# Study on the Evolution Law of Overlying Rock Collapse Induced by Mining Based on BOTDR
## 4 Analysis of Horizontal Optical Fiber Strain Monitoring in Slope
### Indoor Fiber Tensile Test  
To investigate the strain and displacement characteristics of fiber deformation under axial tension during the collapse of overlying rock layers, two indoor fiber tensile tests were designed and conducted to simulate the impact of different collapse modes on fiber strain. Scheme 1: The fiber was fixed at both ends, and a vertical point load was applied at the midpoint of its effective arrangement area to simulate fiber deformation under a hinged collapse of the overlying strata. This test aimed to reveal the strain distribution and tensile characteristics of the fiber when the overlying strata underwent a hinged deformation. Scheme 2: Similarly, the fiber was fixed at both ends, but a \"rock block\" with a length of 60 cm was placed at the midpoint of the effective fiber layout area to simulate fiber deformation under a single collapse of the overlying strata. This test helped to explore the stress and strain distribution characteristics of the fiber under localized rock collapse conditions. During the experiment, the AV6419 optical time-domain strain measurement system was used for real-time monitoring of fiber strain. The measured strain values were then substituted into the strain-displacement relationship model to calculate fiber displacement. Finally, the computed tensile displacement values were compared with theoretical calculations to verify the accuracy and applicability of the model. The test setup is shown in Figure 7.  
The fiber was stretched by 50 mm, 80 mm, and 100 mm at the midpoint position according to Schemes 1 and 2, and the corresponding strain curves were obtained, as shown in Figure 8. The overall fiber strain curve exhibits a slightly higher strain at both ends and a lower strain in the middle. Figure 8 illustrates the strain distribution of the fiber under different tensile conditions. Generally, the strain curves exhibit a pattern where strain is slightly higher at both ends and lower in the middle, indicating that the central part of the fiber undergoes uniform deformation after loading. From Figure 8a, it can be observed that when the fiber is stretched at the midpoint, the strain gradually attenuates toward both ends, forming a \"U\"-shaped curve. The tensile  
Figure 8: Fiber tensile strain curve: (**a**) strain curve of fiber under point stretching, (**b**) strain curve of fiber under single-block collapse. slope remains relatively constant, and the strain values show minimal variation, indicating uniform force distribution along the fiber. From Figure 8b, in the case of localized rock block collapse, a significant strain concentration occurs in the affected region, whereas the strain is much lower in areas away from the collapse zone, forming two distinct \"step-like\" features. This suggests that when localized rock collapse occurs, the fiber effectively captures the strain concentration in the collapse-affected region. Furthermore, in the section from 700 mm to 1300 mm, where the simulated rock block applies compression, the fiber undergoes minimal deformation, resulting in negligible strain variation. Overall, the fiber effectively reflects the strain distribution characteristics under different collapse modes, providing valuable data support for monitoring overlying rock movement using optical fiber technology. Substituting the optical fiber strain curves into Equation (13), the displacement of the optical fiber at different tensile distances is calculated based on strain variations. The computed fiber displacement is then compared with the theoretical tensile length, as shown in Figure 9.  
The calculated optical fiber displacement, derived from Equation (13) based on strain variations, closely aligns with the theoretical tensile distance. This confirms that fiber strain monitoring can accurately compute actual collapse displacement, validating the scientific reliability of using optical fiber strain to represent overlying rock displacement.