Evolution of seepage driven networks in the lab

Abstract. During rain, water infiltrates the ground, where it flows as groundwater toward nearby rivers. There, its emergence can entrain sediments, triggering seepage erosion and thereby influencing the development and expansion of river networks. To investigate this process, we construct an experimental aquifer, made of erodible plastic sediments. A reservoir beneath the aquifer supplies water at a controlled recharge rate. We find that seepage erosion, driven by the resulting groundwater flow, is sufficient to initiate the formation and growth of a drainage network. For a given recharge rate, network growth eventually ceases as the drainage system reaches a steady-state morphology, in which sediments are everywhere at the threshold of motion. This observation indicates that the recharge rate of the aquifer selects the size of the network. In our experiment, the depth of the aquifer  is small compared to its lateral extent, so that the flow of groundwater obeys the Dupuit-Boussinesq equation.  As in natural systems, the water table in our experiment intersects the drainage network at the elevation of the streams. This condition provides the necessary boundary conditions to solve for the Dupuit-Boussinesq equation and reconstruct the shape of the water table around the river network. The resulting numerical solution agrees well with piezometric measurements carried out in the experimental aquifer and reveals that groundwater flow converges toward channel tips, where velocities are maximal. These results suggest that seepage erosion occurs only when groundwater velocity exceeds a critical threshold.