Regularization of Inverse Problems in Concrete Fracture

The crack opening displacements (CODs) contain information on the internal crack bridging forces between the crack surfaces. High resolution image analysis measures the CODs. Theoretical models map the crack bridging forces into the surface CODs by integral transforms. Theory of Inverse Problems defines necessary conditions and procedures for the back calculations of determining crack bridging forces from CODs. Furthermore measurement precision and deviation of the theoretical model from the real situations cause mismatch between the theoretical and the measured CODs. Thus measured COD data are noisy as simulated by the theoretical models. The Tikhonov method of regularization is a good choice for this inverse analysis. The predicted steel bar force matched well with the results of reinforced concrete beam test results.