ARS | Publication request: Empirical sediment transport function predicting seepage erosion undercutting for bank failure prediction

Submitted to: Journal of Hydrology
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: August 17, 2009
Publication Date: October 20, 2009
Citation: Chu-Agor, M.L., Fox, G.A., Wilson, G.V. 2009. Empirical sediment transport function predicting seepage erosion undercutting for bank failure prediction. Journal of Hydrology. 377:155-164.

Interpretive Summary: Seepage out of a stream bank face that transports sediment out of the face, commonly called seepage erosion, is an important factor in causing stream bank to collapse. Seepage erosion has been found to cause of undercutting of banks which results in mass failure. Limitations exist with existing seepage erosion sediment transport functions due to the difficulty in predicting the size and shape of the undercutting. The objective was to develop a sediment transport model that can predict seepage erosion and undercutting with time. This work is based upon soil block experiments that involved a wide range of water level combinations, two soil types, and various slopes and soil bulk densities. The transport function was represented by a water flow velocity equation in which the rate of erosion was related to the difference between the steady state water flow velocity and a critical velocity (R2 = 0.62). The critical velocity is a function of the critical water pressure which was measured in the laboratory using the soil blocks. The relationship between the volume of eroded sediment per bank face area of the undercut and the width of the undercut was also derived. A mathematical expression for the size and shape of the undercut was developed. An excellent relationship was observed between the predicted time and measured time at which a given amount of undercut occurred. The water flow velocity seeping out of the streambank can be used with the sediment transport equation to predict the rate of development and size and shape of the undercut. This enables the prediction of the impact of seepage erosion undercutting on bank stability.

Technical Abstract: 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 were able to predict the observed time at which a given amount of undercut developed (R2 = 0.79). 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.