Numerical calibration of damage indices

• A new numerical calibration procedure is proposed based on incremental dynamic analysis.
• Five well known damage indices are calibrated on the basis of cracks opening width.
• The procedure is generally applicable, robust and efficient.

In this study a numerical calibration procedure is proposed; while its application in some of the most widely accepted damage indices (DIs) used for quantifying the extent of damage in reinforced concrete structures is presented. In particular, without loss of generality of the applicability of the proposed procedure, the Park and Ang local damage index, its modified variant presented by Kunnath, Reinhorn and Lobo; the Chung, Meyer and Shinozuka local damage index; along with the maximum and final softening damage indices proposed by DiPasquale and Çakmak, are calibrated on the basis of the width of crack openings. The estimation of the crack width is performed by means of detailed modelling with hexahedral finite elements for the concrete and rod elements for the steel reinforcement; while due to the computing demands the databank of values for the damage indices under investigation is defined based on coarse models with beam–column elements. These two steps of the proposed procedure are based on the incremental dynamic analysis. Next, the statistical characteristics of the DIs are computed by means of horizontal statistics in conjunction with the maximum likelihood function method and an optimization algorithm.