## 6 Influence of Cavern Span on Stability of Surrounding Rock
### Model Test of 50 m-Span Cavern  
Figure 11 presents the size diagram of the cavern model with a span of 50 m. Figure 12 illustrates the progressive collapse process of the surrounding rock in a cavern with the 50 m span.  
Figure 10: Collapse process diagram, unit: cm. (**a**) The first collapse, where the angle of the model box is 78\({}^{\circ}\) and (**b**) progressive collapse profile.  
Figure 9: Model size diagram of 40 m span cavern.  
Figure 11: Model size diagram of 50 m span cavern.  
Figure 12: Collapse process diagram, unit: cm. (**a**) The first collapse, where the angle of the model box is 67°; (**b**) the second collapse, where the angle of the model box is 82°; and (**c**) the progressive collapse profile.  
From Figure 12, it can be observed that when the model slowly rotates to 67\({}^{\circ}\), the intermediate portion of the cavern's arch roof experiences the first collapse. After observing the model for 30 min without further collapses, as shown in Figure 12a, the width of the collapsed portion is 21.9 cm, and the height is 14.6 cm. The height of the collapsed portion is 29.2% of the cavern span.  
Continuing the slow rotation of the model box, when the model rotates slowly to 82\({}^{\circ}\), a second collapse occurs upward along the arch foot of the cavern, as shown in Figure 12b. At this time, the width of the collapsed portion is 25 cm, and the height is 29.9 cm. The height of the collapsed portion is 59.8% of the cavern span. After observing for 30 min without further collapses, continue to rotate the model box to 90\({}^{\circ}\). No collapse occurs in the surrounding rocks, forming the final progressive collapse profile, as shown in Figure 10b.  
The relationship between cavern span and collapse curve is detailed in Table 1. Through the comparison of stability model test results for cavern surrounding rocks with spans of 20 m, 30 m, 40 m, 50 m, and 60 m, it can be concluded that during the excavation process of small-span caverns, the stress release range of the surrounding rocks is relatively small, and the impact of stress redistribution on the surrounding rocks is minimal. Thus, the stability of the surrounding rocks is relatively easy to control. As the span of the cavern increases, the phenomenon of stress concentration becomes more pronounced. Significant stress concentration occurs at the intersection of the arch roof and the sidewalls of large-span caverns, making these areas prone to initiation of failure and multiple collapses. Non-uniform stress distribution increases the risk of local instability.  
In the model test results, the reason the ground surface remains intact without collapsing is attributed to a combination of factors including the initial stress state of the rock mass, the structural plane orientation, and the mechanical properties of the rock. Specifically, as the span length increases, stress concentration at the arch roof and sidewalls of the cavern becomes more pronounced, leading to a higher propensity for failure and multiple collapses in these areas. Conversely, smaller-span caverns exhibit a more uniform stress distribution and a smaller stress release range, making the stability of the surrounding rock easier to manage. This phenomenon is corroborated with model tests of caverns with varying spans, where the 30 m-span model demonstrated higher stability, compared to the 60 m-span model that experienced three distinct collapses.