In the seismic field, the seismic performance of a structure reflects its damage level under a given seismic demand. Thus, to evaluate this performance, many analysis and design techniques are used, such as nonlinear approach commonly called Pushover is used in this research. On the other hand, predicting the damage level is a random process, where only a probabilistic approach would allow predicting it, as the level of uncertainty, related to the seismic action is important. For this purpose, a statistical study was conducted through simulations with large number of seismic accelerations, generated from a probabilistic distribution law, inspired from the Monte Carlo method, to evaluate the damage rates corresponding to each damage domain. The results revealed the influence of the seismic zone and the location of the structure on the damage rate observed after seismic loading.