A fixed-mesh finite element framework for backward erosion piping evolution with anisotropic resistance and pseudo-porosity transition

Backward erosion piping (BEP) is one of the principal forms of internal erosion and poses a significant risk to the stability of levees, embankments, and earth dams. Its numerical representation remains difficult because pipe initiation and subsequent retrogressive development are governed by the combined effects of local seepage gradients, anisotropic erosion resistance varying with depth, and progressive changes in soil hydraulic conductivity. In this study, a fixed-mesh continuum finite element framework is developed to reproduce the time-dependent development of BEP without imposing a predetermined pipe trajectory. The proposed approach incorporates three main features: (1) a depth-dependent anisotropic criterion for the critical hydraulic gradient, (2) a pseudo-porosity-based transition rule for updating hydraulic conductivity, and (3) a local maximum tracking algorithm to identify the most susceptible element at the advancing pipe tip. The pseudo-porosity parameter is introduced to describe the lag between particle detachment and the full removal of eroded material, whereas the search procedure confines pipe growth to a localized zone controlled by the excess hydraulic driving term. The model is assessed against benchmark tests on regressive erosion, Delta Flume experiments, and foundation seepage tests involving a cut-off wall. For the cases examined, the simulations reproduce the main characteristics of equilibrium arrest, intermittent pipe extension, hydraulic-gradient redistribution, and pipe deflection around a cut-off wall. The proposed method provides a simplified continuum-based approach for modelling two-dimensional dominant-front BEP evolution without prescribing the erosion path in advance.