Method for Developing Motion Damage Relationships for Reinforced Concrete Frames

This report presents formulations for developing fragility curves and damage probability matrices for reinforced concrete frame structures. Three different classes of reinforced concrete frames, based the story heights, are considered. The development of fragility curves and damage probability matrices requires the characterization of ground motion and the identification of different degrees of structural damage.

The ground motion characterization parameters used in this report are the spectral acceleration and the root mean square acceleration. At a given ground motion parameter, an ensemble of ground motions is required for evaluating the conditional probabilities of the different degrees of damage. Autoregressive moving average (ARMA) models and Gaussian stationary models with modulating functions are used for this purpose.

The identification of the different degrees of structural damage is carried out based on the structural damage models. Models for characterizing the seismic damage to reinforced concrete structures are reviewed in this report. The Park and Ang damage index is used in this report for the development of fragility curves and damage probability matrices.

Constrained Monte Carlo simulation techniques are used for evaluating the fragility curves. The comparison of the damage probability matrices for the three classes of reinforced concrete frames, developed in this study, with those in ATC-13 (1985) shows that the ATC-13 DPM's potentially underestimate the damage, particularly at the high intensity levels. Because the existing definitions of damage to reinforced concrete structures are found to be inadequate, a new technique for identifying different damage states for such structures is presented that considers the crack widths and interstory drift ratios.