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

Some agricultural reservoirs in South Korea are vulnerable to situations in which they are unable to function as reservoirs because of essential safety issues. This is because 70% of existing agricultural reservoirs were originally constructed more than 50 years ago; most of these reservoirs have not been maintained or managed since their initial construction. In the worst cases, reservoirs are connected to one another by short distances and/or the sizes of upstream reservoirs are larger than the sizes of downstream reservoirs. Individual components of the reservoirs, such as their 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 (for reservoirs connected in series). 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 (CFD) program that is used for tracking free-surface flows. The values predicted through the simple formula were close to the simulated data (within a maximum prediction error of 5%). The values were updated to reflect the effects of hydraulic pressures on the walls of downstream spillways, thereby allowing the failure probabilities (due to overturning, sliding, and settlement) of the downstream spillways to be computed. This study found that the failure probabilities of independent components in reservoirs are significantly different from the systematic failure values observed in sequential modes.