Inception of stream incision by seepage erosion

Abstract

Because seepage erosion is generated by complex interactions with other processes, associated stream incision process is not well understood. In this study, some fundamental characteristics of incipient incision by seepage erosion were investigated by laboratory experiments and linear stability analysis. The experiments were conducted with various sediment layer depths and gradients. With similar discharges in the experiments, incision spacing decreases with increasing depth of the sediment layer and with increasing gradient, whereas incision width increases with increasing sediment layer depth. A linear stability analysis was performed using the Dupuit‐Forchheimer equation and an expression of the planimetric retreat of the scarp. The retreat velocity of the scarp consists of two terms: (1) a power law function that describes the specific discharge in excess of a critical discharge and (2) a diffusion‐like function that describes the incision edge shapes, in which the retreat rate is enhanced or reduced by the convexity and concavity of the edges, respectively. This analysis shows that the characteristic incision spacing becomes infinitely small when the effect of the edge shapes is excluded. Using the experimental data of incision spacings, the values of the diffusion‐like coefficient in the second term were estimated. Since the weight of a failure block and hydraulic pressure are the driving forces in the slope stability analysis, a relationship was found between the diffusion‐like coefficient and the combination of the two forces.