Toward Distributed Fiber-Optic Sensing of Subsurface Deformation: A Theoretical Quantification of Ground-Borehole-Cable Interaction

Fiber-optic sensing is emerging as a superior means for distributed strain sensing of the subsurface. The ability of an embedded fiber-optic cable to capture accurate strain profiles depends on the degree of rigid mechanical coupling between the ground and the cable. However, a current challenge in this field is to determine the actual level of ground deformation from strain signatures sensed by the cable deployed in the subsurface; addressing this issue has been hampered by the lack of suitable theoretical methods. Here we propose a two-step ground-cable coupling evaluation procedure, whereby we develop analytical formulations to quantify the interaction and interface shear transfer of a ground-borehole-cable system. We constrain key model parameters using a data set acquired with a fiber optics-instrumented borehole for monitoring groundwater-related sediment compaction. Extensive parametric analyses reveal that increasing the backfill modulus and cable gauge length or decreasing the borehole radius and cable stiffness can improve the quality of strain transferred to the cable from the ground; the effect of ground properties is comparably insignificant. Further, we develop design charts and tables at designated transfer thresholds to facilitate the development and field deployment of fiber sensing elements. Taken together, the theoretical quantification of ground-cable coupling should improve the state-of-the-art performance of distributed fiber-optic strain sensing for subsurface ground movements detection and monitoring.