Model for erosion, transport and deposition of tracer stones in gravel-bed streams

A common approach followed by scientists and practitioners studying sediment transport in gravel-bed streams is to estimate the bulk bedload transport rate by relating it to channel-averaged driving parameters (i.e. those of the flowing water) and the corresponding resistance properties of the bed material. Notwithstanding the proven success of this approach in modeling various morphodynamic scenarios, it does not contain the mechanics necessary to explicitly relate the bulk sediment transport rate to the displacement patterns of individual sediment particles. Furthermore, it ignores the intrinsically stochastic nature of the underlying physical processes. The experiments on the entrainment, transport and deposition of marked particles (tracer stones) in a flume presented here were designed to address these issues. Predictors for the statistics of bed elevation fluctuations at short time scales, total and elevation-specific particle entrainment rates, particle step lengths (the distance a particle moves from entrainment to deposition), the probability density function of particle virtual velocities (the particle velocity averaged so as to include both periods when the particle is in motion and when it is at rest, either on the bed surface or buried under it), and the thickness of the active layer (the layer near the bed surface, the particles of which actively exchange with the bedload) have been developed. The main working hypothesis tested in this research is that the statistics of the (vertical and streamwise) displacement patterns of the tracer stones can be related to channel-averaged hydraulic parameters, and thus in turn linked to macroscopic aspects of bedload transport. The experimental results have been used to complete a probabilistic formulation for sediment continuity, which allows the direct tracking of the movement of tracer stones under mobile-bed equilibrium conditions. The new formulation might be used for instance, to investigate how the vertical sorting of the sediment in the bed deposit influences the stratigraphic pattern constructed by a river as it aggrades. From a practical engineering point of view, its application could permit an improved estimation of bedload transport rates during flood events using tracer stones.