The occurrence frequency of failure events serve as critical indexes representing the safety status of dam-reservoir systems. Although overtopping is the most common failure mode with significant consequences, this type of event, in most cases, has a small probability. Estimation of such rare event risks for dam-reservoir systems with crude Monte Carlo (CMC) simulation techniques requires a prohibitively large number of trials, where significant computational resources are required to reach the satisfied estimation results. Otherwise, estimation of the disturbances would not be accurate enough.

In order to reduce the computation expenses and improve the risk estimation efficiency, an importance sampling (IS) based simulation approach is proposed in this dissertation to address the overtopping risks of dam-reservoir systems. Deliverables of this study mainly include the following five aspects: 1) the reservoir inflow hydrograph model; 2) the dam-reservoir system operation model; 3) the CMC simulation framework; 4) the IS-based Monte Carlo (ISMC) simulation framework; and 5) the overtopping risk estimation comparison of both CMC and ISMC simulation. In a broader sense, this study meets the following three expectations: 1) to address the natural stochastic characteristics of the dam-reservoir system, such as the reservoir inflow rate; 2) to build up the fundamental CMC and ISMC simulation frameworks of the dam-reservoir system in order to estimate the overtopping risks; and 3) to compare the simulation results and the computational performance in order to demonstrate the ISMC simulation advantages.

The estimation results of overtopping probability could be used to guide the future dam safety investigations and studies, and to supplement the conventional analyses in decision making on the dam-reservoir system improvements. At the same time, the proposed methodology of ISMC simulation is reasonably robust and proved to improve the overtopping risk estimation. The more accurate estimation, the smaller variance, and the reduced CPU time, expand the application of Monte Carlo (MC) technique on evaluating rare event risks for infrastructures.