The contribution of grain sorting to the dynamics of the bedload active layer

During the last 20 years, flume and field experiments have shown that grain sorting contributes to bed-level fluctuations and bedload pulses. In this work, we propose a new analysis of these experimental data. From the flume data, we derive a model for gravel-bed rivers where both local (bedform-scale) slope and bedload are known to fluctuate through space and time, in the so-called 'bedload active layer'. The model uses standard concepts and empirical tools with reach-averaged data for the hydraulics and sediment transport. It considers a maximum slope for local armouring equal to the mean bed slope (reach scale) affected by a coefficient which expresses the difference in mobility of the coarse fraction considered alone or in a mixture. The minimum local slope for bed erosion is the mean bed slope corrected by a coefficient that depends on the armour ratio A(r) (ratio of the surface to the subsurface grain diameter) and the reach-averaged transport rate. The model is compared with a compilation of scour-fill depths measured in the field. Results suggests that the slope fluctuations in 1D flume experiments are consistent with in-channel bed-level fluctuations associated with scour-fill processes in the active layer. The model also suggests that although the length scale of the maximum scour depth delta is on the order of the bed surface D-90, it is well explained by the product between the mean bed slope S and the active channel width W, with delta approximate to 1.4SW. For the pulse intensity, we provide a justification for the simplified squared slope equation for solid concentration C = Q(s)/Q proportional to S-2 (with Q(s) the solid discharge, Q the water discharge and S the slope), which has often been used in place of standard bedload equations for modelling highly concentrated bedload transport events in mountain streams.