Erosional dynamics of a river driven by groundwater seepage

Seepage erosion occurs when groundwater emerges at the surface of a granular heap. A spring forms and feeds a river which entrains sediments, thus changing the groundwater flow.

We reproduce this phenomenon in the laboratory using a quasi-2D aquifer filled with glass beads, by imposing a water level at one end of the pile. Water flows through the aquifer and emerges at the surface of the granular bed. For large enough water levels this river erodes its bed and the spring progressively ascends the heap. We investigate its trajectory, the evolution of the groundwater discharge and the river depth. Intriguingly, we find that after an initial erosive period the river attains a new equilibrium profile, with an elevated spring.

We model the flow in the aquifer using Darcy's law, predicting the shape of the water table, the position of the spring and the groundwater discharge. By appling Coulomb’s frictional law to the forces experienced by a grain we predict a threshold for the onset of erosion as a function of reservoir height and aquifer length. This prediction provides a dynamical theory for the erosional dynamics of the river. Our combined theoretical and experimental approach thereby helps constrain the response of an idealised erosive river-catchment system to steady forcing.