Comparison of Experimental and Model Simulations of the Dynamic Erosional Growth of a Soil Pipe

Soil pipes are large contiguous macropores that exist in soils or geological materials. These macropore features generally serve as conduits for rapid movement of water through soils or geological material and are generally oriented nearly parallel to the land surface. Soil pipes are important with regard to the genesis of the landscape, leading to formation of gullies or sink holes, and also significantly increase the generation of rapid runoff in response to rainstorm events. They can also lead to dangerous natural hazards such as landslides, or to failures of human infrastructure including levees, dams, or structural surfaces. Soil pipes generally show evidence of erosion by the flow of water flow along pipe walls. The erosion process can lead to pipe enlargement and eventually to collapse of the material overlying the cavity formed by the pipe. Similar to the approach by Nieber et al. (2019), we present a model of pipe flow and pipe wall erosion based on the CFD module of COMSOL-MP (COMSOL, 2021). The solution is based on the Reynolds Average Navier Stokes equations using the for the turbulent flow, and the equation for suspended sediment transport. The erosion of the pipe walls is modelled using the well-known excess shear stress equation containing two parameters, k_e, the empirical erodibility coefficient, and τ_crit, the critical shear stress. The solution in this case accounted directly for the dynamic geometry of the soil pipe as the walls are eroded. The numerical solution is set up to simulate the measurements of pipe and suspended sediment discharge from piping experiments conducted at the USDA National Sedimentation Laboratory (Wilson, 2011). For those experiments the soil pipe was constructed into a soil bed while a constant head of water was applied to the inlet of the pipe. Several initial diameters were tested in the experiment, but for the numerical solution we considered the case with a 6 mm initial diameter. The parameters k_e and τ_crit were estimated using the Hole Erosion Test, yielding τ_crit = 0.009 Pa and time-averaged k_e = 0.0025 s/m. The simulations were conducted with these parameters, and also for the case where k_e was given as a function of time and location along the pipe. Results from the measurements and model simulations are presented in Figure 1.