Bedload transport in the case of seepage flow

The Shields number provides a classical non-dimensionalization expressing the relative mobility of a sediment particle on the bed of a river. It is not commonly recognized, however, that the Shields number implicitly contains the assumption of a hydrostatic pressure distribution in the water immersing the particles. If the concept underlying the Shields number is correct, however, the Shields number should be generalizable to non-hydrostatic pressure distributions. Here such a generalization is attempted for the case of a non-hydrostatic pressure distribution produced by a vertical seepage flow: the effect of both upward and downward seepage flow on bedload transport was investigated (Francalanci, Parker and Paris 2005), suggesting that an appropriately generalized Shields number is needed to capture the effect of a seepage flow on sediment mobility. A theoretical and numerical model is here proposed to account the effect of seepage flow on sediment mobility and bedload transport.