Empirical sediment transport function predicting seepage erosion undercutting for cohesive bank failure prediction

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 remains a challenge. Limitations exist with all existing seepage erosion sediment transport functions, including neglecting the three-dimensional geometry of the seepage undercut and the cohesive nature of soils. The objective was to develop an empirical sediment transport function that can predict seepage erosion and undercutting with time based on three-dimensional soil block experiments covering a wide range of hydraulic, soil type, slope and bulk density combinations. The transport function was represented by an excess gradient equation (R² = 0.54). The critical gradient was predicted by the soil cohesion based on laboratory experiments. Using a three-dimensional Gaussian function, the geometric relationships between the maximum distance and lateral and vertical dimensions of the undercut were then derived. The proposed empirical relationships reasonably predicted the observed volume per unit area of undercut, erosion rate, and time at which a given amount of undercut developed. The flow gradient can be used with the derived sediment transport function, the first ever relationship proposed for predicting the dimensions and the geometry of the undercut, to predict the impact of seepage erosion undercutting on hillslope stability. Users only need to input the seepage layer's cohesion, bulk density, and the hydraulic gradient over time in the near-bank ground water system.