A non-destructive stress evaluation model for anchorage interfaces integrating contact mechanics and ultrasonic nonlinearity

To assess the stress state of contact interfaces in bridge anchorage systems, a theoretical model integrating contact mechanics and nonlinear acoustics is developed. Based on one-dimensional longitudinal wave scattering theory, an analytical expression for the reflection nonlinear coefficient γ R is derived, incorporating first- and second-order interface stiffnesses K 1 and K 2 . An ellipsoidal asperity multi-stage contact model is introduced as a physically based complement to the power-law model, which is concise but relies on empirical stiffness–pressure fitting. Laboratory graded tensioning and ultrasonic tests on a single-strand anchorage system, together with field tensioning and ultrasonic tests on a multi-strand anchorage system, validate the model. Results show that reflection nonlinear coefficient γ R increases monotonically with contact stress P , reflecting interface compaction and stiffness enhancement. The power-law model is convenient within a calibrated pressure range, but its accuracy depends on fitted parameters C and m and does not explicitly encode surface topography or material properties, limiting extrapolation. The proposed model derives the stiffness–stress relationship from rough-surface topography and material parameters, reducing empirical fitting. In the laboratory single-strand anchorage test, the acoustic characterization model based on the contact model gives a coefficient of determination of 0.9460 for reflection nonlinear coefficient γ R . In the field multi-strand anchorage test, the relative error between the predicted and measured contact stresses is 8.49%. These results confirm the field applicability and engineering reliability of the model for quantitative stress evaluation of anchorage interfaces.