## 5 Conclusions  
An optical-fiber-embedded beam (OFEB) based on DPP-BOTDA technology was proposed in this study. The study results provide a theoretical and practical basis for the application of optical fiber sensing technology to monitor subgrade settlement. A model test and numerical simulation were carried out to assess the applicability and monitoring accuracy of the OFEB. The major conclusions are given below.  
1. The results of a calibration test show that beam deflection can be accurately measured by the embedded optical fiber, where the relative error between the measurements of the optical fiber and a displacement transducer is approximately 5%. The OFEB can be used to make dense displacement measurements and is therefore suitable for monitoring large-scale settlement in a subgrade.
2. The results of a test on a subgrade similarity model test show that the OFEB can measure subgrade settlement and settlement variations before the subgrade soil slips or decouples from the beam. The relative error between the measurements of the optical fiber and the displacement transducer is less than 8.1%. The main sources of error are artificial error, the effect of the boundary constraint, and the pipe bending stiffness. However, the OFEB is not suitable for measuring large subgrade settlements.
3. A numerical simulation shows that the optimal ratio of the elastic moduli of the beam and soil lies between 30 and 40. The measurement range of the OFEB can be appropriately increased by selecting a small-diameter beam and by improving the coupling between the beam and the soil. Increasing the interfacial friction can only improve the beam-soil coupling performance to a limited extent.  
Preliminary experiments based on finite fixed-point calibration were carried out in this study to assess the suitability and accuracy of the OFEB for monitoring subgrade settlement. The maximum measurement range was identified as 89.77 mm. Further studies are needed to verify the applicability of the OFEB for detecting realistically large subgrade  
Figure 16: MVD and MCP versus (**a**) the friction coefficient and (**b**) the pipe diameter.  
settlements. The beam fabrication process could be mechanized to achieve \"real optical fiber implantation\".  
Conceptualization, Z.L. and K.Y.; methodology, Z.L. and K.Y.; software, Z.L.; validation, Z.L. and L.-G.Z.; formal analysis, K.Y.; investigation, Z.L. and K.Y.; resources, L.-G.Z.; data curation, Z.L., K.Y. and L.-G.Z.; writing--original draft preparation, Z.L. and K.Y.; writing--review and editing, K.Y. and L.-G.Z.; visualization, Z.L., K.Y. and L.-G.Z.; supervision, L.-G.Z.; project administration, L.-G.Z.; funding acquisition, L.-G.Z. and K.Y. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Shaanxi Province Technology Innovation Guidance Special Project, Grant No. 2021 CGBX-38, the Second Tibetan Plateau Scientific Expedition and Research (STEP) Program, Grant No. 2019 QZKK0905, and the CCCC Scientific and Technological Research Program, Grant No. 2020-ZJKJ-PTJS04, 2020-ZJKJ-QNC09, 2020-ZJKJ-PTJS12.  
Not applicable.  
The data presented in this study are available upon request from the corresponding author.  
The authors declare no conflict of interest.