System reliability analysis of downstream spillways based on collapse of upstream spillways

Individual components of reservoirs such as embankments, spillways, and water intake facilities, have been considered in order to understand the main factors associated with potential reservoir failure. Accordingly, this study aims to estimate the probability of failure in downstream spillways upon the collapse of upstream spillways. A simple equation to calculate the rise in the water level in downstream spillways, which is caused by the collapse of upstream spillways, was proposed. This equation was based on the discharge equation of an overflowing rectangular weir and the scaling law for continuous flow. To verify the proposed simple equation, the water level increments were compared with the simulated results of the commercial software FLOW-3D, which is an accurate computational fluid dynamics program that is used for tracking free-surface flows. The values predicted through the simple formula were close to the simulated data. The values were updated to reflect the effects of hydraulic pressures on the walls of downstream spillways, thereby allowing the failure probabilities of the downstream spillways to be computed.