coefficient of \(\lambda\) = 0.39 with two, three, four, six, and eight preset seams. The best preset seam configuration is determined by analyzing the degree of lining damage, reinforcement stress, and seam opening displacement. As shown in the total damage (SDEG) of the lining in Figure 10, multiple preset seams can effectively reduce the damage factor at the far end of the joints. As the number of preset seams increases, the region with higher lining damage between the seams noticeably decreases. However, increasing the number of preset seams leads to a decline in the overall integrity of the lining. When the number of preset seams reaches six, the total damage is minimized.  
Figure 9: Vertical displacement and maximum principal strain of the surrounding rock after excavation and during operation.  
As shown in Figure 11, it can be seen that when two preset seams are used for \(\lambda=0.39\), the maximum tensile stress in the reinforcement at the seam is 13 MPa, while at the far end, the maximum tensile stress reaches 413 MPa, leading to reinforcement yielding and crack widths exceeding 0.3 mm. With three preset seams, although the maximum tensile stress reduces to 249 MPa, the maximum crack width still reaches 0.32 mm. With four, six, and eight preset seams, the maximum tensile stress in the reinforcement further decreases and is maintained below 200 MPa, with corresponding maximum crack widths of 0.17 mm, 0.12 mm, and 0.12 mm, respectively.  
Figure 11: Rebar stress for different numbers of preset seams.  
Figure 10: Total damage (SDEG) of the lining for different numbers of preset seams ((**a–f**), \(\lambda=0.39\); (**g–l**), \(\lambda=1.50\)).  
The seam opening displacement of the lining is a key parameter in the design of segmented lining structures. Excessive seam openings may reduce the sealing performance of the underground working. In contrast, insufficient seam openings may limit the self-supporting capacity of the surrounding rock. This can reduce the gas storage capacity of the working. Additionally, the opening displacement of a single seam should not be too large, as it could increase the complexity of sealing the seam. Therefore, it is essential to study the seam opening displacement under high internal pressure conditions.  
Figure 12 shows the calculated seam opening displacements of the lining for different numbers of preset seams. It can be observed that with two preset seams, the seam opening displacement at the inner side of a single lining reaches 3.47 cm. As the number of preset seams increases, the seam opening displacement at the inner side of a single lining decreases to below 2.00 cm. Furthermore, as the number of preset seams increases, the total seam opening displacement of the lining increases.  
Increasing the number of preset seams effectively alleviates the excessive tensile stress in the reinforcement at the far end of the seams and reduces the lining damage factor. Additionally, the total seam opening displacement of the lining increases, which better facilitates the release of radial displacement and maximizes the self-supporting capacity of the surrounding rock. When six or eight preset seams are used, the SDEG of the lining is only around 30%, and the maximum crack width under high internal pressure is just 0.12 mm. This demonstrates that using six or eight preset seams meets the design requirements for the segmented lining structure. Considering both construction costs and technical difficulty, the optimal solution is to use six seams.