Calibration of a diffusion model for aggrading channel after sediment overloading experiments with near-critical flow

Abstract

In alluvial streams shaped across geological times, the water and sediment discharges typically are in equilibrium with the corresponding supply conditions, preventing significant scouring or deposition over extended periods. However, various natural and human-induced actions may alter the balance between the river sediment transport capacity and the sediment supply. These disturbances may result in significant aggradation or degradation along specific reaches of the river. Degradation occurs when the sediment inflow discharge is smaller than the sediment load transported downstream of the reach; on the contrary, aggradation happens when the sediment entering the reach is higher than the sediment transport capacity of the channel. The present work focuses on the sediment aggradation problem, that in turn may lead to the increase of hydraulic hazard. Various mathematical approaches have been documented in the literature to predict the aggradation process in riverbeds. In this regard, several studies have focused on deriving an analytical solution for a parabolic diffusion equation. This equation is obtained by imposing several simplifying hypotheses (such as quasi-steady flow, quasi-uniform flow, etc.) on the Saint-Venant-Exner system of equations. In the present work, an analytical Fourier-series solution proposed by Gill in 1983 was applied to analyze 15 aggradation experiments, carried out at the Mountain Hydraulics Laboratory of the Politecnico di Milano (Lecco campus) using lightweight sediment material. The experimental conditions differed in terms of main control parameters such as the loading ratio (the ratio between sediment inflow discharge and initial sediment transport capacity of the channel) and the water discharge. Most of the investigated conditions corresponded to the near-critical flow regime. The same boundary conditions of the experiments were applied to the parabolic model to develop the corresponding analytical solution in terms of space/time evolution of the bed elevation. Upon comparing the analytical bed profiles with the experimental ones, acquired through a proprietary image processing technique, it was found that although for some experiments the theoretical and experimental results were consistent, the a-priori estimate of the diffusion coefficient of the model did not generally provide good agreement. Therefore, a further calibration of the diffusion coefficient of the parabolic model was performed. In this way, the space-time evolution of the bed profile in each experiment could be accurately represented, thus demonstrating the descriptive capability of the adopted simplified model for the investigated experimental conditions (that involved relatively high Froude number for which the applicability of a diffusion equation had not been ascertained). A constant value of the diffusion coefficient was enough to reproduce the evolution within an experiment, but the coefficient needed to be varied from an experiment to another, calling for further research on how the diffusion coefficient depends on the controlling variables.