Mathematical modeling of flooding due to river bank failure

Modeling of flooding events resulting from bank overflooding and levee breaching is of relevant social and environmental interest. Two-dimensional (2D) hydrodynamic models integrating the shallow water equations turn out to be very effective tools for the purpose at hand. Many of the available models also use 1D channel elements, fully coupled to the 2D model, to simulate the flow of small channels dissecting the urban and rural areas, and 1D elements, referred to as 1D-links, to efficiently model the flow over levees, road and rail embankments, bunds, the flow through control gates, either free or submerged, and the operation of other hydraulic structures. In this work we propose a physically-based 1D-link to model breach formation and evolution in fluvial levees, and levee failure due to either piping or overtopping. The proposed 1D-link is then embedded in a 1D–2D hydrodynamic model, thus accounting for critical feedbacks between breach formation and changes in the hydrodynamic flow field. The breach model also includes the possibility of simulating breach closure, an important feature particularly in the view of hydraulic risk assessment and management of the emergency. The model is applied to five different case studies and the results of the numerical simulations compare favorably with field observations displaying a good agreement in terms of urban and rural flooded areas, water levels within the channel, final breach widths, and water volumes flowed through the breach.