Mathematical model for river bed degradation due to gravel mining

Among other remarkable impacts, the most important effect of gravel mining in rivers is river bed degradation. Although there are some methodologies proposed to foresee the effects of gravel mining (giving bed degradation or incision), none of them can be applied to the most common case of a reach subjected to a gravel extraction lasting several years with variable mining intensities and pit locations. To take into account all these features, a source term must be considered in the Exner's equation. In this paper a simple method to predict river incision due to gravel mining is presented. The methodology is based on simple hypotheses regarding water flow, i.e. uniform flow approximation, as well as sediment conservation equation. These hypotheses lead to a non homogeneous diffusion equation that can be solved analytically whatever the sediment extraction function is. In order to test the applicability of the method proposed herein, field data has been collected in the Gállego River, a tributary of the Ebro River, in Spain. A good agreement between river bed elevations predicted by the model with those observed in the field is shown.Postprint (published version