Seismic Reliability of Damaged Concrete Beams

Abstract

A method is developed to estimate the reliability of a seismically damaged structure that will be subjected to future earthquakes. Damage states are defined, and conditional as well as initial damage probability matrices are introduced, in such a manner that the definition of the damage is consistent with the kind of accuracy achieved when the extent of the structural damage is estimated through field inspections. The initial damage probability matrix indicates the probabilities that an undamaged structure will produce various degrees of damage, representative of the corresponding states of damage after it is subjected to an earthquake of a specified intensity. The conditional damage probability matrix is essentially a Markovian transition matrix and describes the transition probability with which a structure in a certain state of damage will reach another state after being subjected to an earthquake of given intensity. The validity of using such probability damage matrices is demonstrated analytically and further verified by a Monte Carlo simulation with the aid of a nonlinear dynamic structural analysis involving artificially generated earthquakes.