Probabilistic assessment of the global damage in reinforced concrete structures

The main objective of this study is to evaluate the expected damage in reinforced concrete structures in a probabilistic way using Monte Carlo simulation. To do that, the mechanical properties of the materials have been considered random and a set of real accelerograms are scaled in such a way that the mean of their response spectra is similar to the elastic response spectra of the Eurocode EC-08. Performing a series of nonlinear dynamic analysis in the time domain, the probability density function of the maximum displacement at the roof of the structure is obtained. Afterwards, the mean capacity curve of the structure is calculated in probabilistic terms. The static and dynamic nonlinear structural analyses are performed with the program RUAUMOKO 2D. The capacity curve allows defining the states of seismic damage of the structures. According to the methodology proposed by the ATC 40, the expected seismic damage of a structure can be calculated from its capacity spectrum and from the horizontal displacement demand at the roof level. In order to calculate the latter, the equal displacement approximation will be applied and will be compared with the demand of the structure calculated by means of the before mentioned nonlinear dynamic analysis. The fragility curves of the structures are then calculated starting from the obtained damage states. The expected structural damage is finally obtained entering in the fragility curves the spectral displacement obtained by using both, the ATC 40 method and the nonlinear dynamic method. The results obtained from static and dynamic analyses are finally compared and discussed from a probabilistic point of view