2D Dam-break Flows over Erodible Floodplain. Comparison of Two Shallow-water Models against Laboratory Experiments: a Saint-Venant - Exner Classical Approach and a Two-layer Description

Dam or dyke collapse constitutes a major danger for the surrounding inhabitants and infrastructures. Indeed, it induces a fast transient flow that may entrain large amounts of sediments and modify the valley morphology. The understanding of the interaction between such a rapid flow and the sediment transport remains a challenge for fluvial hydraulics. A combined approach of laboratory, theoretical and numerical modelling is still needed to predict the geomorphic consequences of a dam failure, mainly in a complex topography. A laboratory study of a dam-break wave expanding over a flat mobile bed in a floodplain was conducted in the Hydraulics Laboratory, Institute of Mechanics, Materials and Civil Engineering, Universite catholique de Louvain, Belgium. The flume was 3.6 m wide and about 36 m long. The rising gate featuring the dam break was 1 m wide, inducing a wave expanding longitudinally as well as transversally. An initial 85 mm layer of coarse sand was put down upon the fixed bed from 1 m upstream to 9 m downstream of the gate representing the dam. Two cases were simulated: (1) an initial water level of 47 cm above the fixed bed in the upstream reservoir and no water downstream; (2) an initial water level of 51 cm in the upstream reservoir and a water level of 15 cm downstream. Time evolution of the water level was measured at 8 points by means of ultrasonic gauges and the final topography was measured by a bed profiler every 5 cm. Only bed-load transport was observed in these experiments. This laboratory test was carried out as a benchmark experiment in NSF-Pire project (http://pire.ce.sc.edu/) and allowed two-dimensional (2D) numerical models from several authors to be analysed. Among these models, two shallow-water models are here compared in details. In the first model, a clear-water layer approach is used: the Saint-Venant-Exner (SVE) equations are solved, using a Manning formula for the friction source term and a Meyer-Peter-Muller closure equation based on an equilibrium solid transport assumption. The second model is a two-layer model (2L), where the flow is described along a vertical by three regions of homogeneous properties separated by sharp interfaces. The upper layer is made of clear water while the lower layer, standing for the bed-load transport layer, is a mixture of water and moving sediments. These layers flow over a motionless bed. Both models are solved on unstructured triangular meshes by a finite-volume scheme with a lateralized Harten-Lax-Van Leer (HLL) flux computation. Interesting conclusions may arise from comparisons between both models and comparisons with laboratory observations. The main features experimentally observed are captured by the numerical models. The water level evolution is better reproduced by the two-layer model than by the SVE model. The final deposition crests near the walls are still difficult to predict by both models.