A constrained cylinder model of strain transfer for packaged fiber Bragg grating sensors embedded in inelastic medium

In this study, the strain transfer rate from an axially loaded, inelastic concrete tube to a glass fiber reinforced polymer (GFRP) packaged optical fiber with Bragg gratings is derived when the radial deformation of an equivalent elastic concrete tube is constrained by the packaged fiber. The concrete strains, both undisturbed and disturbed by the presence of the fiber Bragg gratings sensor, are analytically evaluated, and their difference (up to over 30%) is related to the development length at two free ends of the GFRP package. The mechanism of strain transfer is dominated by a ratio of average fiber and concrete strains in elastic range and by the averaging effect and a ratio of disturbed and undisturbed concrete strains in inelastic range. The analytical strain transfer rate was significantly reduced from 0.95, when concrete behaved elastically, to less than 0.4, when concrete damaged severely. This result was experimentally validated with less than 10% difference prior to concrete fracture. The validated model is applicable to fiber optic sensors that are embedded into concrete structures by a concrete cover of at least 10 times of the radius of the optic fiber.