## 3 Physical Model Test
### Results and Analysis of Shaft Lining Test  
#### 3.3.1 Analysis of No. 1 Shaft Lining Test Data  
In this test, the circumferential optical fibers were distributed along the inner and outer edges of the shaft lining. The measurement points and test results are shown in Figure 6. As seen in Figure 6b, the temperature variation of the shaft lining model remained within 1 \({}^{\circ}\)C throughout the test, indicating a minimal impact on fiber optic measurements (20-30 \(\upmu\epsilon\)). Compared to the overall test data, this temperature effect is negligible. Therefore, temperature fluctuations did not significantly interfere with strain measurements during the experiment. Throughout this article, the term \"location\" on the horizontal axis of all figures denotes the measured distance (m) to the reference point along the shaft lining section. Figure 6c shows the strain monitoring results of the fiber at the inner edge of the shaft lining. The data demonstrate that the fiber can fully monitor strain changes along the inner edge. At points B and F, cracks appeared and expanded as loading increased. However, despite crack growth, the shaft lining itself did not fail (As shown in Figure 7). This provides direct evidence of the potential of distributed fiber optics for crack monitoring in shaft linings, highlighting its practical engineering value. Similarly, Figure 6d shows that the fiber also provides complete strain coverage at the outer edge of the shaft lining. Cracks formed and expanded in segments IJ and LG, but due to the surrounding rock, these cracks were not visible on the surface. This suggests that the mechanical properties of the surrounding rock may affect crack visibility at the outer edge. Fiber optic technology still faces challenges in such applications, especially in areas where cracks cannot be directly observed. Comparing Figure 6e,g, the measurements from strain gauges and fiber optics showed differences of less than 200 \(\upmu\epsilon\) in most cases, indicating strong agreement. However, significant discrepancies were observed in Figure 6f,h, especially at crack locations. Specifically, in Figure 6f, the strain gauge and fiber optic measurements exhibited opposite trends. This mismatch likely resulted from fiber slippage at cracked areas, causing deviations between the actual strain values and the measured data. In Figure 6h, after 1200 s, measurement errors between the fiber and strain gauges increased significantly. This suggests that crack propagation caused fiber displacement, reducing data accuracy in later testing stages. Although the test achieved full-section strain monitoring of the shaft lining's inner and outer edges using fiber optics, significant deviations from theoretical predictions were observed. Notably, at crack locations, strain gauge and fiber optic measurements showed clear discrepancies. These errors may result from large gaps between the outer edge of the shaft lining and the surrounding rock. These gaps could cause the surrounding rock to bear a larger portion of the load, while the shaft lining experiences relatively smaller forces. As a result, strain changes in the shaft lining may appear slower, failing to reflect the true mechanical interaction between the surrounding rock and the shaft lining. To test this hypothesis, a comparative experiment was added to the No. 2 shaft lining model tests. Loading tests were conducted on models with polytetrafluoroethylene (PTFE) plates to study the potential impact of mechanical differences between the shaft lining and surrounding rock. Figure 6: Test results for the NO.