A retrogressive erosion model with automatic adjustment for sediment entrainment dominated and mass failure dominated bed deformation

Retrogressive erosion, a critical process impacting river engineering structures, channel geomorphology, and reservoir sediment management, manifests primarily in two distinct forms: rotating and stepped bed deformation. The former type is dominated by sediment entrainment, whereas the latter is dominated by mass failure. Simulating these processes accurately, particularly predicting which form will dominate, poses significant challenges for existing numerical models. This study addresses this gap by developing and validating a numerical model capable of simulating both rotating and stepped retrogressive erosion with automatic adjustment between the two types. The model integrates governing equations for unsteady nonuniform flow and nonequilibrium sediment transport with specialized modules for each erosion type. The rotating erosion module incorporates sediment entrainment theories suitable for high flow velocities and steep slopes, accounting for shear dilatancy effects. The stepped erosion module employs force equilibrium analysis to predict the critical horizontal erosion distance at the step toe to induce mass failure. A key feature is the implementation of a criterion based on the ratio of shear stresses at the top and bottom of the overfall relative to the critical shear stress, allowing the model to adapt the simulation approach on the basis of evolving hydrodynamic conditions. The hydrodynamic and sediment transport equations are solved at each time step, and the criterion is applied to determine whether the rotating or stepped erosion model is used to further solve bed deformation. Model calibration and verification were performed via laboratory flume data covering various inflow discharges, initial step heights, and bed material properties. For rotating-type erosion simulations, the model demonstrated high accuracy, with Nash–Sutcliffe efficiencies (NSEs) for water surface and bed elevation calculations generally exceeding 0.9. The calculated cumulative erosion amounts also agreed well with the measurements, with relative errors mostly less than 10 % in the later stages. The maximum Froude number, which was located at the end of the foreset reach, increased from 1.72 to 3.40 during the entire test. The maximum sediment concentration was almost constant. For stepped erosion, the model successfully replicated the characteristic headcut migration, although the results were sensitive to the erodibility coefficient. The errors of predicted overall migration rate were within 12.5 % of the measured values. The developed model provides a robust tool for predicting retrogressive erosion dynamics and is uniquely capable of handling both rotating and stepped forms.