Mathematical Modeling of Dam Erosion Conditions When Water Flows Over Its Crest

This study aims to determine the criteria of dam erosion conditions when water flows over its crest. It is well known that in natural disasters, when a stream of water flows over the crest of a dam, spatial erosion of the dam is observed, when an initial hole is formed on a small part of the crest. The continued overflow of water leads to erosion of the bottom part of the initial channel. When the bottom of the hole reaches the foundation of the dam, the flow of water from the reservoir begins to erode the side walls of the hole. The erosion process ends after the reservoir is emptied, with the formation of a final hole that is only a part (often small) of the body of the dam. At the same time, in the experimental studies, the flow of water over the crest of a dam leads to a plane-parallel erosion of the dam model, when erosion occurs uniformly along the entire length of the pressure front with almost complete destruction of the dam body. This paper identifies the reasons for this difference. Based on the mathematical model, preliminary conditions for the implementation of various dam erosion modes are obtained, confirmed by specially conducted experiments, as well as well-known experimental and field data on dam erosion.