Inverse Analysis to determine re-bars' force from external crack widths measurement

Abstract

This paper focuses on the stability of fracturing process in reinforced concrete beams and derives a fracture mechanics based transformation between crack opening displacements (COD) and re-bars force. Bridged crack model is adopted which considers distinct phenomena for damage process in concrete and bridging of cracks by re-bars. The derived transformation yields crack profiles for known re-bar force determined by either RC section analysis or computations having fracture mechanics based approach. Inverse of the integral transformation is ill-posed when experimentally collected COD's are not exact. Tikhonov method of regularization is followed to compute re-bar force from COD where the extremals of the Tikhonov functional is determined numerically. A numerical example proving the applicability of this method with different noise levels are demonstrated. It is observed that current method of numerical inverse analysis on external surface COD can satisfactorily determine location and force of re-bars in the beam cross-section within limited tolerance of noise in data. Application of this method enables the maintenance engineers to retrieve inner cross-sectional information from outer measurements in a non-destructive way.