## 3 Physical Model Test
### Results and Analysis of Shaft Lining Test
#### 3.3.3 Analysis of No. 3 Shaft Lining Test Data  
The test involved the installation of optical fibers along both the inner and outer edges of the shaft lining in axial and hoop orientations. PTFE plates were placed between the surrounding rock and the shaft lining, with the gaps between the PTFE plates and steel plates filled with fine sand. The test results are shown in Figure 11. First, Figure 11b shows that the temperature variation during the test was controlled within 0.5 \({}^{\circ}\)C, ensuring the reliability of fiber optic monitoring. As indicated in Figure 11c, the optical fibers achieved comprehensive strain monitoring at the inner edge of the shaft lining. Notably, significant compressive strain was measured at Points E and C, while tensile strain approaching 400 \(\mu\)\(\epsilon\) was detected near Point A, suggesting localized cracking. However, despite the detected tensile strain, no visible cracks were observed, highlighting the capability of distributed optical fibers to capture micro-strain changes during early-stage cracking, which is critical for practical shaft lining monitoring. In contrast, Figure 11d demonstrates full-section strain monitoring at the outer edge of the shaft lining, where no significant tensile strain was observed, aligning with theoretical predictions. Data from Figure 11f-h reveals close agreement between strain gauge and fiber optic measurements, validating the accuracy of fiber optic technology in shaft lining strain monitoring. However, Figure 11e indicates that near Strain Gauge 1, fiber slippage occurred during cracking, resulting in lower fiber measurements compared to strain gauge values. This suggests that fiber slippage due to cracking may compromise measurement precision in fractured zones. Figure 11i shows that the axial strain of the shaft lining exceeded 100 \(\mu\)\(\epsilon\), supporting the suitability of plane stress state analysis for this structure. After filling with fine sand, the measured axial strain closely matched theoretical values, further confirming the stress state consistency. Overall, the optical fibers effectively monitored strain across both inner and outer edges of the shaft lining, with results consistent with strain gauge data. However, minor discrepancies in cracked regions were attributed to potential fiber slippage. Errors in OFDR measurements caused by slippage are inevitable.  
Figure 10: Test results for the second loading trial of the NO. 2 shaft lining: (**a**) Key point numbering of the shaft lining model; (**b**) Axial strain curve at point b on the inner edge of the shaft lining; (**c**) Axial strain curve at point a on the inner edge of the shaft lining; (**d**) Axial strain curve at point a on the outer edge of the shaft lining; (**e**) Axial strain curve at point b on the outer edge of the shaft lining; (**f**) Radial strain curve of the GA segment of the shaft lining; (**g**) Radial strain curve of the FL segment of the shaft lining; (**h**) Radial strain curve of the KE segment of the shaft lining; (**i**) Radial strain curve of the DJ segment of the shaft lining; (**j**) Radial strain curve of the IC segment of the shaft lining.  
Figure 11: Test results of the No. 3 shaft lining loading: (**a**) Key point numbering of the shaft lining model; (**b**) Temperature variation during the test; (**c**) Circumferential strain curve at the inner edge of  
the shaft lining; (**d**) Circumferential strain curve at the outer edge of the shaft lining; (**e**) Comparison of circumferential strain between Strain Gauge 1 and fiber optic measurements (crack location); (**f**) Comparison of circumferential strain between Strain Gauge 2 and fiber optic measurements; (**g**) Comparison of circumferential strain between Strain Gauge 3 and fiber optic measurements; (**h**) Comparison of circumferential strain between Strain Gauge 4 and fiber optic measurements; (**i**) Axial strain-time curve of the strain gauge.