## 3 Physical Model Test
### Results and Analysis of Shaft Lining Test
#### 3.3.2 Analysis of No. 2 Shaft Lining Test Data  
The strain curves of the inner edge of the shaft lining for two test groups are shown in Figure 8.  
In this experiment, axial and circumferential optical fibers were installed along the inner and outer edges of the shaft lining for comprehensive strain monitoring. Figure 8a,b show the strain curves of the fibers at the inner edge for the first and second test groups. In the tests without PTFE plates, significant measurement errors were observed, especially in the strain variations of the FE segment, which showed notable fluctuations. In the first test group, large deviations occurred in multiple areas, reflecting uneven stress distribution during loading. This uneveness may result from interactions between the outer edge of the shaft lining and the surrounding rock. In contrast, after adding PTFE plates in the second test group, measurements stabilized in most areas, showing clear compressive strain characteristics. In the FE segment, the fiber measurements indicated a tensile strain of 800 \(\mu\)\(\epsilon\), suggesting significant stress changes in this region. These results confirm the hypothesis explaining the large errors in the No. 1 model tests. Detailed results of the No. 2 shaft lining loading test are shown in Figure 9, including temperature changes, fiber optic strain monitoring, and comparisons between fiber optics and strain gauges. According to Figure 9b, the temperature variation remained within 1 \({}^{\circ}\)C throughout the test, ensuring reliable strain measurements. Figure 9c demonstrates that the fiber optics fully monitored strain changes at the inner edge of the shaft lining. Larger compressive strains were observed at points E and C, and the EF segment showed a tendency for cracking, although no actual cracks were observed. This indicates that fiber optics can detect minor deformations before cracks become visible. In the strain monitoring of the outer edge, Figure 9d shows that the fiber optics effectively monitored the entire cross-section. No significant tensile strain zones were observed, consistent with the stress distribution during loading. Figure 8: Strain curves at the inner edge of the No. 2 shaft lining: (**a**) First test group; (**b**) Second test group. Figure 7: The cracking failure mode of shaft lining model: (**a**) The cracking location near point F on the NO. 1 shaft lining model; (**b**) The cracking location near point B on the NO. 1 shaft lining model. Figure 9e,g show good agreement between fiber optic and strain gauge measurements, with small errors. However, in Figure 9f, the fiber optic measurements slightly exceeded those of the strain gauge. This discrepancy may result from the large spacing between Strain Gauge 2 and the fiber, combined with excessive adhesive, which reduced the strain gauge readings. Figure 9h demonstrates the fiber optic response during shaft lining cracking. After installing PTFE plates, the stress transitioned from tensile to compressive zones. The fiber consistently recorded positive strains, likely due to fiber slippage caused by cracking, indicating reduced accuracy in reflecting actual deformations during this phase. In Figure 9i, the axial strain curve shows values exceeding \(110\)\(\upmu\varepsilon\), confirming that the shaft lining behaves under plane stress conditions. The negative values and reverse strain trends in Strain Gauge 4 validate crack formation, aligning with fiber optic data and improving crack location accuracy. These results confirm the effectiveness of fiber optics for strain monitoring in shaft linings, particularly for crack detection. However, factors like cracking-induced fiber slippage may limit accuracy in certain cases. Figure 9: _Cont._  
Axial and radial strain curves at different key points during the second loading test of the NO. 2 shaft lining model are shown in Figure 10. According to Figure 10b,e, the axial strain at point b showed tensile behavior, increasing gradually as the test progressed.