Probability distribution of the seismic damage cost over the life cycle of structures

In the life-cycle analysis, the total cost of damage caused by earthquakes is a significant but highly uncertain component. In the current literature, the seismic risk analysis is largely limited to the evaluation of the average cost of damage, which is not informative about the full extent of variability in the cost. The paper presents a systematic development of the stochastic modeling of seismic risk analysis problem and reformulates the damage cost analysis as a superposition of compound Poisson processes. An explicit analytical solution for the distribution of damage cost is derived in form of a recursive equation. The proposed approach extends the capability of the existing framework of seismic risk analysis, which can be used to optimize initial design and retrofitting of structures.