Two-dimensional operator for bank failures induced by water-level rise in dam-break flows

Bank failure in a stream generally originates from bed erosion at the bank toe. This research proposes a novel two-dimensional (2D) bank-failure operator, based on a simple local failure criterion and on the conservation of sediment mass. This operator is inserted into a 2D Saint-Venant-Exner model to simulate both bed and bank geomorphic processes and their interaction with the flow, especially during dam-break events. This shallow-water model is solved by a first-order finite-volume scheme on an unstructured triangular mesh. After an erosion or deposition update, the bed inclination is compared locally with the sediment stability angles, considering the impact of water-level rise. Assuming material homogeneity, the unstable bed elements are tilted around an appropriate axis of rotation, ensuring mass conservation. The numerical model is tested for a collapsing circular hole and against laboratory tests of a dam-break flow: first in a prismatic channel made of coarse sand and then over an initial bed step.