Backward erosion piping is a failure mechanism of dikes. Numerical modelling is crucial for design and assessment against BEP. Over 30 models have been developed, each with a different purpose and approach. This paper provides a comprehensive overview of the available numerical BEP models, highlighting their limitations, capabilities, and associated challenges. It discusses the different assumptions and their implications on the representation of BEP. Key challenges in the numerical modelling of BEP are (1) the flow (regime) inside the pipe, which is often simplified, even though the impact of this is relatively unknown. (2) The type of erosion (primary or secondary) differs per model, and even within a given type of erosion, approaches vary. (3) Overcoming the difference in scale is a trade-off between the computational effort and simplification. (4) Furthermore, validation of the physics in BEP modelling is difficult due to a of lack micro-scale experimental data.

Backward erosion piping (BEP) is a type of internal erosion responsible for the failure of many dams and levees. BEP occurs when small, shallow erosion channels progress upstream through foundation sands beneath the structure. As analysis of BEP involves coupling two different sets of flow equations to describe the groundwater flow and erosion pipe flow, the solution contains a singularity in the gradient field at the juncture of the soil and pipe domains. In addition, the erosion process is highly localized, often occurring over length scales of 1 cm or less. While it is well known that singularities and localized phenomena cause high errors in numerical solutions, there has been no assessment of the magnitude of these errors in BEP numerical models. This study evaluates the magnitude of error in BEP finite element models through comparison of numerical results to measurements from a highly instrumented BEP experiment. The results indicate that discretization errors related to the pipe geometry can cause 50%–300% error in the solution near the pipe tip when the pipe is represented via linear, 1D elements. These errors are significant and must be considered for models that assess pipe progression based on the local solution near the pipe tip. Results also indicate that the pipe width must be modeled as twice the physical pipe width to accurately represent the pipe flow when assuming a rectangular cross sectional shape for the erosion pipe.

Backward erosion piping (BEP) is a form of internal erosion which can lead to failure of levees and dams. Most research focused on the critical head difference at which piping failure occurs. Two aspects have received less attention, namely (1) the temporal evolution of piping and (2) the local hydraulic conditions in the pipe and at the pipe tip. We present small-scale experiments with local pressure measurements in the pipe during equilibrium and pipe progression for different sands and degrees of hydraulic loading. The experiments confirm a positive relation between progression rate and grain size as well as the degree of hydraulic overloading. Furthermore, the analysis of local hydraulic conditions shows that the rate of BEP progression can be better explained by the bed shear stress and sediment transport in the pipe than by the seepage velocity at the pipe tip. The experiments show how different processes contribute to the piping process and these insights provide a first empirical basis for modeling pipe development using coupled seepage-sediment transport equations.