In this paper, the following analysis is performed by means of theoretical derivation and model establishment. However, in practical engineering applications, factors such as the strain-transfer rate between the flexible substrate and sensing points, the displacement reconstruction algorithm, and the arrangement interval of the sensing points can cause measurement error, which, in turn, leads to a decrease in the displacement-measurement accuracy. The flexible sensor can perform regional and quasi-distributed measurements of the displacement field of the measured structure, and accurately reflect the operating state of the engineering structure. The fiber Bragg grating (FBG) flexible sensor, developed by the combination of flexible material and an FBG sensor, is widely used in geotechnical engineering health monitoring due to its excellent performance. Monitoring geotechnical structures and providing real-time early warning is a key measure to mitigate the impacts of disasters (slope slip, subsidence, dam deformation, bridge settlement, etc.).
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