A seepage erosion sediment transport function and geometric headcut relationships for predicting seepage erosion undercutting

Seepage erosion is an important factor in hillslope instability and failure. However, predicting erosion by subsurface flow or seepage and incorporating its effects into stability models remain a challenge. Limitations exist with all existing seepage erosion sediment transport functions, including neglecting the three-dimensional geometry of the seepage undercut. The objective was to develop a sediment transport model that can predict sediment mobilization (i.e., seepage erosion and undercutting) with time based on previously reported three-dimensional soil block experiments covering a wide range of hydraulic, soil type, and packing (i.e., slope and bulk density) combinations. The transport function was represented by an excess velocity equation wherein the rate of erosion was related to the difference between the steady state velocity and the critical velocity (R²=0.62). The critical velocity was derived from a critical head measured in the laboratory using the three-dimensional soil block. The relationship between the eroded volume per bank face area and the amplitude of the headcut was also derived. Using a three-dimensional Gaussian function, the geometric relationships between the lateral and vertical dimensions of the headcut were then estimated. Linear regression analysis between the predicted and observed time at which a given amount of headcut developed resulted in an R² of 0.86. The ground water velocity exfiltrating a hillslope can be used with the derived sediment transport function to predict the dimensions of the headcut and the geometry of the undercut which enables the prediction of the impact of seepage erosion undercutting on hillslope stability.