Reliability assessment of existing buildings subjected to probabilistic earthquake loadings

In order to mitigate the losses induced by major earthquake, it is important to strengthen vulnerable existing structures. To identify this vulnerability, a probabilistic method is needed in which uncertainties from different sources are incorporated. based on seismic hazard evaluation for a site, a single peak power spectrum is used to represent the intensity and frequency content of the ground motion. Assuming a non-stationary Gaussian model for earthquake time history. Monte-Carlo simulation technique is used to generate a set of time histories. Since the input peaks occur at random time and at different random frequencies, the response of the structural system is also random. A statistical analysis of a suitable response parameter (such as ductility demand or moment demand) is conducted and the Gumble Extreme Value distribution is fitted. The ultimate ductility capacity is assumed to have a probability distribution. The reliability of the structure is evaluated by convolving the demand and capacity distributions. A numerical example is presented for illustration. It is shown that with further modification in the proposed method, one could obtain a reasonable estimation of structural safety based upon which a rational decision for strengthening policy can be made.