A two-dimensional, adaptive finite element approach for simulation of backward erosion piping

Backward erosion piping (BEP) is a type of internal erosion that significantly contributes to internal erosion being a leading cause of levee and dam failures, second only to overtopping. Despite its significance, very few numerical or analytical tools exist for assessing the progression of backward erosion pipes. Further, existing tools do not automatically refine the mesh near the pipe tip, nor do they automatically search for the weakest erosion path in the foundation. Both features are critical for assessing piping when conditions along the pipe path vary due to natural geologic variability or engineered features such as filter trenches and partial cutoff walls. In the present study, a two-dimensional, auto-adaptive, finite element program has been developed that solves the coupled groundwater flow and erosion pipe flow equations in a piecewise, steady-state manner to simulate BEP progression using automated, local mesh refinement. Criteria for pipe advancement and pipe widening are presented that permit pipe growth through the mesh along the path of least resistance, and an approximation to account for foundation depth is introduced. Examples are presented in which BEP progression is simulated beneath a levee to illustrate the analysis method.