Civil infrastructures, such as highway bridges, located in seismically active regions are often subjected to multiple earthquakes, such as multiple main shocks along their service life or main shock-aftershock sequences. Repeated seismic events result in reduced structural capacity and may lead to bridge collapse causing disruption in normal functioning of transportation networks. This study proposes a framework to predict damage accumulation in structures under multiple shock scenarios after developing damage index prediction models and accounting for the probabilistic nature of the hazard. The versatility of the proposed framework is demonstrated on a case study highway bridge located in California for two distinct hazard scenarios: a) multiple main shocks along the service life, and b) multiple aftershock earthquake occurrences following a single main shock. Results reveal that in both cases there is a significant increase in damage index exceedance probabilities due to repeated shocks within the time window of interest.