A network theory for BOTDA measurement of deformations of geotechnical structures and error analysis

The Brillouin optical time domain analysis (BOTDA) technology is gaining immense popularity and increasingly being utilised to measure strains in geotechnical structures. The deformations are usually determined by recording strains of selected points, from which the precaution and early warning of instability can be obtained. The errors of the measured strains using BOTDA are related to uncertainties in different connection methods and accumulated errors of the network in the monitoring zone. In this study, a network theory was derived first to measure the deformations of a geotechnical structure in two-dimensional (2D) condition. Next, two physical models (one with four nodes and the other with eight nodes) were established. The performance of the calculated deformations using the network theory based on the measured strains from BOTDA was examined and analysed by comparing the preset displacements from micrometres. From the test results, it is found that the stress concentration at the connection, which has a direct impact on the measured data, can be effectively reduced when using the rubber gasket. There is a good agreement between the calculated deformations and the preset displacements. The accumulated errors are less than 6% for three groups of relative stable nodes, which demonstrates that the proposed network theory can be well utilised in various fields and practical applications that require high precision.