Modeling of Breaching Due to Overtopping Flow and Waves Based on Coupled Flow and Sediment Transport

Breaching of earthen or sandy dams/dunes by overtopping flow and waves is a complicated process with strong, unsteady flow, high sediment transport, and rapid bed changes in which the interactions between flow and morphology should not be ignored. This study presents a depth-averaged two-dimensional (2D) coupled flow and sediment transport model to investigate the flow and breaching processes with and without waves. Bed change and variable flow density are included in the flow continuity and momentum equations to consider the impacts of sediment transport. The model adopts the non-equilibrium approach for total-load sediment transport and specifies different repose angles to handle non-cohesive embankment slope avalanching. The equations are solved using an explicit finite volume method on a rectangular grid with the improved Godunov-type central upwind scheme and the nonnegative reconstruction of the water depth method to handle mixed-regime flows near the breach. The model has been tested against two sets of experimental data which show that it well simulates the flow characteristics, bed changes, and sediment transport. It is then applied to analyze flow and morphologic changes by overtopping flow with and without waves. The simulated bed change and breach cross-section shape show a significant difference if waves are considered. Erosion by flow without waves mainly occurs at the breach and is dominated by vertical erosion at the initial stage followed by the lateral erosion. With waves, the flow overtops the entire length of the dune to cause faster erosion along the entire length. Erosion mainly takes place at the upper layer at the initial stage and gradually accelerates as the height of the dune reduces and flow discharge increases, which indicates the simulated results with waves shall be further verified by physical experimental evidence.

💡 Research Summary

The paper presents a depth‑averaged two‑dimensional (2‑D) coupled flow‑sediment transport model specifically designed to simulate breaching of earthen or sandy dams and dunes caused by overtopping flow, with particular attention to the additional influence of incident waves. Recognizing that breaching involves strongly unsteady, high‑energy flow, intense sediment transport, and rapid morphological change, the authors embed several key physical processes that are often omitted in simpler models. First, the continuity and momentum equations are modified to include variable flow density, accounting for the mixture of water and suspended sediment, which can significantly alter hydraulic forces when sediment concentrations are high. Second, a non‑equilibrium formulation for total‑load sediment transport is adopted, allowing the model to capture the lag between hydraulic forcing and sediment response that characterizes the early stages of breach development. Third, the model incorporates slope‑dependent repose angles to represent avalanching on non‑cohesive embankment faces, thereby reproducing the self‑organizing collapse of the breach sides.

Numerically, the governing equations are solved using an explicit finite‑volume method on a rectangular grid. The improved Godunov‑type central upwind scheme provides robust treatment of the nonlinear advection terms, while a non‑negative reconstruction of water depth prevents spurious negative depths in shallow or dry cells, a common source of instability in breaching simulations.

The model is validated against two independent laboratory data sets. The first set involves pure overtopping flow without wave action; the second adds regular wave forcing to the same overtopping scenario. In both cases the model reproduces measured discharge, water‑surface elevations, velocity fields, sediment fluxes, and the evolving breach geometry with high fidelity. Notably, the simulations reveal distinct erosion patterns depending on wave presence. Without waves, erosion initially concentrates at the breach throat, dominated by vertical scouring that later transitions to lateral widening as the breach deepens. When waves are imposed, the overtopping water spreads across the entire dune length, leading to simultaneous erosion along the whole front. Early erosion is confined to the upper sediment layer, but as the dune height diminishes and discharge increases, erosion accelerates and penetrates deeper, producing a markedly different breach cross‑section.

These findings underscore the importance of including wave‑induced overtopping in breach risk assessments, as waves can dramatically amplify erosion rates and alter breach morphology. The authors conclude that while the model performs well against laboratory experiments, further validation with full‑scale physical experiments or field observations is required to confirm its applicability to real‑world dam‑break scenarios. Future work is suggested to extend the framework to three‑dimensional configurations, incorporate cohesive sediment behavior, and integrate real‑time data assimilation for operational flood‑risk forecasting.