## 4 Simulation Analysis of Different Tunneling Parameters
### Effect of Disc-Cutter Spacing on Rock Breaking  
To analyze the effect of cutter spacing, the 3D single-disc cutter rock-breaking model (Figure 4) was modified to incorporate a double-disc cutter configuration (Figure 11). Cutter spacings were varied at 30, 40, 50, 60, 70, and 80 mm. Figure 12 demonstrates how cutter spacing influences crack formation. When the spacing was 30-40 mm, cracks from the two cutters merged, producing a smaller rock fragmentation volume. At 50-60 mm spacing, cracks interconnected between cutters, creating larger fragmentation volumes. When the spacing was increased to 70-80 mm, each cutter acted independently, with cracks failing to connect. This led to ridges forming between cutting paths, reducing fragmentation volume and efficiency. Figure 10: Effect of disc-cutter diameter on rock breaking specific energy. Figure 9: Effect of disc-cutter diameter on rolling force. The cooperative action of adjacent cutters enhances rock fragmentation. However, as cutter spacing increases, the interaction diminishes, resulting in incomplete rock fragmentation and lower efficiency. Conversely, excessively small spacings limit crack propagation, causing overlapping cracks and reducing fragmentation volume. The appropriate spacing of cutters directly affects the efficiency of tunnel excavation and the associated costs. If the spacing between cutters is too large, it can lead to incomplete rock fragmentation and reduced drilling efficiency. Conversely, if the spacing is too small, it can cause excessive cutter wear and energy waste. Therefore, determining the optimal cutter spacing is essential for fine-tuning excavation parameters, enhancing construction safety and economy. This study provides scientific evidence on the impact of different cutter spacings on rock fragmentation, assisting tunneling teams in making more informed decisions in practice, thereby improving construction efficiency, reducing resource consumption, and lowering project risks. Figures 13 and 14 depict the effects of cutter spacing on rolling force and specific energy. The rolling force increased with spacing before peaking at 60 mm, then declined. Similarly, specific energy decreased initially, reaching a minimum at 60 mm, and then  
Figure 11: Rock-breaking model by double-disc cutters. Figure 12: Effect of disc-cutter spacing on rock cracks. increased. At 2 mm penetration, the rolling force was smallest, while specific energy was highest. At 4 mm penetration, the rolling force and specific energy were moderate. At 6 mm penetration, the rolling force peaked, while specific energy reached its lowest value due to the higher rock fragmentation volume. A quadratic function was used for regression fitting, and the fitted formulas are shown in Figures 13 and 14. The optimal cutter spacing for maximum rolling force averaged 61.68 mm across penetration depths of 2, 4, and 6 mm. For specific energy, the optimal spacing averaged 61.22 mm. Therefore, a cutter spacing of 60 mm is recommended for tunneling in granite formations to achieve the highest efficiency and lowest energy consumption. Figure 14: Effect of disc-cutter spacing on rock breaking specific energy. Figure 13: Effect of disc-cutter spacing on rolling force. [PERSON] et al. [13] demonstrated that disc-cutter spacing significantly influences the specific energy consumption of rock breaking, while [PERSON] et al. [19] identified the optimal disc-cutter spacing-to-penetration ratio that minimizes the specific energy of rock breaking. Our study complements these findings by offering a more detailed analysis of the relationship between disc-cutter spacing and rock-breaking efficiency. [PERSON] et al. [20] examined the effects of cutter spacing and penetration on rock-breaking performance through experiments and finite element simulations, developing a mechanical model for optimal spacing in cooperative rock breaking. Utilizing the discrete element method, our study expands on [PERSON] et al.